From b077b1fccf15a0ab2a1464513363ca77d1132e7c Mon Sep 17 00:00:00 2001 From: Patrick Longa Date: Thu, 5 Sep 2019 17:09:17 -0700 Subject: [PATCH] Add new compressed variants of SIDH and SIKE --- KAT/PQCkemKAT_434.rsp | 1 + Makefile | 82 +- Visual Studio/SIDH/SIDH.sln | 156 + .../SIDH/SIDHp434_compressed.vcxproj | 657 + .../SIDH/SIDHp434_compressed.vcxproj.filters | 93 + .../SIDH/SIDHp503_compressed.vcxproj | 620 + .../SIDH/SIDHp503_compressed.vcxproj.filters | 93 + Visual Studio/SIDH/SIDHp610.vcxproj | 24 +- Visual Studio/SIDH/SIDHp610.vcxproj.filters | 16 +- .../SIDH/SIDHp610_compressed.vcxproj | 614 + .../SIDH/SIDHp610_compressed.vcxproj.filters | 93 + .../SIDH/SIDHp751_compressed.vcxproj | 623 + .../SIDH/SIDHp751_compressed.vcxproj.filters | 93 + .../test-SIKEp434_compressed.vcxproj | 487 + .../test-SIKEp434_compressed.vcxproj.filters | 33 + .../test-SIKEp503_compressed.vcxproj | 487 + .../test-SIKEp503_compressed.vcxproj.filters | 33 + .../test-SIKEp610_compressed.vcxproj | 487 + .../test-SIKEp610_compressed.vcxproj.filters | 33 + .../test-SIKEp751_compressed.vcxproj | 487 + .../test-SIKEp751_compressed.vcxproj.filters | 33 + .../test-SIDHp434_compressed.vcxproj | 487 + .../test-SIDHp434_compressed.vcxproj.filters | 33 + .../test-SIDHp503_compressed.vcxproj | 487 + .../test-SIDHp503_compressed.vcxproj.filters | 33 + .../test-SIDHp610_compressed.vcxproj | 487 + .../test-SIDHp610_compressed.vcxproj.filters | 33 + .../test-SIDHp751_compressed.vcxproj | 487 + .../test-SIDHp751_compressed.vcxproj.filters | 33 + src/P434/AMD64/fp_x64_asm.S | 76 +- src/P434/P434.c | 2 +- src/P434/P434_compressed.c | 374 + src/P434/P434_compressed_api.h | 109 + src/P434/P434_compressed_dlog_tables.c | 28967 ++++++ src/P434/P434_compressed_pair_tables.c | 4123 + src/P434/P434_internal.h | 43 +- src/P503/AMD64/fp_x64_asm.S | 125 +- src/P503/ARM64/fp_arm64_asm.S | 86 +- src/P503/P503.c | 4 +- src/P503/P503_compressed.c | 377 + src/P503/P503_compressed_api.h | 109 + src/P503/P503_compressed_dlog_tables.c | 81954 ++++++++++++++++ src/P503/P503_compressed_pair_tables.c | 4936 + src/P503/P503_internal.h | 49 +- src/P610/AMD64/fp_x64_asm.S | 55 +- src/P610/P610.c | 4 +- src/P610/P610_compressed.c | 379 + src/P610/P610_compressed_api.h | 109 + src/P610/P610_compressed_dlog_tables.c | 50579 ++++++++++ src/P610/P610_compressed_pair_tables.c | 7781 ++ src/P610/P610_internal.h | 46 +- src/P751/AMD64/fp_x64_asm.S | 64 +- src/P751/ARM64/fp_arm64_asm.S | 183 +- src/P751/P751.c | 2 +- src/P751/P751_compressed.c | 389 + src/P751/P751_compressed_api.h | 109 + src/P751/P751_compressed_dlog_tables.c | 49654 ++++++++++ src/P751/P751_compressed_pair_tables.c | 11018 +++ src/P751/P751_internal.h | 44 +- src/compression/dlog.c | 182 + src/compression/pairing.c | 644 + src/compression/sidh_compressed.c | 1219 + src/compression/sike_compressed.c | 96 + src/compression/torsion_basis.c | 433 + src/config.h | 53 +- src/ec_isogeny.c | 173 +- src/fpx.c | 680 +- src/sidh.c | 38 - tests/PQCtestKAT_kem434_compressed.c | 233 + tests/PQCtestKAT_kem503_compressed.c | 233 + tests/PQCtestKAT_kem610_compressed.c | 233 + tests/PQCtestKAT_kem751_compressed.c | 233 + tests/test_SIDHp434_compressed.c | 22 + tests/test_SIDHp503_compressed.c | 22 + tests/test_SIDHp610_compressed.c | 22 + tests/test_SIDHp751_compressed.c | 22 + tests/test_SIKEp434_compressed.c | 19 + tests/test_SIKEp503_compressed.c | 19 + tests/test_SIKEp610_compressed.c | 19 + tests/test_SIKEp751_compressed.c | 19 + 80 files changed, 253367 insertions(+), 322 deletions(-) create mode 100644 Visual Studio/SIDH/SIDHp434_compressed.vcxproj create mode 100644 Visual Studio/SIDH/SIDHp434_compressed.vcxproj.filters create mode 100644 Visual Studio/SIDH/SIDHp503_compressed.vcxproj create mode 100644 Visual Studio/SIDH/SIDHp503_compressed.vcxproj.filters create mode 100644 Visual Studio/SIDH/SIDHp610_compressed.vcxproj create mode 100644 Visual Studio/SIDH/SIDHp610_compressed.vcxproj.filters create mode 100644 Visual Studio/SIDH/SIDHp751_compressed.vcxproj create mode 100644 Visual Studio/SIDH/SIDHp751_compressed.vcxproj.filters create mode 100644 Visual Studio/kem_tests/test-SIKEp434_compressed.vcxproj create mode 100644 Visual Studio/kem_tests/test-SIKEp434_compressed.vcxproj.filters create mode 100644 Visual Studio/kem_tests/test-SIKEp503_compressed.vcxproj create mode 100644 Visual Studio/kem_tests/test-SIKEp503_compressed.vcxproj.filters create mode 100644 Visual Studio/kem_tests/test-SIKEp610_compressed.vcxproj create mode 100644 Visual Studio/kem_tests/test-SIKEp610_compressed.vcxproj.filters create mode 100644 Visual Studio/kem_tests/test-SIKEp751_compressed.vcxproj create mode 100644 Visual Studio/kem_tests/test-SIKEp751_compressed.vcxproj.filters create mode 100644 Visual Studio/kex_tests/test-SIDHp434_compressed.vcxproj create mode 100644 Visual Studio/kex_tests/test-SIDHp434_compressed.vcxproj.filters create mode 100644 Visual Studio/kex_tests/test-SIDHp503_compressed.vcxproj create mode 100644 Visual Studio/kex_tests/test-SIDHp503_compressed.vcxproj.filters create mode 100644 Visual Studio/kex_tests/test-SIDHp610_compressed.vcxproj create mode 100644 Visual Studio/kex_tests/test-SIDHp610_compressed.vcxproj.filters create mode 100644 Visual Studio/kex_tests/test-SIDHp751_compressed.vcxproj create mode 100644 Visual Studio/kex_tests/test-SIDHp751_compressed.vcxproj.filters create mode 100644 src/P434/P434_compressed.c create mode 100644 src/P434/P434_compressed_api.h create mode 100644 src/P434/P434_compressed_dlog_tables.c create mode 100644 src/P434/P434_compressed_pair_tables.c create mode 100644 src/P503/P503_compressed.c create mode 100644 src/P503/P503_compressed_api.h create mode 100644 src/P503/P503_compressed_dlog_tables.c create mode 100644 src/P503/P503_compressed_pair_tables.c create mode 100644 src/P610/P610_compressed.c create mode 100644 src/P610/P610_compressed_api.h create mode 100644 src/P610/P610_compressed_dlog_tables.c create mode 100644 src/P610/P610_compressed_pair_tables.c create mode 100644 src/P751/P751_compressed.c create mode 100644 src/P751/P751_compressed_api.h create mode 100644 src/P751/P751_compressed_dlog_tables.c create mode 100644 src/P751/P751_compressed_pair_tables.c create mode 100644 src/compression/dlog.c create mode 100644 src/compression/pairing.c create mode 100644 src/compression/sidh_compressed.c create mode 100644 src/compression/sike_compressed.c create mode 100644 src/compression/torsion_basis.c create mode 100644 tests/PQCtestKAT_kem434_compressed.c create mode 100644 tests/PQCtestKAT_kem503_compressed.c create mode 100644 tests/PQCtestKAT_kem610_compressed.c create mode 100644 tests/PQCtestKAT_kem751_compressed.c create mode 100644 tests/test_SIDHp434_compressed.c create mode 100644 tests/test_SIDHp503_compressed.c create mode 100644 tests/test_SIDHp610_compressed.c create mode 100644 tests/test_SIDHp751_compressed.c create mode 100644 tests/test_SIKEp434_compressed.c create mode 100644 tests/test_SIKEp503_compressed.c create mode 100644 tests/test_SIKEp610_compressed.c create mode 100644 tests/test_SIKEp751_compressed.c diff --git a/KAT/PQCkemKAT_434.rsp b/KAT/PQCkemKAT_434.rsp index d71b65f..5f969bb 100644 --- a/KAT/PQCkemKAT_434.rsp +++ b/KAT/PQCkemKAT_434.rsp @@ -699,3 +699,4 @@ pk = D10B725FA678E2B06C026AF41AB8728C777C643D959AFF59DD51698CF563D171F3187C6BFCC sk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ct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ss = A047B7E873C8EA4ECE4B143C3E0896E9E9C7863511508292 + diff --git a/Makefile b/Makefile index 1dc57b2..68cb1a5 100644 --- a/Makefile +++ b/Makefile @@ -83,8 +83,12 @@ OBJECTS_434=objs434/P434.o $(EXTRA_OBJECTS_434) objs/random.o objs/fips202.o OBJECTS_503=objs503/P503.o $(EXTRA_OBJECTS_503) objs/random.o objs/fips202.o OBJECTS_610=objs610/P610.o $(EXTRA_OBJECTS_610) objs/random.o objs/fips202.o OBJECTS_751=objs751/P751.o $(EXTRA_OBJECTS_751) objs/random.o objs/fips202.o +OBJECTS_434_COMP=objs434comp/P434_compressed.o $(EXTRA_OBJECTS_434) objs/random.o objs/fips202.o +OBJECTS_503_COMP=objs503comp/P503_compressed.o $(EXTRA_OBJECTS_503) objs/random.o objs/fips202.o +OBJECTS_610_COMP=objs610comp/P610_compressed.o $(EXTRA_OBJECTS_610) objs/random.o objs/fips202.o +OBJECTS_751_COMP=objs751comp/P751_compressed.o $(EXTRA_OBJECTS_751) objs/random.o objs/fips202.o -all: lib434 lib503 lib610 lib751 tests KATS +all: lib434 lib503 lib610 lib751 lib434comp lib503comp lib610comp lib751comp tests KATS objs434/%.o: src/P434/%.c @mkdir -p $(@D) @@ -102,6 +106,22 @@ objs751/%.o: src/P751/%.c @mkdir -p $(@D) $(CC) -c $(CFLAGS) $< -o $@ +objs434comp/%.o: src/P434/%.c + @mkdir -p $(@D) + $(CC) -c $(CFLAGS) $< -o $@ + +objs503comp/%.o: src/P503/%.c + @mkdir -p $(@D) + $(CC) -c $(CFLAGS) $< -o $@ + +objs610comp/%.o: src/P610/%.c + @mkdir -p $(@D) + $(CC) -c $(CFLAGS) $< -o $@ + +objs751comp/%.o: src/P751/%.c + @mkdir -p $(@D) + $(CC) -c $(CFLAGS) $< -o $@ + ifeq "$(USE_OPT_LEVEL)" "_GENERIC_" objs434/fp_generic.o: src/P434/generic/fp_generic.c $(CC) -c $(CFLAGS) src/P434/generic/fp_generic.c -o objs434/fp_generic.o @@ -139,7 +159,7 @@ ifeq "$(ARCHITECTURE)" "_AMD64_" objs751/fp_x64_asm.o: src/P751/AMD64/fp_x64_asm.S $(CC) -c $(CFLAGS) src/P751/AMD64/fp_x64_asm.S -o objs751/fp_x64_asm.o -else ifeq "$(ARCHITECTURE)" "_ARM64_" +else ifeq "$(ARCHITECTURE)" "_ARM64_" objs434/fp_generic.o: src/P434/generic/fp_generic.c $(CC) -c $(CFLAGS) src/P434/generic/fp_generic.c -o objs434/fp_generic.o @@ -191,7 +211,31 @@ lib751: $(OBJECTS_751) $(AR) lib751/libsidh.a $^ $(RANLIB) lib751/libsidh.a -tests: lib434 lib503 lib610 lib751 +lib434comp: $(OBJECTS_434_COMP) + rm -rf lib434comp sike434_compressed sidh434_compressed + mkdir lib434comp sike434_compressed sidh434_compressed + $(AR) lib434comp/libsidh.a $^ + $(RANLIB) lib434comp/libsidh.a + +lib503comp: $(OBJECTS_503_COMP) + rm -rf lib503comp sike503_compressed sidh503_compressed + mkdir lib503comp sike503_compressed sidh503_compressed + $(AR) lib503comp/libsidh.a $^ + $(RANLIB) lib503comp/libsidh.a + +lib610comp: $(OBJECTS_610_COMP) + rm -rf lib610comp sike610_compressed sidh610_compressed + mkdir lib610comp sike610_compressed sidh610_compressed + $(AR) lib610comp/libsidh.a $^ + $(RANLIB) lib610comp/libsidh.a + +lib751comp: $(OBJECTS_751_COMP) + rm -rf lib751comp sike751_compressed sidh751_compressed + mkdir lib751comp sike751_compressed sidh751_compressed + $(AR) lib751comp/libsidh.a $^ + $(RANLIB) lib751comp/libsidh.a + +tests: lib434 lib434comp lib503 lib503comp lib610 lib610comp lib751 lib751comp $(CC) $(CFLAGS) -L./lib434 tests/arith_tests-p434.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p434 $(ARM_SETTING) $(CC) $(CFLAGS) -L./lib503 tests/arith_tests-p503.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p503 $(ARM_SETTING) $(CC) $(CFLAGS) -L./lib610 tests/arith_tests-p610.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p610 $(ARM_SETTING) @@ -204,6 +248,14 @@ tests: lib434 lib503 lib610 lib751 $(CC) $(CFLAGS) -L./lib503 tests/test_SIKEp503.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike503/test_SIKE $(ARM_SETTING) $(CC) $(CFLAGS) -L./lib610 tests/test_SIKEp610.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike610/test_SIKE $(ARM_SETTING) $(CC) $(CFLAGS) -L./lib751 tests/test_SIKEp751.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike751/test_SIKE $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib434comp tests/test_SIDHp434_compressed.c tests/test_extras.c -lsidh $(LDFLAGS) -o sidh434_compressed/test_SIDH $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib503comp tests/test_SIDHp503_compressed.c tests/test_extras.c -lsidh $(LDFLAGS) -o sidh503_compressed/test_SIDH $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib610comp tests/test_SIDHp610_compressed.c tests/test_extras.c -lsidh $(LDFLAGS) -o sidh610_compressed/test_SIDH $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib751comp tests/test_SIDHp751_compressed.c tests/test_extras.c -lsidh $(LDFLAGS) -o sidh751_compressed/test_SIDH $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib434comp tests/test_SIKEp434_compressed.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike434_compressed/test_SIKE $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib503comp tests/test_SIKEp503_compressed.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike503_compressed/test_SIKE $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib610comp tests/test_SIKEp610_compressed.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike610_compressed/test_SIKE $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib751comp tests/test_SIKEp751_compressed.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike751_compressed/test_SIKE $(ARM_SETTING) # AES AES_OBJS=objs/aes.o objs/aes_c.o @@ -228,16 +280,36 @@ lib751_for_KATs: $(OBJECTS_751) $(AES_OBJS) $(AR) lib751/libsidh_for_testing.a $^ $(RANLIB) lib751/libsidh_for_testing.a -KATS: lib434_for_KATs lib503_for_KATs lib610_for_KATs lib751_for_KATs +lib434comp_for_KATs: $(OBJECTS_434_COMP) $(AES_OBJS) + $(AR) lib434comp/libsidh_for_testing.a $^ + $(RANLIB) lib434comp/libsidh_for_testing.a + +lib503comp_for_KATs: $(OBJECTS_503_COMP) $(AES_OBJS) + $(AR) lib503comp/libsidh_for_testing.a $^ + $(RANLIB) lib503comp/libsidh_for_testing.a + +lib610comp_for_KATs: $(OBJECTS_610_COMP) $(AES_OBJS) + $(AR) lib610comp/libsidh_for_testing.a $^ + $(RANLIB) lib610comp/libsidh_for_testing.a + +lib751comp_for_KATs: $(OBJECTS_751_COMP) $(AES_OBJS) + $(AR) lib751comp/libsidh_for_testing.a $^ + $(RANLIB) lib751comp/libsidh_for_testing.a + +KATS: lib434_for_KATs lib503_for_KATs lib610_for_KATs lib751_for_KATs lib434comp_for_KATs lib503comp_for_KATs lib610comp_for_KATs lib751comp_for_KATs $(CC) $(CFLAGS) -L./lib434 tests/PQCtestKAT_kem434.c tests/rng/rng.c -lsidh_for_testing $(LDFLAGS) -o sike434/PQCtestKAT_kem $(ARM_SETTING) $(CC) $(CFLAGS) -L./lib503 tests/PQCtestKAT_kem503.c tests/rng/rng.c -lsidh_for_testing $(LDFLAGS) -o sike503/PQCtestKAT_kem $(ARM_SETTING) $(CC) $(CFLAGS) -L./lib610 tests/PQCtestKAT_kem610.c tests/rng/rng.c -lsidh_for_testing $(LDFLAGS) -o sike610/PQCtestKAT_kem $(ARM_SETTING) $(CC) $(CFLAGS) -L./lib751 tests/PQCtestKAT_kem751.c tests/rng/rng.c -lsidh_for_testing $(LDFLAGS) -o sike751/PQCtestKAT_kem $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib434comp tests/PQCtestKAT_kem434_compressed.c tests/rng/rng.c -lsidh_for_testing $(LDFLAGS) -o sike434_compressed/PQCtestKAT_kem $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib503comp tests/PQCtestKAT_kem503_compressed.c tests/rng/rng.c -lsidh_for_testing $(LDFLAGS) -o sike503_compressed/PQCtestKAT_kem $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib610comp tests/PQCtestKAT_kem610_compressed.c tests/rng/rng.c -lsidh_for_testing $(LDFLAGS) -o sike610_compressed/PQCtestKAT_kem $(ARM_SETTING) + $(CC) $(CFLAGS) -L./lib751comp tests/PQCtestKAT_kem751_compressed.c tests/rng/rng.c -lsidh_for_testing $(LDFLAGS) -o sike751_compressed/PQCtestKAT_kem $(ARM_SETTING) check: tests .PHONY: clean clean: - rm -rf *.req objs434 objs503 objs610 objs751 objs lib434 lib503 lib610 lib751 sidh434 sidh503 sidh610 sidh751 sike434 sike503 sike610 sike751 arith_tests-* + rm -rf *.req objs434* objs503* objs610* objs751* objs lib434* lib503* lib610* lib751* sidh434* sidh503* sidh610* sidh751* sike434* sike503* sike610* sike751* arith_tests-* diff --git a/Visual Studio/SIDH/SIDH.sln b/Visual Studio/SIDH/SIDH.sln index d4cad1a..161cbf7 100644 --- a/Visual Studio/SIDH/SIDH.sln +++ b/Visual Studio/SIDH/SIDH.sln @@ -35,6 +35,30 @@ Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp610", "..\kem_tes EndProject Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIDHp610", "..\kex_tests\test-SIDHp610.vcxproj", "{6BC0CAC3-5769-4B86-B56E-6AF3086B09F0}" EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P434_compressed", "SIDHp434_compressed.vcxproj", "{D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P503_compressed", "SIDHp503_compressed.vcxproj", "{A025CB78-542D-423C-8E8F-C43291C7C053}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P610_compressed", "SIDHp610_compressed.vcxproj", "{0BC26A55-1492-4DD0-9299-BB5C8D57F535}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P751_compressed", "SIDHp751_compressed.vcxproj", "{42CE9192-A45B-4B27-9BF0-A5E0F2705890}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp434_compressed", "..\kem_tests\test-SIKEp434_compressed.vcxproj", "{F7A30C83-5B6A-41E6-A19F-E351670BDF4B}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp503_compressed", "..\kem_tests\test-SIKEp503_compressed.vcxproj", "{6CB47494-FA0E-41B7-A7E9-822818C2A210}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp610_compressed", "..\kem_tests\test-SIKEp610_compressed.vcxproj", "{8228E3E5-E952-4B43-AEF0-861A8D199C9D}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp751_compressed", "..\kem_tests\test-SIKEp751_compressed.vcxproj", "{B5E698E1-767B-4F89-9516-3EEC96990A40}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIDHp434_compressed", "..\kex_tests\test-SIDHp434_compressed.vcxproj", "{0F110149-40C2-4A4F-8A06-2E9C794093A7}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIDHp503_compressed", "..\kex_tests\test-SIDHp503_compressed.vcxproj", "{D8BBA46C-427B-4D2A-826B-D2251C552276}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIDHp610_compressed", "..\kex_tests\test-SIDHp610_compressed.vcxproj", "{6AE66111-165B-4F57-BD88-BB1D4D222D0F}" +EndProject +Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIDHp751_compressed", "..\kex_tests\test-SIDHp751_compressed.vcxproj", "{6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}" +EndProject Global GlobalSection(SolutionConfigurationPlatforms) = preSolution Debug|Win32 = Debug|Win32 @@ -221,6 +245,138 @@ Global {6BC0CAC3-5769-4B86-B56E-6AF3086B09F0}.Generic|Win32.Build.0 = Generic|Win32 {6BC0CAC3-5769-4B86-B56E-6AF3086B09F0}.Generic|x64.ActiveCfg = Generic|x64 {6BC0CAC3-5769-4B86-B56E-6AF3086B09F0}.Generic|x64.Build.0 = Generic|x64 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Debug|Win32.ActiveCfg = Debug|Win32 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Debug|Win32.Build.0 = Debug|Win32 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Debug|x64.ActiveCfg = Debug|x64 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Debug|x64.Build.0 = Debug|x64 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Fast|Win32.ActiveCfg = Fast|Win32 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Fast|x64.ActiveCfg = Fast|x64 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Fast|x64.Build.0 = Fast|x64 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Generic|Win32.ActiveCfg = Generic|Win32 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Generic|Win32.Build.0 = Generic|Win32 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Generic|x64.ActiveCfg = Generic|x64 + {D3BD913F-5112-4FCE-A4E6-4C1A59396E0C}.Generic|x64.Build.0 = Generic|x64 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Debug|Win32.ActiveCfg = Debug|Win32 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Debug|Win32.Build.0 = Debug|Win32 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Debug|x64.ActiveCfg = Debug|x64 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Debug|x64.Build.0 = Debug|x64 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Fast|Win32.ActiveCfg = Fast|Win32 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Fast|x64.ActiveCfg = Fast|x64 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Fast|x64.Build.0 = Fast|x64 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Generic|Win32.ActiveCfg = Generic|Win32 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Generic|Win32.Build.0 = Generic|Win32 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Generic|x64.ActiveCfg = Generic|x64 + {A025CB78-542D-423C-8E8F-C43291C7C053}.Generic|x64.Build.0 = Generic|x64 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Debug|Win32.ActiveCfg = Debug|Win32 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Debug|Win32.Build.0 = Debug|Win32 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Debug|x64.ActiveCfg = Debug|x64 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Debug|x64.Build.0 = Debug|x64 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Fast|Win32.ActiveCfg = Fast|Win32 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Fast|x64.ActiveCfg = Fast|x64 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Fast|x64.Build.0 = Fast|x64 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Generic|Win32.ActiveCfg = Generic|Win32 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Generic|Win32.Build.0 = Generic|Win32 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Generic|x64.ActiveCfg = Generic|x64 + {0BC26A55-1492-4DD0-9299-BB5C8D57F535}.Generic|x64.Build.0 = Generic|x64 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Debug|Win32.ActiveCfg = Debug|Win32 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Debug|Win32.Build.0 = Debug|Win32 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Debug|x64.ActiveCfg = Debug|x64 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Debug|x64.Build.0 = Debug|x64 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Fast|Win32.ActiveCfg = Fast|Win32 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Fast|x64.ActiveCfg = Fast|x64 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Fast|x64.Build.0 = Fast|x64 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Generic|Win32.ActiveCfg = Generic|Win32 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Generic|Win32.Build.0 = Generic|Win32 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Generic|x64.ActiveCfg = Generic|x64 + {42CE9192-A45B-4B27-9BF0-A5E0F2705890}.Generic|x64.Build.0 = Generic|x64 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Debug|Win32.ActiveCfg = Debug|Win32 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Debug|Win32.Build.0 = Debug|Win32 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Debug|x64.ActiveCfg = Debug|x64 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Debug|x64.Build.0 = Debug|x64 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Fast|Win32.ActiveCfg = Fast|Win32 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Fast|x64.ActiveCfg = Fast|x64 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Fast|x64.Build.0 = Fast|x64 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Generic|Win32.ActiveCfg = Generic|Win32 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Generic|Win32.Build.0 = Generic|Win32 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Generic|x64.ActiveCfg = Generic|x64 + {F7A30C83-5B6A-41E6-A19F-E351670BDF4B}.Generic|x64.Build.0 = Generic|x64 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Debug|Win32.ActiveCfg = Debug|Win32 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Debug|Win32.Build.0 = Debug|Win32 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Debug|x64.ActiveCfg = Debug|x64 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Debug|x64.Build.0 = Debug|x64 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Fast|Win32.ActiveCfg = Fast|Win32 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Fast|x64.ActiveCfg = Fast|x64 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Fast|x64.Build.0 = Fast|x64 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Generic|Win32.ActiveCfg = Generic|Win32 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Generic|Win32.Build.0 = Generic|Win32 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Generic|x64.ActiveCfg = Generic|x64 + {6CB47494-FA0E-41B7-A7E9-822818C2A210}.Generic|x64.Build.0 = Generic|x64 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Debug|Win32.ActiveCfg = Debug|Win32 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Debug|Win32.Build.0 = Debug|Win32 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Debug|x64.ActiveCfg = Debug|x64 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Debug|x64.Build.0 = Debug|x64 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Fast|Win32.ActiveCfg = Fast|Win32 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Fast|x64.ActiveCfg = Fast|x64 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Fast|x64.Build.0 = Fast|x64 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Generic|Win32.ActiveCfg = Generic|Win32 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Generic|Win32.Build.0 = Generic|Win32 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Generic|x64.ActiveCfg = Generic|x64 + {8228E3E5-E952-4B43-AEF0-861A8D199C9D}.Generic|x64.Build.0 = Generic|x64 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Debug|Win32.ActiveCfg = Debug|Win32 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Debug|Win32.Build.0 = Debug|Win32 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Debug|x64.ActiveCfg = Debug|x64 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Debug|x64.Build.0 = Debug|x64 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Fast|Win32.ActiveCfg = Fast|Win32 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Fast|x64.ActiveCfg = Fast|x64 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Fast|x64.Build.0 = Fast|x64 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Generic|Win32.ActiveCfg = Generic|Win32 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Generic|Win32.Build.0 = Generic|Win32 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Generic|x64.ActiveCfg = Generic|x64 + {B5E698E1-767B-4F89-9516-3EEC96990A40}.Generic|x64.Build.0 = Generic|x64 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Debug|Win32.ActiveCfg = Debug|Win32 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Debug|Win32.Build.0 = Debug|Win32 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Debug|x64.ActiveCfg = Debug|x64 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Debug|x64.Build.0 = Debug|x64 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Fast|Win32.ActiveCfg = Fast|Win32 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Fast|x64.ActiveCfg = Fast|x64 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Fast|x64.Build.0 = Fast|x64 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Generic|Win32.ActiveCfg = Generic|Win32 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Generic|Win32.Build.0 = Generic|Win32 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Generic|x64.ActiveCfg = Generic|x64 + {0F110149-40C2-4A4F-8A06-2E9C794093A7}.Generic|x64.Build.0 = Generic|x64 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Debug|Win32.ActiveCfg = Debug|Win32 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Debug|Win32.Build.0 = Debug|Win32 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Debug|x64.ActiveCfg = Debug|x64 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Debug|x64.Build.0 = Debug|x64 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Fast|Win32.ActiveCfg = Fast|Win32 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Fast|x64.ActiveCfg = Fast|x64 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Fast|x64.Build.0 = Fast|x64 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Generic|Win32.ActiveCfg = Generic|Win32 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Generic|Win32.Build.0 = Generic|Win32 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Generic|x64.ActiveCfg = Generic|x64 + {D8BBA46C-427B-4D2A-826B-D2251C552276}.Generic|x64.Build.0 = Generic|x64 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Debug|Win32.ActiveCfg = Debug|Win32 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Debug|Win32.Build.0 = Debug|Win32 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Debug|x64.ActiveCfg = Debug|x64 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Debug|x64.Build.0 = Debug|x64 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Fast|Win32.ActiveCfg = Fast|Win32 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Fast|x64.ActiveCfg = Fast|x64 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Fast|x64.Build.0 = Fast|x64 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Generic|Win32.ActiveCfg = Generic|Win32 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Generic|Win32.Build.0 = Generic|Win32 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Generic|x64.ActiveCfg = Generic|x64 + {6AE66111-165B-4F57-BD88-BB1D4D222D0F}.Generic|x64.Build.0 = Generic|x64 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Debug|Win32.ActiveCfg = Debug|Win32 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Debug|Win32.Build.0 = Debug|Win32 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Debug|x64.ActiveCfg = Debug|x64 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Debug|x64.Build.0 = Debug|x64 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Fast|Win32.ActiveCfg = Fast|Win32 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Fast|x64.ActiveCfg = Fast|x64 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Fast|x64.Build.0 = Fast|x64 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Generic|Win32.ActiveCfg = Generic|Win32 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Generic|Win32.Build.0 = Generic|Win32 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Generic|x64.ActiveCfg = Generic|x64 + {6ECD0EDA-00EB-4B32-8DD0-1CFEEFA4F3A9}.Generic|x64.Build.0 = Generic|x64 EndGlobalSection GlobalSection(SolutionProperties) = preSolution HideSolutionNode = FALSE diff --git a/Visual Studio/SIDH/SIDHp434_compressed.vcxproj b/Visual Studio/SIDH/SIDHp434_compressed.vcxproj new file mode 100644 index 0000000..ef577b1 --- /dev/null +++ b/Visual Studio/SIDH/SIDHp434_compressed.vcxproj @@ -0,0 +1,657 @@ + + + + + Debug + Win32 + + + Debug + x64 + + + Fast + Win32 + + + Fast + x64 + + + Generic + Win32 + + + Generic + x64 + + + Optimized-fast + 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Studio/SIDH/SIDHp610.vcxproj index 7193b68..c58cbdf 100644 --- a/Visual Studio/SIDH/SIDHp610.vcxproj +++ b/Visual Studio/SIDH/SIDHp610.vcxproj @@ -545,32 +545,20 @@ - true - true - true - true true - true - true - true true - true - true + true + true true + true - true - true - true - true true - true - true - true true - true - true + true + true true + true diff --git a/Visual Studio/SIDH/SIDHp610.vcxproj.filters b/Visual Studio/SIDH/SIDHp610.vcxproj.filters index ac47fe9..0078ef8 100644 --- a/Visual Studio/SIDH/SIDHp610.vcxproj.filters +++ b/Visual Studio/SIDH/SIDHp610.vcxproj.filters @@ -42,18 +42,18 @@ Source Files\sha3 - - Source Files - - - Source Files - Source Files\x64 Source Files\generic + + Source Files + + + Source Files + Source Files @@ -68,10 +68,10 @@ Header Files - + Header Files - + Header Files diff --git a/Visual Studio/SIDH/SIDHp610_compressed.vcxproj b/Visual Studio/SIDH/SIDHp610_compressed.vcxproj new file mode 100644 index 0000000..d321520 --- /dev/null +++ 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false + $(SolutionDir)$(Platform)\$(Configuration)\ + $(Platform)\$(Configuration)\SIDHp751_compressed\ + + + false + $(SolutionDir)$(Platform)\$(Configuration)\ + $(Platform)\$(Configuration)\SIDHp751_compressed\ + + + false + $(SolutionDir)$(Platform)\$(Configuration)\ + $(Platform)\$(Configuration)\SIDHp751\ + + + + + + Level4 + Disabled + __WINDOWS__; _X86_; _GENERIC_; + AdvancedVectorExtensions + + + Console + true + + + + + + + Level4 + Disabled + __WINDOWS__; _GENERIC_; _AMD64_; + AdvancedVectorExtensions + MultiThreadedDLL + + + Console + true + + + kernel32.lib;user32.lib;gdi32.lib;winspool.lib;comdlg32.lib;advapi32.lib;shell32.lib;ole32.lib;oleaut32.lib;uuid.lib;odbc32.lib;odbccp32.lib;%(AdditionalDependencies) + + + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__; _X86_; _GENERIC_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__; _X86_; _GENERIC_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__; _X86_; _GENERIC_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__; _X86_; _GENERIC_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__; _X86_; _GENERIC_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__;_OPTIMIZED_FAST_; _AMD64_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__;_OPTIMIZED_FAST_; _AMD64_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__; _FAST_; _AMD64_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__; _GENERIC_; _AMD64_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + Level4 + + + Disabled + true + true + __WINDOWS__;_OPTIMIZED_GENERIC_; _AMD64_; _GENERIC_; + AdvancedVectorExtensions + + + Console + true + true + true + + + + + + \ No newline at end of file diff --git a/Visual Studio/kex_tests/test-SIDHp751_compressed.vcxproj.filters b/Visual Studio/kex_tests/test-SIDHp751_compressed.vcxproj.filters new file mode 100644 index 0000000..e9517f3 --- /dev/null +++ b/Visual Studio/kex_tests/test-SIDHp751_compressed.vcxproj.filters @@ -0,0 +1,33 @@ + + + + + {4FC737F1-C7A5-4376-A066-2A32D752A2FF} + cpp;c;cc;cxx;def;odl;idl;hpj;bat;asm;asmx + + + {93995380-89BD-4b04-88EB-625FBE52EBFB} + h;hh;hpp;hxx;hm;inl;inc;xsd + + + {67DA6AB6-F800-4c08-8B7A-83BB121AAD01} + rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms + + + + + Source Files + + + Source Files + + + Source Files + + + + + Header Files + + + \ No newline at end of file diff --git a/src/P434/AMD64/fp_x64_asm.S b/src/P434/AMD64/fp_x64_asm.S index 8d1a2c7..4d88878 100644 --- a/src/P434/AMD64/fp_x64_asm.S +++ b/src/P434/AMD64/fp_x64_asm.S @@ -809,57 +809,87 @@ mp_add434_asm: //*********************************************************************** -// 2x434-bit multiprecision subtraction -// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2]. Returns borrow mask +// 2x434-bit multiprecision subtraction/addition +// Operation: c [x2] = a [x0] - b [x1]. If c < 0, add p434*2^448 //*********************************************************************** -.global mp_sub434x2_asm -mp_sub434x2_asm: +.global mp_subadd434x2_asm +mp_subadd434x2_asm: + push r12 + push r13 + push r14 + push r15 xor rax, rax mov r8, [reg_p1] mov r9, [reg_p1+8] mov r10, [reg_p1+16] mov r11, [reg_p1+24] - mov rcx, [reg_p1+32] + mov r12, [reg_p1+32] sub r8, [reg_p2] sbb r9, [reg_p2+8] sbb r10, [reg_p2+16] sbb r11, [reg_p2+24] - sbb rcx, [reg_p2+32] + sbb r12, [reg_p2+32] mov [reg_p3], r8 mov [reg_p3+8], r9 mov [reg_p3+16], r10 mov [reg_p3+24], r11 - mov [reg_p3+32], rcx + mov [reg_p3+32], r12 mov r8, [reg_p1+40] mov r9, [reg_p1+48] mov r10, [reg_p1+56] mov r11, [reg_p1+64] - mov rcx, [reg_p1+72] + mov r12, [reg_p1+72] sbb r8, [reg_p2+40] sbb r9, [reg_p2+48] sbb r10, [reg_p2+56] sbb r11, [reg_p2+64] - sbb rcx, [reg_p2+72] + sbb r12, [reg_p2+72] mov [reg_p3+40], r8 mov [reg_p3+48], r9 mov [reg_p3+56], r10 - mov [reg_p3+64], r11 - mov [reg_p3+72], rcx - mov r8, [reg_p1+80] - mov r9, [reg_p1+88] - mov r10, [reg_p1+96] - mov r11, [reg_p1+104] - sbb r8, [reg_p2+80] - sbb r9, [reg_p2+88] - sbb r10, [reg_p2+96] - sbb r11, [reg_p2+104] + mov r13, [reg_p1+80] + mov r14, [reg_p1+88] + mov r15, [reg_p1+96] + mov rcx, [reg_p1+104] + sbb r13, [reg_p2+80] + sbb r14, [reg_p2+88] + sbb r15, [reg_p2+96] + sbb rcx, [reg_p2+104] sbb rax, 0 - mov [reg_p3+80], r8 - mov [reg_p3+88], r9 - mov [reg_p3+96], r10 - mov [reg_p3+104], r11 + + // Add p434 anded with the mask in rax + mov r8, [rip+p434] + mov r9, [rip+p434+24] + mov r10, [rip+p434+32] + mov rdi, [rip+p434+40] + mov rsi, [rip+p434+48] + and r8, rax + and r9, rax + and r10, rax + and rdi, rax + and rsi, rax + mov rax, [reg_p3+56] + add rax, r8 + adc r11, r8 + adc r12, r8 + adc r13, r9 + adc r14, r10 + adc r15, rdi + adc rcx, rsi + + mov [reg_p3+56], rax + mov [reg_p3+64], r11 + mov [reg_p3+72], r12 + mov [reg_p3+80], r13 + mov [reg_p3+88], r14 + mov [reg_p3+96], r15 + mov [reg_p3+104], rcx + pop r15 + pop r14 + pop r13 + pop r12 ret diff --git a/src/P434/P434.c b/src/P434/P434.c index 214b63a..154a74c 100644 --- a/src/P434/P434.c +++ b/src/P434/P434.c @@ -101,7 +101,7 @@ const unsigned int strat_Bob[MAX_Bob-1] = { #define fp2inv_mont_bingcd fp2inv434_mont_bingcd #define fpequal_non_constant_time fpequal434_non_constant_time #define mp_add_asm mp_add434_asm -#define mp_subx2_asm mp_sub434x2_asm +#define mp_subaddx2_asm mp_subadd434x2_asm #define mp_dblsubx2_asm mp_dblsub434x2_asm #define crypto_kem_keypair crypto_kem_keypair_SIKEp434 #define crypto_kem_enc crypto_kem_enc_SIKEp434 diff --git a/src/P434/P434_compressed.c b/src/P434/P434_compressed.c new file mode 100644 index 0000000..23f3237 --- /dev/null +++ b/src/P434/P434_compressed.c @@ -0,0 +1,374 @@ +/******************************************************************************************** +* Supersingular Isogeny Key Encapsulation Library +* +* Abstract: supersingular isogeny parameters and generation of functions for P434_compressed +*********************************************************************************************/ + +#include "P434_compressed_api.h" +#define COMPRESS +#include "P434_internal.h" + + +// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points: +// -------------------------------------------------------------------------------------------------- +// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format). +// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position. +// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position. +// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32. +// For example, a 434-bit field element is represented with Ceil(434 / 64) = 7 64-bit digits or Ceil(434 / 32) = 14 32-bit digits. + +// +// Curve isogeny system "SIDHp434". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p434^2), where A=6, B=1, C=1 and p434 = 2^216*3^137-1 +// + +const uint64_t p434[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFDC1767AE2FFFFFF, + 0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x0002341F27177344 }; +const uint64_t p434p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xFDC1767AE3000000, + 0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x0002341F27177344 }; +const uint64_t p434x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFB82ECF5C5FFFFFF, + 0xF78CB8F062B15D47, 0xD9F8BFAD038A40AC, 0x0004683E4E2EE688 }; +// Order of Alice's subgroup +const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000001000000 }; +// Order of Bob's subgroup +const uint64_t Bob_order[NWORDS64_ORDER] = { 0x58AEA3FDC1767AE3, 0xC520567BC65C7831, 0x1773446CFC5FD681, 0x0000000002341F27 }; + +/* Basis for Alice on A = 6, expressed in Montgomery representation */ +const uint64_t A_gen[6*NWORDS64_FIELD] = { 0x6E18D3A63313A738, 0x1DCC496DD6DDE298, 0xA35F3F7DAFBE2B43, 0xC6B9A5CC670071EB, + 0x2EA3DB085283675A, 0xFDFE173A0297F36, 0x0002200804EB824D, // XPA0 + 0xB999E9E259F7BFA8, 0x2584D67D0C2EEAA9, 0x80AB07D4E9625724, 0x781DA616A7A76E54, + 0x9BE449736374F491, 0x8C6F86E8B0C4D74A, 0x0001C1D4812CBD98, // XPA1 + 0x257DBD53095FD263, 0xBBB3C7A7B4EDB1D4, 0xA817B7FDDD5BB8DA, 0xF5DE963B242B7AB3, + 0x7F51B5362FC94CB6, 0xE7D2496B526DFF16, 0x0001E962CF69118C, // XQA0 + 0xED9DC89467FB039D, 0x17C71E114B5803D0, 0x816C3379BE9647BF, 0xB07F441A15434B64, + 0xCC65C1804AF4CBD1, 0xF06BF5F074032C77, 0x0001A251F94CF02C, // XQA1 + 0xA26194AB4BD1A16F, 0xCFCD9F7F04D5AB10, 0x1BB4A7C04C37482C, 0x71DEE733632DA36D, + 0x7335784B5ECF957F, 0x66AE2381533A7F09, 0x000232BFFE6FA42F, // XRA0 + 0x60ACBE5D899CFA6A, 0x82AC55A556E5A22F, 0x437D8C2AC83FDC6B, 0x620A8DA602543EDE, + 0xD19ABA8092A1E8C2, 0xAFF1AA61981C95D3, 0x0001A7232B0C035E }; // XRA1 + +/* Basis for Bob on A = 6, expressed in Montgomery representation */ +const uint64_t B_gen[6*NWORDS64_FIELD] = { 0xE172658571249BA8, 0x9D8F52CB15829DA0, 0xE3A7C7F9F0E3F832, 0x8B825DD0B9410D30, + 0xF42F815734752EDA, 0xCB35DD9160997586, 0x00018B3AAAAD0F79, // XPB0 + 0xCF0B435C40C1375D, 0x58AC8A63992B36EF, 0x416D0B3DFB0C1DF5, 0xB257E9CFE8985F15, + 0xA493D98A7A1D6DF2, 0x6D6781A5B3FDE61F, 0x000179AC0D886A3F, // XPB1 + 0xE172658571249BA8, 0x9D8F52CB15829DA0, 0xE3A7C7F9F0E3F832, 0x8B825DD0B9410D30, + 0xF42F815734752EDA, 0xCB35DD9160997586, 0x00018B3AAAAD0F79, // XQB0 + 0x30F4BCA3BF3EC8A2, 0xA753759C66D4C910, 0xBE92F4C204F3E20A, 0x4B698CAAFA67A0EA, + 0xD73282EDB73B40B1, 0xFF94DE30CDC73A36, 0x0000BA73198F0904, // XQB1 + 0x9F7367022EFDF650, 0xA8C21C687A91D6BC, 0xDDB909C497C4BFED, 0x66FD362A30232EBF, + 0x84AC5026408590E1, 0x5378004CB74DA4ED, 0x00008AA46B9E55B2, // XRB0 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0 }; // XRB1 + +/* The x-coordinate of lB^(eB-1)*QB, expressed in Montgomery representation */ +const uint64_t XQB3[2*NWORDS64_FIELD] = { 0x821E631A922B742C, 0xDA3EB61A6B066600, 0xBE9BF948971BD406, 0xAEF5D42FAF04075A, + 0x70165C6A99378F7F, 0xEEE1058485DD1F9A, 0x1B20B9F7D4D95, + 0x787CA8B336944EF3, 0xD29EBA9AF11A6EB, 0xE0BC6DA29BB99844, 0xF583F3C8DA2FB5FA, + 0xBBCB2EAAD861B7E8, 0x2487A88C3E782D0A, 0x11BA37E3442A5 }; + +/* Basis for Alice on A = 0, expressed in Montgomery representation */ +const uint64_t A_basis_zero[8 * NWORDS64_FIELD] = { 0x6E18D3A633148F91, 0x1DCC496DD6DDE298, 0xA35F3F7DAFBE2B43, 0x3B18175B7C0071EB, + 0x62E0C886CC6A1260, 0x75482A45DD52E0F9, 0x1C5C62D4E6CBE, + 0xB999E9E259F7BFA8, 0x2584D67D0C2EEAA9, 0x80AB07D4E9625724, 0x781DA616A7A76E54, + 0x9BE449736374F491, 0x8C6F86E8B0C4D74A, 0x1C1D4812CBD98, + 0x9B989BE60CFF0D15, 0x8B80A32171813F53, 0xF4F067606A56228E, 0x48F8237E159577B0, + 0x42529574B9E74156, 0xD8D26313F4AA9F9C, 0x1279AC6BC876C, + 0x9597544CBE9D88DF, 0x13801F440DF32748, 0xE4ECAFF9C15D0CEB, 0x7867D92EB045A646, + 0x2399062BA8C64EF, 0xE9258C0BDF8BBFF7, 0x1CE4BBF872205, + 0x257DBD530960BABC, 0xBBB3C7A7B4EDB1D4, 0xA817B7FDDD5BB8DA, 0x6A3D07CA392B7AB3, + 0xB38EA2B4A9AFF7BC, 0x4D3A923D8F9760D9, 0x18F20F7CBFBFE, + 0xED9DC89467FB039D, 0x17C71E114B5803D0, 0x816C3379BE9647BF, 0xB07F441A15434B64, + 0xCC65C1804AF4CBD1, 0xF06BF5F074032C77, 0x1A251F94CF02C, + 0x6239F7D1AD27CE42, 0x717E2E83920EF08C, 0xAA9328D01C5FDF24, 0x824E9DEA2B1F02F9, + 0x20B1D0984E195350, 0x4A5AFBFD02EF9414, 0x228BCA648BAFF, + 0x7DEDAD20B53F2C9A, 0xE7DD8746364EACC1, 0x743BABC72A5096D4, 0xDDA2FBF4E96A5174, + 0xE05A5B3B71083AF0, 0x69AB2A817C72ADCC, 0x216CFFC723E3C }; + +/* Basis for Bob on A = 0, expressed in Montgomery representation */ +const uint64_t B_basis_zero[8*NWORDS64_FIELD] = { 0x214C34BB192F67A0, 0xDD49D3D02115D30, 0x700652C1A7B66ED, 0x1F856B48F4FF0024, + 0xFBDE6F4E6A705221, 0xB951A3D6C93D87B8, 0xAE8ADB818ED6, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x51D889FE197209C1, 0x191BCD9DBE4FE0EF, 0x447818CF5E54DD8A, 0x3F42710E8562A583, + 0x647BDBB01C66DCB5, 0xF402D36C15EA12E1, 0xA1E1D287C14C, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xDEB3CB44E6D0985F, 0xF22B62C2FDEEA2CF, 0xF8FF9AD3E5849912, 0xDE3C0B31EE00FFDB, + 0x7FE7ED29C6E85C82, 0xB3AABBFFB887989D, 0x185944B95E46D, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x51D889FE197209C1, 0x191BCD9DBE4FE0EF, 0x447818CF5E54DD8A, 0x3F42710E8562A583, + 0x647BDBB01C66DCB5, 0xF402D36C15EA12E1, 0xA1E1D287C14C }; + +/* Full 3-torsion for Bob on A = 0, expressed in Montgomery representation */ +const uint64_t B_gen_3_tors[16*NWORDS64_FIELD] = { 0xD697601DCA7CA4B5, 0xD16726DCBE0FD988, 0x8119DD7AF0E6C87C, 0xD1E1BDAB620C8DF9, + 0x27ABDBB336AF35D0, 0xC36900B91B5F4914, 0x1E21CCC021AE9, // XPB30 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, // XPB31 + 0xDAEB901A8B0B1BF6, 0xCFA413FEE3DEEB, 0xD8A152FC022EDD7F, 0x69AEE6F393ADDBE5, + 0x45F3B54D85AB6DDE, 0x19F7181A0B697BAB, 0xE1C0ED0125C4, // YPB30 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, // YPB31 + 0x29689FE235835B4A, 0x2E98D92341F02677, 0x7EE622850F193783, 0x2BDFB8CF80F37206, + 0x541A80C4FAA978D3, 0xA9935F1D6665D742, 0x52025B15585A, // XQB30 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, // XQB31 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, // YQB30 + 0xDAEB901A8B0B1BF6, 0xCFA413FEE3DEEB, 0xD8A152FC022EDD7F, 0x69AEE6F393ADDBE5, + 0x45F3B54D85AB6DDE, 0x19F7181A0B697BAB, 0xE1C0ED0125C4, // YQB31 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, // XRB30 + 0xFC42C90C960A3D15, 0x815F603FE9413385, 0x640A06136E6DF1BA, 0x71E4C95A57555FE7, + 0xBF7BAC5BE8654D6F, 0x27CD8B340B46A743, 0x259C6CF43995, // XRB31 + 0xFF585E4DCB517F6A, 0xEFFCE64BA91FBE1C, 0xFAEB260583830D6E, 0xEB68E9A0F32E8E96, + 0x419A555BABEC214B, 0xBA7A5BFD1EA7D14F, 0x220892411AA66, // YRB30 + 0xA7A1B234AE8095, 0x100319B456E041E3, 0x514D9FA7C7CF291, 0x12588CD9EFD17169, + 0x3A2C071C856C8D58, 0xB28203D9631D4F07, 0x13960305C8DD, // YRB31 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, // XSB30 + 0x3BD36F369F5C2EA, 0x7EA09FC016BECC7A, 0x9BF5F9EC91920E45, 0x8BDCAD208BAAA018, + 0xBC4AB01C48F36134, 0x452ED4A2767E7912, 0x20E82BA2339AF, // XSB31 + 0xFF585E4DCB517F6A, 0xEFFCE64BA91FBE1C, 0xFAEB260583830D6E, 0xEB68E9A0F32E8E96, + 0x419A555BABEC214B, 0xBA7A5BFD1EA7D14F, 0x220892411AA66, // YSB30 + 0xFF585E4DCB517F6A, 0xEFFCE64BA91FBE1C, 0xFAEB260583830D6E, 0xEB68E9A0F32E8E96, + 0x419A555BABEC214B, 0xBA7A5BFD1EA7D14F, 0x220892411AA66 }; // YSB31 + +/* Pre-computed pairing ReducedTatePairing(R0,S3,lB^eB) on A = 0 */ +const uint64_t g_R_S_im[NWORDS64_FIELD] = { 0x410F318D49162E42, 0x6D1F5B0D35833300, 0x5F4DFCA44B8DEA03, 0x908ADE1CD38203AD, + 0x100CD330A23B7494, 0xE0A2D716A265D0DA, 0x1C5F4777BD5A5 }; + +/* Pre-computed pairing ReducedTatePairing(phiR,phiS,lB^eB) on A = 0 */ +const uint64_t g_phiR_phiS_re[NWORDS64_FIELD] = { 0xE3F6DD5BAE3DA160, 0x893B9874EAD27B9A, 0xAEB72FD8BCC2583, 0x2FFCCC8FAFA395E, + 0x2303AE01DD252409, 0xC6AD33482DFD53FA, 0x978AD00D3221 }; +const uint64_t g_phiR_phiS_im[NWORDS64_FIELD] = { 0xC728DE8E32AF6622, 0xF179EECB0D4F3D28, 0x37CA8F90B93772D7, 0xA349AE99A7B40196, + 0xD81D98E9D4891BF8, 0x4767F6BC20C22291, 0x19AF8C13C99B8 }; + +// Montgomery constant Montgomery_R2 = (2^448)^2 mod p434 +const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x28E55B65DCD69B30, 0xACEC7367768798C2, 0xAB27973F8311688D, 0x175CC6AF8D6C7C0B, + 0xABCD92BF2DDE347E, 0x69E16A61C7686D9A, 0x000025A89BCDD12A }; + +// constant Montgomery_RB1 = (2^NBITS_ORDER)^2 mod Bob_order +const uint64_t Montgomery_RB1[NWORDS64_FIELD] = { 0xE63F0179FFC3EF1B,0x47AF4CC2440BEB81,0xEC3CD079857407E7,0x8BF47C}; + + +// constant Montgomery_RB2 = -(3^OBOB_EXP)^-1 mod 2^NBITS_ORDER +const uint64_t Montgomery_RB2[NWORDS64_FIELD] = { 0x7A9991106B9F6535,0x7E06A4ACAEA6DA73,0x3D4C8710FC0ECD0E,0xAE3D0E8DC11F55F1}; + + +// Value one in Montgomery representation +const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x000000000000742C, 0x0000000000000000, 0x0000000000000000, 0xB90FF404FC000000, + 0xD801A4FB559FACD4, 0xE93254545F77410C, 0x0000ECEEA7BD2EDA }; + +// 1/3 mod p +const uint64_t threeinv[NWORDS64_FIELD] = {0x5555555555557C0E,0x5555555555555555,0x5555555555555555,0x3C30F5A8EB555555,0x9A84C9F93D7058B4,0x410E5C007655D5E8,0x1C70EFCA40721}; + +// Fixed parameters for isogeny tree computation +const unsigned int strat_Alice[MAX_Alice-1] = { +48, 28, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 13, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, +1, 1, 5, 4, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, +1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1 }; + +const unsigned int strat_Bob[MAX_Bob-1] = { +66, 33, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, +2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 32, 16, 8, 4, 3, 1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, +1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 }; + +// Fixed traversal strategies for Pohlig-Hellman discrete logs +const unsigned int ph2_path[PLEN_2] = { // w_2 = 4 +0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 13, 13, 13, 14, 14, 15, 16, 17, 18, 19, 19, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, +27, 27, 28, 28, 28, 28, 28, 29, 30, 31, 32, 33, 34, 34, 35 +}; + +const unsigned int ph3_path[PLEN_3] = { // w_3 = 5 +0, 0, 1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 20, 20 +}; + +// Entangled bases related static tables and parameters + +// Constants u and u0 where u = u0^2 in F_{p^2} \ F_p used in entagled basis generation +// For the 2^eA-torsion basis generation: +// Two tables of 17 elements each for the values r in F_p such that v = 1/(1+ur^2) where r is already converted to Montgomery representation +// Also, 2 tables for the quadratic residues (qr) and quadratric non residues (qnr) v in F_{p^2} with 17 GF(p^2) elements each. +// For the 3^eB-torsion basis generation: +// A table of size 20 for values v = 1/(1+U*r^2) + +const uint64_t u_entang[2*NWORDS64_FIELD] = { +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0xE858,0x0,0x0,0x721FE809F8000000,0xB00349F6AB3F59A9,0xD264A8A8BEEE8219,0x1D9DD4F7A5DB5}; + +const uint64_t u0_entang[2*NWORDS64_FIELD] = { +0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA,0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA}; + +// Tables for quadratic residues and quadratic non residues v with 17 elements each. + +const uint64_t table_r_qr[TABLE_R_LEN][NWORDS64_FIELD] = +{{0xE858,0x0,0x0,0x721FE809F8000000,0xB00349F6AB3F59A9,0xD264A8A8BEEE8219,0x1D9DD4F7A5DB5}, +{0x244DE,0x0,0x0,0xA1CCD72326000000,0x407B7FF8496D02DF,0xB402E5F8D9CA0493,0x386AF88303BD}, +{0x2B90A,0x0,0x0,0x5ADCCB2822000000,0x187D24F39F0CAFB4,0x9D353A4D394145A0,0x12559A0403298}, +{0x3A163,0x0,0x0,0xCF3B3CB737000000,0x4CBA127218F35AB9,0x29D831F766AA763,0xCB17C8A31D0A}, +{0x4158F,0x0,0x0,0x884B30BC33000000,0x24BBB76D6E93078E,0xEBCFD773D5E1E870,0x1B80670604BE4}, +{0x5E641,0x0,0x0,0x710813DA5D000000,0x8D35926A62605D99,0xB6A069185034ABF6,0x10382C12620C7}, +{0x7B6F3,0x0,0x0,0x59C4F6F887000000,0xF5AF6D67562DB3A4,0x8170FABCCA876F7C,0x4EFF11EBF5AA}, +{0x82B1F,0x0,0x0,0x12D4EAFD83000000,0xCDB11262ABCD6079,0x6AA34F1129FEB089,0x13BEDB9A92485}, +{0x89F4B,0x0,0x0,0xCBE4DF027F000000,0xA5B2B75E016D0D4D,0x53D5A3658975F196,0x228DC61665360}, +{0x91378,0x0,0x0,0x87335C8C98000000,0x1EDFFE125B40B7E,0xD00B97E36728124D,0xE1ABE20C0EF6}, +{0x987A4,0x0,0x0,0x4043509194000000,0xD9EFA4DC7B53B853,0xB93DEC37C69F5359,0x1CE9A89C93DD1}, +{0xAE42A,0x0,0x0,0x6FF03FAAC2000000,0x6A67DADE19816189,0x9ADC2987E17AD5D3,0x2D2832D1E3D9}, +{0xBCC82,0x0,0x0,0xE21027B4BA000000,0x1A6B24D4C4C0BB32,0x6D40D230A06957ED,0x20705824C418F}, +{0xCB4DB,0x0,0x0,0x566E9943CF000000,0x4EA812533EA76638,0xD2A91B02DD92B9B0,0x1ACC3AAAF2C00}, +{0x10563F,0x0,0x0,0x27E85F8023000000,0x1F9BC84D2642124E,0x684A3E4BD23840BD,0x43BC4C3AD5C6}, +{0x10CA6B,0x0,0x0,0xE0F853851F000000,0xF79D6D487BE1BF22,0x517C92A031AF81C9,0x130AAF3F804A1}, +{0x113E97,0x0,0x0,0x9A08478A1B000000,0xCF9F1243D1816BF7,0x3AAEE6F49126C2D6,0x21D999BB5337C}}; + +const uint64_t table_r_qnr[TABLE_R_LEN][NWORDS64_FIELD] = +{{0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA}, +{0x15C85,0x0,0x0,0x2D6E659411000000,0xC3E9279CF8657DA,0x4E9A9D269CA0A2D0,0x92ACD020194C}, +{0x1D0B1,0x0,0x0,0xE67E59990D000000,0xE4403775252604AE,0x37CCF17AFC17E3DC,0x17F9B77DD4827}, +{0x32D36,0x0,0x0,0x13ECBF2D1E000000,0xF07EC9EEF4AC5C89,0x86678EA198B886AC,0x2124847FD6173}, +{0x489BC,0x0,0x0,0x4399AE464C000000,0x80F6FFF092DA05BF,0x6805CBF1B3940926,0x70D5F106077B}, +{0x4FDE8,0x0,0x0,0xFCA9A24B48000000,0x58F8A4EBE879B293,0x51382046130B4A33,0x15DC498C33656}, +{0x57215,0x0,0x0,0xB7F81FD561000000,0xB533ED6F0CC0B0C4,0xCD6E14C3F0BD6AE9,0x16941968F1EC}, +{0x65A6D,0x0,0x0,0x2A1807DF59000000,0x65373765B8000A6E,0x9FD2BD6CAFABED03,0x1F07168E34FA2}, +{0x6CE9A,0x0,0x0,0xE566856972000000,0xC1727FE8DC47089E,0x1C08B1EA8D5E0DB9,0xA940E9890B39}, +{0x742C6,0x0,0x0,0x9E76796E6E000000,0x997424E431E6B573,0x53B063EECD54EC6,0x1962F91463A14}, +{0x9FBD1,0x0,0x0,0xFB91CE1BAD000000,0x362AED5F9F9AB683,0x3573E0B5A4517410,0x876A0A6EF968}, +{0xA6FFD,0x0,0x0,0xB4A1C220A9000000,0xE2C925AF53A6358,0x1EA6350A03C8B51D,0x17458B22C2843}, +{0xB5856,0x0,0x0,0x290033AFBE000000,0x42697FD96F210E5E,0x840E7DDC40F216E0,0x11A16DA8F12B4}, +{0xC40AF,0x0,0x0,0x9D5EA53ED3000000,0x76A66D57E907B963,0xE976C6AE7E1B78A3,0xBFD502F1FD25}, +{0xD2908,0x0,0x0,0x11BD16CDE8000000,0xAAE35AD662EE6469,0x4EDF0F80BB44DA66,0x65932B54E797}, +{0xD9D34,0x0,0x0,0xCACD0AD2E4000000,0x82E4FFD1B88E113D,0x381163D51ABC1B73,0x15281D3121672}, +{0xE1161,0x0,0x0,0x861B885CFD000000,0xDF204854DCD50F6E,0xB4475852F86E3C29,0xB5153B7D208}}; + +const uint64_t table_v_qr[TABLE_V_LEN][NWORDS64_FIELD] = +{{0xB91B91B91B91BAE5,0x1B91B91B91B91B91,0x91B91B91B91B91B9,0xE6BB9DE0C91B91B,0x18879A47F2F0700D,0x32C54E927DB88A64,0x40658CB2BA6D}, +{0x37237237237228D7,0x2372372372372372,0x7237237237237237,0x8A63A78A7E723723,0xB7898A3899D52E3B,0xD6D1EB429400CD35,0x30F2C1819FDA}, +{0x9DF0A569883D6A65,0x59DF0A569883D6A5,0xA59DF0A569883D6A,0x93172790C79883D6,0x298B605E3417DFB7,0x81016F426986717,0x1AE3C15954874}, +{0x26FFB1636401381F,0x726FFB16364013A7,0xA726FFB16364013A,0xEDF3527199364013,0xBDFF43E957D8E920,0x74E1DFE3B43CAA6,0x1E902BD6A68C3}, +{0xB29534AE62D85A79,0x73A1CBC35EA5FE1F,0x1FB29534AE62D85A,0x19C5E5E8785EA5FE,0x6B6158A5E8F068E6,0xCECA7AEFD88C24A,0xCF8664C37D4D}, +{0xC6092EF433268DDD,0x7A7EB10D61508715,0x15C6092EF433268F,0x83BED59416615087,0xDA8AD203B0BCEA94,0xDC0EF2686153C430,0x1217CC87DEA8B}, +{0xA1597A9A1597A9A3,0xA9A1597A9A1597A9,0x97A9A1597A9A1597,0x47173487D07A9A15,0x3062918D06B8B8BB,0x5EF6E4246C346412,0x5CDEB10B32FD}, +{0x5342B2F5342B2E6A,0x2F5342B2F5342B2F,0x2B2F5342B2F5342B,0x4305EAA744B2F534,0x71C32BD0E142A474,0xE23E2A390CBEBE56,0x20B54D66A6931}, +{0x31D09D29093CBD5A,0xA279F28F044339E9,0x1C3591FDDFA2ABE3,0x7A95272488FA8224,0x7A5F257CDC0C28BB,0x2F3DFE9FC01A2996,0x1366E89ECB66C}, +{0x79FC8C0827902CB2,0x2ED4817F4D755A6E,0x26199D587B0F39F3,0xA3A0E2151F79A526,0x1386C93E197B9F03,0x6B7E90520EBF0D2E,0x1E10076731598}, +{0x5DD68140F43AA56B,0x4AA53DAEB55472EF,0xA60F1009929BD460,0x3D4DD25C8193C341,0x35733EAA8A1EA07B,0x99783B0926D5C757,0x1D6A91F47E8D5}, +{0x1AC9583D8A91979F,0x71D48F5496803FF6,0xC01CD35C6E4198DD,0x941E3BB5DBE83352,0x421F7BB430992C92,0xDA40000C2EA98E76,0x23324E9FB029F}, +{0x952DEB9E62D9C2BE,0x7B98EE26B6AE484E,0xA57575A4B923F963,0x7F6E921069A934B5,0xD34628FB53F37E0,0x84CD034670F66804,0x233E185011583}, +{0x2E520464D0564CC2,0xF0B64C978A80BE93,0x6CCC6215FCC6ED62,0x3727B865F5F6FDE0,0xA5963EE8317E2563,0x3AEEFD45F2BC2A1D,0x8B27F67FAD8C}, +{0x6B7A7DCC7F3B44FC,0xBA2952F78F79D85C,0x58AA10FC845A4938,0x38607CDC19E40DE8,0xF782E6EB3A1CBDE0,0x98DAE7F75A012666,0x1E9CFDCCA840A}, +{0xF1F1925DF1F95FED,0xC765FD5CD394560F,0x918500D0FB76A868,0x5C3B831FAFBCCBDF,0xB1E4D8E96D477318,0xC4EB9AA3919CE98F,0xCA5C17F444A8}, +{0xF505266D38669368,0xAD2B0AFD3D136E5D,0x3CA7F0C0A4792B2B,0xF6CC2F16221333E8,0x74FDE820A0C50733,0xD749F43FD6060D30,0xFF30BAB231A0}, +{0xF7799FF6EEB44369,0x9C9B01C9BF32BB02,0xEE5B00B022443ED1,0x16418A8BDAD79B04,0x264771819C98C2EB,0x7CB8EF625BB1BCE,0xDC5C646444C8}, +{0xA52C6022C70D3B7D,0xF9B79B1003C84AFA,0x765C85B2883915A,0x3C54570B229D2FC2,0xA59E1613FB354422,0x88D1CAF4B3C2622E,0x9178DE51F8AB}, +{0xD5539351F6A61891,0xA23B6DF42E15B0BB,0xE1EDE32164D9C3B3,0xA7DECA9161CAC1A8,0x875FC6BEE0404B9D,0x907741C12EF25428,0x18B79DBCD1C48}, +{0x18A1E0F1292838F7,0xBAE67B6B45CF66EC,0x2982C916B06A06F1,0x9A53622D7C86DA5A,0x9314B3E18DD3A3B7,0x36BB18009CF1A383,0x1BFC9236F3E65}, +{0x22470120336BBA45,0x11EAC8697B6F6693,0xFB672FD432B4132A,0x27792DC88E63B55C,0x30D776047CAC287C,0xDE79BC44A0443180,0x1F651F5F1A9A7}, +{0x3E09917AC9688DC1,0xEC94402B3F3397BE,0x56025A9144380945,0xA1AE22A2253250,0x891F8847B8B78A7D,0xDA0443EFF16C706F,0x22368A03A9304}, +{0xD4F15775A9821722,0x64DF3D6397D527E8,0xF568724D03D64557,0x5B53D0D1B29D967C,0x7E629228475B7DAB,0xE2F8D30C52E943C7,0x493BB0D3CEFE}, +{0x57EF7EC9AC7CE353,0xB563E360103A5DD6,0xC42C5BD044455DBC,0x41EA4366B0C69229,0xE97382F193D45A27,0x8B63E6E956D7C174,0x190B9B4F7F000}, +{0x972A66E90C6F6DE7,0x8772CAA4BC06BFF,0xF5BB1C1771A8F362,0x7609CCF88A4C136B,0xB995935C846B7647,0xF7C843EA8188B335,0x1542E019C30FC}, +{0x4246FA13382275B5,0x4734FBDCE5228591,0x4024F01C044310A0,0x764F2B4888774196,0x7F3EFA9545B4D464,0xCD48FEF1A7C24D0E,0x371FB2198997}, +{0xD444A482CEF0AC6,0xDB7957048C8DE64A,0x1DC15465E53A2A4B,0x17829A8B38E47B7,0x1394CE02BBC42752,0x30B81EE68A7D7B3B,0x1B89AA7B09560}, +{0x91E8F43CA01721C0,0x39ABE9BE4138C9F2,0x342B58F5DC8FD7C4,0x8BEBB3AD3C59CBD4,0x14A504F2E2D58BF,0x63B43021EDEEB875,0xCC6FC5A0F66}, +{0xA9571A2B15CA47C5,0x136159ABA10347FA,0xC91B46A6CF975D38,0xC91B144F43D03B6F,0x764A2DFFD44DAC62,0x9DC2BEE6D762D341,0xA472F28BA413}, +{0xE22367F18819D3B6,0x581661D0BA67F352,0xBB446CC1C435EC24,0x234DE0F57175551C,0x22DCB9526AB8B42A,0x9B132D68572887FF,0x106208C8243C0}, +{0x61524ABE5BC5AA7B,0xE09DD59654379389,0x1E2CCF9B77486349,0x401627FB5217B2B5,0xA0ABBE33F68582CB,0x5FDCEBB71DBF474A,0x1A6CA9A638D47}, +{0x743A7ADEC4CBEB9,0x47D5F3C3612D8380,0x2AB1A136944C1875,0x1A465F3FB9F85ABF,0xEE93D67ED7FD59F4,0xAECA171A0F106B4E,0x58273E8B0400}, +{0xCC45DEE3E386734,0x9A5A0BDFB68C83AE,0x5C1D5047058C14ED,0x9FB2AA0ED2404366,0x166F7D427E758FC3,0x95C498C32ED2863F,0x18C4775225D1C}}; + +const uint64_t table_v_qnr[TABLE_V_LEN][NWORDS64_FIELD] = +{{0x6666666666667DA2,0x6666666666666666,0x6666666666666666,0xBDB6F9CBC0666666,0xC31C792F24DD0205,0x27089D99E099E6BE,0x11108FDFC0447}, +{0x33333333333304BB,0x3333333333333333,0x3333333333333333,0x825382E362333333,0xF58D6A19E79EAA98,0x1EEB24A2C09152D8,0x120D2B1F6AB6}, +{0x8B6BE9F1D2505894,0x38B6BE9F1D250583,0x838B6BE9F1D25058,0x9C0909AB631D2505,0xEA75FE266DA83956,0xB98D22E1CCB2BBBE,0x7DB423F53C56}, +{0x32698CFF3659C593,0x32698CFF3659CC0,0xC032698CFF3659CC,0xFC24A25976F3659C,0xEE93EFA540E7611C,0x15016B5024486E43,0x22DF13C37023D}, +{0x7722377223772254,0x3772237722377223,0x2377223772237722,0x36D7BAAAFB223772,0x7AA4C5D72FC85655,0x3369C65060D08696,0x104009788DC36}, +{0x1BB911BB911BB571,0x11BB911BB911BB91,0x911BB911BB911BB9,0x35E9BD3E8B911BB,0xEC06B024EB2770F5,0xF590D385807C1241,0x8DC059443A3B}, +{0xE6111C7042F3A8E9,0xA8E6111C7042F3A8,0xF3A8E6111C7042F3,0xE2F2B515761C7042,0x530947C450F471E0,0xFE9688F7B8604C8D,0x5C0ECF10587A}, +{0xED731D065EB956BE,0x57ED731D065EB957,0xB957ED731D065EB9,0xFB2E1576F91D065E,0xF2D84E5C17F75228,0x5A258E938774B74D,0x4472D355531}, +{0x3337C993650C0D08,0xD089EDE9FF52557D,0x7620D4C829513EF7,0xDA1743C426DBF666,0xA107EC0033174F2C,0xAD15D89173C23C09,0xF99F9FB462F5}, +{0xFC6A84D90E95D167,0x143E213087AD362F,0xB659C39FB886CE65,0xD6153F7A8F277FF3,0x39C5C5A13D9EDBF8,0xAAAC1FF0ADC9568B,0x11A1FD239C2DA}, +{0x87736309DDA6A943,0x91F6A7837911C71,0x743D3FD9AC58005,0xE763272C18E09F9A,0x26B8C4C17D8D30CA,0xA460F26C8AFDB3DA,0x14E6984FF9B2E}, +{0xF4EC60AC7873FE1A,0x604D5A5B78D31CAD,0x21E19A43B14CFB3D,0x1179D702BA92065,0x4EA04B3126A1C70,0xEA50BE0D9B0E2C6D,0x131C643902465}, +{0x8614211F80B1616D,0xF7B81FD3A7A49E4E,0xF80B1616D86C5E7A,0x7BF548F41614211,0xC37DA826EB2AE8DF,0xC0411FD8C5ED8C6F,0x1F341510F9157}, +{0x295ABC8F38726461,0x50DC31E366CDE7A9,0xF387264C8615B5A9,0xC75E33E8F95ABC8,0x5D38EFF0970FFA71,0x461FA2CC981D3869,0x418CBED84E70}, +{0x87700C2E778D8075,0x43A87500FA58EEAF,0x9CE75275C96D2A5C,0x5FA19F2E462F399A,0xDF0F017B7DD8C4F2,0x280013794FEDAE61,0x94ED77FF8063}, +{0x9C6D58D8EF534C70,0x660CD680A7D28338,0xBDC9BBA390D722B8,0xA71C6310BFAFCB3F,0xB99B4BBB58195F7C,0x6691D6254221D44,0x12108224A3BF7}, +{0x2195F504EC8CE821,0x9D41075B38625AA5,0x9014203CA406BB05,0x6D62CB6D8B2DF2C3,0x1C86F3E3A5CCF863,0x203E5B5903F00EDA,0x164F4C3C7C43C}, +{0xF6674D58304FF4E1,0x93B111A6E31CA9BA,0xBC9F5567AC2B4021,0x38B75040103B443C,0xA69C3BA57D6DCDCB,0xA75A1F558C7AE4E1,0x906E5FF4617C}, +{0x94129AFB594129AF,0x129AFB594129AFB5,0x9AFB594129AFB594,0x2900F1CD82B59412,0x20D6A4CA5E4BAF82,0x6793F3042CF7FB07,0x1D02041A5E76A}, +{0xDACA094D7DACA05A,0xCA094D7DACA094D7,0x94D7DACA094D7DA,0x4B05B38CC6D7DACA,0x5BB2D964C0D0DE02,0x801FF33FFAFD404E,0x1AAD724D92DFC}, +{0xE166CDB3BE58BCD0,0xE77C60E75642CDFD,0xC39472A9783BE7F,0x96A7FC14FBC96ABA,0x5CC689CB13C56A4D,0xC328410D8CB268EB,0x1A8A8A5004ABD}, +{0xB346305840760AA7,0xB1B19541D3651803,0xC76AE6F315D7AC5C,0xF0B9349859647081,0xA9244A61C30F5B9B,0x6A76EE9B87BC5C4F,0xAF0668ACA050}, +{0xADA031682113D6D1,0x17CF7EC83494C4A,0x33EF143065596ED1,0x276B5923C8389FE,0x822C190F53979AC,0x33C32FAC0249AB9F,0x11975648F1F39}, +{0x6FF3CFA74C02322E,0xD98760896B12B35E,0x5DEE8FFD24640437,0x3069F716185FB36D,0xA97ABED04F5F5959,0xDBDAA58A321B6B1F,0x491708DEB2B8}, +{0xA6D19EFB46E8A47A,0xB4DDF0D82FF93FF2,0x7EF791FD729C9B0F,0x1CBEBA7707E84CC6,0xE949FCCBE6E9F9A6,0x85AFF3FCD75590B,0xF96FFCFE49F3}, +{0x7475B90FC40CE223,0xDC4E0065C0F5C12D,0xB2928765F52DD4E,0xCB9E763FBEB91EC8,0x44396405161C4326,0xA0D8B0D51BD60EA8,0xA27A2002EA20}, +{0x49EC0E19DF71A633,0x2A457AC271C844D8,0xDBF40F545519A32C,0x318D60D527180CFE,0x19A398A08B929CDA,0xCF17763B94DCBD5B,0x1DD4F8A136584}, +{0xFD97B0A56ABB6CB8,0x404AD893F967E82A,0x4C00B1B353FCAE77,0xF75B9E618F05FC7F,0x9C6E7902F4787FCE,0xE4E698A7B7077008,0xCF2A0C917171}, +{0xC0BAAADC355770BB,0x9D7581EB3277D7EA,0xCDBA0DAFF2A59F6E,0x3E461B402A9B65B2,0x5F0D156E1A7A3ED,0x69A1891EBDCC6A7C,0x1281AFCFED68C}, +{0xB5896529877D4FE7,0x71F064AE68975B99,0x4F9211F7BBCE7B39,0x19AC9E4507FDCF34,0xE4F185BB956F52E1,0xE327A4E691DAE76D,0x46219384EE75}, +{0x1B49FE6D324A903E,0x4E33D89D1655631F,0x1E1C101410671389,0xE332832DFB6C742D,0x38CDD49E02180B90,0x1279178D8097B588,0x119E5683A4805}, +{0x1FBB103663B9C88C,0x2374EF7AF79F0D48,0x4AAEF2ECAB3EA292,0xA0FA2CB6396F22C4,0xBE1E1F8EC2B4A5CA,0x43D353300E514A3B,0x1288094A6D8E5}, +{0x998BF5138DDDD5D2,0xD1F015AF4EA7BF66,0xE3DAF7886068D9AD,0x99E9067025D583AF,0xCC498E253E868EF6,0x618AE02455C9B20A,0x2322145632832}, +{0x333A0330E480A5E0,0xD37D31D37894FFB3,0x4E09921C2CCDB4FD,0xAC7069BEE6F95173,0xA05EDFF1E57DBBEF,0x5C3678A72B135234,0x1BB5DA10EE9DF}}; + +const uint64_t v_3_torsion[20][2 * NWORDS64_FIELD] = +{{0x999999999999BC73,0x9999999999999999,0x9999999999999999,0x9C9276B1A0999999,0x24AAB5C6B74B8308,0xBA8CEC66D0E6DA1E,0x1998D7CFA066A,0xCCCCCCCCCCCCC12E,0xCCCCCCCCCCCCCCCC,0xCCCCCCCCCCCCCCCC,0x1EE5F99502CCCCCC,0x1A381FE09EEA2DA1,0xD978110991782CF7,0x1AB9AA8197120}, +{0x41FAB8BE05474CC2,0x54741FAB8BE0547,0xB8BE054741FAB8BE,0xC9AE7F39FF4741FA,0xB1F4EE9D1CDDE556,0x1650D500E95EBA31,0x5023E95DDE16,0x54741FAB8BE04FA9,0x8BE054741FAB8BE0,0x1FAB8BE054741FAB,0x16655C7EB0E05474,0xD849DDDEC437B020,0x2E677A183619E2D7,0x19324B6AFA19D}, +{0x8536718536718A34,0x3671853671853671,0x7185367185367185,0x88EBEF311A718536,0xA7D32684ABC9D6E9,0x86FFA027C5EA41ED,0x1EF2D26807E04,0x8B01288B012888A3,0x1288B01288B0128,0x288B01288B01288B,0xF2CAF7B478288B01,0xB30406DB0864DD0C,0x7DE19AB6317E9551,0x1499080A4B0D6}, +{0x497819E2B03FF6AB,0x43C254E3A3E0C8FE,0xA1F98753F0030B9C,0x9D08AFDF66CDC06D,0xDC9B4D2060AC66D4,0xAA1B0432076D8C12,0x8C728C65FAC7,0x7787B5638B83E57E,0x4BC0CF1581FF9E8C,0x1E12A71D1F0647F2,0xF874D414C6185CE2,0xB1C3CEFB8EF40E5E,0xD974CD64813E2AD0,0xEF9B64A50B19}, +{0x4FAC336C14F326D0,0xF324FAC336C14F32,0xC14F324FAC336C14,0x7A441A68B4FAC336,0xF55ABB9E02E51BCD,0x7DF241E5CC125D82,0x20CD99B418553,0x79927D619B60A6B2,0x60A79927D619B60A,0x19B60A79927D619B,0xC1836ABCD19927D6,0x56ED5F9FA770E50,0x938A248852AF05FF,0x180454EC85AD4}, +{0x8FC8F97836B765C9,0x79F3DDD74597E657,0xF40F4D525855A12C,0xB504F4CAE1D399D4,0x5B3EBD1F2ED83FF2,0xE84645130B2D0DBA,0xDA2062334ED3,0xC71EA489199E8B2C,0x4CA048F486023DBF,0x7D1F0775331F6A61,0x238045677D90A29A,0xA9A61EA8DBC1A3F4,0x7D71C1C648CD9742,0x1075C2F69D7C4}, +{0xC3A939DD014D003A,0xA92F1F17B5248C25,0x7399C8DD37028F40,0x78F15EE9E1AEC3C9,0x9C6EC31DE809B64F,0xADC32BB57B097A2B,0x182925F9D25CA,0x37B92BC3BEB5AFB9,0xC389002039BCC790,0x769F328FEC87C89C,0x45F48B81136118A1,0x771813745D6BBD3E,0x1DB0C12AB3EBFB1D,0x14733DD55FF54}, +{0x8D3D7757053F25DE,0x1BB0A5534AD2D44F,0x6A5D806D0822AA3D,0x81D30F00C5FE0658,0xDD7EDBA5455F0CBF,0x321F8C3287B5561C,0x10C3B9266397A,0x58AFE48B66934683,0x2BD00D3BE2D0F3F0,0x366476DBC465DF23,0xCF46D882997C04CA,0x100047EAE7B1B0CA,0xE98B984D9BA8857B,0x19D8D87E9F5E7}, +{0x16255E514230CE8B,0x4CEE6DB1C53E2C2B,0xE69FC4293B640916,0xBEDB813769959101,0x75374AFDF84FA267,0xA08A7C370DEA787F,0x1C42814BBDFF3,0xCA970CCFC4688815,0xB0EF9A5F6A27C77F,0x57FF227293F58D8B,0x2782596E2D3675FA,0xF3B4D13FBB928B8E,0x5F9B384AE0301D97,0x15DD020A61A84}, +{0xB9758CA6605A88DC,0x9B0E00E773B0BE3F,0x8D1CB3F2BBA35FE1,0x5BD852F804F988BA,0x5AB812185EC1F54A,0x81EE7303B3B11EF8,0x167A5C4B8EC00,0x537E31BF0E7887B0,0xF28A3A23236AEF0A,0x49B722040DA1FB99,0x89C14F4BF6ADE22F,0x8303646A89C2A6D6,0x4446EB8898043332,0x1C1BE6A2BAA3F}, +{0x60904BED92E6F0A1,0xB75830F83D32BDCE,0x5303D79E3A35E71C,0x57F1D1FBF1F6424,0x9D29AFFCD4B9F82,0xDE6CF6ECF1EDB33,0x1B330E4A5A838,0x9DBF7B0AE6C58C5,0x45E3E366E4AFF3A9,0x29E3BFD3FA3102E9,0x4F66726AC8918DDF,0xAC46D1291B0F682A,0x197E0510E123E22F,0x141E2A18F39E4}, +{0x611E67F5AFE0C95,0x73F50769BEADF858,0x5FF1EF605FF0AD88,0xC80A90794F63FDDE,0xA435619598EC3001,0x34AF362A0C54F5EA,0x17A9719011B55,0xE183ECD15F816A3A,0xF6F117C4395997BE,0x67AAE2316B369528,0x618723D3BFE02D5,0x947CE54AACCA22AF,0x4963179F500215D8,0xA69EB2B134C5}, +{0x4512C7CB549E0613,0x58B3138052AC291F,0xBDB21A1D0DC8E1F3,0x8F33DE426C49F38,0x78ED469B002924BC,0x94FBCA884C534ECE,0x16411608F666E,0x76DCF643092ACD65,0x87827A6E7863F18A,0x5FBB99DF645C6BDD,0x26E3468335753344,0xC6BB91D8121B199B,0x3BC17926E87E395D,0x7D5A5FF0E692}, +{0x2CD377F7AF7A3996,0xFE915A6848EB6335,0xE2796F2ACB922496,0xD5FEAE7013EC2D63,0x1B264179788453F2,0x3A50528DF123CA80,0x3C2B61484D9B,0xCD1CFE4E128028C,0x7E6F33F849117206,0x422F91D71D67A4CB,0xA9C6E809C409E2D9,0xD3D9B2D66BAC46C7,0x68CEEB5277B8DDD3,0x381E05A78010}, +{0x4F4EBAA4A85CBB5A,0xF6A3476ECCE55C,0x6DF6C3C9230F72FA,0xDCB283C6564F0BA,0xA82B8AC12EDC42E9,0x5FBD7E3CB399C776,0xFFF6BD7C7E3E,0xDC68551ECFC41D23,0xC237308737FA469E,0xE6A81586A6FCD565,0x3DED4572B5A03B45,0x6946056BDF996305,0xE2F1389B1D6CF35C,0x10CD02839AEB3}, +{0xA5959A668F12A176,0xB310CEBDA555CD7D,0x78B28C38E9A01DF,0x6197E0DCCE65322A,0xA8D2A1E798A9702A,0x753603AD399F0CAA,0x105A74C730C51,0xC8D0CA6784B4551A,0x45D4AE4A0850F0C8,0x391DDCAFE0C29DC1,0x8270BF6B173AC986,0x73770F0EAA80DDEF,0xBB7C9EE74BD61C23,0x7A592BC0228D}, +{0xA302403B141A0385,0x9188DF46965BF724,0x666234B05EB3A268,0x37AB02DCD5D0FB01,0xED9FA4ABF47BF81A,0x31B87D353910E9E3,0x1E931A394CEF8,0x9E46F21160F6FEAF,0x6359F8041E2E0FEA,0x4AE82F18B6A502F1,0xCC2D17C159C53B16,0xDC5076C57AEF74C5,0xA4D66592DBF0E267,0x12E32E3B2202}, +{0x9237E2347B57BBD8,0xE16C142FE156484A,0x87E8A48B3B14220,0x34B6225A95A547ED,0xD26CBF294A3E2E72,0x33C06874E35A7F57,0x17DFC7A25D7B7,0x91ECC77A8220B97E,0xBD3818A24751F785,0x2E3FD75D7AE703AB,0xD7E8692B70CA482C,0x53C8B5DDEBA21D6D,0x5FC1E218D7085E99,0x129CD0E49FE6F}, +{0x3945471CC48EF6BB,0x7C3FB717D0165DC8,0x92F83793BFEBC75A,0xD5BF95D93BFE5316,0x209E198DB1F16A4,0xE2086C62914F403A,0x19D6352AA2CC,0xBFFF0BF092E15611,0xFA429EEA322007B3,0x99EFB4184EBBD84C,0xF6C5230835D383A8,0xF1CD8283C93674AF,0x41C64F9EA1AC8458,0x2CD68D0A2571}, +{0x570C567E928211B1,0x70459EE4560443C6,0x1FC204B885DBB2C0,0x7C99D3BCAF19BE0E,0x5BFFD67B5AA530E7,0xF8701F7AE35B9C57,0xF056DF1DFCBE,0x4183962A42D28AD1,0xFF8B6A5752A5FAEB,0xA4B714F92FE41B11,0x8CC5D5EEFFAFB58B,0xA53A15C837E4CFC9,0x1A79CF6122569F16,0x1FE4DB81AE342}}; + +// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions +#define fpcopy fpcopy434 +#define fpzero fpzero434 +#define fpadd fpadd434 +#define fpsub fpsub434 +#define fpneg fpneg434 +#define fpdiv2 fpdiv2_434 +#define fpcorrection fpcorrection434 +#define fpmul_mont fpmul434_mont +#define fpsqr_mont fpsqr434_mont +#define fpinv_mont fpinv434_mont +#define fpinv_chain_mont fpinv434_chain_mont +#define fpinv_mont_bingcd fpinv434_mont_bingcd +#define fp2copy fp2copy434 +#define fp2zero fp2zero434 +#define fp2add fp2add434 +#define fp2sub fp2sub434 +#define fp2neg fp2neg434 +#define fp2div2 fp2div2_434 +#define fp2correction fp2correction434 +#define fp2mul_mont fp2mul434_mont +#define fp2sqr_mont fp2sqr434_mont +#define fp2inv_mont fp2inv434_mont +#define fp2inv_mont_bingcd fp2inv434_mont_bingcd +#define fpequal_non_constant_time fpequal434_non_constant_time +#define mp_add_asm mp_add434_asm +#define mp_subaddx2_asm mp_subadd434x2_asm +#define mp_dblsubx2_asm mp_dblsub434x2_asm +#define random_mod_order_A random_mod_order_A_SIDHp434 +#define random_mod_order_B random_mod_order_B_SIDHp434 +#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp434_Compressed +#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp434_Compressed +#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp434_Compressed +#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp434_Compressed +#define crypto_kem_keypair crypto_kem_keypair_SIKEp434_compressed +#define crypto_kem_enc crypto_kem_enc_SIKEp434_compressed +#define crypto_kem_dec crypto_kem_dec_SIKEp434_compressed + + +#include "../fpx.c" +#include "../ec_isogeny.c" +#include "../compression/torsion_basis.c" +#include "P434_compressed_pair_tables.c" +#include "../compression/pairing.c" +#include "P434_compressed_dlog_tables.c" +#include "../compression/dlog.c" +#include "../compression/sidh_compressed.c" +#include "../compression/sike_compressed.c" diff --git a/src/P434/P434_compressed_api.h b/src/P434/P434_compressed_api.h new file mode 100644 index 0000000..dfd9ff1 --- /dev/null +++ b/src/P434/P434_compressed_api.h @@ -0,0 +1,109 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: API header file for P434 using compression +*********************************************************************************************/ + +#ifndef P434_COMPRESSED_API_H +#define P434_COMPRESSED_API_H + + +/*********************** Key encapsulation mechanism API ***********************/ + +#define CRYPTO_SECRETKEYBYTES 239 // MSG_BYTES + SECRETKEY_A_BYTES + CRYPTO_PUBLICKEYBYTES bytes +#define CRYPTO_PUBLICKEYBYTES 196 // 3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES + 2 bytes for shared elligator +#define CRYPTO_BYTES 16 +#define CRYPTO_CIPHERTEXTBYTES 209 // COMPRESSED_CHUNK_CT + MSG_BYTES bytes + +// Algorithm name +#define CRYPTO_ALGNAME "SIKEp434_compressed" + +// SIKE's key generation +// It produces a private key sk and computes the public key pk. +// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 239 bytes) +// public key pk (CRYPTO_PUBLICKEYBYTES = 196 bytes) +int crypto_kem_keypair_SIKEp434_compressed(unsigned char *pk, unsigned char *sk); + +// SIKE's encapsulation +// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 196 bytes) +// Outputs: shared secret ss (CRYPTO_BYTES = 16 bytes) +// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 209 bytes) +int crypto_kem_enc_SIKEp434_compressed(unsigned char *ct, unsigned char *ss, const unsigned char *pk); + +// SIKE's decapsulation +// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 239 bytes) +// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 209 bytes) +// Outputs: shared secret ss (CRYPTO_BYTES = 16 bytes) +int crypto_kem_dec_SIKEp434_compressed(unsigned char *ss, const unsigned char *ct, const unsigned char *sk); + + +// Encoding of keys for KEM-based isogeny system "SIKEp434_compressed" (wire format): +// --------------------------------------------------------------------------------- +// Elements over GF(p434) are encoded in 55 octets in little endian format (i.e., the least significant octet is located in the lowest memory address). +// Elements (a+b*i) over GF(p434^2), where a and b are defined over GF(p434), are encoded as {a, b}, with a in the lowest memory portion. +// +// Private keys sk consist of the concatenation of a 16-byte random value, a value in the range [0, 2^216-1] and the public key pk. In the SIKE API, +// private keys are encoded in 239 octets in little endian format. +// Public keys pk consist of 3 values of length OBOB_BITS, one element in GF(p434^2) and 2 bytes. In the SIKE API, pk is encoded in 196 octets. +// Ciphertexts ct consist of the concatenation of 3 values of length OALICE_BITS, one element in GF(p434^2), 2 bytes and a 16-byte value. In the SIKE API, +// ct is encoded in 3*27 + 110 + 2 + 16 = 209 octets. +// Shared keys ss consist of a value of 16 octets. + + +/*********************** Ephemeral key exchange API ***********************/ + +#define SIDH_SECRETKEYBYTES_A 27 +#define SIDH_SECRETKEYBYTES_B 28 +#define SIDH_PUBLICKEYBYTES 196 +#define SIDH_BYTES 110 + +// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys. +// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016. +// Extended version available at: http://eprint.iacr.org/2016/859 + +// Generation of Alice's secret key +// Outputs random value in [0, 2^216 - 1] to be used as Alice's private key +void random_mod_order_A_SIDHp434(unsigned char* random_digits); + +// Generation of Bob's secret key +// Outputs random value in [0, 2^Floor(Log(2,3^137)) - 1] to be used as Bob's private key +void random_mod_order_B_SIDHp434(unsigned char* random_digits); + +// Alice's ephemeral public key generation +// Input: a private key PrivateKeyA in the range [0, 2^216 - 1], stored in 27 bytes. +// Output: the public key PublicKeyA consisting of 3 values of length OALICE_BITS, one element in GF(p434^2) and 2 bytes encoded in 196 bytes. +int EphemeralKeyGeneration_A_SIDHp434_Compressed(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA); + +// Bob's ephemeral key-pair generation +// It produces a private key PrivateKeyB and computes the public key PublicKeyB. +// The private key is an integer in the range [0, 2^Floor(Log(2,3^137)) - 1], stored in 28 bytes. +// The public key consists of 3 values of length OALICE_BITS, one element in GF(p434^2) and 2 bytes encoded in 196 bytes. +int EphemeralKeyGeneration_B_SIDHp434_Compressed(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB); + +// Alice's ephemeral shared secret computation +// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB +// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^216 - 1], stored in 27 bytes. +// Bob's PublicKeyB consists of 3 values of length OALICE_BITS, one element in GF(p434^2) and 2 bytes encoded in 196 bytes. +// Output: a shared secret SharedSecretA that consists of one element in GF(p434^2) encoded in 110 bytes. +int EphemeralSecretAgreement_A_SIDHp434_Compressed(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA); + +// Bob's ephemeral shared secret computation +// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA +// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^137)) - 1], stored in 28 bytes. +// Alice's PublicKeyA consists of 3 values of length OALICE_BITS, one element in GF(p434^2) and 2 bytes encoded in 196 bytes. +// Output: a shared secret SharedSecretB that consists of one element in GF(p434^2) encoded in 110 bytes. +int EphemeralSecretAgreement_B_SIDHp434_Compressed(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB); + + +// Encoding of keys for KEX-based isogeny system "SIDHp434" (wire format): +// ---------------------------------------------------------------------- +// Elements over GF(p434) are encoded in 55 octets in little endian format (i.e., the least significant octet is located in the lowest memory address). +// Elements (a+b*i) over GF(p434^2), where a and b are defined over GF(p434), are encoded as {a, b}, with a in the lowest memory portion. +// +// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^216-1] and [0, 2^Floor(Log(2,3^137)) - 1], resp. In the SIDH API, +// Alice's and Bob's private keys are encoded in 27 and 28 octets, resp., in little endian format. +// Public keys pk consist of 3 values of length OBOB_BITS, one element in GF(p434^2) and 2 bytes. In the SIKE API, pk is encoded in 196 octets. +// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p434^2). In the SIDH API, they are encoded in 110 octets. + + +#endif \ No newline at end of file diff --git a/src/P434/P434_compressed_dlog_tables.c b/src/P434/P434_compressed_dlog_tables.c new file mode 100644 index 0000000..c153e7e --- /dev/null +++ b/src/P434/P434_compressed_dlog_tables.c @@ -0,0 +1,28967 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: precomputed tables for Pohlig-Hellman when using compression +*********************************************************************************************/ + + +const uint64_t ph2_T[DLEN_2*ELL2_W*2*NWORDS64_FIELD] = { +0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA, +0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x1456085945D0BBE6,0xA23060443A427246,0x6414C3E45A2D4823,0x31199D4A05995ECD,0x708B6618CB10EB64,0x2E199015E016EEFB,0x2333EFDB53522, +0xE1BE789DA9B9430A,0x6CA157BABC640F89,0x18DF05CDB35D8457,0xF5A852399993032E,0x9813A5F96E1A6F99,0xEBF778DB119C8E69,0xFEF5F10D76D6, +0x89208B6FDF956BDA,0x312AC4F6E9C85F61,0x1B23FBBED83E9D36,0x1EF851C1C2EB17BC,0xA92211A301627063,0xE7CE55FD626D5223,0x13BE0680A3675, +0xF5B897CFAF9FE076,0x1E7165DEB9D50571,0x6C811BEFA0DCF16,0x20DB0016EA256AF9,0x9E976F1C93520308,0x81ECE186530EA978,0x2286AFB77C08F, +0x7F01E1B3ACDE3D61,0x60B5805D38581CCF,0x5910ADAEFF8407E6,0x7D3C32FD2CC99FE,0x26017F0905DD06BA,0x705FDFD4AFB2B286,0x50904E766D96, +0x2A178B7B01445B4B,0x4F8CC070A1E3F827,0x9C57D7998F0FA40A,0x294C04A269F86F56,0xFC195697B2307E76,0x700D13217667C845,0x2F744FB2317D, +0x93F88D69798C984C,0xA9CC28230B2C73E8,0x159DB9A1745AE7A9,0x9E243A74A4FC1532,0x5FC2EFD47B68C49A,0xEEE33086820795A4,0x98956B5DA6B, +0x6D09B7EDABFE7AFC,0x12DCB2F666F066A3,0x60B97552D60A0DCE,0xD0530437CAEF853A,0x833A5BEC1C3E38C6,0x68E9208208B6C649,0x18145BA177798, +0xBDAE367B872D445D,0x1B41D5394F010B68,0x20AE4B45BE601BE4,0x9F7683B5A8A36BD2,0x5B208FAFF4874E68,0x36D4A78A0638FE13,0x1CAB44915868, +0x5413918A9C6AC04B,0xCC9AFAE9FE8DEF18,0xD1F1F828B7832254,0xE22C8D0E43FD51C3,0x84FADF17B3AF5989,0xD86D999F0763C569,0x4868CD118175, +0x4BE2D77B660001E9,0xEE67F358638B0348,0x1D2C0F8D8C883D3F,0xB6DD7E48326F1A95,0x2C3359677B50F984,0xE7CE202AE925DEDE,0x21AFFA487FEB0, +0xB64077578236B48A,0xE4F02BAF7936E01E,0xC7732BD164CDE847,0x178830150B442F78,0xB868604C0E1DB4B2,0x3DB54785C9924535,0x1DEDA1E127F32, +0x88CC7258461DF40A,0x1C1C0238BFDC8D5D,0xB739C1B9124E80F,0x467304C785304B0,0xC438C5DC4C138A44,0xEE637878D2BDCC56,0x106F1CFF98A6A, +0x50E03E36C8E537D6,0x9FE082583E09E678,0xBD50F262866500C4,0x1611AD005AB676B9,0x3D70DE4149F512C3,0xA5FE0A8AF42F9B28,0x1FA096A6B5BF4, +0x2E737AFC3279C736,0x5C80BE5804AB5121,0x334CE5B896B20A2A,0xB0B7628931F14103,0xF452229220177C66,0x479B76B25A8F2EB1,0x8C24E4BE0212, +0x52D2E72D5C3D7C61,0x462D101651DDE024,0xE874DEE1A884C6FB,0x2D7667BF2F86E7E8,0x13DCFF8FDF529F1B,0x30315CB0BD0DACA4,0x3525067AAF90, +0xBA41BF62B985EEF5,0x37AD6A1FAD0DFEB8,0x39FA5FA1657E0709,0x8E911E6A1CB7EF8A,0x42CD070A86756FC7,0x8D315D5C2C64EFEF,0x13A32B6C89375, +0xFE5D6F7FCEB95BE3,0xDEAF36DF50427E4F,0x5381138C47614B13,0x9E742C0B94F3EBD6,0x7F5107286107FD8B,0xB51F147B718005F7,0x16F2CB8A81EFD, +0xCF4B274B2A4AE81A,0x1070E2CD8B996D68,0xE4104D53F174B340,0x95462E13386FD3CC,0xBFEA7BBAA0730B6F,0x5F06C12F454CF925,0x90471DD82E55, +0xAFBC6933CB813453,0x984D1D6A04AF1989,0xB29E46E0C72EDBB6,0xA1353C491C157CED,0x8D29FD5846148F4D,0xEF9542062F842624,0x102968A025139, +0xC1B6690A6C84BA1F,0x7F40F753AAB17A54,0xC60C72D039C3AC93,0xAE31798A36B6A6A5,0x5EB938051FE62A90,0x7C8D5D4509701D1D,0xFF868F6F3007, +0x6226DA2192B980AD,0x83C10A4EEC3A1EC6,0x4C718AC9F6FB4DE0,0x110CED3727F66B17,0xD0EA0554055672B3,0x3EEFD070578ADC29,0x120B5B8AFC3CB, +0xF491D7F062E73049,0x29DD7C77A9B2555A,0xFB2AD5233488022D,0x212F7DFDC7CD0074,0x3306459EDF0474A8,0x553C979E2CACB087,0x10D27DD11727A, +0x9E3E1CBA73781ECF,0xC354290C0B23ABE1,0xA6723F937CDFE36A,0x1F2773A8579A7E68,0x2B90F0AA4ED43D25,0x821AFD9741A08CD6,0xF3F4259E6BD6, +0x54BBB1D9E8AD75AE,0xF71C6F8C26BA729F,0x2025EC60ED4D1806,0xCBECBB8CF05300A7,0x29A0C91093794F60,0x8926B06A132ACD6D,0x1F09F6BC20D25, +0x359820E91E01EC2C,0xA169E79B59162BB5,0x15EAA57F5AFAB428,0xA29795FB3687EE30,0xF2D8F53512C1294A,0xC4F027858BEB96E8,0x83F492BC7BE5, +0xB88DC7A4B6F8376,0x40575F5524B708C1,0x5D974B0DAE2C337D,0xB88F5FCD0128CA8,0x3807A30450C18AC7,0x242192BB43E1F585,0x1F94FC591027C, +0x144E12A5A2354AAF,0x40D7883A0E872DE2,0x490ABC9A55C8C82E,0xE78D576B83905EC9,0xD04E3EE3AC70726F,0x33FCCB8601E80DDD,0x17076684EB087, +0x67A39CB25226D252,0xCCEEABF643601A5,0x8C27F1460DC9ED75,0x1453024085A44EDC,0x775D3D601E4B45C8,0x2CA100E59952945B,0xA13108406EC, 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+0x6263A3DDA1BCBD39,0x3884DDEB7C542501,0x4B09E30172434E3E,0xE6618A7CA54A4B2D,0x38AA3C484A7A59C6,0x4FB5B5B7DD88D00A,0x1922704B96FD5, +0x4ECC0C645C8AB896,0x2DD42C054D5638DB,0xE52E2A447CEA474D,0x32BF52C92E831087,0xDC0EBBAA482DB8A0,0x21E3A039E1179A64,0x1AD4DF754B17, +0xFDE8E47142A9938F,0xA19A504C8671F14D,0xEFBDA9AE096A070B,0xF7EEFE285EC3E73F,0x5BC0AD996EAE40FD,0x931919E827701977,0x129B91EAFACB4, +0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0xFFFFFFFFFFFF8BD3,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0x44B18275E6FFFFFF,0xA3C4B77CDBB901CF,0x83CA0B82224DDF49,0x147307F5A4469, +0xB133F39BA3754769,0xD22BD3FAB2A9C724,0x1AD1D5BB8315B8B2,0xCB0223B1B47CEF78,0x9FB7A0CDE92AF603,0x4B18BF9CA0AD85F1,0x2194A47A2282D, +0xFDE8E47142A9938F,0xA19A504C8671F14D,0xEFBDA9AE096A070B,0xF7EEFE285EC3E73F,0x5BC0AD996EAE40FD,0x931919E827701977,0x129B91EAFACB4, +0x9D9C5C225E4342C6,0xC77B221483ABDAFE,0xB4F61CFE8DBCB1C1,0x175FEBFE3DB5B4D2,0x431C202FE6DE54DD,0x1D46AA1EA43C504C,0xA1F8225E036F, +0x6263A3DDA1BCBD39,0x3884DDEB7C542501,0x4B09E30172434E3E,0xE6618A7CA54A4B2D,0x38AA3C484A7A59C6,0x4FB5B5B7DD88D00A,0x1922704B96FD5, +0x2171B8EBD566C70,0x5E65AFB3798E0EB2,0x10425651F695F8F4,0x5D27852843C18C0,0x2005AEDEC2AA6DA6,0xD9E345EE5A5506DF,0x10A660867C68F, +0x4ECC0C645C8AB896,0x2DD42C054D5638DB,0xE52E2A447CEA474D,0x32BF52C92E831087,0xDC0EBBAA482DB8A0,0x21E3A039E1179A64,0x1AD4DF754B17 +}; + + +const uint64_t *ph2_T1 = {0}; +const uint64_t *ph2_T2 = {0}; +// Assume W_3 = 5 therefore only using ph3_T1 and ph3_T2 +const uint64_t *ph3_T = {0}; + +const uint64_t ph3_T1[DLEN_3*ELL3_W*2*NWORDS64_FIELD] = { +0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA, +0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x37ED7978F7323982,0x4936C76D51F21F5,0x16050C18A973EE88,0x72F7BF23AB9375D3,0x47C989C9C28BA7B6,0xDF611D74933C983D,0x1BC0CBF2A04F4, +0x8A0EAC4B85F5303,0xB686A96CB86BBC16,0x8F36EBD4A443E09C,0x948222B2B2D156F6,0x8A66ACFAE2CCD48B,0x98DEEDA161F27B50,0x103F846A96DB5, +0x694F92DFDA192A6A,0x53DB650F045FBB94,0x914D7DD5D24B8A7D,0x332A4681B4537855,0x77B22ED3C97AA0A8,0x29F51E43F01EEBF0,0x2BE99CC2EA3F, +0x50AADD31483272BD,0xEF71AFF18F5CD2A7,0x2718B25973322EE9,0x4AA70233D7135E34,0x18E840E9D3D8137D,0xCC10E80D37099E81,0x611A286EE0D1, +0xA9354A35B269FF9F,0x6FD04B074DF96AF6,0xC3106A5031DDC3E7,0x96D97DB085DE52CB,0x52E69CD3E0656B33,0x413B47B6FD5C630A,0x99B4D7906FA4, +0x4773AACD7C006827,0x6E0D9C18E227CEB2,0x970AA29DDA4FC705,0x7DB2A73DC99EB,0x503DA274C8A57B9C,0x456519435726C6BD,0x1269589CECCC9, +0xF03E85B4AA764A,0xD6A2D3F58CFCB874,0x92DA0409FD01266B,0xADCC6564A5D4F6F7,0xC02F15A74EC243E8,0x7730B32C01DE2F53,0x7E846A2516F7, +0xE133F07C2ED3E1D8,0xB4326C2931139F04,0x6A51505413E95C84,0x736ACF58BEEF524F,0x538B2008AF8272BD,0x4BA606901671E978,0x177FF06B895C4, +0xFDC3EBCDD657CD6E,0xA247E9F561464943,0x3C1009CB51346175,0xF002A2B6FA005AEF,0xEDDF64F46D2A177C,0x83518EC200172743,0xCCB04068DD44, +0x45C5EF8ED846E9A1,0xC594E2935A404A15,0xF1FA86D9065998F9,0x3177F334A98AB972,0x683137B06187B6C5,0x763E818699AF9A82,0x25CDBC8D6DE3, +0x27AE2A62883696B6,0x591D09EF41B582E3,0xAA5B4530E1582194,0x99CCB2BCAD4E2F47,0xAF7B2BBC1BFAEF2A,0xD2D3BCB820C00A6B,0x184CF997B843D, +0xD149B9FF09F549CC,0xE7CFAEAB0F338F18,0x9EA6958AE87055F5,0x408E4C22C8263BC8,0x17E57438EEDDC7DB,0xD58BB12D4423F92F,0x1D7D0C433AD30, +0xC7DCBE1AEC6D7C2D,0x8F6FB8EDACEED8A3,0xA92B7BA065B357F1,0xF6A92D93E4F369B4,0xD0B517306D4B0BAF,0xF53ABA5B52BEFB27,0xC56412AA646B, +0x4B826A4831175010,0x67D08097812EF865,0x1950DA79789DA00D,0xED0B99011BB1215C,0x5E5B32AC7AE8C701,0x561D7DE509792047,0x1C21010F2BCCF, +0xF057F3BC88DF9B21,0x8B8EE060C16EE48F,0x2FDAC5C9B23B3ECB,0x6AAEE97E18D02869,0x5EF58C8866A37082,0x9D42D0D7D776AAF7,0x9106AA9E5BF6, +0x7F7F72CA5B66613B,0x49FF121C8796E2,0x446921D8A9193C4D,0xC46710A67EF0094C,0xEFEA22E111B76E16,0x2132DDE3208096C8,0x158537695C848, +0xC9B7E0C49271E5E6,0x9232D78410486561,0x15CB972066F892E8,0xA221C57C5BC43FDF,0x3CD91966B44E4005,0x4313785071F6AAD4,0xCC4419E3E98C, +0x83EF71190034677F,0xB73C0DA961FBF58C,0x2D2FA4D06846EF77,0x249169E3A3B98786,0xBC1076683BEB81A4,0x45D0E9EB5D1324FE,0x627AFD457D2E, +0xA2D211FD38E81A4E,0xE74DF34D9BDAAD83,0xFA9276E47ABCF316,0xE306ACDDA72C24FA,0x5B68BF41E7F5BF84,0x322D98FD53020106,0x8902F84E1521, +0x8C44089102E680E8,0x4CE3AD9309B0D800,0xE2AFBFE63C21F2F6,0x51D7493A7E0E5F24,0x5F4EBD5D1CCA229E,0x6B49826312FF74D8,0x91AB97F84071, +0xC363D921AA5766B4,0x5F78F0E41B0F5359,0x4A43F68C67C5BCE2,0xFEAC89F6BF98C204,0x9D7AC06DBF4FC7B4,0x26989B3B2D44C774,0x1B6C805550CB5, +0xD253F7739CCDB075,0x8318538FAD5D33A2,0xDBF3CCADFDE3674E,0xC6773568F794E12D,0xD6A71F2C69C17A5B,0x53FD7701967BFE2A,0x5CB62ADF7B66, +0xF1876400E4AEBCEC,0xDB7D4068365A6399,0x8D2B3C07E3AA1D93,0xB763B70480DB937E,0x6B209F9E89C1C38E,0x99F233803462481C,0x1703585A8F941, +0x53651286AF21B7BD,0xB5DC8DE712CB9D2B,0x8C8653F83462375E,0xA13993C7C4E915F2,0x964055D5E5966731,0x357C020389033773,0xCC534E50DED, +0xFF72F3C9C8A650F0,0xCE49F4C2868EF761,0x458103FE62D5D7EC,0x5EDF0259B91D5E5F,0x1D08EB6816BD60E5,0xA946F4C5D79C5C1B,0x223E0CC250BC, +0x2B51A049820E158D,0xB0AE40314ADDBCED,0x7ADA8CE98928AE66,0x54CB91E1C6E32237,0xC5BA6BBE489D3E92,0xC61076FBB6204480,0x16725A031428C, +0x3A92D6D06B0B6EDB,0x1ADE21C97654BE73,0xE271928261B0076,0x6B9DF8D0E09C8992,0x27F786EDA59B3C9,0x975A8BEE7B5EC4C9,0xAFA0FDA363FE, +0x9047EE7C050CBED4,0xF3781E1D85D49BB3,0xAD873DF315248617,0xA9E7355B2CEAE96B,0xE90FC31DC64DCD64,0x6F45178E5A29321C,0x1A618CAFD119B, +0x5672D70BE990A15,0x3FEF40FC149C3FE8,0x9C81EFCBAE70DD6C,0x9F964655DA5913E7,0x59432E918D96F444,0x2B59102B23F4D2,0x4A425F24DDE6, +0x324BAAAE2FDEAB86,0x63607B03D45F6A9A,0x230D76A303A8C8CE,0x97B3C313174CBBCC,0x5A24B5DD77C206A8,0x751AF2A1299B204,0xCF767AC97B04, +0xF75A643B16C5B398,0x1255224D230C319D,0xC733F9FEA0EF30B,0xAD99BC3033C58A98,0xB44F5CFA20F22066,0xBFD0350548D89E1F,0x6E52ABE1C15E, +0xCD910AF82A8CA8B2,0x6F15C4A286951548,0x6EFC3CAA976400E2,0xD18FB293397D4F45,0x116CD09871E669AF,0x966F0985B71EFBBC,0x647457D4C9C5, +0x6714EEC0AA9B8FCD,0x6A777B8393705E2D,0xD12CD81353E9679A,0xD3D53268A2806B43,0xA68F82D9345F3C9D,0x414851DB9E366422,0x1B32707A898C9, +0x334E85C9B2A3107A,0x21D049D0C092EBD5,0xD1CCD08A75B38964,0x32029A5740ED5DAD,0x8090D84FF425DA83,0xD4544D90A1AF897A,0x1C6A8E8D424C3, +0xC03CD433DBFD1940,0xAD1049F408EAFDC6,0x9413F0B3B5F855D2,0xB466E1E85E7E45E1,0xD353B33DE6AAFDBF,0xAF62EC1EE44B00A9,0xEE42010787DB, +0xEF422805A8ECF8B2,0xEFC179F15231A992,0xBC9F1827039347A,0x60D8FBD734560515,0x60E378BBF16EA78D,0x96AF9D3C96D4CDAF,0xC16C643E295B, +0x36D16CD0263A9AB9,0xD87BC4D53C6E1211,0x2AE87901381D15FA,0x209C834F76D467B6,0x55B2BD003C7E8269,0x701814E0F24A5C4E,0x3CF57DCFD233, +0x749C38DC298B7F9A,0x371C8F3940AC9690,0x895CC8DA0846BD84,0xE970194C504D02D1,0xEB495492BCEEFAEC,0x97BC3276F515D0E1,0xE1C5118185A1, +0x2EE8E7ABC8098A2B,0x67C75F3B45A2875B,0x10918167956B7F5E,0x4D3BE6F465F3E297,0xFDFD202F29DFFCBA,0x5D04E97F6619600,0x14475CE430F93, +0x34E47AE7DBCEB9D0,0xF8478BE803AFC918,0xD5798299E2A62AE8,0x55F75A9703FA6DE6,0x66D6427BA3A1F840,0xF4E9BF5C0F04CC6B,0x2204CD8AAEE0A, +0x193A0D15F7350DC5,0xE79F588318E1E782,0xDDB4B5F58336AF43,0x89E77C897292E4E1,0xE0B36791D63FB443,0x225A19E20E67C086,0x161F727194FBE, +0x93A5A681B53DD22E,0x6E013311BE9B4392,0xFA300B3DFAD4763C,0x790A43D65BA4875F,0x349334D35ACB270F,0x5E8237B1B1CFA852,0x231D841E935C8, +0x510D3F267F7DA78A,0x70BB4BAC53909066,0x30532EB396A82BCA,0x3F3B26C7C7CF9A9,0x2AEF32AE78AC179,0x6163ADB1AF2BF0F2,0x1ED121B74EE8, +0x3A6860FA56380021,0x613CD8D1C7DA09F7,0xC705ED31F5CD3BF9,0xEAE3B3F59774158B,0x287CCCB2114E5F11,0x5C3404192C065307,0x20E905E0F024D, +0x6AE64194AE1B5C0C,0xF322C8CBE5F2A1B5,0xE030A2A09E212E90,0x5B0DF6EEC8B864EE,0xC8B4B86F2EB5CCC4,0x9CF2A12A8C439E0C,0x1E0366566EF7F, +0x839968BB4B100D67,0x2A913C4CA9F8D213,0xCBDA82E3742C3DDB,0xCB87AC7D728E8FC5,0x6CAD812E2874436,0xFD40F2D7298EAAA7,0x201B7D988430, +0x3EE21729D80A3C10,0xECE93D61791DAC1F,0xDCA3594C2A1C133F,0xD5FDAD0DF683BACC,0x8499D710A97E98E1,0x3151ED382A2DF84F,0x1BE89904FD7ED, +0xD62D77E34232DC33,0x870D8843706E31ED,0xAB2D4DDDB453188F,0x5B5B6F24C74D4D36,0x8EB8D4749A090D27,0x4E1D298669BB2388,0x18FD0F5CE711F, +0xEEE231DD313EC727,0x4F6B715B352FC32C,0xBFC9F2BA24E82C7,0x575F6918FF4DD55D,0x1CD8849EAB6FC8F1,0x7CDCF28CFB53A84E,0x16E04BB1F4944, +0x5255ACC85A3A70DC,0x552C28DB8AA92710,0x62155C80F3115FC5,0x9A0A8CFBDCE72DF7,0xF3EE5CE93CC46061,0x9EB9554C8CF9F458,0x17671AAEC0A64, +0x14BFFE93F44331F4,0x5971011EC5077996,0x437CEC1D8FC8FE7C,0x5B3797BA4B089F2A,0x6C63871A19A23BBC,0x2FA8FD85E9319982,0x230C7336AC471, 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+0xBEF0CE72B6E9D1BD,0x92E0A4F2CA7CCCFF,0xA0B2035BB47215FC,0x6D36985E0F7DFC52,0x6BB989478F1D3A0F,0x8C5988BFDF5F4F7C,0x6E2AAF9B9D9E, +0x15D9717B534B56F9,0x57ED5C5F28EEED33,0xAA224149D1792C1,0x2B663432FFF290C3,0x65B645B7893F3761,0x8C45450423A64BF5,0x2072BDFEECFDF, +0x2E9A77227F6B4DC7,0x26A6145E0CD52870,0xE8E7255BCCFF6551,0xC04097B01E64680A,0x56B98EE30BBE9A40,0xF3BD5AE69AE90DEB,0x1ADE268AB0C0B, +0x15D9717B534B56F9,0x57ED5C5F28EEED33,0xAA224149D1792C1,0x2B663432FFF290C3,0x65B645B7893F3761,0x8C45450423A64BF5,0x2072BDFEECFDF, +0xD16588DD8094B238,0xD959EBA1F32AD78F,0x1718DAA433009AAE,0x3D80DECAC49B97F5,0x250CCD95259A1463,0x793F04EFE6DC126B,0x863CBE6C6738, +0xFFFFFFFFFFFFC5E9,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xA1397C7864FFFFFF,0xFC589FA8688D839,0xF86335AC52097FD0,0x1BDA7D338DBD6, +0x410F318D49162E42,0x6D1F5B0D35833300,0x5F4DFCA44B8DEA03,0x908ADE1CD38203AD,0x100CD330A23B7494,0xE0A2D716A265D0DA,0x1C5F4777BD5A5, +0x2880FCA6BFC771FC,0xE8A1ED366C5EAF41,0x26DEC38C89ACC9AE,0xF433245E87B28253,0xED43C4B08B4E1835,0xC605E763F1368AD7,0x15274B28B2E38, +0x897467983BA2B43B,0xB297D33E561E6331,0xE0FEA7EA579AEB2C,0x65BFB50A8ABAD92D,0xCC49CAF44749DE58,0x6BCC9B9136C1E1D0,0x11149D163881A, +0xC1A591DDECED3709,0xBF70B66A6AB2638B,0xCE7F185ED93BA38F,0xDBE994643E5AECE9,0xA492AE884E240DB0,0x87AD9344EEAD69DF,0x10E9DBBB4E870, +0xB80EDEBABB0E0203,0xD93DE79C62F38BA1,0xC9E5CD46249A507D,0x283ED63FC61F4138,0xA73CFD5F21AFC9F5,0xF28D96A14FE5CF65,0x8B0D12F720E1, +0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA, +0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0xC1A591DDECED3709,0xBF70B66A6AB2638B,0xCE7F185ED93BA38F,0xDBE994643E5AECE9,0xA492AE884E240DB0,0x87AD9344EEAD69DF,0x10E9DBBB4E870, +0x47F1214544F1FDFC,0x26C218639D0C745E,0x361A32B9DB65AF82,0xD582A03B1CE0BEC7,0xD4895F190FA8E4AE,0x7A6EC93531DF50F0,0x1A91214205262, +0x2880FCA6BFC771FC,0xE8A1ED366C5EAF41,0x26DEC38C89ACC9AE,0xF433245E87B28253,0xED43C4B08B4E1835,0xC605E763F1368AD7,0x15274B28B2E38, +0x768B9867C45D4BC4,0x4D682CC1A9E19CCE,0x1F015815A86514D3,0x9801C170584526D2,0xAF7C9183EA0ED04B,0x12FC4454B033E85,0x122D555B3EB2A, +0xFFFFFFFFFFFFC5E9,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xA1397C7864FFFFFF,0xFC589FA8688D839,0xF86335AC52097FD0,0x1BDA7D338DBD6, +0xBEF0CE72B6E9D1BD,0x92E0A4F2CA7CCCFF,0xA0B2035BB47215FC,0x6D36985E0F7DFC52,0x6BB989478F1D3A0F,0x8C5988BFDF5F4F7C,0x6E2AAF9B9D9E, +0x15D9717B534B56F9,0x57ED5C5F28EEED33,0xAA224149D1792C1,0x2B663432FFF290C3,0x65B645B7893F3761,0x8C45450423A64BF5,0x2072BDFEECFDF, +0x2E9A77227F6B4DC7,0x26A6145E0CD52870,0xE8E7255BCCFF6551,0xC04097B01E64680A,0x56B98EE30BBE9A40,0xF3BD5AE69AE90DEB,0x1ADE268AB0C0B, +0x15D9717B534B56F9,0x57ED5C5F28EEED33,0xAA224149D1792C1,0x2B663432FFF290C3,0x65B645B7893F3761,0x8C45450423A64BF5,0x2072BDFEECFDF, +0xD16588DD8094B238,0xD959EBA1F32AD78F,0x1718DAA433009AAE,0x3D80DECAC49B97F5,0x250CCD95259A1463,0x793F04EFE6DC126B,0x863CBE6C6738, +0xFFFFFFFFFFFFC5E9,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xA1397C7864FFFFFF,0xFC589FA8688D839,0xF86335AC52097FD0,0x1BDA7D338DBD6, +0x410F318D49162E42,0x6D1F5B0D35833300,0x5F4DFCA44B8DEA03,0x908ADE1CD38203AD,0x100CD330A23B7494,0xE0A2D716A265D0DA,0x1C5F4777BD5A5, +0x2880FCA6BFC771FC,0xE8A1ED366C5EAF41,0x26DEC38C89ACC9AE,0xF433245E87B28253,0xED43C4B08B4E1835,0xC605E763F1368AD7,0x15274B28B2E38, +0x897467983BA2B43B,0xB297D33E561E6331,0xE0FEA7EA579AEB2C,0x65BFB50A8ABAD92D,0xCC49CAF44749DE58,0x6BCC9B9136C1E1D0,0x11149D163881A, +0xC1A591DDECED3709,0xBF70B66A6AB2638B,0xCE7F185ED93BA38F,0xDBE994643E5AECE9,0xA492AE884E240DB0,0x87AD9344EEAD69DF,0x10E9DBBB4E870, +0xB80EDEBABB0E0203,0xD93DE79C62F38BA1,0xC9E5CD46249A507D,0x283ED63FC61F4138,0xA73CFD5F21AFC9F5,0xF28D96A14FE5CF65,0x8B0D12F720E1, +0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA, +0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0xC1A591DDECED3709,0xBF70B66A6AB2638B,0xCE7F185ED93BA38F,0xDBE994643E5AECE9,0xA492AE884E240DB0,0x87AD9344EEAD69DF,0x10E9DBBB4E870, +0x47F1214544F1FDFC,0x26C218639D0C745E,0x361A32B9DB65AF82,0xD582A03B1CE0BEC7,0xD4895F190FA8E4AE,0x7A6EC93531DF50F0,0x1A91214205262, +0x2880FCA6BFC771FC,0xE8A1ED366C5EAF41,0x26DEC38C89ACC9AE,0xF433245E87B28253,0xED43C4B08B4E1835,0xC605E763F1368AD7,0x15274B28B2E38, +0x768B9867C45D4BC4,0x4D682CC1A9E19CCE,0x1F015815A86514D3,0x9801C170584526D2,0xAF7C9183EA0ED04B,0x12FC4454B033E85,0x122D555B3EB2A, +0xFFFFFFFFFFFFC5E9,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xA1397C7864FFFFFF,0xFC589FA8688D839,0xF86335AC52097FD0,0x1BDA7D338DBD6, +0xBEF0CE72B6E9D1BD,0x92E0A4F2CA7CCCFF,0xA0B2035BB47215FC,0x6D36985E0F7DFC52,0x6BB989478F1D3A0F,0x8C5988BFDF5F4F7C,0x6E2AAF9B9D9E, +0x15D9717B534B56F9,0x57ED5C5F28EEED33,0xAA224149D1792C1,0x2B663432FFF290C3,0x65B645B7893F3761,0x8C45450423A64BF5,0x2072BDFEECFDF, +0x2E9A77227F6B4DC7,0x26A6145E0CD52870,0xE8E7255BCCFF6551,0xC04097B01E64680A,0x56B98EE30BBE9A40,0xF3BD5AE69AE90DEB,0x1ADE268AB0C0B, +0x15D9717B534B56F9,0x57ED5C5F28EEED33,0xAA224149D1792C1,0x2B663432FFF290C3,0x65B645B7893F3761,0x8C45450423A64BF5,0x2072BDFEECFDF, +0xD16588DD8094B238,0xD959EBA1F32AD78F,0x1718DAA433009AAE,0x3D80DECAC49B97F5,0x250CCD95259A1463,0x793F04EFE6DC126B,0x863CBE6C6738, +0xFFFFFFFFFFFFC5E9,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xA1397C7864FFFFFF,0xFC589FA8688D839,0xF86335AC52097FD0,0x1BDA7D338DBD6, +0x410F318D49162E42,0x6D1F5B0D35833300,0x5F4DFCA44B8DEA03,0x908ADE1CD38203AD,0x100CD330A23B7494,0xE0A2D716A265D0DA,0x1C5F4777BD5A5, +0x2880FCA6BFC771FC,0xE8A1ED366C5EAF41,0x26DEC38C89ACC9AE,0xF433245E87B28253,0xED43C4B08B4E1835,0xC605E763F1368AD7,0x15274B28B2E38, +0x897467983BA2B43B,0xB297D33E561E6331,0xE0FEA7EA579AEB2C,0x65BFB50A8ABAD92D,0xCC49CAF44749DE58,0x6BCC9B9136C1E1D0,0x11149D163881A, +0xC1A591DDECED3709,0xBF70B66A6AB2638B,0xCE7F185ED93BA38F,0xDBE994643E5AECE9,0xA492AE884E240DB0,0x87AD9344EEAD69DF,0x10E9DBBB4E870, +0xB80EDEBABB0E0203,0xD93DE79C62F38BA1,0xC9E5CD46249A507D,0x283ED63FC61F4138,0xA73CFD5F21AFC9F5,0xF28D96A14FE5CF65,0x8B0D12F720E1, +0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA, +0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0xC1A591DDECED3709,0xBF70B66A6AB2638B,0xCE7F185ED93BA38F,0xDBE994643E5AECE9,0xA492AE884E240DB0,0x87AD9344EEAD69DF,0x10E9DBBB4E870, +0x47F1214544F1FDFC,0x26C218639D0C745E,0x361A32B9DB65AF82,0xD582A03B1CE0BEC7,0xD4895F190FA8E4AE,0x7A6EC93531DF50F0,0x1A91214205262, +0x2880FCA6BFC771FC,0xE8A1ED366C5EAF41,0x26DEC38C89ACC9AE,0xF433245E87B28253,0xED43C4B08B4E1835,0xC605E763F1368AD7,0x15274B28B2E38, +0x768B9867C45D4BC4,0x4D682CC1A9E19CCE,0x1F015815A86514D3,0x9801C170584526D2,0xAF7C9183EA0ED04B,0x12FC4454B033E85,0x122D555B3EB2A, +0xFFFFFFFFFFFFC5E9,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xA1397C7864FFFFFF,0xFC589FA8688D839,0xF86335AC52097FD0,0x1BDA7D338DBD6, +0xBEF0CE72B6E9D1BD,0x92E0A4F2CA7CCCFF,0xA0B2035BB47215FC,0x6D36985E0F7DFC52,0x6BB989478F1D3A0F,0x8C5988BFDF5F4F7C,0x6E2AAF9B9D9E, +0x15D9717B534B56F9,0x57ED5C5F28EEED33,0xAA224149D1792C1,0x2B663432FFF290C3,0x65B645B7893F3761,0x8C45450423A64BF5,0x2072BDFEECFDF, +0x2E9A77227F6B4DC7,0x26A6145E0CD52870,0xE8E7255BCCFF6551,0xC04097B01E64680A,0x56B98EE30BBE9A40,0xF3BD5AE69AE90DEB,0x1ADE268AB0C0B, +0x15D9717B534B56F9,0x57ED5C5F28EEED33,0xAA224149D1792C1,0x2B663432FFF290C3,0x65B645B7893F3761,0x8C45450423A64BF5,0x2072BDFEECFDF, +0xD16588DD8094B238,0xD959EBA1F32AD78F,0x1718DAA433009AAE,0x3D80DECAC49B97F5,0x250CCD95259A1463,0x793F04EFE6DC126B,0x863CBE6C6738, +0xFFFFFFFFFFFFC5E9,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xA1397C7864FFFFFF,0xFC589FA8688D839,0xF86335AC52097FD0,0x1BDA7D338DBD6, +0x410F318D49162E42,0x6D1F5B0D35833300,0x5F4DFCA44B8DEA03,0x908ADE1CD38203AD,0x100CD330A23B7494,0xE0A2D716A265D0DA,0x1C5F4777BD5A5, +0x2880FCA6BFC771FC,0xE8A1ED366C5EAF41,0x26DEC38C89ACC9AE,0xF433245E87B28253,0xED43C4B08B4E1835,0xC605E763F1368AD7,0x15274B28B2E38, +0x897467983BA2B43B,0xB297D33E561E6331,0xE0FEA7EA579AEB2C,0x65BFB50A8ABAD92D,0xCC49CAF44749DE58,0x6BCC9B9136C1E1D0,0x11149D163881A, +0xC1A591DDECED3709,0xBF70B66A6AB2638B,0xCE7F185ED93BA38F,0xDBE994643E5AECE9,0xA492AE884E240DB0,0x87AD9344EEAD69DF,0x10E9DBBB4E870, +0xB80EDEBABB0E0203,0xD93DE79C62F38BA1,0xC9E5CD46249A507D,0x283ED63FC61F4138,0xA73CFD5F21AFC9F5,0xF28D96A14FE5CF65,0x8B0D12F720E1 +}; + + +const uint64_t ph3_T2[DLEN_3*ELL3_W*2*NWORDS64_FIELD] = { +0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA, +0x0,0x0,0x0,0x0,0x0,0x0,0x0, 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+0x35CFCAA5921C7D40,0xA53E0DBB227FEDA,0x6603F49BB5A87243,0x1CD2B946DF9D2512,0x3933D7936DFFA0AB,0x2E7BB406174278FA,0x18D15D6CE4D23, +0x94747DE95EBA3DAD,0x6153BA2FA01D449D,0xE6CCB30D62922F3C,0x621940A023A262AF,0x1E1765A6F7EAAFAE,0x65084E461A39AA9,0xB6265C7D9074, +0x19B581B643E2F454,0xF02A090EC3C6221B,0xA897CBB34542F824,0xC29C7F93272B5E90,0x42F2C17A4DA84E7D,0x2C6F10AD56455537,0x3D1A5806C57D, +0x529A98F90FB6B43,0x636BADD6951C6E5D,0xE3C69E3E5822D8BC,0x34CC5C43F5459C7,0x1CA19A068EAD9C4A,0xC5F411EA50E85259,0x1BA8FD736BDFC, +0x507F630AB41C095D,0xB32DD30F2E567D82,0x7E04DD2CDCB2C0C7,0x2875B21696420008,0x59AD83290152AE3B,0x3DCBD1D4EDD44273,0x1F167A8CBBFDD, +0x7C9E71B5088BD450,0xE377B6299A84EC23,0xB283FCD8652C0821,0x9ED4A93C9A53B760,0xD3895089CBB76193,0x248C2AB502D79774,0x86E9551D6334, +0xB3217D1B2A878DF1,0x76831535DC90BBF9,0x2B83F145151BEAB2,0x761862A087481F5,0x743FFBB844FD8CFE,0xD407536C88C3CC0C,0xB8A627AD39A8, +0xF152430FBB0B1DBE,0xE3568C1C356BF46F,0x1364FC57DF940142,0x53A0739714D93EDF,0xA7E14F8906B19D5,0x84C8104B46A7DD44,0xDB2434BADA3B, +0xE0C0801C81E9187B,0x71B8BC4069D7A4BA,0x34DEB95B46E5D1E7,0x49D6C5C34F8FCA22,0xE4C759E8F979AEF1,0x54810DBC25076750,0x16CA6BEF5ADC0, +0x84EF739E89074420,0xF7756424F99DE4BE,0x4379E183A608DABB,0x7DBDEBBE169AEF00,0xBE1665D536F68CCF,0xE1CD3876BC9C435D,0x1055E38120373, +0xC6F2BFD31A2C23BB,0x7305F5C98849AEA0,0xA4A2677AEA1FA0B3,0x93C77F38393DD26F,0xED5AD62AC21A8508,0x19B49B3B2DA839EF,0x22549833CEC49, +0xA02F0C97DFAE7E47,0xB637B49189CB0814,0xC3F74B323BE03840,0xB31534EB340465AD,0x3234E3EB38BFDD68,0x7DC07CCB02369028,0x1F414C8FDA45B, +0x4420E85EE76076D1,0x1C948FE8EE14511C,0x6DB9146A79AC5EE4,0x79F3810916C522B3,0x523081DE1FFA875E,0xEA27FAA23D185F4,0x1C7B70B81F459 +}; + diff --git a/src/P434/P434_compressed_pair_tables.c b/src/P434/P434_compressed_pair_tables.c new file mode 100644 index 0000000..bc8371c --- /dev/null +++ b/src/P434/P434_compressed_pair_tables.c @@ -0,0 +1,4123 @@ +/************************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: precomputed tables for pairing computation on E0: y^2 = x^3 + x when using compression +***************************************************************************************************/ + + +// T_tate3 contains 6*(eB-1)+4 elements from Fp. There are (eB-1) 6-tuples (l1,l2,n1,n2,x23,x2p3), each corresponding to a single step in the Miller loop. +// The values l1 and l2 are the slopes of the doubling and point addition to compute the tripling, n1 and n2 are coefficients of the corresponding lines and +// x23 and x2p3 are the product and sum of the x-coordinates of the intermediate double and the tripled point. The last Miller iteration only needs four +// precomputed values. + +const uint64_t T_tate3[(6 * (OBOB_EXPON - 1) + 4) * NWORDS64_FIELD] = { +0x87CF42AB4DB902F, 0x2DC7847A25C2D0BB, 0x2EA717C1089170B, 0xD648387AF59D578F, +0x16EC71A5BDA7D98B, 0xC02025B1BDE6B5F1, 0x482FED00DCBB, 0x8AD7A8F0578700AE, +0xB317427ECCC5FA27, 0x43EE31091EAF92, 0x2D317292BB029F77, 0xFBBB529BB4CBB2B4, +0x60580C9725507661, 0x112DF39343123, 0xA434F3F0FDB57E43, 0x1F19074AF93E2F11, +0x543519D9822F9BCD, 0xA37D58CA3D49D484, 0xBF5FA675ABF1AF8C, 0xFB287704C7B40291, +0x1BF7E42435225, 0x87EE9673F98AC980, 0xBA0821247ABC3FA4, 0x15E15DE1E6F42728, +0xC0113FC5F784DFF1, 0xBEF4D30A12CEFB55, 0xDA6EDD9E69F8D979, 0x5095BF6E331A, +0x8712D8BFF33A915F, 0x6FA3BBA2BCAD2B3D, 0x3DA66FC51C479D41, 0xE4664DED73E4F4F8, +0x1DC84EF123484BDF, 0x3830A0CBC1A1FB32, 0x2093CD1FD32C3, 0x52BE5D7415D580B0, +0xA038215031E30913, 0x5D7CF2307F86F392, 0xB6F68C9CA159295E, 0x7C91CA90411DDBD2, +0x738CEC7107271928, 0x104B080B38D23, +0x782F2E6790E469ED, 0xC4B78003E1050FA0, 0xE0CA084A7EE5B883, 0xAB2ACCCF86F46C37, +0x1F32B66BFB23DD49, 0xD5960A518B29111E, 0x11F1B4E73A529, 0xEFC5D3474A129A11, +0x5576852523BA0748, 0x6B93C9ADD44CFFC0, 0xCE812E5B9151006E, 0x2C9F8A0911FE0C97, +0x910D0523327E636C, 0x11B72F214EA79, 0x1A0321DD62C5B1B9, 0x3F9DD61C3034ADA0, +0x94741AF0B2D3B8E6, 0xC74C38965B4D0043, 0x21C00F3322E375AB, 0xC26D7F847AC9EAAF, +0xBCCD45776F12, 0x799308ADD29259EA, 0x6B7CD64D6C3B7F04, 0xAC37BFD305C534DD, +0x7A5D6FB2163561D0, 0xAC47BF7A3D8DCAE1, 0xAEBCD5A1549AE57F, 0x10AEB563DEFA5, +0x870E74E9DDB6717F, 0x887B67035BB681CE, 0x6C589E63249B07D5, 0x23462ED5BC57928D, +0xA0911EE4D14324FC, 0x86C5A1C6E6D7610A, 0x6EE385585755, 0xF99C75D5FD1C99C8, +0xBD786788169F0B16, 0xD870C3F4FC4D3405, 0x883E82ADAA7EBAAB, 0x45F9810FBA0BB397, +0x742954D5E7597601, 0xBC1CEB24C698, +0x567D28386337D588, 0x451A058E61D82479, 0x9682171F6F2EF6B9, 0xA30AD92F6A21E952, +0x6835DA5DA162FFBA, 0xCFFCFC13DBE63182, 0xE18A5A20B5E, 0x7CF1E2C85A4336BF, +0x3BD672C9E247B93B, 0xE64AC73819FD063A, 0xB6229AC036E0CA04, 0xA02326A8503A3520, +0x2A0755DAAF4169B4, 0x1E6959E0B87C9, 0x8D6D2A7F6F30837C, 0xBF902E6320D3235F, +0x21647994DA640189, 0x5C1E206F4038BD47, 0x33BEF2EA45AEE25D, 0x160FFA08EA8FD067, +0x13202524ECD23, 0x8B52AD13442077CE, 0xE55F2B037EA7ADDC, 0xBB4EE449E9D97433, +0x3C9C89020167F595, 0xEA9B9E3A82ADCB66, 0x1E08BA4129BD5B25, 0x1CA2DA5BFC577, +0x4299DCB647918CB2, 0xAF86EB07DE2A69D2, 0xCE24B54DD0C4B65F, 0x4231A1A4B650B923, +0xEE6DFBA9BBEBABE8, 0x195BE1CE395BCA2, 0x1840939C66720, 0x9AE6708F03788550, +0xBFC33006F72C5178, 0x6FB8B0073442F23B, 0xDCC091F52DBAEFF, 0xF34F1009782EE835, +0xF567D3A9073710E5, 0xBD48650F0ECA, +0x590DE17FB7AFC380, 0x7F7A56940C607B76, 0xEA34A1DED0626E92, 0x2A5E86FC27A7919D, +0x2A939C77E67228A, 0x902EC93718A484D8, 0x1D525EC65922E, 0xA338F9FEA0D9FD2B, +0x3AE49152EFF3EBB1, 0x72EACC005FA0B6F4, 0xEC65DCD4E95F675A, 0x7CDCC1D8A54EEEC6, +0x1963678E2115897C, 0x68C906CC71D, 0x4ED2850CD8521CAA, 0x37B668E8B3464B4, +0xB0538F23955CC4A0, 0x89317CA4D87495E6, 0x682016748E5AF9CE, 0x8E8731A96729969, +0x19CA49150D970, 0xC8CBAB39A17258A8, 0x33177D7C5D70BC99, 0x4F766FC8ED881455, +0xAE27E8930854CD7A, 0x3D422E5E0D4FB34F, 0xE52EC94774679E91, 0x158125921CDFD, +0xD958C12302FCB427, 0xCC1C7CE47DA3923A, 0xF48BEB644D67B3B4, 0xCB3E85E981789F1, +0x690E38488F855778, 0x8DF571936B9DE3C1, 0x1697A828BD480, 0xBFB5E671A41DE11, +0xCB6E6ADD07E16041, 0x7F6F7E1F0F59312C, 0xA0C84CC72C66CF2C, 0x1BFACA064061C7D1, +0x81920D03644F54B7, 0xF51E62948FFB, +0x10BC57E9486532BE, 0xFAF9AEC6841ED41A, 0x2A4104E64469CE3C, 0x202B80D69318DB79, +0x417CA89D2A5935D2, 0xA991C6404CEC3BEC, 0xB47B0A935EF0, 0x6E7687B28A998E7D, +0x2BC789694ECBD01C, 0x3F6E60BDAEB97F, 0x556D30AD5D42D1FD, 0x60C2A6D0B08E7835, +0x867D4D0F64B409AB, 0x2192BBD62698D, 0x37CFB96EC731556A, 0xACD0CCD8FB2E14F7, +0xEEB912564ACA878D, 0x3EDF98CDDA176443, 0x36A39D2C28ADB9A8, 0xEE9427130BF5E0A, +0x13944C7977D23, 0xE71E70C0472421C5, 0xE5EB07ADE978903, 0x2960B1C908E63B43, +0x5E5C8461A3D6BB04, 0x25449D5F39BE1CD9, 0x7D38319C4E8FA1D6, 0x1B28945723E0, +0x2E4D063B45948CB, 0x5FCDCF2209C009DB, 0xE86EA48B5B6F3F39, 0xB84BF12AD9132FE2, +0xDC6D825944811BB9, 0x381B81898F0A201E, 0x22059964BCBC4, 0xDA3C7C2FCB5DAAFA, +0x74F84B725AB8E5A3, 0x720E9D56CF17EBEB, 0x736024360E3A21E6, 0x529A2C8828A26EC0, +0x869C50C4297976A4, 0x61588CFE53A, +0x858EE17E03A95FB3, 0x6D179EB603320ECD, 0xA79F512866434C99, 0x89A85A54E50F173, +0xFEC0CC93361E6BEB, 0xFFDE8D620EA6E9AB, 0x21A20B4098F6A, 0xCA888F57ACA873C0, +0x9A50D95DE7A71205, 0xBC7CBEB3C8A98062, 0x2A2905DF61B87ADA, 0xB291F326FC02A2AB, +0x3E609C4E7ECD502C, 0xF4589C2CE8DF, 0xADAE53CEF38551E7, 0x34D0CFFBDE9619CA, +0xAC9A701D7B5C7C0F, 0xB14E1F10C87D96E6, 0x48D6572A797B36FE, 0xB9683A45FC90701A, +0x13DDB71DE40BC, 0x2F9C779613D1EB20, 0xBD55351AF620C75D, 0x97E623955DE2C6F1, +0xF00BDBD7698387C, 0x51CBBA19E50C3C61, 0x5F3642423EA425A5, 0x1B81B90642DDE, +0x4C2EAEF1CEFCDBE7, 0x736480464AA31966, 0xCA127B84714F101C, 0x7E419C0DAD15DD90, +0x7CCCDAC3DC01253E, 0x1FB3B5BDE2C93EBF, 0x17C77D3B6FD3B, 0xE6F54C1EEFA787D6, +0xEFD4296AC605632A, 0x8EE5AE0226B2A8D2, 0x9ECDD8D398024EEC, 0x2E1CB33EA04D00CF, +0x464AE77AA92E13A9, 0xAFF71032B956, +0x8477DAECBBF7AFEE, 0xC4CEA77FC65DD0AF, 0x708D21475374EE8A, 0xA9071AA7FFD218D2, +0x74299452AA96A753, 0xC1D694EE1C0F6758, 0x307B19DD1825, 0xFC7252D4FBF8C849, +0x269C191CC6929A6, 0x9ACC9148C0F65B26, 0xED2DBBCAE7A3E486, 0x45B19AB48ECE5D56, +0x5F7CD50692571186, 0x19B34DCB42909, 0x20D1D5FDDFFE608F, 0xEF7F528260E40225, +0xA1A23C15C212B507, 0x3DA7B29B1EC33EA6, 0xCBAB15C5235A0297, 0x609F3E2D4D738CE3, +0x1542B656331C8, 0x1E65EAE77C59C667, 0xD17B6DD36F481322, 0xA3DEF060B572C354, +0x9C5A706D158433DE, 0xF2F48D157A95AC5C, 0x5AE4305B0A56F366, 0xD438B9D41AE7, +0x8FD509195F1D6C55, 0xB06FA1C951ECE50F, 0x3E9BE721FCF076FD, 0x85B2919E8DF876C2, +0x79636DCF86FD975C, 0x84C4EC3664D33000, 0x7C341F157510, 0x137F69B41C015930, +0xC13C66ACA7C5CD52, 0x6492B4371600668E, 0xABD67760352A65CE, 0x895F4E4B73A9CAFE, +0xA1AA295248E45B89, 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0x23161CF7FB53F10D, +0x5F83324EB5FEE38E, 0x3AEB3384E9A0, 0x205BF5E1D01C2F64, 0xBCDF65CAF5666AC0, +0x462E5E85DE28CE61, 0xF4BC578D3A6BB9F9, 0xE8D9B3AD7474C53A, 0x5B8D49F5AAD392CB, +0x18E4B09E124BA, 0xEF25C97FF51F3A62, 0x2577DC6B020FFC1E, 0x744F55983FE8E346, +0x7A63DF17ECF6CF8, 0xCCDC763CD26146F5, 0xC471CC32DE906BD2, 0x225ED685EC9E2, +0x7421D058AC7D2220, 0xBC8992B1F58C4B72, 0x90E1F967281025CC, 0x7C867141220A1A02, +0xE4C31003C23B1D91, 0x40BE0113AB833129, 0xE532E89CBC00, 0x5AB1471A2E5EEFFA, +0xB559E403E9011070, 0xBCFDE4E620886765, 0x454A1AF7C2F0BA52, 0xE7E6171A4DE5E2E5, +0x4DBD77E72E8E0737, 0x447CF92D4892, +0xBB61C03A2757760B, 0xE0ABC84AE56A9F7B, 0xD89E2334734408B, 0xC135DE9C48F9B2C5, +0x33296DD9165AB6F4, 0xC661CB9FB1D28DDC, 0xD3A1CB03836B, 0xCECE3CB3AD8F4747, +0x6FBE8942DE44F934, 0x4C913B2499235245, 0xA50C3BC53BD95B6E, 0xA955339216B2A0E6, +0x1A99C1BD757A6D86, 0x1CA72D5586936, 0xD4D1B12363BE4D51, 0x552FCD74E342461D, +0xD820FA1DD8037BC5, 0x194E362595C5AE8B, 0xD5B504C7E46C29EB, 0xF3B5A7E2082CE03, +0xEDFDE0C92D0F, 0xD79C7F75C04FD59F, 0x76B6946C8CC2E920, 0xCDCC45DD0C650DB3, +0x952A6A18E05D1C53, 0x5165330F22BE6EC, 0x1011B88C0E8B0896, 0x1D38A69628F43, +0xACF16BDF5C30539D, 0x87B0EA08B7823C54, 0xD0E725FB113F852E, 0xCC3AF005823BB87D, +0x393CD91F62E68700, 0xE31D2A515634A676, 0xBAECB314D06C, 0x523A215F16204966, +0x595E201A8749CC27, 0x10B8FF2A6BB221C5, 0xB1ADBFAB8BF9D413, 0x718AEE5191498513, +0x29B01E970C06B8A2, 0x3C332116D61D, +0x27A8A9594DE0F58, 0xCA960B3C06FDFDD4, 0xA02B1283F46E00E6, 0xE3BF8B4E7676FB7E, +0x11B9737503EE84AD, 0xC3EAEB2F6E1515AB, 0x1C8A0DB5D41BE, 0x9295530DBAF3D8E5, +0x90325DC5A0AE629B, 0xABA90A925136AE80, 0x87F46357F54D9C73, 0x90E474CE183BB014, +0xF937D341E6022FE3, 0x1E58B7113FBFA, 0x67C93C38DE354A5B, 0x999D84156DCD8796, +0x88C85619FCE161D2, 0xE88DB0B5749A5B30, 0xFB3AC5D8006224F9, 0x2404810D81F068CB, +0x1CB0D4BA98E26, 0x7F66E1755045A0DC, 0xD4198C361E9ED5B, 0xF44AA277690B8A71, +0xF3DC5B683DE8E854, 0x592771F75BBF2DF6, 0xADD2311BBBB0FC1A, 0xE76DB8CE11CD, +0x1D84F50443FDDB56, 0xB18B72DF571AF5E, 0x5BCEF3C9D00424BE, 0x771D8857E619C19E, +0x98320E7BAFF0C5F5, 0x4F2166BEDBB30443, 0x1D830CE1C6DB7, 0x108EDC760FDB446E, +0xA7AAA4979978C8B5, 0xA28279203E30484D, 0xF810F5C8F3CEC86E, 0x2CC66BD3F8BB23D0, +0x7F9D4587381E5A74, 0x1E4CF7EFBE302, +0xDE2A873C0D7635FC, 0x745262516BF50C2A, 0xEED570958B8B3432, 0xE135D5C68B80007F, +0xA3336407D1BEE140, 0x47BF95A9297E4E16, 0x17DE2564D3EDB, 0x4300C2E7FBC7F047, +0x3C9809B85C4E1417, 0x809ED788EBFDD244, 0x2E8A7BC30AEF1E17, 0x22F7BE2F92CE3957, +0xD9F14433D5428C4F, 0x1D1480DE5CD02, 0x2211D15F8E262331, 0xBC78BD1CA3153A7F, +0x3D431742689C7926, 0x9880A8E1336AA5EF, 0x6D19C5B42E302B48, 0x5CFD361762089D64, +0x27ED3F6E656E, 0x9FD607AB7F5BFB8B, 0x601D1E8F28061F97, 0x9D98562D23CE58F2, +0x867F1AFF9E856FAD, 0xB32AE445CE79EE33, 0x28A8152261DF92C0, 0x21322D6719C7C, +0xA7D064F19A3B766C, 0x6C70FFF87FC880EF, 0x64A71182A8173CC9, 0xDC01420CBCE0F083, +0x1CE34E007DF3E10E, 0xA27CDA41DCB50501, 0x788394289850, 0x321A468385F3C4CB, +0x2E8B87337E5B2DF4, 0x55CE68D7346011D, 0x211C4F75F283503D, 0x760E7474AA7D4D65, +0x4A0E0253F940ED40, 0xA916FD5EE6AD, +0x50110D646390C270, 0x86E8D3951EC20D9C, 0xB6FD16E075C5BD48, 0x5F07F24970C115A1, +0xCEFBAF35044B271C, 0x3FA8653FA6D2C397, 0x21FB7CF70963, 0xAD63406878A34C94, +0xA450503F2F889C83, 0xB6F2A238CAD9FF55, 0x5023DDF6E6251AD, 0xBDB4345F05DE7BC3, +0x2B5CE771D30634FD, 0x128240CBCB559, 0x2CE714EDC3BDF356, 0x217E6C473EB94A0F, +0x57920D655C05E18C, 0xBB126101B6C25A13, 0xE30A2B768E1C6796, 0xEE3FA706678A73D6, +0xC3FD63D644FA, 0xB735C051475DB5A5, 0x3BF1095B6D64E1C6, 0xAA49CC37E57D16EE, +0x26C0E20CD9F6600, 0x35B1C16E1F053607, 0x230EFF870D31C882, 0x67D73F288421, +0x25ADCA312A6EAE9C, 0xE3E1C51C5694C8E0, 0xFE82EF9822A4B866, 0x27BD4C7D0BB97C92, +0xBAFC69C4A8C421A6, 0x53F5C5C0CA06323B, 0xE1F46E647D51, 0x5A2BF604D8C1763, +0xF2B50258CF506E30, 0x6EA0D11B05D949C3, 0x8314B9C8331B9A16, 0x531F09DFA1D95CED, +0x15379B7AD194C054, 0x1372AC736D509, +0x3BACD1724318472E, 0x8DBE4C45864051CE, 0x3281343E3E81F7BE, 0x69515F477DC165A9, +0x21DB1C63E82703C7, 0x567227C494402924, 0x194E16265B465, 0xFB088C7573C04246, +0xD9D2BB685BA4D2A6, 0xE9F226E6A4EC0009, 0xF1E0A5436D1514E1, 0x2F3C22902F310CCE, +0x2CD76D2984306B2A, 0xA404531E770E, 0xE7572FDD04B018E0, 0xCE009909ABBD420F, +0x82E5E15477934400, 0x21DC976085B80962, 0xF8542C3F9344F4CB, 0x6D6F2EC047746A4E, +0xCA2CE1C26D48, 0xA5D6195D7BCB4C0E, 0x7DD8EADA8BE3D256, 0x3C1B81966558900F, +0x3EEF54ADA4962011, 0x76F07142D675804F, 0xDEF95C79D5787504, 0x72EB27BD775, +0xC18A3DDDE53E66E8, 0x61B300BB1D994D8F, 0xC7320432EEE78FA, 0xB727166634FAB1E9, +0x889A27FB7D155BA8, 0xA5D21E1C141244FA, 0x13299C740CC26, 0xDC9EC3CA3562323, +0x8F093AE1772A81FB, 0xC45E9E3A45EEF070, 0xC231FCFF6FD14E9F, 0xC36CE3ADCB07F4AD, +0x18D79D4E8872C8BB, 0x1BE584D130CE2, +0x5B38B7ACFFF69FDB, 0xDE8175476D96A43D, 0x35AC0492BE5961C0, 0x98AE41101E7A91CF, +0xC054957B5B674A2A, 0xE3ACD33058015675, 0x3EF049C9C556, 0x249A1FE943A1AB78, +0xFFBA40FB0B3D3BB7, 0xE9241DC45B3DE8FE, 0x2EA0032E8D6BE2D7, 0xCC7BBF86DA3C2673, +0x54081B7288F687FE, 0x143372CF1353F, 0xE9340A646C3D6336, 0x792C64E4919239E6, +0x1CD7F6FC0AE998CE, 0xE47E45DCD6F1D39C, 0xEB64A7DE32637127, 0x19E930C01DB61B28, +0x1A14586E66FA9, 0x5F7F36ACFF66E52B, 0x336CD8997CA7A2D, 0x6600E5645BF5B406, +0x83E0D73530A99859, 0xD984C3549A5F9C6E, 0xBD3F256ACD1832B2, 0xBFBECE59FE03, +0xCE52ADD9B13961B8, 0x32139337A15B9FA3, 0x8D60C99085A75A75, 0xD79AF63122564C76, +0xB05DE5BD32C812BC, 0x8BC4F1EAE4D26168, 0x220801F9818EE, 0xB29276B081A880BE, +0x4720DDF0CD2B3198, 0x66AD048931E14380, 0xB4823652C5495F31, 0xC61DB15B6731F3E5, +0x86AF90528124EB39, 0x1F9A90488EA90, +0x64D9B4792067E15C, 0x26EB9580D7573612, 0x4B2B9BECE0C15118, 0x1F123C825B8BEAD2, +0x7EC28F7E437BF1C7, 0xDD65FAD83A0D051D, 0x1F824EA6FB3A5, 0xFEC1D7BADBED9BB5, +0x17FE5E55FC1B0FC0, 0x5A596858014EAED6, 0xA6A1753568BD0C67, 0x2B967FE08968A92D, +0x84358A7999C86278, 0x1CE063451AC53, 0xDEC3C3D557271CB5, 0xB1E6C62B09DBEBEC, +0x5AC67448586F9A57, 0xA0B622450784A3D0, 0x5A60BC95BA23D068, 0xB1039D856CEAE08B, +0xD1B5A75F36BA, 0x9C230F1BA354319C, 0x8617F024A6F4C893, 0xB46F0030B2797C5D, +0x17DF4FF2274CB434, 0xDD9D91CCCEB67F3, 0x80DC6AD4DDB3237E, 0x14F958130A42D, +0x7973A16188DDB1B0, 0x89979C9C0357798C, 0xFFFD7C78AE3AB490, 0xA069B5648991C1AF, +0xFA4E0CB7C176FE5, 0x539A085F4C9E957, 0x122CEC918D3AA, 0xB4999DFB62B2F209, +0xB95281F59FC290DF, 0xDFE07954A9C00208, 0xB17F7F2BB2D43655, 0x64E68AC1C936A797, +0x8FE6337825E96E18, 0x2BD519660667, +0x2AC6449E13C4492C, 0xD97807C01BAAE84A, 0x6B906B1A303C6FF7, 0xCA8A866D61061BFF, +0x2243F350913B539D, 0xD875D65B5B17A7E5, 0xC6FE838E9C4, 0x2DFE0C7D9D82F12E, +0xD2AD3EF092CB42E8, 0xDC0684C29F47D1F5, 0x9F1C8289161952C2, 0x798E8AA232B42171, +0x94CCFAAA86213CE6, 0x2306FFD022510, 0x9D2E23C936E0A543, 0x7C9D6265D35F598D, +0x24134294A6359F5, 0xBA94C6CC3541DB2F, 0x944DF32A94D860A4, 0x8635906C03DEDBFF, +0x210DCCC627733, 0xEE3FA10811682C45, 0x9D329A0B021BF33A, 0x36A1F8895E4533B8, +0x488B32CB52369293, 0xF9ED9B78413CCA40, 0xF0FF66E3A63A3397, 0xABC2AA32C41, +0x6124A70277F1D15C, 0xC149800072287933, 0x78B4F3DDA0B24173, 0xB12C514941670022, +0xF794BF268229589A, 0xDB62AB898CEFB25F, 0x9CF4C4D12225, 0xF04D98170810855F, +0xFFB6B417564FCE74, 0xBE9FC0C057F7AB6, 0x38B7BB8A63575670, 0xF1CC9EC1E031685C, +0x570921D01EB88A87, 0x1575DC510BE2, +0x9FDA088A5FA2876C, 0xC7CCA6229BEDA074, 0xEC88EC0498439475, 0xF4A89D7DE5A1D984, +0x19D978E372302083, 0x9F2A444BB54F36D4, 0x9089056D8DC, 0xFA8ED7BD6BA567F3, +0xB849A18C68BA3397, 0xA6E2409DA5E46E7E, 0xAD41CAFD1D1F857D, 0xFC18D3401F016204, +0xDC60D8378D80BE0D, 0xC42E1B0A1B38, 0xDAC964848C952111, 0x134B8EAAA786F5EB, +0x76F738494920F34D, 0x86D7E8768F1BBA44, 0xF1154A3E03BC7F41, 0x6BD4E97463BDAC89, +0x13E65360D5A86, 0xA9C4262D03C9088D, 0xF8C761483E64F21B, 0xD820EF12E39D86D8, +0x43E1B9B7663B4A82, 0x62B431BF20E21131, 0xE2140E9E875FCF44, 0x79D64AE8FAD0, +0x81DF8CA3A850A74E, 0xBA5A2CD79C3A71B9, 0xEFFBB2D8905094A0, 0x7B1CF2C7149FA99A, +0x1E87E02164A50F1C, 0xDC33C8090B4188BB, 0x15E0A16D8B8E6, 0x944BF31371F77FB1, +0xE984B27B708C2AE7, 0xC01EE730E35EE82, 0xC36CDC432770EDB1, 0x66C4FAC4D9EDAB4F, +0x760F0C021937821, 0xF4DCFC4C5C1C, +0xD697601DCA7CA4B5, 0xD16726DCBE0FD988, 0x8119DD7AF0E6C87C, 0xD1E1BDAB620C8DF9, +0x27ABDBB336AF35D0, 0xC36900B91B5F4914, 0x1E21CCC021AE9, 0xDAEB901A8B0B1BF6, +0xCFA413FEE3DEEB, 0xD8A152FC022EDD7F, 0x69AEE6F393ADDBE5, 0x45F3B54D85AB6DDE, +0x19F7181A0B697BAB, 0xE1C0ED0125C4, 0x374B1CE5F2781984, 0x71D5AD70126A6664, +0x4389E57D7715FCAE, 0xE3EFE78A9BEAC09E, 0x455C8B14585F1F17, 0x5F372F4049EBCCF7, +0x1AD446F6FFF06, 0xD697601DCA7CA4B5, 0xD16726DCBE0FD988, 0x8119DD7AF0E6C87C, +0xD1E1BDAB620C8DF9, 0x27ABDBB336AF35D0, 0xC36900B91B5F4914, 0x1E21CCC021AE9 +}; + + +// Precomputed values for the first Miller iteration of the Tate pairing on the +// 2^eA-torsion of E0: y^2 = x^3 + x. Contains a triple (x,y,l1), there the +// coordinates x and y of the double of P are in Fp, the slope l1 is in Fp2. + +const uint64_t T_tate2_firststep_P[4 * NWORDS64_FIELD] = { +0x16747C943533BF87, 0xB4497C90231C8CF6, 0x5ABB26BC14FB0710, 0x457A7E552E14B4D2, +0x6E92EEF549069079, 0x565AB7E75A1BA5C, 0x21F0CABC7F726, 0x39645C6B7CF4AD82, +0x72CA8B9E5285631B, 0xB778021E0CE0E39B, 0x1255EAC0AC0F8ABA, 0x6A43AE42E0830B36, +0xC85CCEC4E3F3764B, 0x10F16B11E4DF3, 0x44D662245513A8F6, 0x4926CA3671265135, +0x1BD215535DA13B6D, 0x18FE224B9795814C, 0x4010C29A1FC10E03, 0xB72E6E05D7DDD73A, +0x4ECD639F7DE7, 0xDFA0E79BF5633D28, 0x5F9B46F9C06602E, 0x22B17FDA14F3A36A, +0x44E15C64A71346D5, 0xAA9205DED17FC6DA, 0x59B8583E58373D72, 0x77D7B7A0BE52 +}; + + +// From here on all values are in Fp. The table contains eA-2 triples (x,y,l1). + +const uint64_t T_tate2_P[3 * (OALICE_BITS - 2) * NWORDS64_FIELD] = { +0xEC805BF7BF3C44F4, 0x9544F219309FD605, 0x57266A162ABDBD16, 0x19BB58DC7DB2C684, +0x94AC03F73CAF41E7, 0xE74ACBA50EDF2704, 0xC3C8774EB007, 0x8D6C83984DF44C50, +0xE0465877BEE21C8, 0x84AF8716D3A72CA4, 0xB24BA37D544FF41A, 0x55AE1D1FDDE2CF50, +0x1FC6005B0A3BF598, 0x1F03B0D3AB5AD, 0x9DECCF4D9DED8FCF, 0xB174F8838F39077A, +0x57F83822E25CAFEB, 0x3102E1391CAB6155, 0x227FA1883A32B238, 0x16017735CEB0AC74, +0x148CD6FD6DB5D, +0x2A01D357301F926A, 0xCB4D81CD7FBABD64, 0x6B82DEA4A30AB815, 0x76E5F2AF75BEC38E, +0xD26B0D0ABA831A53, 0x1B9143452E5F9339, 0x472E47104E30, 0x6580B4E8616255FE, +0xBEB1D48213D4135A, 0x8B8E530E0979FFBB, 0x7332BF0175E66A6C, 0x1FC991982AE560F1, +0xA63089887981F8A2, 0x10651DF93EDBB, 0x138A40B5B601F403, 0xDBEBDEEF56F7172C, +0x850B270EBB655B18, 0xEA99413F5D06C2EC, 0x62E8C519B38D16E3, 0xD6A087AEE5AD7907, +0x13BF25988A35B, +0xBDA4E8A80BD58554, 0x8F5AD2D24CA205E9, 0x9FB501A9A3361E8B, 0x795D391E5533B114, +0x7AE37A1A8755126D, 0xDF2E2F4B20CB4625, 0xCC1D3836F3A4, 0xBA317AE90A9F1F40, +0x5CD96B10E8B594F2, 0x363A99B394562375, 0x16D9907278F5B7B8, 0x3AD00C23270F99C, +0x268847B06792AB18, 0xEDC9BAA4479B, 0x9B6A0789351E26F8, 0x232122287972F869, +0xABF334899D2596EF, 0x3ED05B4EC3155259, 0x7D153AE088BEB1A1, 0xEE1400032F6CA07E, +0x22F95CC45C80F, +0x7E95894918D79779, 0x928ECBB76806A6E7, 0x4E2B5CADC7FF9D7E, 0x3EF12F8FFE36B356, +0x6D737A7E43CD3BA0, 0xE4806271B8F12A28, 0xD0A7EBEEE94C, 0x408E6739BCCDB794, +0xAFA9839E9ED686F5, 0x9EE7977709708BFA, 0x25F8FF292CBE439F, 0xC9592A5D7646E46F, +0x41A47FDC9F47D842, 0x36971DB625B, 0xD7DE6837A1ABBEBB, 0x20FCE0F370405436, +0x8869DB8FC8418E06, 0xA5C42D3B0B9BB347, 0x7FFA3574D7D5EF0D, 0xD16DA2322F7EE3F6, +0x78CFBA1DCF15, +0xA815AEF0BF8399F4, 0x8CDFE4B9C791F68D, 0xB69B40AB65F50C78, 0x7A99360A56DEB801, +0x73F1372B37835BAA, 0x52B46F01879A8491, 0x196D0BCBEA9F4, 0x66D9042B7AD20631, +0xE2F40994B640041E, 0x803BAB14A520E115, 0x4B8FB04BB4407C75, 0x2746731DF016AEF1, +0x52D95DC473A19231, 0x1E688353A84FF, 0xEADB60B1FA225B1C, 0x5829844ECDE44538, +0xA8BA69D1157F1438, 0x9A5013CE37BBEB9E, 0xA55A58B80006659A, 0x4B36EA4E5661125C, +0xE65382B5CD2A, +0x26656337D53A935E, 0xFE987B7E89B1904E, 0x436D2F9722F581AF, 0x8F8B3F66A8F46A4, +0x9FF207863CB9DD39, 0x7513BB4EFB10A0DA, 0x1F93DB55F5B81, 0x791730F0307313B9, +0x7FE8FF1A56374977, 0xD2955E67E5C7E2BC, 0xC9B6294FEF5D4306, 0x30A601C9B98C9AEE, +0x284BF19491A4209B, 0x830D23D448DD, 0x8D8A5A0DF5A3B0E3, 0x54A28EABFA1FFB3C, +0x5BA10B3F803A058E, 0xC54D364353A14233, 0xABB9A859710CB096, 0xF8F1F93A83990040, +0x14978080CDB86, +0x1AA49D3AFA98A463, 0x6C6DA2FA9F14B6CF, 0xE26903D621527B64, 0x547FC7310D472B4B, +0x181E14EB3AA253E3, 0xA0721B617FE0783, 0x1E99EEA34B165, 0xA9B8C03406426554, +0xF2B4C5825F09678A, 0x981530252C4749C7, 0xF29F3AF85B7E7AB9, 0xECFEA4DF9FA9F013, +0x51A67D8E5665BB0A, 0x9F3012AFD23F, 0x5530A83019C37B7A, 0xAF5AFDC8C3EFBAC9, +0x809F533BC34A7F8D, 0x3533941DD50EC17, 0x89B4146CADFFB9CE, 0xE4EDE6B5180628CA, +0x193D642291ACD, +0xC52680F5A1D5D7F5, 0xF26A16EA220A67C4, 0x51683DEA555E736, 0xC9307DF26CF08349, +0x3400369D2D68531, 0x6CD36316EFEBDD37, 0x835FCF304968, 0xE9EEED9A49FC4107, +0xC111AB8833D02EDB, 0x1577C41960237790, 0x759869DEB441D1BF, 0x271966E27233557D, +0x7EFB1183747CA62, 0x180C94F1A1040, 0xAA64A278C44DB707, 0xB40B3790036F4F6E, +0xF2F57F2AA9B2F7B4, 0x6D586DB0589D399B, 0xE2A3BB7BFEDA900, 0x98D09766D631F998, +0x21B347969E01B, +0xB506D47E4BFEC3F7, 0xB25652C1BCF5DA48, 0xEA70506FC28B1499, 0x2A3666DED90E9479, +0x9E1E6860FD9C462D, 0x67FFC42CB5322928, 0x179434D8F8A0A, 0x9728BC42F646B3AB, +0xF1AEE70E07D4D70F, 0x59EEB6357C35AC9, 0xB23E0EBA39E1B2F7, 0x5A4542BC35E8FD34, +0x4E017D5C7725B7C3, 0x27CF73C827B9, 0x64A527550DCD5907, 0x3678D09161817EFE, +0xBED115C5EA63801B, 0x9736263ECDB012C6, 0x6B903280A8E74DAD, 0xBD6C18152B8296A9, +0x12F2A1077202B, +0x48D9422DB4A3B891, 0x3EDCDEE2B344539, 0x25B146C62D60B2AF, 0xA4F160649E0326AA, +0xA291E261A82338AA, 0xEEE5E3064E0B77DA, 0x105BD35B40E, 0xF4783294C135E1E, +0xA5056685C34208E6, 0x821C7ADCCB5496AF, 0xFAB3049F340E60F3, 0xB290A6682B4ED813, +0x8E099C0AF76DE046, 0x124785BE30A9D, 0x6FDD10D2556F813, 0x2810FEE45663F2C8, +0xC1846948C575D352, 0x56DB785BE231144F, 0xD696AD1BA6CE96CA, 0x29514A98D851387, +0x15571AFD5B61E, +0xE8CBF8001C741815, 0x77B0355995A8F28B, 0xBE4CFA44D8EDFB3B, 0xE03758C6281A9E95, +0xBD2BF821C2AC5C54, 0x6F7CF1D311270F5B, 0xF6A83D28167C, 0xE00134075CEA80D2, +0x39F53D0CD51BDF6C, 0x9EA5BF410C5C3222, 0x4DCE756CCEEDF29D, 0x3CDD9D8B9B946992, +0x4AC197F2379A720A, 0x21A5EC40B60D6, 0xEB17AE69CFA246C0, 0x32AB8A55FAF11D62, +0xA34108F3AC58ABB6, 0x26B8F2F3195613EC, 0x14C63EAD61B4D5E2, 0x365E422661915515, +0x1A24591098012, +0xE2E6D1E1474947ED, 0x42FA4D623EC16323, 0xE90EDE5521144F5C, 0x91CE2D331E2A7E0E, +0x850E6D98B922CB75, 0xB556CB1D67A349A2, 0x2114FE415E8BF, 0x779255107AE35E3E, +0x9E6D0061AC12A9D, 0xBC60D00D01AE4026, 0xA49F8250E4538090, 0xFDBEC6D26803DBF2, +0x86C1FE821736C7C4, 0x24C6915F258F, 0xCE8BA2749878FA9B, 0xE859F9258EDD3175, +0x8A4265D885141FC2, 0x4E51167C4F0E592C, 0xCFBB67893372F87, 0xEC365D0DC5C4EB2D, +0x556EBB8E388B, +0xCBECFFEE9D0E49E8, 0x4BA22118880EBAA6, 0x78BB39B967C71E2B, 0x887CC2D8910B6D72, +0x6CAA7599C21DE9C5, 0x5F38FCA2D8BB592A, 0xD29EDB7D6BCF, 0x65B7E0A8477B667D, +0x29DEBF940550FAF1, 0x8B31EA5E76AD46A5, 0x732860309056EACE, 0xED98A8EFBCC1B997, +0x19FFE4D0F727DBDA, 0x3BA2B40F82CB, 0x60E457EAE729D731, 0x600EF128147DBECC, +0xB9590B8C64F9BB28, 0x5E3C420EF97F4680, 0x93476B581D6CA303, 0xE6E9F1CF72812AB4, +0x5003F03BFC0B, +0xD439D6D5EAA73560, 0xF06A3C80062AAAC4, 0xAF4335CAE37F5A58, 0x74BA9BF16A7DD5BD, +0xC89A68E2F9A0BF53, 0x900E6ECAC98A891F, 0x1932C987ABB0, 0x3CA109071F25F058, +0x758DA3DE20BBD2D4, 0xA5B958E96387B49B, 0xD9BD787164AF5633, 0x4FB1B19C44984020, +0x3AB302C4F7C2158A, 0x12515483B15A3, 0xB6528F8CB35D3BF, 0xBA4769181A02C48C, +0x3537B032B2D8FF07, 0x1C69541832F46446, 0xFBE2C41D50D0E1AE, 0x21DE168D7F787302, +0x7220AFEDB032, +0xAF7867D34F3BF6B0, 0xDB4C91FCD5DAD187, 0xBDFDF76F7B17064C, 0x232BAFFA1A02AC8E, +0x50549D1F80C29BC, 0x10AE173A14542B1C, 0x1BDD3A653C0CF, 0x2E539937FDFE7D29, +0xAE7ED2C03C24C3F4, 0x4AA63D4EB4F8504C, 0x2346DDD13B081DF7, 0x13A0D691575A35BF, +0x7AFB1EC81E8194D5, 0xF4F8F2A2C320, 0xBF23B1F69D1EDAC2, 0xA39ECD16B70125EE, +0xB0E53A50D9EECE0B, 0xB22CC704EE8439F4, 0x4840F99D830FB492, 0x1DD8BA3FAD131F16, +0x18EFA369142E7, +0x60DA859ED995FB4A, 0xEC5EB0B7C3E7244E, 0x6CE35165BC3C9E09, 0x94740EA96A023CE0, +0x32E556A128025F16, 0xBA45528485F4EDD5, 0xEFF0985033CD, 0x6E158D126DB2DEE0, +0x82FB9165FB521F54, 0x3564147F9581D527, 0x37A57CEE7A3654BC, 0xE9156B8B4E47EF3, +0x3A7D3FD6D9A54B83, 0x5B1C49C6BCDA, 0x559DB8E736B4F3F9, 0xA519659F1124F25B, +0xF2477A0585F8AE45, 0x5671E973CD91B9BE, 0xDCD7A48C8C3C97F0, 0x214CBA473CF8B1CF, +0x9FD2B65E417D, +0xCF52D82628DCF1D8, 0x97FEB86048FC880E, 0x450231D4783A4B19, 0x847F6411A65722FF, +0xA95CE3350E7B3566, 0x97B2F0D1C47A68A7, 0x1208EF04B340, 0x3BE0EF689F5BB450, +0xC76F8D29CF9B6BDB, 0xF9AAC51986968F4A, 0x56256F725F6F30BF, 0xA5E1B70EEFB49BE2, +0x8BCC908A33938A96, 0x18AB876B614C6, 0x6612C9C5D1794A59, 0xB29357609F4C37E5, +0xCC887976729B553D, 0xD0B386D693FC0827, 0x1FDEB4D44B64A1D7, 0x565F7D573A7E9B5C, +0x2191576EEF553, +0x85879C670E2DC088, 0x12242C35BB697A0C, 0x8526D3EE0EDE7472, 0xDB5DC97753DEB6E5, +0x2399900DDB6F8C0D, 0x573146154B32DD6D, 0x325F55372262, 0xBA994F6EA5431FFA, +0xF5C3F913134C3318, 0xA8EF722CB20BD1D6, 0x9A11E85CCDEAC7CB, 0x3EA776C6945B7DF8, +0xEECFE2889EE181F2, 0x20537B246E1DC, 0xEBFF24875AED5B33, 0xDAF5286243D128F9, +0x23F33DCC4A5ACDB1, 0xD224F507EC30453D, 0x9A22A4BEFC7FA3D6, 0xCAF88503AB48F569, +0x1178C5516E662, +0x18E6027D4233E649, 0xE9EDEBF20EEAD413, 0x6B09697E29352C33, 0x736EE33D69F9A9F4, +0x8267768A86DEC9E8, 0x16A7CFE6294D02B5, 0x3A43907C8837, 0x8D80F73732FD5C8C, +0xEBC5B2707CD96B0F, 0x4F58A96ECAA4DDFE, 0x1178709A071EC1EE, 0xDAFC4B5BF4C91023, +0x58E37310B575C8CF, 0x1CD2F757C98D, 0xD2D24D9C3DEC9B66, 0x55764D2A3FB0C42A, +0xB64D4B8317F30545, 0xDA8E716688B68F63, 0x97C17DFDD366C677, 0xCE7245F1198A0F0E, +0x13EAAFF0D6029, +0xE6E48A44B43C89E5, 0x729CEBE84B6942D2, 0x164E27D64781A163, 0x1CAC477220437833, +0x45A3E96D49BF87D4, 0xC6FE846712ED2BA1, 0x21B72315663B7, 0x7A469AB0A6702F84, +0xAEA9F8638D12D040, 0xBB052C5B755AA1, 0xEE52128794CDAF92, 0x495DA559392F87B, +0x1E2C02254A1FEA57, 0x12231DD7E481D, 0x187273C1C37C6622, 0xC9C7517D5C0B6928, +0x34A7092D320B11B1, 0x9249DD4C05620084, 0xCA9EFB8591C88F3F, 0x52D28AF4714725B5, +0x1DD56B54910A7, +0x60E6F39B5C74C7AC, 0xB5030DD06DA1667A, 0x2175642C60F3D7F5, 0x308ECAD7DFEAE2BB, +0xF73516A21B97FB78, 0x1BA5B72190DCB248, 0x814A4017C80A, 0xE67E5CE4B226D943, +0xCE154A47A33B21C4, 0x94D875AB1FE1C199, 0xD5483DBF0A988DE5, 0x441C1EA4E829DB4F, +0xD561CF220941ED83, 0x96749EDC2A04, 0xBF73DF457B525792, 0x3C58A39EF96E0273, +0xFF83338BE7542DDA, 0x3630AABC466C745F, 0x60B9D65A3C4FE8B4, 0x871BB8EB8F9B9AD5, +0x1135758AB7C72, +0x40CE9D13DF0E370E, 0x6DDAAD3CCCC6C750, 0x4FBC4D2E53A9992B, 0xEB4E8EEB80C686A9, +0xC85F619F10828C06, 0x50D4DAD71D81060F, 0x54D92587DEDD, 0xAE06A87F5BD90662, +0xE9627C4A7A64B6C4, 0xBB743848A6AE2604, 0x374FA0A07416144E, 0xB233F465B37BFD12, +0xF61D02CAE88CCD3F, 0x185A97C9D19A4, 0xAD696B376924772C, 0x5AC02B5A506A3610, +0x80A03934B03DBE7, 0xC33F4BFB9450D0EB, 0x56667418085DAC07, 0xB4572857CAF0DC9D, +0x24230F6CBCCF, +0xA1AAB1BAA37583C5, 0xC22CA59BF0E0333A, 0xE03E802AB9B4DEE4, 0x3B29042FCFCBFB40, +0xDA929CD11E32E8B0, 0x66077E4869255DAF, 0x2830C635D6BE, 0x177F1811FA04CAA8, +0x4836D14C30233589, 0xE1EE4266BB52CBE3, 0x20D5F503A51D4190, 0xCA43478014143DA9, +0x59D3E7173954F91, 0x19A435D18674F, 0xE3967A755C076502, 0xD0BFEF602071471A, +0xA58FBFADBEFF7AB9, 0x433DA2CE99EB6B74, 0x391960B98B84626F, 0xC00B7E1F1977AE49, +0x27D260A8B5A4, +0x5A836453DE1CBA8B, 0xFD616603A337363B, 0xF9393B0BF8671490, 0x3AC8527CABB7905A, +0x8D1BC7B150AC6087, 0x5A5B1535DF3F9442, 0xEFDD3198BE80, 0x274D0598A60C7C7E, +0x95202DD451175148, 0xE2FEFDF91D536F91, 0xC470BA28B4F3ADC5, 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0xD1C3EBA4F5A4, 0x6E9E623A006B7FDA, 0xE570EA2F6E57C69E, +0x668725A90D995223, 0xE00987B98C5290A8, 0x5BEE2C4D49F48591, 0x14960C315FDC6FD4, +0x1700AEC7DA845, +0xE92044731DEF1AED, 0xABF8B2737E298E6B, 0xC4A65180B676C2A3, 0x29050C0F7B4349A7, +0xB289FA5D6249A91F, 0x59B7A8626D9A8A90, 0x15E1E1423FA3C, 0x18D17F18C6502B45, +0x3FDEC7BFE1F5789F, 0xD45C729F42B81362, 0xCE9CF6090E2E7FC6, 0x3A14D6B7FF21B790, +0x41E58BB03D532CC8, 0xF99601B0E71E, 0x7B89BB899167644C, 0x8582F6D7E3521C22, +0x3AEB37DE39DF42AA, 0xB8F203CE27EDBDBD, 0x6DB03359CBD94B41, 0xFC64822FF1D62C4, +0x1B14973FD16FD, +0x175B144B2092B503, 0x46F8542E2DA36003, 0x9333CCDA0BE10C58, 0x6574F4D7F9F1246D, +0x88134479D0B920CE, 0xA1E7C3D606CE330, 0xAC3F2C0AC417, 0x6DF32EABC2E82DFC, +0x36CC436913AD233A, 0x6C515FAA12B6BB69, 0x32B798A9D5165D61, 0x8EEB1056C8806008, +0xD0B8729094194671, 0x154014D45EB57, 0xDA05C4D21992A737, 0x5DE6DE9938307D3C, +0x356A6074009158A0, 0xFA5D7C1FCE001389, 0xC686F8A324BA46DC, 0xCE3F61A7893AC10F, +0x1699470F035E1, +0xE56F3C89DD88827E, 0x54C2DDA7D67C72B9, 0x9597ED45A77C7ADF, 0xE9A8D40A47CBD095, +0x3C763B1CFB3A28C, 0x24779FA2A9BB62D2, 0x3CEFB9AB456A, 0xCDBC4B19E670D500, +0xD60BEF4F82667437, 0x18049C63FCC8790, 0xD7854E3EF9824064, 0xA3E8F23F3F20AE72, +0xE2346EB12B286EC1, 0x175DE81E67D97, 0xC936C115D2074BC, 0x69E75EE93135AEDB, +0x36BFFB9FD0DC6A99, 0xB1FBA35023F17FAE, 0x7522E95DE309556C, 0x68D4BDC75560F8F1, +0x1FCE2B47CFD1D, +0xEAF9C5ED2AF7FE7B, 0xAD1400B4E61AD2F2, 0x8CE64A8BC6FDEFB7, 0xEE4B0104E91EF51A, +0x757EDC61BBE15B24, 0x40F0C89BEC91C483, 0x12D2202634609, 0x8C738AE3EABF4F3E, +0xFE89CF744B096129, 0xF6294A1659578553, 0xDAB2034B763F6E12, 0x1F69F8232FEFC826, +0x8BF00BCEF2A7D837, 0x2E1D491D2E2D, 0x8F994AF5702E337B, 0xAA076EC11F16BECC, +0x4A3D03B1C1946C0E, 0x43E956551AC23B6E, 0x9111ADAF6DB54B91, 0xB0F73A3D7B60840E, +0x1EC29D12CACFC, +0x4F26A97B509701F8, 0x20038DA5D24ABC38, 0xBE819956470BFA04, 0x856441F6BE71EF4D, +0x7E80B190AAF15BBC, 0x241A9E050C1FA794, 0x1A833D6CD6BDF, 0xCEDBCB3808B8EAF8, +0x5521C674B7F3C238, 0x3969460EE8175E2D, 0xB3AE5CB32FB9C850, 0x4CA2C90D1426F39B, +0xD1FB460902647BE8, 0x1AC8AE3032E8A, 0xB3208C7EAB19A50E, 0x9BAE8940B45A638D, +0x786C30F5D9BE629A, 0xF2A8C2F9A06E21C, 0xF8DD91C9084488EC, 0x9C9652FE0B22EF60, +0x21B52407F008, +0x10004CF4EF9A2778, 0x7BB915417928FCFB, 0xE436A88FE206E42D, 0xFDACF0DC0906AA43, +0x2CB2AAE91AF6ACFA, 0x53ABB62D4C13AC52, 0x48B7B5A1BA72, 0xF7278050566E9249, +0x300F4FAFAFDCB153, 0xB203C65DFE4BF5BD, 0x9B2316CE116926DC, 0xE068D39489B9E2B3, +0x32DC2F27ABD7EF43, 0x129D4DBAA1DBD, 0xF881AB66A8565072, 0x5129D22EB84CA725, +0x64DFBFACD7D97E38, 0x617095B8CEB2829, 0x4F0648F9A8D4D397, 0x862ABA78ABD6F1E1, +0x9CA0BA951C7, +0x33BCCB49A10F6CCF, 0x722A27581E91A825, 0xDE9CACE4487370CF, 0x2B13C432C62C6E2E, +0xC4FB6140991FEC89, 0xB96520008DE2DA04, 0x17C6B378DFF7, 0x5F810376E65C5E64, +0x2545C5FF7E725327, 0x64243E7E04CA2540, 0xDD85A177D84F2C26, 0xBFED32F42167E35, +0xEEC049DF3F761609, 0x146F7CC513DEB, 0x1F467D1130299114, 0x399CA3044A276FC, +0xD697A305417ABA1E, 0x13704E1F1DD64EF5, 0x31453A4AD52CB3D9, 0xBF05ADCF8E8DADC9, +0xE3F3D27616B, +0xBB53D0FE83464E86, 0xBF445D9784300712, 0xFFA8EB2455C27BB7, 0x4D6C52C7E4F20B48, +0x9B981F403C4BAD5A, 0x524AF53683B6BC36, 0x53B3B31EA192, 0x103842ED515C2F19, +0xF66AB3B74BAE4B16, 0xF533354981EBFC0C, 0x6210648B721EE08B, 0x34D76F38143C125, +0xB11284AE3BD5AC0C, 0x11A0EDB895DDF, 0x4FCE2114A73458A9, 0xB14E0A5E226A58E, +0x39A3E15E82EFC52, 0x97FF4631FD2AE50D, 0x6966FE8CA9E23D39, 0xD867C32E7F94B69B, +0x8365EC759703, +0x76717089790C96EC, 0x1DEC88520EAF6BFA, 0xD3D873FA36F2C707, 0xA46FBBF3FAD6D34A, +0x346EDBC445D9A69F, 0x8BE85426317A0024, 0x19AF1E1BADEE1, 0x0, 0x0, 0x0, 0x0, +0x0, 0x0, 0x0, 0x4BA72CA59B6001BB, 0xE5FD2ABD4CB6A33E, 0x8A98D19511F78FF8, +0x2C5C5AFB9A978D78, 0x73C9F51BE2B16F40, 0x671834E521007F4D, 0x451B04879668 +}; + + +// Precomputed values for the first Miller iteration of the Tate pairing on the +// 2^eA-torsion of E0: y^2 = x^3 + x. Contains a triple (x,y,l1), there the +// coordinates x and y of the double of Q are in Fp, the slope l1 is in Fp2. + +const uint64_t T_tate2_firststep_Q[4 * NWORDS64_FIELD] = { +0x6448CB5BD9770D67, 0x3092CF8C8803D8B4, 0x2542331C81C2C2F8, 0x8066DFBFF024AA32, +0x5F4E163CD158E1A, 0x87C8B0AC7FF6B89F, 0x18466971777FB, 0x414795F6A70D543E, +0xDC7D2E0B9229A814, 0x679CD711C5B2AC8E, 0xCC92A943030F0D18, 0xC2BB3CDA074E0076, +0x19332E71DC423BA4, 0x1C95A2FC045DD, 0x6DB3A00833C75E25, 0xEF23EDA1ACBDA616, +0x72B19555F79DDE6E, 0x9DBA3A0E78EBE79E, 0x1D187EE5215D71B3, 0x1D24D175B4C3C65B, +0x10AEB3555065D, 0x508F3D07E0AE1491, 0x1C7EF18B886FDB38, 0xAA1001FC42642F0C, +0xD5536205F2F93C34, 0xB647092B16484B6E, 0x899C89AEA084752F, 0xD0C508EA68B4 +}; + + +// From here on all values are in Fp. The table contains eA-2 triples (x,y,l1). + +const uint64_t T_tate2_Q[3 * (OALICE_BITS - 2) * NWORDS64_FIELD] = { +0x750FCD24D96F498D, 0xE74B7652658B6360, 0x54FB85D2945C71AD, 0xA530239B59D34B1A, +0x5E729DB52488A584, 0x8EF15300FCCB833, 0xCF9B1759A390, 0xB751C3B1450C3CFB, +0xFCD2CDCDC975A71C, 0xB205AE03102DA534, 0x2A92457AFE850487, 0x11C5DE0150BB9277, +0x92583FABF57B00B, 0x1DB45E9F74BA0, 0x6E2824B9A6CD94A6, 0x326996F14616B5B, +0xB8B059926FC41E14, 0x81C1902B47804230, 0x4AED4C52162CE0C2, 0xFDF011A61D93A862, +0x1EF5325739A5E, +0x78B9C0B9A3BD2967, 0x71CB2BC7320553C6, 0x316F5C32407BD0A7, 0xE55D1AF3CE7A86A1, +0xADA2BE65BC44F08B, 0x6DFECE85DFCA3C66, 0x1FC0E23853261, 0x2DDD455D97F32363, +0x46045C35F348D058, 0xEBED02F21182F5E7, 0x945CE83599BB7C39, 0xBFFC17B98D65562A, +0xF2939B5BA82E954, 0xA00560C80C10, 0x474F1C272489BC2F, 0xA564E546E5A201CB, +0xB957D75CFF3FF629, 0x3A76D34BC39747A6, 0xAA8D48E8E9B4698, 0xCCA8F309E4BDB606, +0xCAA0E8A11964, +0x976CCC8431FB6C34, 0x8C8284AF61466CBB, 0xB0AF134D7B823472, 0x1A04747E8B17FAF1, +0x5E2440D685E770E9, 0x3DDB066DB9B420C9, 0x625F7441AC17, 0x7CFA008777AD43F9, +0xA4B6C0632363D1AE, 0x9336E4719A6D77FC, 0x5EABF971D76F3F31, 0x626FAB5A44137369, +0xF40400CBD713FCCB, 0x14F6A0CDB44DC, 0xFDB139668120B384, 0x1DED27FD8F13D564, +0x9AC2B6A0F21A8FE1, 0x67C90AA701E803E0, 0x8D43D97FBF09947C, 0xFEC1313BA4FE8713, +0x1F2633D52B220, +0xFF1D65CA3CEC7022, 0xB42F77A4ECD38FDD, 0x10D4A99EF3C7A955, 0x1B2303D6B0FD913E, +0xA572DE48DA807A48, 0x502F9A6E3E3A37E8, 0x37CC76C9CAFA, 0x2780B7621B977D32, +0x7C0DEF25CD7EA965, 0x4DD4316EEEB248A1, 0x305AC1CBF3AAAE7D, 0x76EE1B4562B0B550, +0x448B64F5350DB407, 0x5445283D28B8, 0x7D0C48FCF2971A51, 0x5603D7D476DA47F4, +0xF3EA2E2B18DB0180, 0x9FB26BEE17EB7153, 0x9979BEB62FE54A8F, 0x7BEA62C58A6755ED, +0x433EE8B58E9E, +0xEBECB7300254B1E1, 0xD0BA966A73B96166, 0x6A80F889DA560535, 0xBA5F9AB3FF24BF95, +0x83ED7166FCD75963, 0xBDAC93405D97A232, 0xD861C6B948F9, 0xE3BE6182E764F224, +0x207EEC37228E7DDE, 0xE63CED9839EA5FE0, 0x25C5DEC25FDD4617, 0x1F8E938E85B1CDB7, +0x75274B7A209FC0E6, 0x1839F3198378E, 0x6B6F952BF801101B, 0x3B790104ACBCA620, +0x8732A25B16A39F6F, 0x58838C50A4F42CF7, 0x6CF709BFB949B38F, 0xF7B30AD8E2FBE8BE, +0x10AFD93F23D73, +0x5BC1E231775DB25D, 0xBD14AAB4EF0F7D0E, 0xB16B666A646CDD6D, 0xA4B23B30157407A5, +0xCC196DB00BAECEB0, 0x823C20C85890BA32, 0x166D4CE5942EB, 0x92E0CD7EAC79931D, +0x98AC6027E2E6E739, 0x7C5B6749716ED8F0, 0x9587208313A6421A, 0x1A264889F1AB32C6, +0x986D989217672862, 0x6F058AD03407, 0x8A28D792AC68A4EF, 0x758DBEC36CFDC047, +0x4A3BB5480742B492, 0x737F130B7B7B07EC, 0x2C2410E5B8112DD8, 0x88461660FCA94625, +0x1A9B7CA9A7EBD, +0x3F0D55442DF08455, 0xC6FCFD68C4543DF4, 0xE8FDDA0B8B397428, 0x553102BC463B8655, +0xE5FBA8DFDBD0EE7B, 0x2259D7A195D96B6F, 0xAE763E0E16F1, 0x7C873A06F4E87392, +0x483291D3C46E6149, 0x630FCF37481539B1, 0x55749A6554255C40, 0xE93BD8E4541A00BA, +0xD6052323E9AB7DBC, 0x1D9E8E2B76ACE, 0x4C2240A028DFD1C8, 0xE5E61CBE05C1B35C, +0xABB89AB8647CCD2, 0xA652181A694CD8A5, 0xBE23EB2730D0E41E, 0x93A4368F83A8C22F, +0x7F25F33AE96B, +0x9BB49112E1992786, 0xFF567E8A6A208CC3, 0xE82B79721517C379, 0x3D25B6E13998867B, +0x2B1759EC761146E5, 0x848B6C4C60858B, 0x1581E213BE60B, 0xFAA58AB579DC241D, +0xDB9AD8ADF806E6C1, 0x8DD926E84E3C8530, 0x21A6AB3DC79E86B, 0x815E030F6666EF52, +0x83273E8F1FEC66D7, 0x910F40660D28, 0xE9D5AE8EF786F7C8, 0x381ADEFD696AE953, +0x11775446545AFE, 0x61047775DC13B67B, 0xD1CD714D5B833F65, 0x630DC4B85564086E, +0xF9019F945C63, +0xD3696E6951EAC453, 0x8D3A301B3D438D24, 0xC92AE0676C6F85F6, 0xF08D5878E41056CB, +0x5F01D4CC3F1C6991, 0x7A46CB006E86FCF9, 0x1ACB66191B170, 0x5DAB8F66ABC12F71, +0xD31ADC09529629FD, 0xCA5462533F93EBF4, 0x1FD9239820B35EF2, 0xC4006DB9D099E737, +0xD33F192F3C60176F, 0x194C33CCE9747, 0x34FEAF8B42A7E67, 0xAB831F7FA796DBB0, +0x1C079D015E7E2DBE, 0x9FD78DC14C4FB1D5, 0x32AE7FF62C72850F, 0x7CAAC8E174CCA7BA, +0x22041D2B129E2, +0xD6D341AA9C65FA0A, 0x269CE4DA19787A0F, 0x5C40364FBEDB730D, 0x1E5BDDF054C72EDA, +0xDAE41EFA9FD3DE60, 0xB9E24619E36B6BBA, 0x15662A66F5914, 0x5CD18C2F5D6C35C4, +0x9BED59102C378CCB, 0x2D42AF0D2A5D691F, 0xDACEE58A11F684A1, 0x197C8D9EA914E123, +0xFE0106C5A328B9DC, 0xF9958E1DD8EB, 0xE1DCB01D0EC5BB24, 0xA8C8965084B59D42, +0xF2AB73AF5445D89C, 0x353F3DA2A09B895D, 0x448A1BDA9F45BB88, 0xED4CA9F58D3CD69C, +0x18641D1221F20, +0x99766C73104FDD34, 0xA0EC15986B4E96BF, 0x56FD2630B8FE894D, 0x37F6E0A38F687DE4, +0x7155F8F92BD9CF3A, 0x10BAD4A97A19C91D, 0x2D12F4F62D7C, 0xBEEC749EB21AD7B3, +0x7E4A5802AF46E40E, 0xCBBDB4823045A57, 0x16C2AAF84AC0A36D, 0x73FCB5D8C923A60C, +0xC81696869435882C, 0xE7FBAC22A3A8, 0x1FA28C25DEC25548, 0xCD267A99D02AAA05, +0xA06C218D03F4830A, 0x88AA3FC65324C470, 0x3A1643BD10F7D37A, 0x2C077987A57ED136, +0xF8D12F1E90B4, +0x982B36BB77C84893, 0x21351AB71BB1755B, 0xD170325D69937E8E, 0xC9FFC37128F13C3C, +0x2BB1EA58B3E3B52B, 0x497FC1C7DB647619, 0x1BFF4F5970419, 0xA849C7DA82EAFD6A, +0x432F43E215122330, 0xE0697EE4307E6357, 0x8AFA2C96D5906B08, 0x62910BCC532ABA04, +0x8365333F5666343F, 0x17AB82A1C17DB, 0x20B0BC62AD66E26C, 0x83C5E378CA181D81, +0x30CDDC6C68519055, 0x2EE7B32CE5A3C27F, 0xED3BED5F9729B254, 0xF462AB18AF63ED41, +0x9B903749BD4E, +0x9E8B6D6ED4F2013B, 0x26B43C36DA612DD9, 0x15B847B36354D5D3, 0xA973422CC6C26BBC, +0x9090C35E8C528BE1, 0xAC6900114D2426EF, 0x222E4EB1A855D, 0x368DEBFE21C9F228, +0x7DA13C45615E58B4, 0x7A1EEF8121CF946E, 0x1389B603541060B7, 0x35939F7C849FAD98, +0x5612D5495886080A, 0x126D9F7666C62, 0xA59E23FFC30D7F08, 0x4E863412FBF7537A, +0xE12D5C2B11B3EA72, 0xFA2DA80117B7E529, 0x829D2C4BC870471A, 0x55D25AF55CAF0CE3, +0x17E58E9A60B00, +0xAE7AE0E86C75F5FF, 0x5F731A8E705CDE2, 0x58D769F2E36FF7DE, 0x695C5EA9378A6292, +0x3800F94F79ED92D7, 0x95571F8C30FCC4B2, 0xF95830B84254, 0x736DF6FCAFEE78CE, +0x4187189B5DC95A2F, 0x624AC9761F193886, 0xDDB9D8115854F372, 0xC0A14EFFC8B7CFB1, +0x98AB4109ABB6B169, 0x9A3B57476653, 0xFA5379F67D64F895, 0xE8DA1DC75B85E197, +0x66AB894EFFFEFF69, 0xD07F3ED21FD321A0, 0x50CF0F089CAD08FF, 0xF41CC7E5C71FCF78, +0x49CF3C122C1A, +0x8839927AF53F1372, 0xDB5E77050B6270A8, 0xDF500C79F8D3E234, 0x7397E4AF21489137, +0xFB074F540CF5B358, 0x24937D8B699276A4, 0xE2BEB58E1F43, 0x6C09EEBC3B808501, +0xD08F5CCBE480B4DA, 0x18A7DA53E2FA206E, 0xD1475AEF5FF06038, 0x224C25D316F1BDDD, +0x9DF5FBF015F68464, 0xF6CF4101CB6F, 0x77D66053CB379B05, 0xC30F832597978504, +0x2502B8604C8092DF, 0x3B8505BED298AFD6, 0x16A7F7AAA19AE877, 0x489084A274644201, +0x1520AE384EB88, +0x4ED3669DF211CE2F, 0xA947F59FB6D56130, 0x5638C08919F3E836, 0xC752FADE9CC53F0C, +0xA0F96535831E8618, 0xFC2AB5351383C7A1, 0x592D92B69080, 0x6E5D4DBA90CEA065, +0xF18827A2148F9149, 0x2D95C2B574EEE1C6, 0xE45DF60BA50CD91D, 0xF186C5FB7061474F, +0x748912DFBE7E289C, 0x12C5D5F96EE84, 0x9AAFE769FA51D697, 0xDE1047885327BA69, +0x6A5E24FF211F8572, 0xBADE71E4BCC6ACBD, 0x84775B0F03B8ABA6, 0x3A0B4AF076484734, +0x1EE715D2BAA11, +0x112166B515BA4D19, 0x86EC702AF6897D6, 0x15A1E4A44D712A9B, 0x7992F8B85FD31C2A, +0xA11306EAE3E7FFEE, 0xB886F4D254477E21, 0x8989E6AA5B25, 0x6840E0ACE4B22049, +0xFB9993EACC8508, 0xFAE632398F41F6E3, 0x6EEC63929229AABF, 0x67B8C615A76C3FC3, +0x6735EEA6B63DB765, 0x10C989056CD98, 0x5E0E035D4869CACF, 0x6478EE750E4BC97F, +0xE4510F8F46C1539C, 0x55BC95BCC99271FC, 0xFB9C777517663A, 0x6F3E119669FF2B5D, +0x39292ECF566, +0xAE520B158A1FF06C, 0x80A75BF1A049CF, 0xCB34F7C15C6EF9D2, 0x37BD230485704A36, +0x371D40187C0F944E, 0xDBC6C6F6859511C2, 0x22CC2104AFB41, 0xC4F21C38C5B85958, +0x77FC5A339ED63183, 0x7149B5D638A75E1F, 0x8384F5A1B6181170, 0x195FFD7ABAB3096F, +0xF85F05D350A77AAA, 0x119E4DD8CA9C9, 0x45C5BAC286EE7FB0, 0x4344528D50651C4A, +0xB6495C96DCA65927, 0x42904F323A584C6E, 0xC10D98101270F3C, 0xC7562A3AC2978FDE, +0x8B416F91D036, +0xEEAE7E7259BCB358, 0x18AF927D1101692E, 0x78987E28398D7C06, 0x3AF66C5F09A98CCB, +0xDF2555D6732D3EB8, 0x6C92E1BF5F717600, 0x138E67EF2A448, 0xF8319F1300F7D2DD, +0x91939965262F1B40, 0x51891307FA41820, 0xDED0AAF0E9A4011A, 0xA991918474E277AE, +0xC8341FFC284AD381, 0x1011F23114641, 0x92EEB0CD4A3EDA72, 0x37A29A8CCAC3443D, +0x5D9F1528FBBF870, 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+0x9911F3EFF893, +0x76F41226DC8A3023, 0x7BE200A488E52102, 0x487627195F3851FA, 0x4178EA05091B286A, +0xC5821D7BBBC8D1AE, 0x39E8A975376BCBEE, 0xAEEB22142B4C, 0xB8E3FB4B8368EAD5, +0xFA2CEACDC78819FD, 0x8C7B0736A4F4235D, 0xDB39AF50D758F37, 0xEFAB2A6C37EEAAB8, +0x32471BF3E9437ACA, 0x1698D34A2FFC4, 0x94E779CBB06174FF, 0xA710C2D17913F265, +0x74CF8CEBC8216BB0, 0x873E3C89E109A2D2, 0x33CBDAD174E42AF2, 0x556B6E273C9CBED7, +0x4CDEF5523B5B, +0x59479F58397D7D49, 0x6E409F3B94C939AF, 0x8199507BE7FC16C9, 0x31D51A16516BB8DA, +0xCF4F30A5246D95A6, 0x6D367CB671A8DB5E, 0x19943E87FF1EF, 0x58700FE8CAC4CA63, +0x9DC551B810381FD, 0xDAD8CF1B6AE8A85, 0x46198234D62C5A6C, 0x58083F4F805ADAB0, +0x33E7758B76EB139D, 0x219BA0312203F, 0x3C42CFE6210B3F5C, 0x941A71AF0DFBD2AE, +0x507B75FF78D4748B, 0x69B2CBDECCB89C5A, 0x94C898B57C8B59DE, 0x98CA17DAA6DBCF26, +0xFB3627D437F8, +0xCC63B1CEDCE3A0B0, 0xCD32D70C9B3CC30, 0xD5613FFC0ADC8958, 0xD5701D8FCB0B23E8, +0x4224B275443B8D16, 0x9EFD16964724195E, 0xBC4AC548ACBC, 0xC4F50564AB0A898F, +0x1191E0E421D96F90, 0xE60159DAE586D25F, 0xA5B3DD9044641C78, 0x1439F6A2AEEF7B09, +0xEF77FC9113AB6B8F, 0x52D98B48B1E6, 0x9313E6BEB895D0E, 0x6AF38699D035397A, +0x4FBE29CCDA8B85CD, 0x6C564B1A52E8E3B5, 0xC8D117642E9549AF, 0x1BFFCC77AD0410BB, +0x131387CD80395, +0xA894DE296055FB87, 0x5DB8470A2CA41235, 0xFEF5B8443725D1B2, 0xFCA66DE405FEC730, +0xC4C544BFCFE70903, 0x74CE0044E253EB18, 0x18259F34D009B, 0xC3273CA14AE62F90, +0xE31E217F636B3E94, 0xA41C63C97C7965C8, 0xF8991686F607B1FE, 0xE37BC311F302B66C, +0xE2EF85D8FE6FE9DE, 0xD1664DFC3881, 0xC4D90C0F00D51B8B, 0xE59718F079173E13, +0x608CD12E7902DD75, 0xCCEAC254C5BEB15F, 0xAC5F815370ED6199, 0xD3295DDB1DFAE34C, +0x19D86F9D8651D, +0xFE2A6047FA56CB14, 0xD004D6A4BA6949A2, 0x24689EB3FDCAAFC6, 0xE1EF935B69FE5C5B, +0x6CDFF99FC1866C35, 0x212117C3E11F21E4, 0x79BCA3AB78F9, 0x82FF06210E3EDFFA, +0x272E07A6431EFD5E, 0xE719B1822C5E921B, 0xA906001B221DF812, 0x52E6585D606220B, +0xED05E3331F99E229, 0x579083AA0038, 0x367FD304A45FC4E2, 0xFA11EA91F1C6ABF5, +0x39E59FAA6DC66EBD, 0xCF88A0A6432AF727, 0xA62C398E372E227A, 0xAE74A8E35645BAC1, +0x15EEB6E65BEC4, +0xC634C4819A1ED8F, 0x632268FEB06EE93B, 0xBECF722F1E15D90B, 0xC951162D2DA8FB4C, +0xB02A1B6BE8A9AB68, 0x9C324ACCCCC8C38C, 0x1B695A42186A, 0x8E53D97D3EACBB01, +0x1546816422E55F82, 0xDED0DAD160D3FD5D, 0x8249B64710AD203B, 0xFCA69B2EA8E86113, +0x7AAD296BB1437B7D, 0x125423B1330F9, 0x7091AB1ED7539F4B, 0x28419925E4BAD20D, +0xE39DCE03BC0C1115, 0x49EB10415FF2C1E1, 0xD56389BA809F1E88, 0x53122F69D5CBAAE5, +0x2572A0410415, +0x94408985DF01B82D, 0xD7EDAADFA0E53F14, 0x4A245907960DB392, 0xBB226A43832CCB13, +0x7B277BF33DE3D23B, 0xC4AEDAA89EB73B67, 0xD21752580643, 0x84AED6258A895C6E, +0x36B24217E57E7491, 0x9E6F1E0A51D27F06, 0xE4F5E0643E93D39, 0x3896A837DD4BC3A9, +0xFA18FDAC49BBAB04, 0x34EA6AE877E5, 0xDFB4F8B82B5C4CB0, 0x545BB1A058955AFC, +0xD01068891A87987F, 0x79F9D88F405217D3, 0x9AB64DD5C53DFFC8, 0x940D7DB71D845B97, +0x199FBF16DE3A0, +0xD9379C3602EFA740, 0x14DB81FE5A32C517, 0x419B8B23501EBE3D, 0xA6D8EE39DA5D0125, +0x56107A9442B7C580, 0xEAA6A10898EE23FD, 0x22EFAC42E1589, 0x992694C146B577DE, +0x910F1157BBB6981, 0x637CB38160574E0C, 0x92D8EB069447957E, 0x63EA8765CB69E1C8, +0xDC9E59ADEAF236E7, 0x12D7DCC203D36, 0x3AABADA2FB2A69D3, 0x5EDAFF782EC99D1E, +0xF10BB55F7ACB3D91, 0x177BDF5BD06D132D, 0x34F24DB9ED124120, 0x54114B5129B22F2A, +0x49050C0B45AF, +0x2F5CA0C247A406A8, 0xDDE367BF0F642412, 0x58B8950278FB5185, 0x29050BF178AB4D40, +0xDAED76DCF5437F7E, 0x4CA8F29E78198058, 0x1063F8ED2EE7D, 0x86399023050A95F3, +0x1C06CD3E959204F, 0x1A417A70FF5A7888, 0x2B66036DD80951, 0xCAC6D940A116FCCF, +0xAF420C1858C09DAD, 0x73B6B8943D47, 0xFBF1853CF4CA38C1, 0x64076146CE220140, +0x7D44FD9728E266C, 0xE1D1C30AAE15B92C, 0x2C65251123C21040, 0xE84884BB24035B65, +0x185D07ABC9FC7, +0x2CF9C3DD57549E80, 0xFF75C7C5C8411D8A, 0x5AC86B4329AA1E30, 0xD4A1454728E83789, +0x88F9A8848737DB2D, 0xEE329A298C8E04A1, 0x1DFC97FF288BE, 0xC44DD075B441C425, +0x64B249A6E8D7A3A, 0xE5E67E0D973363DE, 0x6E7E9B098493454D, 0x5B0C18272FEA045B, +0x463CC69FF3B34692, 0x1993BD0E6A84B, 0xD82AB92BDFDEE8F1, 0x6BE4121F868511E8, +0x9FCBFD369DBD1FB0, 0xF4E3CE88DBBC3646, 0xA53FC3CD2515EEAD, 0x611EE870BCBA5C35, +0x1CDC2390317B, +0xD4A38D9831C8757D, 0x17181235735820DA, 0xCD59E34A61783856, 0xDCB8A1A8584EB55F, +0x156CAFBA65D8FFC, 0x4D8CC567AA9D3DE6, 0x64B26D614845, 0xBFEBB868B8908A57, +0x5237682F9B452750, 0x59CCF79AF996FB66, 0xC05F593FFBF60426, 0xC182D64E091F751, +0xEB0EEF94889460C9, 0x1B5E585AFAA16, 0xFFF263E252B6E6F7, 0x6215F00F1EF47715, +0x85124C7B65F1FED, 0x90F179181E54CF0D, 0x5BD793B9654C55A4, 0xEA53F96F9A483B6C, +0x10602D666D5AA, +0x4E5E5DE514C96F13, 0x2AC2C798BBF7B098, 0x976EE2F3D5641BC4, 0x74576C261CEA95, +0x871FDC0176077F2D, 0x2BEA33718ADB38B8, 0x207B71701C5BC, 0x50D3ADC2CCB580A4, +0xAB07618076260833, 0x18126A46026F52B0, 0x74FA761F2E4CCD0B, 0x4567554AC3F5659A, +0xAD891EDE812893AB, 0x193060A996EDB, 0x764D68EC155F7730, 0xB7F19DB9A5ACF80C, +0x677FAFC16F572F8A, 0xCCE364F015C2E6C8, 0x3B6AF86FA7CD3340, 0x2BC1F998297666CA, +0x200C6C4126A35, +0x15C85, 0x0, 0x0, 0x2D6E659411000000, 0xC3E9279CF8657DA, 0x4E9A9D269CA0A2D0, +0x92ACD020194C, 0x898E8F7686F2F4E6, 0xE21377ADF1509405, 0x2C278C05C90D38F8, +0x9E033CFCCF292CB5, 0xEB1C3830C73809D3, 0x64DE17327298FF7B, 0x1E05DC4B6D8CC, +0xC4CFCE6E8DD591D4, 0x48AF4FEACAA71C92, 0x6B4756EE0C56E2CB, 0xEE12A8E041F3BDE0, +0x67C6B65234E8CA53, 0x61A3D36CDB18D779, 0x819B29E8027E, +0xE858, 0x0, 0x0, 0x721FE809F8000000, 0xB00349F6AB3F59A9, 0xD264A8A8BEEE8219, +0x1D9DD4F7A5DB5, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x898E8F7686F2F4E6, +0xE21377ADF1509405, 0x2C278C05C90D38F8, 0x9E033CFCCF292CB5, 0xEB1C3830C73809D3, +0x64DE17327298FF7B, 0x1E05DC4B6D8CC +}; + diff --git a/src/P434/P434_internal.h b/src/P434/P434_internal.h index acc4816..b7de184 100644 --- a/src/P434/P434_internal.h +++ b/src/P434/P434_internal.h @@ -55,6 +55,34 @@ #define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8) #define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8) +#ifdef COMPRESS + #define MASK2_BOB 0x00 + #define MASK3_BOB 0x7F + #define ORDER_A_ENCODED_BYTES SECRETKEY_A_BYTES + #define ORDER_B_ENCODED_BYTES SECRETKEY_B_BYTES + #define COMPRESSED_CHUNK_CT (3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES + 2) + #define UNCOMPRESSEDPK_BYTES 330 + // Table sizes used by the Entangled basis generation + #define TABLE_R_LEN 17 + #define TABLE_V_LEN 34 + // Parameters for discrete log computations + // Binary Pohlig-Hellman reduced to smaller logs of order ell^W + #define W_2 4 + #define W_3 5 + // ell^w + #define ELL2_W (1 << W_2) + #define ELL3_W 243 + // ell^(e mod w) + #define ELL2_EMODW (1 << (OALICE_BITS % W_2)) + #define ELL3_EMODW 9 + // # of digits in the discrete log + #define DLEN_2 54 // ceil(eA/W_2) + #define DLEN_3 28 // ceil(eB/W_3) + // Length of the optimal strategy path for Pohlig-Hellman + #define PLEN_2 55 + #define PLEN_3 29 +#endif + // SIDH's basic element definitions and point representations @@ -65,6 +93,16 @@ typedef felm_t f2elm_t[2]; // Datatyp typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates. typedef point_proj point_proj_t[1]; +#ifdef COMPRESS + typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates + typedef point_full_proj point_full_proj_t[1]; + + typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates. + typedef point_affine point_t[1]; + + typedef f2elm_t publickey_t[3]; +#endif + /**************** Function prototypes ****************/ @@ -82,7 +120,10 @@ void mp_add434_asm(const digit_t* a, const digit_t* b, digit_t* c); // Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit unsigned int mp_sub(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords); -digit_t mp_sub434x2_asm(const digit_t* a, const digit_t* b, digit_t* c); + +// 2x434-bit multiprecision subtraction followed by addition with p434*2^448, c = a-b+(p434*2^448) if a-b < 0, otherwise c=a-b +void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c); +void mp_subadd434x2_asm(const digit_t* a, const digit_t* b, digit_t* c); // Double 2x434-bit multiprecision subtraction, c = c-a-b, where c > a and c > b void mp_dblsub434x2_asm(const digit_t* a, const digit_t* b, digit_t* c); diff --git a/src/P503/AMD64/fp_x64_asm.S b/src/P503/AMD64/fp_x64_asm.S index 5f8fafd..7578ce6 100644 --- a/src/P503/AMD64/fp_x64_asm.S +++ b/src/P503/AMD64/fp_x64_asm.S @@ -1515,64 +1515,103 @@ mp_add503_asm: //*********************************************************************** -// 2x503-bit multiprecision subtraction -// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2]. Returns borrow mask +// 2x503-bit multiprecision subtraction/addition +// Operation: c [x2] = a [x0] - b [x1]. If c < 0, add p503*2^512 //*********************************************************************** -.global mp_sub503x2_asm -mp_sub503x2_asm: +.global mp_subadd503x2_asm +mp_subadd503x2_asm: + push r12 + push r13 + push r14 + push r15 xor rax, rax mov r8, [reg_p1] mov r9, [reg_p1+8] mov r10, [reg_p1+16] mov r11, [reg_p1+24] - mov rcx, [reg_p1+32] sub r8, [reg_p2] sbb r9, [reg_p2+8] sbb r10, [reg_p2+16] sbb r11, [reg_p2+24] - sbb rcx, [reg_p2+32] mov [reg_p3], r8 mov [reg_p3+8], r9 mov [reg_p3+16], r10 mov [reg_p3+24], r11 - mov [reg_p3+32], rcx - - mov r8, [reg_p1+40] - mov r9, [reg_p1+48] - mov r10, [reg_p1+56] - mov r11, [reg_p1+64] - mov rcx, [reg_p1+72] - sbb r8, [reg_p2+40] - sbb r9, [reg_p2+48] - sbb r10, [reg_p2+56] - sbb r11, [reg_p2+64] - sbb rcx, [reg_p2+72] - mov [reg_p3+40], r8 - mov [reg_p3+48], r9 - mov [reg_p3+56], r10 - mov [reg_p3+64], r11 - mov [reg_p3+72], rcx - - mov r8, [reg_p1+80] - mov r9, [reg_p1+88] - mov r10, [reg_p1+96] - mov r11, [reg_p1+104] - mov rcx, [reg_p1+112] - sbb r8, [reg_p2+80] - sbb r9, [reg_p2+88] - sbb r10, [reg_p2+96] - sbb r11, [reg_p2+104] - sbb rcx, [reg_p2+112] - mov [reg_p3+80], r8 - mov [reg_p3+88], r9 - mov [reg_p3+96], r10 - mov [reg_p3+104], r11 - mov [reg_p3+112], rcx - - mov r8, [reg_p1+120] - sbb r8, [reg_p2+120] + + mov r8, [reg_p1+32] + mov r9, [reg_p1+40] + mov r10, [reg_p1+48] + mov r11, [reg_p1+56] + sbb r8, [reg_p2+32] + sbb r9, [reg_p2+40] + sbb r10, [reg_p2+48] + sbb r11, [reg_p2+56] + mov [reg_p3+32], r8 + mov [reg_p3+40], r9 + mov [reg_p3+48], r10 + mov [reg_p3+56], r11 + + mov r8, [reg_p1+64] + mov r9, [reg_p1+72] + mov r10, [reg_p1+80] + mov r11, [reg_p1+88] + sbb r8, [reg_p2+64] + sbb r9, [reg_p2+72] + sbb r10, [reg_p2+80] + sbb r11, [reg_p2+88] + mov [reg_p3+64], r8 + mov [reg_p3+72], r9 + mov [reg_p3+80], r10 + mov [reg_p3+88], r11 + + mov r12, [reg_p1+96] + mov r13, [reg_p1+104] + mov r14, [reg_p1+112] + mov r15, [reg_p1+120] + sbb r12, [reg_p2+96] + sbb r13, [reg_p2+104] + sbb r14, [reg_p2+112] + sbb r15, [reg_p2+120] sbb rax, 0 - mov [reg_p3+120], r8 + + // Add p503 anded with the mask in rax + mov r8, [rip+p503] + mov r9, [rip+p503+24] + mov r10, [rip+p503+32] + mov r11, [rip+p503+40] + mov rdi, [rip+p503+48] + mov rsi, [rip+p503+56] + and r8, rax + and r9, rax + and r10, rax + and r11, rax + and rdi, rax + and rsi, rax + mov rax, [reg_p3+64] + add rax, r8 + mov [reg_p3+64], rax + mov rax, [reg_p3+72] + adc rax, r8 + mov [reg_p3+72], rax + mov rax, [reg_p3+80] + adc rax, r8 + mov [reg_p3+80], rax + mov rax, [reg_p3+88] + adc rax, r9 + mov [reg_p3+88], rax + adc r12, r10 + adc r13, r11 + adc r14, rdi + adc r15, rsi + + mov [reg_p3+96], r12 + mov [reg_p3+104], r13 + mov [reg_p3+112], r14 + mov [reg_p3+120], r15 + pop r15 + pop r14 + pop r13 + pop r12 ret diff --git a/src/P503/ARM64/fp_arm64_asm.S b/src/P503/ARM64/fp_arm64_asm.S index 7510d32..608aa36 100644 --- a/src/P503/ARM64/fp_arm64_asm.S +++ b/src/P503/ARM64/fp_arm64_asm.S @@ -4,7 +4,16 @@ // Abstract: field arithmetic in 64-bit ARMv8 assembly for P503 on Linux //******************************************************************************************* -.data +.text + +// p503 +p503: +.quad 0xFFFFFFFFFFFFFFFF +.quad 0xABFFFFFFFFFFFFFF +.quad 0x13085BDA2211E7A0 +.quad 0x1B9BF6C87B7E7DAF +.quad 0x6045C6BDDA77A4D0 +.quad 0x004066F541811E1E // p503 + 1 p503p1: @@ -31,7 +40,6 @@ p503p1_nz_s8: .quad 0x4066F541811E1E60 -.text //*********************************************************************** // Field addition // Operation: c [x2] = a [x0] + b [x1] @@ -690,58 +698,78 @@ mp_add503x2_asm: stp x5, x6, [x2,#80] stp x7, x8, [x2,#96] stp x9, x10, [x2,#112] - ret + ret //*********************************************************************** -// 2x503-bit multiprecision subtraction -// Operation: c [x2] = a [x0] - b [x1]. Returns borrow mask +// 2x503-bit multiprecision subtraction/addition +// Operation: c [x2] = a [x0] - b [x1]. If c < 0, add p503*2^512 //*********************************************************************** -.global mp_sub503x2_asm -mp_sub503x2_asm: +.global mp_subadd503x2_asm +mp_subadd503x2_asm: ldp x3, x4, [x0,#0] - ldp x5, x6, [x0,#16] ldp x11, x12, [x1,#0] + ldp x5, x6, [x0,#16] ldp x13, x14, [x1,#16] subs x3, x3, x11 sbcs x4, x4, x12 + stp x3, x4, [x2,#0] + ldp x7, x8, [x0,#32] + ldp x11, x12, [x1,#32] sbcs x5, x5, x13 sbcs x6, x6, x14 - ldp x7, x8, [x0,#32] - ldp x9, x10, [x0,#48] - ldp x15, x16, [x1,#32] - ldp x17, x18, [x1,#48] - sbcs x7, x7, x15 - sbcs x8, x8, x16 - sbcs x9, x9, x17 - sbcs x10, x10, x18 - - stp x3, x4, [x2,#0] stp x5, x6, [x2,#16] + ldp x9, x10, [x0,#48] + ldp x13, x14, [x1,#48] + sbcs x7, x7, x11 + sbcs x8, x8, x12 stp x7, x8, [x2,#32] + sbcs x9, x9, x13 + sbcs x10, x10, x14 stp x9, x10, [x2,#48] ldp x3, x4, [x0,#64] - ldp x5, x6, [x0,#80] ldp x11, x12, [x1,#64] + ldp x5, x6, [x0,#80] ldp x13, x14, [x1,#80] sbcs x3, x3, x11 sbcs x4, x4, x12 + ldp x7, x8, [x0,#96] + ldp x11, x12, [x1,#96] sbcs x5, x5, x13 sbcs x6, x6, x14 - ldp x7, x8, [x0,#96] ldp x9, x10, [x0,#112] - ldp x15, x16, [x1,#96] - ldp x17, x18, [x1,#112] - sbcs x7, x7, x15 - sbcs x8, x8, x16 - sbcs x9, x9, x17 - sbcs x10, x10, x18 + ldp x13, x14, [x1,#112] + sbcs x7, x7, x11 + ldr x11, p503 + sbcs x8, x8, x12 + ldr x12, p503 + 8 + sbcs x9, x9, x13 + ldr x13, p503 + 16 + sbcs x10, x10, x14 + ldr x14, p503 + 24 sbc x0, xzr, xzr - stp x3, x4, [x2,#64] - stp x5, x6, [x2,#80] - stp x7, x8, [x2,#96] + // Add p503 anded with the mask in x0 + ldr x15, p503 + 32 + ldr x16, p503 + 40 + and x11, x11, x0 + and x12, x12, x0 + and x13, x13, x0 + and x14, x14, x0 + and x15, x15, x0 + and x16, x16, x0 + adds x3, x3, x11 + adcs x4, x4, x11 + stp x3, x4, [x2,#64] + adcs x5, x5, x11 + adcs x6, x6, x12 + stp x5, x6, [x2,#80] + adcs x7, x7, x13 + adcs x8, x8, x14 + stp x7, x8, [x2,#96] + adcs x9, x9, x15 + adc x10, x10, x16 stp x9, x10, [x2,#112] ret diff --git a/src/P503/P503.c b/src/P503/P503.c index a376afd..bbc6696 100644 --- a/src/P503/P503.c +++ b/src/P503/P503.c @@ -106,7 +106,7 @@ const unsigned int strat_Bob[MAX_Bob-1] = { #define fp2inv_mont_bingcd fp2inv503_mont_bingcd #define fpequal_non_constant_time fpequal503_non_constant_time #define mp_add_asm mp_add503_asm -#define mp_subx2_asm mp_sub503x2_asm +#define mp_subaddx2_asm mp_subadd503x2_asm #define mp_dblsubx2_asm mp_dblsub503x2_asm #define crypto_kem_keypair crypto_kem_keypair_SIKEp503 #define crypto_kem_enc crypto_kem_enc_SIKEp503 @@ -121,4 +121,4 @@ const unsigned int strat_Bob[MAX_Bob-1] = { #include "../fpx.c" #include "../ec_isogeny.c" #include "../sidh.c" -#include "../sike.c" +#include "../sike.c" \ No newline at end of file diff --git a/src/P503/P503_compressed.c b/src/P503/P503_compressed.c new file mode 100644 index 0000000..20761d0 --- /dev/null +++ b/src/P503/P503_compressed.c @@ -0,0 +1,377 @@ +/******************************************************************************************** +* Supersingular Isogeny Key Encapsulation Library +* +* Abstract: supersingular isogeny parameters and generation of functions for P503_compressed +*********************************************************************************************/ + +#include "P503_compressed_api.h" +#define COMPRESS +#include "P503_internal.h" + + +// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points: +// -------------------------------------------------------------------------------------------------- +// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format). +// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position. +// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position. +// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32. +// For example, a 503-bit field element is represented with Ceil(503 / 64) = 8 64-bit digits or Ceil(503 / 32) = 16 32-bit digits. + +// +// Curve isogeny system "SIDHp503". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p503^2), where A=6, B=1, C=1 and p503 = 2^250*3^159-1 +// + +const uint64_t p503[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xABFFFFFFFFFFFFFF, + 0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E }; +const uint64_t p503p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAC00000000000000, + 0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E }; +const uint64_t p503x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x57FFFFFFFFFFFFFF, + 0x2610B7B44423CF41, 0x3737ED90F6FCFB5E, 0xC08B8D7BB4EF49A0, 0x0080CDEA83023C3C }; +// Order of Alice's subgroup +const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0400000000000000 }; +// Order of Bob's subgroup +const uint64_t Bob_order[NWORDS64_ORDER] = { 0xC216F6888479E82B, 0xE6FDB21EDF9F6BC4, 0x1171AF769DE93406, 0x1019BD5060478798 }; + +/* Basis for Alice on A = 6, expressed in Montgomery representation */ +const uint64_t A_gen[6*NWORDS64_FIELD] = { 0x3353B596D45A95A6, 0xDF7E0A94A39B96C0, 0x715DC90A72A3223F, 0xCB73F56E5AD9430F, + 0xE4B5DA591AEE475D, 0x322F1CE730413BD7, 0x4EEA4028D168DAD2, 0xB254087875FFA, // XPA0 + 0xAC3985C5BB18D89D, 0x45F2445C680A1E40, 0xF59454B450FBAB11, 0x95DC27D8152A0DAE, + 0x42A4FD439715E500, 0xB958FBA1CD4CC505, 0xC4E5AB2ABB732FC5, 0x268ED322F62ACA, // XPA1 + 0xDD27E5ADF7F57AB4, 0x7C1379D2B09F0434, 0x6E267408F1C8C89F, 0xC3BB383C07B60035, + 0x9268C9183A95ECD5, 0x9327EC043E0F021F, 0xE63D2D907A9DE5A5, 0x3110B6B4E0CD93, // XQA0 + 0x40B6BC5F5C2675E6, 0x62AD4B61EEDC2C5C, 0xA1CCA6B5091EF540, 0xC6273D4E1D8FC7FE, + 0x266D8B99EE63A78F, 0x39604E6927906566, 0xAB8BA8F2C6A977F8, 0xCD759EE7AB739, // XQA1 + 0x1482EA2C7A8F5FA0, 0xB42C8B9C007E5FE5, 0xCFCFF2625C69E7FD, 0x8334C3F384C268F5, + 0xD71E78E25FA4DB2F, 0x64BECFBE41708879, 0x103FF021EF7BF9, 0x2695BB8221E83B, // XRA0 + 0xA08787E922A1030, 0x8D34581F64BCE547, 0x2FA5BED41306271A, 0xEC24812ABD206DCF, + 0x978FA888C3CC6366, 0x2BFF991CDB7CE058, 0xA0BCCC1A447CF056, 0x2425429A072D82 }; // XRA1 + +/* Basis for Bob on A = 6, expressed in Montgomery representation */ +const uint64_t B_gen[6*NWORDS64_FIELD] = { 0xB810321963CF561F, 0xACA612873FBC647F, 0xE5C29CB78215B634, 0xB277ACABE764F907, + 0x76DBA8FCCDFF4721, 0x1B4E6541441EB543, 0xDAAB92E8B2DD0517, 0x1ECAA65407E4C9, // XPB0 + 0xF7EEE8D8D30365E6, 0x48F0AF97691E0303, 0xA8AC75108BFDA627, 0x7C0F65DCF8450F1, + 0xCD74E9CA0E92BECA, 0x342E232149CA1DFA, 0x8E841EC6D7725DE3, 0x2429A4E9A12CB0, // XPB1 + 0xB810321963CF561F, 0xACA612873FBC647F, 0xE5C29CB78215B634, 0xB277ACABE764F907, + 0x76DBA8FCCDFF4721, 0x1B4E6541441EB543, 0xDAAB92E8B2DD0517, 0x1ECAA65407E4C9, // XQB0 + 0x81117272CFC9A19, 0xB70F506896E1FCFC, 0x57538AEF740259D8, 0xA43F09A2307BAF0E, + 0x45937210137F28D6, 0xE76DD3A731B45FB4, 0xD1C1A7F7030546EC, 0x1C3D5057DFF16D, // XQB1 + 0x6E3DEF7C8A5A47D2, 0x12D9AF90F92FC868, 0xCE33D50FC931894B, 0x2927354E05ED037C, + 0x4864AD1D8B6E4E56, 0x2C6BB7E4CD4284DD, 0x50A30A93843DDC28, 0x38195667C39958, // XRB0 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0 }; // XRB1 + +/* The x-coordinate of lB^(eB-1)*QB, expressed in Montgomery representation */ +const uint64_t XQB3[2*NWORDS64_FIELD] = { 0xEE99D64B76EDCAB8, 0x24081A5326BA0FF9, 0x2BCFD2861E3D63FA, 0xA0964C6F4D7EB493, + 0x171019237F558103, 0xA19A27B706871B49, 0xECC7384313612D3C, 0xA3EC9B9537811, + 0xA7CD1086A7F15A87, 0x21A78B0FFA3920DC, 0xBDBDD8A49264C6D1, 0x925A193B79F45BB9, + 0xD3E14C9F15E21C4E, 0x6A218D16356EE2CE, 0x9D0D5E4AAA37DE6D, 0x17C49B586430A4 }; + +const uint64_t A_basis_zero[8 * NWORDS64_FIELD] = { 0x3353B596D45A9D99, 0xDF7E0A94A39B96C0, 0x715DC90A72A3223F, 0x8773F56E5AD9430F, + 0x9943B35C469A0526, 0xB964613981C02523, 0x43F68F92C55B886, 0x18B5A8D224F483, + 0xAC3985C5BB18D89D, 0x45F2445C680A1E40, 0xF59454B450FBAB11, 0x95DC27D8152A0DAE, + 0x42A4FD439715E500, 0xB958FBA1CD4CC505, 0xC4E5AB2ABB732FC5, 0x268ED322F62ACA, + 0xBC88BB85404378E5, 0x61071195BC44BF8F, 0xC92D13994CE9B8B3, 0x9ED615392DCF6CA2, + 0xC4A95165FB25BFDA, 0xEEEA8545EBEAEC62, 0xAC09C1C3E91B41FD, 0xB43AC79A90A0C, + 0xE8B38A79E90EAADB, 0x840B284661CCFC39, 0x6D5091432C311AD, 0xDAFBD9CD646033B, + 0x3FAF77BC98339AF0, 0x75F0C7A7AA5D03A3, 0xD188DA98DE124C6A, 0x2780B2B7B1C9CC, + 0xDD27E5ADF7F582A7, 0x7C1379D2B09F0434, 0x6E267408F1C8C89F, 0x7FBB383C07B60035, + 0x46F6A21B6641AA9E, 0x1A5D30568F8DEB6B, 0x9B925660D58AC35A, 0x3EA11EFF7E621C, + 0x40B6BC5F5C2675E6, 0x62AD4B61EEDC2C5C, 0xA1CCA6B5091EF540, 0xC6273D4E1D8FC7FE, + 0x266D8B99EE63A78F, 0x39604E6927906566, 0xAB8BA8F2C6A977F8, 0xCD759EE7AB739, + 0x986343072253CB59, 0x675F6504D2978FEC, 0xA0A52D48BA2141EA, 0x623302893A18D8D1, + 0x56B48005611F5B79, 0xE398D5F901FB591F, 0xE5A41D9AFCF35177, 0x391CDEF0EEFA35, + 0xE9B1DB43D63D7EE9, 0x8BC7B3CEB5A89BAE, 0xC0DDDEFB4D9CDCD, 0xB9873A36C1B0B949, + 0x97FCE091A32E2501, 0x838C61141A0FB449, 0xA4B61F965220A71F, 0x16978E2D5FBE08 }; + +/* Basis for Bob on A = 0, expressed in Montgomery representation */ +const uint64_t B_basis_zero[8*NWORDS64_FIELD] = { 0x4256C520FB388820, 0x744FD7C3BAAF0A13, 0x4B6A2DDDB12CBCB8, 0xE46826E27F427DF8, + 0xFE4A663CD505A61B, 0xD6B3A1BAF025C695, 0x7C3BB62B8FCC00BD, 0x3AFDDE4A35746C, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x440192590061240E, 0x60C942451EC3E20D, 0x2195638E3B7632CA, 0xBA84AC322AA59D16, + 0x3751CBF97048E02D, 0x6A583E4C816EAC44, 0x7A984D4F477762C1, 0x27B5AB2E503D63, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xBDA93ADF04C777DF, 0x8BB0283C4550F5EC, 0xB495D2224ED34347, 0xC797D91D80BD8207, + 0x14BDF59D4D0C4184, 0x44E8550D8B58B719, 0xE40A10924AABA412, 0x56916F74BA9B1, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x440192590061240E, 0x60C942451EC3E20D, 0x2195638E3B7632CA, 0xBA84AC322AA59D16, + 0x3751CBF97048E02D, 0x6A583E4C816EAC44, 0x7A984D4F477762C1, 0x27B5AB2E503D63 }; + +/* Full 3-torsion for Bob on A = 0, expressed in Montgomery representation */ +const uint64_t B_gen_3_tors[16*NWORDS64_FIELD] = { 0xAA6FCA1A7DB3B9C1, 0x8D12C496B3D530CE, 0x909089D6DB66CE9F, 0x26979B12182E911, + 0xD838DEA96EFB14F2, 0xC70C12A9DB5E8DEB, 0xBB4D79F4A6E1AEEA, 0x2F6E7532C0487D, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x565D24EF17871BCA, 0x5547441AA7195322, 0xACA179D99F24388F, 0xF764EBCF575D78CF, + 0x6890A45614A3A134, 0x545AF60FF4DCA38, 0x4730B86C7FC40E22, 0x25DC757FF39EDC, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x559035E5824C463E, 0x72ED3B694C2ACF31, 0x6F6F762924993160, 0xA996864EDE7D16EE, + 0x3ACF7D30B316D2AE, 0x548FE41EA01FEFC3, 0xA4F84CC93395F5E5, 0x10F8800EC0D5A0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x565D24EF17871BCA, 0x5547441AA7195322, 0xACA179D99F24388F, 0xF764EBCF575D78CF, + 0x6890A45614A3A134, 0x545AF60FF4DCA38, 0x4730B86C7FC40E22, 0x25DC757FF39EDC, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xA71C6ED6210C87CC, 0xC8DFD8D415B8B348, 0x6F6F7629249932AF, 0x4196864EDE7D16EE, + 0x367B30E71EAF8BE3, 0x880DD782D08D9134, 0xE6A3EACE9EDA18D, 0x2542106DA2CDE1, + 0xDC6CDA78FBC6D660, 0xAB35FE4E0DB497, 0x4CD08BF7B90D948B, 0xDD38F40AED30B440, + 0x5C9D9A2A66152FA5, 0x8143357E694594D8, 0x4331EA627E400226, 0x274E4E416D3346, + 0x239325870439299F, 0xFF54CA01B1F24B68, 0xB32F740846F26B74, 0xCEC70BF512CF4BBF, + 0xB66AC1AFBBFCB7FA, 0x9A58C14A1238E8D6, 0x1D13DC5B5C37A2A9, 0x1918A70013EAD8, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x58E39129DEF37833, 0x3720272BEA474CB7, 0x909089D6DB66CD50, 0x6A6979B12182E911, + 0xDC8D2AF303625BBD, 0x938E1F45AAF0EC7A, 0x51DB8810F08A0342, 0x1B24E4D3DE503D, + 0xDC6CDA78FBC6D660, 0xAB35FE4E0DB497, 0x4CD08BF7B90D948B, 0xDD38F40AED30B440, + 0x5C9D9A2A66152FA5, 0x8143357E694594D8, 0x4331EA627E400226, 0x274E4E416D3346, + 0xDC6CDA78FBC6D660, 0xAB35FE4E0DB497, 0x4CD08BF7B90D948B, 0xDD38F40AED30B440, + 0x5C9D9A2A66152FA5, 0x8143357E694594D8, 0x4331EA627E400226, 0x274E4E416D3346 }; + +/* Pre-computed pairing ReducedTatePairing(R0,S3,lB^eB) on A = 0 */ +const uint64_t g_R_S_im[NWORDS64_FIELD] = { 0xF74CEB25BB76E955, 0x12040D29935D07FC, 0x95E7E9430F1EB1FD, 0x844B2637A6BF5A49, + 0xEF53270066899336, 0xA235B168E9C24121, 0x813113E8A462D7E0, 0x2C1B13A2B9155C }; + +const uint64_t Montgomery_R[NWORDS64_FIELD] = { 0 }; +// Montgomery constant Montgomery_R2 = (2^512)^2 mod p503 +const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x5289A0CF641D011F, 0x9B88257189FED2B9, 0xA3B365D58DC8F17A, 0x5BC57AB6EFF168EC, + 0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771 }; + +// constant Montgomery_RB1 = (2^NBITS_ORDER)^2 mod Bob_order +const uint64_t Montgomery_RB1[NWORDS64_FIELD] = { 0xC2615CA3C5BAA99,0x5A4FF3072AB6AA6A,0xA6AFD4B039AD6AA2,0x10DA06A26DD05CB }; + +// constant Montgomery_RB2 = -(3^OBOB_EXP)^-1 mod 2^NBITS_ORDER +const uint64_t Montgomery_RB2[NWORDS64_FIELD] = { 0x49C8A87190C0697D,0x2EB7968EA0F0A558,0x944257B696777FA2,0xBAA4DDCD6139D2B3 }; + +// Value one in Montgomery representation +const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x00000000000003F9, 0x0000000000000000, 0x0000000000000000, 0xB400000000000000, + 0x63CB1A6EA6DED2B4, 0x51689D8D667EB37D, 0x8ACD77C71AB24142, 0x0026FBAEC60F5953 }; + +// 1/3 mod p +const uint64_t threeinv[NWORDS64_FIELD] = { +0x55555555555556A8,0x5555555555555555,0x5555555555555555,0x7555555555555555,0x7CF1276D98503E1C,0xCF0186C74B5465B9,0xA3B114D6FC634CB0,0x227636AD3027D0 }; + +// Fixed parameters for isogeny tree computation +const unsigned int strat_Alice[MAX_Alice - 1] = { +61, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, +4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, +1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 29, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, +1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 13, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, +1, 1, 2, 1, 1, 5, 4, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1 }; + +const unsigned int strat_Bob[MAX_Bob - 1] = { +71, 38, 21, 13, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 4, 2, 1, 1, 2, 1, +1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 17, 9, +5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, +1, 4, 2, 1, 1, 2, 1, 1, 33, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, +2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, 2, +1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 }; + +// Fixed traversal strategies for Pohlig-Hellman discrete logs + +const unsigned int ph2_path[PLEN_2] = { // w_2 = 5 +0, 0, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 14, 15, 16, +17, 18, 18, 18, 19, 20, 20, 21, 22, 23, 24, 25, 25, 25, 25, 26, 27, 28, 29, 29, +30, 31, 32, 33, 34, 35, 35 +}; + +const unsigned int ph3_path[PLEN_3] = { // w_3 = 6 +0, 0, 1, 2, 3, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 17, +18, 19, 20, 21 +}; + +// Entangled bases related static tables and parameters + +// Constants u and u0 where u = u0^2 in F_{p^2} \ F_p used in entagled basis generation +// For the 2^eA-torsion basis generation: +// Two tables of 17 elements each for the values r in F_p such that v = 1/(1+ur^2) where r is already converted to Montgomery representation +// Also, 2 tables for the quadratic residues (qr) and quadratric non residues (qnr) v in F_{p^2} with 17 GF(p^2) elements each. +// For the 3^eB-torsion basis generation: +// A table of size 20 for values v = 1/(1+U*r^2) + + +const uint64_t u_entang[2 * NWORDS64_FIELD] = { +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x7F3,0x0,0x0,0xBC00000000000000,0xB48DD9032BABBDC8,0x87354452517EE94B,0xB55528D05AECDDB4,0xD90684A9D9488 }; + +const uint64_t u0_entang[2 * NWORDS64_FIELD] = { +0x3F9,0x0,0x0,0xB400000000000000,0x63CB1A6EA6DED2B4,0x51689D8D667EB37D,0x8ACD77C71AB24142,0x26FBAEC60F5953,0x3F9,0x0,0x0,0xB400000000000000, +0x63CB1A6EA6DED2B4,0x51689D8D667EB37D,0x8ACD77C71AB24142,0x26FBAEC60F5953 }; + +// Tables for quadratic residues and quadratic non residues v with 17 elements each. + +const uint64_t table_r_qr[TABLE_R_LEN][NWORDS64_FIELD] = +{ {0xBEC,0x0,0x0,0x7000000000000000,0x1858F371D28A907D,0xD89DE1DFB7FD9CC9,0x4022A097759F1EF6,0x348C1710ACEDDC}, +{0x17D9,0x0,0x0,0x3400000000000000,0x1DA98B098303395A,0x959FCCF6F47CBBE3,0x1FFF7A7110C6991D,0x28B138DFD8BD9A}, +{0x23C6,0x0,0x0,0xF800000000000000,0x22FA22A1337BE236,0x52A1B80E30FBDAFD,0xFFDC544AABEE1344,0x1CD65AAF048D57}, +{0x2BB9,0x0,0x0,0xB400000000000000,0xD787FBA45F279FFF,0xD9D6FC60827AC448,0xB5317D1B06DAF0F8,0x2A66C2F9A221E0}, +{0x2FB3,0x0,0x0,0xBC00000000000000,0x284ABA38E3F48B13,0xFA3A3256D7AFA17,0xDFB92E2447158D6B,0x10FB7C7E305D15}, +{0x33AC,0x0,0x0,0x7000000000000000,0x8C15D4A78AD35DC8,0x610C40B2D3F9AD94,0x6A86A5EB61C7CEAD,0x37F72B443FB669}, +{0x3BA0,0x0,0x0,0x8000000000000000,0x2D9B51D0946D33F0,0xCCA58E3CA9FA1931,0xBF9607FDE23D0791,0x5209E4D5C2CD3}, +{0x3F99,0x0,0x0,0x3400000000000000,0x91666C3F3B4C06A5,0x1E0E2BCA1078CCAE,0x4A637FC4FCEF48D4,0x2C1C4D136B8627}, +{0x478C,0x0,0x0,0xF000000000000000,0x45F4454266F7C46D,0xA543701C61F7B5FA,0xFFB8A89557DC2688,0x39ACB55E091AAF}, +{0x4B86,0x0,0x0,0xF800000000000000,0x96B703D6EBC4AF81,0xDB1016E14CF7EBC8,0x2A40599E9816C2FA,0x20416EE29755E5}, +{0x5379,0x0,0x0,0xB400000000000000,0x4B44DCDA17706D4A,0x62455B339E76D514,0xDF95826EF303A0AF,0x2DD1D72D34EA6D}, +{0x5773,0x0,0x0,0xBC00000000000000,0x9C079B6E9C3D585E,0x981201F889770AE2,0xA1D3378333E3D21,0x146690B1C325A3}, +{0x5B6C,0x0,0x0,0x7000000000000000,0xFFD2B5DD431C2B13,0xE97A9F85EFF5BE5F,0x94EAAB3F4DF07E63,0x3B623F77D27EF6}, +{0x5F66,0x0,0x0,0x7800000000000000,0x50957471C7E91627,0x1F47464ADAF5F42E,0xBF725C488E2B1AD6,0x21F6F8FC60BA2B}, +{0x6360,0x0,0x0,0x8000000000000000,0xA15833064CB6013B,0x5513ED0FC5F629FC,0xE9FA0D51CE65B748,0x88BB280EEF560}, +{0x6759,0x0,0x0,0x3400000000000000,0x5234D74F394D3F0,0xA67C8A9D2C74DD7A,0x74C78518E917F88A,0x2F876146FE4EB4}, +{0x6B53,0x0,0x0,0x3C00000000000000,0x55E60C097861BF04,0xDC49316217751348,0x9F4F3622295294FC,0x161C1ACB8C89E9} }; + +const uint64_t table_r_qnr[TABLE_R_LEN][NWORDS64_FIELD] = +{ {0x3F9,0x0,0x0,0xB400000000000000,0x63CB1A6EA6DED2B4,0x51689D8D667EB37D,0x8ACD77C71AB24142,0x26FBAEC60F5953}, +{0x7F3,0x0,0x0,0xBC00000000000000,0xB48DD9032BABBDC8,0x87354452517EE94B,0xB55528D05AECDDB4,0xD90684A9D9488}, +{0xFE6,0x0,0x0,0x7800000000000000,0x691BB20657577B91,0xE6A88A4A2FDD297,0x6AAA51A0B5D9BB69,0x1B20D0953B2911}, +{0x13E0,0x0,0x0,0x8000000000000000,0xB9DE709ADC2466A5,0x44372F698DFE0865,0x953202A9F61457DB,0x1B58A19C96446}, +{0x1BD3,0x0,0x0,0x3C00000000000000,0x6E6C499E07D0246E,0xCB6C73BBDF7CF1B1,0x4A872B7A5101358F,0xF45F26466F8CF}, +{0x1FCC,0x0,0x0,0xF000000000000000,0xD237640CAEAEF722,0x1CD5114945FBA52E,0xD554A3416BB376D2,0x3641A12A765222}, +{0x27C0,0x0,0x0,0x0,0x73BCE135B848CD4B,0x886E5ED31BFC10CB,0x2A640553EC28AFB6,0x36B143392C88D}, +{0x37A6,0x0,0x0,0x7800000000000000,0xDCD8933C0FA048DC,0x96D8E777BEF9E362,0x950E56F4A2026B1F,0x1E8BE4C8CDF19E}, +{0x4393,0x0,0x0,0x3C00000000000000,0xE2292AD3C018F1B9,0x53DAD28EFB79027C,0x74EB30CE3D29E546,0x12B10697F9C15C}, +{0x4F80,0x0,0x0,0x0,0xE779C26B70919A96,0x10DCBDA637F82196,0x54C80AA7D8515F6D,0x6D6286725911A}, +{0x6F4C,0x0,0x0,0xF000000000000000,0xB9B126781F4091B8,0x2DB1CEEF7DF3C6C5,0x2A1CADE94404D63F,0x3D17C9919BE33D}, +{0x7346,0x0,0x0,0xF800000000000000,0xA73E50CA40D7CCC,0x637E75B468F3FC94,0x54A45EF2843F72B1,0x23AC83162A1E72}, +{0x7740,0x0,0x0,0x0,0x5B36A3A128DA67E1,0x994B1C7953F43262,0x7F2C0FFBC47A0F23,0xA413C9AB859A7}, +{0x7B39,0x0,0x0,0xB400000000000000,0xBF01BE0FCFB93A95,0xEAB3BA06BA72E5DF,0x9F987C2DF2C5065,0x313CEB60C7B2FB}, +{0x8B20,0x0,0x0,0x8000000000000000,0x1515143C04FECE86,0xDD824BE2E1F23AC8,0x145E12A5BA8E66FE,0xBF6C6B481BDEE}, +{0x8F19,0x0,0x0,0x3400000000000000,0x78E02EAAABDDA13B,0x2EEAE9704870EE45,0x9F2B8A6CD540A841,0x32F2757A911741}, +{0x9F00,0x0,0x0,0x0,0xCEF384D6E123352C,0x21B97B4C6FF0432D,0xA990154FB0A2BEDA,0xDAC50CE4B2234} }; + +const uint64_t table_v_qr[TABLE_V_LEN][NWORDS64_FIELD] = +{ {0xD640973CA6FDA33,0x30D640973CA6FDA3,0xA30D640973CA6FDA,0x9630D640973CA6FD,0xB9B362A86413EF5,0x291A8D3DCCB3503C,0x28AA7266E86C4410,0x3E57A5066529FA}, +{0xEF755DBC422A858,0x90EF755DBC422A89,0x890EF755DBC422A8,0x8890EF755DBC422A,0x85ACA658F4ABDC07,0xD196BC04A493216,0xE8EBEE1D04CCCD7F,0x2513A427F72A8B}, +{0xEADE47323668C519,0x19083ECD7DC0E6AB,0xABEADE47323668C5,0xF919083ECD7DC0E6,0xB14832196A6135B,0x65C238AE07A19315,0x33892F2EF24CBA75,0xEB6BD00093E7D}, +{0xF17BF9E0B28890E7,0xF5AE5634A1BF1FA5,0xA5F17BF9E0B28890,0x5CF5AE5634A1BF1F,0x25C93809E47AEFCD,0x36BB725E0DF4FAB5,0xE60CED675C5D80CD,0x23712156F96CCD}, +{0x1C678311555200F,0x4D5264E0DACE9D42,0x12A66D44591361B5,0x5631C420E42BD0E8,0xC7CA70C8F9037B,0x345253296A40C7FC,0xF44CE094886CA2C1,0x3DAD6A1ADCE6F6}, +{0xE067F0F08021B5E6,0x11DC29B589407C3A,0x32AEDABFA1BC2B45,0x4481E32F9C45CD24,0x1AA9DD8D9554F1DC,0xB6F1C1F604160937,0x11DEFDB2CC29708D,0x37004EEAE4323C}, +{0xE36097357D9260F6,0x439C0A04D12BD483,0x66E8351E74487091,0x1421CC574D451882,0xAEB61FAD8599E2CA,0x48EF54E42C5C665F,0xED1A8E11AC6A738D,0x16259CACCC3BDD}, +{0xEB10F6F4BA05720,0x167E877244911B53,0xB87DC936138596AE,0x680CD578F4AED4BA,0x1694318AE2679DB1,0x1CEEBA16962876FF,0x73CAE996B2A0D8BA,0x323A5E254D4A2D}, +{0xAF443325C49FC9C7,0xF3368ED80D8E2E2D,0x5C49FC9C7474942E,0xCCD8E2E2DAF44332,0x471B92FFA7F05FFB,0x8C55AC5DD5163AAD,0xD41A2EDB81C0F26E,0x12B9411FE82E2A}, +{0xD3467582CC3CFFCC,0x629F4CF0C00C0C9A,0x2CC3CFFCFCD94B2E,0xFC00C0C9AD346758,0x3FB8C3F63F740571,0x2ECB1038CC7F3A82,0xF9707F59B63157EB,0x115F359929F1C8}, +{0x3218F78BA3CBAE8D,0x19C8ECF809D7722F,0x7097E87F9E319229,0x1FCB0DEE58D468E5,0xD0E9B55BF73DCF1F,0x1EFE4FCE69BC0416,0xEF0693CEC4EE816A,0xBD45626E7A975}, +{0xDB0929A1BD138997,0xF4B72083018B3DAF,0x576F0781228D05BB,0x59E79B4EB78D8111,0xDA7D2741F2CC8972,0xDF9C5CCEC9E387F5,0x1A7CC1B8C08AB119,0x3AFC9BC0E8ABC4}, +{0xEEAAAB192225A66F,0x3D36F4A6197D1682,0x95351AD9A4013A92,0x737FCA70517EACFE,0x546BE45BE532FB91,0xCC1BAF4DF9C83B85,0xB7F98958BFF6909C,0x3A327C901E0790}, +{0x77FF3DD1F9D16F4B,0x6565F407321E6DD8,0xB8A6CD6DB5D70AF0,0x6D5E2690BF53E87D,0xDCA29E4346D90AC4,0x1C4B31AB442130F8,0xAA4B89D4E4CCD33D,0x16F0F5CF7D95E7}, +{0x8CAE1CD478CAE1CD,0xAE1CD478CAE1CD47,0x1CD478CAE1CD478C,0x1878CAE1CD478CAE,0xFAD9099BBD3A4347,0x67F1D575139CB5BF,0x38293A715DDCB486,0x123FF210860EF6}, +{0xA3C6570E6A3C656E,0xC6570E6A3C6570E6,0x570E6A3C6570E6A3,0x266A3C6570E6A3C6,0x28B12AECF9AF8B71,0xDB47D42F34B82DE3,0x9556758ADED2F1DF,0x3AD3BE4F8540E2}, +{0xCA6337B265BAB821,0xDFD5196D5A6AC701,0x5931D9A74BA1FF5A,0xD0C5E74C37D3F402,0x4D621242F79E2216,0x57F1976F8DF43182,0xF052D77BBE57890B,0x26C6CA2E21363A}, +{0xB4DB046E7F5DEAF1,0x6C97A33321B84377,0x39D110888DF1A1F9,0x3F0E8712AF7E5A0E,0x318610A741127CA6,0x8FAE99D54C14A492,0xB8E11ABEDF29D523,0x3610D24823BB34}, +{0xBCEE07864886985B,0x893DFD453F69DBD8,0x846663A2582C0992,0x90BD04A8B4E03846,0xAC8F553BEBE4AAA3,0x21D7DE00A60E1DBA,0xD25E1FED110FEECB,0x2A3CA66830CF45}, +{0x28AEC74774664D80,0xEF2BB2B32771F6BB,0x973B002353CD00B8,0x42E8DC31DFA1491E,0x913BAEE3CA3D9E30,0xABF6D1605464DDAE,0xF3BBF0EC6297B06D,0x1F94C96F693152}, +{0x13C45267DD75029B,0x2A5B4B4FF8E045B9,0x3A2CEEEDFA82F7D8,0x9E84B2F89B9CECA,0x6F9D9229FB56184A,0xE7CFAA7031AA43EF,0xAB559E585413397D,0x3410E7C5B657C2}, +{0xE59C162702DD0330,0x117686788B4FC859,0x9130D016E8C6193E,0x95ACF6377DD58B43,0x886E99BF17505709,0x5785149D522C7B5C,0x35A0C131A77598A4,0x3CE98183E3A406}, +{0xF66188E646E44D38,0x1DDB967838C24787,0xF0DDC924163B32D9,0xF3085EC466F80420,0xCDC2841D90A1671D,0x42C7CECE348BFCC8,0x56B81B6CB2CA11DB,0x3514702E4A9A0A}, +{0x5F325943F0BC0122,0x19AF0969616185E4,0x395F6F8BF027BB07,0x3059A95AA6306371,0x4C8AC22B51821D99,0x8CA5493A42F7F073,0x3159D0CAF4E03BA1,0xBA85326656B98}, +{0x355770484B8F9E78,0x3CE74F9FB70AE2AF,0x29C66659490DA55A,0x4A4908AB5BFCCAB2,0x28E847CF76744D1B,0xD73C1DA7E9743E83,0xBC0814A45DE92E,0x231BAF63ED339C}, +{0x8CA1F537B87311CF,0x4C08EDED850327E5,0x5A0D0300159AA110,0xAA2A2BCDD5424BAF,0xD5DE3F3F3DB4665A,0xB414A9EB85AEED8A,0xF42B8C9A1B8CC578,0xFA3EDA9B597BB}, +{0xA67D8C524B3E4E75,0x86499A8DBF7A9491,0x72F4B7F3EA4620AD,0x4817A8E2631DE824,0xBB8AFA3312167C4A,0xFC6430A72CDFEFB7,0x8D35B46A38FE2241,0x175BFA3B8577D}, +{0xCB088DAD679EF165,0xB4C8822258637092,0xB2C43661C46CF323,0xB9880541F96B5BFA,0x107BCA3032B41FAD,0x269816DB16A086AB,0xB5B0180593043903,0x38FD7D2B147838}, +{0x475B7B82B2D288B0,0x22C1F565B3292571,0x59C43DCA0D6C8F10,0xE1F36E62396C705C,0xF83EB8755AE3C245,0x8AD232E4B45B2625,0x877CD62B7C9672AD,0x89DA6104B553C}, +{0x934EEBD2D80093F8,0x48EFC56B31172CE1,0xAFCA4B6A73ED7336,0x995F04639C835D11,0x5B3B9A208FA56837,0x47FD72D865F2357E,0x9E3CAC4107E83532,0x31CC176CE59261}, +{0x4AD8213DCC0EE2E4,0x4CB861B5AE488639,0xA51A5B14C15122A6,0x11D3BAEAD457C643,0x69F81BA8151F4289,0xBBF7FD30D142B1CF,0xEFF9B4443C1F00D,0x3A8516A2E48A25}, +{0xBA9071A25161B713,0xD23BF87F90FB216C,0xCCEFA630B8101BA,0x95CCD7CE9070EAC0,0xB8CEE68602DD9A73,0xD60E96A7B6065216,0xF90F1CEBF826728B,0x1F67DF31E4041C}, +{0xB826A44841FE3FCD,0x5D362655AAD7FF01,0x92B4DD765A16E5F5,0xFCDB74BC0D0D0A6B,0xF41E518CAA1A182E,0xF07FC9B18F378B80,0x5C70AB82A854E783,0x1DD88FB06EF820}, +{0x33EC5C7825F89FD2,0x2199AC18FDD5A835,0x75EAB3F2E9965093,0x162128FDABBAA756,0xED6618E12EA9E8AA,0x300CF4246FAB5DDF,0xBE8FFF323060A819,0x147D4620F25FE7} }; + +const uint64_t table_v_qnr[TABLE_V_LEN][NWORDS64_FIELD] = +{ {0x6666666666666731,0x6666666666666666,0x6666666666666666,0x7A66666666666666,0x566281F7D63AE371,0xBFF8182310E4EED8,0x260EA261A835DB3,0x3B5180C26A5D29}, +{0x333333333333319C,0x3333333333333333,0x3333333333333333,0x6333333333333333,0x794BB3C497AE085E,0xB747BD4AD5331DAD,0xBBC9B92F7FE88E38,0xA2AE8FE2D81EA}, +{0x42F42F42F42F4303,0xF42F42F42F42F42F,0x2F42F42F42F42F42,0x3EF42F42F42F42F4,0xEDE69F6C16FE9C49,0x5F14E71311869A6F,0x4A3D210B203EC110,0x361A6419F55969}, +{0xE85E85E85E85E7E1,0x5E85E85E85E85E85,0x85E85E85E85E85E8,0xBC5E85E85E85E85E,0x160587963688731A,0xC89C86E2D4409C4A,0x4FFF66D7F74F792D,0x11FD93FADD078A}, +{0x2FF402FF402FF403,0x2FF402FF402FF40,0x402FF402FF402FF4,0xF002FF402FF402FF,0x10AD8E578684D15D,0x7D8BE80CE669C6B0,0x2F6BF0AEC5EAAB99,0x3FBFC2D75908E7}, +{0x17FA017FA017F80,0xA017FA017FA017FA,0xFA017FA017FA017F,0x7FA017FA017FA017,0x4B59B05371A2C857,0xC201D772A296DFE0,0x1B3AC1E2919F26D3,0x14E64D4502A6E6}, +{0x95C05529A8FEAB59,0x595C05529A8FEAB5,0xB595C05529A8FEAB,0xDF595C05529A8FEA,0x2F45F28BB8ED273E,0xFA436C90BD54C61A,0x1062C7B1DEDB1074,0x315A8AEDC8909C}, +{0xC06F5DDCFE428877,0x8C06F5DDCFE42888,0x88C06F5DDCFE4288,0x948C06F5DDCFE428,0xAA9C9EF112689F32,0x53976445D5B6748E,0x7756462EC170E4DB,0x2C003A897F5825}, +{0xFFEB87D96821E700,0xE6FFEB87D96821E6,0x21E6FFEB87D96821,0x6821E6FFEB87D968,0x536BACDAEA5360A5,0x587DE91F62936769,0xF9873A3AF7BA1771,0x1AC726662E629}, +{0x7D5FEC6230591FD,0x9207D5FEC6230592,0x59207D5FEC62305,0x27059207D5FEC623,0x49E0E7C0B24AB790,0x72A0A655B60DE2BB,0x9B0D09A6BA29F50C,0x1D311492A73E49}, +{0x3DBF0903DBF0903D,0x903DBF0903DBF090,0xF0903DBF0903DBF0,0xDFF0903DBF0903DB,0x2E57678E6F6B36FA,0x6D14F41B551BD544,0xA9A9EBE547506451,0x340F0593481A65}, +{0x207B7E1207B7E118,0xE1207B7E1207B7E1,0xB7E1207B7E1207B7,0xE7B7E1207B7E1207,0x8FB1896621AA9BD5,0xACE233C79D786D08,0x4762CA7D1868CBD4,0x2250D8F8670982}, +{0x840F89EF8D6AD1D9,0xD860EB4F2F6A9A25,0x59D8EC2E0086586E,0x12947D34DB3512E9,0xF63A898976A47748,0x501E5E834CF73F95,0x8EAC965E265BB2A6,0x34B4D6B0074D55}, +{0xD3DC3CD9848C0DD4,0xF4482A22F4B792B0,0xCE877C0F970AE966,0xABFE2EB4BE8939B1,0xD39F645922FB329F,0x183041DAFBDED6FF,0x35DDD811FD020363,0x14AD647102E09E}, +{0x9A9AC56B775830E6,0x349D4969F781C5FE,0x4A96A3BBEA5CCC22,0xE413030F74832A1C,0x4CD1307BD96041FD,0xAFCB8545E06F5E57,0x1C86CB1828C75997,0xEC2C4397DD1A7}, +{0x4301B37140F51F76,0x6F2795BD0148D223,0xC955484121E76B9F,0x3AE35055972784AD,0x109E0D0B1EE661B7,0x8530AF7BBFEFB9DF,0x2A20E1C05CCEC0E4,0x9F5C0FEBB8ECA}, +{0x4E3AF17430022B8A,0x35839EC8DB54E2A4,0xA3C6E03E4E9EFCD7,0xDA418C66D7C8A36C,0x1FD4F171FE1732C8,0xC625B70E60138FC9,0xA4E5092E399B6337,0x21F760DFCCB761}, +{0x5EEAD7AB9B19B13B,0x2CD37E80CA584907,0x38F9B3527D092219,0x2400FFCCCCFF04B6,0xCE2C4B82E6F44CF0,0x83A9B6663589197B,0x66030DD337B55803,0xA2179BE9ED7BA}, +{0xDD28279CDC678A67,0x4D6331D441594443,0x8D052A7E726EC043,0x24C4928EE44B7AD9,0x371ECF34320A1AC3,0xF7E715563D9223CA,0x7D4F1577FFD8B72B,0x113FAE041A1084}, +{0xE28435CF3C6F7D49,0x2A0448B3C90AABEC,0x4FDB34DA65E72DAE,0x8DB6017694201827,0xBBBDA1163D75E61D,0x7DD994DF4E8BB61C,0x4376D272F53F0160,0x2F782D31FCAD7B}, +{0x13CC56E70A95B922,0x3E79A643C48D1142,0x193B7E19EC380834,0x1F43A718BEE0BD64,0xAF07EEDBAAC36417,0x1479E0460B4E85E0,0xE997B33A457870E1,0x12792B8A001D25}, +{0xBC6BB8DF2AF20DFE,0x56E5A0EC1FF64B46,0x739BA13928CDC001,0xD9A0886EDF77FAE5,0x641A73F9F6B41ACE,0x1DAA1F63D364ED8F,0x797D94D0849C5333,0xED06FE444692E}, +{0x5FDF74D731C8412A,0x6FA3CCC72BC442E7,0xF7A328C581FF9506,0x9D43E8D9CE513419,0xE0969762B591CA14,0xA7A20D5B0A226CEE,0xE652DF72F7ACDBA7,0x98B2737AA6855}, +{0x15D2521AEA43D912,0x7DC88B6270806BCC,0xF1FE1E4FDEBEDBB6,0xAFD018F26E77AD62,0xF8BB0C784D9A7776,0x8F933FA003570378,0xB7A3F4080B1BBFAF,0x3043D63A75E546}, +{0x2254A8771FEA02B3,0x8398EEA5EF546F3E,0xA6062563B110D486,0x5AD887813EF3AE86,0xEAE29AC17FA58A77,0x924599311ED77B3C,0x3DF2835E75922318,0x2EEB5411B26C76}, +{0x9CBF7A679A9D0048,0xB4B201453651D31E,0xA4C91B0B01A9AE32,0xBD873B3D5E9CDD40,0x1869D6517CD803A,0x5F3A2180D299CEE,0xD46EDCD4F9A5E5C9,0x2901D3472FBC49}, +{0xBC9C88687B4C473D,0xB37349E2D384219,0x86A75F99B9FEA3F6,0x32FAC92124206663,0xBE37BE6B4BCC19CA,0x8F77567E888968B4,0x4308A1AB82A632E2,0x28B00FD8816E8}, +{0xF0C7DF924D5127BA,0xCB86F4707F9FBAC5,0xB643FD9963502BF,0x5125F52EC4BF48C7,0x87F7A3330AF723A0,0x1455E18791E932FD,0x4DE936B1F7BAE4CF,0x6F35FFA98F53D}, +{0x459FB6EF424D1859,0xF492057CEBD9391E,0xE70ACB8F885C8084,0xCEBCCFF5FF922454,0xEA056AA88BDD2C5B,0xB33F747126069D2B,0xABC8F606165AB077,0x280CA098BAD483}, +{0xAD7B42377A2CF64A,0x62877A76DB1B5C49,0xDAAFDC58FABA0793,0x6501BFB81B604B74,0xA5EC0D8847E461DF,0xE730BEA141B807F7,0x16209BF6A0544D52,0x1C131448A178B3}, +{0xF09679A75D6EDB8A,0x85E0E32FA20333FD,0x659E89AE27506F5D,0xCBE8610A2E1C126F,0xCA328C6CB821E1A4,0xB0F6B45C68433733,0x996850439E5A4FA7,0x3D91026425288B}, +{0xC70416DFD912112,0x7B03BDB79F9194DC,0x1ACDFCB1F1986D14,0x572978ED23C5581B,0xFB1B4CAD724370B0,0x7DCCA0FBB9D5A84A,0xA33D15155FB6D48B,0x861CA17970496}, +{0x22BCBF7871766C3A,0x9395C19D8E87CC4C,0xB92EF7084D0FEBD8,0x8A60E143C87DB915,0x3FDCB6ED258F6167,0xFB9943E3BF11D380,0xE116C209F87D2108,0xE76DDE2391409}, +{0xC8A69E75B7B72831,0x300BCE8A5E86484D,0x34F0183CB8FBECCB,0x590030B5DC767075,0x2D8B65503007FE01,0x8F397E3E796F3B98,0xC77FB29679EAF434,0x13554730291BD2} }; + +const uint64_t v_3_torsion[20][2 * NWORDS64_FIELD] = +{ {0x9999999999999ACA,0x9999999999999999,0x9999999999999999,0xE199999999999999,0xF80F9506B04F6159,0x922628D05B98276C,0x536E7BDA3A893A25,0x38C6C682DEFCAE,0xCCCCCCCCCCCCCC67,0xCCCCCCCCCCCCCCCC,0xCCCCCCCCCCCCCCCC,0x98CCCCCCCCCCCCCC,0x5E52ECF125EB8217,0x2DD1EF52B54CC76B,0xAEF26E4BDFFA238E,0x28ABA3F8B607A}, +{0xB61A6449E59BB678,0xE59BB61A6449E59B,0x6449E59BB61A6449,0x161A6449E59BB61A,0xB0A7A696AD14F403,0x5908519429BF6752,0xF8F5C2FDB95D626B,0x3415A91EB9B01B,0x59BB61A6449E5991,0x449E59BB61A6449E,0x61A6449E59BB61A6,0xEDBB61A6449E59BB,0xDCBBFD66B1210ED0,0xD1759BAF69F0DE7F,0x151E605BC94FFF1C,0x1AF11E41BC9044}, +{0x865EFC865EFC868A,0x5EFC865EFC865EFC,0xFC865EFC865EFC86,0xCE5EFC865EFC865E,0x4CC228DC36501857,0x73987670F8421161,0xE0DF934DDA9372B7,0x2EFD8AF527F647,0x548FA3548FA3547A,0x8FA3548FA3548FA3,0xA3548FA3548FA354,0x5C8FA3548FA3548F,0x370CE767DB69F0A1,0x148A42FD9FA8E75E,0x95D3497A1836567A,0x3B176D3CEE7B7D}, +{0x50217FB6E959A5E1,0x55D744B5F5B8D09B,0xF7A01245A9968DFD,0x5E2ED28291CBD92B,0x327D6A4F12ED9197,0x22F38DE9B94342A8,0xF08F9207C0BC4954,0x92CA7D85CB62,0x554517694148E5E0,0x810BFDB74ACD2E40,0xAEBA25AFADC684DA,0x3D00922D4CB46FEA,0x9B6A27893DA502ED,0x70CDC63D75720D1A,0x79E291279150591,0x1EF28157438CF6}, +{0x59D483698ADF25AD,0xDF259D483698ADF2,0x98ADF259D483698A,0x47698ADF259D4836,0x8A409FE323B0C564,0x7776BA73BB1425E9,0xA9C30185C47DDDD5,0x17CB3BFFF6729E,0x6F92CEA41B4C56F1,0x4C56F92CEA41B4C5,0x41B4C56F92CEA41B,0xE2A41B4C56F92CEA,0x9D076460B8435788,0x54F113B72EB92D94,0x2A66E44EFC731303,0x12A4AB560F3F66}, +{0x2B1FB984943A94A8,0x30572CDCDFF75824,0x86B44D20E248E0BD,0x91D67FBFB355D2A2,0x1FB62ABAE68FD35D,0x3C9EB762B7B42EE1,0x9F02146D035C6473,0x2E16E82F80CE94,0x57721BBE9E5A5800,0xA2061AF8C6275649,0x3BD12A9F2030397F,0x11812DB680FC4074,0xE65278C2B095007B,0x8F2E2CBAE91FE5D5,0xED8F5676C276CA45,0x3DF6D70A1D206A}, +{0xBE8AB88AA30ECFE7,0x4BA78C308192D1B7,0xB3E24AC5F8070CA1,0x96351F2D30F7BBD,0x81FEFCEA948AD196,0xD3C5B4543AD9805F,0xA75812F48753D9,0x1724C5EDAB3470,0x2827F23CACB56FB9,0x157BD32FB57A7B7,0x70A9DAFDB132D060,0x792BEEB65C0F9BF7,0xE56FC183B1F50CE1,0xCCAD12C0789DBF02,0x8C2146875FF342E2,0x1CE0B3C0517507}, +{0x49B33CFF3F381BC6,0xD8CAC1728CCEDAAE,0x1DF2FD00097B2467,0xAB713DCFD459086,0x8836E5EA1B2EDAB,0x1716275997ADF384,0x191CA247A36D2F50,0x32176EFFF620B5,0x4C8D46F27B6D17EC,0x50F8ADEAE3D0F0C7,0x545DC5F4131C3561,0xE5B904096E80374E,0xA86F14DB302AE72D,0x8F42BC329DB7D7E0,0x83BAE6D9FEE5F302,0x31094190A0F887}, +{0x8EB074F53A76A870,0xB126FDBA6CC46493,0x555A9BBF86580EF5,0x2D766D1384CC6DD9,0x488C1D0E043C69F6,0xE46574481370F9B8,0x20011A2950633B25,0x2C90D406DC97FF,0x25760E200D5A3CC9,0x5B029C9D13C41968,0x4CF262816A003763,0xECB895F7DEFD5B79,0x5500D603F7586E63,0xD3B73E937238582B,0xE0717E4434F561B4,0x24B97B8A231B62}, +{0x3B59E87672CD3132,0x39065FDDB46E42BB,0xDFF1DBFCEE9FB3C5,0x95D0A17ADF5B0686,0x4F4AE55C15F6F6,0xEC7A661AF31BEEA2,0xCA7A05464470274,0x32630B4C55211E,0x9DB227BAE1A18E5E,0x2D8003402FC924D9,0xDBBA9E0412D57B42,0xE3590E03813384,0x50E5FD1EE6160BE7,0x319EE53F2DE7E963,0xAFBEDCC8195A0FE7,0x1D66C22AE5E03D}, +{0xFA1D721B8012AD24,0x4D5A34CA856360AA,0x2C74166DA03E082F,0xA334C1A0A8C0EECA,0x4BD3029C76081336,0xC17E91F7FE1620AB,0x602C6464DF6D7B5A,0x37C56195A01609,0xF42E70CB53B77D89,0x971CD3CDB95DCA98,0x98BED2110CEA97D7,0x29E8E40FDE89CEA0,0x66762394F501B5D,0x768E393C98EDB0DC,0x7B7177B9782A051C,0x2419F31B5536B7}, +{0x6B9078F75FB9FD5A,0xAAE697DEF085EE62,0x55F0635BB0920820,0xB6EB4C44F59DA609,0x9D20534E797B55E3,0xE586320878C2E00C,0x4B2C04D2265832BF,0x2B7A08CADF8ABE,0xA28AD65405737E37,0x1A7AD3DA645AE6C,0xA007C768042513DE,0xB862E5834961B9AB,0xD751FD817FF50BD6,0xD40A969925029B74,0x38326A08AA3FE933,0x33A720FE49B1C0}, +{0x6F33A8DC20803BD8,0x2846C4B267C2FEA9,0x3007D269048CB91D,0x149AF087F10343DC,0xA411643250BFE57D,0xFE05DA28BEBBD6A2,0xA1CC30AB16469EDF,0x73147428B8D6E,0x14144FB077BA07EC,0xBDDB35BAB1D76D69,0x161ED689F2678887,0x635E2E3996327A7D,0xEF1D6C7CA5686991,0x50B90BE915F46926,0x1CA4E335B9AB5FD5,0x27BAA66DCED0C5}, +{0xEFA7AC2F83918F15,0x1180A29870F3D459,0x90347A6E04DDB73E,0x80D765C86450E8FF,0xB872718F0F19F98D,0xD6A86F096DCF4922,0xB38BB34120254D9,0x2E5A1621B615F2,0xB2D181BD4FA52AA2,0xDC904B3EB8AF6F02,0xD6B25DF9558317E8,0x85BF914F31A23BAC,0xBDA3E9AB557B29B7,0x5CD5E1D426B1789D,0x8A6AED659E678CD3,0x1C56D6E1BB93F5}, +{0x924E6058D015A38D,0x1E2EC7DD7A5132B7,0xA97C2194346DA32D,0x41EF1F31CD51333B,0xFB89E6E30C1162AA,0x4061678E5962580A,0x9ECCCCB3B6FAD5A,0x37AF58627A887A,0xE8F5D903F0BD0269,0x200E1FFA8489B9DA,0xDE882C8D3156A460,0x8C4DABC11F877458,0xD54C3B40CD538F2F,0x41674635284DFEBB,0xAD9B8330BFF569FC,0x30C2633BF078F7}, +{0x75C1E6ED473130D0,0xFD624B7CC04D355F,0x313DC4BCA820911E,0x449D8112D71CF106,0x23A25A83664B420E,0x16A55C6AF6910691,0xDA58FB0631B2EAD0,0x2D42B72E1FA0F5,0x4AF98FC17BA992CE,0x19C1F944FD5AB7F4,0x68ACC73E0CE942CF,0x7B3F9FA6C110FEFD,0x3DEFD9B6CFCF2AD2,0x4B080446336C5FA5,0x19508DFD60080814,0xFD442DBA88642}, +{0x4EE43F3D8CAC1374,0xAF2E7784E2460F7,0x50133AD8519FCCA1,0xBDB81ECD10C888CF,0x675791FE9112FBA,0x364B5F4D282C51A3,0xA3A53FD5546E97E0,0x261C6F73A8BA64,0x13DE8B19DF5E0FEE,0x1D05A6FE505FEA21,0x634E634AA1C25DBB,0x2C49E6E62282B432,0xE989B2E0D9775E22,0x104ABC59A97037E8,0x3DFAB907857260E,0x3B8179D525D960}, +{0xAA3BFB6CB8587768,0x515E32FD38308C38,0x927E612E9CE18C76,0x13B2195A5D867C54,0x857274100A6ECFD0,0x10CAD97274DDC646,0x30BCDB9A79ECA27,0x7F0790BC050BA,0x67F4FD27FF7B7A3B,0x7528EF9DFC6790F9,0xD34442AA02F00A58,0x51935D736DE84027,0xFEA3DCBAF9002F2,0xB3D055C2572AD741,0x9F0EF6D70050CCC5,0x10611302FDA1B4}, +{0x8894D7E86C5358CF,0xE01ED56C2E374D80,0x1EB04AACFBB0B60D,0x1B0F1031360154CD,0x52257CF78935DF2,0xD1759C3E61E7823C,0xC5CBD367AD3EB0AB,0x377C52E4424CF4,0xED5FFE6B5FB024BD,0x65B8965C7A3F1BB,0x61A0E4FB6BAAF40F,0xD8ACB4A3CC9A6C24,0x38FAAD404A5D6211,0xF59F595458B10D72,0x13FDB0B2371936A0,0x1934F680EC8F88}, +{0xF6DC60A5C5734661,0x9CD9E9A6DA083A88,0xEDA465D0EAA7F9BB,0x87FEE132D788E4CA,0x94D57ED92F0D0A7B,0xA157AC0056BDBFE8,0x62DAF28EE0E30FC9,0x10E9FA4557999D,0x78942F9DE083A353,0x5FDAC52AEBA63CE5,0x905BC434EA6102CF,0x9CC2E0667372C509,0xE22094C33879AFDC,0x820B3999B77E5E28,0x7076A18C8D100A7D,0x1B55229ADA2623} }; + +// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions +#define fpcopy fpcopy503 +#define fpzero fpzero503 +#define fpadd fpadd503 +#define fpsub fpsub503 +#define fpneg fpneg503 +#define fpdiv2 fpdiv2_503 +#define fpcorrection fpcorrection503 +#define fpmul_mont fpmul503_mont +#define fpsqr_mont fpsqr503_mont +#define fpinv_mont fpinv503_mont +#define fpinv_chain_mont fpinv503_chain_mont +#define fpinv_mont_bingcd fpinv503_mont_bingcd +#define fp2copy fp2copy503 +#define fp2zero fp2zero503 +#define fp2add fp2add503 +#define fp2sub fp2sub503 +#define fp2neg fp2neg503 +#define fp2div2 fp2div2_503 +#define fp2correction fp2correction503 +#define fp2mul_mont fp2mul503_mont +#define fp2sqr_mont fp2sqr503_mont +#define fp2inv_mont fp2inv503_mont +#define fp2inv_mont_bingcd fp2inv503_mont_bingcd +#define fpequal_non_constant_time fpequal503_non_constant_time +#define mp_add_asm mp_add503_asm +#define mp_subaddx2_asm mp_subadd503x2_asm +#define mp_dblsubx2_asm mp_dblsub503x2_asm +#define random_mod_order_A random_mod_order_A_SIDHp503 +#define random_mod_order_B random_mod_order_B_SIDHp503 +#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp503_Compressed +#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp503_Compressed +#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp503_Compressed +#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp503_Compressed +#define crypto_kem_keypair crypto_kem_keypair_SIKEp503_compressed +#define crypto_kem_enc crypto_kem_enc_SIKEp503_compressed +#define crypto_kem_dec crypto_kem_dec_SIKEp503_compressed + + +#include "../fpx.c" +#include "../ec_isogeny.c" +#include "../compression/torsion_basis.c" +#include "P503_compressed_pair_tables.c" +#include "../compression/pairing.c" +#include "P503_compressed_dlog_tables.c" +#include "../compression/dlog.c" +#include "../compression/sidh_compressed.c" +#include "../compression/sike_compressed.c" diff --git a/src/P503/P503_compressed_api.h b/src/P503/P503_compressed_api.h new file mode 100644 index 0000000..2c58acb --- /dev/null +++ b/src/P503/P503_compressed_api.h @@ -0,0 +1,109 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: API header file for P503 using compression +*********************************************************************************************/ + +#ifndef P503_COMPRESSED_API_H +#define P503_COMPRESSED_API_H + + +/*********************** Key encapsulation mechanism API ***********************/ + +#define CRYPTO_SECRETKEYBYTES 280 // MSG_BYTES + SECRETKEY_A_BYTES + CRYPTO_PUBLICKEYBYTES bytes +#define CRYPTO_PUBLICKEYBYTES 224 // 3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES + 2 bytes for shared elligator +#define CRYPTO_BYTES 24 +#define CRYPTO_CIPHERTEXTBYTES 248 // COMPRESSED_CHUNK_CT + MSG_BYTES bytes + +// Algorithm name +#define CRYPTO_ALGNAME "SIKEp503_compressed" + +// SIKE's key generation +// It produces a private key sk and computes the public key pk. +// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 280 bytes) +// public key pk (CRYPTO_PUBLICKEYBYTES = 224 bytes) +int crypto_kem_keypair_SIKEp503_compressed(unsigned char *pk, unsigned char *sk); + +// SIKE's encapsulation +// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 224 bytes) +// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes) +// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 248 bytes) +int crypto_kem_enc_SIKEp503_compressed(unsigned char *ct, unsigned char *ss, const unsigned char *pk); + +// SIKE's decapsulation +// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 280 bytes) +// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 248 bytes) +// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes) +int crypto_kem_dec_SIKEp503_compressed(unsigned char *ss, const unsigned char *ct, const unsigned char *sk); + + +// Encoding of keys for KEM-based isogeny system "SIKEp503" (wire format): +// ---------------------------------------------------------------------- +// Elements over GF(p503) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address). +// Elements (a+b*i) over GF(p503^2), where a and b are defined over GF(p503), are encoded as {a, b}, with a in the lowest memory portion. +// +// Private keys sk consist of the concatenation of a 24-byte random value, a value in the range [0, 2^250-1] and the public key pk. In the SIKE API, +// private keys are encoded in 280 octets in little endian format. +// Public keys pk consist of 3 values of length OBOB_BITS, one element in GF(p503^2) and 2 bytes. In the SIKE API, pk is encoded in 224 octets. +// Ciphertexts ct consist of the concatenation of 3 values of length OALICE_BITS, one element in GF(p503^2), 2 bytes and a 24-byte value. In the SIKE API, +// ct is encoded in 224 + 24 = 248 octets. +// Shared keys ss consist of a value of 24 octets. + + +/*********************** Ephemeral key exchange API ***********************/ + +#define SIDH_SECRETKEYBYTES_A 32 +#define SIDH_SECRETKEYBYTES_B 32 +#define SIDH_PUBLICKEYBYTES 224 +#define SIDH_BYTES 126 + +// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys. +// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016. +// Extended version available at: http://eprint.iacr.org/2016/859 + +// Generation of Alice's secret key +// Outputs random value in [0, 2^250 - 1] to be used as Alice's private key +void random_mod_order_A_SIDHp503(unsigned char* random_digits); + +// Generation of Bob's secret key +// Outputs random value in [0, 2^Floor(Log(2,3^159)) - 1] to be used as Bob's private key +void random_mod_order_B_SIDHp503(unsigned char* random_digits); + +// Alice's ephemeral public key generation +// Input: a private key PrivateKeyA in the range [0, 2^250 - 1], stored in 32 bytes. +// Output: the public key PublicKeyA consisting of 3 GF(p503^2) elements encoded in 224 bytes. +int EphemeralKeyGeneration_A_SIDHp503_Compressed(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA); + +// Bob's ephemeral key-pair generation +// It produces a private key PrivateKeyB and computes the public key PublicKeyB. +// The private key is an integer in the range [0, 2^Floor(Log(2,3^159)) - 1], stored in 32 bytes. +// The public key consists of 3 GF(p503^2) elements encoded in 224 bytes. +int EphemeralKeyGeneration_B_SIDHp503_Compressed(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB); + +// Alice's ephemeral shared secret computation +// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB +// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^250 - 1], stored in 32 bytes. +// Bob's PublicKeyB consists of 3 GF(p503^2) elements encoded in 224 bytes. +// Output: a shared secret SharedSecretA that consists of one element in GF(p503^2) encoded in 126 bytes. +int EphemeralSecretAgreement_A_SIDHp503_Compressed(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA); + +// Bob's ephemeral shared secret computation +// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA +// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^159)) - 1], stored in 32 bytes. +// Alice's PublicKeyA consists of 3 GF(p503^2) elements encoded in 224 bytes. +// Output: a shared secret SharedSecretB that consists of one element in GF(p503^2) encoded in 126 bytes. +int EphemeralSecretAgreement_B_SIDHp503_Compressed(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB); + + +// Encoding of keys for KEX-based isogeny system "SIDHp503_compressed" (wire format): +// ---------------------------------------------------------------------- +// Elements over GF(p503) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address). +// Elements (a+b*i) over GF(p503^2), where a and b are defined over GF(p503), are encoded as {a, b}, with a in the lowest memory portion. +// +// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^250-1] and [0, 2^Floor(Log(2,3^159)) - 1], resp. In the SIDH API, +// Alice's and Bob's private keys are encoded in 32 octets in little endian format. +// Public keys pk consist of 3 values of length OBOB_BITS, one element in GF(p503^2) and 2 bytes. In the SIKE API, pk is encoded in 224 octets. +// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p503^2). In the SIDH API, they are encoded in 126 octets. + + +#endif diff --git a/src/P503/P503_compressed_dlog_tables.c b/src/P503/P503_compressed_dlog_tables.c new file mode 100644 index 0000000..09832dd --- /dev/null +++ b/src/P503/P503_compressed_dlog_tables.c @@ -0,0 +1,81954 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: precomputed tables for Pohlig-Hellman when using compression +*********************************************************************************************/ + + +const uint64_t ph2_T[DLEN_2*ELL2_W*2*NWORDS64_FIELD] = { +0x3F9,0x0,0x0,0xB400000000000000,0x63CB1A6EA6DED2B4,0x51689D8D667EB37D,0x8ACD77C71AB24142,0x26FBAEC60F5953, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x85B6F6614C5479F1,0x125041AA45F3D3F8,0x71E9FEFE8A5D5695,0xB34124002BB38B60,0x83397A0DD88EFBAC,0xBA9505B09077EAC4,0xF66DA4912B0DF68F,0x2C381431E2BA3A, 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+0xD0605099745D3CD8,0xC8C39181EF7276F2,0xCCF7487120657325,0x6EDA70F77EC46F20,0x43DA20C227072698,0xE6E32D4D1D5AC0F2,0xEBBC5F10274F5B0A,0x29210825190FCD, +0xFFFFFFFFFFFFFC06,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xF7FFFFFFFFFFFFFF,0xAF3D416B7B3314EB,0xCA33593B14FFCA31,0xD5784EF6BFC5638D,0x196B467B71C4CA, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0xBDEED4832E1C525D,0x2E75D4C62228BB24,0xDE8B525B98E1C5AD,0x329E283DE990E07,0x523DAEFC12681C5B,0xFB41377E83547ED5,0x1A7788F89F9A83DE,0x56955F92F900C, +0x2F9FAF668BA2C327,0x373C6E7E108D890D,0x3308B78EDF9A8CDA,0x3D258F08813B90DF,0xCF2E3B17FB0AC108,0x34B8C97B5E23BCBC,0x748967ADB32849C5,0x1745ED1C680E50, +0x1466ABECBC90153E,0x13FA4A4B6EA544E3,0xBEFA3823091CB000,0xF18E70EAB661ABC6,0x2D17AEAE098EF1C9,0x655B3A21E4448B49,0x4841893D3729816A,0x3C83FDC04A8688, +0xBB8DEE3E69808717,0xE3171073A8989DB3,0x73A762FCC404CBE7,0xE4DAD49D30F79B16,0xB8E167E22887F110,0x36B9C4A7365AC473,0x16FA457EC2CBF010,0x3725B3919486BE, +0x123D14887026B926,0x87B89B004B0A9F1F,0x93D6B359A2F4126B,0x24816BBAE36DD1BD,0x7FE14990096D19B2,0x20B2CBCD9DC9135E,0x73DC4D732E422CD7,0x1400D10E9B874, +0x61CC4A98F36F8215,0xC07BA4B8E63EB3D1,0xA137FA8ECCE82F30,0xE78CC9A4A03882D7,0xB4E8CAAD3634B70,0xDDC44DA9679D3B53,0xAF161AEB7C6D2565,0x280C10C6BABE21, +0xE263D6EEA7C1B1D,0x551EAE12F0F2E18B,0xB0AA582A236EA512,0xA51292B0FC177133,0xF6B9D6691CAE6B30,0x347DB3BAB12BA379,0x1638CF7B22D4ED26,0xA918D47C9E6EA, +0xF1D9C2911583E4E2,0xAAE151ED0F0D1E74,0x4F55A7D5DC915AED,0x6ED6D4F03E88ECC,0x1C4E857105637C70,0xE71E430DCA52DA35,0x4A0CF742B7A2B7A9,0x35D567F9B73734, +0x9E33B5670C907DEA,0x3F845B4719C14C2E,0x5EC805713317D0CF,0xC473365B5FC77D28,0x7B9CF2F4EAE9C2F,0x3DD7A91F13E1425C,0xB12FABD25E0A7F6A,0x185AE47AC65FFC, +0xEDC2EB778FD946D9,0x784764FFB4F560E0,0x6C294CA65D0BED94,0x877E94451C922E42,0x9327124A18A4CDEE,0xFAE92AFADDB56A50,0xEC69794AAC3577F8,0x3F26E8309765A9, +0x447211C1967F78E8,0x1CE8EF8C5767624C,0x8C589D033BFB3418,0xC7252B62CF0864E9,0x5A26F3F7F989F68F,0xE4E232214523B93B,0x494B813F17ABB4BF,0x94141AFEC9760, +0xEB995413436FEAC1,0xEC05B5B4915ABB1C,0x4105C7DCF6E34FFF,0xBA718F15499E5439,0xE5F0AD2C1882F5D6,0xB640BCA69739F265,0x18043D80A34E2365,0x3E2F781369796, +0xD0605099745D3CD8,0xC8C39181EF7276F2,0xCCF7487120657325,0x6EDA70F77EC46F20,0x43DA20C227072698,0xE6E32D4D1D5AC0F2,0xEBBC5F10274F5B0A,0x29210825190FCD, +0x42112B7CD1E3ADA2,0xD18A2B39DDD744DB,0x2174ADA4671E3A52,0xA8D61D7C2166F1F8,0xC0CAACDE0FA9CB45,0x205ABF49F829FED9,0x45CE3DC53ADD20F1,0x3AFD9F48518E12, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x3F9,0x0,0x0,0xB400000000000000,0x63CB1A6EA6DED2B4,0x51689D8D667EB37D,0x8ACD77C71AB24142,0x26FBAEC60F5953, +0x2F9FAF668BA2C327,0x373C6E7E108D890D,0x3308B78EDF9A8CDA,0x3D258F08813B90DF,0xCF2E3B17FB0AC108,0x34B8C97B5E23BCBC,0x748967ADB32849C5,0x1745ED1C680E50, +0x42112B7CD1E3ADA2,0xD18A2B39DDD744DB,0x2174ADA4671E3A52,0xA8D61D7C2166F1F8,0xC0CAACDE0FA9CB45,0x205ABF49F829FED9,0x45CE3DC53ADD20F1,0x3AFD9F48518E12, +0xBB8DEE3E69808717,0xE3171073A8989DB3,0x73A762FCC404CBE7,0xE4DAD49D30F79B16,0xB8E167E22887F110,0x36B9C4A7365AC473,0x16FA457EC2CBF010,0x3725B3919486BE, +0xEB995413436FEAC1,0xEC05B5B4915ABB1C,0x4105C7DCF6E34FFF,0xBA718F15499E5439,0xE5F0AD2C1882F5D6,0xB640BCA69739F265,0x18043D80A34E2365,0x3E2F781369796, +0x61CC4A98F36F8215,0xC07BA4B8E63EB3D1,0xA137FA8ECCE82F30,0xE78CC9A4A03882D7,0xB4E8CAAD3634B70,0xDDC44DA9679D3B53,0xAF161AEB7C6D2565,0x280C10C6BABE21, +0xEDC2EB778FD946D9,0x784764FFB4F560E0,0x6C294CA65D0BED94,0x877E94451C922E42,0x9327124A18A4CDEE,0xFAE92AFADDB56A50,0xEC69794AAC3577F8,0x3F26E8309765A9, +0xF1D9C2911583E4E2,0xAAE151ED0F0D1E74,0x4F55A7D5DC915AED,0x6ED6D4F03E88ECC,0x1C4E857105637C70,0xE71E430DCA52DA35,0x4A0CF742B7A2B7A9,0x35D567F9B73734, +0xF1D9C2911583E4E2,0xAAE151ED0F0D1E74,0x4F55A7D5DC915AED,0x6ED6D4F03E88ECC,0x1C4E857105637C70,0xE71E430DCA52DA35,0x4A0CF742B7A2B7A9,0x35D567F9B73734, +0xEDC2EB778FD946D9,0x784764FFB4F560E0,0x6C294CA65D0BED94,0x877E94451C922E42,0x9327124A18A4CDEE,0xFAE92AFADDB56A50,0xEC69794AAC3577F8,0x3F26E8309765A9, +0x61CC4A98F36F8215,0xC07BA4B8E63EB3D1,0xA137FA8ECCE82F30,0xE78CC9A4A03882D7,0xB4E8CAAD3634B70,0xDDC44DA9679D3B53,0xAF161AEB7C6D2565,0x280C10C6BABE21, +0xEB995413436FEAC1,0xEC05B5B4915ABB1C,0x4105C7DCF6E34FFF,0xBA718F15499E5439,0xE5F0AD2C1882F5D6,0xB640BCA69739F265,0x18043D80A34E2365,0x3E2F781369796, +0xBB8DEE3E69808717,0xE3171073A8989DB3,0x73A762FCC404CBE7,0xE4DAD49D30F79B16,0xB8E167E22887F110,0x36B9C4A7365AC473,0x16FA457EC2CBF010,0x3725B3919486BE, +0x42112B7CD1E3ADA2,0xD18A2B39DDD744DB,0x2174ADA4671E3A52,0xA8D61D7C2166F1F8,0xC0CAACDE0FA9CB45,0x205ABF49F829FED9,0x45CE3DC53ADD20F1,0x3AFD9F48518E12, +0x2F9FAF668BA2C327,0x373C6E7E108D890D,0x3308B78EDF9A8CDA,0x3D258F08813B90DF,0xCF2E3B17FB0AC108,0x34B8C97B5E23BCBC,0x748967ADB32849C5,0x1745ED1C680E50 +}; + + +const uint64_t *ph2_T1 = {0}; +const uint64_t *ph2_T2 = {0}; +// Assume W_3 = 6 +const uint64_t *ph3_T = {0}; + +const uint64_t ph3_T1[DLEN_3*ELL3_W*2*NWORDS64_FIELD] = { +0x3F9,0x0,0x0,0xB400000000000000,0x63CB1A6EA6DED2B4,0x51689D8D667EB37D,0x8ACD77C71AB24142,0x26FBAEC60F5953, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x9C988666C8802654,0x8184EAC95BD2440C,0xE200344E0D5D28F9,0xC9BA078F1956DBA5,0x2906BC1E03C540B7,0x547D46164CD844B4,0xB1F040F7A98DCAEC,0x149C072F5EB3E1, +0x7F0D799C1910B629,0xBD86D4FE2D8DA37E,0xD093E71B785A0563,0xE3CE2A52349EBCE7,0x21843952BAE5404E,0x901EC526F4BB88C0,0xDA7FF2CC132EA904,0x36A6DB4332CCE8, +0x9C98F5B6D5C81D00,0x1E85D999D78C8540,0xB72ED89EFBDC2D38,0x872FFBF30252896,0xE24A83FF782611A9,0xC174117B147D3FB2,0x93702F73CCE04D63,0x279143ECB8AA7A, +0xA3B0A72938D02581,0x7972EA180357F6B1,0xA240CE057EFE1076,0xE0736E8251B1BA71,0x2D710EA358B4FC76,0xABB60C1ECD9CFE18,0x17AE912AF3591E5C,0x3E86FE0F9EB0B9, +0xAC6B631F67D056B0,0x592176278AD019D0,0x8C681ADF943DCF80,0x8B534119923CBCFA,0x8DC5AC3D0DD5A847,0xB346DDF4C6CFDE16,0x1D852513DE83B7B4,0xECA0BFB5A4B7B, +0xD2666711F049454B,0x7E454BE952117089,0xD3F999FFAE1B21CC,0x5CC07F0AE4984E8A,0x2B9C84A51DCCCC3E,0x1A76A2495250B61D,0x6F594C9CE6AEF270,0x155EBF4ED9D36E, +0xCF0EEDEE483D60F5,0x4AFB2C4D7F9DB8D3,0x9658325FBCE90413,0x97130CF056D15346,0x9F94EF01022B7B86,0xF53C8DF574E06AF9,0xDA2ABF66E22C84E7,0xD751467B84986, +0x507E896424C44313,0xDA0EA3BAD8D5CB8F,0x5AB1B42D97251EEB,0xF56EE4D0B8D7B88B,0xC1E1CE9F96BB65B7,0x1729EF296ECBF6CB,0x55AACAA7CE1DCB59,0x13017F00154667, +0x78D22D0C97EBF8E0,0x18597966B7386399,0x53735DCF43F1061B,0xA5AC480D2846C991,0xC0EE9E1228E59BB3,0x4A161A71AC030EFD,0xEE9FC4D499C05B89,0x3F54865C2A4A02, +0xDEBBE76F1D22A738,0x8C8CD4B910C8719C,0x38877D494DF4FABA,0x77F2CB203884E2FD,0x6353D7B8C6632982,0xC701C3FDC2597FED,0x612A54C833D66F28,0xFE5F367ACBC39, +0x62FAD5A60041DA2A,0x7DD1A770A066F36C,0x566D7F581E9E39DB,0x2D7BC50C204AB39A,0x2256883E7DF85482,0x618034F61CAAF443,0x2DFD0844BBB8105,0x25C9CA351A2E77, +0x546669B3472C36F6,0xA2E071EF3F64843B,0x9DBA1EA75EB35A4A,0x7B4651D77CEE37A,0x80825DCE2C14BF80,0x2E887EBD2669B73B,0x834813581E66FA1B,0x3139F77D99E40, +0xA90BC0631CF6E5AC,0x52FA636BD1BDE54A,0x4569C1E84D737D5D,0x7AF91E7B8F45FF79,0xD382D3650601FF6F,0x41CBC0BEC2980F9C,0x645DC6F280A28864,0x190E4A54AA2EF5, +0xE518AE940B80EBB5,0x8F15EE0BD2B84DC8,0xC06452E6DA589432,0xB17EC5E19BE7E192,0x9B49EE5A181C8D4E,0x1175EEF9987380D6,0x2265C9A44EC1C1E2,0x203D92A40728AC, +0xD3C8687DDD8C0F3,0x1719CD406BFEAA24,0x42884019B6625731,0x4B234660D441FB57,0x434275AD468E7A7E,0x17A7296E893D8B15,0xC243EDBF870C8B0A,0x2EF57CBF885576, +0xAD5C7265891471D4,0x29729F561C8ED100,0x512590D6FA5C206D,0xEB134103EA32CB25,0xE9241137F91476EC,0x38C7EEEB1E271836,0x5DFB4F9F5AEDF5F5,0xE5B36891B85CF, +0x3AD78FFDCE75375B,0xB6FA684A8E9F7971,0x4808B4D98EDD7ABC,0xA8859CD33A43B90D,0x737D8D5E550A41C,0x63670E0C46594321,0xA2C2B55E84BA804B,0x1F73293B5D3588, +0xE3B936DBEA5D1B2B,0xFE361969EB9A153B,0x60364FFA640EE8F,0x24ACD933CE45BE83,0xB6A042BD7209BD3,0x82522A1B55F3082,0x820244F73E8468AE,0x288698C2CBAE40, +0x115B174D8BE8887E,0xC4509994CED876C6,0x81F6A9050C32625F,0xE12F6ECA4B5BA601,0x5FCA4F5B0CEDA62,0xB76C8398E23A1065,0x79E613D8DE35EE2E,0x31F6B174435810, +0xCD09C27EFB4569BA,0x801BC242D4A240E1,0xBC7CECB19D0FEBAB,0xEF770D9F566CF40E,0x2D9F7EF61BF2510B,0x7B79B80AE1D267AD,0xEE8BF3FB6F61A79,0x1A7305A8B38DEF, +0x62E0B307DAE8E929,0x327737D48348FDBE,0xCAE811F7A8359B15,0x7FB113BF97FF9BCD,0x14142F90896BD74E,0x2400F3C256E311C7,0x5368A50F2817B421,0x39E0B5E5DF18EA, 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+0x556CC8E9B2E56453,0x858DC088D1F67FA6,0x10AC6A3CA7756C0C,0xC38CE121F5A0CDC1,0xB658208DD4B7260C,0x66CA6A967B9F98E5,0x244A44EA95C0464E,0x161E199585A02C, +0xA510A89A28E80484,0x7C35801850320E82,0x9E0201DC8A2598F8,0xC3AD664AC0D13837,0xF9F2275A3B8E65F1,0xFA6F3248AB4064A4,0xAD2069004C4EB521,0xAD59DAF6DE8C3, +0x555BC38B5DE27CBB,0x32938A3BFB8F095,0x722EC4D62E5DA841,0x462749FFB350348E,0xFA79AF401E0C111D,0xCCA7317CDE7D3525,0xD72E631242F84C39,0x40448094414E2E, +0xFECEC24BA9DA8C58,0xAEF80A36454D4A69,0xA113C434F31B805A,0x71EC83B82B6F348,0x5865E36DCD8C435,0x9EED85177FEC1655,0x8F5CB681351310FD,0x3F927FA5EB22AB, +0x3BADC1A21C233411,0x664B55838DFC3017,0x3FBD34F8FB07AF21,0x33BB141BEAD159ED,0x2C2806D6A31AD57B,0x7E63F9DE0458061A,0x2EA14E842EDDDBAC,0x1F015D99540727, +0x1D6B777DA600F5B3,0x15AAB2660F8077E9,0xA0F1B8A23428E590,0x43821B573E1B83A5,0x5DC6D8079A739E5A,0x423B4F4F46106BE0,0x492E02B3FAE0985A,0x3C320DE43D104A, +0x21205669B06F54E3,0x1CFE26227EFDE61B,0x5231EC89A13CEDDF,0x91BD0AF81C1323B9,0x75344679B08B0E88,0x7922BF713EE6B2C,0x1E0AB48FB8B43D77,0x218AA4E053ECEB, +0xDBD43A843471FC2A,0x48B835D64A7E22BD,0x2D9E937CFC1F81E3,0xAA084E33C512FA45,0x27EC71CD5962D27A,0x312136DC78F00958,0x15E797DBE0D2EEDC,0x138FD914B1CC3E, +0xE14CAEADA8A2EA44,0x89223DDFD813DCF4,0x946484500C6C01AB,0x6C0A34703EC5E0B,0x8CDCAADCCDF6AE44,0xC32D9313BB7426B0,0xD2FA80B904B4864A,0x37E569CE3B72A5 +}; + + +const uint64_t ph3_T2[DLEN_3*ELL3_W*2*NWORDS64_FIELD] = { +0x3F9,0x0,0x0,0xB400000000000000,0x63CB1A6EA6DED2B4,0x51689D8D667EB37D,0x8ACD77C71AB24142,0x26FBAEC60F5953, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x9C988666C8802654,0x8184EAC95BD2440C,0xE200344E0D5D28F9,0xC9BA078F1956DBA5,0x2906BC1E03C540B7,0x547D46164CD844B4,0xB1F040F7A98DCAEC,0x149C072F5EB3E1, +0x7F0D799C1910B629,0xBD86D4FE2D8DA37E,0xD093E71B785A0563,0xE3CE2A52349EBCE7,0x21843952BAE5404E,0x901EC526F4BB88C0,0xDA7FF2CC132EA904,0x36A6DB4332CCE8, +0x9C98F5B6D5C81D00,0x1E85D999D78C8540,0xB72ED89EFBDC2D38,0x872FFBF30252896,0xE24A83FF782611A9,0xC174117B147D3FB2,0x93702F73CCE04D63,0x279143ECB8AA7A, +0xA3B0A72938D02581,0x7972EA180357F6B1,0xA240CE057EFE1076,0xE0736E8251B1BA71,0x2D710EA358B4FC76,0xABB60C1ECD9CFE18,0x17AE912AF3591E5C,0x3E86FE0F9EB0B9, +0xAC6B631F67D056B0,0x592176278AD019D0,0x8C681ADF943DCF80,0x8B534119923CBCFA,0x8DC5AC3D0DD5A847,0xB346DDF4C6CFDE16,0x1D852513DE83B7B4,0xECA0BFB5A4B7B, +0xD2666711F049454B,0x7E454BE952117089,0xD3F999FFAE1B21CC,0x5CC07F0AE4984E8A,0x2B9C84A51DCCCC3E,0x1A76A2495250B61D,0x6F594C9CE6AEF270,0x155EBF4ED9D36E, +0xCF0EEDEE483D60F5,0x4AFB2C4D7F9DB8D3,0x9658325FBCE90413,0x97130CF056D15346,0x9F94EF01022B7B86,0xF53C8DF574E06AF9,0xDA2ABF66E22C84E7,0xD751467B84986, +0x507E896424C44313,0xDA0EA3BAD8D5CB8F,0x5AB1B42D97251EEB,0xF56EE4D0B8D7B88B,0xC1E1CE9F96BB65B7,0x1729EF296ECBF6CB,0x55AACAA7CE1DCB59,0x13017F00154667, +0x78D22D0C97EBF8E0,0x18597966B7386399,0x53735DCF43F1061B,0xA5AC480D2846C991,0xC0EE9E1228E59BB3,0x4A161A71AC030EFD,0xEE9FC4D499C05B89,0x3F54865C2A4A02, +0xDEBBE76F1D22A738,0x8C8CD4B910C8719C,0x38877D494DF4FABA,0x77F2CB203884E2FD,0x6353D7B8C6632982,0xC701C3FDC2597FED,0x612A54C833D66F28,0xFE5F367ACBC39, +0x62FAD5A60041DA2A,0x7DD1A770A066F36C,0x566D7F581E9E39DB,0x2D7BC50C204AB39A,0x2256883E7DF85482,0x618034F61CAAF443,0x2DFD0844BBB8105,0x25C9CA351A2E77, +0x546669B3472C36F6,0xA2E071EF3F64843B,0x9DBA1EA75EB35A4A,0x7B4651D77CEE37A,0x80825DCE2C14BF80,0x2E887EBD2669B73B,0x834813581E66FA1B,0x3139F77D99E40, +0xA90BC0631CF6E5AC,0x52FA636BD1BDE54A,0x4569C1E84D737D5D,0x7AF91E7B8F45FF79,0xD382D3650601FF6F,0x41CBC0BEC2980F9C,0x645DC6F280A28864,0x190E4A54AA2EF5, +0xE518AE940B80EBB5,0x8F15EE0BD2B84DC8,0xC06452E6DA589432,0xB17EC5E19BE7E192,0x9B49EE5A181C8D4E,0x1175EEF9987380D6,0x2265C9A44EC1C1E2,0x203D92A40728AC, +0xD3C8687DDD8C0F3,0x1719CD406BFEAA24,0x42884019B6625731,0x4B234660D441FB57,0x434275AD468E7A7E,0x17A7296E893D8B15,0xC243EDBF870C8B0A,0x2EF57CBF885576, +0xAD5C7265891471D4,0x29729F561C8ED100,0x512590D6FA5C206D,0xEB134103EA32CB25,0xE9241137F91476EC,0x38C7EEEB1E271836,0x5DFB4F9F5AEDF5F5,0xE5B36891B85CF, +0x3AD78FFDCE75375B,0xB6FA684A8E9F7971,0x4808B4D98EDD7ABC,0xA8859CD33A43B90D,0x737D8D5E550A41C,0x63670E0C46594321,0xA2C2B55E84BA804B,0x1F73293B5D3588, +0xE3B936DBEA5D1B2B,0xFE361969EB9A153B,0x60364FFA640EE8F,0x24ACD933CE45BE83,0xB6A042BD7209BD3,0x82522A1B55F3082,0x820244F73E8468AE,0x288698C2CBAE40, +0x115B174D8BE8887E,0xC4509994CED876C6,0x81F6A9050C32625F,0xE12F6ECA4B5BA601,0x5FCA4F5B0CEDA62,0xB76C8398E23A1065,0x79E613D8DE35EE2E,0x31F6B174435810, +0xCD09C27EFB4569BA,0x801BC242D4A240E1,0xBC7CECB19D0FEBAB,0xEF770D9F566CF40E,0x2D9F7EF61BF2510B,0x7B79B80AE1D267AD,0xEE8BF3FB6F61A79,0x1A7305A8B38DEF, +0x62E0B307DAE8E929,0x327737D48348FDBE,0xCAE811F7A8359B15,0x7FB113BF97FF9BCD,0x14142F90896BD74E,0x2400F3C256E311C7,0x5368A50F2817B421,0x39E0B5E5DF18EA, +0x6671633D77B71F3F,0x2205E5F39540643A,0x400ECAEC05E94E79,0x581446F77AFA1E71,0xACF0CA2CCD7D9263,0x87BA351589031753,0x8902F4BF4223B754,0x1F0CE138A430CF, +0xF304A171E9F7AF70,0x46572158652C9587,0xA92CCF2E7EE0F8E9,0x6D060B26ADEBBE0E,0xC334BE167E88C81C,0x48685E40E8E64029,0xA98E761AEED92A19,0x3877A0759267DF, +0x4AB164CFEC84DCEF,0x6EDCF2C6C1F0A10D,0x5D15DC872CFCD260,0x6F5FC91B80DD5BC8,0x87CF65FFE9BDD69F,0x68121155AED7F3E1,0x16B4F4CBF7BF6A1,0x1BAA62EFDFF6B2, +0x9B296C0B5A1AC63A,0xC5716037BF82A646,0xA62DB264B742BA86,0xD12906CE154598EE,0xA7CEF23AE634A18F,0x6C72484F4EEE38C6,0xD139D576E8449DCA,0x3927CFCFE5E3CB, +0xFC24CB6BA03DC80A,0xB47566D5B14A1768,0xE218F1668F74998C,0x8B78C509CCC58B96,0x23BE099151A6A8FC,0xF3FCC4F15F5CA7F2,0x6D3F3E146B3ABA0F,0x2348E2192D5E0B, +0x495178F1AFEB40D6,0xF8E612C088BCB976,0xB90B50F541B4FD87,0x621E5D075ED38B57,0x86BD4C1B53BE22B3,0xFCAB10A59D53300,0xC48CF4B00905C114,0xE0070FA10EFFF, +0x4C49F2C0BA288D38,0xA597644CB4E92268,0x2593965553A80BEC,0xCC852A89AABD30E5,0xF097FAAD430D2323,0xA610EC67E9B89891,0xB9377CE24AE17EAD,0x3884E6C68F781E, +0xEDC81B23128A27EB,0xECFEA31F10E40F06,0xB257577BF4F1AE6B,0x76EBE3A4899CED39,0xA08039167B6B4D1E,0x78E27103A9A92D2F,0x25EFF7923095A50D,0xC965E5EDCE745, +0x80F8E1C80BBC3A89,0x75E115D846F3C63D,0x5A3B0510A8DFE54F,0xE7720CD09FA5EDCE,0xE149549271927EE8,0x3D3D2211852A18A4,0x5716F81982EC71EC,0x1A1AF17EE9446B, +0x1688A581CEA6B4C0,0x6FD9B8166DAFBEAA,0x4B039DFF9B55447,0xE19E9B56FB3B6065,0x85FB1955218DD3D0,0xEE8ECDD7ADF40455,0x99FE22E29E8ED1B3,0x3A44FC76A85F58, +0xF51431B856CE6F3C,0xF77AD6F5791CE626,0x85E80AD35DB01E90,0x9D46CA7875E50CFF,0xEC833AC7FA64A7C3,0xF64759BCF61981B,0x259D05D8318AA3D1,0x2BF0A39723AB84, +0xDE78EB90CC56D5AC,0x12E80CE39A1050FA,0xFC753C60C5A3D8CA,0x9082CD49F93C39AA,0xBE55451BD97BBA65,0x327708E29C8C0B24,0x4993025A3F73D528,0xA73C4F83483C3, +0x852B7D2D57B4198,0xE59C883A240EF98F,0x450C8283CFB3AACE,0xA7A6CA75A6B5D2B2,0x1A204BB56BEE8032,0x5DA19104E43CFD24,0x3CC0C8E8FAE422FF,0x1EDAFC8AC0B9BF, +0xA5EFEF37A5F47F71,0x28852AB6851361CD,0xB3A9602B0ADE4C5A,0xF27DDCBC17A1DD09,0x85AD5543F5A30451,0xEE4F05B247D6CA22,0x65B0514B60657151,0x37453F5548770, +0x6A32F13D004228CA,0x5BC8F7325DFFB852,0xB9459DA52F952157,0x209E9051D4717F9B,0x2AE04A696B7CA6C2,0xC76B2DF9B76D34C8,0xFFFF00086EC29B6B,0x209A7ECDF95549, +0xCE27FD51091CAC02,0xA85D2E141FA40A0E,0x2F3F365BB932FD72,0x55847D11C59D5608,0x2686A304C527A1EA,0x8BE2D18958AD2507,0xE9F74E0E25442CDB,0x1E5631680969AA, +0x4ADA9AF4D368880C,0xA61BECB194C25965,0xEAA3DCFE45EB6BCC,0x9A7613C058B148BB,0xB3CF7F5BAFC4FBB3,0x5C5907E58D01482E,0xC94AE3CE3B100221,0x3726D3065DEE12, +0x77F9C1623D99985A,0x19CA642B485A7050,0xBEA207D536763C69,0x21A0D8349045DA43,0xA8E68E8A3C754848,0x82FBE26FFDBBEAE8,0xED0683CAC648B238,0x2BE17AE27352DD, +0x446B4CAA2A231781,0x4B79FAB18740A8F3,0x5F9F6786E719B5C1,0x6EA73BBDF9D4729E,0x57EA2EE1C2830F59,0xA1CACED0B194E00F,0xC244B637CD6285C,0x3CF7E5407F399E, +0x654BB52EA16EAB06,0x815598307379EAA4,0xE4FA4FEF96807DA2,0xB030DCC0C9F365B5,0xC0746A4415CCCA55,0x2D77BB495E9A8045,0x942FA79FDBF1AF3A,0x3F4076C3AF3CC4, +0xE4139F7B65868134,0x4840BED770A52F86,0x97DDD5B8318C8968,0x3D793F3D5CCE47D7,0xA7F2B3236D15974F,0x168242B12DF77D5C,0xDEFD54DE85FE1F9F,0x370E59E812FEAF, +0xE876871F460AEF89,0x98A279F53F6C3711,0xBE9C2493E309F40A,0x4E4517179BE8CB8E,0xABDE296A87E07680,0xF6B40F210504ACEE,0x1F60898E32BBF408,0x16825AE36A2673, +0x1E53436047049BD5,0xE0F87287640B0639,0x40F746D36524ECD5,0xC0C8F59E2EC65DC9,0x4683F4F16329B168,0xCB1819DD77102C95,0x97CA7FC82AA4172,0x2463A96B90AFD, 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+0x4A58D86E159F74D4,0xA2CCB262F07731D7,0x44373B3F9E3576A,0x59CC51A2D0D7B37F,0x44C94695BCE57B26,0x578F9AA0379502A5,0x98826F7757D85C40,0x1FF23E84BD3F14, +0xBD87083A3F6315AD,0xFCF9268083C28759,0x4CEB94AB84636F1E,0x362D35B761BD1F30,0xA1F5B0934CCD2809,0xF44CA709DEE37FF7,0x8543745948035DB2,0x2EC511B875DECF, +0xA738C594CB451397,0x62DB69DBEF5CA275,0xF1753B10DF3E9405,0x5C1157DCA3EE7AD,0x62DC07E1403EA0E3,0x4262741C1922D2B5,0x8DB101876C1BB906,0x1EC63957DD9DF6, +0x3AF177EE1317FA22,0x1FDEB771B727C7,0xC4495A6C8E4BE3A3,0xCB913D94D50887ED,0xB7A038A39D849E41,0x90D145739298A9FA,0xC63D798B685A438A,0x145909F186BE9D, +0x34565238872DA0DD,0x34378EDFFCAD5833,0x2940A927CD3B2B87,0x4515B4116A6A315E,0x5C94475F58AE4FF,0xA0595D8F7B81594B,0x461247F34B230409,0x3036B1993523F3, +0x4E84262D85F57F25,0x75CDE2C94803B9C4,0x8682C5820FA824C0,0xCEE17D04A050B57B,0x6CF30EFA2C768E26,0xC098E800A193FC96,0xBF022EE6075E80C4,0x2172AC064456FB, +0x27833BA6EE12ECC9,0x402CC8299C61FE34,0x894E549F5810A908,0xF8F41E01D9E15076,0x8C3F84D91916AA84,0xB67314EE8B4A5F1,0xD25477E80486C660,0x2A2DE7BCF6E8DE, +0x56D6E43C52BD27D3,0xD279CE375B457035,0xDAD23ACD15B33DB4,0x2C611934F6E94157,0x2F8E3B2D218E1CC4,0xF62702817E93820F,0xFCCB19E26FFF25FE,0x904D7FF560D3A, +0xB7A65ED834F6F16A,0x260CA4485C8158A2,0x8F8802EBBF6F0D01,0xECBB4DCB02F3FBCC,0x68FD6A7B16182915,0xEB9B623E1BCDA856,0x5C7D9799213D2DE9,0x2D424FF3B0C5BA, +0x343C78A6E771B50C,0xE26E0DAB0B462F18,0xC97491799F247BA9,0xC6CBE227F09D6884,0xE3A1A94AED9B6C69,0x8FC0F0BBF6D61067,0xF891AF6A747624D8,0x2F7E85E99DECF7, +0x912CB02186640490,0xB9EFED1B48803C93,0x8CFCBEBE2F9F555E,0xE477621ABAFF7B7F,0xE95A7C0EA2EA6F10,0xA38753D8807F91C1,0xFC063DCD93F73DBF,0x3AFA464C3AC6F, +0xC8429C712330C23,0xEFC9FD168384433A,0x744836F34EDF28,0x6F111074CC0ED5EC,0x342BA15FAAE35A98,0x4A7C81E411CD4D92,0x74DC23CD4691A9CD,0x10526427733F7C +}; \ No newline at end of file diff --git a/src/P503/P503_compressed_pair_tables.c b/src/P503/P503_compressed_pair_tables.c new file mode 100644 index 0000000..79d2a4f --- /dev/null +++ b/src/P503/P503_compressed_pair_tables.c @@ -0,0 +1,4936 @@ +/************************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: precomputed tables for pairing computation on E0: y^2 = x^3 + x when using compression +***************************************************************************************************/ + + +// T_tate3 contains 6*(eB-1)+4 elements from Fp. There are (eB-1) 6-tuples (l1,l2,n1,n2,x23,x2p3), each corresponding to a single step in the Miller loop. +// The values l1 and l2 are the slopes of the doubling and point addition to compute the tripling, n1 and n2 are coefficients of the corresponding lines and +// x23 and x2p3 are the product and sum of the x-coordinates of the intermediate double and the tripled point. The last Miller iteration only needs four +// precomputed values. + +const uint64_t T_tate3[(6 * (OBOB_EXPON - 1) + 4) * NWORDS64_FIELD] = { +0xC8958D5CEAEE9961, 0x15656BE866831334, 0x3DBF0E58FFD1403F, 0x2A2E6D76A5BD8030, +0xCB8B87470EB10976, 0xBF2B2AC3FF0E5842, 0xAA01464195495DC7, 0x3301FE417ADEE4, +0x1774317C1AE747D8, 0xF622B72338E21067, 0x66B109C419F65B51, 0x3D8711EDC6BBD998, +0xB63D65AEBC6BA7DC, 0x1291072426592F1, 0x1BD9936571211946, 0xDD17AD4188A2F, +0xF88254ED9673F23C, 0xFE13BC2A7A60FD32, 0x5C477D4791512FC9, 0xB60D285940223FBA, +0xD4F04D230B01D6D7, 0xAED3BA7AF814D35F, 0x50DE8541ED8EB69, 0x70D8A04CD0C5F, +0x8F6D06DEB1BEEBA7, 0x728845EFC2E41EEF, 0xC0899F1BE099641C, 0xB2D53A9A6FFB638B, +0x81DFFB91EE670A12, 0x7F6ED051EF6DD383, 0x56FE7CC0F271EBC2, 0x27A62D7A33CAE4, +0x52F209522A9A8F2, 0xBF15EC49DA5F9607, 0x164BD51C1FC2F4DC, 0x2E24296622C7558F, +0x578D487C382796A2, 0xAB9ADD2F0B1DAB27, 0xA71611FFD3196A6A, 0x1C93380BC6A35F, +0x6FEBC2CFB6E541F0, 0xA0E90B20492B299F, 0x58D1C7665561D204, 0x726AB02F7704DD1E, +0xADCAF51273B66C35, 0xAFEC72698D7A86F8, 0x6B938FF75A01AD1F, 0x25E913D3900041, +0x3D782D5FBF4E9D25, 0x8CE0A7CD3D244A6A, 0x5DE270BA6D676D73, 0xC7137CB67CD0CC07, +0x8A42A49B803C1B06, 0xA6C6BE61B5F9D23, 0xADB2D782169A7FF5, 0xCC514CA84D8C8, +0x494C083C726D319A, 0x6A7A0544AA7CFB48, 0x20BF934A99D0A326, 0xFDE6116074F7AFB, +0x9CF64B6FC92E8B3B, 0x1996D1A2E28860F, 0x9C527774AD244155, 0xCCAB220E2CC6A, +0x558C076E1F240A33, 0x4E11EA9EA5AEC610, 0xC5E1F18FFBCDBC66, 0xC9A0DE18266F12AE, +0x83E9A9054C991729, 0x64F28BF07DC4BBC0, 0x4F98AB9C8248C641, 0x380130CBD158A5, +0x13B583F5FE1445EF, 0x2E28143407376486, 0xC3388A75AFF33517, 0x1180CEEC3264360E, +0x9AA81B55A88A713E, 0xB0B585C6D4E7871A, 0x7727044C3A91B54F, 0x34090B82AED8CA, +0x43B9DA643352346E, 0x5CD80A2E547931A9, 0x52C64DEFA2869297, 0x42550BF0D51F925B, +0x7A5C596ECA3ED13B, 0x41315CCCBCB0EF42, 0x59A69D5A2907E724, 0x18FA7EBEF3D7A0, +0x17B4FF96AE5486AB, 0x98A04C523C0F8004, 0x7588FD11603A8967, 0x75D3A9FA885976C9, +0x319EB1383D272E66, 0x390D6ED7B9D98336, 0x4F178CBFE6278E11, 0x10FFD3C9A1690F, +0x59B95A5F65DC83B1, 0x611AE8D14E568ECB, 0x104FFA7B7F94B97F, 0xF0EBFF6D81837480, +0x3E0FC0257BF0208B, 0xA335B99DB95D061C, 0x3A05D7396AF06A4A, 0x25BFEFD95D3454, +0x777847DB261D0C8E, 0x316D64AD0DF8761E, 0x1F7BDFB78BDFC95C, 0x12D68D75520F6CE5, +0xAD8922594DA44BD6, 0x52D2196B26BEE2C, 0xF56F8AC4937139B4, 0x337B4607E54134, +0xE28F853A3580BBC7, 0x6AC658838B3D9CAE, 0x75711438ADE90FF5, 0x90B042B090FDD7E7, +0x396F3E95707FB6A6, 0x903D06BCB61F51F1, 0x7A89595551A0AF7D, 0x3823C2BCB4ACF8, +0x30FBC722A0A8D1E5, 0x5C20FB9E09682F63, 0x5EDA785D78735AC6, 0xEACDEFF413E25C76, +0x5B6CCE16AF1FBFFE, 0xBAA204B461C736D3, 0x3A2C5DA9681E38F4, 0xD873080ABDF7, +0x48EA7D1A8EAA38C8, 0x817C468377955430, 0xB36941B46040DF4F, 0xD4D353AC3A3506AE, +0x88875C3AA6E17B17, 0x913E3089EEAEA7FA, 0x4A756EC91340AE78, 0x23799D07E58FE5, +0xDB8BF50A3795D736, 0x91F358BC8714D0C5, 0x94653037769E2588, 0x71391585F29F6D3, +0x3323D1202F4B91DE, 0x1537C77A96148FF3, 0x6056A81907D4C433, 0x2121EC34AF435E, +0x215197FE6EA6E31A, 0xF99AD791E0E90BF1, 0xCBF0A844BC107235, 0x92998285C0447A1E, +0x7B6D6B57A26B0385, 0x163308F350FFD8A1, 0xD75DB0B3BD04C81F, 0x380259EBA432E2, +0x3A1B603C9748B921, 0xE442778BF7E68F7B, 0xC18D7F7912EB3BA8, 0xA97738AA6A94B292, +0xCA75DC8EBDBA768A, 0x9EA20EE8BE90961, 0xBFC40FB0608DDE23, 0x3437B4025F50CF, +0x59ADBCD79A4CD43D, 0xDFBB504AC907DE13, 0x1B320674C30D8AF7, 0x19130F0C4D890FAD, +0xA51C4182DE07371E, 0xD51E6A288043EA17, 0x77C9D0181A5D7095, 0x1474DCC530DE65, +0x2FFF407EA2A5AC4, 0x4C1F998FAE9AEA08, 0x1F18404A859AF280, 0x58D9E124B68B9102, +0x558683EE964318EE, 0xC70041AF357A5CA0, 0x7BF6DA77FB7FFBF4, 0x24F2DBE4601F9E, +0x410262939B802A04, 0x1C6C3272E99EA472, 0x2CA3BABFC6D7B31B, 0x1B27459EC0530457, +0xFBCE8F37D551AF07, 0x1CA4F10EC70009F5, 0x45E564B687157DF7, 0x2619882EC74442, +0x41FD94D3816493F, 0x3C43AD27D4DDE1BD, 0x8E6524D5E6F70274, 0xF124A431D2885B3B, +0x77D49DF03BF4ED70, 0xCB719BBCC7F877EC, 0xBDD570A4AE5F4E6, 0x35C1B86C412524, +0x5C27C52F336B093C, 0x760E352F13CE0F9F, 0x3005961C7E83724F, 0xB910D0879B11A93C, +0xCA6250054F49E93F, 0xC2B4EA9E521006D6, 0xCC7F250134D90E4A, 0x109F0DA2F06B04, +0xB31A22E737D960F1, 0x54F35A87C8BF3BAD, 0xB64A22864F9DE445, 0xE76935A149ABDCC3, +0x3A314D980FE6562D, 0x89CFE04D814E533C, 0xBC988C62FBD1175D, 0xE89CDC935EF7, +0x32AF9BC2289DB649, 0x1748FB4EA48F5876, 0xB59B2185EE4AE2A7, 0xF67B98DB2060ED3, +0xD6A0940F2E8DDB73, 0xFE11002C43D00FE8, 0x8FE34DB948A55EB9, 0x8FA142A65DD9A, +0x3A07B154D3BFBB8C, 0xA89023C326755A79, 0xEEEF615D4B42338C, 0x6F85FD4BDEA87EBA, +0xCB0A581FB61C8CF5, 0x5A3D9879C6DB166D, 0xED45C7CF88EE4C19, 0x22D56528470E3, +0xA13D9D61964CD379, 0xDA8C473E933BF48B, 0xDBFA60AC3B60F7ED, 0xE82F50C2AD350D3D, +0x36A822C9786ABF2A, 0xA590A2E855277A, 0xF40625E007D6CE4, 0xED96BB72BCFCB, +0x55DEF0577BBFE8C4, 0x550A31D9A1652217, 0xC72D388FF8569303, 0xD85B0FF4F21A2163, +0x344702DC9E36C473, 0x3A3738B89E55EAE7, 0x77BBD889350CF856, 0x20D9667170E607, +0xEE654EBBCFD99BF4, 0xA51754E593C8BD24, 0x9EE410583CE28A66, 0x959A3A1C0637EEF0, +0x25B018DB2AC757CA, 0x5C999C11E8BE1A71, 0x406E15821AEFD399, 0x23E566DBF968CD, +0x8B0556A8CBDD09A5, 0x29A330F02CB9BC71, 0x2C7A4CA49EE08EDA, 0xA20BC85C23DE7881, +0x2B008CB2ABA75ECE, 0xD9DAD51971C97CE3, 0xC299DF6E1090B2F, 0x3D366FA90735DE, +0xC4A80F061484271E, 0x57FAD14D646659E6, 0xAC47A7E1EE5915BD, 0x79228C14AAA868EC, +0x9FAB6233F405979B, 0x9FAEAEDDCD5C0B7B, 0xB1ABF3654CE77537, 0x2B7EB1000F0EEE, +0x1ACB510F9BDD6C9, 0x300626F7AB298E48, 0x19D4AB3BA42040D0, 0xF2244C65099634E6, +0xAC98B66BE249B8A3, 0xD54BFE9A19638B55, 0x38BB6F006099B783, 0x3EAD979CFAB042, +0x562B64097C0E3D15, 0x617A23EC3EAD0D16, 0xC16ED610D3E26DB9, 0x39CFD8008287C87F, +0xC086978264A3CF3F, 0x976297406CCCDE6, 0x4D29A168F4C24E5C, 0x2BC6550814EAEC, +0x21B04A0861AB56AF, 0x81AD267496B0723A, 0xD0A6B1330F2658A, 0xAA43D8AE67E02AEB, +0x8C758B566009EE53, 0xDB673CB9F69599D1, 0xC7817897B57ABC15, 0xD6E2530200C64, +0xF3BB67FB8D15AEB, 0x6A373275A0F9691D, 0xC82F999933CFDCE7, 0xF3C21A92123729D3, +0x2AAA8D42CFF0166F, 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0x30B7CFFE411326, +0x4AD803219AEA015, 0x3B127AED74E9E6E2, 0xA1B372DC9EA15C09, 0x66104E6C7DF26B58, +0xB0CE79CEAA320AF2, 0x96AF9F8DD1AF658A, 0x8137A8794E772FE0, 0x16F36E5CC82192, +0xA248F9A712FC0334, 0xFABC190A39DB8D58, 0x6A02F0A7A4A35818, 0x473967E98A1ADC3A, +0x430DDB76CDEB9D9B, 0x4F2EE227219D8B73, 0x34F82CBF436DA16A, 0x35ABF270F9B859, +0xF3C5BE4290AD367, 0xED0365BD00803009, 0x78560A61C5EFCAED, 0x492093FE7B818F3E, +0x70BDBE48D8841644, 0x96635901DE8FD7B0, 0x1A89B1784B12AA52, 0x25109649384628, +0x2011DA342AABE4F5, 0x382CDE111D8F56BD, 0x2D9018C8ED7CDF3A, 0x842BD9A95C4119E6, +0xBABEBBA8BDA512FC, 0x63764C8C023EE439, 0x7B2CD5A52963D9B8, 0x5675588287901, +0x364705CAC2B9E31F, 0x963501D713DF38AD, 0xBA575E9986DD6C80, 0xFAA3E9DA370E4E12, +0xE1EF838042543A94, 0xE20081234EF456FD, 0x14DAEAAF6EFD7D11, 0x1EC2CE718A3EC2, +0xD4771D5ECC381EA9, 0x10A20021D425B7ED, 0xE60FBB275A22C6CA, 0x6732C6FD0836D17, +0x79B3EE79BAC2E4, 0x6783645AD86DF950, 0xA1EBED41E9A54BE1, 0x2D1771D5777358, +0xD5EEA9841C7BA200, 0x8FAF2AC75417114E, 0xFBA2266E67798488, 0x8ED17ACBCF483CA5, +0xB9034E006419C405, 0x20CCDD4E5AF18868, 0x5A79BFC89466B013, 0x273D781F6DC679, +0xA58C50E6B57D8223, 0x1DC2B7FC09D1AC0F, 0x5F0A1690F731EAB1, 0x73A3024D44F7E4C6, +0xAD7ADB9CA9424E51, 0x9C81A715ECDBA06B, 0x5D17407821590129, 0x8F100FBEC8A6, +0x66528367A9F40798, 0xEC9E7778ED29211C, 0x690D671E36B643F0, 0x2A9F229689450856, +0xA2B92585F1D8862F, 0xC029B63C0755CC6F, 0x6DD0BE9D437BEE07, 0x115CB39157EA4F, +0xED374F0AFC9ABD7F, 0xD078941413D0F4EF, 0xBDC4CD48B58A34A6, 0x2B35D43376FF9510, +0x72C7DCD49E00991F, 0x1479364B573E5AC, 0x3C061DF3ADBE3130, 0x2AA23122F56111, +0x99B2AE22BBCC28DA, 0xBFEC81FFADC6EC30, 0xE1401303CDF33BC0, 0xE650107832288D09, +0x2044562384E2F0BF, 0xF02F2F05C83C075B, 0xC68724995FFD394, 0xA9E9D2B8C94BE, +0xDB33B34A10888926, 0xF2D0DA74613B1D1C, 0xEF68956ECD83A03E, 0x84518FA4351C56BB, +0x328AAF3AB61BA04A, 0x57FC7A343D5B74AF, 0xA1C871D002F1BEEA, 0x348341CCA32194, +0x7F5EC5B888B9F865, 0x9E5C9E22D66CC5DE, 0x6525CE2F727A1015, 0xDB8325B20C320F36, +0xF89EF08798378634, 0x39E1D4A39E714E13, 0x67357AF27E9F3CD6, 0x20348CFD0EFE4B, +0x7C9241B464165481, 0x15F85190C4F7D5E6, 0x78B9C23B339FF7B6, 0x39614CCE4CE2CE83, +0xBFACB512355C8F8A, 0x2F49FE11BA9C6809, 0x7CDFD252F09C197C, 0x120E9EB6761AFC, +0xBA5F153D0AB59BFF, 0x9072CAD46A1E59BF, 0x775D5DB04F989048, 0x98DE6DAF455DD684, +0xFC80EDF40678F837, 0xC0472DBA504A75EB, 0xD0C9588234AF4436, 0x369CCAFDA69382, +0x139F6A61F2E4A98B, 0xE332FE2085106157, 0xBC57CAEE869F816D, 0x6DEECC5DBB591660, +0x2BD39864D3850D4, 0xA7F9C7F7B1320CE0, 0xEE1A72C0A1A8CC8B, 0x2C9B648E485241, +0x85F50F2868AF152A, 0x8BBCC9945859D4FB, 0xF60A234877AE9F3B, 0x523530E9567B73F5, +0x8C9A49760628D5F5, 0xC93E1D8AF2DD7BEE, 0x819178A8E7CEBDC2, 0xB4A097CA258E, +0x3612D264B4725676, 0x5D7BAC06AE94B7C0, 0x10AABA2A5F15FD79, 0xA7BD19CBA25A6394, +0x129864CCD972F4AC, 0xFE3EB380055473D8, 0xACC358640642C937, 0xADE6C3102BBDE, +0x7356C641AB543BC8, 0xFA35C706BD5B9D30, 0x5BFB0B59C014402D, 0x395188374158EC5B, +0x743A219DFD2E63A4, 0x339759CDE854A98, 0x9AB65D7F129B8934, 0x177622BDF2DAF, +0xEF68F3A169AF128E, 0xCB6CAA002759CFD8, 0xDD7B7EA14732B81E, 0xD5A5CD2735175146, +0x59FC41486CFD5743, 0xBA0706C64FD4C9D7, 0x352770138259D369, 0xCC3EEB7F475AA, +0x633B1A93CC9A599E, 0xA0D8E8676E93D37A, 0x442B24D022EF33AF, 0xC7929F968F907A7C, +0x7A0E256C43F4148A, 0xADF9C85830E93578, 0x7FD8CCB35B764628, 0x1A15602F5FFB28, +0x19A4FA8B85928919, 0x4B27C6942EB897BF, 0xBDAB4D549F06CE93, 0x6007D16CA5610221, +0x8A59DE2796C40195, 0x3762F014B088C4B4, 0x29997AAB63EBB7B8, 0xB4F034CDC3BD, +0x30552236DB32D68D, 0xFEC3C7B9ECD181FC, 0x4E3590DF10CA8896, 0x5C9CAB3B380B57D3, +0x6B20E4ACC1A218, 0xB580D9E8D4FFABDF, 0x9C4743BD4086AF5F, 0xFD322D9F3FD84, +0xAEE7ACF01B3EDCD3, 0xDCCED786BA3AA8F7, 0x5F5D3823DC8585D2, 0x1D416CA9A3ABDF01, +0xEA91AB88345237F0, 0x852E19ABC77B57A9, 0xF32CE825D352BA43, 0x20891B2ECB9492, +0xFC621D9694F86FF8, 0xB1BA185A3ABCA920, 0x2184C4BE6BC533C1, 0x6E695597FB6F2927, +0x77B2AAF092E92F14, 0xAFF1E40F88007EA0, 0x3081ADEAB631F670, 0xC1EFF74E15585, +0x48E51512BF3D46BA, 0x24903B794C62D4F7, 0x8D86469E68D9DF0B, 0x2EC50BDD1338704D, +0xE5572ABDAE3B8467, 0x884398292EC3F8F9, 0x7D84E7C31F8DC84E, 0x19A46DC94F19F3, +0xE656202F676F6C40, 0xCD8FC839052033A4, 0xAB143FB3256F4C51, 0x5A97FFCE66B1C257, +0x2BF35CF67FAF9F07, 0x17A8AE8B521B02F3, 0x8DBFC8929D2EEE05, 0x20629FF9623D0E, +0x93BD99E046E9911B, 0x15B9DE0502C6E79B, 0xEB42504C86C8303C, 0x1B956670A4C32F65, +0x1473DBC179311247, 0xD60AFEED3B65B487, 0xD5FC98D115B8DD15, 0x3773E18AB36630, +0xEB824734D2473888, 0x8146C5DA08388822, 0x8DFBC6CDE26325F4, 0xACED0DCE8ADEB80B, +0x5F8469180FA11791, 0x3E002FED2A4D7ADD, 0xD018400BF0022613, 0x5B63BCFD85195, +0xF9652105CACB8B73, 0xCA5B4F88BB963C32, 0x3FC224B1E5F5ADEA, 0x30E94D86F8359FC9, +0xCCAE232C6BB25801, 0x2F984EF62E4C643C, 0x9F1A9B03F550856, 0x3056D862D0FF96, +0xAA6FCA1A7DB3B9C1, 0x8D12C496B3D530CE, 0x909089D6DB66CE9F, 0x26979B12182E911, +0xD838DEA96EFB14F2, 0xC70C12A9DB5E8DEB, 0xBB4D79F4A6E1AEEA, 0x2F6E7532C0487D, +0x565D24EF17871BCA, 0x5547441AA7195322, 0xACA179D99F24388F, 0xF764EBCF575D78CF, +0x6890A45614A3A134, 0x545AF60FF4DCA38, 0x4730B86C7FC40E22, 0x25DC757FF39EDC, +0xBF8E2EAE49386E91, 0xB99940C92BD7882B, 0x60C7FB2173F8D4DA, 0xA764A666D970DBC8, +0xBFF3C598783486B7, 0x8431A95843DB6C8, 0x3CC7639BF98D01AC, 0xCA9360BFA6359, +0xAA6FCA1A7DB3B9C1, 0x8D12C496B3D530CE, 0x909089D6DB66CE9F, 0x26979B12182E911, +0xD838DEA96EFB14F2, 0xC70C12A9DB5E8DEB, 0xBB4D79F4A6E1AEEA, 0x2F6E7532C0487D +}; + + +// Precomputed values for the first Miller iteration of the Tate pairing on the +// 2^eA-torsion of E0: y^2 = x^3 + x. Contains a triple (x,y,l1), there the +// coordinates x and y of the double of P are in Fp, the slope l1 is in Fp2. + +const uint64_t T_tate2_firststep_P[4 * NWORDS64_FIELD] = { +0xAEC40A3D269C8FEF, 0xC901D47D0A3E4250, 0xF92DBCF459BDCB5F, 0xD1FCEC504243AC4E, +0x35513B7F3D8DA9E, 0x4BCF1E8DFB823BE0, 0xB644A35C2747C746, 0x1387681059CD8F, +0x6A2A72A338B50096, 0x8060F6343072AE2B, 0xA41CAE35AE87535E, 0xD1B133E259ECD08F, +0x51410B1347F9CF32, 0x2AFC37844B4AB202, 0xBC46C5B8E68E0B83, 0x11FB79CDC2C0B8, +0x4F5496068AC8BABB, 0x2650DB615718D577, 0xD0B19FC68436E291, 0x243E6839C95A5B7A, +0x300115D56D3DF938, 0x5D16DD7EEE5A01ED, 0x2EE0160F48638C9E, 0xC5AC73FE3B483, +0xFBD0D3459E1F91EE, 0x81858CC7C1478D5E, 0xF96E35FDC26A7257, 0x925AED6C82566ACD, +0xFA2BA728C44C8FAA, 0xE6F6402117FCA3C5, 0x58A8F674A28C12BE, 0x2BFFC6D4ED3CAA +}; + + +// From here on all values are in Fp. The table contains eA-2 triples (x,y,l1). + +const uint64_t T_tate2_P[3 * (OALICE_BITS - 2) * NWORDS64_FIELD] = { +0xE15E54C7E1BF6AE1, 0xBBE023A52C58B9BD, 0x4773C7868E2AECDF, 0xD0F31194C4F0F0A6, +0x9B6996444464D978, 0x65E876D83C354F, 0xDA6CBD8E40EF5ACF, 0x15CCA1A19B1051, +0xEFDF6E4E6C0536E5, 0x649BB3639B1EAC0C, 0xC18DB1639A6E0FA3, 0x6162920D5DF367D2, +0xA709862B237844E9, 0xC50C4249DB3BD4E8, 0xE5D92B58A4AEA3BD, 0x29697FDB257476, +0x3B872D3AD7E0BEDA, 0xAAAC956261023780, 0x70190ADB81D6FABC, 0x4E1CE92ECBA70616, +0xF500301D56BCEAC2, 0x87051A2B36A943E6, 0xD63B6735CBC97B42, 0x1ACE03FE60013E, +0x66AF64372C624662, 0xF696F2290E102519, 0x41F369211B7B7552, 0x9A322E5A79C55355, +0xC7D1D9FA4DE54101, 0x717587C03144A77F, 0xB32C380222BB1B21, 0x302D39CD6ED1E9, +0xAEBB7B2EA3FCEECB, 0x53D3CA97FC288CE1, 0x7A398038449AA9B6, 0x7CC60D7C50D8AE90, +0x36973C257530E81E, 0xF1C27F812B8AD4A4, 0x1430510471B0B075, 0xFB3305F079FA7, +0x6DAA239526566852, 0xB2995FE00B68E765, 0x8593F0492DE80A85, 0xA5CA6D4055578C57, +0x532E561A76D8257A, 0x28EBED3231F7F11E, 0x62D6F52397EF8068, 0x28E7267745552, +0x468BBC2D95772E19, 0xB2E1C62CA88A7120, 0xEB10936312056DA3, 0x806C9EF9B1561726, +0xE72249A802556594, 0x80ED06392AA902CB, 0x4CE543889ED8364E, 0x27F87C1458480, +0x69E441ECF8772463, 0x9DF9DA550F8E6201, 0xA53686138BB14EFD, 0xB84A64E46493ACC7, +0xCFCBB2003A302D56, 0x5C02C10EC256DE4A, 0xDC60F48476A2E8D4, 0x395CACD38AE3B5, +0xB87F059172C6ED76, 0x2932FDFCCE69E4D0, 0xB416F82BD24B0FA, 0xB6DCCC6B4E8A9CFC, +0x93701AF5335830AC, 0x29F75A15087323B7, 0xFF003D2F00D8D34E, 0x3A26CEE191368C, +0xF3EF2C0AFBA895B8, 0x6D45204E9C4D19B9, 0x28DBE2644D7528DA, 0x38E371EE6E15EFDD, +0x127CECE338AB45A, 0x13D4C7E1893B91F0, 0xB962D4CCBAA4FAB0, 0x16D176542EDE88, +0x42203947D6C06948, 0x4BB905BF6EBB203F, 0x2B7BE18BA628ACBE, 0x72B234EEA79086C7, +0x5160DCDBC5D7E8BF, 0x2FD811B105ED10C8, 0xF9DA215B8DFAC028, 0xF625997335100, +0xFF17C2F57ABB9030, 0x54DE338756C482A2, 0xFA364465D449501F, 0x9175FB41E0496DBE, +0x166DF21B0335172A, 0x19187B7174B5BF20, 0xB0741C7C46FBABB1, 0x25BA7896023A07, +0xFEFFC7D2AC702A6E, 0x59CE9CBAD2F27073, 0x113DA67315FC5E2E, 0xD76BF86E8CA8DB50, +0xC9EB985911FC4FE, 0x49069554D8B3C6DC, 0x41A1C5BE8B94E11C, 0x257E4F254EDD01, +0xED61E2ED61F58EFC, 0x41C3760267FBC88F, 0x85CAE320285D4075, 0xC6B780661903771B, +0x94D0C0810B0F72EA, 0x3DF026AAB87F4582, 0x93F673FA15A9D880, 0xACC3C203E7351, +0xB42AEAC8F7D6E27B, 0xBD6409E19C8019A6, 0xAD50331C834B566D, 0xDAD3689BC01AB78, +0x32C457DACF80DFF1, 0x224F6C8340B17255, 0x8841166DBB02149E, 0x3F31ECF46340C0, +0xF18441D4124FDE87, 0x3350ED0247BC0F93, 0x30C8FBAFA5DE4AE1, 0x45753E34C9F8CAF7, +0x63514595E095D04E, 0xC07ADE75971DE0C, 0x7CAF53BC83C4FD5E, 0x1B1752B7623A1E, +0x54FF46192257CED6, 0x401B2CB2E4EA9C35, 0xFB92995B7BA05295, 0x333B487DC95D7D3, +0x47F05B6B620CA279, 0xBD79CB7931683638, 0x65C0E17D2DDE2BF2, 0x204550CCA8F1A9, +0xF0939C1464755345, 0x719FAB828BD4584F, 0x202ED13B395D9A6E, 0x47A80BD43374AD35, +0x4101CC3E3FD46C8E, 0xE1B571BB2650968D, 0xDEB1D79F1370DF78, 0xE5919C57A925D, +0x541BEB354356A59E, 0xEB6F34C2C221E394, 0x59819227414959E0, 0x48ED4FC8A982379, +0x4F70CBED553F2465, 0x2E9C67D2CEFFC9F0, 0x9320E7440CECEBE3, 0x169264BC38A393, +0xDDCDE127F7786D1B, 0xB1547D524EE3F5B4, 0xB7C90DE3E6C5A4CF, 0xD120ACB3A8D1E78B, +0x73109B5A0C8C81B6, 0x43D3A78713601B46, 0x6EA91624375C33D1, 0x2275A20DD0F9B6, +0x10DC9C67F752F6DD, 0xD374D09CDE8D0636, 0xE841BB01CBE857F9, 0x8E6E1C3FC97617E8, +0x663386301E371F4, 0x620AC2ECBCD0F210, 0xB9FC4B559E6D1679, 0x1A84D56A203C53, +0xC3140AB54B0EA626, 0x350A5021A22B7ED3, 0x32FDC484C8A39896, 0x5906F7BA27D83AC, +0xF48EB70C4659CA80, 0xFE18D249DDF54EEA, 0xFF3932E4A2C9AB91, 0xB2BDCE81EAD63, +0x7723EBFA12852698, 0x35317D2737EDD95F, 0x93118E00AFDAA29, 0xBB8E773126124A98, +0xBFCF8A04A71671EE, 0x2583A77FFBC73C7D, 0xC65A1506078DD6BF, 0x3F591B9B315F78, +0x8D96EC7B17C33B63, 0x1629EF29EC637531, 0xD29F473876086E9E, 0x78AC820EA27CA6DA, +0x65242C0BA614DFD9, 0x9026FE6F40536C3F, 0xEDC685E952B61740, 0x104B43844D672E, +0xD90E6480A3D0338C, 0xF27B240BC2B47195, 0xE7AB41432018AEF, 0x2759024B28277E7, +0x98839685CA190A0A, 0xE01E8C369429D5D3, 0x199E73C5E0764E75, 0xAE85D34F87FC5, +0x8180BAECAD2D95ED, 0x757F3E2E72B7223D, 0x6A524E49C732A555, 0x7F09CFE7F3ED8E79, +0xE299410DDE3848AE, 0xDBB6C0B3E9DC1A15, 0x4E5A9E4381CDF2FA, 0xFA6C13B498AC6, +0xB94BC01EFFC7241, 0x5934EB3D0742D36D, 0xAB906E08DD6C95D8, 0x7F754AE680FC9348, +0x9B805513A2C4EB18, 0xFE6E684DB6BE15C6, 0x3D461BAECB444065, 0x3E4589F0CF6657, +0xFE9773AE0CCAB40C, 0x8B8D4183DAC892D1, 0x303ED6A006012B62, 0x543FDF8863221EA2, +0x685DE9BE01CB15E7, 0x3BE65844FA2EC03C, 0x5D0B380B54A6FBC6, 0x303761F84C8DFF, +0xEB673F469BBEDC35, 0x7D0EC3CEDBCFFF3F, 0x9EC6E3E2F93A8327, 0xF3C345078E0D035D, +0xAB3010C3EB051645, 0x78F1FA0B868103C5, 0xCF970083593EF175, 0x2837E8F43E261F, +0x6C91AEFF22E99502, 0x2BBF067C8577B4E7, 0x813886523F7A19DE, 0x8AD6CE1F64DB3007, +0x447F06C6248A1604, 0xD15AAAE2ED3A8A6A, 0x284188CBDBAC1FD9, 0x10F5BF9DBDD49A, +0x2DE4B9D7281CF59, 0x86FE4C992432A428, 0x1AB88AE7A8D8746B, 0x1A99FC14E55D4E4F, +0x821D34ED734EDAE9, 0x3E82D47EAD64052D, 0x152B70F4A4C31142, 0x1E3B40AADE9355, +0xDEB33E75EBA16598, 0x870E35EE440FBAE7, 0xCC95E3809C694B70, 0xD15B0620C34851C, +0x176D52306FB9DF6F, 0xD7544F9CC04DB893, 0xE5C54205DAC38489, 0x39AEA9039DBDF, +0x5E632A108F996BFA, 0x92FBADF8465B9DB2, 0x60A4C123D378619, 0x2B659207E80244CF, +0xCA891F118A2C6DAC, 0x17FE4F9123B9EB3E, 0xC4A161771F33CF44, 0x33EF5A1AE1046F, +0xC85AAF1294CDA307, 0x65D11275AC77D8B, 0x57635D778C0C73A5, 0xD7D10390AF4009D2, +0x7D582C16FDF86FBE, 0xDFDB7E204D69B52A, 0x7F9C59F6F32EF670, 0x1B9CD228B30FD9, +0x849CAEE5B64618A1, 0xADA0CC1A2AFE278C, 0x271E9E0BC8C529A3, 0x56B4B88631584390, +0xC7B8A2E97FD23384, 0x8A867C6CD1CDF122, 0xA1E040315001939E, 0x1115280F06D680, +0x889F9CFF478EA3DD, 0xF3F7DB1DD1560A57, 0xF5385C325AD9CAE6, 0x7B5A9E3A75AC080F, +0x13A9E90AD8AED44E, 0xFED2A810E4107104, 0xE8D41A737013F7D4, 0x20E4C39F6CC64, +0xE9904305CC595E34, 0x507F09FC05DF37EC, 0x97A2F0F6FCFE8C65, 0x48B1DEC2DF99EF7F, +0x324DB7D20FEFF200, 0x251B93E5BE3289D1, 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0xBB5D8B9A4CD9E1B6, 0x2A3FF76BE4C221, +0x2FC7F14CB8DBD522, 0x7AE4C5F5357C6609, 0x4B1E2E3743B27E8E, 0xCF074325A98D7923, +0xFF3FD435E1638180, 0xE861A2D529E203E5, 0xB8762C9344F6845D, 0x124E887DCCE057, +0xCED385CBD5C9E783, 0xEA683083EAF8E56F, 0xEBDAA67FD155292, 0xAC0F997B58E6C3CF, +0x9F54A2E39DEF2E9A, 0xDB822C8FAC33EA4F, 0x3FBB722693535E76, 0xB2187CA097BEE, +0x2CB6BF2A9637161D, 0x2DB144BB0D694018, 0x24C67A2F1F7F4136, 0x3F696AE6B78340C6, +0x330025E48FC265C, 0x7C94C33FFC74D76F, 0x12326E8B0C6DD6B9, 0x3FAF416EA7637C, +0xEE06FACCE7CFCE76, 0xA15A6C012A143581, 0x7E777001191582BC, 0xCCB204A40E62CB2F, +0xE3080B2462518A5D, 0xF84872AD413DC5D2, 0x68E7CC15CCF69371, 0x3E98DA9DE5A9BB, +0xC851A6CF483DA816, 0x2A1B4005D4FAD2AE, 0xFF2B47C57EA4E0DF, 0xFEBACE6FF1AF1777, +0x70E8F47215607F99, 0x5926DC818360265C, 0x3483DAB66AB6EAC3, 0x321C3D75D2D916, +0xD75C5214121877ED, 0x924EEAF7BE22C198, 0x748F4F8FB7B2970E, 0x165BF3843CB47D28, +0x1C3920E2138D17DC, 0x2F5E8E2D6726F3CE, 0xBB17ED78C94E336E, 0x21D184F2413119, +0x4B440DFA95AD7F4D, 0x8E06AEC8A3324C9A, 0x776722DEC5ADED4E, 0xD2FC6EFD81FE3084, +0x2A1B79DBBE448845, 0x912A8719D0BDA80A, 0xCAAC07C4C7775BA1, 0x8B0B0E0189EAD, +0x66270CA73B796CD7, 0x783CF42ECDA34DED, 0xEC6DE1D7354DACB4, 0xF73D914ACD4A2A66, +0xB83119669AAEA264, 0x7429D9F36657F492, 0x96632147E62B966C, 0x12E66B895305F7, +0x5B80667254A592AB, 0xB71AEF88FBF9F606, 0xB798CF330072CF89, 0x516B1A50BAEC773A, +0x237616F2F15CEA18, 0x559761AB47194203, 0xBC6B1B50AD83AD0A, 0x3AC206E23E1CCC, +0xDB8C53C65D05917A, 0x31A2183C5CDAA49F, 0x9EB2800F95566346, 0x45653F022788ADEC, +0x5F362ADFEA283A2F, 0x3CE597FE0387AD5E, 0x9B3EB20DEC97E4B7, 0x355BC9CC1645B6, +0x5FC25BE4716A9B73, 0x23559011B3331F92, 0x9CD8DCAF28793B2F, 0xD0258D3F4F35EB5E, +0xF9E7F175DFA82C33, 0xA708544114536C9B, 0x93D78E9B98FB4F05, 0x1CF2A5E4290356, +0x18A9778FE95D3B88, 0xBEB84B5F58E35360, 0xEA75D1ECC1D9279D, 0x69FBCD5EF57B8738, +0x2767B1B2BB60E09F, 0x8EEC6F75B7714B71, 0x7908225F04AE3CCA, 0x9F6537B454193, +0x96E122751EEC6A9B, 0x66DCA93565826745, 0xF6BDE0DCBF7452A9, 0x5988008B2D03B02, +0xC625B54CE6DD5618, 0xBCB7BB6888D993BF, 0xD6DBA33F03FB2481, 0x34102E96B804F6, +0x1A262D31010051B0, 0xEE2ABD5AEE8F0AF2, 0xB161A380FB46F6FA, 0xB1A9B198ED72D9C5, +0xC6317D896D1E7C2C, 0x8D745EA65CA029D3, 0x7D5DFD564A8E4BA0, 0x14A06940896B3E, +0xE3611850E445542B, 0x59FC6E330B4036FE, 0xFE7E25498E723FD9, 0x76556269ED0417B6, +0xD0A81CBF4B18DD62, 0xD58A9744B5844554, 0xA28B72E895EF4DC8, 0x371459525FA15D, +0xDBB716892E46CF36, 0x491F6A0295DC6058, 0x9A91F876794893A0, 0x22D0F37C83FF2A8F, +0x54D0F524BF4B3C29, 0xDC12596C35098CDD, 0x16D60675A4724844, 0x12A6667BCFF443, +0x44DDA42510C9F463, 0xCDB409382D930CA2, 0x74CA40002DDAD19F, 0xF4D49F9640B3A84A, +0x789097C3C9DBFE4F, 0x670084653218197, 0xD27FDDBF2285F0A7, 0x38FF2F47BB4043, +0xFD4FBB6379CE7D04, 0xAC71A42222C0CD1A, 0x49E3F2B5BAC5AD30, 0x44CE7BD50186AA92, +0xE418F0D809E35307, 0x5EBFEA43AFE48723, 0x41215226A36A2D94, 0x48F0750A31AE0, +0xB192C198C942F93E, 0xC1FE4E122497A11F, 0xA3E666DDB601D122, 0x9D3B1E4BD8A42201, +0xCE7DC1080C876DA3, 0x793135B80200E7C2, 0x4D0CB90A78C893AD, 0x397D7573DB19B8, +0x4FEABC5543CA4EEC, 0x632DBB55232B201A, 0x86D767840FED4818, 0x98C3D439E9870915, +0x8B359B227DAE6DA5, 0x51E09E10A2964BAA, 0xB9B01646D180C3A1, 0x17B717E57CF2DB, +0x38585DB4436B2322, 0xE1F46490F42D85FA, 0x536B5062B93BF41B, 0xEC48915CA8A837A, +0x5ACD711FC9EE441E, 0x5DA2694B93B7594C, 0xF13F56A7AC858172, 0x2BC59E609A529D, +0xCBF18AA402150616, 0x5B340DCAD2D76D2E, 0xEECAACE002125040, 0x21AEFFFB8766AC4, +0xDA400C1733763C1E, 0xEE6C0573C5076EE7, 0x2F0BAD7E6467AF8A, 0x3240528CB38E3F, +0x3127D9EBE2965B5A, 0xB1C7D7C5E6F4C16D, 0xA823927FC33E70A9, 0xBC7CE44D996DBFB2, +0xFEB8576991650DAA, 0x7D8114418CFF2DB7, 0x2A6B22A74FDEC85, 0x2A3EF36E60CAF6, +0xF1FD80E6F0289D57, 0xE9BC8E9B75BF993A, 0x81F423EABB202915, 0xDA0D616810DA4947, +0x4868042A078B4A67, 0xAD472A9D3D9E4D7F, 0xF173DB1BE5FD6B67, 0x2ED99F229D55E4, +0x207A86AC5A3302EC, 0x98F7E8AC8986C1D2, 0xF845A1E1CD25235F, 0xF4CEA81350E5FBC0, +0xFC8248CEABEDB8B4, 0x6012FDFC2AAFC9D5, 0x90E4604C4EDBF288, 0x11718BA3424E5, +0x477E1D5140841A8A, 0x700FDE069A778B7C, 0xE4550563D5460F39, 0x1D98C40D3D50884E, +0x47B9516BB969D615, 0xC69B41B795BAD650, 0x801F27D2AA632CC6, 0x1B85A287B22BE6, +0xCEBEA794E5EBFB99, 0xC3CB84134D81CEDD, 0xA4768B92FCA3F853, 0x26907CC33E383B83, +0x67051B01DEE8D620, 0xA68FADA8251E53B3, 0x89C564DC2C89669F, 0x22FA0FD2990075, +0x3BB6AE42F3169FA4, 0x89F4309FC453823D, 0xEE86BB406176A768, 0x94B89AF9737BEB87, +0xBF6A603823F02E76, 0x61A1CA522802FD36, 0x51CD7464AC883E51, 0x643B230A01A4A, +0x57D33E4E4B602067, 0xCF7388C77A9CC1FD, 0xC3F9F80CFB7A4D75, 0x7C968AAF75ECA7C4, +0x295EA90D8242A1E2, 0x8A0691AA45BED0E9, 0x649142FE7FCB581, 0x12759741A959BF, +0x692051BD1AFAE33D, 0x741EED4CA5FE84CF, 0x60DF37006E48801B, 0x42D7A7FF449B4186, +0xABED0A24AE308180, 0x7D852F3A11D1672E, 0x574E76B34A8F8D59, 0x21963866ADFECD, +0x5B8849921318DD07, 0xDB388953E12106C9, 0xB0186BFF2C172ED4, 0x8D021A5A501CF59C, +0x60769B3C3C4B5F51, 0x47E94467352679E5, 0x7A963E251C933A6C, 0x14D156B4ED2359, +0xC91EB9501ADE5584, 0xE6A3730836663311, 0x9F4BE3F1B86FBA05, 0x32EF4AFAE436F37C, +0x81A95F357E59CB60, 0x86ACAFA64461AB42, 0x9335BEC52E6DF854, 0x6BD43ED3A8763, +0xE4DF3A317803A47E, 0x2DE4E28249B668EA, 0xCDADDB2D2C486D85, 0x63CE86EDB349C1D0, +0x235927C0D81FEBEF, 0x4E8E7FB04AD5E1AD, 0x1897E39DEBDABBC0, 0x240089C34BA61A, +0x24D177980F692F00, 0xC800C45DB8E57D21, 0x9C52F93E3FE21C24, 0xA0F8023DE96F8BED, +0x7F131EAF0151EEDA, 0xE322309781340EFB, 0x547B6343A88E2B2F, 0x17C118BE89C777, +0x13598CF2892BC6C2, 0xAB7DA12E2F2FC734, 0x5E0C0D69DF2A5A3D, 0x2C2023945336CF75, +0xEEC09C0D4CB46E73, 0xC8964C9657F29DFF, 0x2A6B0FF457209735, 0x85C93E4D5259, +0xC451CA144B4EFA82, 0x10A3F56DCC62B12, 0x73E9264875F0EA4, 0x207166B1A7452203, +0x7A9C3E44BB41505C, 0xBA133E768A63FADC, 0x296F9604A44B7AFF, 0x20A55F6128F55A, +0xBF610B6FB52E1DB0, 0x91F3203B0875205F, 0x497645CB6C9F70A8, 0x257734B956B9923, +0x670B028BA3E9196E, 0x326D91A3145F8244, 0xE3F11602051EE8E1, 0x6B8F1047A4053, +0xA8501000BC480776, 0x4FD7CB82693C403B, 0xBD4AD98AC34CA6A6, 0x199BA22710A86AEB, +0x3DD8E8CC5A8B2870, 0x25D2370C36FC23E5, 0xD7F8BEB5FB9452, 0x7207CF250F345, +0x349D07C84D8D1ED3, 0xB67A29115CBD65F4, 0x4954E43D2A8A790E, 0xC8A6924649DC5CF9, +0x1285FE9428FBC3A5, 0xEE30554ED7E6EDC9, 0xCB568AA0E4FF6B01, 0x1060B748841C08, +0x7B58DCED84780B47, 0x6B6C14FCBF98C90, 0xB2E8D725668EE1AA, 0xF196D3912FCEF04, +0xF89FB34163CD0D0E, 0x37DB5E81FC238CF6, 0xC5721E4D4D0E82F5, 0x36C92AC0527A52, +0x1DA6A55F9582951D, 0x80E28B3D4DA77A72, 0xED558FF9883CF6, 0x62DDBED0AA59985A, +0xD4F6786DBB4F088B, 0x44AE2026C2884CFB, 0x23D1A1E456061E6C, 0x10B0BC75341D61, +0xF466F60AF65532EB, 0x82077D7C185A79F8, 0xD1277A0796348B3E, 0xE7CB5ED03B288DFF, +0x137BE7C37484D751, 0xFB35800A9B1FFB4A, 0xB5F82469F742968E, 0x41CA1761BA250, +0x613CB00507B423FC, 0xD2984D57450FC9A0, 0x6B0EA24CBFF5625B, 0xC5A7C2CA0DCF1AB1, +0xF832FD36764C72D0, 0x67D747EFBA98A4CA, 0xF40D39FD06F2B09F, 0x2D3253701E0875, +0x640D0B7ED2040A18, 0x6E69B17628BCF469, 0x713ED3A3F801AF4A, 0xA269F921925CD9DC, +0x577A29B48205D0E0, 0x29C2E66E71AAE2CC, 0x2E985D266C9036E8, 0x58258BFF58EAA, +0xCBD778C5BB434D69, 0xFA9FCE8561DAE905, 0x545AB790010B1322, 0xED6923D780971672, +0x4F13D21FF2F41AE1, 0x50A4918CC107AEE7, 0x5999C125A9476B85, 0x3B89E7DB44AEE2, +0x7C60A6213FD93E67, 0x8A80A06925A4C403, 0x830698A08342FD62, 0x7831B8249CD6CA0, +0xEF6923F19A4F5E3B, 0x5C65EDEC8F6BAA7B, 0x479662E847FBBE5C, 0x25AE05A40A644E, +0x3BCA8F118FE5C56E, 0xA1F2B27B8BE0E1E1, 0xFCCF54306E5D7385, 0x1AEE6DD57A750F11, +0xF5DCC41FC69C75C2, 0xC0AC6E4896015546, 0x2F80752B8A3A5D09, 0x215EA4FBD4523C, +0xC7398F0D12FC3A2F, 0x2751D507CFB1BF47, 0xAC9E1AF3DE9D43F, 0x5406D5631941F0AB, +0xDA1FB2B7DCCE6D55, 0x607C999F04451B4A, 0xC2C87FE3CD30FF08, 0x12BA80DC37E685, +0x15BC795994BB700C, 0x2A9E086B8E1D9687, 0x5259ACEB963FFA17, 0x38BF1665794F1824, +0xDCCD88FA728967AD, 0xC05BF42047244590, 0x38EC07C9692C939B, 0x7153536A190DA, +0x87AF4E23452D1D33, 0xCFD4696764E7DBF5, 0x715556542E7E0D4A, 0xB4DE7F21066290B6, +0xB47C1FB725FCA9, 0xD5582FE0FD390600, 0xCB11418A98365314, 0x35E72B43A05135, +0xB755E3445AC4D025, 0x7D51012DDB24B560, 0xC160A773E31D7704, 0xE6AD5A9E8FEF95EE, +0x6F4B3BDC30C4A0D4, 0xF4F52B6E36FC7AA8, 0x6EECD53DB666B51C, 0x2DF30F94871E13, +0xB10514173E7A23D3, 0xF51AA9EE1BF46125, 0x9FF0221A0E16672A, 0x3F6AE38C6B9189B3, +0x510870D8AE88CF60, 0xD590F20ECC00031B, 0xF009459159234D5E, 0x132CBD570E2E07, +0x3310E94E704202F2, 0x3F26CF6ECCE36F36, 0xB58EBCBF288520D1, 0xF3BA7775C96A1E28, +0x209DE4B65F82E151, 0x20D1241C3E4184CB, 0x26D7D0BD7EF5B854, 0xE94382A380048, +0xD8215C231998DCDE, 0xCCF89A92C86DF92D, 0x51AF622F834ABA0F, 0x4262B81F46F39DA0, +0xEC0622A19882FAA2, 0x8516C9BE30E53B30, 0xFD048A25ACF756D1, 0x58A7AB0C20642, +0xC7670A44560F8F91, 0xAB8547B43C3479D3, 0x3D569F5772456BB6, 0xFB5B53C0FA23B31, +0xE75E43A12A8B4FCA, 0x13D88118CBCFB9F8, 0xDCDAD7C80EE953C5, 0x2F8C069DCB4740, +0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xB1678C5AC22E6CF3, 0xD3997F70E6B1F497, +0x56C3B1478B8F394B, 0x90B563F098BC13F7, 0xE33BA6C4F7BB082D, 0xD51B497D2F1C4BE0, +0x3DE4316EA65A30B2, 0x7F44E0C9DA7C7 +}; + + +// Precomputed values for the first Miller iteration of the Tate pairing on the +// 2^eA-torsion of E0: y^2 = x^3 + x. Contains a triple (x,y,l1), there the +// coordinates x and y of the double of Q are in Fp, the slope l1 is in Fp2. + +const uint64_t T_tate2_firststep_Q[4 * NWORDS64_FIELD] = { +0x273F6C464CB9B30E, 0x83722DBAE9836B36, 0x7236DD158D1A1BBF, 0xCE84ED2FD6FC9B11, +0x96804584C42BBFDC, 0xE3D6BF4D45241A13, 0xC4D8AF04CC4F6BEE, 0x653193B290C00, +0x3E3209393CB32A2, 0x689964CCAB348A84, 0x74471EFFCED8819B, 0x661D7240B28E2790, +0x71AAE7BAAE2179CA, 0x5DA64F579D150D5B, 0x17919259B69EA954, 0x77328AA89BBC7, +0x3906E0889D1C2FC0, 0xC75AE81624C4EC7, 0x8B7480889B54EE7, 0x64943C09942FDB32, +0x44E4802923DF1D79, 0xF56CE97EE0F89851, 0x1DF1A01FA1863680, 0x315A043E1D0C15, +0xF50FC07FBDA91B34, 0x617F5AFB158C037C, 0x31A682FAED0AB32D, 0x4CB68F9AE1F01D7F, +0x4F468A61D183C4E9, 0x692707D7F3EBE901, 0x5084C7D3D549991F, 0x136698F774A6F6 +}; + + +// From here on all values are in Fp. The table contains eA-2 triples (x,y,l1). + +const uint64_t T_tate2_Q[3 * (OALICE_BITS - 2) * NWORDS64_FIELD] = { +0x85C7CA3E9EADB8EE, 0x97873829844CF9A5, 0x96510E240E86B156, 0xEEDE7282E40EE2EA, +0x834790477C5D787E, 0x3B30922B819FBB12, 0x503CBCFF9F6EEA85, 0x310DB49979557B, +0xB19D04E98B392C8E, 0xD2E39BFF2A5E96F1, 0x1360F52AE4A91741, 0xABE9E841F06BD82F, +0x9B0F10004369DA05, 0x9773A80A2D5B4968, 0x150F402F78BA17EA, 0x267889EDDA82D1, +0xE4F3317EB16BD357, 0x8CB1BCD465AAAACD, 0x5BD63B8AD1EA3E14, 0x75F4CE2332B5240D, +0x58D711071848D94B, 0xC3A1D6B6ADEFFDC6, 0x2E60A7A9993D40BC, 0x2A4DF4CCDEDB41, +0xC1BD72B10DA4FA9, 0x84A26F4EE4496FA, 0x34589B9528ECBF9C, 0xB6222BA5EECE380, +0x27A5FA02EAD7F3F8, 0x7663FDF274804B47, 0x4954C526AFA4A7E1, 0x36648BE8A9460, +0xCB251808FD734F84, 0xEA1DB9DBA11457A8, 0xBE247A8E2EE186D, 0x275FE19B2EB7F43, +0xDBC4D02713E06C40, 0x5C7D6AEA148B13DD, 0x657E84E0CBDAB22B, 0x2432F09DC4483B, +0x1637A27855823819, 0xC3DC5597D4F788D7, 0xD251D69BE7F1CE68, 0x785BF32F873C30E8, +0x4AD8725177438524, 0x45DCB744C6F8F13, 0xD216FC7A1F74ACFD, 0x619711080F21C, +0xE01B02B0FFABF430, 0xED5F88D2590604A9, 0xADA943FA1DD8403F, 0x5E330D59DC77889C, +0x139080687DC5E98F, 0x1CF2B81CD54F9FE8, 0x4BB02BF0902937A0, 0x188104988B2CB4, +0xB7D8CACDD61A57E7, 0xB1AFF074D0533E5D, 0x6A5C95740929D714, 0xBAB26BB2A69E78A5, +0xF277141029706195, 0xC9AEF881ADC3BA1E, 0xE5715B4D01CCC2B, 0x176A061CC47CC7, +0xC09FEE1625AE485F, 0x8633DAD9226734EB, 0xBF88C965D8CA54AA, 0xEBCBD4B6E769FF87, +0x543DD3C8707D9014, 0xD35E50A6F9FD3B4B, 0x7A28A562FCB3C67F, 0x405843C342F10F, +0xF238C2032DBAFB12, 0xE29F7AAF15F306FB, 0x45DFA909E7653EBC, 0x9325C090B921F541, +0x7D18BD7B8A2FA1DE, 0xC3036FC258CD9EC9, 0x7D744123622097A4, 0x10E3ED466E3E8C, +0x8132CD2F847DA8B8, 0x4AFC83F0068DECEB, 0x30DAEE5EFF8CEA14, 0xD89FDB2B91756EBE, +0x3BF36981E1ECF64E, 0xEBC4FE8E9E8212CF, 0x31D29511C2723BA7, 0x3C1E06F04F5653, +0xCBD8B07F4A9A3E45, 0x1443092D9F914C9F, 0x33A88AA7136FDD85, 0x17F517BE8449ABD1, +0x8A4E91AB3AA503F1, 0x8372BD7EAEDDEACF, 0x56450B847931748D, 0x6FDFC54AA439E, +0xF6D3936A7E8712C4, 0x525FDE819DBEBAE0, 0x2874E4ECC2630B74, 0x1FBC2C7D26CB7E36, +0xF75681CF0E5462FB, 0x93909F88676FC573, 0x295E93A843BE4E64, 0x33CEAF9B01127F, +0x9B8A62C5089194EA, 0x2474CD26C67ACF1C, 0x9776C45076A0977C, 0xE805E224A4E0EAFD, +0xACB7D10D3BAB10E9, 0xF8F389F69B8F5367, 0x86A9B41152D32C07, 0x20E2F3D52A54BF, +0xF4314B5F9E42A846, 0x4721BB5334E50C10, 0x2AF52E2277F6A2A0, 0xFEC9E0B07EF0A81E, +0x64D012D951925CEE, 0xC1B86D0291FE861, 0x279EDD2B4083148E, 0x3843ED590AC7F2, +0xBE269B61D16536B5, 0xD03EF1FEF08E1497, 0xB699A3117FA61D4B, 0x512788543423CF68, +0x6C7F64B39A4E2E15, 0x6B4E8D0ADCE0BEED, 0x52ED5CE2D6FF84C8, 0x2271E0661F2B91, +0xF66F83C841E5822A, 0xC4334FE8A1E1D72A, 0xA042BDCD86E19192, 0x570E5ED7AB554437, +0x76E232A73F137EE0, 0x2BF11712838E81B9, 0x620CAD3081CF4F40, 0xABFA98FA91B55, +0x3E51D21636E0A903, 0x9CFA6AABDBB555A5, 0x8785D31D6B816F69, 0xA7AC7754211FD4, +0xB0301E0BB9F4D945, 0xC1592A4A7959CE02, 0x9E4549F8438B08FC, 0x196357117C9D02, +0x8C24774ABB7FA431, 0x5341695414714243, 0x7673CE34ADCB8932, 0x9E4D78196166C3EC, +0xB32797EA20E361FE, 0x328A84C13F177314, 0x78E496C747C09D29, 0x1350733DF5ABC1, +0xB7042BF0D6B8E130, 0xC6A689E163EB578A, 0x593BCBC303ABF6E8, 0x1E4B4F8C9A09B9FE, +0xE15DBF9ADD7DD378, 0xBEF91FDA06BAFC65, 0x6A21A6C54EEDF611, 0x2F3FBE51ABF33, +0x8CD0DA012FA7D205, 0xA86097FA989CF40A, 0x4A7285B013F66F1A, 0x5A7FA82A56ADE8F7, +0x68637425CD3F8883, 0xDA57D6A35D194D22, 0x94EA55988E64D5E2, 0x11FD6C675540C6, +0x4A3BEA3AE93960B1, 0xE03E165866FDBEDD, 0x925C330C1E7D8226, 0x30FB772BB1A85AFC, +0x436A12091E97D9D1, 0xEE98C9A0EB42B05C, 0xF63CD3C900A0A350, 0x1D17A39BDD6600, +0x6086DE8F8146C8B0, 0x40566185C25BA161, 0xE901C89884636E6A, 0xB578BE00D22D4401, +0xB58916BFA27EE2F6, 0xBB29C4CD5D3D1370, 0x561BFAC5817EA571, 0x3261F12EAF245B, +0x51C69FE4C2BD6C90, 0xBA93C7516B3E3562, 0xC914015B590A73D, 0x112F9F42FB703305, +0xE86D0D63682C6968, 0x89D08909C7F53035, 0x95D8E48B6CEF33E8, 0x224CDEE2EB9524, +0x655858D5FD89F1DD, 0xE47C518457856AB0, 0x6EDE0F13DF8B80D2, 0x1A7A03582B70F298, +0x62B5A5C54B3D490D, 0xAA840FD16257E005, 0x67E4472CFA384456, 0x48C971ACB01E7, +0x5AB1C2CA90CBEB5C, 0xA25F64938BC48A66, 0xEC946017823C05DF, 0x896C703B4F137BC2, +0x32EA49999D906542, 0xC8B0D06EEB790E74, 0xBA60C32EC55C62D7, 0x1AA03D36CF8502, +0x86DB15CBA6040955, 0xAF4C4A5B90F3C56A, 0x2DF9587824678BA0, 0xAE49AC5DDD49376B, +0xB39B01B40BD1D99D, 0xD968B251D800B4CA, 0x1FB9A82972F38C8C, 0x1A2DE56B250C3, +0x9E8FFAF253556784, 0x308D2F92623A0758, 0xE283E03D68849D09, 0xA62A3E8DC4720855, +0xBE933CA1DEA1F275, 0x6009F11D5EEB04C7, 0x48CF021AD85286E2, 0x352903B55112B8, +0xD043C2E2D1B77306, 0x63FF12D119064271, 0x36F29C4ADBA2CEE6, 0xFDB6B49216D3743F, +0x97583BFB1634421C, 0x62F50B77D0D5602B, 0x4BBB0B43D24A746E, 0xE9F0633ED51C6, +0xDFB8B695F3B4F26C, 0x5926C2AAE5838D27, 0x91BCA10F9B44E726, 0xD1FFF3CF57DA04CD, +0xA557509AE62E5C1E, 0x50B1A18402085750, 0x899F58D853D855A, 0x2E5F28E5B5A275, +0x5E3A092F11893DD2, 0x7CE31E0C582ED837, 0xAB07330F1F006699, 0xDB71C77A33D38014, +0x37D84F386EE42EB5, 0x77A216FB5ED21C3, 0x826FC664DDB3B6CB, 0x39BA5D5EE95E97, +0x455360834F72B7BE, 0x5965D9CAB8F4EE6B, 0x232B72F1FD1FE273, 0xA230386D4DCA331F, +0x94A0A28561ABDD7D, 0x54A05FB6BB2173CA, 0x7175AA2C518B12C, 0x117D3E02839973, +0x5B11E861840A8078, 0x5B447B97205FC6DB, 0xCA02CFA6A69FE8B0, 0xC07409C6A41936E, +0xB589C55662216004, 0x28B0E362E168B785, 0x11D6CC0D36BCE4BB, 0xC53B7973EEB92, +0xCA9A36B9F4CD5A25, 0xA2D743ED9D94288F, 0xE11854245C2BE3F9, 0x18DD5D0EA9C62B77, +0x71B5DDF069A38239, 0x462FF85D662B5739, 0x8F0775F6EB9F7067, 0xE9028CEA5F5FD, +0xEF7DDA0A270B0FAC, 0x8D5B15C4B85CFDC5, 0xA3DE0BFBA5540069, 0xA6910D57AB8EFF6E, +0x4781ABC5C99EA8FB, 0x8CC560CA2BCF0E00, 0xAE945E2C3B9CB9D2, 0x2AADD1B133219A, +0x3B176193FED733A2, 0x8BCA4B181A55CBD3, 0xCC578CEF7ADE923C, 0xBFE1BE006218D884, +0x841B3859467B2940, 0xC77D877F581800BC, 0xD98044F56633E791, 0x3983D8E1C488E2, +0x8F23E62C402FDECB, 0x947EF73A4794033E, 0xDF63C67CFBDEF4C2, 0xC7A1E3299594F62D, +0x2C3F5E6251D15207, 0xDAE5AC00D90CCED1, 0xBC7E64AEE5638D51, 0xBA3C4739DA95B, +0x93FFE0DE8250187B, 0x1D145333E5899F46, 0x1904EEEE43EBB312, 0x1383058CF8C03C87, +0xF92EE48461F96224, 0x2DA38D983DDB17E8, 0x6D2186D33E59C36B, 0x250774ECFFA4DF, +0xB368385C28DF4763, 0x931E6BF4DAC47FAC, 0x34A28F276A7C3C07, 0x34E6BE5555D20E25, +0x3423691989928F92, 0x598AF984C0AE13FF, 0x3DF9238A7426BC3C, 0x1867401DE4D7EE, +0x216C54D5330CCE0B, 0xBC2C3DB4CE0888C2, 0x2C92AA85C95B4DA6, 0x9D0E9A4B6E7210B1, +0xF6E6762771B5AC97, 0x2EC536B830889B61, 0x807C10D3B11DDF68, 0x3FF77B9E0A89F8, +0xC8144E0C41F30695, 0x3E3216EF624A9A97, 0x1CEC3E595606677F, 0x25EC1B46F719664E, +0xD3988CCE8D90BEE4, 0xA6225EEEAC9FA979, 0xBA1D02D6F0F81FC3, 0x16E7C4EE3397F9, +0x35DCCFD70EF557F5, 0x8D1980542AD4762E, 0x5E0B1073DFE2159F, 0x827FAEFAD1E0137E, +0x34B5552A179F9441, 0xF6246D207B94E9D4, 0x93007594B4F7E044, 0xFE2D687655527, +0x60DD66091EF9F724, 0x1713DA394C304A7C, 0x93650F486A1E3823, 0x4748A18300898763, +0x5CF0D9565529F133, 0xE04370653045DB14, 0x4C826D11D78C4CE4, 0x33AD7C5A501721, +0xD9942C04B985BA1B, 0xA04C0FCD1FE51A92, 0x9CA6E9006C195EFD, 0x4C4553E980A95FD3, +0xF8BE423B25A8A7D, 0x5A1F67D1FFB29FE4, 0x91A5BE542B0A932C, 0x63B25B749D19F, +0x16A29B9201E906BA, 0xB10E1938815305BC, 0x5608FC5B5B876DC8, 0xA5F59F40A6141C4F, +0x198990E366A4AEFD, 0x1F3483AB7FB179ED, 0xD0BCC3CF8F74995F, 0x1BFAC67531314A, +0x36080686BF9215B5, 0x602D018177CD81D2, 0xE3641F6027AF998D, 0x3B8E0FDFBB079394, +0xD2A122A54B97B729, 0x17F44B964268FFC6, 0xAE4D570FDE71BFA3, 0x14C7D16D56D1E2, +0x6466107E7069561, 0x346E8735EDF6CFE9, 0x8555074D6550572C, 0x2BE3DD8E6CE42FE1, +0x7D49E486C984BDFA, 0x7E1FC7D4C20D1613, 0x55C7A2DB2D5E0698, 0x1D9DDA3B632481, +0xDB9B3258205C48FA, 0x67D583A5A421505E, 0xB3527021E1986A5C, 0x33C4DCECEB1A6B45, +0x48D6918C40FE9C8A, 0xCC046BDC8FF41783, 0xB2D54654918CC0A8, 0x3EE566368BFC87, +0x4C1AA9CD5080A8C7, 0x12415F1D2B7C1C47, 0xE42D8F52EA34738E, 0x2CDFE05607ADE66B, +0xA3C5939C4B7FCF1D, 0x8DDF73AF50F16E3E, 0x31398F59CA516063, 0x1CAC742C9EA0D0, +0x4736685D0DC78377, 0x7A9E13039FE5298F, 0xF11631E4026205C3, 0x6525796BAEED916D, +0xCC54E633784977F6, 0xDDF4964C37E2E2B, 0xD24A23B4B6FADBD6, 0x3DEFD9719D7A6, +0xE322D17049627462, 0x1FBDF2EC1BC4D507, 0xABC696715CF3BCFD, 0x91AB243F06E274EC, +0xFC5422F7E78C36AC, 0xFDE102D5DF6E66B5, 0x45790CC96C4AEBB4, 0x331AF62D67FA57, +0xC2B0DCCD96D923B4, 0x84FA2BAC0D3C859B, 0xC17ED893C59886, 0xBF948BD94C3DC842, +0xE5E8E516AD745041, 0x51DEF67C63D51EBA, 0xFF263CB3B7DD9069, 0x4C7694FFB5BC8, +0xAEBE3F2B5F1491C6, 0xC44EEEF5E128DD2C, 0x8254867236B5A579, 0x28009270DB328E6B, +0x519CA7E8917CE06F, 0xB44DB1F9E9B4DB12, 0xE3334898D9E5610D, 0x393DAB9885267C, +0x85A06E3AE4FEC073, 0xA3D647A36A446ABE, 0xED36ADC92A5A996F, 0xF8CDEF4AC24F3746, +0x5842BCE637F98D69, 0x5E77EAC96EFC10EE, 0x63FD47C69362DAA7, 0x1712B1AE643E7, +0x7D304F8AE560CC28, 0xF5DAC6B99A25356, 0x1CF4C58415593775, 0x7FCA44231F25C19A, +0x4CDBC8ABC051A5E4, 0x72D8EDD946CDAA49, 0xB46753FF109F5760, 0xC307D695E4A56, +0x86062BA4B21EB80C, 0x3B42184AA93CD213, 0x5A116C8CE0189032, 0x501CF7F8103717DB, +0x284CBEFD3305DA3C, 0x6A08B7B622A34532, 0x712CD8F1816AD4F9, 0x1FD9B26CA27AF0, +0x4DD5D695E595A32A, 0xA077A742183FC75, 0x598989699CC18805, 0xC2617B819981E73A, +0xBE7C7DF06238CAB5, 0x75ACC7DF17ABCC3C, 0xA07B0F723DDFAB29, 0x3E6FC04801B1E2, +0x2F9420C8E8DD440A, 0xD50455326469FF7A, 0x6D2A21A9C77AEB7, 0x1888356EB4EFD335, +0x17C9E871EAC65AC8, 0xD9FD6DCCAF50F40C, 0x44903FCF9BFB1D85, 0x32C96C494E613A, +0x33DFEBF9BF435BA8, 0x8DE71856F6276769, 0x8C0443A3D1BD7CF3, 0xFA2F513362F81A32, +0x3388B27A29F79BE9, 0x8009AE009FC0B146, 0x7C83CBC4821BB624, 0x21AA6406D46979, +0x7BEA4D6BF644AC2A, 0x715A3391352B1354, 0xA8D5ACDA8730C050, 0x60EBE04F5D109161, +0x456FFE0E23BFE4CF, 0xA3BEEEABE95EE8E9, 0xF7294F5AD4EE823A, 0x4101A0480A75C, +0xC9667FEEE14BCBF9, 0x3ABDA0FF19DD27E4, 0x11E9C4C666AF0D2B, 0xB8DB81838D7FB021, +0x355EE3390DD73CDB, 0xDE5F26E8A1BD10EE, 0x64BEBD1EBF5151B5, 0x18135EE1C69533, +0x29A01240B1C2EE1E, 0x67CAD17532A3C508, 0x54E1853DA437B5C8, 0x6A8BE5F77FB465BB, +0x3C076A2CF29A6C19, 0x5624367DB7953190, 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0x5A78799C25406073, 0xE2E1955125177B8E, +0xB43CD4A41CDABE74, 0xF738D7CC5B93EB6, 0x3557A4AAEB8D122D, 0x35F943E6E56A54, +0x908BB99BAD39CF34, 0x3F7FF7687372BE08, 0x5355B6151C63B096, 0x908B8CA2FD6F040A, +0x7B1EF9D829AC3C4D, 0x6457557F7A089E7E, 0xBF486DAE6783F72E, 0x1EA9B3533B073E, +0xDB85E3A2D08C244C, 0x3104C3A075E320FC, 0xC1098114FF2918DA, 0xEEE371F097F26ED0, +0x331FFF33D4A6BD76, 0x316F0986CF3F2150, 0x83350FD149EA113, 0x356E8D9FD432D7, +0x87B4D7A5346090FE, 0xAE760E523D10C41F, 0xBE85B02F41FCC1E5, 0xDB8A8032A88D91C8, +0x246B1AD0A387B293, 0x46101DDED3B23072, 0x9EA5A3D57FD730B8, 0x3F9A5FCF7CC873, +0xAFA7846A7A7C2FEB, 0x737EB536F3340B23, 0x426A25A2E267C427, 0x71E08C109D2DC8E7, +0xE13A8A3822FFC4F8, 0xB5BFCDADD5919D0A, 0xDB0821B34F8901E, 0x3B09FAA2F4DAA, +0xF9BE25D26E759627, 0xC022DF1B38C7D305, 0xAF8E510B4CD7E2B2, 0x6F2952C7FBF662D0, +0x450E3653D813E400, 0x3D01DE38C78F6160, 0xCD68EF802ABA7C19, 0x23756C2690B1E9, +0xEC015B20598D3949, 0x219FB828424697A8, 0xF64982521E7353BA, 0xA17F4726D124E30A, +0x721B335373702AA3, 0xCC134076C36DDABC, 0x8666CB7F1C069C6C, 0x1E11618E8FB770, +0x291B18E78005586C, 0xC4457E4EACCE410C, 0xAA634B593BF7D7DA, 0x3B564DE164DF11BD, +0xA3280F50E8F5473F, 0xD1157A83C81BB173, 0x2294112A430AA68A, 0x1B8704A90FE9E5, +0xF35ECDED4E7F3276, 0x8B10B7F4A9543332, 0xE608366934CF9F30, 0x432B8C52FB7683D8, +0x39A07B1A743B689B, 0x33D32CDB4382158F, 0xABC25C233708D34, 0x211A5EE1867669, +0x56B7E5F1CADF3313, 0x47B6351D7109C43D, 0xDD5666E5339FC4F0, 0xDA8946080066E593, +0x36994943E044F666, 0x6A2B8F4464FB3E3B, 0x6775ECBA97140B33, 0x2F0B20C119E257, +0x4CBE7B2A035321B7, 0xB31EEDF4016AFC9E, 0xF853E0F9EBD7E953, 0xC88E9F8FE1BE7272, +0x7DB096E448017615, 0xD6FBF30304DA0BB7, 0xFEF5D9A874327177, 0x3AC6FA54D7DC62, +0x82005D007C9AED13, 0xE0B6EA116A5D23B7, 0xAD65717EA4DE6487, 0x15639FFD0B558EA8, +0x76BFC178C5F2BDC9, 0x461944B49557A700, 0xC66079DF0C57F9D2, 0x3B7DE01528082D, +0xD5693E97D8B53A88, 0xE4365A9243F7C564, 0xF4FC3F444CC54747, 0xDB2BF03B2AA1BFC2, +0x3382B49DE21B8238, 0xB839CE1A807B14E7, 0xD648CB971E2DF0F2, 0x195B1F31C8B985, +0x5CF601EF691C8411, 0xFB61B0468185AE7B, 0x9C8370B8A4F911F1, 0xC7FEB02F1F842E0E, +0xB516DCD90887BFE9, 0x8B713061E5E0E4BD, 0x2C17AD49DE6AD232, 0xFE60868C75312, +0x4F2A7CF74F28C8DF, 0x52A61BF256662287, 0x46D63444B75DAD47, 0x99F19B8F1ED887CC, +0x5BF09FA62D79BE44, 0x7C053959512E0DEA, 0x3980E77E98AEDAEE, 0x1AB407D73E50A0, +0xAABA9D1340B05A22, 0xFA67356ACC404A0D, 0x5C87FC45FE5BC1F1, 0xC24F06241A283FD7, +0x5873FF137240B6B7, 0x4F2202DAC0407A09, 0x7622F95D076787DF, 0x3E32D3538BA52D, +0x71CF043B02F4029E, 0xF2E0C6DCDE4B5E4B, 0x9B20D0ABD80ADB52, 0xA342518DA9C937DA, +0x506C510850829AE7, 0x47C6CD2CCD05EF9D, 0x205D8CA94920A22B, 0x381E7404CE0CBC, +0xECE83AD9352C2823, 0x3860D22F6A9F1B74, 0xF6F983EE0F555ABB, 0xE54974EA7B8F545, +0xAF6EF5DD3F2DA352, 0x3175C4C42E185DD, 0xFE146E5AABAA6307, 0x2E82CAB178E922, +0xAE98986FBA003312, 0x99AC6AC39159C882, 0xBF9ECFC393993307, 0x65762C6F29AC779D, +0x387A8CC25D4529CC, 0x65C1CE3A619696B6, 0x7E64DCB7C333CEED, 0x13E4983CB2C9A4, +0x4DED04C4720EE33, 0x5A64CEAFE858F85A, 0x8AF32312E11774D7, 0x274CFA6AA509D361, +0xF7A0488C63B5A4CC, 0xC5584635A10FC961, 0xB0398F65333BC999, 0x291F2ABF0E10EF, +0xD92E86099675CDC8, 0x803A569E83862284, 0x5308E8DA552D68FF, 0xC796FFF8CA7256D6, +0x1AEA521AC7316631, 0x4FF75D83A7D6C6F9, 0x4F81F1D8F31119AD, 0x1770DB9DF8F60, +0xA1076A18D981D2A, 0x8F06FCF5D6DE4C70, 0xCEC9733838097057, 0x50FB065EA1CD9094, +0x93161ACF5A59E2A9, 0x845983D6512FFF79, 0xCD0E1C06541D52E5, 0x42C7AAAA0BB1F, +0xE285AA7217ED5CFB, 0x13F7367D4AE539C0, 0xFB9C59AAF663AA40, 0xABD3304310774662, +0xE4214D6AD98968E8, 0x5CE1BC2F5FBBEB13, 0xEA77DEFD87B7B3ED, 0x2AC905FEE0F8AC, +0x9FA860ADBC72C2D2, 0x989C4D2948CD6DDE, 0xB18EE90BE1AD4BB5, 0xD685F9B04E49181D, +0xF38D785033731986, 0xDA8FAB3E7AD81DC9, 0xC327E652862489A5, 0x22ADE9F9C0FA37, +0x7A813D7910A7AE4D, 0xCD7698379F20810A, 0xC2BD0C335C47DA8C, 0xEDBCDEB6E1651F37, +0x20C9C7D4D4E5B3B3, 0x6694BF77D77167F3, 0x9A99ADC1AFEB8EF8, 0x1CB2E021CCF274, +0x4FE2DCF4FFDF1F06, 0x9A604B6CFE16FB30, 0xEC3E031F268C7972, 0x10E9199993B50D99, +0xB089A13E702AE83A, 0x8385530BDCA34E51, 0xD870E484F8FC7945, 0x3B2EA55231BB81, +0x449D115DA5EABF56, 0xAFC072E8F24A38EE, 0x2ECE330359640FE7, 0xF6E985D905956893, +0x58182C9B435CB992, 0xAC2A8C54344AC281, 0xA192F7AC0DB51A0, 0x1B294C2F036521, +0x30F634EBB1F06E94, 0xB17576DAA833A32F, 0xA256DA0896115659, 0x5FA67941E88E3639, +0x1350EB959F2EF3B5, 0x788BE520132861DB, 0xBE9D413D9492119E, 0x2B2D7430BE22E7, +0x1E07E360D490BC33, 0xCEE2D395831BEC36, 0xB0A948F75E8A1614, 0xC1D62A8E9571A44A, +0x945A1DD9B4339624, 0xD48311E2151A0EA3, 0xC77D6FB21B8CB73E, 0x3054E58242A23A, +0x2EADFD02C8B1622D, 0x17BC72FB655AB2F4, 0xB2D0DF3CDE1EC71C, 0x2F4239B2A43FFC20, +0x390D4F85A306641, 0x5F003E2968FEE3A1, 0xBF137C501F23C0C4, 0x264CF89AD79961, +0x1BF08B36A5181E07, 0x6FEE26D63FD6D9F3, 0xF4600638B8A000AD, 0x95A71A77F83EF707, +0x66C290996DBEC194, 0x179D3ACC9A54B8D7, 0xDB9334DF62BF7313, 0x142B500FC6EA78, +0x8DC81B1791577D69, 0xDBE49752CD507631, 0xCE2795AAF59E2BB7, 0xB38CC1B3220C2762, +0x2BDBF7C667CFD33D, 0x2F8658F790565B53, 0x172AE38594D0A033, 0x25DAD03A1C2361, +0x4BAFD338530545F5, 0x882026B53661251D, 0xA8861C4BEF1BEE28, 0x8406C5861729CD70, +0x28D90BC89980F9F, 0xD1F68357340D9715, 0x61851BF560009B7B, 0x14447D3F8D7749, +0x41FBF1E190B4C6B8, 0x86BC4E8C911F7164, 0x683816115099D136, 0x952357ADE621076, +0x9A4ACDD90EE870B3, 0x3F1A3B5C44294382, 0x36E78468EB62B975, 0x35D80D75E99C3B, +0xA8FE70D5806CC71F, 0x10E16A8D72145F33, 0xD612B61A2EFAB7AF, 0x3CFF7BD03534952E, +0xC28FD239BAE71B72, 0x34CFE87FE7424E58, 0xF669A119840A237F, 0x35B3566567FA80, +0xA8D5FF10491C8F8F, 0xCBC997451C543D13, 0x3E59F3855CF7E03D, 0x85B0BE9B87591599, +0xCCBCA3F11DD449CE, 0xAAD1CAD2C2C7C11B, 0xAB5BC2FE400F8C07, 0x4FF9C26E7AB5A, +0x4A613CC203EE5C02, 0xC81E767D21690F5D, 0xF40BD4B57DA764A9, 0xC8DEF84F2C7F5874, +0x35CB6541E748483D, 0x6E58BBE9A3E1440, 0xFDA85604AAB25CEF, 0x309686C84AAC8, +0xFCAA9EDB82A6065F, 0x9BF1A72FD4BA7F2C, 0xDE57A3A05DA9E64C, 0x1A20E92C1DED19A5, +0x6DCADAEC9FA7F808, 0x5CA8E407A2A37175, 0x2A95C7A08B7DC3E0, 0x290DEE95F437F0, +0x7EF9A695A17391F2, 0xE2471E611CF41741, 0xB1DBCC0CE323B56F, 0xD200C280E6F8A664, +0xA32C246ACAFAD250, 0x1DA20FBBADCF29A8, 0x41580A644CE4FC5A, 0x39BA2590AC90CA, +0xBEC, 0x0, 0x0, 0x7000000000000000, 0x1858F371D28A907D, 0xD89DE1DFB7FD9CC9, +0x4022A097759F1EF6, 0x348C1710ACEDDC, 0xC7670A44560F938B, 0xAB8547B43C3479D3, +0x3D569F5772456BB6, 0x17B5B53C0FA23B31, 0x38210235AF583ADE, 0x49A527DDB6CFEFC7, +0x76288D14F23F037, 0x1620C022598276, 0xEE37B8F9A6021865, 0x8C5C41CEA26276CE, +0xCE9D8BF310132F9F, 0x876B5274C3DE6C59, 0x59A9CD65B71D224D, 0x5246877E7BEF62F3, +0x109010B83B8E355E, 0x34CD34FD408568, +0x7F3, 0x0, 0x0, 0xBC00000000000000, 0xB48DD9032BABBDC8, 0x87354452517EE94B, +0xB55528D05AECDDB4, 0xD90684A9D9488, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, +0xC7670A44560F938B, 0xAB8547B43C3479D3, 0x3D569F5772456BB6, 0x17B5B53C0FA23B31, +0x38210235AF583ADE, 0x49A527DDB6CFEFC7, 0x76288D14F23F037, 0x1620C022598276 +}; + diff --git a/src/P503/P503_internal.h b/src/P503/P503_internal.h index c0f7409..c68a811 100644 --- a/src/P503/P503_internal.h +++ b/src/P503/P503_internal.h @@ -55,6 +55,34 @@ #define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8) #define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8) +#ifdef COMPRESS + #define MASK2_BOB 0x03 + #define MASK3_BOB 0xFF + #define ORDER_A_ENCODED_BYTES SECRETKEY_A_BYTES + #define ORDER_B_ENCODED_BYTES SECRETKEY_B_BYTES + #define COMPRESSED_CHUNK_CT (3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES + 2) + #define UNCOMPRESSEDPK_BYTES 378 + // Table sizes used by the Entangled basis generation + #define TABLE_R_LEN 17 + #define TABLE_V_LEN 34 + // Parameters for discrete log computations + // Binary Pohlig-Hellman reduced to smaller logs of order ell^W + #define W_2 5 + #define W_3 6 + // ell^w + #define ELL2_W (1 << W_2) + #define ELL3_W 729 + // ell^(e mod w) + #define ELL2_EMODW (1 << (OALICE_BITS % W_2)) + #define ELL3_EMODW 27 + // # of digits in the discrete log + #define DLEN_2 50 // ceil(eA/W_2) + #define DLEN_3 27 // ceil(eB/W_3) + // Length of the optimal strategy path for Pohlig-Hellman + #define PLEN_2 51 + #define PLEN_3 28 +#endif + // SIDH's basic element definitions and point representations @@ -65,6 +93,16 @@ typedef felm_t f2elm_t[2]; // Datatyp typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates. typedef point_proj point_proj_t[1]; +#ifdef COMPRESS + typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates + typedef point_full_proj point_full_proj_t[1]; + + typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates. + typedef point_affine point_t[1]; + + typedef f2elm_t publickey_t[3]; +#endif + /**************** Function prototypes ****************/ @@ -82,7 +120,10 @@ void mp_add503_asm(const digit_t* a, const digit_t* b, digit_t* c); // Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit unsigned int mp_sub(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords); -digit_t mp_sub503x2_asm(const digit_t* a, const digit_t* b, digit_t* c); + +// 2x503-bit multiprecision subtraction followed by addition with p503*2^512, c = a-b+(p503*2^512) if a-b < 0, otherwise c=a-b +void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c); +void mp_subadd503x2_asm(const digit_t* a, const digit_t* b, digit_t* c); // Double 2x503-bit multiprecision subtraction, c = c-a-b, where c > a and c > b void mp_dblsub503x2_asm(const digit_t* a, const digit_t* b, digit_t* c); @@ -116,10 +157,12 @@ bool fpequal503_non_constant_time(const digit_t* a, const digit_t* b); // Modular addition, c = a+b mod p503 extern void fpadd503(const digit_t* a, const digit_t* b, digit_t* c); extern void fpadd503_asm(const digit_t* a, const digit_t* b, digit_t* c); +void fpadd503_inline_asm(const digit_t* a, const digit_t* b, const digit_t* p, digit_t* c); // Modular subtraction, c = a-b mod p503 extern void fpsub503(const digit_t* a, const digit_t* b, digit_t* c); extern void fpsub503_asm(const digit_t* a, const digit_t* b, digit_t* c); +void fpsub503_inline_asm(const digit_t* a, const digit_t* b, const digit_t* p, digit_t* c); // Modular negation, a = -a mod p503 extern void fpneg503(digit_t* a); @@ -132,11 +175,13 @@ void fpcorrection503(digit_t* a); // 503-bit Montgomery reduction, c = a mod p void rdc_mont(const digit_t* a, digit_t* c); +void rdc503_asm(const digit_t* ma, digit_t* mc); +void rdc503_inline_asm(const felm_t ma, felm_t mb, felm_t mc); // Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p503, where R=2^768 void fpmul503_mont(const digit_t* a, const digit_t* b, digit_t* c); void mul503_asm(const digit_t* a, const digit_t* b, digit_t* c); -void rdc503_asm(const digit_t* ma, digit_t* mc); +void mul503_inline_asm(const digit_t* a, const digit_t* b, digit_t* c); // Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p503, where R=2^768 void fpsqr503_mont(const digit_t* ma, digit_t* mc); diff --git a/src/P610/AMD64/fp_x64_asm.S b/src/P610/AMD64/fp_x64_asm.S index 33cd261..527a3de 100644 --- a/src/P610/AMD64/fp_x64_asm.S +++ b/src/P610/AMD64/fp_x64_asm.S @@ -990,11 +990,16 @@ mp_add610_asm: //*********************************************************************** -// 2x610-bit multiprecision subtraction -// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2]. Returns borrow mask +// 2x610-bit multiprecision subtraction/addition +// Operation: c [x2] = a [x0] - b [x1]. If c < 0, add p610*2^640 //*********************************************************************** -.global mp_sub610x2_asm -mp_sub610x2_asm: +.global mp_subadd610x2_asm +mp_subadd610x2_asm: + push r12 + push r13 + push r14 + push r15 + push rbx xor rax, rax mov r8, [reg_p1] mov r9, [reg_p1+8] @@ -1055,11 +1060,51 @@ mp_sub610x2_asm: sbb r11, [reg_p2+144] sbb rcx, [reg_p2+152] sbb rax, 0 + + // Add p610 anded with the mask in rax + mov r12, [rip+p610] + mov r13, [rip+p610+32] + mov r14, [rip+p610+40] + mov r15, [rip+p610+48] + mov rdi, [rip+p610+56] + mov rsi, [rip+p610+64] + mov rbx, [rip+p610+72] + and r12, rax + and r13, rax + and r14, rax + and r15, rax + and rdi, rax + and rsi, rax + and rbx, rax + mov rax, [reg_p3+80] + add rax, r12 + mov [reg_p3+80], rax + mov rax, [reg_p3+88] + adc rax, r12 + mov [reg_p3+88], rax + mov rax, [reg_p3+96] + adc rax, r12 + mov [reg_p3+96], rax + adc r12, [reg_p3+104] + adc r13, [reg_p3+112] + mov [reg_p3+104], r12 + mov [reg_p3+112], r13 + adc r8, r14 + adc r9, r15 + adc r10, rdi + adc r11, rsi + adc rcx, rbx + mov [reg_p3+120], r8 mov [reg_p3+128], r9 mov [reg_p3+136], r10 mov [reg_p3+144], r11 - mov [reg_p3+152], rcx + mov [reg_p3+152], rcx + pop rbx + pop r15 + pop r14 + pop r13 + pop r12 ret diff --git a/src/P610/P610.c b/src/P610/P610.c index 8474712..0f67636 100644 --- a/src/P610/P610.c +++ b/src/P610/P610.c @@ -109,7 +109,7 @@ const unsigned int strat_Bob[MAX_Bob-1] = { #define fp2inv_mont_bingcd fp2inv610_mont_bingcd #define fpequal_non_constant_time fpequal610_non_constant_time #define mp_add_asm mp_add610_asm -#define mp_subx2_asm mp_sub610x2_asm +#define mp_subaddx2_asm mp_subadd610x2_asm #define mp_dblsubx2_asm mp_dblsub610x2_asm #define crypto_kem_keypair crypto_kem_keypair_SIKEp610 #define crypto_kem_enc crypto_kem_enc_SIKEp610 @@ -124,4 +124,4 @@ const unsigned int strat_Bob[MAX_Bob-1] = { #include "../fpx.c" #include "../ec_isogeny.c" #include "../sidh.c" -#include "../sike.c" +#include "../sike.c" \ No newline at end of file diff --git a/src/P610/P610_compressed.c b/src/P610/P610_compressed.c new file mode 100644 index 0000000..e2a81d5 --- /dev/null +++ b/src/P610/P610_compressed.c @@ -0,0 +1,379 @@ +/******************************************************************************************** +* Supersingular Isogeny Key Encapsulation Library +* +* Abstract: supersingular isogeny parameters and generation of functions for P610_compressed +*********************************************************************************************/ + +#include "P610_compressed_api.h" +#define COMPRESS +#include "P610_internal.h" + + +// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points: +// -------------------------------------------------------------------------------------------------- +// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format). +// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position. +// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position. +// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32. +// For example, a 610-bit field element is represented with Ceil(610 / 64) = 10 64-bit digits or Ceil(610 / 32) = 20 32-bit digits. + +// +// Curve isogeny system "SIDHp610". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p610^2), where A=6, B=1, C=1 and p610 = 2^305*3^192-1 +// + +const uint64_t p610[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x6E01FFFFFFFFFFFF, + 0xB1784DE8AA5AB02E, 0x9AE7BF45048FF9AB, 0xB255B2FA10C4252A, 0x819010C251E7D88C, 0x000000027BF6A768 }; +const uint64_t p610p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x6E02000000000000, + 0xB1784DE8AA5AB02E, 0x9AE7BF45048FF9AB, 0xB255B2FA10C4252A, 0x819010C251E7D88C, 0x000000027BF6A768 }; +const uint64_t p610x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDC03FFFFFFFFFFFF, + 0x62F09BD154B5605C, 0x35CF7E8A091FF357, 0x64AB65F421884A55, 0x03202184A3CFB119, 0x00000004F7ED4ED1 }; +// Order of Alice's subgroup +const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0002000000000000 }; +// Order of Bob's subgroup +const uint64_t Bob_order[NWORDS64_ORDER] = { 0x26F4552D58173701, 0xDFA28247FCD5D8BC, 0xD97D086212954D73, 0x086128F3EC46592A, 0x00013DFB53B440C8 }; + +/* Basis for Alice on A = 6, expressed in Montgomery representation */ +const uint64_t A_gen[6*NWORDS64_FIELD] = { 0x31C8AF7FFC0DE9FA, 0x8A8AD55D2AC8A709, 0x95A4DC49B64E5B2C, 0xF08C77AAE90ABE83, 0x675E4FF97C95845D, + 0xF8A22591248401F0, 0x73F573A4FF34A84A, 0x37D18A6C3D989158, 0xEE73973862A3E95, 0x24084FCCB, // XPA0 + 0x4B8C9CED6DEF0B8B, 0x652C800D926AB992, 0x3DFA6D6B8FD37D80, 0xA30C578CD98EFD79, 0x9FC067E58CCBD32E, + 0x2B0599AEAF150FDB, 0xBA321B31886F3292, 0xE0011F56247547A1, 0x28CA0747910BFAE2, 0xFC020A14, // XPA1 + 0x2728178178DEAFBD, 0xD377C4656DBC71F0, 0x968642007B807932, 0xB8B04B1039062A21, 0xF824771B468A977C, + 0x260F1C50354F46AB, 0x78A3D37CDBBD4DC5, 0x1FB1BAC6851BA175, 0xA73444F1CAC4A10, 0xF3A5C2BB, // XQA0 + 0x4F828B752E825BB4, 0x82CEA210AC766C69, 0x8B1BBC87DAD8BEDD, 0x9BFC5B9CE215B423, 0xF7E1BCC0C541177C, + 0x7727E3A0F1A1AF24, 0xFBCFE4177D2B0221, 0xBB15BDCC160D902A, 0x3FE1467B4A911446, 0x1A495CB35, // XQA1 + 0x38687702D78D1A93, 0x58C09FD23B1E1B56, 0xC54917327D5C0FAB, 0xB6D55B7BE801A3C, 0xEB3AE21C8B93E9E9, + 0xECB45AD6D24FF76A, 0x850645B4F39EC5F2, 0xE6F78202586C9B3A, 0x2923209A250F7F66, 0x26FB150F, // XRA0 + 0x5AC7B27F9096F718, 0x487DDD2820132C83, 0x6B21AC48569E12D8, 0x57B54E5A827D1CD9, 0xDB7C4BEB143E4130, + 0xB6781CA1DA245EAD, 0xCC09878A2A6D7C45, 0x980726C5232C75E5, 0x50D3A7350792C35F, 0x172B595DB }; // XRA1 + +/* Basis for Bob on A = 6, expressed in Montgomery representation */ +const uint64_t B_gen[6*NWORDS64_FIELD] = { 0xD4A2CF040BC56F2C, 0x58F1D1D2B190EDE7, 0x2229F10D3BC7BA47, 0x769AB0F0EDD86AA4, 0x97F1214B80D8463, + 0x9B23774D13ED3EEE, 0x9A182E846DAA95C6, 0x343741369B273442, 0x61FB37462569D4BB, 0x1815EF8B9, // XPB0 + 0xF380CA27C26BF32E, 0xD594C3EA0698D298, 0x21D388E632D1CA2E, 0xDD1E0B34330E0AB0, 0xEA7B89CAD59CA8C2, + 0x28C129BFC584BEC1, 0x48D1E802FC7418CF, 0x11F3A548C5DFFDF7, 0xDB0E9AF98D314F67, 0x219918D2B, // XPB1 + 0xD4A2CF040BC56F2C, 0x58F1D1D2B190EDE7, 0x2229F10D3BC7BA47, 0x769AB0F0EDD86AA4, 0x97F1214B80D8463, + 0x9B23774D13ED3EEE, 0x9A182E846DAA95C6, 0x343741369B273442, 0x61FB37462569D4BB, 0x1815EF8B9, // XQB0 + 0xC7F35D83D940CD1, 0x2A6B3C15F9672D67, 0xDE2C7719CD2E35D1, 0x22E1F4CBCCF1F54F, 0x838676352A63573D, + 0x88B72428E4D5F16C, 0x5215D742081BE0DC, 0xA0620DB14AE42733, 0xA68175C8C4B68925, 0x62651A3C, // XQB1 + 0x4F62205A5DAFB369, 0xA2B75D5BC06C691F, 0x6B82C9B893D51C38, 0x2C2467D7AB7DAA2C, 0x8A8D5AC13C2C5ADD, + 0xBC3AEC544F8953F5, 0xBC43C1BE1B1DC069, 0xB8CDA0908AEBCD84, 0xA213356DB0FBFCFF, 0x15F063030, // XRB0 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0 }; // XRB1 + +/* The x-coordinate of lB^(eB-1)*QB, expressed in Montgomery representation */ +const uint64_t XQB3[2*NWORDS64_FIELD] = { 0x4E8DA387C42D31D0, 0x83AFE0DEB4FCE84B, 0xE819FEA7B6AE32CB, 0xA3DA371FFE9EE0F2, 0x4765959DBFECDE2D, + 0xDB446F20746721E0, 0xE2596FFE42E2D7A8, 0x1FC46DF0BC2B8759, 0x9F5106F3AD0A27F8, 0x161083808, + 0xA88E809BEF28310C, 0x506DB48241A76019, 0xE9FB9219833DF071, 0x342D697582036AEE, 0x25F078F10F357AFB, + 0x43CE96BEE1668B06, 0xC540E958A6494D2, 0x46EB300B952B437D, 0x898338D77E9F811D, 0x1FC9961CB }; + +const uint64_t A_basis_zero[8 * NWORDS64_FIELD] = { 0x31C8AF80CA277BC7, 0x8A8AD55D2AC8A709, 0x95A4DC49B64E5B2C, 0xF08C77AAE90ABE83, 0x2DC44FF97C95845D, + 0xE25D5D22CB0C4641, 0xEDA1E4D340EC56D7, 0x2AE81B9DCDAA0FF1, 0xB4292D8E409BC484, 0x1D5B8282A, + 0x4B8C9CED6DEF0B8B, 0x652C800D926AB992, 0x3DFA6D6B8FD37D80, 0xA30C578CD98EFD79, 0x9FC067E58CCBD32E, + 0x2B0599AEAF150FDB, 0xBA321B31886F3292, 0xE0011F56247547A1, 0x28CA0747910BFAE2, 0xFC020A14, + 0x3CA84837D69D8728, 0xB2BDFE3304CB7401, 0x8C840937950AD3E9, 0xCE8094A539AA6C49, 0xF0802AAE490F29A0, + 0x5458A8E61BB9D01F, 0x3592A73DE4758511, 0x7DEA75B85A60F316, 0xF835EEAC9B12CC1D, 0x11C4E0162, + 0x87A90900552B058, 0xF34899FE9411DC6A, 0x3807CF5B95B0168, 0xC986BAF1E3FFDED4, 0x1D10EAC33AA0781A, + 0xD9569230F9A2D512, 0xF8295F6189DBAAF3, 0x26B44D4CECB1A5E8, 0x9CA4CE754143DAA4, 0xAF517DFC, + 0x2728178246F8418A, 0xD377C4656DBC71F0, 0x968642007B807932, 0xB8B04B1039062A21, 0xBE8A771B468A977C, + 0xFCA53E1DBD78AFC, 0xF25044AB1D74FC52, 0x12C84BF8152D200E, 0xAFB53869D71DCFFF, 0x88D8EE1A, + 0x4F828B752E825BB4, 0x82CEA210AC766C69, 0x8B1BBC87DAD8BEDD, 0x9BFC5B9CE215B423, 0xF7E1BCC0C541177C, + 0x7727E3A0F1A1AF24, 0xFBCFE4177D2B0221, 0xBB15BDCC160D902A, 0x3FE1467B4A911446, 0x1A495CB35, + 0x59DD6DAF69D05BED, 0xD76AC76FF586B73A, 0x7FE9D57BA40A785A, 0xD14A8A25B5B1A187, 0xA96A1F6746EC4DCB, + 0x3D12E7FA86078B0A, 0x37816E342D89C86B, 0xEF93BD5D8E68FE5, 0x582A083E04E4D83D, 0x1A402EB75, + 0x439B3817B316DC12, 0xAAC33FB9DB2CFE99, 0x103161162202C633, 0x3C38BFDA7559D6F5, 0xB4BC209633AB8D22, + 0xA1724B6332EFE4FE, 0x81919EE777E6B9E1, 0xD15DFC6FAB242CF4, 0xD69C41AF15E2B7FC, 0x274D72579 }; + +/* Basis for Bob on A = 0, expressed in Montgomery representation */ +const uint64_t B_basis_zero[8*NWORDS64_FIELD] = { 0x203596CF0245B227, 0xFE7D4CB978F11517, 0xEC79574E9D7DD13A, 0xD24627B69D4DFF63, 0x85B4D3B2B5426BBF, + 0xFF0237C357683FCA, 0x2C3E0FE7792534B1, 0x8B68DB1AFC3F9CDE, 0x5AFD2B5021786921, 0x16CFF1918, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xDFE1CAFF47350FFB, 0x7F6641B5806DBD07, 0xD558CE2B43292C47, 0x28EB4A4147C77BD6, 0x143218EB29F5FB6C, + 0x5F457BD167A2260F, 0x26D9639E9DD4A15D, 0xEC9DFA3764433777, 0x9D8C59E2D257CACF, 0x1D2D65779, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xDFCA6930FDBA4DD8, 0x182B346870EEAE8, 0x1386A8B162822EC5, 0x2DB9D84962B2009C, 0xE84D2C4D4ABD9440, + 0xB276162552F27063, 0x6EA9AF5D8B6AC4F9, 0x26ECD7DF1484884C, 0x2692E572306F6F6B, 0x10EF78E50, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xDFE1CAFF47350FFB, 0x7F6641B5806DBD07, 0xD558CE2B43292C47, 0x28EB4A4147C77BD6, 0x143218EB29F5FB6C, + 0x5F457BD167A2260F, 0x26D9639E9DD4A15D, 0xEC9DFA3764433777, 0x9D8C59E2D257CACF, 0x1D2D65779 }; + +/* Full 3-torsion for Bob on A = 0, expressed in Montgomery representation */ +const uint64_t B_gen_3_tors[16 * NWORDS64_FIELD] = { 0x1930B476A230B7BE, 0x3A42EE16DC949E2, 0x838416CC861CB74D, 0xE43303F18BFF483E, 0x30C6C49AC1829C11, + 0x40DD7E521AF62273, 0x33AA27D882B23CB2, 0xA970F369B7A93C6, 0xDBAC55CF2FEFF179, 0x1967E10A3, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x4709DA258D7CF239, 0x68142BD88204D1EA, 0xAE14B528AE909088, 0x8D813E124214BFD6, 0x8E6949403E0D509B, + 0xF795CE2041AC8CA6, 0x20F1E1F2A851B359, 0x89B489710FA8BD76, 0x1608B910A609EED8, 0x1F957263F, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xE6CF4B895DCF4841, 0xFC5BD11E9236B61D, 0x7C7BE93379E348B2, 0x1BCCFC0E7400B7C1, 0x3D3B3B653E7D63EE, + 0x709ACF968F648DBB, 0x673D976C81DDBCF9, 0xA7BEA3C375499164, 0xA5E3BAF321F7E713, 0xE57896C4, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x4709DA258D7CF239, 0x68142BD88204D1EA, 0xAE14B528AE909088, 0x8D813E124214BFD6, 0x8E6949403E0D509B, + 0xF795CE2041AC8CA6, 0x20F1E1F2A851B359, 0x89B489710FA8BD76, 0x1608B910A609EED8, 0x1F957263F, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xF4209DFFD5BA5848, 0x5B5A41268B033DBF, 0x7487D67F15941658, 0xE0C6754A260143AA, 0xDC40C6C153BD4F30, + 0xA37675E3DD939202, 0x71830795095B5791, 0x204F7BB4612B47A, 0x196818C06A9FA46F, 0x1C82644E6, + 0xC41ECDCAECF46668, 0x3303A35DC32C0272, 0x6A10EEBB3E7C798D, 0x800B26C6B6F0F2B7, 0xE0AA44F811ECA6C6, + 0x38BB298B83C41423, 0x5C8E988E2C1B6909, 0xD61B6FE6260A9672, 0xE249E98EF30D4401, 0xA91ADF39, + 0x3BE13235130B9997, 0xCCFC5CA23CD3FD8D, 0x95EF1144C1838672, 0x7FF4D939490F0D48, 0x8D57BB07EE135939, + 0x78BD245D26969C0A, 0x3E5926B6D87490A2, 0xDC3A4313EAB98EB8, 0x9F4627335EDA948A, 0x1D2DBC82E, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xBDF62002A45A7B7, 0xA4A5BED974FCC240, 0x8B782980EA6BE9A7, 0x1F398AB5D9FEBC55, 0x91C1393EAC42B0CF, + 0xE01D804CCC71E2B, 0x2964B7AFFB34A21A, 0xB050BB3ECAB170B0, 0x6827F801E748341D, 0xB3D06282, + 0xC41ECDCAECF46668, 0x3303A35DC32C0272, 0x6A10EEBB3E7C798D, 0x800B26C6B6F0F2B7, 0xE0AA44F811ECA6C6, + 0x38BB298B83C41423, 0x5C8E988E2C1B6909, 0xD61B6FE6260A9672, 0xE249E98EF30D4401, 0xA91ADF39, + 0xC41ECDCAECF46668, 0x3303A35DC32C0272, 0x6A10EEBB3E7C798D, 0x800B26C6B6F0F2B7, 0xE0AA44F811ECA6C6, + 0x38BB298B83C41423, 0x5C8E988E2C1B6909, 0xD61B6FE6260A9672, 0xE249E98EF30D4401, 0xA91ADF39 }; + +/* Pre-computed pairing ReducedTatePairing(R0,S3,lB^eB) on A = 0 */ +const uint64_t g_R_S_im[NWORDS64_FIELD] = { 0x58B92E3BB6DC9E31, 0x3E280F90A5818BDA, 0x8BF300AC24A8E69A, 0x2E12E47000B08F86, 0xB01B3531200990E9, + 0xF63C539B47B5A4FE, 0x9F70EF0C3FFAB9BA, 0xCFBD59EBE2438F9B, 0x1E7E8AD9F5361552, 0xC2DDA200 }; + +const uint64_t Montgomery_R[NWORDS64_FIELD] = {0}; +// Montgomery constant Montgomery_R2 = (2^640)^2 mod p610 +const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0xE75F5D201A197727, 0xE0B85963B627392E, 0x6BC1707818DE493D, 0xDC7F419940D1A0C5, 0x7358030979EDE54A, + 0x84F4BEBDEED75A5C, 0x7ECCA66E13427B47, 0xC5BB4E65280080B3, 0x7019950F516DA19A, 0x000000008E290FF3 }; + +// constant Montgomery_RB1 = (2^NBITS_ORDER)^2 mod Bob_order +const uint64_t Montgomery_RB1[NWORDS64_FIELD] = { 0x4FDA7CB300F00BFB,0x8559FEAD08AF7CE1,0x6C728679071D8D77,0xFBFABAAF1825440F,0x8D0536062AB9}; + +// constant Montgomery_RB2 = -(3^OBOB_EXP)^-1 mod 2^NBITS_ORDER +const uint64_t Montgomery_RB2[NWORDS64_FIELD] = { 0x5BAEA880514636FF,0x32B4BD3B3F4460CB,0x4802A8E49DA81538,0x9F99CD971298B1A8,0xE333BBA90FAF20FE}; + +// Value one in Montgomery representation +const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x00000000670CC8E6, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x9A34000000000000, + 0x4D99C2BD28717A3F, 0x0A4A1839A323D41C, 0xD2B62215D06AD1E2, 0x1369026E862CAF3D, 0x000000010894E964 }; + +// 1/3 mod p +const uint64_t threeinv[NWORDS64_FIELD] = { +0x5555555577AEEDA2,0x5555555555555555,0x5555555555555555,0x5555555555555555,0xDE11555555555555,0xC488963F0D7B28BF,0xAE18B2BDE10BF15E,0x463CB6074578F0A0,0x5BCDAB7A2CB98FBF,0x5831A321}; + +// Fixed parameters for isogeny tree computation +const unsigned int strat_Alice[MAX_Alice-1] = { +67, 37, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, +2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 16, 9, +5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, +1, 4, 2, 1, 1, 2, 1, 1, 33, 16, 8, 5, 2, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, +1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, 2, 1, 1, +4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 }; + +const unsigned int strat_Bob[MAX_Bob-1] = { +86, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, +1, 3, 2, 1, 1, 1, 1, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, +1, 1, 2, 1, 1, 1, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, +1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 38, +21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, +9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 17, 9, 5, 3, 2, 1, 1, +1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, +1, 1 }; + +// Fixed traversal strategies for Pohlig-Hellman discrete logs + +const unsigned int ph2_path[PLEN_2] = { // w_2 = 5 + 0, 0, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 14, 15, 16, 17, 18, + 18, 18, 19, 20, 20, 21, 22, 23, 24, 25, 25, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, + 35, 35, 35, 35, 35, 36, 37, 38, 39, 40, 41, 41, 42 +}; + +const unsigned int ph3_path[PLEN_3] = { // w_3 = 6 + 0, 0, 1, 2, 3, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 17, 18, 19, + 20, 21, 21, 22, 23, 24, 25 +}; + +// Entangled bases related static tables and parameters + +// Constants u and u0 where u = u0^2 in F_{p^2} \ F_p used in entagled basis generation +// For the 2^eA-torsion basis generation: +// Two tables of 17 elements each for the values r in F_p such that v = 1/(1+ur^2) where r is already converted to Montgomery representation +// Also, 2 tables for the quadratic residues (qr) and quadratric non residues (qnr) v in F_{p^2} with 17 GF(p^2) elements each. +// For the 3^eB-torsion basis generation: +// A table of size 20 for values v = 1/(1+U*r^2) where U = 4+i + +const uint64_t u_entang[2*NWORDS64_FIELD] = { +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0xCE1991CC,0x0,0x0,0x0,0x3468000000000000,0x9B33857A50E2F47F,0x149430734647A838,0xA56C442BA0D5A3C4,0x26D204DD0C595E7B,0x21129D2C8}; + +const uint64_t u0_entang[2*NWORDS64_FIELD] = { +0x670CC8E6,0x0,0x0,0x0,0x9A34000000000000,0x4D99C2BD28717A3F,0xA4A1839A323D41C,0xD2B62215D06AD1E2,0x1369026E862CAF3D,0x10894E964,0x670CC8E6,0x0,0x0,0x0,0x9A34000000000000, +0x4D99C2BD28717A3F,0xA4A1839A323D41C,0xD2B62215D06AD1E2,0x1369026E862CAF3D,0x10894E964}; + +// Tables for quadratic residues and quadratic non residues v with 17 elements each. + +const uint64_t table_r_qr[TABLE_R_LEN][NWORDS64_FIELD] = +{{0x670CC8E6,0x0,0x0,0x0,0x9A34000000000000,0x4D99C2BD28717A3F,0xA4A1839A323D41C,0xD2B62215D06AD1E2,0x1369026E862CAF3D,0x10894E964}, +{0x19C332399,0x0,0x0,0x0,0xFACE000000000000,0x84EEBD0BF76B38CF,0x8E40A1A187FF56C5,0x9882D55D30E7225D,0xCC13F8F7C6CAE46A,0x1A65CFE27}, +{0x338664733,0x0,0x0,0x0,0x879A000000000000,0x58652C2F447BC171,0x819983FE0B6EB3DF,0x7EAFF7C0510A1F90,0x1697E12D3BADF048,0xD0C354E7}, +{0x39F731019,0x0,0x0,0x0,0x21CE000000000000,0xA5FEEEEC6CED3BB1,0x8BE39C37AE9287FB,0x516619D62174F172,0x2A00E39BC1DA9F86,0x1D9583E4B}, +{0x4067FD900,0x0,0x0,0x0,0x4E00000000000000,0x422063C0EB0405C2,0xFB45F52C4D26626C,0x71C688F1E11B9E29,0xBBD9D547F61F7637,0x65F68046}, +{0x46D8CA1E6,0x0,0x0,0x0,0xE834000000000000,0x8FBA267E13758001,0x5900D65F04A3688,0x447CAB07B186700C,0xCF42D7B67C4C2575,0x16E8B69AA}, +{0x53BA633B3,0x0,0x0,0x0,0xAE9A000000000000,0x79755E0FB9FDC452,0x7F3C7E943201E515,0x37933C394197EEA5,0x7484CBD136BDAB64,0x103BE950A}, +{0x5A2B2FC99,0x0,0x0,0x0,0x48CE000000000000,0xC70F20CCE26F3E92,0x898696CDD525B931,0xA495E4F1202C087,0x87EDCE3FBCEA5AA2,0x20C537E6E}, +{0x609BFC580,0x0,0x0,0x0,0x7500000000000000,0x633095A1608608A3,0xF8E8EFC273B993A2,0x2AA9CD6AD1A96D3E,0x19C6BFEBF12F3153,0x98F1C06A}, +{0x7A5F2E919,0x0,0x0,0x0,0x6FCE000000000000,0xE81F52AD57F14173,0x87299163FBB8EA67,0xC32CA2C802908F9C,0xE5DAB8E3B7FA15BD,0x23F4EBE91}, +{0x9A932D599,0x0,0x0,0x0,0x96CE000000000000,0x92F848DCD734454,0x84CC8BFA224C1B9E,0x7C0FE740F31E5EB1,0x43C7A387B309D0D9,0x27249FEB5}, +{0xA103F9E80,0x0,0x0,0x0,0xC300000000000000,0xA550F9624B8A0E65,0xF42EE4EEC0DFF60E,0x9C70565CB2C50B68,0xD5A09533E74EA78A,0xFEE840B0}, +{0xA774C6766,0x0,0x0,0x0,0x5D34000000000000,0xF2EABC1F73FB88A5,0xFE78FD286403CA2A,0x6F267872832FDD4A,0xE90997A26D7B56C8,0x2077D2A14}, +{0xADE59304D,0x0,0x0,0x0,0x8966000000000000,0x8F0C30F3F21252B6,0x6DDB561D0297A49B,0x8F86E78E42D68A02,0x7AE2894EA1C02D79,0x941B6C10}, +{0xB4565F933,0x0,0x0,0x0,0x239A000000000000,0xDCA5F3B11A83CCF6,0x78256E56A5BB78B7,0x623D09A413415BE4,0x8E4B8BBD27ECDCB7,0x19CB05574}, +{0xBAC72C21A,0x0,0x0,0x0,0x4FCC000000000000,0x78C76885989A9707,0xE787C74B444F5328,0x829D78BFD2E8089B,0x20247D695C31B368,0x294E9770}, +{0xC137F8B00,0x0,0x0,0x0,0xEA00000000000000,0xC6612B42C10C1146,0xF1D1DF84E7732744,0x55539AD5A352DA7D,0x338D7FD7E25E62A6,0x131E380D4}}; + +const uint64_t table_r_qnr[TABLE_R_LEN][NWORDS64_FIELD] = +{{0xCE1991CC,0x0,0x0,0x0,0x3468000000000000,0x9B33857A50E2F47F,0x149430734647A838,0xA56C442BA0D5A3C4,0x26D204DD0C595E7B,0x21129D2C8}, +{0x135265AB3,0x0,0x0,0x0,0x609A000000000000,0x3754FA4ECEF9BE90,0x83F68967E4DB82A9,0xC5CCB347607C507B,0xB8AAF689409E352C,0x9DC814C3}, +{0x2033FEC80,0x0,0x0,0x0,0x2700000000000000,0x211031E0758202E1,0xFDA2FA9626933136,0xB8E34478F08DCF14,0x5DECEAA3FB0FBB1B,0x32FB4023}, +{0x26A4CB566,0x0,0x0,0x0,0xC134000000000000,0x6EA9F49D9DF37D20,0x7ED12CFC9B70552,0x8B99668EC0F8A0F7,0x7155ED12813C6A59,0x13B902987}, +{0x2D1597E4C,0x0,0x0,0x0,0x5B68000000000000,0xBC43B75AC664F760,0x12372B096CDAD96E,0x5E4F88A4916372D9,0x84BEEF8107691997,0x2442512EB}, +{0x4D4996ACC,0x0,0x0,0x0,0x8268000000000000,0xDD53E93B3BE6FA41,0xFDA259F936E0AA4,0x1732CD1D81F141EE,0xE2ABDA250278D4B3,0x27720530E}, +{0x670CC8E66,0x0,0x0,0x0,0xF34000000000000,0xB0CA585E88F782E3,0x33307FC16DD67BE,0xFD5FEF80A2143F21,0x2D2FC25A775BE090,0x1A186A9CE}, +{0x6D7D9574D,0x0,0x0,0x0,0x3B66000000000000,0x4CEBCD33070E4CF4,0x729560F0B571422F,0x1DC05E9C61BAEBD8,0xBF08B406ABA0B742,0x2E24EBC9}, +{0x73EE62033,0x0,0x0,0x0,0xD59A000000000000,0x9A858FF02F7FC733,0x7CDF792A5895164B,0xF07680B23225BDBA,0xD271B67531CD667F,0x136B9D52D}, +{0x80CFFB200,0x0,0x0,0x0,0x9C00000000000000,0x8440C781D6080B84,0xF68BEA589A4CC4D8,0xE38D11E3C2373C53,0x77B3AA8FEC3EEC6E,0xCBED008D}, +{0x8740C7AE6,0x0,0x0,0x0,0x3634000000000000,0xD1DA8A3EFE7985C4,0xD602923D7098F4,0xB64333F992A20E36,0x8B1CACFE726B9BAC,0x1D481E9F1}, +{0x8DB1943CD,0x0,0x0,0x0,0x6266000000000000,0x6DFBFF137C904FD5,0x70385B86DC047365,0xD6A3A3155248BAED,0x1CF59EAAA6B0725D,0x61202BED}, +{0x942260CB3,0x0,0x0,0x0,0xFC9A000000000000,0xBB95C1D0A501CA14,0x7A8273C07F284781,0xA959C52B22B38CCF,0x305EA1192CDD219B,0x169B51551}, +{0xCE1991CCD,0x0,0x0,0x0,0xB066000000000000,0xB01C62D467945597,0x6B7E50B3292AD5D1,0x486A2C0733645917,0xD8CF73F29CCFE895,0xC716AC33}, +{0xD48A5E5B3,0x0,0x0,0x0,0x4A9A000000000000,0xFDB625919005CFD7,0x75C868ECCC4EA9ED,0x1B204E1D03CF2AF9,0xEC38766122FC97D3,0x1CFAB9597}, +{0xDAFB2AE9A,0x0,0x0,0x0,0x76CC000000000000,0x99D79A660E1C99E8,0xE52AC1E16AE2845E,0x3B80BD38C375D7B0,0x7E11680D57416E84,0x5C49D793}, +{0xE7DCC4066,0x0,0x0,0x0,0xAB34000000000000,0x350B1FE05EFF8E67,0xF9BEF254B12A2C97,0xE0ED0164644B7B74,0xA4E36CEA639ACCFF,0x26D73AA5B}}; + +const uint64_t table_v_qr[TABLE_V_LEN][NWORDS64_FIELD] = +{{0xCCCCCCCCE168F4FA,0xCCCCCCCCCCCCCCCC,0xCCCCCCCCCCCCCCCC,0xCCCCCCCCCCCCCCCC,0x76D8CCCCCCCCCCCC,0x3E565465D2C0BCB,0xB12E9DDC577A588F,0x1F35C932D0B247B5,0x521DAB18F8F36B0,0x231AFE7CE}, +{0x666666663D2E160A,0x6666666666666666,0x6666666666666666,0x6666666666666666,0xEE52666666666666,0x5B25D1449A5D48C5,0xD37242D15A2B4239,0x263FD38E8023BAE9,0xF8DC6C2184B143B9,0x948D7F34}, +{0x2B7522B7524531E5,0x22B7522B7522B752,0x522B7522B7522B75,0x7522B7522B7522B7,0xED882B7522B7522B,0xF1639645024AE01,0x4F035B12DE5E50A0,0x73C4980ACDD7F1A1,0xA42840C6580DE412,0x1DD62C7C0}, +{0x915BA915B759C347,0xA915BA915BA915BA,0xBA915BA915BA915B,0x5BA915BA915BA915,0xD2C915BA915BA91,0x71F86F2E9E45744B,0x40364B61A6454DC2,0xF1CB7911E8296CFF,0x22098A2EFDE7A36E,0x26EBD6120}, +{0xAD9149BAD91637DA,0x9BAD9149BAD9149B,0x149BAD9149BAD914,0xD9149BAD9149BAD9,0x9F25149BAD9149BA,0xD62B18FB0FE869F1,0xC55BADFBDB1E3966,0xD3983013C35F72D3,0xCDCBA5EC343A38C7,0xA9663F71}, +{0x375B229374E412DD,0x29375B229375B229,0xB229375B229375B2,0x75B229375B229375,0x77BBB229375B2293,0x2DE6294756311D89,0x7FD8288210926F0E,0x959F6E4E9B17AAF0,0xD0DF547715963752,0x23F992A62}, +{0x95AB46517CB6558,0xF00AC4C8322D018D,0xC4BBB5E824213413,0xFE54FF999E981B8B,0x457485163ADB696E,0xB3837BF2C2444F67,0xAE6D4CC9D80D6369,0x16560F053370AC84,0x23263644FE26E906,0x70C8ECA4}, +{0x1499D806F149DE33,0x192F79503F8504C0,0x8136E31922FD0B62,0xE3640C9A3BE918D,0x827DC7EEC12747C3,0x816C63BC5D0BB5E8,0x2B161316CBD65F8F,0x113FC50958EB09DD,0x6F238E5A72A41216,0xABCB36F8}, +{0x84665F30F3CF95E5,0xC3B84BD34725A330,0x3A6AF0FAC575EE0A,0x9C71AFCF5C78A658,0xB84BA4EE269DDBC3,0x8E25FEED6714479A,0x6FA95E8F73EA96FC,0x4E8F67FDBB4C1B14,0x9F723476F170C736,0xBA3A5C22}, +{0x9005A1C185D2E4DD,0x1804C2F06A988218,0x5C73BC15BBDE0797,0xC72EA5FFC1BE0B12,0x5F5D25F1D4AC4F2D,0xD90ACB26BB0EA9D3,0x771734D57DE89542,0xB9B7016789BF68DA,0x4AFADFDC405345FF,0x114409A09}, +{0x69E362D42702ACE6,0x9FC36EB7EA12F1E0,0x9CCA7DF3BC005DFF,0xD8FB897860F89087,0x684E603A54569145,0x59A0620287865C95,0xA1EE61177C586BBF,0xDDBC6767DA8F6EE1,0x9C092A6A8396897F,0x27991721C}, +{0xE70C93731F788DA2,0xF9415624BA1759DB,0xC894EF9847A7245A,0xE2380C3455075FCD,0x63CD08DC462AABF8,0xA1CFF8CECB706A7,0x5BBB070AC484296B,0xF8E970373DD450FB,0xF985BF0108DCBA20,0x243AC61BE}, +{0x886DC36536F16AC0,0xCE46420B9809323C,0x8F0CE1E1A569DA62,0x574F7A978263CAAD,0x93BE116009D2DB5C,0xE47CE9FDE2BCB17A,0xAEFCD1BFDE2FB352,0x6596D37050A6FE96,0xA936C53A6B044AC2,0xBAE5C165}, +{0xDF14045D75410E1C,0xA73CCCB143DBAC13,0x20FDC4139A3DA98B,0xB91023F5D83E66D9,0xE7D50F33079A6014,0xA6117DAD2E4A7E4B,0x78B9C7A26D42C39F,0x8856BF64102261B1,0x31F624C6B2E5E24B,0x1A9000C99}, +{0x4D1B7C9879B8F55E,0x2A149D570FBDDE34,0xB2B6E11841366015,0xBCF5C4F2C545EF76,0x939396F37CA988F0,0x2F66041FC5F19298,0x60D9027E6FDDE5C8,0x594434D0D278B451,0xDABB15ADAEA1D3E7,0x24D1C996F}, +{0xEDE936859CC846A4,0x906F12AFE543BFE9,0x57F752DC24BCDF97,0xA7AA6C41ECE9523E,0x70D8DB291C664F5E,0xC2D8762B1F0A0862,0xF538248730EF2597,0xE1699BCD8E10BBF7,0x4A5EA2590DDB6DCC,0x22EEB1551}, +{0xF2A95939B0FDB788,0x220AC9E23E53C0A,0x37C7FB2D043F1549,0x17A39CE70F0B8E54,0xF8D84DD2D87A4331,0xCC560AC3C2D4ECB1,0x29AFE290E4B8470D,0x5FD3854406911AD1,0x16284324DEA12E26,0x265A1E3E1}, +{0x72512896E203613D,0x42909204E70C74C1,0xF2787ADE891C95AA,0x726631D78DAFCFF5,0x812D335F7915E3B4,0x602D763CFDD14E0D,0xF09DBF94B4B8587D,0x95CEDD56F23A03B9,0x35067361D5A1D79E,0x1FD8BE4EB}, +{0x401CA1FC04E9C123,0x90C26307F5CC0A0F,0x485D5BE49E59B0C3,0x4FE729949842C2E,0xDFE318C2AE76911B,0xD12311AD4DD78EA1,0xE40CA0745241900F,0x3D124917B409965B,0xBFD7D5AFE6476F0,0x6D74FB8C}, +{0x2F3F273A24BD4ACD,0xBBC4B38CC68BA0FD,0xE8B2D539670B7871,0xEA60CBAEA93B6577,0x487E2AEFF59AC1CB,0xD2D62FD5A457C222,0x778BDCA33D649C39,0xD6463F406CBC16A4,0x726CA44086DD4B26,0x1D3824D0D}, +{0xBDB1260A3702AD09,0x2D6B1A339991FEBC,0xAA9F6C83305EA847,0xA046C8AD7DFDC0E3,0xD44F15831B61D266,0xE5069559BBEFA954,0xD78E56E41C84CC4E,0x760438E0D334C5E,0xAD70552405CB2442,0x26FADBB00}, +{0x62D4D20873F55316,0x9E0A17CCEF05AEAA,0x3297B1A6560ABFB3,0xC178F3490A1BFF80,0x30F33204C7CD322E,0xBF67D1323DD3AF36,0xC26B4425CDECACD6,0xFD1804929AF46345,0x6C6AD7A3773EB3E9,0xA0F5703F}, +{0x7B5586A15EEE987A,0x712704F03450E84C,0x6FDC36F98F02AC0C,0xA1B5EBF84C82B74F,0x70B06DBC6C6FBB4,0xF49DA4BBBBB4A081,0xD539B581C8C78E70,0xC505DC913CDC308A,0x79302B7361615850,0x1FDAD6EA8}, +{0xC864A00E76FB7862,0x7F79E3208CF1BA8D,0xCEBB9173B4F3EB3F,0x65B5CD9A69BCEE1F,0x2FFC82DF6866F802,0x372294003EFDDFB6,0x2B4A606D7D21B67A,0xFCCF899A749472DD,0x60AD6F3318245C4F,0x8A94EC6B}, +{0x3B540A505CFDE08A,0x1F4FA2605E47B5FD,0x545260EAD2FAFEEF,0xEACCE2AB9D6A73E1,0x4DE929F08605608A,0x7FD4E8C4330111E9,0xACA7C41ABA9F32CB,0x81CE18FFB987259B,0xCF27FAA2E00078FC,0x13C2D3CF2}, +{0xAC298794E336248F,0xA36E730E1546DE9E,0xACF027D5C26DA122,0xF5F2E5A8A5CC01FA,0xBBDC81BC339A2257,0x70D7847A7AC291EB,0x653A274765BB19A2,0x4AD77CDA41E716D9,0x909862AA50015453,0x214843766}, +{0x28DCFDDEE7E75520,0x926112237D3B1FF5,0x1C7EF82595F8671,0x1506781F7F3CBDFF,0x6085630169990327,0xE99E1AB62629523A,0xF5124A3DA6D4B381,0x6238E3E6BA5CD147,0xFF73FD00F4AE2505,0x267B4E1A7}, +{0x4562207B3C7D2A3C,0x5326B1E0C543FDBD,0xDB4DEB9EFDF44D2C,0x4127DC9D580DE9A7,0xB5A21F4968C0B6A,0x551995E644DD6F9D,0xA410258D02B6BD1A,0x38AD3333153D132C,0xBC05805A3AF78F5E,0x118462D9D}, +{0x6BCC76AD0919255E,0x1CE349F8E0113FDD,0x9FDDB44D41754041,0x17B14F71175D7A86,0xFF025B1D9403E728,0xB066EF99669BAC1,0x823A70C11307F544,0xE302A74F2C217B92,0x44959A86BE1185DF,0x1AAAE7CC1}, +{0xBBA91C2845FB1C23,0xFDAEBA39658D3CB,0xD20FA6CF11D6712F,0xE1F96B50E371876C,0x8FCBEAD568182A6E,0x7470BD4B6F6ECAC0,0x854B204F3377B675,0x1A4069A8A9B7FEE1,0xD94275FEBB51BF6B,0x278D27918}, +{0x6426BB8949C81154,0xF8E70C86ACAADADD,0x254018F73FF1D13,0x299DE9B99FB375F3,0xFAD85F5B9455BC3D,0x75B38230DECC8C86,0x84D8352EC4455A3E,0xC63E8F4D14896C61,0xABDCAF24FBE2620C,0x18DD5BB6F}, +{0xF983D3F93B7E21FB,0xA1EFB325856DFD63,0xB40DBF77DDD2F2C6,0x90765A64B6E3095A,0x5C97784B64B13624,0xA66B10ECDB13601E,0x56B0519E348B08D7,0x377A62607E2C784,0xBD9E2E4BF13D82CB,0x1FF451525}, +{0x10BEA3C10F74187C,0xD1A28B48103C996B,0x71DE9B27B2DEE637,0xCCD9CF6314DF24F6,0xA3509CFF5B01D17C,0xBD870219DBDE553D,0xC24847905D600F2,0x3F6029BE326908F1,0x956902BB0608AF31,0x19FBAFFCD}, +{0x43909A8B57B3D387,0x11CAD4DD5E94732,0x5ACD10DE50BD4786,0xA485CF553F041B2F,0x78621C881B370A7F,0x54D76CE547ACAC13,0xD2BAF160F13C3B9E,0x4FDE5E64A3480204,0x2501DA6825E2CC9A,0xD63111F9}}; + +const uint64_t table_v_qnr[TABLE_V_LEN][NWORDS64_FIELD] = +{{0xAD4AD4AD4C6A88FF,0x4AD4AD4AD4AD4AD4,0xD4AD4AD4AD4AD4AD,0xAD4AD4AD4AD4AD4A,0xA6D6AD4AD4AD4AD4,0x9AEFF6AA14208728,0x25F686D3A6B965DD,0x89CFD24F7B8B05D6,0x3277900023742A0A,0x181A60983}, +{0x95A95A959CABB803,0xA95A95A95A95A95A,0x5A95A95A95A95A95,0x95A95A95A95A95A9,0xEF5495A95A95A95A,0x9FD9D03AB2C137A2,0xD6D285BBE104B16D,0x2D2DEC66777C8B23,0xF413D3CA7DE5EA6B,0x5EA0F8F0}, +{0x890EF755DC154E99,0xA890EF755DBC422A,0x2A890EF755DBC422,0x22A890EF755DBC42,0xE6F8890EF755DBC4,0x992CEA18AE912E4D,0x78C13445EFF8450A,0xFC7F0B40B903DCD5,0x3DEB2380F4A72BD3,0x14B83DE77}, +{0x5CF29BF686807934,0x25CF29BF68C35902,0x25CF29BF68C3590,0x9025CF29BF68C359,0xE9A5CF29BF68C35,0x298A955A6155A056,0x8F77CBC74E2AE5F6,0x366A3337A563ECA7,0xB5182885FF4D6097,0x1885CE5B2}, +{0x1060A07FBF2642F,0xE01060A07FBE7D7E,0x7E01060A07FBE7D7,0xD7E01060A07FBE7D,0x832001060A07FBE7,0xED7D83B8855A105B,0x61124019E05FD124,0x17593771A74013B3,0x65ED650971772921,0x27986C521}, +{0xCCD20A70CAA86EA0,0x3CCD20A70CCB7D63,0x63CCD20A70CCB7D6,0xD63CCD20A70CCB7D,0xE023CCD20A70CCB7,0x46FB7D673A1F3731,0x4BB2D66D1167EA52,0x455020A49BCB6949,0x65C58A1BD6024304,0x79DA31E3}, +{0xC8A714319269CBF,0x3EE6C5324FB03682,0x820C8A7143192186,0x863EE6C5324FB036,0xEB040C8A71431921,0x136A320C0C040BB6,0x168E5DED014E95FF,0x823E3A98411D42EC,0xBF3B909BE84CA071,0x20313C368}, +{0x79102520ED23EA0D,0x4F1889D99670AB6C,0x6C79102520EE923E,0x3E4F1889D99670AB,0x415279102520EE92,0x70DBE13BE1C34F41,0x5B5EAA3FAF145AD4,0x783FC4CF8CF9BE6B,0x137330EF8AE1C880,0x1B4499FA0}, +{0x4634145CDBBC7D65,0xBE4634145CDBB9BE,0xB9BE4634145CDBB9,0xDBB9BE4634145CDB,0xFC11B9BE4634145C,0x2FE8FEBF758B8693,0x62828E9265ECF9A0,0x1C4ED813B3BC7207,0x846F272559B2E04B,0xB0BF2182}, +{0x20103473E1D7FF3A,0x2920103473E2E529,0xE52920103473E2E5,0xE2E52920103473E2,0x896EE52920103473,0x11F70027A281C06D,0x3B5E57817B07BF75,0xAB30DBCF075069D5,0x7934D8F49EE1D2A2,0x1E5CF7B77}, +{0x9A1999347725E051,0x99B2E2369C46A0F7,0x477258EE57C21979,0x69C46A0F79A19993,0x56DA2197999B2E23,0xCE319B8B5D5BF252,0x5FFDE836E4511966,0x3C4EE6DEE16E12B3,0xF9D395517385C677,0xC56DA3A3}, +{0xA333A4F9F563A486,0x16C18290308AE972,0x9F5BF3DD45A35733,0x308AE972A333A4F,0xF74E3573316C1829,0x6C7C6702DC7153B0,0x77D40082BF6132B4,0xD95D312C4920072E,0x7E9DE8AED502DB52,0x1795EC244}, +{0xBFAD90149BFAF2C4,0xAD90149BFAD90149,0x90149BFAD90149BF,0x149BFAD90149BFAD,0x7E72D90149BFAD90,0x6866E05B5982496,0xC0A9956428181AA3,0x692DDBE0498CF749,0x8D9D8E6C9C0C1C9F,0x123FACCAD}, +{0xA4DFD6C80A1A7714,0xDFD6C80A4DFD6C80,0xD6C80A4DFD6C80A4,0xC80A4DFD6C80A4DF,0x8425FD6C80A4DFD6,0x8E0BC711DB513DD0,0x7A798B500484E43A,0xB493DF45AE3AFC5,0x35B299EB698262E2,0x251C8F93C}, +{0xF106BA2361C0BBFC,0x267751BCCB188710,0xCF04E54D6488BC95,0xE9C02260C68B4DBC,0xA0F2D5B56BFB777B,0xC62C2D54EEB3DD6D,0x8C3B7A47FF6C7E8D,0xE7AD379C550443FF,0xE820CAF499D9CD06,0xBB9BA44B}, +{0xCECFBC1D4AD7905D,0x269973BD729F0BBF,0x96F247430346373F,0x3C32617FB97A7BB4,0x170F7C62323C3A3A,0x1B9DB0A6D879BD7E,0xDA82AC8B59360996,0xA26FE113F634C7A,0x7130F589581CBC64,0x13858DF6C}, +{0x7E5D2D52571E03D0,0xF75D1072B445F79B,0x706331C41D88D1D5,0x265B33A4D24975E8,0xC97488655D632ABE,0x6D82AC11CD7F6048,0xB030079E0A9EBAD4,0xA7E87B1B62EAFB16,0x9522F6F141D35D44,0x82B24B60}, +{0x242547937C0658FA,0xDC6E5DA7AEE53E68,0x84EA07953DACDA65,0xE92546CBB60D8BA3,0xA612BF6B9CFBCEAE,0xB2353AB9010C800F,0x1BBAD6158193C629,0x5464119263DFE2DF,0x50E7B308405743DC,0x20FCCD43A}, +{0x6D72564707F57DA7,0x44E62AEA7A94D72F,0xC60D55CE4D3ABF28,0xC819D3C0BC081DE5,0x161317D2034B91E3,0x9A84FE10A373C3D5,0xD73276492F6D4036,0x5332ED7A2830AE9E,0xCC28BE76FB2DF00A,0x120CA3CCB}, +{0xFAB2620720D754B4,0xB0B9E340EEDF8BC9,0x1653DB4EA86AA228,0xAF4A45B466A291F5,0x6F2D8FB5B3D8182E,0x7774D2D36F2E881F,0xC3D2516E474E557D,0x92B45DD23EC32833,0x3984A07B8619C7C9,0x1CAB80BBA}, +{0xE7CC90E6EE298EA,0x99D3392BBC06C468,0xE8F51B6B2D8C36DD,0x7477C602BFC793C0,0x4CC9A5B9824BBB8D,0x66B8B5F5427D3453,0xCC9FA954AA043A0,0xE68FEBFA58A0024E,0x1C4E709FC346F24B,0xE0867832}, +{0x16134C45F74D2894,0x645075230AF517E,0x638788BD12EAF884,0xBB57CA874264F15D,0x83B306DD1713D2A4,0x623C0C908B287197,0xBA8FC5C2734F4A9E,0xFC971C3F17C55B04,0x61546665082121F8,0x18551EAB8}, +{0x47236352CCCCD4B,0x807700F6D1EDDCEE,0x17537341BAEA6CBA,0x504419A64B50C73D,0x2591E7171ACC64DE,0xEB04A5C122391E85,0xD96557BF89D24F8E,0x780CD38FF64726CB,0xFDAFF780CC4EB54E,0x11861577}, +{0x302306EE9997BC4D,0x3E045AB634949BFF,0xCC742F753994DECA,0x7E7F0333368EA0FF,0x8A8430A2AB229760,0xE1D75408F952D6F,0x4F3D600657F280B3,0xDE89E80487A538B0,0x68D1E57A19D64620,0xD0027A4E}, +{0x5970FB914A91F4D4,0xEF97BEC7A9F0D144,0x693EE802E571FE58,0xCE320E8569E81BC7,0x2FE521976533C96E,0xE5D7F9268E7D0519,0xFAFD246C31C4833,0x7218544447E13899,0xEA1FFC738CF3C5D3,0x95EB5BCC}, +{0x5B105189D0CA2ADE,0xCEDD8AD3AABF2386,0xA052407BEE2D471,0xD51FFCA04EBD31DF,0x7CFF2C4FBFF9840F,0x68E863DD7BE0FB3F,0x71ADC0F419B76B2F,0x9F2486034EC06308,0xEE7F083774F1E588,0x1782E172E}, +{0x26B06F653E426CA3,0x653E426B06F653E4,0x6B06F653E426B06F,0x53E426B06F653E42,0xCD29653E426B06F6,0xE25934934CDB47A9,0x368EE07F45083838,0xFF81E126E2784509,0xB7FBA2C6FB2C0307,0x66F35905}, +{0x7C84D60DEC9AE6B4,0xDECA7C84D60DECA,0xC84D60DECA7C84D6,0xDECA7C84D60DECA7,0x5F6E0DECA7C84D60,0x5E606F56135F2DCD,0x6D881359A8F60397,0x381AE539FC37E98C,0x29BF8428D894967B,0x12918EDC8}, +{0xBF924F1BF0EB7ADA,0xC78EDA5EA1CEF780,0x48C247D7D53CFE2,0x3FE9A831F3E25AF8,0xC4223C70A27E8F90,0x51DCF86B78B6D4C0,0x29A14DBF09A8A42,0x35B0B186FFA03AA9,0xB34DDE1D41C9D131,0xF56A46E3}, +{0x253AF4484C94CA03,0x32A226E35D2A4AA2,0x4FB18C5BBCF1589A,0x3E17070314360DE9,0xB94BC9B9873E96C0,0x8A3E6EFEA06EB882,0xC06DE286FA2EECCD,0x124298F6432B070E,0x25CB59755BA0A18B,0x14B1CD916}, +{0xBF83218A8CCC3E78,0x5BD5A5F17E801598,0x2F948F576364D3E7,0xF9D2270EC3408B6F,0xC00D05257D2C78BC,0x3CA32AC0114D7EAF,0x16D9296AC7B7D2D4,0x6E661F03BA457337,0x3F69FD67E3F62F31,0xA70AFB41}, +{0x67B914B86B6BD1E0,0x9E7D53018B3CF47E,0x4A5172C659663E8A,0xCE0F42ACA114BBDA,0xCF29856D865D954F,0xDC1EF1F853824B06,0x8D28378F21C8EB01,0x8140F83D8E9FBBA9,0xEF3B3FBF4817BA,0x1CEA072EF}, +{0xB04ACFA73EA0C46C,0xCF933F68BB9B3F4A,0x15AE5CE2F27DB04C,0x1695B1823A1F6D59,0xD753A316CA51CB6,0x7445E2D99B0BA50B,0xB6F9A9A580E786,0x51545996DACD4F17,0x112B452323F4F0A3,0xAFBF4B5F}, +{0xA8982A5E43B37B3,0x4D1DFB947C1F2BC7,0x7A938628C766F64A,0x545AB97381CCDA04,0xD8ACCB93F83D4C5B,0xCA5959634A186221,0x9E72DEA20E161486,0x3FB2EF9969B4F6C,0xA62EC7356550C78,0x1C0F7BD25}}; + +const uint64_t v_3_torsion[20][2 * NWORDS64_FIELD] = +{{0x6EB3E454124AAF4,0xEB3E45306EB3E453,0x3E45306EB3E45306,0x45306EB3E45306EB,0x286B3E45306EB3E,0x375E62F5BC7C82AF,0x650BCBF202B9AE38,0x3FDD465F450DFCFD,0xC63A99445C986900,0x250ED785C,0x2983759F1FCF38D7,0x83759F22983759F2,0x759F22983759F229,0x9F22983759F22983,0x4EEA3759F2298375,0x87430979EEB424F2,0x4D75F319566660DA,0x30CD05437A146239,0xA2641600BDE8C04,0x712AA3BE}, +{0xCF43C7FB897F2FE2,0x3C7FB84C2F0E011E,0xFB84C2F0E011ECF4,0x4C2F0E011ECF43C7,0x751C11ECF43C7FB8,0x1D007C113B5D095,0x4235B0D5E66773CE,0x9E42B6C94350F39E,0xB98F10656ABF493B,0xA2738C79,0xC023D9E87818892A,0x3D9E878FF70985E1,0xE878FF70985E1C02,0x8FF70985E1C023D9,0x52445E1C023D9E87,0xC4A56A1DB3037852,0xBE1F9B0F8C463146,0xD7DB04211C8A255B,0x87C4C4B67CF93C1C,0x96C2BFBD}, +{0xBB5E4448409D1B64,0x9650668A321ACCD8,0x48D39ADBC2F1339E,0x8F7071B9DA7AD093,0xDC2BFF88AE51552D,0x67B12046E4504FA2,0xDAC40568A6E7ACA6,0x62ACCE83A2BE7FE7,0xCEBB880D5DC0D19E,0x25FA2A502,0x12FE408DB093593F,0xAAF044FB38FAC1A9,0x2726CD500D0CEF1,0x1605D37D0757467F,0x1B66F6542117A77,0x1350C0D1B1A7435E,0x51F0069F69135871,0x203791450029A4BC,0x42B7E3FCB870BE19,0x1CDC6F300}, +{0x7B5CB802B56792C7,0xBD1E27BB33DC664B,0xC2399B484A347FD4,0x5CB802B42E1D844C,0x7699BB33DC664B7B,0xA62220120D0CB91A,0x24AAF6ED9C3527F0,0x1FA962A3FE0A08F3,0x219A48CC422DF1B1,0x118AF1785,0x2085638DAFEB8A83,0xFD68A923B68BC5DE,0x9743A21DF7A9C724,0x85638DB029756DC4,0x9A323B68BC5DE20,0xDC5A0F3CC5799C18,0x3CDBDDF993C3E933,0x399816785890182E,0x3DDF5FEAA7F4990C,0xAC3F3421}, +{0x63BDA9468BD342F5,0x7403E8DA50E41EF7,0x7B32C72BE3C39E62,0xA4AEF030E69A6DAF,0xC8E9EC938255BB45,0x5AE36274AC3BB919,0xAF73A8FEA01C6E98,0x6C9E0C391AEA075A,0xDE3F1DFEA825A09A,0x495C0A99,0xCDBBE48241B79B59,0x29FF396B0854C507,0xC91466B43E7DC219,0xA46772E1FAE15C03,0xC113B29586A5D8CF,0x44FE6A6E5B9FB7B0,0x11825F97D892585E,0xC1F3209A0E0006B4,0x313425C4139E19C4,0x14DB5D37A}, +{0x3011EB8A0C610EAE,0x8632968FCBEC6D1D,0xEF749BB7DE6283EB,0x1038A58CDB855B10,0x5574052BEBB46182,0xB3E1CF3C83597C0F,0xA718ADD06AD56610,0x359FB5AA447520F6,0xCDF6E662B8EB669C,0x9CC50ACC,0x4E213592827CF602,0xB80C916F6BF2EBB6,0xD05F9D238FE11743,0x5FC7793D16D042BF,0xBD58FD8E99F594EA,0xC1100B4C07C4A897,0x29F16A0996A54969,0x3A7EB43A7FC5530D,0xB3EF41DC7BE3CE6C,0x4A3A4407}, +{0x32CEC987C02E1E16,0xB7E44C9BBD497EE5,0x59C0313782E83DF1,0x2C71AF09B871F5DE,0xE44DFBF49F9CEA51,0xC4BD0DF1CC341EB3,0x7EC7C21EE53DE39D,0x2B1B1BB9C6276C2C,0xF86DE3A5ABE9539E,0x2302FFE8B,0x28DF22C8DCD7982F,0x426541E94DCF04E7,0x98CA1BA8F9B2855A,0xF4067E6F7EA49E1D,0xD03034D68F095472,0x7D26821B325A3A85,0x87DB2B11EC3322D6,0x73BAAA33C117FB57,0x92225964AC014B47,0x12E0D7FE7}, +{0xDF2479A490E3F3DA,0xE07894F7FF684C36,0x9A5E7229EF62380A,0xE88DF8EE954C69A4,0x800A8000EAE4D453,0xAE77A73EF2BD6B7D,0xDA18723BBC2CA8D7,0xF186FA30727D2A31,0x291452F619104C5B,0x1E7F1399,0x3732F21D651B1FEE,0x8DDCCB2BDD071E43,0x9641B49A54A8A116,0xDA68148CA4D341DD,0xC32B7A049A23B8F4,0x24932D3124EB482F,0x84AE00B5C46870B9,0xCEAE14C3C3D55562,0x97148EC2C4193A5,0x1D94CB43}, +{0x5DDBBCF90B937BD9,0x3E84379AA3442E8,0xCC25DC2808E0C528,0xFB444A0D98465DEB,0xD69F5A96BE71AC2C,0x13938F1D6E581318,0x37AE0B4F7DAC04ED,0x863F2AD318BF5A7F,0x397673E27BAC9DEA,0x1216A9621,0x904B65B8E15A658,0xC7BB97BD7B0C45E2,0x93CD91DECA863B07,0x7E159E553BF8497,0x5075FEF394A53914,0xE7E384970BABE75A,0x5968B82EF98ECFC6,0x29B5FE78CEF214F8,0xE3F63B7F9DF9725C,0xFDF9B378}, +{0x57CC8084740AF239,0x5703E093ED1DEC26,0x700B10597FE6838D,0xBDADB8A8DE7E5988,0x3EEB9E3F634109D8,0xC632284A295D87A2,0xFF7ED47380421F0,0x46A42D85372D6D51,0xCEB02C53FD6561AD,0x68700397,0x94083C312FDD1CCF,0x8D8BBEBC2683FDD4,0xDF6AA14583575AC1,0xDF3FF19FF44AEEA3,0xCEBEB4FB032ECD7D,0x9CE783658636286,0x7B3D4444C53B3D32,0xB8749FA7F3A9070,0xC415DCDB6A0AD61E,0xB7869319}, +{0x139CF42869D49482,0xBC6F0C720A8973B,0x28E407583814A9E0,0xF00EFBF2ED7F95AF,0x7D480A57AEF5BFD3,0x7EC46EDF97D9EAC2,0xB3F987339979273B,0x699F07E12CA4729D,0x7A1D6F1D94D877DD,0x24F8BFBDA,0x971EC29363AFF4EF,0xA525D0504E28FD9,0xB1499925B9A9134F,0x3790DCE6BA9C9907,0x9E2EB2BD7D2BDE58,0xB1A37E98CE909692,0x4C9EB9AB58C0D4A9,0x77A16CF26A2492C6,0xB2121E58A818AFB2,0x5FF8FB81}, +{0xD59C657588B26B4C,0xB824E399449753E5,0xB2EA59D067504894,0x2E77C98265BE8415,0x3A34AD15D89E7895,0x6AA2E3EAB0F65905,0x3A464491A81B6AD6,0x64AFCC145F1EE37C,0xEF30841D92867D4C,0x1653C11AC,0xC4A62DC72662944A,0x4BC6EC7683E05B2E,0xDE0AB70705491613,0x7FC5FD6400FBAE3A,0xBE093F12B7441F4E,0x754D61F85BE9B748,0xED144F4AD57B89A0,0x4B6DFB51DECE2551,0x67980426FCD240D0,0x75699852}, +{0xD3D4BB413D7061BE,0x18AEC9D6854ECB25,0x74912785EEF65EF3,0x428B21B602840579,0x7BEDFBC19961AB28,0xE537045DFA2E6F0C,0xAF709EC9946F55BB,0xD4633E3CA2BBFE3D,0xDDF84B965ACD8170,0x1837A2775,0xFB8249F345205225,0xDC81B2C34B0B30FC,0xF5B9D98AC4766CBA,0x8B37B96AC565EDF5,0xAB88EC455AB3E730,0xF99410A2815AE199,0x926C8A85493EB093,0xC7082D622A51444B,0xFE11910D6EC752C1,0x22D0E6336}, +{0xFBDC842A96D96B13,0xEE3034ABA5D2EC9A,0x5D4BFE83ECA3D306,0x10CE1C3DB0210EC,0x645EB45E9AC10E46,0x99085D8D171BC2BE,0x9F361AF1FC456B18,0x8D9D38D8C416A25,0xB071C0B7D59CE33C,0xD89DA6CB,0x770A7B6239055C1F,0xE9767FC8D42B73D3,0xFCC1954DC3AC1EE7,0x1251746D17D4CA40,0xD83FEEE6736971D,0xB0210B1F8D0AB262,0x3DE49D676CD13FB7,0x1657FEBB10C212AF,0x2F61A2D8A3F81312,0x18E3342F8}, +{0xD08AB92DAE048DB1,0xAFDFB841D45B6CDB,0x4E16B9F649DBDAD4,0x8F7BD80A86CD6FE4,0xE9D860EE31368282,0xAB87FA97EF9B4B4E,0x595B5FD6D5CD3C22,0x8B2AF45E9CDA91B3,0x2DFE5B32A817912D,0x1FB079EE,0x6B3EC443091B482D,0x9248D66829014899,0x638D81CC4AE199D,0x5E8DE73EEB6DE96A,0x55771848724D17F0,0x734CB651B4339600,0xFD2432CB79D99C1B,0x373869CEA55DDEC4,0x39D83CB6F4815AF5,0xD31D84E9}, +{0x8FC08908D008677E,0xF50D53E90F7118D4,0x38984342BC5C5F12,0x9EF8ADEE9D890053,0x2E9134B510F28488,0x8951AC1CA56CA72C,0x7CFED4FEED36EDEC,0xCDF3038414AC384C,0xA2C3889B433C8C6F,0x27A01960F,0xA3526DB518930119,0xDC37B0E13644ED3F,0x6E31E890F08A37BD,0xA37A5E57024A8AA0,0x40B194BE09CD892F,0xF8D9FD2F6BFCA6BD,0x20DFBAEF4B42549B,0x45F0B1D7FBC11721,0x5E7E3BB644063BE0,0x171428956}, +{0xB637BBC305F67791,0x204FF0D2AEDF672E,0xF92D3782494289DB,0x24F7EB7320299A80,0x977CC127123CD922,0xB6C51C2947B68DB4,0xBEFC8E5B0AE18F09,0xFABDF4A65AAD3791,0xAEBB5AA66A4EC660,0x9F9CF17F,0x110C3AF5E13E1951,0xF40DC401CC686B06,0x68EEA45A46B10505,0x325395A25A0F0DE9,0x1C92E56F56D28E24,0xD0F8A55787894E1F,0xEEEC7393357C5523,0x5FB696B3518CC792,0xD39D05F3A9382E5A,0x26B74CDB1}, +{0xBDF8A208F713F4A9,0x18481280856177D9,0x10BD738108662F2C,0x1EF37C1AB5531600,0x98D3C52040B3E9DB,0x8E988D26C011FF69,0x18AE98AA255688B,0x8E60CDC1B136648B,0x7E91BFE825833F56,0x13DB93F4A,0xC90DED2C7313B98,0x82F6CE5855C8D3AC,0xD22BF07E7380D124,0xE912C49BBF549FD8,0xBD34790D9C351C45,0x4A1A372896AB66BF,0x44E6AD3D3CB7D968,0x473B9962DF10B605,0x2DC4E87221525887,0xD61465}, +{0x3E77A9B726C4E35A,0x72508865383E24E9,0x703A850A1795B24B,0xB744F39B78F82E6,0xBCA3D4CB44C8DE88,0x98BB9A1523EDC1A1,0x1055B9EF0ED241A1,0xDF619C4A7A3305B,0xD3CAD19AFBE71CE8,0x8A810A03,0x78553A5AD2AFD1FC,0x87C486E5D053F7C5,0xD49A2C8D3988259,0xD059B9BB567D1CB1,0x5D10F35FBB64BF63,0xB6A58DE0F78BF9DD,0xCD0DEBAFEA4B0478,0xDAF46A0964D3FD0A,0x8E33C74FE2F70AFC,0x21CAAD2F8}, +{0x3BABE989C4B7C8C6,0x2BF8F447EF3BDD7D,0x20EAAD8C5457CF18,0x8C176F27BA3E5B6D,0x6994DF1010BAB10B,0xC508E30E46C0CA1E,0xA48AA3C16405257B,0xFDA00D371BEC4681,0x9D86B52EDF6EC9F8,0x1C34BB8B6,0xADB4F379816C780A,0xC25F504173CEACF5,0x1DA0375FEB0BBE8C,0xB87264B37860585,0xE0E1B8080C0215AB,0xA4E2CD906374B7FC,0x5326260B7A3021ED,0x168C806A9FD020B4,0xDD2E356F2066C037,0x110BD582B}}; + +// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions +#define fpcopy fpcopy610 +#define fpzero fpzero610 +#define fpadd fpadd610 +#define fpsub fpsub610 +#define fpneg fpneg610 +#define fpdiv2 fpdiv2_610 +#define fpcorrection fpcorrection610 +#define fpmul_mont fpmul610_mont +#define fpsqr_mont fpsqr610_mont +#define fpinv_mont fpinv610_mont +#define fpinv_chain_mont fpinv610_chain_mont +#define fpinv_mont_bingcd fpinv610_mont_bingcd +#define fp2copy fp2copy610 +#define fp2zero fp2zero610 +#define fp2add fp2add610 +#define fp2sub fp2sub610 +#define fp2neg fp2neg610 +#define fp2div2 fp2div2_610 +#define fp2correction fp2correction610 +#define fp2mul_mont fp2mul610_mont +#define fp2sqr_mont fp2sqr610_mont +#define fp2inv_mont fp2inv610_mont +#define fp2inv_mont_bingcd fp2inv610_mont_bingcd +#define fpequal_non_constant_time fpequal610_non_constant_time +#define mp_add_asm mp_add610_asm +#define mp_subaddx2_asm mp_subadd610x2_asm +#define mp_dblsubx2_asm mp_dblsub610x2_asm +#define random_mod_order_A random_mod_order_A_SIDHp610 +#define random_mod_order_B random_mod_order_B_SIDHp610 +#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp610_Compressed +#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp610_Compressed +#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp610_Compressed +#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp610_Compressed +#define crypto_kem_keypair crypto_kem_keypair_SIKEp610_compressed +#define crypto_kem_enc crypto_kem_enc_SIKEp610_compressed +#define crypto_kem_dec crypto_kem_dec_SIKEp610_compressed + + +#include "../fpx.c" +#include "../ec_isogeny.c" +#include "../compression/torsion_basis.c" +#include "P610_compressed_pair_tables.c" +#include "../compression/pairing.c" +#include "P610_compressed_dlog_tables.c" +#include "../compression/dlog.c" +#include "../compression/sidh_compressed.c" +#include "../compression/sike_compressed.c" diff --git a/src/P610/P610_compressed_api.h b/src/P610/P610_compressed_api.h new file mode 100644 index 0000000..bb2b48a --- /dev/null +++ b/src/P610/P610_compressed_api.h @@ -0,0 +1,109 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: API header file for P610 using compression +*********************************************************************************************/ + +#ifndef P610_COMPRESSED_API_H +#define P610_COMPRESSED_API_H + + +/*********************** Key encapsulation mechanism API ***********************/ + +#define CRYPTO_SECRETKEYBYTES 336 // MSG_BYTES + SECRETKEY_A_BYTES + CRYPTO_PUBLICKEYBYTES bytes +#define CRYPTO_PUBLICKEYBYTES 273 // 3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES + 2 bytes for shared elligator +#define CRYPTO_BYTES 24 +#define CRYPTO_CIPHERTEXTBYTES 297 // COMPRESSED_CHUNK_CT + MSG_BYTES bytes + +// Algorithm name +#define CRYPTO_ALGNAME "SIKEp610_compressed" + +// SIKE's key generation +// It produces a private key sk and computes the public key pk. +// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 336 bytes) +// public key pk (CRYPTO_PUBLICKEYBYTES = 273 bytes) +int crypto_kem_keypair_SIKEp610_compressed(unsigned char *pk, unsigned char *sk); + +// SIKE's encapsulation +// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 273 bytes) +// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes) +// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 297 bytes) +int crypto_kem_enc_SIKEp610_compressed(unsigned char *ct, unsigned char *ss, const unsigned char *pk); + +// SIKE's decapsulation +// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 336 bytes) +// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 297 bytes) +// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes) +int crypto_kem_dec_SIKEp610_compressed(unsigned char *ss, const unsigned char *ct, const unsigned char *sk); + + +// Encoding of keys for KEM-based isogeny system "SIKEp610" (wire format): +// ---------------------------------------------------------------------- +// Elements over GF(p610) are encoded in 77 octets in little endian format (i.e., the least significant octet is located in the lowest memory address). +// Elements (a+b*i) over GF(p610^2), where a and b are defined over GF(p610), are encoded as {a, b}, with a in the lowest memory portion. +// +// Private keys sk consist of the concatenation of a 24-byte random value, a value in the range [0, 2^305-1] and the public key pk. In the SIKE API, +// private keys are encoded in 336 octets in little endian format. +// Public keys pk consist of 3 values of length OBOB_BITS, one element in GF(p610^2) and 2 bytes. In the SIKE API, pk is encoded in 273 octets. +// Ciphertexts ct consist of the concatenation of 3 values of length OALICE_BITS, one element in GF(p610^2), 2 bytes and a 24-byte value. In the SIKE API, +// ct is encoded in 273 + 24 = 297 octets. +// Shared keys ss consist of a value of 24 octets. + + +/*********************** Ephemeral key exchange API ***********************/ + +#define SIDH_SECRETKEYBYTES_A 39 +#define SIDH_SECRETKEYBYTES_B 38 +#define SIDH_PUBLICKEYBYTES 273 +#define SIDH_BYTES 154 + +// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys. +// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016. +// Extended version available at: http://eprint.iacr.org/2016/859 + +// Generation of Alice's secret key +// Outputs random value in [0, 2^305 - 1] to be used as Alice's private key +void random_mod_order_A_SIDHp610(unsigned char* random_digits); + +// Generation of Bob's secret key +// Outputs random value in [0, 2^Floor(Log(2,3^192)) - 1] to be used as Bob's private key +void random_mod_order_B_SIDHp610(unsigned char* random_digits); + +// Alice's ephemeral public key generation +// Input: a private key PrivateKeyA in the range [0, 2^305 - 1], stored in 39 bytes. +// Output: the public key PublicKeyA consisting of 3 GF(p610^2) elements encoded in 273 bytes. +int EphemeralKeyGeneration_A_SIDHp610_Compressed(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA); + +// Bob's ephemeral key-pair generation +// It produces a private key PrivateKeyB and computes the public key PublicKeyB. +// The private key is an integer in the range [0, 2^Floor(Log(2,3^192)) - 1], stored in 38 bytes. +// The public key consists of 3 GF(p610^2) elements encoded in 273 bytes. +int EphemeralKeyGeneration_B_SIDHp610_Compressed(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB); + +// Alice's ephemeral shared secret computation +// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB +// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^305 - 1], stored in 39 bytes. +// Bob's PublicKeyB consists of 3 GF(p610^2) elements encoded in 273 bytes. +// Output: a shared secret SharedSecretA that consists of one element in GF(p610^2) encoded in 154 bytes. +int EphemeralSecretAgreement_A_SIDHp610_Compressed(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA); + +// Bob's ephemeral shared secret computation +// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA +// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^192)) - 1], stored in 38 bytes. +// Alice's PublicKeyA consists of 3 GF(p610^2) elements encoded in 273 bytes. +// Output: a shared secret SharedSecretB that consists of one element in GF(p610^2) encoded in 154 bytes. +int EphemeralSecretAgreement_B_SIDHp610_Compressed(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB); + + +// Encoding of keys for KEX-based isogeny system "SIDHp610" (wire format): +// ---------------------------------------------------------------------- +// Elements over GF(p610) are encoded in 77 octets in little endian format (i.e., the least significant octet is located in the lowest memory address). +// Elements (a+b*i) over GF(p610^2), where a and b are defined over GF(p610), are encoded as {a, b}, with a in the lowest memory portion. +// +// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^305-1] adn [0, 2^Floor(Log(2,3^192)) - 1], resp. In the SIDH API, +// Alice's and Bob's private keys are encoded in 39 and 38 octets, resp., in little endian format. +// Public keys pk consist of 3 values of length OBOB_BITS, one element in GF(p610^2) and 2 bytes. In the SIKE API, pk is encoded in 273 octets. +// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p610^2). In the SIDH API, they are encoded in 154 octets. + + +#endif diff --git a/src/P610/P610_compressed_dlog_tables.c b/src/P610/P610_compressed_dlog_tables.c new file mode 100644 index 0000000..392942c --- /dev/null +++ b/src/P610/P610_compressed_dlog_tables.c @@ -0,0 +1,50579 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: precomputed tables for Pohlig-Hellman when using compression +*********************************************************************************************/ + + +const uint64_t ph2_T[DLEN_2*ELL2_W*2*NWORDS64_FIELD] = { +0x670CC8E6,0x0,0x0,0x0,0x9A34000000000000,0x4D99C2BD28717A3F,0xA4A1839A323D41C,0xD2B62215D06AD1E2,0x1369026E862CAF3D,0x10894E964, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0xB1662745692C51F9,0x7D112F9529E3CB65,0xD197985FE3BA9E35,0xC7218B1D6F96D08C,0xF81C88AB84530BB9,0xDAEB3FA2025F5139,0x8FC68EF3278C667C,0x11F0CF3A469A94FD,0x8705518AE0C2CCB0,0xFCBD2A01, +0x36DA26A97883B0B,0x2475DAD3D5536A6C,0x5864894F54B94DE0,0xF4588A5A494D4152,0x50CC014F35902C17,0x3182C1C74E8C210C,0x6EA72DB01A895A9A,0xD0D7CC58929E30D5,0xA2E804E67E87A33,0x1177BB1E8, +0xF2C529E73E9A02A0,0x70DAC74CCCCF18F9,0x13456B350B54B453,0xB1638FA335F950D2,0x3942573057561275,0xD877977B47DBAE51,0x4D74BF15D4409920,0x57029818490F5F1B,0xBEE9B373411DD41A,0x118DACB6C, +0xBD0BFE66DCEA15DA,0x1C11F9C6914F1B1D,0x71F4555569EC06EA,0x4648AC1FE55300CF,0xB90D7A66B7089591,0x137DB0778655BF6A,0xFE361335F06EC68E,0xACA05F38ACEBEF34,0xAFFBAA5877E6B512,0x1AAB822AF, +0x77F26AC0E2A4877E,0xBACEBB2B5B676442,0x810B019FB10A1A5B,0x637F6B73B0607AD,0xFAB656F7DE8D6ECE,0xF94034B552AAE862,0x5D824C5DBE90B0A,0xFA6B0E57BBBC2D6D,0xA1AC2946E855A23E,0x12307F13F, 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+0xA0F896E0A8F5F891,0xD0D6227C27250BE5,0xEEFEF5AC5190D9EE,0x5F1D1955E37E17A4,0xC68B9B133134C106,0x583846BFEF02F022,0xF9A36AFBBDCD3ED8,0xAB4EDA2E9E71CD61,0xAFC6D01EE592C9D1,0x1BA188040, +0xF2F8F5B499E64AC6,0x832A15C6069B2B91,0xF797DFB661EE87D1,0xA11AF1AEF484AD,0xEDA42010A021C449,0xF93DB64723686963,0x6751CB2FA70875BC,0x43132B1C80B67AC3,0x9B4B243FA666F7D0,0x323E62B9, +0xE9862C5119DFF1E7,0xAF97AD5F0E7A1907,0xD7DD50183125095E,0x3F44DA450F117011,0xF94CD0EB56CFD9AF,0xABCD01589BFABD2D,0x27731BE9F852637F,0x5956994FFFBDAE2D,0xA414C03BDEC2AAC6,0x11B0B8360, +0xEF6504D05C86EFAC,0x4FA4A676813301F8,0xEC46ED611A74D0C0,0x951640C7ED0094FF,0xD9BCC8D9FBEF1EFD,0x9320A2FFFC9C04C3,0x24D40B5D598D1939,0x31DAB1686547F538,0xEDCBD62CD326D25A,0xDD64BA85, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x670CC8E6,0x0,0x0,0x0,0x9A34000000000000,0x4D99C2BD28717A3F,0xA4A1839A323D41C,0xD2B62215D06AD1E2,0x1369026E862CAF3D,0x10894E964, +0x1679D3AEE6200E18,0x506852A0F185E6F8,0x2822AFE7CEDAF6A1,0xC0BB25BAF0EE8FEE,0x74B52F14A9302650,0x5AB4C900E5FF300,0x7374A35B0C3D962C,0x58FF19AA110676FD,0xDD7B508673252DC6,0x160EB2407, +0xEF6504D05C86EFAC,0x4FA4A676813301F8,0xEC46ED611A74D0C0,0x951640C7ED0094FF,0xD9BCC8D9FBEF1EFD,0x9320A2FFFC9C04C3,0x24D40B5D598D1939,0x31DAB1686547F538,0xEDCBD62CD326D25A,0xDD64BA85, +0x5F07691F570A076E,0x2F29DD83D8DAF41A,0x11010A53AE6F2611,0xA0E2E6AA1C81E85B,0xA77664ECCECB3EF9,0x59400728BB57C00B,0xA144544946C2BAD3,0x706D8CB725257C8,0xD1C940A36C550EBB,0xC1DE2727, +0xF2F8F5B499E64AC6,0x832A15C6069B2B91,0xF797DFB661EE87D1,0xA11AF1AEF484AD,0xEDA42010A021C449,0xF93DB64723686963,0x6751CB2FA70875BC,0x43132B1C80B67AC3,0x9B4B243FA666F7D0,0x323E62B9, +0xDFC02A9F94D30101,0x6C6174875633DC0,0xEF34FBB6A23E74AF,0x8DB9228A9C2BB961,0x14199B97C3E015A9,0x279C29251002AD68,0x8D39A363CF0EA572,0x70FC9CBBD4A5F460,0x6E7D0456ECFF9BFD,0xB10233ED, +0x6BD954CA55EEABE4,0x86271714EB2B5502,0x66E0BE067A1F6866,0xEFF51D69878AA021,0xAAB2AA55B7712426,0xEB7F46FB7530FB2E,0xA9F9C43216E77869,0xCEFACFBB6EAF1CF,0x11B07D2D08796D90,0x8556071F, +0x419C81786E20741D,0x2252EC4ABF8BEF2B,0xB9F0AE3FDF226929,0xF32D714E1DC68C3,0x2D4C221259908AA6,0x9FEFF5FF0FE1F1CB,0x8CB2B08CAC934821,0xC0E927A123E53081,0x93F6379AD5F874F8,0xD72D9220, +0xBE637E8791DF8BE2,0xDDAD13B5407410D4,0x460F51C020DD96D6,0xF0CD28EB1E23973C,0x40B5DDEDA66F7559,0x118857E99A78BE63,0xE350EB857FCB18A,0xF16C8B58ECDEF4A9,0xED99D9277BEF6393,0x1A4C91547, +0x9426AB35AA11541B,0x79D8E8EB14D4AAFD,0x991F41F985E09799,0x100AE29678755FDE,0xC34F55AA488EDBD9,0xC5F906ED3529B4FF,0xF0EDFB12EDA88141,0xA56605FE59D9335A,0x6FDF9395496E6AFC,0x1F6A0A049, +0x203FD5606B2CFEFE,0xF939E8B78A9CC23F,0x10CB04495DC18B50,0x7246DD7563D4469E,0x59E864683C1FEA56,0x89DC24C39A5802C6,0xDAE1BE135815439,0x4159163E3C1E30CA,0x13130C6B64E83C8F,0x1CAF4737B, +0xD070A4B6619B539,0x7CD5EA39F964D46E,0x86820499E11782E,0xFF5EE50E510B7B52,0x805DDFEF5FDE3BB6,0xB83A97A186F246CA,0x3395F4155D8783EE,0x6F4287DD900DAA67,0xE644EC82AB80E0BC,0x249B844AE, +0xA0F896E0A8F5F891,0xD0D6227C27250BE5,0xEEFEF5AC5190D9EE,0x5F1D1955E37E17A4,0xC68B9B133134C106,0x583846BFEF02F022,0xF9A36AFBBDCD3ED8,0xAB4EDA2E9E71CD61,0xAFC6D01EE592C9D1,0x1BA188040, +0x109AFB2FA3791053,0xB05B59897ECCFE07,0x13B9129EE58B2F3F,0x6AE9BF3812FF6B00,0x944537260410E102,0x1E57AAE8ADBEAB6A,0x7613B3E7AB02E072,0x807B0191AB7C2FF2,0x93C43A957EC10632,0x19E91ECE2, +0xE9862C5119DFF1E7,0xAF97AD5F0E7A1907,0xD7DD50183125095E,0x3F44DA450F117011,0xF94CD0EB56CFD9AF,0xABCD01589BFABD2D,0x27731BE9F852637F,0x5956994FFFBDAE2D,0xA414C03BDEC2AAC6,0x11B0B8360, +0xFFFFFFFF98F33719,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xD3CDFFFFFFFFFFFF,0x63DE8B2B81E935EE,0x909DA70B616C258F,0xDF9F90E440595348,0x6E270E53CBBB294E,0x17361BE04, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x109AFB2FA3791053,0xB05B59897ECCFE07,0x13B9129EE58B2F3F,0x6AE9BF3812FF6B00,0x944537260410E102,0x1E57AAE8ADBEAB6A,0x7613B3E7AB02E072,0x807B0191AB7C2FF2,0x93C43A957EC10632,0x19E91ECE2, +0x1679D3AEE6200E18,0x506852A0F185E6F8,0x2822AFE7CEDAF6A1,0xC0BB25BAF0EE8FEE,0x74B52F14A9302650,0x5AB4C900E5FF300,0x7374A35B0C3D962C,0x58FF19AA110676FD,0xDD7B508673252DC6,0x160EB2407, +0xD070A4B6619B539,0x7CD5EA39F964D46E,0x86820499E11782E,0xFF5EE50E510B7B52,0x805DDFEF5FDE3BB6,0xB83A97A186F246CA,0x3395F4155D8783EE,0x6F4287DD900DAA67,0xE644EC82AB80E0BC,0x249B844AE, +0x5F07691F570A076E,0x2F29DD83D8DAF41A,0x11010A53AE6F2611,0xA0E2E6AA1C81E85B,0xA77664ECCECB3EF9,0x59400728BB57C00B,0xA144544946C2BAD3,0x706D8CB725257C8,0xD1C940A36C550EBB,0xC1DE2727, +0x9426AB35AA11541B,0x79D8E8EB14D4AAFD,0x991F41F985E09799,0x100AE29678755FDE,0xC34F55AA488EDBD9,0xC5F906ED3529B4FF,0xF0EDFB12EDA88141,0xA56605FE59D9335A,0x6FDF9395496E6AFC,0x1F6A0A049, +0xDFC02A9F94D30101,0x6C6174875633DC0,0xEF34FBB6A23E74AF,0x8DB9228A9C2BB961,0x14199B97C3E015A9,0x279C29251002AD68,0x8D39A363CF0EA572,0x70FC9CBBD4A5F460,0x6E7D0456ECFF9BFD,0xB10233ED, +0x419C81786E20741D,0x2252EC4ABF8BEF2B,0xB9F0AE3FDF226929,0xF32D714E1DC68C3,0x2D4C221259908AA6,0x9FEFF5FF0FE1F1CB,0x8CB2B08CAC934821,0xC0E927A123E53081,0x93F6379AD5F874F8,0xD72D9220, +0x419C81786E20741D,0x2252EC4ABF8BEF2B,0xB9F0AE3FDF226929,0xF32D714E1DC68C3,0x2D4C221259908AA6,0x9FEFF5FF0FE1F1CB,0x8CB2B08CAC934821,0xC0E927A123E53081,0x93F6379AD5F874F8,0xD72D9220, +0xDFC02A9F94D30101,0x6C6174875633DC0,0xEF34FBB6A23E74AF,0x8DB9228A9C2BB961,0x14199B97C3E015A9,0x279C29251002AD68,0x8D39A363CF0EA572,0x70FC9CBBD4A5F460,0x6E7D0456ECFF9BFD,0xB10233ED, +0x9426AB35AA11541B,0x79D8E8EB14D4AAFD,0x991F41F985E09799,0x100AE29678755FDE,0xC34F55AA488EDBD9,0xC5F906ED3529B4FF,0xF0EDFB12EDA88141,0xA56605FE59D9335A,0x6FDF9395496E6AFC,0x1F6A0A049, +0x5F07691F570A076E,0x2F29DD83D8DAF41A,0x11010A53AE6F2611,0xA0E2E6AA1C81E85B,0xA77664ECCECB3EF9,0x59400728BB57C00B,0xA144544946C2BAD3,0x706D8CB725257C8,0xD1C940A36C550EBB,0xC1DE2727, +0xD070A4B6619B539,0x7CD5EA39F964D46E,0x86820499E11782E,0xFF5EE50E510B7B52,0x805DDFEF5FDE3BB6,0xB83A97A186F246CA,0x3395F4155D8783EE,0x6F4287DD900DAA67,0xE644EC82AB80E0BC,0x249B844AE, +0x1679D3AEE6200E18,0x506852A0F185E6F8,0x2822AFE7CEDAF6A1,0xC0BB25BAF0EE8FEE,0x74B52F14A9302650,0x5AB4C900E5FF300,0x7374A35B0C3D962C,0x58FF19AA110676FD,0xDD7B508673252DC6,0x160EB2407, +0x109AFB2FA3791053,0xB05B59897ECCFE07,0x13B9129EE58B2F3F,0x6AE9BF3812FF6B00,0x944537260410E102,0x1E57AAE8ADBEAB6A,0x7613B3E7AB02E072,0x807B0191AB7C2FF2,0x93C43A957EC10632,0x19E91ECE2, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0xFFFFFFFF98F33719,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xD3CDFFFFFFFFFFFF,0x63DE8B2B81E935EE,0x909DA70B616C258F,0xDF9F90E440595348,0x6E270E53CBBB294E,0x17361BE04, +0xE9862C5119DFF1E7,0xAF97AD5F0E7A1907,0xD7DD50183125095E,0x3F44DA450F117011,0xF94CD0EB56CFD9AF,0xABCD01589BFABD2D,0x27731BE9F852637F,0x5956994FFFBDAE2D,0xA414C03BDEC2AAC6,0x11B0B8360, +0x109AFB2FA3791053,0xB05B59897ECCFE07,0x13B9129EE58B2F3F,0x6AE9BF3812FF6B00,0x944537260410E102,0x1E57AAE8ADBEAB6A,0x7613B3E7AB02E072,0x807B0191AB7C2FF2,0x93C43A957EC10632,0x19E91ECE2, +0xA0F896E0A8F5F891,0xD0D6227C27250BE5,0xEEFEF5AC5190D9EE,0x5F1D1955E37E17A4,0xC68B9B133134C106,0x583846BFEF02F022,0xF9A36AFBBDCD3ED8,0xAB4EDA2E9E71CD61,0xAFC6D01EE592C9D1,0x1BA188040, +0xD070A4B6619B539,0x7CD5EA39F964D46E,0x86820499E11782E,0xFF5EE50E510B7B52,0x805DDFEF5FDE3BB6,0xB83A97A186F246CA,0x3395F4155D8783EE,0x6F4287DD900DAA67,0xE644EC82AB80E0BC,0x249B844AE, +0x203FD5606B2CFEFE,0xF939E8B78A9CC23F,0x10CB04495DC18B50,0x7246DD7563D4469E,0x59E864683C1FEA56,0x89DC24C39A5802C6,0xDAE1BE135815439,0x4159163E3C1E30CA,0x13130C6B64E83C8F,0x1CAF4737B, +0x9426AB35AA11541B,0x79D8E8EB14D4AAFD,0x991F41F985E09799,0x100AE29678755FDE,0xC34F55AA488EDBD9,0xC5F906ED3529B4FF,0xF0EDFB12EDA88141,0xA56605FE59D9335A,0x6FDF9395496E6AFC,0x1F6A0A049, +0xBE637E8791DF8BE2,0xDDAD13B5407410D4,0x460F51C020DD96D6,0xF0CD28EB1E23973C,0x40B5DDEDA66F7559,0x118857E99A78BE63,0xE350EB857FCB18A,0xF16C8B58ECDEF4A9,0xED99D9277BEF6393,0x1A4C91547, +0x419C81786E20741D,0x2252EC4ABF8BEF2B,0xB9F0AE3FDF226929,0xF32D714E1DC68C3,0x2D4C221259908AA6,0x9FEFF5FF0FE1F1CB,0x8CB2B08CAC934821,0xC0E927A123E53081,0x93F6379AD5F874F8,0xD72D9220, +0x6BD954CA55EEABE4,0x86271714EB2B5502,0x66E0BE067A1F6866,0xEFF51D69878AA021,0xAAB2AA55B7712426,0xEB7F46FB7530FB2E,0xA9F9C43216E77869,0xCEFACFBB6EAF1CF,0x11B07D2D08796D90,0x8556071F, +0xDFC02A9F94D30101,0x6C6174875633DC0,0xEF34FBB6A23E74AF,0x8DB9228A9C2BB961,0x14199B97C3E015A9,0x279C29251002AD68,0x8D39A363CF0EA572,0x70FC9CBBD4A5F460,0x6E7D0456ECFF9BFD,0xB10233ED, +0xF2F8F5B499E64AC6,0x832A15C6069B2B91,0xF797DFB661EE87D1,0xA11AF1AEF484AD,0xEDA42010A021C449,0xF93DB64723686963,0x6751CB2FA70875BC,0x43132B1C80B67AC3,0x9B4B243FA666F7D0,0x323E62B9, +0x5F07691F570A076E,0x2F29DD83D8DAF41A,0x11010A53AE6F2611,0xA0E2E6AA1C81E85B,0xA77664ECCECB3EF9,0x59400728BB57C00B,0xA144544946C2BAD3,0x706D8CB725257C8,0xD1C940A36C550EBB,0xC1DE2727, +0xEF6504D05C86EFAC,0x4FA4A676813301F8,0xEC46ED611A74D0C0,0x951640C7ED0094FF,0xD9BCC8D9FBEF1EFD,0x9320A2FFFC9C04C3,0x24D40B5D598D1939,0x31DAB1686547F538,0xEDCBD62CD326D25A,0xDD64BA85, +0x1679D3AEE6200E18,0x506852A0F185E6F8,0x2822AFE7CEDAF6A1,0xC0BB25BAF0EE8FEE,0x74B52F14A9302650,0x5AB4C900E5FF300,0x7374A35B0C3D962C,0x58FF19AA110676FD,0xDD7B508673252DC6,0x160EB2407 +}; + + +const uint64_t *ph2_T1 = {0}; +const uint64_t *ph2_T2 = {0}; + +const uint64_t ph3_T[DLEN_3*ELL3_W*2*NWORDS64_FIELD] = { +0x670CC8E6,0x0,0x0,0x0,0x9A34000000000000,0x4D99C2BD28717A3F,0xA4A1839A323D41C,0xD2B62215D06AD1E2,0x1369026E862CAF3D,0x10894E964, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0xEFE0B1246E1B15D8,0xCE5E59D2C6A938B7,0x9421DA239FF6D260,0x96F33702CD2DAAC5,0x45CC46BDE3A5FCE,0xE855F2AEFA620E36,0x96D60B35087BA313,0x587DEC7923493D74,0xE9FDFA81772DFB58,0x1A4BC61E5, +0xFCE11250E1823AA,0x7DE75D693DB489FA,0xDB547584F4D310CE,0xDEDA13FBB2D3E2C4,0x73E82F442A99394B,0xF41360FBC0F94A94,0xD5D12F662BDB097,0xFE4093C5B907F763,0x5F5BCA5AD0110C1F,0x9612E327, +0x86FD022EC9F94DBD,0x5343F05AB1097F09,0xA3125120920E316E,0x4D2C9F0629D2DC17,0x767954328D9D6A46,0xD8B5FC2F6A5748EF,0x603DABBFFB73D6F0,0x1A9B4211D79384A,0x89704DFD1BA13165,0x22F662552, +0x7F75B2FBE4552BA8,0xD8BBCA8D0697B755,0xAB964F06BC50D80B,0x68656927DA935A51,0xDB2C7A908DEE21C5,0x54207A7E2064E50B,0x548C5E27C54C5BAD,0x30663353362BFF6E,0xB229CA37822C2336,0x1F1C65245, +0x6AAA0FFDA5BBBCD7,0x618EBEE72EA4F88B,0xFB440030DEC39C4C,0x156362DCA5EFC0E4,0xC7B9A7AA365C9745,0xF0CFDB90838A770A,0xDE36F85314F5540B,0x6934C51A2512C49B,0x90F6E835EEF6A55B,0x236073F7B, +0xD61111C3019E6B9D,0x71995AFD6009DDA0,0x998D49598316D2E6,0x130E2EE2B4BDBE1D,0x235974B164108C76,0xF3C53A408E0FE7EC,0xB59255A6AD3B36DE,0x6D61681687E31845,0xF813C38433A7C7CD,0x2377A56C5, +0xE9D68FB4864F476C,0xB73DADF725508865,0xB34B60AD7B5BF9FF,0xC9E642EA8FE13116,0x5FA481C91A5B6698,0x5D2B63305833C75A,0xC74579F19E78EBE4,0xC58D31F9ED86CA9D,0xB0696DE0B73C8891,0x7617FDF4, +0x802E0B51FB6B186E,0xF8F6B70C9A398EB6,0x597A0959EBA4B53C,0x7B830DF4C24E2ED8,0x66B76D85642AA97,0xB003463AA38532E7,0x9AA87FF5006105AD,0x8D092F92733BD14D,0x4FD1ED446DF801D1,0x2ADA2E43, +0x2352C7F5AF84E69D,0x14AEF2842031743,0x5C05FAC0CC876757,0xB8769C806EA6E20D,0x6EEC48E698AE64FA,0xF4B7B352C35612B0,0xD0CBC9DE5AEEA58E,0xB6FD9411C0784F87,0x15A85CC228A7D03B,0xE40F365E, +0xEB75CFE28431D5E7,0xA5D634681EF68AF0,0xF22746B4BA4E42CF,0x545C96BA2069B50C,0x5F2EB55ED4CAF6D2,0x844DA1C7A89E93F9,0xCC7898A710274475,0x354A048276409157,0x167920483AC16CEA,0x1811ED046, +0x9C3ABCC6E68E705B,0xE34DF217202355E5,0x107569E54CB351EC,0x1925215A7CDC64E8,0xF96FEB136EA58363,0x1370BA7C0A9B0989,0x9BBAB20692F31A5F,0xF2C57EAAC7BBDD17,0x45D63B1D687EE446,0x2DFCCAD3, +0xFCC1F2BC081F84B8,0xB0631C98B1C51C,0x396E1D3A3322B175,0x1B2BDFCE9C2303E0,0x6D81852F855146D0,0x5CCB40C9522BBC56,0x454B4035A269E9D2,0x21081A95A6296B71,0x21A10AACF9574325,0x1C36A00A, +0x73BCF7EFE36E9207,0x5906A4F704D3630E,0x427C426D7D84BCBE,0x1184EEAC60A368EC,0x9AB2BAAA38AF05BB,0xF8D210A9D02EE04F,0xB850A422E4834D64,0x68336583BABF0131,0xA8AA1FE153DC6AF,0x24CD8115F, +0x94BB71F0DA02B0CE,0x7D055AB794B75E38,0xDFD876C4DD403D18,0xC15712997E7D36C6,0x4A1AD99ED1E83D9B,0xB33BB91E43784CCC,0xC802292D0AD68926,0x48E972B2ADDCF657,0x573DED5A51F69BBD,0x12EF39CDC, +0x7206A16ACF028ED9,0x75F903438FC844C1,0x40F5F4D472A0AFCA,0xF9BD4FA7924BE49A,0x51081EDF59D780BB,0x9ADFBDBD0837D98A,0x47CAA05ABC98E2EB,0x86799F7A022D8FBD,0x7E07FEB593E35542,0x1EF3B1212, +0xE38A0306AF13B214,0x8AA0ADDD6977AC15,0xBE55B1F99F93BA50,0xEE1C9D36512B8B96,0xE9FEBEC1E48D730B,0x7EDADBD9F466E6CE,0xF5C21935AC12E135,0x5074543ADD0B48F2,0xE2FC51409687AB83,0xDA2848F5, +0xD58BE275ABA921A0,0x253A619C05AF312F,0x4BBC5C7DA24E4128,0x9501240F9BDAD1B7,0xCA14B0D23480D387,0xB3DE9FFBA6AEB736,0x473386736CF86606,0x92EB0B81FC674853,0x34FECF52DE6B40EC,0x803D786F, +0x8FDB621E6BE55588,0xA9583254021E0437,0x807352FFE89037B8,0x7F212D4E7789D170,0xC254AF485B369469,0x6843BD9750ED6A69,0x781C1C13A76717E2,0x72501AC3225F591F,0xD15447E859830ABA,0x272F02DA6, +0xD75ACAB0E0186235,0x9E03194519000128,0xCCB68D2B09807776,0x12C528F07F57922,0x1C968F8C79F188AF,0x3CF5D459B51D5334,0x79C445C479277C36,0x4E4F2C9A5662DDE,0x80BFD5FFDF2D8739,0xB7E1B432, +0x66E69AB48B168BE1,0x4D14AC49DE2124DE,0x7CF689514DC14115,0x1457520A30F5E1C2,0x471251A605CF44B6,0x6ED1FB06EB71B001,0xB2E6E11C867856DE,0xC47B1AC7BAB20E16,0x488074D655E28E46,0x1C05B6443, +0x84B87E8A05A91B40,0xB8FED3A9167E8667,0x8AC620666A78DE55,0x65B90DA63045158B,0x18BB62C862C36755,0xE8A0C97416FCD448,0x77504BA92CCB0D6D,0x6EBC2F6C6AFCEC2E,0x5CC7D24DCC67A365,0x69A610D5, +0xEAF11B6AC0A05972,0x59DFB58B494F40B8,0xDE2EBD4F7EBB6817,0x73423090E2221DC5,0xBC61FBBF34996194,0x313F36343A94CA01,0xF022CB0DE06DF3B2,0x13ADA8AAB93A7C,0xD29F434A616B53F4,0x275C2A309, +0x17F6ED15E7EBA15F,0x4B5E365E24C6D45,0xB384F482F7E60084,0xC22E5513C923C902,0xA65BBA8935170485,0x10016C207EDA2E33,0x32B1294C484E9BC8,0x8A5AAE4285858DF5,0x34ECFF8E3BE421EB,0xD3A282C4, +0x10B5CFC56AB8F4EC,0xD6A5CC925ED60961,0x2E4C5CEDB6AE037D,0x7AB85146E3AC9FF1,0x559D6D5EC6EDF91F,0x6B9E6F216F70530A,0x5308947A204335C5,0xEC084C5E5211D3CE,0xCA992290752334A1,0x1BA2526EF, +0xEE2AFF6029EF934D,0x39E3FB207F461056,0xADEB0F1174DD8AFF,0x989DA97CB54EDAA5,0x914C7B1E8AA1916,0x851D974682DFE3AE,0x69988E4DB1528B62,0xBADD2489D9FC9AB1,0xE420E7FCAC4DF9F,0x121E3CB48, +0x7517545FDE166EE1,0x8D70FFF9A4881D6D,0xA84984DA240111D4,0x27FF89F3B7068D57,0x177C32DB1E5114E6,0xBF4277883CDB255A,0xD750941BBB9D680A,0xDDE4A87FAEB647E3,0xB196258879219747,0xFAD0457D, +0x72FDB820609AA32F,0xCD1EDAD8F377549C,0xDFA18140CE6F7B5A,0xD57CBAE08D5EE21A,0xB96FF0602A49F1D9,0xDADB154BA5E0D0CE,0xB8B69B4DB70E443C,0x43E80C54D41E99C1,0xA4B01492F9495715,0x2522EF309, +0xBFDE2D873906D91B,0x2200E0B5A65DFE27,0x33BF0F42C8A210AF,0xEC0086A8EE05CB30,0xDD05BE4F558CAA60,0x413677D80C6AD7FC,0x42E681C1ADA081E7,0x834CC253E8CF7C99,0xD9D9A7623A5D9549,0x253778F2, +0x652978A4B5107972,0xCB5BDE5B94F31BBF,0x578E3A09CC15BC7F,0x36C89E1121AB7A4C,0x227AACF6BA8D564C,0xD3ECCEA133920104,0x126CFE5CF7E163BD,0x7F8C45CFF3D3CC02,0x143BF3DCF75DE779,0x1027E16B5, +0x35DD40442B9965E2,0x559408A05F7E1E5F,0x122634303810DCAC,0x41BFC1A2B90D451F,0x85578CC4479DE334,0x4F1D50302EA0552E,0xF411C970EC48770C,0x9CE5BCB62510B238,0x8FBBC606B3F60DCD,0x26797D664, +0x3C8BD9C1E7F5D73F,0x72FFE2422611B02A,0x7E948385A4DDDA2A,0xA45CCB9CB19BC2D7,0xC49E238ED6F7394F,0x531D11B51B0DFB7D,0xC5187EC8F06BF182,0x4DF89D3F6962875A,0x4F66587BA8258016,0x23C4B31CF, +0x97D0E77A1A047A6,0xAC797987C3C2A43B,0x9F0CD17DEE039058,0x3576899B087304E8,0x997BB84A9B467DB3,0x63DD667AE3E89434,0x33ECAA96F7C847EE,0x30A9D7B7EAC996D4,0x77A6799051BA1DB4,0xD2C26673, +0x76F74E501E64CF22,0x2CDAACC26E4033B,0xB814DDFE80002EC,0xFE332792FD583161,0xB681FF76EB9110FF,0xFB2C669EC247442F,0xD69DF42D1E75B039,0xA349402D3C7B15EE,0xCEB66789ECA7DFE8,0x957527C, +0xB485BAED9EB4AD17,0x3BDC001E388E4488,0x93676219591567F1,0xA883C36D914276E9,0xF5564444D3BDD118,0xFD25E3176B1B571D,0xF4B2EF669D035154,0xD5853799BACC6121,0x2AEC92D5F9C5917,0x1DFCC76CD, +0xCAEFDEB4F78C232F,0xB6C0B7A24A17B873,0x49F970D156B116F6,0xF5C00601064F5BC,0x7CAA96287BF3AD7D,0x1B824728C8A53214,0xA76A0A351F1B49FC,0x5314CA2A8AD7FF8F,0xBDA788728C17DCC4,0x1D1248EE0, +0x142237FF7E09BDBD,0xC52B6920FB553B75,0xD21F059807A827E6,0x5CCD530AA4AB0E9C,0x809AD790E75B2F74,0xF54BE97D9E5BB114,0xABF631785DD8E749,0x71651FCC0A36E0FF,0x5F684F23EDE00446,0x135805122, +0x318EE02D89D56D67,0x38FE1CB0DFCFC2CE,0x581A24B8FD2CC6AE,0x955FA2E369213AA5,0x216E50A8290B53F8,0x365232A047B0ABE8,0xE81D8770C0FD1D91,0xDED67DFD1DE5B526,0x33D4D2738D56A9AF,0xCBCEA413, +0xC6E97EBB2C79E788,0xDADA725F723FED67,0x430A123A77AC7519,0xD7534980D432360F,0x27E7D551CF6C0335,0x8426E8796E7B81CD,0x928A0C6FE3C72678,0x46E8F9CF89283A88,0x858E848B1563131B,0x56C59565, +0x82A597D6376D3E4F,0x921D59A8F1734106,0x51670BFF348F19D7,0x3599B65DC237818A,0xA332AB57D0449B84,0x7BE2BC16175D9190,0xD05B975E01BC6A28,0x15D3450689CEA045,0x398D40A6217F9F01,0x1F7EC8E87, +0x1D70BF6E8B62544F,0x806B9B10A74FE397,0xF95AC05157F6BA7E,0xB203DB5C2AC91EC3,0xB7FC78D2BD145D87,0xB6141C9BFB9E17E6,0xE852B775C059853B,0xC115B453BBF96EA9,0xB150B61DAE932D0D,0x263FC6948, +0xDCC9C79CE101263E,0x34C581D2F04EDA38,0xD8883F07FFF7D194,0x7C26F650334F4D27,0x584B313D7D5E348,0x2E0E559C6ADCEF80,0xB98FC4035A98442,0x4E8C771773E0E9EF,0x8DBF97FA7021C8CC,0x1360D1B65, +0x3630958C722CCBFC,0x1B49D735F839B1E0,0xE1650757554B0E31,0x713FBD4BC3616ADB,0xE609E4C3453FC4AE,0xE80B520981D6B9CC,0x6F16DDC74011A85D,0x79604029D593B6D6,0x1089096F0CE13B2,0x10169513F, +0xF03C057287624C53,0x1D5631EF0D31297A,0x1C3882BFD08362ED,0x6802C425C528F94E,0x45C3E979DA62D6EC,0x7BFF5E6882D7DD67,0xCA59E6D5AADC9ED4,0x47511909A6807E08,0x60112C73CCBC6BC9,0x16A51737F, +0x7910BBE3721F5802,0xF8E5F14CA609C2DF,0xF38C0E3881BFC818,0xA1FDD95B42BD8F79,0x7A98E14E33E64122,0x9020EB08EA4B009A,0x19A8CA6586165540,0x5D1C0A0A15DA9856,0x3818B4BBF710D53F,0x16AD233B0, +0x309900F3F551CFE,0x604D975AF89CEDDE,0x693CDE2945F1EFCE,0x59019B480E6E95D3,0x92CB86483BC9ED66,0xA47FA1E747ECFBBD,0x4F83974AA95BAC09,0x70BE3E4C34014735,0xCB72C5A94E6047DD,0x2175E7E59, +0xAF55689235DE2A6A,0xD43386B29C9C1F2D,0x15B87C4E49406AC2,0x4C591220CAB54187,0x4D39FA798E8AC1C8,0x57718962F3D871A,0xEB0B971C0ECF741,0xDA61D7A294691643,0x5D136FCC29B8B0B,0x3A57B757, +0x5DC3F4ED1BC714B0,0x3C33BBE4C3E2A6BF,0x8355612B6B0B01EA,0xCC7CFC0B51067B33,0xF6A931B8C7BBACA2,0x361FEC952AE7F23D,0x3B701ABCD1A634AD,0x7AE3E58D826F9B78,0x52122FE547E5C196,0x265F23C48, +0x52546BB1A58FA5C3,0x9C6007E9E18CF542,0x4FBF65A02D40E29,0xC2B00EE10DAAB1D4,0x2ED87522976E8D70,0x20B696F94DE535E0,0xF0F7A43C9E3A61BB,0xF81088F4E97E1E3B,0x562CDD87C176C47A,0xBABF4C01, +0x5D90481320C62A5F,0x51E4FD119516E65D,0x65B70FEF9085C540,0x677BCCFB0A076489,0xC414BB3F4272EEEF,0x52AF6DFF4971A351,0x28702C1BF52CEDB8,0x8EF083D5A72865D9,0x5084F248DEA57B41,0x17E5D2556, +0xAC69C3E55BE5567C,0x2BA40B26F35FD58F,0x9A305685B61F2422,0x44AA03A904229A7B,0xADAC7416F9CDB7A9,0x2A6375341BBD94DC,0xA1FB00F5D8FAA475,0xBA4F029E99A766C8,0x9C4CDAE87DD625B9,0x172D6152A, 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+0x1B227AA981B7128F,0xF131F744A68EB68,0x4A48CE2F749D84C7,0x424C7F085D1FCD24,0xC760F7AC6633BBA6,0xDD8B56B235692EB9,0xE17C9E655978602E,0xCE79BB195637E2B9,0x9AFEA82F896C4945,0x19D3508D, +0xAE7C56D6A5E96A99,0x31E3C2A4D56889B3,0x442E109844154B5B,0x76E6B0900206A453,0x8E074F2B432EA36A,0x1FA706E1635BEE5F,0x248BCB254C26F90C,0xBC3D5191929169F1,0xF94EC254E38418B5,0x7B8CD1DC, +0x77EB5A1E69B302D6,0x8D44754E7157C47F,0x992A3EFF7F2B6FC,0x21AE3FF65276E89F,0x3BFAFF510B3D035E,0x45DAB70700E1C88B,0xC2D81AF9978D3FC6,0xB3F1138E4DF49CC9,0x7CCC6169465B69FA,0x1013B5CC, +0x411FF17944B437AE,0x7B0BE1F7FC95DBDB,0x40EF7BDD4E8E2ECA,0xB1AF96E9030CB2AB,0x71D92670BD54FBE3,0x9C73F635EF35753B,0xB1312FECC3ADCC7D,0x49BCBDBD02C1E88E,0x8B22394A1AEAF43C,0x1BDB2425C, +0x6D110CD59C19A5D0,0xEF5F64D5E9FA88AF,0x74CE68FEFCC30B9F,0x69338BD5F6F51A31,0xC208A1A19AF2BE90,0x637410F2A37C853B,0x25BCCA0A2CEA0C59,0xA1F7212958220910,0x3CE9F648117CAE8F,0x24DB5095D, +0xF49CC14293952054,0xEDBF2CD454C904EC,0xF0B4D1959625CDC3,0xB86BFBFEE49BEBAB,0x61A4CF545DD3F732,0xB554BDCBE818C202,0x7E136A8CF346DD35,0xB2CA4D377E7313AA,0x91C30F9AEB0A0A5D,0x212AF3CE9, +0x6193AEFFB6C9EAA9,0x26E508B9113EB81C,0x5E604091ED9507A5,0xDB87F6163C330251,0xE9CC8083FCB5193,0x72C2CEAD446DAD3F,0x2E7A95567713870B,0xF851EAC727F104E4,0x2DF6F852F553388F,0x2399AE12C, +0x7D460B334CE74C19,0x9640A08A630A9FD4,0xC1074EADC0705C28,0x827880949F8C0DC0,0xF9471A99B5E4EB3D,0x24633C8005570601,0xAD49219B6F86A09,0xE8297C3EA1AD9BF0,0x334C7B1752CB797B,0xD3A14823, +0xB86CD3455784D082,0x578BB9CBF9B15C81,0x86157867CBF13AE9,0xE061305A7D8D47AA,0x5AF8E25FE2DBF8B7,0x9C7C0F2114035933,0x653FC70C6B597F63,0xD3865BFF784BB309,0xA48E257921EEBCF7,0x22EB5E945, +0x4375B93832E97F2F,0x155C9FCB7588AD35,0xF3ECDE88E92D068C,0x25940E08B9A7B57,0x1508BA5A9D8EE205,0xB8A4B6CECBF073A8,0x4F31ADF1DF761471,0x16226771628BFD76,0x13BD7C612CC682A8,0x2690AF836, +0x2F6AEF2C37F27953,0x9A3D08EEBBEBF86D,0xA5EB62B880347D2,0xC36A13BAFC780955,0x38C2A4B5B463BBF1,0x61F7FF2550D92F7D,0x936310E1E67E7ACF,0xBE125FC14F8AFE12,0x3E35901158C8D306,0x12CCB8D94, +0x9E19866CE51C0B0B,0x6C9941CD7808ECB1,0xA64198B02B420B9C,0xE646A3508C9C1DFD,0x1F3B15579510F3E3,0xF28FCA23C7D1BE4B,0xAD1478E018D60F64,0x48DD5A8F33ABA020,0xE8CCC7A3F2515B7D,0xC09F15E8, +0xC8C5354063F39D2B,0x6DFA81C07B23655B,0x1F2FA87F8E777A43,0x5B3D9A8B9F775BEE,0x6DE9646C13EE9878,0x589A17EA8AA17C15,0xF8A04EEDCD26FF8E,0x40CEFC8E2D4EADFD,0x1DFED52CBF0A5A6,0x161F5C8, +0x216FC83D0E3A7447,0xB7F0CC7A94684D2B,0x42FA80FD55A40C7A,0x8960448D33FD8EC9,0xFAA6270BCE4F5874,0xBC5E2220AF5E2B4F,0x9A2A51C03F8C8B22,0xA4FD45C2188F9A84,0x1D680F935A592CA4,0xD718A3B1, +0x587A32AA98438160,0x682EEE4FAEDEBBF5,0xB385989F4C2C5F0E,0x1FEC48A9040E0B3D,0xB1572BC0EB3D6B9,0x30190E5E04D08CB9,0x27CD833F07A2CD7D,0xBA491F3D881821C7,0x969C81C9C3DB6174,0x9A25C370, +0xF094BDEA6B8DD1A5,0x4F4E4D39F331462C,0x938A08FC58153F5A,0x8CF5BCF9ABADDD8B,0x41C72999BF8DED53,0xBBBB221CC7D4A5B4,0x6345BFBAAE39F4A7,0xAD901516CD63C75B,0x15D84CB8EB5B13E2,0x166CCBADF, +0x6EA16E87C8740F11,0x7825BD108CF0E3D6,0x7DFE5CB7BC6DB243,0x4CDDD111CB6B6DBE,0xA006977B1A8E92B1,0x6483697A4BF02E8F,0xD9CF793C6CEE1767,0x5DAFD4A6E2AC962,0x7A00CB5760E79941,0xC74E7349, +0xCB52939FB4CD1F39,0x8855F2279B3D62AA,0x1AB1311E100E886A,0x3B7D4DC3B9960B26,0x9F41B27126D1454A,0xA5EECD227E24ACEB,0x4217FFDF1F3AD9D,0x2AEB73C606656187,0x417E568F73F693B2,0x18F3C1E4D, +0x6B1B60204C950778,0xB546319FC9C63C98,0x34D4DD6548524D3B,0xEF92A56AD833BC34,0x48F7F3B44C2A2F95,0x5FFC27B974A72B72,0x26ACDE8625321CFF,0x61B567A5A48CA3BE,0xCAE4D974F2AF1F3C,0x5336CB65, +0x1835ACDC0852DD27,0xF28493F7D010E6F1,0x2012518C8259AA8B,0x8A776F1299A6B513,0x48FE2663BA2CFF85,0xF50A5E8BF0FFEEA2,0xF2011438711E9F2F,0xEBC90E3B0FCCA8E7,0x80062F05DD83E1AC,0x204803748, +0xC61ED39FED3BBEB5,0x989424D3392C16C3,0x3576E7340E9E319,0xA8EAE64FF210DCBE,0x23A19AE363FB32B1,0x73A0E0DA74855CDD,0xC4E200C4D937CA7F,0xE8AF2FF7C941FC23,0x9964D01AEE2DF567,0x106CAE8A1, +0xDDF2D092C3F8029E,0xE51563CA13630A67,0xED016046C968DE79,0xC86284E1B101F073,0x72D11D89F1E5D848,0xD69C7FC451C863E,0x3197898DC1708E28,0xD6D70F97B0D18564,0x153E12F61F99CE86,0x2636F833, +0x1E6E2933A3915161,0x9670240451C7549C,0x746E7D54C5BA499A,0x483FDB310FA1ECAB,0x67F391B061730660,0x9D71C9A0F0726BAF,0xD47E72D36460E77F,0x36F941A4DEF129BE,0x1E764DBDAA70176C,0x2230C9B45, +0xA3C0B3101E41A848,0xEB94AB6A6FEC3C54,0x8544A97F9A02C5B7,0xC6FB87218FC4C0BA,0xB80039D006CA4BB8,0xEE1D30FEFB700947,0x614C7C8E36BBBA9D,0x6FB1AE08781FA72C,0x7F1351836E1CA12B,0x560EC85F, +0x5D77E4876D2134AA,0x698CA660D98EE747,0xAC98857F7B08C2BC,0xFB72AC1F3F684FE3,0x16988B3E5357AA04,0xC3A2D468F3A5C4D3,0x5D99DEFB3E146BF7,0xBF3157B2659ACC42,0x74EBEC42661101FC,0x23BCACAF7, +0x23C63E44D3C67456,0xC041DFF7AC12B7D9,0x8B7CF235A29F5FD6,0xB4FA3F1F73DA68FB,0x6D869C6166E05F6C,0xE573496FA481AD43,0xD6D1B0C83010D30,0x2412781687293D14,0xB393732469B796CB,0x1F30F0130, +0x32028CE4B469F6F9,0xD0E03CC1EEEDB878,0xFFE1A82795706FC2,0x89F0F4D328C7D1DA,0xA14B93BAB5D7D151,0xF97349B5713BC602,0xABA65CAB908846DC,0x8F30EABC091CF67A,0xE92A2AC7A3DDF61,0x27787B4E4, +0xF37F2A02191C9F85,0xE4F64329EE20AC16,0x892C9797F3BAA392,0xB196FC38E3E42843,0x3E2E3011F443CF62,0x46B871517ED46391,0x499DA2ED3A9CA636,0x610D070E0ED45F6B,0x7397668F471EB9D0,0x47345D18, +0xD538C4BAF07E1232,0x1D7CA654B413C84E,0x6AF4671F0F52E012,0xD0EC9736D345138E,0x5AF62A6E5714F98F,0x91471078D3FE90E8,0x59EB305A02E7069,0xD026EA5D718C1729,0x4112DCFA94FA1FDD,0x1D4ADA955, +0x34CBE31424A38DDE,0x5D1B6B5E0BD94EE6,0xC70511DB778315B3,0x49B7853B78C84F6,0x1F657707A5804911,0xDD71652338A91881,0xC45F32E90555A164,0x765A77E36A0ADB14,0x7701F728B0580380,0x27BF2F8A9, +0xE6A6B3B3015B8DD,0xFEE380B09443C919,0xD13A0E1F6665D7A7,0x846C860481F38F3B,0xBF2F638B18B47F94,0xCF860B844ADED493,0x5AD1088ED29417CD,0x92E335E1E735C284,0x734633B5708E42A5,0x16FB90FF, +0x45F1532681D6C166,0x8FB73F873DF92D13,0xF549F27110B0C9C9,0x98418E8B5CD7C8D5,0xCC1221CE5D315336,0xA8006252EFFC5A7E,0xBDF1E75828A40B8C,0x1E6BBF6A7A430E34,0x7946F463E1FC836D,0x9D02136C, +0x809D0BFF23D562C5,0xF69D5CDE67A463C8,0x862182D57E528228,0x488367FE02F287F2,0x3A3C7192FA7BA0F2,0xC1C119D89515FEDE,0x4FD2D887C7B4CA92,0x5490AF775EAAB273,0xCC528C4E0A343155,0x1E655F828 +}; + +const uint64_t *ph3_T1 = {0}; +const uint64_t *ph3_T2 = {0}; \ No newline at end of file diff --git a/src/P610/P610_compressed_pair_tables.c b/src/P610/P610_compressed_pair_tables.c new file mode 100644 index 0000000..9bf022c --- /dev/null +++ b/src/P610/P610_compressed_pair_tables.c @@ -0,0 +1,7781 @@ +/************************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: precomputed tables for pairing computation on E0: y^2 = x^3 + x when using compression +***************************************************************************************************/ + + +// T_tate3 contains 6*(eB-1)+4 elements from Fp. There are (eB-1) 6-tuples (l1,l2,n1,n2,x23,x2p3), each corresponding to a single step in the Miller loop. +// The values l1 and l2 are the slopes of the doubling and point addition to compute the tripling, n1 and n2 are coefficients of the corresponding lines and +// x23 and x2p3 are the product and sum of the x-coordinates of the intermediate double and the tripled point. The last Miller iteration only needs four +// precomputed values. + +const uint64_t T_tate3[(6 * (OBOB_EXPON - 1) + 4) * NWORDS64_FIELD] = { +0x1ACACEE95C25B36F, 0x8283860F86A452E9, 0xE463E8A5F4ABDF67, 0x5F4496B7DAFFDFB8, +0xB96E4571923D8135, 0xC0A7D039BB9DBC00, 0x5B4B7691B62F4EB9, 0xD5DB546FC843767A, +0xBB5D5CB6F297EDE, 0x8683C34F, 0xD51008F74037048C, 0x8C9DA54F68721E6, +0x6E6BBBA73729328E, 0x16A7B8815DA44FCF, 0xB9103FC3DFB5402A, 0x4344E673E040795C, +0xF6CBC30639B40D70, 0xB5B2A09F36AF62F4, 0x391A008C7948C385, 0x22259942F, +0x2E7021FB37C11B7E, 0x135FA1CCFD99A476, 0x6DFD54E21ACB8758, 0x48F64935DF5A5CA8, +0x1541ACB019E2466C, 0xA9EB8C72617BAA9F, 0x52EAFB8F96828E74, 0x12699D6A31D85792, +0x98E48A0A28C02C46, 0x177CA30BB, 0x8F692C912C63FA8C, 0x9DD48425F0A9B9EF, +0x5793C472BE67B781, 0xF1D532FA444D9A39, 0xB181C2847E631112, 0x6D791AE36802A83A, +0xFE5F4F1D7D5803B2, 0xD87D8AB8CFE2A161, 0x76D777B51A654279, 0x35C64E9D, +0x5527494F2E46C083, 0xB43900E98786EDCE, 0x60E4E9E9EC328495, 0xA48B3D4A7745C7F7, +0xCD9EE90CBBE6CABE, 0xEAA8C52F8FDDB50F, 0x4FAD073D21E314B3, 0xA6D657EC69C36C0, +0x67E409EAC1891280, 0xDBADCBFA, 0x6D33BE2991DEC70B, 0x512447B1C4BDC002, +0x1AED6BCADA4185C3, 0x3079F4483460C2AC, 0x6B116A3D4AA94F2F, 0xC07C8496E931546D, +0x1AE8CDFD601C143, 0xD92303156AA0F57A, 0x1DE0BA566C5629B5, 0x15B563596, +0xDA3DE36BE80D087, 0x22FC2AF2844A8C06, 0x646D8D7BD0712EF1, 0x5E4D6D5F34C4A489, +0x3BB015996D1117A7, 0xDC0EE37A9D34567B, 0x19404A3D28B8A0F2, 0xB1CE29B6375A6D5, +0x4989F4887D3277A9, 0x24C07B525, 0xF90274631CCC83A4, 0xAEBBC3B48C46ED79, +0x8C02C364901C02B1, 0xEA3FFF739ABCBDF, 0x48ACA55813A71C62, 0x791A160A5D4F457B, +0x862129402458149C, 0x146C4F8AF0DE533, 0xF72D8EBE27DCA178, 0x2A011EBB, +0xFB9191F0337FD0D7, 0xB9F089316C0ABEFD, 0x4EABAB267D5DDDB1, 0x1302D1CE0AFA532A, +0x29C636375CEFA2E7, 0x3A20872AFE799023, 0xCCE299E108929F5A, 0x33C9880A78D6CC28, +0x1766177816D08D0C, 0x232633AEC, 0x6ABB765D111280F4, 0xB3FA0F69FBE5FE6, +0x2CC308C221F6BC60, 0x7B531D96DF381494, 0x696941BC179450CC, 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0xBD03A79B805BEA3A, 0xB6C1E699384E27B0, +0x82675FEDEDFE37AD, 0x535228FA, 0xA8B0122BCD12DA71, 0x5B96E8122F53015E, +0xD0341687C5841242, 0x4FDB59FA5CC4B088, 0x5B898956A9B6EA4C, 0x95D069CC76067D92, +0xEA62207276E7DD7E, 0xAD64F2C7EF1E99ED, 0xF22EBD3F4175829B, 0x264E33ADF, +0xA034207978A4CB62, 0x16C5934BB4E742B6, 0x1552D5DCE5329C23, 0x2BFE231BB5FC4BFA, +0x9B33EFA49C6FC93D, 0x8131F22FF8F1DA49, 0x31F859AF529FB508, 0xBEC4134A398991EE, +0xB1EEE30DF6B43A6A, 0x2390BA54B, 0x3CA9CA5DBA1FF9A9, 0x1010A095753B125C, +0xABF4B85892DA7284, 0x1E4FDBFBCF5A1330, 0x12F9579375C70980, 0x5B73BD9B50C75C5C, +0xEABF95C6C28ECFB7, 0x11F0684A2E8AC911, 0xD164CD55548C29AA, 0x72232303, +0x30415AFF3D8A8F7C, 0xA28793A9FB3A6582, 0x6C5BB1132814CBB2, 0xF4BF41BC91ABB70A, +0x3EF7C68D4784215D, 0x4166557BD2BF1CB3, 0xF99E3258CE82EFA7, 0x22A97D44058A9C4D, +0x6607A0D24C84D55A, 0x10FD42BBE, 0xB8392C4B50FCAFA0, 0x7DEE2A7216988DE4, +0xD8A4C4B5134591D9, 0x695810DC6208E33E, 0xAEB0CD02F6A062FA, 0xE3A3953841019421, +0x9F0D7E1C0F2B7616, 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0xFDCD309E1C6754F9, 0x6051AD4CE665CB6F, +0xA2305997B126EF5C, 0x5BA7E7FE4C817A12, 0xDEEE75BD7C0C115A, 0x1191DC0AE, +0xEF950C7F013E2223, 0x39203D9D630A2ABD, 0xACD3C238CDEF43DB, 0xEFF4103631A62EB7, +0xB6ADEE709D268EF3, 0xAE9BCE4CA9162D8F, 0x9F24A42B34F1E8ED, 0x2EBD57218FFCB1AB, +0x716216E508D89B33, 0x9B689A9D, 0x78E244CA0219E48E, 0x7A2D307D0A737223, +0xF670FA144D8BC456, 0x9A74DB7B055F4ED1, 0x8627041BB2D88339, 0x86D7062F334E50DC, +0x4F484EE6EE9E26B3, 0x848AD550BC46AB7D, 0x46E6E7A4C069540A, 0x2EA20458, +0x582BB2ED9A4E0918, 0x8675C45CAC0B6D14, 0x4C126A61FA214A23, 0xF1CDF08EC408291, +0xE1ED57E0CD6A1919, 0xFD1F302223501434, 0xE892EFD3F9333F45, 0x32022F2513894023, +0x60340741C3AE49A2, 0xB74B383C, 0xBB6D441E03B8AAA6, 0x3128465494250FF2, +0x6F68711AA8C780F8, 0xD3330794A3C08CEB, 0xD12012CCCD1AFD08, 0x88027F17655F1BDB, +0xB7C7623413D53B19, 0xCE033ED211D2A153, 0x71CF2B4FC05AC24F, 0x222BCC4B0, +0x36AE29E4956BD8EC, 0x1C5DF86D7416A61B, 0xFDF709A41AEBAC0E, 0x4A37541E71A07DF8, +0xD996EAC9517D6074, 0x6E0C897BB5169719, 0xEC05969BE842FBB9, 0x61C551EAE91D23D0, +0xA0E99F35288D53B4, 0xF8F4C59E, 0x4C8B7851698B461C, 0xD19202585AF17B0C, +0x76B1FF9E843B2EC5, 0x2F6527BFC6CE4033, 0x1689054FC2E1B617, 0xA088575F2185F60F, +0x6A8400E80C500E87, 0x5020F2F620E2C2A5, 0xE901B0125A296F14, 0xDA17FCB4, +0xAAD3B148F575CD34, 0x8EDB88C64B59D124, 0xB5DA9C5BE69A712B, 0xC6443B686E73D77C, +0x79C32A6C6CCD24E3, 0xD809A0A9FA18773A, 0xF62FDAFB3247BBE4, 0x18790C2A3B5C1CE6, +0x29A44BA35A185DBE, 0x200E8B0E1, 0xDD6137A9651C4DFD, 0x5347F33689B5F49C, +0x92BAF0557A191850, 0xBDF69256B0A08F0E, 0x9A646DCAA103EADA, 0x92167949A4218486, +0x140DE6B7B7A91D2D, 0xBAEC00E8F0749E64, 0xA9EF5509DEA4FF8A, 0x6C31F5C2, +0x8AEFE447FBA8C4DD, 0xA87A62BC9582F00C, 0xDD2E40ECD736A7FF, 0xE512F4058850BD44, +0x979854A1C0983D4C, 0x63336CE80569B317, 0x1DFFD6349D8F43B5, 0xE93D441C92AE245B, +0x649ACC4EA6327794, 0x1D34BA0A9, 0x76BFD0E3F30D12D3, 0x358E6CB6149FB7, +0xD6A74899568C067F, 0x850A916890FC0908, 0x82983AE7DEF4AD8D, 0xD836CCD300B8E4ED, +0xE4A9F4E76E8BAEB0, 0xE78205FF031C4A0C, 0x1ACB19D2AEFA3139, 0x1243F0F5D, +0x22110174DA40044E, 0x5958DBE87C362954, 0x514AF2BB004E2324, 0xA7B88D048C4C2DE0, +0x7FFEAE45A926CE7D, 0xB62AD2ED1D15D14D, 0x29E23771B32606D7, 0x97BF87A0E8E8A4CD, +0xC9075E9E70D8B915, 0x2739419C9, 0x7222823C717159DD, 0xA8C765C9C884FEAC, +0x17F365B3DE206905, 0x8EB32C6B963BD378, 0xD6E5AA5BB91174DC, 0xAAED6ED507FA7C36, +0xD005C00223DD614A, 0x2E588A31229BBD18, 0x93AAE1109A6AEA88, 0x1127F527D, +0xEFF581A20BAF5954, 0xD4B42FB4290B152, 0x2841C54885F20DAB, 0xD4E0B3813184F3DC, +0x3BA483D11DBA6126, 0x3EEA29DA0B5F21F3, 0x57253FC50CF68877, 0xC17EC43D9E0D44D8, +0x67C9B867DAC47FB8, 0xDB9D13D8, 0x72DD7C8676A64099, 0xF8E278EB669274AE, +0xC9A905024896F728, 0x3CEDBDB82F72E065, 0x3AB694BE481B520E, 0x78DCDCEFDC683AC0, +0x2778DC6C510708EE, 0x424083014F9FB042, 0x27A5D839F47E4F81, 0x14AAB2028, +0x5082858B0A0B8428, 0x78A4FA5C7713C78D, 0x44706D95C45C97E5, 0xAB766E9168FE1B39, +0xD5EBAE33F6FEA2C4, 0xB26999E52727A3B2, 0x55AB58EFBDE0E8BA, 0x2B02C319D2F50BC9, +0x5164D6C3F3787AF2, 0x22C8DE677, 0x20F6593713F8D435, 0x7103886461790D6C, +0xFD66809D30CD836A, 0xD01CF3A6AA702A7F, 0x9406E9DC0BE4A91E, 0xEB17E8B213E4257F, +0xCEBD98CB15066FA5, 0x89AD5E3E1D795BBA, 0xA8E3F1879B3CFE9, 0x2845AA8C, +0x18B4498B24BDC3F4, 0xB637DE7A64682E96, 0xB712FAF1ED95B31A, 0x4B57DCFE61FB196C, +0xEAEE824924DC7FF, 0xED55063690D924E2, 0xA34D23A45780D8C, 0xF6D38C51AE094C7C, +0xA4066D9D5400AE6, 0x113DB1AEB, 0x975BFFE38A592117, 0x434D8982391CFD9F, +0x79E9161681ACCC1C, 0x742D032771422EF9, 0x4DE65B59F83AB4F8, 0x1CBA7EDEDBB8BF71, +0x242BFF6B07827888, 0xB148F6A3D2C2330B, 0x1FEE2C095FA526C7, 0x15C3A9111, +0x66912F32CF70939, 0x7A5179496BF4AC16, 0x342E657D1EF9661F, 0x33024408228D2BC1, +0x23F90BD93F1D426D, 0x2775B3F30CE8ACE5, 0x20EF451E5341EC88, 0xF37B4D9DCA345C2C, +0xCC08E207E1C25FAB, 0x1BB69BE10, 0xDE37935D39574114, 0x80BDB6A011201144, +0x52B5DD2E3987743, 0x1083FE03781A1EEA, 0x1DD99D5C8D12EF64, 0xBF878DACA3694BB9, +0x4903BB6BCC836B1B, 0x388BE9E6DFB97258, 0xF667665C70C1A0CA, 0x97B676C2, +0xA69BB712736F8E6E, 0xEE83EC6359D1D7A3, 0x4034587C2086EDB3, 0x545DB8C8CD973BB3, +0x645FED637BF9324, 0xA3F6E562D12ED17F, 0xEACE0609E2187FBA, 0x51F650C93B7A32, +0xA0DE576ABF66F09E, 0x211E784C6, 0x6F9A09D7C468CF55, 0x319A0C17F03806C2, +0x43D341E7E3A3590, 0x9C32F137E7D4C255, 0x4B8FB5F860601A13, 0xF1CD6AEC71BED0F4, +0xCE88D8EB924AA31D, 0x5F852A8EE925DBA6, 0x8B97F59A8F3E858E, 0x232B5CD8C, +0x6B3FDD15E24ACA60, 0xFBE291EB3850743D, 0x16C0C4E51196A33E, 0xE3FD7643B041F847, +0x5188EBD9C79D61B7, 0xB306AF9D6478800C, 0x34C4F93353DA8802, 0x3274B2EDACB5B9D1, +0x7D4D747F08C62529, 0x1EF6CA7B3, 0xADCBDFCE73D505A, 0x72B3E2B46529F9D2, +0x625FA10CC94120CB, 0x29337BD25133CB9B, 0x19D482B3B3E262B9, 0x3EB45862500EF7E, +0x4D5A959ECC1F5909, 0x7D16E246FE9D87CE, 0x10A4157365E4A491, 0x1DFB74E20, +0x1930B476A230B7BE, 0x3A42EE16DC949E2, 0x838416CC861CB74D, 0xE43303F18BFF483E, +0x30C6C49AC1829C11, 0x40DD7E521AF62273, 0x33AA27D882B23CB2, 0xA970F369B7A93C6, +0xDBAC55CF2FEFF179, 0x1967E10A3, 0x4709DA258D7CF239, 0x68142BD88204D1EA, +0xAE14B528AE909088, 0x8D813E124214BFD6, 0x8E6949403E0D509B, 0xF795CE2041AC8CA6, +0x20F1E1F2A851B359, 0x89B489710FA8BD76, 0x1608B910A609EED8, 0x1F957263F, +0x73CFFC32E9B7CA37, 0xF67644739E040DB6, 0x820A54C0C46F61B, 0x95137B08505FA716, +0x981FE9E46DCC3ECA, 0x81B2061969F6DDEC, 0x2588EE0651AD8E2E, 0x9BEC9F1B09B345EA, +0x67E641D1CC333321, 0x1A98DA956, 0x1930B476A230B7BE, 0x3A42EE16DC949E2, +0x838416CC861CB74D, 0xE43303F18BFF483E, 0x30C6C49AC1829C11, 0x40DD7E521AF62273, +0x33AA27D882B23CB2, 0xA970F369B7A93C6, 0xDBAC55CF2FEFF179, 0x1967E10A3 +}; + + +// Precomputed values for the first Miller iteration of the Tate pairing on the +// 2^eA-torsion of E0: y^2 = x^3 + x. Contains a triple (x,y,l1), there the +// coordinates x and y of the double of P are in Fp, the slope l1 is in Fp2. + +const uint64_t T_tate2_firststep_P[4 * NWORDS64_FIELD] = { +0x5BE1ED524F33C52B, 0xE82A6C9C95E44A2, 0x35AC19AA3D2D0C8F, 0xC48D5A6EF316DCEF, +0xA75B1FAE1C70541F, 0xBF4709C0460AB142, 0x6B989E232D21267C, 0x1C8F0D2F1F827A73, +0x7A1EF44C4B138F94, 0x76F38CA3, 0x1E89B04824B7F00F, 0xB0CECBD277603CC8, +0xA7D3D9FCEF3F333A, 0x96A48E39362C5CDF, 0x562632BF879C83F5, 0x36E6479094FC0145, +0xA58ECF8D41DDE052, 0xDC3DA3C376FAA4AC, 0x6658A30D41B00A4A, 0x1AC7A7CC0, +0x4505A22B44048A6, 0x19F3A6862BD40254, 0x7C43EF221BCF02B5, 0x6B2DFEA48B5098B6, +0x6E06586FDB2FB0AF, 0x1097E2BCBF9ADEDA, 0xB4EC7813CE4DA07F, 0xD12393C9E4990B29, +0x3FEE313BA5FD37A2, 0x1A17AA2A, 0xF167C294F154F59C, 0x8A597350936E94C2, +0x9FA898086E4BAAB3, 0xE81E3DDE95E49C58, 0x3FCCFAEB8E00D887, 0x731B0E03E4A278D4, +0x4A66222E70B0D80B, 0xA63038C5CF23DEB0, 0xFA9EA4C23B762257, 0x35EB2E52 +}; + + +// From here on all values are in Fp. The table contains eA-2 triples (x,y,l1). + +const uint64_t T_tate2_P[3 * (OALICE_BITS - 2) * NWORDS64_FIELD] = { +0xE76420CC37DD8308, 0xA92FF26EE4745DAB, 0x377A25B425FFB178, 0x2AF8E297BFCE0D1F, +0x2589D47C051EF1EE, 0xDB00E9682F7F9205, 0xE9967060F9E3EC7, 0x154FE450E6CE6B92, +0xDA2544169F466B8B, 0x21CDD1EC, 0x79CD0FC4738F4FC5, 0xCEC3E5C7DBCAD38B, +0xA94B3CFA13400C01, 0x10E6396CABA4A834, 0x72E8F09F76B2EDA3, 0x669163F4DC456D51, +0xBDA1AACA2C93BB37, 0xD239CAE9D0D64DBF, 0xF72FC60D1961F96A, 0x1A017D00, +0xB2215859497ACD04, 0xA752EE064241DAD5, 0xA76D04E5DE9CF1CF, 0x823007A316BF06D, +0x30A19BF25506241F, 0x8757C8F92E225574, 0x74F318F5980DBEE0, 0x4F61DA2CF0B3BD1C, +0xD12DEF2F28060036, 0xB854AB5F, +0x611A44C308A6CF4, 0x921C2D38B4AEA068, 0xF71BAE5E2F48A77D, 0x47F3F57089A01C34, +0x27177E7F6FDDA550, 0x4B470FC33533A72B, 0x400774262E5F56F5, 0x9B8C3B105B3C883A, +0x5BA5C8655ADD44DD, 0xB4BA6DC5, 0x474076BF2DFCD8B5, 0xA8EC91566930A7E5, +0x4DF93554A0B82B92, 0x2BD5736F76063698, 0x61EFCA5F3FBB56E6, 0x176E73E317EB5415, +0xFC9C5732C9773153, 0x9BBA66FB3D0E0D3C, 0x2BBA98162A1E811A, 0x191E8A2F9, +0x5CCBF592A41F9C47, 0x477BC6E5F680BFAD, 0xA3BDC29575D57A6B, 0x2A6767D8EE5A4FF7, +0x3275482178B202, 0x48FD1178BCD644B8, 0x1449677E9BB6D2CD, 0x841E2100C7643702, +0xE56970CF517A5A45, 0x4988AD97, +0xDCAE6F11D7427B31, 0x48806E91A39CFE89, 0xA4849BCEA8102C03, 0x8E560FF5C279EEF6, +0xD3BE8E4604A31BEB, 0x5812DE6ECE9D598E, 0xCD5F2849753C339E, 0xD67B5B8417E81027, +0x94CC38B6A28B2B8D, 0xF2EA33DE, 0xCD71A58E3A9F4EBF, 0x95D0C9FE2DD1E9BE, +0xD636165223448FD3, 0x6ABB6BC4DFA92689, 0xED46D50784214072, 0xCBD1ACE6988F45C9, +0x36E5F1FBE59DD554, 0xDE08F9F492F0C1D, 0x30E441A59E5F4778, 0x27B9F69FE, +0xAFA56A94C9CF483D, 0x2192A57F6B1EEE3A, 0x6F936772964C8407, 0x84941A3BC590A2CA, +0x15F3BD3F6B677BD1, 0x9D7D7560E771A039, 0x4E381B7E59A38FB0, 0x5B6A32FE1C82DF2D, +0xB97614E6ED143343, 0x52D26742, +0xF810F7E3F4935152, 0x6FD1CED8B51B14D9, 0xD7684DAD708166CA, 0x770BE11C32D8A0AC, +0x2F4F7AA5390A0DFE, 0xE64CF61B5E914CCC, 0x8EF26F27A5898206, 0x7938B247C3675069, +0x3882B198890C175A, 0x16D795D57, 0xB5BECEAE19C633DA, 0x6FE9C2EE9D63CE60, +0x7AD23A78A93A5F7A, 0x8D93B66E673424AC, 0x2144807DD60D5324, 0x9F20C0BCFA9259, +0x93B4379BF699746B, 0xB6CFBCD8DF2AA34B, 0xCE1E247732921F0, 0x26D3A1A70, +0x72307622E528A148, 0xDED7BE01E4138773, 0xE386945F26C2F9EE, 0xF1D3B7F082E3DCB2, +0xD9A4D835F6BD545D, 0x8B3E666CE7062319, 0x224F19D6903000DA, 0xCFFF4EC9583E5055, +0xBE625F853687F2E3, 0x1F47531E9, +0x60AEB69F0F12FF49, 0x920740A6171F31A2, 0x264301AFC2E17945, 0x1CF025E2B63DBB10, +0xDF9AC49BD709F687, 0x1258DDE964761EE1, 0x43F01D4A52B7EDC3, 0x915AA0928721B0C6, +0xEE8CF27857A3EEA1, 0x20CC71243, 0x7B3E0F8C1E67B876, 0x7849E97064612AA0, +0x55D9C72DA054EF1F, 0xB587DF4503C95FD5, 0x41211FD23DEA9BFB, 0xFADC50A252B22A1A, +0x62250BB1EE9AE790, 0x687DB2EB4C1EDC59, 0xAE555824C68D3085, 0x268C77918, +0xE64028043D9145AA, 0x51A41D2047159B5, 0x9AFA848999D9EBDB, 0x757283C61A603CFB, +0x9627FD75F5CAA530, 0x7BA6322369D5CA66, 0xD55E3D1B51685784, 0x5362FAA489789D67, +0xF39972999BF3B6A2, 0x279BB97A, +0xAED1216787341C3E, 0x908C6A7BA6B01037, 0x9BE89656D0A36351, 0xC8ECC4A1C7C34628, +0xE826D224B22FE427, 0x28087201B385B63C, 0x995D7CA3814C7CD0, 0x861C6BAF8C50B65E, +0xAF2C1646F2F8C01A, 0x14FC86E03, 0x15829DDC1C8BED71, 0x4EE455BEAF68966B, +0xADCF0B3CE10416BD, 0x205A26EAFAD24065, 0xF9B1423C42BDFE7C, 0x275664B9C7E4A57D, +0x60328D087BB6B69A, 0xDDED5244047A515D, 0xBC7C716EB05A45AD, 0x7C2BD20D, +0x2251B27901ADC2BA, 0x220C9711C773827C, 0xA20B17312E44F884, 0xC88AADC105C5F445, +0xDE09F493916EBD95, 0xD0B10F356B40F22A, 0x93AB334CBC5796E8, 0x592B6F2CED55E2C9, +0xE758384132E52C0, 0x1F65576A7, +0x405961B9774C8761, 0xE67D960CD77FCB54, 0x7D6D34BA3898949A, 0x2BA7BB1D9668BD8, +0xAA1E7935632DF103, 0x2F90954953A09BD7, 0x9F98D7CE473C0EC3, 0x8DB0A93865E6223A, +0x3CA39555922E04F2, 0x3E57684F, 0x896080ED05DF7596, 0xBD5C1C6F7EA8812D, +0xAFAD6A5F800B2232, 0xCBF98BEA3CE9573B, 0xCBC1F2F3CAFE767F, 0x4057675C8D4BB81D, +0x46A123D9FC0A4ACE, 0x2B490E814AF89C16, 0xDB090953996C364B, 0x1F40C886F, +0x89359E4181E5D9F3, 0x289DD05377DB78E6, 0xB3B0C07ABCFC4A04, 0xBD9EFC5F8B614723, +0x4EB2CDD0E5A5B679, 0x3643AD7B6003F281, 0xBB07F8621EB37434, 0xD32525E1627940B5, +0xAFEC13AED2DC5FFC, 0x1F2BC16C7, +0x4F25ED51F2DA86EA, 0xA5BBEA03A85E0E41, 0xC6ED4765BFEFCA1C, 0xCE64415005DFA33D, +0xF5E879A55E55E458, 0x83DF89E567D053A1, 0xB394FE355FC88700, 0xBD45B34EBA3AEF57, +0x634DB44F8252C18E, 0x20C521A1B, 0x5D414B47ED6DB7B6, 0x2BBDD0E469704FCC, +0xD1DFEF455A164A5E, 0x446561D0FBBAA3A9, 0xC63ECEDDD494A83E, 0xC8B89E35D49D21AE, +0x83C69A46B3163CA9, 0x96649CB8B176E336, 0xB585F986D6152C3B, 0x27832BD3A, +0xAB284D12BF6EF07, 0x724015760DF5BECA, 0x3ABEE6F09B1F3D87, 0xFA2FF92B57F927DF, +0xF31033DCC310F9E7, 0xEBE0F34846D0CDB4, 0xEBE9AF6B6C2837C7, 0x9BAC7EF70985D8B5, +0xDA4729D6ADD221EF, 0x1F03B652C, +0x6E506EBAFF26728D, 0x7FBADEB1174BBCCE, 0x2510BFF6FDFB8243, 0xCD05098C173FD8AD, +0xAF4E01D40BC210E2, 0xF9D81C76768C197D, 0xA3CAC6108C447368, 0xA530B13CD0530348, +0x49FAB031A6F487E2, 0x11F4F7A6F, 0xE3147613CB95CE, 0x17FD57ECD5A6298C, +0x649AEC524CB72202, 0x626005084F0EE06E, 0x3F6A9C7186D64CED, 0x4445B842868A7C72, +0xD492216BC9D38B43, 0xB90D2D9A90124185, 0xED282ED0FEBF8921, 0x177D113A1, +0xE0FB4E10339F6732, 0x32F1F5FFEDFB7FFF, 0x49E129B87D8D095C, 0x16B2B8E489B9F77, +0xF68CC1FC6766A782, 0xD8BA1B1398F7A9CC, 0xC3DB37DA9680463E, 0x800986502D924078, +0xD3D39E201323B77B, 0x9A39C58D, +0x219D3FA18644ADB0, 0x7987936057F48063, 0x778328676CA162A1, 0x4571CE486E4F4C91, +0x4B249772A513320B, 0x78E49BEBEB112997, 0xDADB1B2F08F4B59C, 0x213CE1247E80CB01, +0xE7C599AF93153182, 0xB5C8029D, 0xCD9C7A4CAC8A0140, 0x5C7436524631F66D, +0x363CD9D6BCCEC2EA, 0xD9BB67FBBD221151, 0xF87FCAB6EC617EC1, 0x61496D9B4BA33C9B, +0x86D21FADD8F971B1, 0x846B5D081BD0BBAA, 0x4246650BDAEB66E4, 0xBB8839A2, +0xA4168E3E2662097B, 0x7CCE694E6257FAA6, 0x4090C55FAF7D4F5A, 0xAD41323B1BFDEF80, +0x17C9A0E3301B3FBC, 0xC0A32CF7B884B6F0, 0x62B12714EDCE57B5, 0x250A56A91AACEB3D, +0x326B8110C4E42D44, 0x1A1127288, 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0xD1C7A173A802B83F, 0xB7EE3028B71062B0, 0x473A7FC33D8E1289, +0xCE03BC683339C669, 0x2345AAB4D, +0xA4AE8821BFF63F5F, 0x1AF0018526BB10D4, 0x2E6AD8BC3C1B1B46, 0x6C062F6970930866, +0xD035BB446A5CABEE, 0xBA9CB66439132ED8, 0xFF99839B9C12C3B3, 0x68A6D925B9966110, +0xA671B5C4953A9F6E, 0x2C99FFC4, 0x8C081E2E424E27FD, 0x7AB8769F1F5729B2, +0x39A28F443B9A06E4, 0xD43B1E3187C02043, 0x5452C2FC04E9C6E, 0x1192D0B877B0C7BE, +0x477A32A9829ECF0, 0xD8DEBB29A29326AB, 0xDD2852AA42362606, 0x18917924C, +0xD816DE34622BBC54, 0xEF56D2993D83789C, 0xF064B5153B3ECA24, 0x34F16E299DB1B3CB, +0xB3A69B58620EC092, 0xEE4A8B3E9192446D, 0xD354180277B2CF7A, 0x23B73E125C2185B0, +0xAB8CDFDD31BDF0D6, 0xB2E1021C, +0x1EBBCC8567C392B8, 0x45A4D6C7A43EAE58, 0xD2655F25307DD679, 0x262B3369C00C9215, +0xDCD91DA835FEFFC, 0xE634D37237E4B9C5, 0xBD7468A11010D9FB, 0x33364B56974C061E, +0x11A04E52C9E5F1D7, 0xA5589C08, 0x4CF8AB5E4DE0E4F9, 0x3750809C7B60D368, +0x7BA7D4CDC3EA6191, 0xD056BE205538C5CD, 0x6450E19E6DA10290, 0x6AA842183D5913DA, +0x967A68C5933F9E8, 0x2B9A24F73C225FB1, 0x7E8428E55E7DB958, 0x2729A7AD1, +0xF91E48849C962FF2, 0xE5C7488818DE6C4, 0x2C6111811070FD4F, 0xAFF891EC66F1EDB0, +0xCF7ED22142322A3C, 0x1235AD106F8B0106, 0x7F4A4B073FAB7581, 0x905E32270AB1B002, +0xD5D67C7A5A20138E, 0x9E540DAF, +0x3E13196EBF9DC095, 0xA2A42B888455A773, 0x558E46B450BA1558, 0xFBC62A6861C0CD5E, +0x6F7CE81DDE8F4023, 0x9EEC254636E0F319, 0xC22C337F5BDA7677, 0xDA9830F1E8B1FFE3, +0x2DC4B7E70DAF3781, 0x201F93974, 0x69C7FC3367AD16ED, 0x7457A140AFD54B38, +0xAF7D02793271D96B, 0xD881EF6593716C43, 0x2425F6A12C64C45D, 0x318A2D7703F5AB1E, +0x579919F2DC862FCF, 0x47AD8B3743F9A5F5, 0x970A88FE96FA8B21, 0xC85F550D, +0xF186EDA5495FDB48, 0xEE120B859DB55A68, 0xAF14DDF9F20A0B9D, 0xA6E1A83F0AC80D78, +0xD8D3B0097865E071, 0x2670A77C35FA9C6C, 0xA4EE8C164F2DF90C, 0x256FADA08BCDBD14, +0x382DABC63D77149F, 0xFD38C940, +0xFD76FA53ABA996E8, 0x498B96EC73E3F9EF, 0x6717EEC29E68E758, 0x65AA9E664C5F439A, +0xB4019D87BB18EC36, 0x2EA3DC5CE74898CB, 0x684B0BDD8DBB2088, 0xB2E1AD4A50EDC3F1, +0x7EF7A263BFBC0526, 0x23875A19A, 0x4ACA209030AEEBCD, 0x486878D8D9833A2, +0xC11066E3596C45D, 0x223AC0F5D6738E12, 0xDD1D165862648D96, 0x4864F1610C1F200B, +0x997DA376D8EFAECC, 0x98D48CA3FDF8AA0D, 0x4F2259B29C57B1DB, 0x3CBFA567, +0xF6972B4C696B4959, 0xEAE41ED219B82510, 0xE81BDC9862219998, 0xAF0302433D6FF329, +0xE1E4FE35C830F23E, 0x2194D5D8D0C254F3, 0x7C6962CF4CDB005B, 0x7C523DE3C19E6B29, +0x9FDA4431C9D63B2C, 0xBC1EF428, +0x3ABEAFF39166DE60, 0xB1457C6D0704B87, 0x6786D8B641DAAE2C, 0xB2647BD423BF5BE9, +0x1419C7C15A8CC388, 0x8F02F20F3518E15F, 0xDFF2C9A11BB7FA07, 0xAD2AA843A505C72B, +0xFE4B0BF56D6E97EE, 0x2E7D20BD, 0xD3BE5FD9FA6AC95E, 0x90E0E13DDDE2E0BF, +0x227A7CCD74DDC04C, 0xE5B0097526EB02F9, 0x573BD5584A8E3E84, 0x3CF8CAFE5600E3A6, +0x8D7BC7C1A195E974, 0x3C7C651EAE33C50D, 0x9E04F49D0BC1B253, 0x25E4ACA71, +0x352246AB3F6E64B5, 0x45CA7B4AB0CF1D9C, 0x5AED22E075337169, 0x93348F17C5028A3B, +0xC0E5D42637ABE2DD, 0x13209290D9B115CA, 0xEF3332F33FC130E6, 0xA04FAEAD6DDD5F62, +0xED4AA026B365A2CD, 0x1027E8301, +0xB8D371D1A4535B9B, 0x59D8A02A90F5DA19, 0x1C3B23412198B9BD, 0x4A4542C256928731, +0xC1630900837869BF, 0x3A73388ACBBDAC8, 0xCE965F4E5412ED75, 0xBEF0AF451BF2BDA5, +0xBA478679D37103D7, 0x11E0F3F01, 0x6BB2877E0AEB57DD, 0xF3DC7E6D52626B37, +0x5151018772163C71, 0xF3D8ED6659CE726D, 0x57AD24C8953EC45C, 0x983499F90C4DB3AA, +0xD104663D31FE5CCB, 0x4AE2CE8134B73B4F, 0x10A571A16670D9C0, 0x30790CD7, +0x3DED0D19173914D3, 0x86151A214D1D7AFB, 0x59483D66F4A207F4, 0x1A2B86AFF634FCD6, +0x77BA4A5102DAE3EB, 0xCFF0DC5F221A5B92, 0x8178D10D92C724B8, 0x5A4AB5095B82C5A1, +0xB11559C36784046B, 0x245D93820, +0x5FDBFD64BAD1CF6A, 0x7E8DE5BE0F9702D9, 0xDB4FC8664FEC408F, 0x776F7C993505D0C2, +0x3BB363C15A036C22, 0xD43D2B8B14E65DCF, 0x91C862EF8E5880E3, 0xA9C78B7FB4063A88, +0xEA0CABC25C3286C3, 0x62C30F36, 0x5C9CC4CB803A182, 0x4FF7B5FC04C7A8F7, +0x60F6587962FC256B, 0xF5A361D59823C27, 0x80CE1B22C2BB9562, 0xB1A44EA5E6C2A491, +0xB3DB5DCF94904A16, 0x63B802C7A2E32910, 0x3148C244F15003B2, 0x20C7438EF, +0xB1BEEDE607683829, 0x43B31D7F8CF6F63A, 0x6EB311EA4938AB79, 0x8396270E10B589EA, +0x9123B111C3D9AB74, 0x35D268F9150261BA, 0x42675809C0ECD498, 0xD642B4487BF39FB, +0xCF0FEE6D975C0BF0, 0xC6529582, +0x5DA52DE2E62B02F0, 0x8AD499E1D30B71B5, 0xD150DB9FDB01AF9F, 0x22849B2AFF2FEEE3, +0x2A9BB481B64461AA, 0xBDE0D7867F35DD76, 0x106B2FC48688AE0, 0x4E296EF9F5658A9A, +0x74BD0DC8A72456FE, 0x10A432664, 0xBDC781D6EAB85413, 0x1F6B72302B6F7437, +0x83609B5F775E5DD3, 0xBD284763B66056D3, 0x4187EF60E9115701, 0x45FC3392FF997702, +0xC816564334EDA76A, 0x2E069C976C6EB91D, 0xEE640D22DFD304F7, 0x13DB1DCAF, +0xC652E92E49B7F7CD, 0x8A36721FC2159DFD, 0xEE0C2DB716CE6358, 0x358BAD009C67E421, +0xCC23F014446D8AB0, 0x674F5B0C1D9E3D4E, 0xB64E9575A013FEAE, 0xC41B28D1370EE4C4, +0xC805538035FF1607, 0x93C1EB96, +0xE691943DD99B64C3, 0x69E342214B22EB44, 0xE64C8FA68312CAA2, 0x8527AC642DECA70A, +0xEF3B7DDAAB73DDA, 0xA730C91204F5DA78, 0x1079839ED0960C60, 0x8EF09BC8D9F97BDE, +0xB20ED42772429620, 0x26824A853, 0x571E9C8D909F906C, 0x1C2F274697A0DE4B, +0x2ED47380C6AAD9DD, 0x2748EA50CD296289, 0x444669CF3B7478F9, 0x1235EBCF7ECC29F5, +0x7D91D7E64D9941D, 0xAA186C7AD5103363, 0x48579431F80CBBE5, 0x8EF4B421, +0x3B32FBBE2DB2BC9F, 0x24DFE9DD88711824, 0x73B1989BC29D8584, 0xB8EFAF902A50BDB9, +0xAE70FCACEAA8BD93, 0xC84BBD15BBA034A8, 0x4235C4E1BE2ABE76, 0x2CB69E58FF330EAD, +0x4F2C8C52A2769A9, 0x275AEC34D, +0x66E4B3BC6D503D2A, 0x967DDC2786DA3FDC, 0x75DE885CF7077A28, 0xD0288C02809C42E9, +0xDF4C0C8F0E59D67E, 0xCC7043DD7D4B15A2, 0x9FE1D369BDB20957, 0xC4B4B251DD69F196, +0xAA90E17EFAB7CC6, 0xFD8C050D, 0xC9C28A5F1D4A607D, 0xCB1FB025E68AF2CF, +0x1936CBB5A252574E, 0x301C1488C512D81B, 0x74A84B4D26E3DB9B, 0x8826758EB226CA7B, +0xCC3F25C91DC5190A, 0xA30A13ADB1404396, 0x4638B7DEF1FF8366, 0x126C77397, +0xBBC24311B22BEE1, 0xAA26492DF7FEE2AC, 0x37613616E23B9490, 0x3D288FC114138A32, +0xA04622912DE0AEF2, 0xE516AA8786FB3B64, 0xC681F1173291948E, 0x810BE75C3C995C9E, +0x48D6E4625744072, 0x2693FA1BD, +0x7C4495E28C08FB40, 0x6CC20EC7C5501A6D, 0xE1A423281D5727D8, 0x3CDA803A747AE42B, +0xF293BDFE899FE942, 0x6A63727D6EB6A7B9, 0x4F577551A8B93A75, 0x9D4FE5F3F2A6C738, +0x2A52219A2AB66B2C, 0xEE73A837, 0x76DF701AFE0A7892, 0x9C01ED466F2C4FDA, +0x1EB87874BF72C942, 0xC22A46E7CA64CEB0, 0x40282D499F872916, 0xE6CC47E467A1C936, +0xE4720EDF18686A2D, 0xDE157AD320F659A5, 0x28512D44AB3D19AE, 0xD92FF5E1, +0xB80A80FD2F99F5E5, 0xB0C648671D058E3F, 0x34933005264DB7D7, 0xAD514A0980ACBE52, +0x64B81574A82EFA99, 0xAFB2AF6776022E88, 0x808C34FA35FD53A9, 0xC25994A4D9B06CF9, +0x10D46CE00D4E1F41, 0x192860BD3, +0xE3CEB0FAB5C3B9EF, 0x3AF90E09AEBFF02, 0x7227045F656C3C36, 0x221CD85B3F2E9139, +0x82986E2D3BB7C0A4, 0xBF844AB18BF02E11, 0xDF10E1B7AB5B277D, 0xA370AC999D3513C2, +0x1A1EF9E71E4B2688, 0x17919AE71, 0xA389C48D3968F3D7, 0x6DFBE9608EE8DCD7, +0x14B8BA30674040CB, 0x1A41A5E3B1A737CA, 0x9C88FF1429C60C17, 0x55882E4B4E4B409E, +0x2560C7465957AFC9, 0x26822C716C02F0DA, 0xC8B691285F10AE6A, 0x278EF07ED, +0x7D398EEE46D9347E, 0xC098092213D67999, 0x33FD761B970885D0, 0xE2B97C428DEF6DBF, +0x75F6AD9BDEF9CDCE, 0x7D40893748FD8573, 0x7FC848842D59C12F, 0xA34C8FC72205F1F4, +0x766B8C0058E83EB, 0x1324FD0E1, +0xAF0D1780F3C98E2B, 0x9205F12E21EF47F8, 0x191809A403552F0D, 0xFB6EFBF4B2C4C9D7, +0x3DBA39AA7A88748F, 0xFC49A0B4DF1E28, 0x81D083F6D2B4B31, 0x9DD30B48CA4DEA40, +0x86E0951C7372FB69, 0x22E552E72, 0x38C19A28E142FE07, 0xEF2AF32D5F2ECF78, +0x9AC7734A0910907E, 0x4A7E68756F234589, 0xB3D9DB49F6A8CCE8, 0xC42A1CED1C9EFE07, +0x1C3984B9FEE33B29, 0x2B0ED24F3A456F5C, 0xDAB17C348E29BB01, 0x1741C17AE, +0x209F42F8455894F8, 0x6FA8A3A1B7BD3BE1, 0x9F32DC8B3C0FA504, 0xBAB1B4758D6078DC, +0xD52D3CC33689B40A, 0x9B3E0ADED2218157, 0xE5CB64BA7A79EBC3, 0x98F145A388451DE0, +0x5EAA8449598957D8, 0x25AC64FBA, +0x67205E15175078E, 0x894BB12AFE2FBCAD, 0xE7C2B8FF7C89A4A4, 0x3CCB5C538771A30E, +0x1AFC884966422A98, 0x3226153F17164CED, 0x2880A9F90F294C6A, 0x30EE7C6EBF29F024, +0x3C6FDBFCD1B524A5, 0x254215F1E, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, +0x0, 0x13A2C637E95545A4, 0xCE90FCF423F58113, 0x59162A1251761C47, +0x22F6B23510F407B0, 0x3FB40A7A3898A0BC, 0xB3BA446746BCA3B2, 0x7A837A4454F01666, +0x79A9A22B85C4EE99, 0xE1093BD17C27343A, 0x1737968C6 +}; + + +// Precomputed values for the first Miller iteration of the Tate pairing on the +// 2^eA-torsion of E0: y^2 = x^3 + x. Contains a triple (x,y,l1), there the +// coordinates x and y of the double of Q are in Fp, the slope l1 is in Fp2. + +const uint64_t T_tate2_firststep_Q[4 * NWORDS64_FIELD] = { +0x2C9E53071352D43, 0xEF4088AD3E54C6DD, 0xC18E7055D2CFF348, 0x24B3268C87D5F690, +0xA3E6D94ADE7B0A93, 0x489BAD43902F0B0E, 0xA1A300A465CBB34A, 0x1E3D0279D17C14C0, +0xCC6901CA8B4EB6EE, 0x6DEB13A0, 0xB84B1E242A63879E, 0xD3A74C3D2770FA06, +0x49DF32C277DE73A3, 0xCA452CB04EBA1741, 0xE36EC74B21763CF, 0xEE808C414124F7B3, +0xCDBC7C4C7FA2F565, 0x6EC6A04436A3B6DD, 0x655153FCAC56E490, 0x1C8AE36CC, +0x49FBC511D3BA2DF8, 0xDAB619C2019157EC, 0xDA5C5F3D92BBAE54, 0x49DFA8B23EA68649, +0x4B0ACA57CA833E4A, 0x5897077C5879B49B, 0x2292FCCA2466BE33, 0x67ED07E1BDBC7A44, +0x524DABA6A86CF688, 0x1A291037F, 0x66B1FBDA9D4C0E29, 0xF387AF93CD5EDB70, +0xD7046A31DFDDCF13, 0xBF285B931FFC64B3, 0x200D028613109DA4, 0xA8503FE4DEED0131, +0xBC04855F33EE906, 0x287557FA56072977, 0xDE18AF410CCD4F3A, 0xF7B7EBD +}; + + +// From here on all values are in Fp. The table contains eA-2 triples (x,y,l1). + +const uint64_t T_tate2_Q[3 * (OALICE_BITS - 2) * NWORDS64_FIELD] = { +0xD8A293B6CF2BB40, 0xE1B641C07DDEAD64, 0x752811982A639080, 0x5EF082EEF14391C0, +0x4E69530B77F63838, 0xE5342EEF727F6792, 0xF833326993E90187, 0xACCA058E8710D072, +0x55F4B4F98DF5D0C5, 0x24DBF832, 0xAD40559D73A22753, 0x4FEA70030F3D7C30, +0x9D351D611C377861, 0xBEDDEEC5B19EF48D, 0xEB85498B19F2BB0B, 0x81699D09B184FE3B, +0x5192C626B954608F, 0xBE03D730E9EAFD39, 0xB1CB16413A4315A2, 0x16254F779, +0xC8864C028ED7D0CD, 0x5915417919728699, 0xFD11B78802FA9E8, 0x69FBB78B682C26B2, +0x65F142FD521EF5F0, 0xE5F9EB77B3BE7118, 0xFE0A2027A9ED7638, 0xD7BA06F4CB96D138, +0x80F1310134488F3C, 0x45BF80D6, +0x535C6E813E9D518A, 0xAD64453323044A7, 0xB68696F72CAFB024, 0x67ACF707BBC8B400, +0x4DEB973E18A70792, 0x64C75184C18B7735, 0xC143A2C5B37680B4, 0x37002C2DB2585AE6, +0x7137052C44ED8446, 0x50623905, 0x25AF94FA7F46084B, 0xFA16E40C4015BEB4, +0x30B5F128BD2D717D, 0x3001A48F6C04ABA9, 0x1EBAC5083C31DC97, 0x3E2216F817DFD05B, +0x34D63D8988B80FAC, 0x53D6DBBF58318C8C, 0xEE135C318B0B4FBD, 0x61BE9479, +0xDCC602C47929F513, 0xCBB3BA8A118AB151, 0x3561D931143F076B, 0x7A5650B3B71E4440, +0x81852B1B6CB1C60A, 0x19A793E2D2032748, 0x209ED381A703C869, 0x90DB88EBE4C731E4, +0x7AA62EF4EC9D7127, 0x1615D6152, +0xB7306FE6C6C844AD, 0xCADFDF1D57932310, 0x4FB22989A00760AD, 0x4DE5D4CCE59DBC2F, +0x9AA0897142B34383, 0x7DD86FC4567E949D, 0x9260F5E77BF68C2B, 0x7A3E0578161B1F91, +0xDD7175E107F0E9DE, 0x2313D9822, 0xB209045D4051D0EC, 0x27A160D0E5FC64BF, +0xCD99808EB0E7CD46, 0xF89ECDA143F74D6C, 0x416622BF3824146F, 0xFA7FB456AE512FB6, +0xB0E4F93CC69D314B, 0x97729DC4A7F13D8B, 0x5C2D47D495FEB5EF, 0x1079A6B9A, +0x9AE4D9DD682A3F7C, 0x7DB6EBEA0F950DAA, 0x7E32B56F928BFBF2, 0x89BF1FE99DC0BDB5, +0x87612D25779867BB, 0xDAB5C143F03C478, 0xCADFA7901D346B96, 0x6A760FD92C65CE15, +0xACF2085B33A86416, 0x198758E70, +0xE3EB3AB8143F2340, 0xDAE56670F6991736, 0xA79D1B2DE9F5E2B4, 0x490044836A4C4FCD, +0xA6E9EEE8B7FF06AB, 0xA7D5C63BB0227849, 0x25D81CBF5F39EF75, 0x949DCC7DA7D8BE9A, +0x4A7DE4544BFED9CF, 0x179E0634D, 0x7503D6D3CFA98967, 0x7A3DBF374FD281B5, +0x8503065669A8E21C, 0x8550407D68B26BF2, 0xB177C65F71B8DB7A, 0x5A0D45B0B9A837CA, +0xDC8077F4A3FB45C4, 0x153F3C5CB9E7C411, 0x17D2017D1D0E9A84, 0x2E11E8F, +0xB706C3A63A31B996, 0xCED12C91DEFD3A2F, 0xD463340FCCF53A95, 0x551D854425B67A71, +0x28DE78F7E4FB7D17, 0x6E194BB2BB980245, 0xF5B88FB1AEE07F32, 0x85F35A860C5069CE, +0x5F90EA8F44B15C19, 0x1AB064103, +0x5F22068AE94C4166, 0xC7432715BDAC1304, 0xAB480DDE9A1BC065, 0xD162573FDEC6853B, +0x35DA082590792F4C, 0x2DEB1D9A1F6B404E, 0x604CE900AD128374, 0x8F33FA9A1D79371F, +0x3D7A20EDA39EBA74, 0x11D8D4C4F, 0x4495FF76C0BEE7A0, 0x3AD1B456FDD7F86B, +0x12AB903D9992AA49, 0x8E3BE3D4211FA9E7, 0x6A9534CE89C10EF4, 0xECBBA15E69F5C65A, +0xFDDCE4D0CE5CBCD8, 0x481729622964F7A8, 0x36377FB17C18D508, 0xFBE3B978, +0xA3C3156AD16D1967, 0xB588C8A52CE721EC, 0xF6E7479F9D828F3E, 0x40FF05D220618A1B, +0x74EDB36E785AA55B, 0x2BCF392004736123, 0x9E86DE8F1E9DCAB1, 0xCDBD9B5424A7145B, +0x592DC689502FED68, 0x11366FFE6, +0x13BBB9C1B414E1C, 0xD9AAE4D9D8B2AF0C, 0x6D732141024FD8B, 0x437658E4F1FC83E2, +0x6AF94F0A48D4088C, 0x3526A5FFED777880, 0xC0AEAF3F9C1BD66E, 0x5ADD0233869DAA1C, +0x660415191C524BA2, 0x1B1C818C, 0xA0B9F640337949B4, 0x743D4EDE527AD851, +0x2B0805A428E85026, 0x4B8021D7FCA4208B, 0xDC579898CFD992AA, 0x9DD7BD0AE4FB28A5, +0xA2CBE0BF4FE509DE, 0x34697254C6428572, 0x327B9DCFD35FBD38, 0xCC1395C9, +0xF1361CB3925213A1, 0xDC63BF3604B80029, 0x5E5D30D348944CB0, 0x8BACC140FBB0CA2A, +0x3B4B28636898829F, 0x67C2F0F0545F5FF6, 0x921EF314EB6E797C, 0x103F92B66822A959, +0x673BDF2F3FA93052, 0xF60342C0, +0x8F9948543B99ACA6, 0x36F97D42A2D36739, 0x7DBAB23D616B79C8, 0xAD727678D082265F, +0x9AA4ED08A53063F6, 0x62A93AADCA656130, 0xEE4EB68243F93FB1, 0x919EF72927726452, +0x43387AE2E23418A, 0x1A8D88C04, 0x114A5F37C004E7CB, 0xF214DAC001515C4F, +0x341693E0B4C0FDB3, 0x84D8576224802B1A, 0xE0ED480067011D08, 0x1A2BCC2E5532D8BC, +0xA040F74C0C3D2A48, 0x9C77DA5CBBFC1E72, 0x440E480406862351, 0x16FAEF420, +0x32FC47412AA23764, 0xAEB94B77E74747F6, 0x4A5DB04DCAC62563, 0xA966ABA8C195D200, +0x6D573C118E654059, 0x2FA9AB15674CC9CE, 0x161EDBB4AD079952, 0xCD9A458D8C76B2CC, +0x7F007FB0DC570B73, 0x263A27A36, +0x2BED0C1FE378F2A8, 0xDA2A696BC0B3494F, 0x50C4F1CF4E48D8AB, 0xDFCD6052BA3FAC7A, +0x8335F1E373F5AE6F, 0x85C65A19416959AB, 0xFCE4314639429572, 0xFF7FDF47AD3E1FAB, +0xFDB0F6514C9A30C2, 0x78783D53, 0x230D045A79B18DB2, 0x1E68580164026785, +0xD671CE8CAB69255D, 0x1134FD7E383D9F01, 0x29034B57E92E00D6, 0x781A01B4CB80F823, +0xD5B0BEE3168BF4E8, 0xC84C3CA6DAA23D1D, 0x278D4719D946E4B2, 0x1E90610D0, +0x7048353A8BDC45EE, 0xC5EA8E4DF6503627, 0x75D7FD7A14AC3D5E, 0xAF2A17C0FBABF167, +0xB2F06FDBE7168BA2, 0x61CECB7C4F8FA68C, 0x11A1A27F43B0705E, 0xFEAA2B8F812D86C7, +0xE469C3E3B3559E03, 0x18240EC9F, +0xA92675E44A8C4C37, 0x658E0A94E9D4D9A5, 0x6BC9B662F494C1B, 0xDAFE8559BA3E1DF8, +0xDE44293B06D5A0CA, 0x1A7F9CCBF38731D4, 0xFCCB6B8068CB4CCC, 0x59AECCD0BC88B911, +0x7EB6963EAC6DA86B, 0x187BA26B2, 0xBAB5987121504DDB, 0x366C3B3DF4114A58, +0x2EEC6F679CA0C63C, 0x6C070FA1C6EDEA55, 0xCD878F98CF05090E, 0x6F5A044649225DFC, +0x7081A7B7459EF13, 0x1F31F9530B2DB722, 0x412FABDF800B31EB, 0x148B46D40, +0x495AF93A016E5F58, 0x46F75E958C209690, 0xA400E4CCA631A6A8, 0xA82752772D4A4496, +0x89BCEFC688FA5429, 0xC5A5483286443D0F, 0xBFBEFC4D167ACCF3, 0xA45795FF298A98DC, +0x6CB2FAED780DF603, 0x5A4E860, +0x74F374F3AFDDD98B, 0x44C89434120D6D2E, 0xF401B2042193889A, 0xB93371C269702247, +0xD01997514733E4D3, 0x48580EB8358BCC72, 0xF040C70DDE52DAE2, 0xB89401A0BB11FA5D, +0x9CBED1BF6FBAEB3, 0x13CDF2630, 0xD66A304FD62CB10A, 0x5B5F6AC0883DC531, +0x41C3E11A22F343C3, 0x499823BA6C3922A6, 0xCC2F58B528A4EC64, 0xF91BCE15545EFA56, +0x9B00731D9A250208, 0x5142E922E648D89A, 0xC1B3F3739F808B89, 0x14D663531, +0x59AAED308D3B1704, 0x5CF6CDF81E0B0FDB, 0xCDFCC18AA85D884E, 0x83AAD261D1D6216C, +0xEF9D9332F29B9805, 0x3AF7649EE92D4F8E, 0x2BA88ED38A6C41A1, 0xCBA08376808CEAAF, +0x66E9914C13EB39B8, 0x1FCA1944, +0xD3D42403679AD82, 0x62DBC05C75294BCA, 0xE621CB241200ECB6, 0x6360EBAC16390DA6, +0x336FBC81DF7482B9, 0x3EEB6169B100559A, 0x784432B3F3631AF1, 0xEBE5214715ACA3F, +0x61F930A38AC1C914, 0x1C3F2DCB5, 0x4B7933C7EA55A06, 0x38807524175D9E98, +0xF6B8841D7F83A4A4, 0x69DE1EEEA7509380, 0xE98831716E539DB4, 0x920B78B60CD4E9E6, +0x669165E748E8CA78, 0x296083B2D2C98BE4, 0x55197B31435F32E1, 0x17436B5F7, +0x56B471BC3178BEDE, 0x5E024E620DFF6883, 0x8E9D78FB5ABA96D4, 0x7569549D47F84F24, +0x7D0A66C2029075A5, 0x16478E4B61EE69BB, 0xBD72EB2EB1A90D44, 0x80AC7479F21D9E24, +0x8B212D95644AD21F, 0x143A4984F, +0x28B5AF5D56CDBFFC, 0x528CB9D9B21CC751, 0x72D66CC56F07FA93, 0xC1210F83201EE242, +0x6916FF2CD2A8CD73, 0x186C8E31B277DE6A, 0x646D3D76ACBD4965, 0x43A2A3081CD0C090, +0x16059CDC55D8DDBF, 0xBA5900E, 0x192FC0A416495766, 0xD9AB13F2A667A98F, +0x891AB6E2EF60C157, 0xD218A531C411B34A, 0xD2E05758A116E190, 0x7A5163330070EA6C, +0x482EDB3DACF094BF, 0xAF9383D30193419A, 0x8B268C74BC4E749B, 0x8184D5F0, +0xA172DBFC9CADCE6B, 0x2754699F27C56FEE, 0xB8F2EE436D9DB687, 0x4B12A71BB0758D50, +0x156E8F7635D205AD, 0xA58EE00AC06C3BA6, 0x1DA197092F116EF0, 0x20F9A93530ACE49E, +0x9935E367B10DF943, 0x1A2165C35, +0xD60B3DE7D04B4D80, 0x8815DBC4E44E3949, 0xC120B9BC6535BE7A, 0x4334403ED19F8D29, +0xE3269DEFFE38083B, 0xB066EB77DA9B1CA5, 0x85D7EDB2C71559F3, 0xE69AEC407C4FD60D, +0x65751C3A74E029CB, 0x1330C7AAE, 0x2681CDE9AFB1EFD2, 0xE6B61A7C87E4849D, +0x55495CDE8A96479A, 0x229446DBB1932328, 0x70EDF88FA8EE5F0D, 0x4B2511B06B9DDD93, +0x703FFA7685AB4275, 0x3D1163B24F38E828, 0x3A1B34198EBFDFBA, 0x16C893BF8, +0x8A08D4ED3362009B, 0xCEEACB8BB44BE9DE, 0x8961D64EB8CA89A0, 0xF8381AAAFD9F5D11, +0x22C56EB5C7DA1592, 0x770A0671AF79C0D3, 0x86B99FD0A62CDFF2, 0xF2B41EC94289C975, +0xDF3CC4DD537DE087, 0x2201BCEF3, +0x2AA8CD224B2F7D6D, 0xA6734DABF1B6BFED, 0x8010A84842280324, 0x104C2556EAF398E5, +0xB188B68834B313CC, 0xA0EAFD30AFC12DE8, 0xCEF3BAC1BA435682, 0xDD7293935A5E5D37, +0x75A4C9ADB6BDBBAD, 0xCDDFC49F, 0x63EA2C96339E24B2, 0x4C3F97341C55C784, +0xA3974C7A01DC0F91, 0x72616595A7342D84, 0xB7958C056A4A1F02, 0xFFA025C32A63C8B, +0xA9FB257805E123DD, 0xAED191BDA4085C54, 0x12D2F4D76B5CE484, 0x1AFF682C1, +0x87C03132A936A5B3, 0xB553676B57FCBC5D, 0x39067649CAAF734A, 0x69F0C81D2BE357C9, +0x69B41B8C5756D129, 0x47F50EB03D7EF088, 0xFB2A61CF14F43BEB, 0xC65A6B0A530672E9, +0xBB159DC1AC175C6B, 0x210CCA106, +0x1640B0318C462826, 0x6AEC0D11CF5F1EA3, 0x9B3A4CA591917194, 0xCDAB2BE379984218, +0x2763FB622D58A965, 0x66E25E7CFB808E9C, 0x2DEB005666D03312, 0x59922AB6C7454D82, +0xE3A1BE83680C0D75, 0x20CA9844F, 0x8C6B9C391A4D94D8, 0x12F89D9CF053BF6D, +0xE9026ADE0C74B24, 0x4A06C288C4C46E42, 0x479B6699573D91D0, 0x14630ED1B17B6165, +0xE1036C2B198DEA43, 0x463D14DADFA2D7C1, 0x32BCB895A5597179, 0x12544B648, +0x63472E2CD585A951, 0xF610C3BA6E356666, 0x289AAD47B7E3C0EE, 0xA7E1D26EF70E4868, +0x312EB338F08A9961, 0x1253FC5BBA3515E8, 0x49F306062D992603, 0x6C083754F9F8B791, +0x53F299CB9249149A, 0x1F7AE9E8A, +0xFAFA7038F98ACA3, 0x3587A7ADDD62850F, 0xBFC0D0555338C346, 0x49F0225252A047F3, +0x83DCBD167BFA5429, 0x4175569B93323F5C, 0xCB61DF6362EF1491, 0x5205BE9E01A38294, +0xCF84BFF4EEDF165E, 0x23D3431E5, 0x9BF2CD69EF0EAA0A, 0xAB6336EC548E87AB, +0xDD8B11B294063FA3, 0xE01F6F890639B576, 0x7416F6C266ACC44C, 0x239BFF3120466A1E, +0x6CEDBCC733143B00, 0x8A36D478DCF9FEE8, 0x7224E36B685F2B57, 0x599F8DF4, +0x789C284669952B5, 0x1D8162DD3D730A08, 0xEB136E49C82EF7E5, 0x75224A5398187B85, +0x47DC4FECD3A32FB9, 0xC4FA0F31758940C5, 0x8303B8F766ED82BC, 0x3B9957A4F623A483, +0xDFCF87DCFE83BADB, 0x241E755CA, +0xC1EF4933FCEE677E, 0xAEF34A2D8CDA036D, 0x49D8A63D61663C0D, 0x43B856CC72ED457A, +0x897A9DD7571C3983, 0x95554C1070A3188C, 0xB10BC5D8F6A0D62F, 0xA6B9633BDCFDDA97, +0xB067E99984D1F23B, 0x12DA40E31, 0x6288F3663EF7B740, 0xC930178F7535C7A8, +0xB07C04D81B422E94, 0x60CD417134853362, 0x643A14DB580B196, 0x24CC07A55ACB952B, +0x16493E1849FB2B87, 0x2A252D48539D6975, 0x4A5237B3BC682CC9, 0x15028C557, +0x987A15C4130C74CA, 0x6C095214377DDD5E, 0xF316E6FD9F15953E, 0x820B30BEE5D2165, 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0xDD11E0D59ABFC30F, 0xCEB09AFBED0D4F41, +0x9C561B3A64BCA0B6, 0xE2B8A4F28FE9FA2C, 0xCD0E79D5C9BB6510, 0x45FB81F5C643F66A, +0xB84C52C98B281460, 0x45EEC506, +0x135265AB3, 0x0, 0x0, 0x0, 0x609A000000000000, 0x3754FA4ECEF9BE90, +0x83F68967E4DB82A9, 0xC5CCB347607C507B, 0xB8AAF689409E352C, 0x9DC814C3, +0x67205E1B881D075, 0x894BB12AFE2FBCAD, 0xE7C2B8FF7C89A4A4, 0x3CCB5C538771A30E, +0x472E884966422A98, 0xCE478A13952D16FE, 0x97E302EDADBD26DA, 0x514EEB8A7ED09CDB, +0xCE48CDA905F9FB56, 0xE0BFA119, 0xCBE3D6D2008C6231, 0xCA857181A6CAE47, +0xDE5F7ED987BA1F46, 0x2846BC6BBD212B7, 0x8A5E804280871124, 0x48D564480F8ADB7E, +0x2DE4D3C9FD8DFC83, 0xEBEC3D5643333E56, 0xDB539F526557088F, 0x23C5B48EA, +0xCE1991CC, 0x0, 0x0, 0x0, 0x3468000000000000, 0x9B33857A50E2F47F, +0x149430734647A838, 0xA56C442BA0D5A3C4, 0x26D204DD0C595E7B, 0x21129D2C8, 0x0, +0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x67205E1B881D075, +0x894BB12AFE2FBCAD, 0xE7C2B8FF7C89A4A4, 0x3CCB5C538771A30E, 0x472E884966422A98, +0xCE478A13952D16FE, 0x97E302EDADBD26DA, 0x514EEB8A7ED09CDB, 0xCE48CDA905F9FB56, +0xE0BFA119 +}; + diff --git a/src/P610/P610_internal.h b/src/P610/P610_internal.h index a73a34f..ecc4dba 100644 --- a/src/P610/P610_internal.h +++ b/src/P610/P610_internal.h @@ -55,6 +55,35 @@ #define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8) #define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8) +#ifdef COMPRESS + #define MASK2_BOB 0x07 + #define MASK3_BOB 0xFF + #define ORDER_A_ENCODED_BYTES SECRETKEY_A_BYTES + #define ORDER_B_ENCODED_BYTES (SECRETKEY_B_BYTES + 1) + #define COMPRESSED_CHUNK_CT (3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES + 2) + #define UNCOMPRESSEDPK_BYTES 480 + // Table sizes used by the Entangled basis generation + #define TABLE_R_LEN 17 + #define TABLE_V_LEN 34 + // Parameters for discrete log computations + // Binary Pohlig-Hellman reduced to smaller logs of order ell^W + #define W_2 5 + #define W_3 6 + // ell^w + #define ELL2_W (1 << W_2) + #define ELL3_W 729 + // ell^(e mod w) + #define ELL2_EMODW (1 << (OALICE_BITS % W_2)) + #define ELL3_EMODW 1 + // # of digits in the discrete log + #define DLEN_2 61 // Ceil(eA/W_2) + #define DLEN_3 32 // Ceil(eB/W_3) + // Length of the optimal strategy path for Pohlig-Hellman + #define PLEN_2 62 + #define PLEN_3 33 +#endif + + // SIDH's basic element definitions and point representations typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 610-bit field elements (640-bit max.) @@ -62,7 +91,17 @@ typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatyp typedef felm_t f2elm_t[2]; // Datatype for representing quadratic extension field elements GF(p610^2) typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates. -typedef point_proj point_proj_t[1]; +typedef point_proj point_proj_t[1]; + +#ifdef COMPRESS + typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates + typedef point_full_proj point_full_proj_t[1]; + + typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates. + typedef point_affine point_t[1]; + + typedef f2elm_t publickey_t[3]; +#endif @@ -81,7 +120,10 @@ void mp_add610_asm(const digit_t* a, const digit_t* b, digit_t* c); // Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit unsigned int mp_sub(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords); -digit_t mp_sub610x2_asm(const digit_t* a, const digit_t* b, digit_t* c); + +// 2x610-bit multiprecision subtraction followed by addition with p610*2^640, c = a-b+(p610*2^640) if a-b < 0, otherwise c=a-b +void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c); +void mp_subadd610x2_asm(const digit_t* a, const digit_t* b, digit_t* c); // Double 2x610-bit multiprecision subtraction, c = c-a-b, where c > a and c > b void mp_dblsub610x2_asm(const digit_t* a, const digit_t* b, digit_t* c); diff --git a/src/P751/AMD64/fp_x64_asm.S b/src/P751/AMD64/fp_x64_asm.S index 2e26d2d..5598df4 100644 --- a/src/P751/AMD64/fp_x64_asm.S +++ b/src/P751/AMD64/fp_x64_asm.S @@ -2770,11 +2770,16 @@ mp_add751_asm: //*********************************************************************** -// 2x751-bit multiprecision subtraction -// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2]. Returns borrow mask +// 2x751-bit multiprecision subtraction/addition +// Operation: c [x2] = a [x0] - b [x1]. If c < 0, add p751*2^768 //*********************************************************************** -.global mp_sub751x2_asm -mp_sub751x2_asm: +.global mp_subadd751x2_asm +mp_subadd751x2_asm: + push r12 + push r13 + push r14 + push r15 + push rbx xor rax, rax mov r8, [reg_p1] mov r9, [reg_p1+8] @@ -2849,10 +2854,61 @@ mp_sub751x2_asm: sbb r10, [reg_p2+176] sbb r11, [reg_p2+184] sbb rax, 0 + + // Add p751 anded with the mask in rax + mov r12, [rip+p751] + mov r13, [rip+p751+40] + mov r14, [rip+p751+48] + mov r15, [rip+p751+56] + mov rdi, [rip+p751+64] + mov rsi, [rip+p751+72] + mov rbx, [rip+p751+80] + mov rcx, [rip+p751+88] + and r12, rax + and r13, rax + and r14, rax + and r15, rax + and rdi, rax + and rsi, rax + and rbx, rax + and rcx, rax + mov rax, [reg_p3+96] + add rax, r12 + mov [reg_p3+96], rax + mov rax, [reg_p3+104] + adc rax, r12 + mov [reg_p3+104], rax + mov rax, [reg_p3+112] + adc rax, r12 + mov [reg_p3+112], rax + mov rax, [reg_p3+120] + adc rax, r12 + mov [reg_p3+120], rax + adc r12, [reg_p3+128] + adc r13, [reg_p3+136] + mov [reg_p3+128], r12 + mov [reg_p3+136], r13 + mov r12, [reg_p3+144] + mov r13, [reg_p3+152] + adc r12, r14 + adc r13, r15 + adc r8, rdi + adc r9, rsi + adc r10, rbx + adc r11, rcx + + mov [reg_p3+144], r12 + mov [reg_p3+152], r13 mov [reg_p3+160], r8 mov [reg_p3+168], r9 mov [reg_p3+176], r10 mov [reg_p3+184], r11 + pop rbx + pop r15 + pop r14 + pop r13 + pop r12 + ret ret diff --git a/src/P751/ARM64/fp_arm64_asm.S b/src/P751/ARM64/fp_arm64_asm.S index 4b22c40..50009ce 100644 --- a/src/P751/ARM64/fp_arm64_asm.S +++ b/src/P751/ARM64/fp_arm64_asm.S @@ -4,7 +4,18 @@ // Abstract: field arithmetic in 64-bit ARMv8 assembly for P751 on Linux //******************************************************************************************* -.data +.text + +// p751 +p751: +.quad 0xFFFFFFFFFFFFFFFF +.quad 0xEEAFFFFFFFFFFFFF +.quad 0xE3EC968549F878A8 +.quad 0xDA959B1A13F7CC76 +.quad 0x084E9867D6EBE876 +.quad 0x8562B5045CB25748 +.quad 0x0E12909F97BADC66 +.quad 0x00006FE5D541F71C // 2 * p751 p751x2: @@ -28,7 +39,6 @@ p751p1_nz_s32: .quad 0xDFCBAA83EE381C25 -.text //*********************************************************************** // Field addition // Operation: c [x2] = a [x0] + b [x1] @@ -1117,81 +1127,114 @@ mp_add751x2_asm: stp x9, x10, [x2,#144] stp x11, x12, [x2,#160] stp x13, x14, [x2,#176] - ret + ret //*********************************************************************** -// 2x751-bit multiprecision subtraction -// Operation: c [x2] = a [x0] - b [x1]. Returns borrow mask +// 2x751-bit multiprecision subtraction/addition +// Operation: c [x2] = a [x0] - b [x1]. If c < 0, add p751*2^768 //*********************************************************************** -.global mp_sub751x2_asm -mp_sub751x2_asm: - ldp x3, x4, [x0,#0] - ldp x5, x6, [x0,#16] - ldp x7, x8, [x0,#32] - ldp x9, x10, [x0,#48] - ldp x11, x12, [x0,#64] - ldp x13, x14, [x0,#80] - - ldp x15, x16, [x1,#0] - ldp x17, x18, [x1,#16] - subs x3, x3, x15 - sbcs x4, x4, x16 - sbcs x5, x5, x17 - sbcs x6, x6, x18 - ldp x15, x16, [x1,#32] - ldp x17, x18, [x1,#48] - sbcs x7, x7, x15 - sbcs x8, x8, x16 - sbcs x9, x9, x17 - sbcs x10, x10, x18 - ldp x15, x16, [x1,#64] - ldp x17, x18, [x1,#80] - sbcs x11, x11, x15 - sbcs x12, x12, x16 - sbcs x13, x13, x17 - sbcs x14, x14, x18 +.global mp_subadd751x2_asm +mp_subadd751x2_asm: + sub sp, sp, #16 + stp x19, x20, [sp] - stp x3, x4, [x2,#0] - stp x5, x6, [x2,#16] - stp x7, x8, [x2,#32] - stp x9, x10, [x2,#48] - stp x11, x12, [x2,#64] - stp x13, x14, [x2,#80] - - ldp x3, x4, [x0,#96] - ldp x5, x6, [x0,#112] - ldp x7, x8, [x0,#128] - ldp x9, x10, [x0,#144] - ldp x11, x12, [x0,#160] - ldp x13, x14, [x0,#176] + ldp x3, x4, [x0,#0] + ldp x5, x6, [x0,#16] + ldp x11, x12, [x1,#0] + ldp x13, x14, [x1,#16] + subs x3, x3, x11 + sbcs x4, x4, x12 + sbcs x5, x5, x13 + sbcs x6, x6, x14 + ldp x7, x8, [x0,#32] + ldp x9, x10, [x0,#48] + ldp x11, x12, [x1,#32] + ldp x13, x14, [x1,#48] + sbcs x7, x7, x11 + sbcs x8, x8, x12 + sbcs x9, x9, x13 + sbcs x10, x10, x14 + stp x3, x4, [x2,#0] + stp x5, x6, [x2,#16] + stp x7, x8, [x2,#32] + stp x9, x10, [x2,#48] - ldp x15, x16, [x1,#96] - ldp x17, x18, [x1,#112] - sbcs x3, x3, x15 - sbcs x4, x4, x16 - sbcs x5, x5, x17 - sbcs x6, x6, x18 - ldp x15, x16, [x1,#128] - ldp x17, x18, [x1,#144] - sbcs x7, x7, x15 - sbcs x8, x8, x16 - sbcs x9, x9, x17 - sbcs x10, x10, x18 - ldp x15, x16, [x1,#160] - ldp x17, x18, [x1,#176] - sbcs x11, x11, x15 - sbcs x12, x12, x16 - sbcs x13, x13, x17 - sbcs x14, x14, x18 - sbc x0, xzr, xzr + ldp x3, x4, [x0,#64] + ldp x5, x6, [x0,#80] + ldp x11, x12, [x1,#64] + ldp x13, x14, [x1,#80] + sbcs x3, x3, x11 + sbcs x4, x4, x12 + sbcs x5, x5, x13 + sbcs x6, x6, x14 + stp x3, x4, [x2,#64] + stp x5, x6, [x2,#80] + + ldp x3, x4, [x0,#96] + ldp x5, x6, [x0,#112] + ldp x15, x16, [x1,#96] + ldp x17, x19, [x1,#112] + sbcs x3, x3, x15 + sbcs x4, x4, x16 + sbcs x5, x5, x17 + sbcs x6, x6, x19 + ldp x7, x8, [x0,#128] + ldp x9, x10, [x0,#144] + ldp x15, x16, [x1,#128] + ldp x17, x19, [x1,#144] + sbcs x7, x7, x15 + sbcs x8, x8, x16 + sbcs x9, x9, x17 + sbcs x10, x10, x19 + ldp x11, x12, [x0,#160] + ldp x13, x14, [x0,#176] + ldp x15, x16, [x1,#160] + ldp x17, x19, [x1,#176] + sbcs x11, x11, x15 + sbcs x12, x12, x16 + sbcs x13, x13, x17 + sbcs x14, x14, x19 + sbc x0, xzr, xzr - stp x3, x4, [x2,#96] - stp x5, x6, [x2,#112] - stp x7, x8, [x2,#128] - stp x9, x10, [x2,#144] - stp x11, x12, [x2,#160] - stp x13, x14, [x2,#176] + // Add p751 anded with the mask in x0 + ldr x1, p751 + ldr x15, p751 + 8 + ldr x16, p751 + 16 + ldr x17, p751 + 24 + ldr x19, p751 + 32 + ldr x20, p751 + 40 + and x1, x1, x0 + and x15, x15, x0 + and x16, x16, x0 + and x17, x17, x0 + and x19, x19, x0 + and x20, x20, x0 + adds x3, x3, x1 + adcs x4, x4, x1 + adcs x5, x5, x1 + adcs x6, x6, x1 + adcs x7, x7, x1 + adcs x8, x8, x15 + adcs x9, x9, x16 + adcs x10, x10, x17 + adcs x11, x11, x19 + adcs x12, x12, x20 + stp x3, x4, [x2,#96] + stp x5, x6, [x2,#112] + stp x7, x8, [x2,#128] + stp x9, x10, [x2,#144] + stp x11, x12, [x2,#160] + ldr x1, p751 + 48 + ldr x3, p751 + 56 + and x1, x1, x0 + and x3, x3, x0 + adcs x13, x13, x1 + adc x14, x14, x3 + stp x13, x14, [x2,#176] + + ldp x19, x20, [sp] + add sp, sp, #16 ret diff --git a/src/P751/P751.c b/src/P751/P751.c index 63ca8b4..df8d30e 100644 --- a/src/P751/P751.c +++ b/src/P751/P751.c @@ -111,7 +111,7 @@ const unsigned int strat_Bob[MAX_Bob-1] = { #define fp2inv_mont_bingcd fp2inv751_mont_bingcd #define fpequal_non_constant_time fpequal751_non_constant_time #define mp_add_asm mp_add751_asm -#define mp_subx2_asm mp_sub751x2_asm +#define mp_subaddx2_asm mp_subadd751x2_asm #define mp_dblsubx2_asm mp_dblsub751x2_asm #define crypto_kem_keypair crypto_kem_keypair_SIKEp751 #define crypto_kem_enc crypto_kem_enc_SIKEp751 diff --git a/src/P751/P751_compressed.c b/src/P751/P751_compressed.c new file mode 100644 index 0000000..5286d04 --- /dev/null +++ b/src/P751/P751_compressed.c @@ -0,0 +1,389 @@ +/******************************************************************************************** +* Supersingular Isogeny Key Encapsulation Library +* +* Abstract: supersingular isogeny parameters and generation of functions for P751_compressed +*********************************************************************************************/ + +#include "P751_compressed_api.h" +#define COMPRESS +#include "P751_internal.h" + + +// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points: +// -------------------------------------------------------------------------------------------------- +// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format). +// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position. +// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position. +// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32. +// For example, a 751-bit field element is represented with Ceil(751 / 64) = 12 64-bit digits or Ceil(751 / 32) = 24 32-bit digits. + +// +// Curve isogeny system "SIDHp751". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p751^2), where A=6, B=1, C=1 and p751 = 2^372*3^239-1 +// + +const uint64_t p751[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xEEAFFFFFFFFFFFFF, + 0xE3EC968549F878A8, 0xDA959B1A13F7CC76, 0x084E9867D6EBE876, 0x8562B5045CB25748, 0x0E12909F97BADC66, 0x00006FE5D541F71C }; +const uint64_t p751p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xEEB0000000000000, + 0xE3EC968549F878A8, 0xDA959B1A13F7CC76, 0x084E9867D6EBE876, 0x8562B5045CB25748, 0x0E12909F97BADC66, 0x00006FE5D541F71C }; +const uint64_t p751x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF, + 0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED, 0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38 }; +// Order of Alice's subgroup +const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0010000000000000 }; +// Order of Bob's subgroup +const uint64_t Bob_order[NWORDS64_ORDER] = { 0xC968549F878A8EEB, 0x59B1A13F7CC76E3E, 0xE9867D6EBE876DA9, 0x2B5045CB25748084, 0x2909F97BADC66856, 0x06FE5D541F71C0E1 }; + +/* Basis for Alice on A = 6, expressed in Montgomery representation */ +const uint64_t A_gen[6*NWORDS64_FIELD] = { 0x2584350E0C33C304, 0x51E9C29E234DC61E, 0xC6E65A7BF90ACC05, 0xB1333E2E19B3A930, 0xA4F7CA2F7F66909F, 0xE01E9E6F6704BF9E, + 0xE2345D48C0219D6D, 0x70F37AD9933FC182, 0x7B9D4D5870CFACA3, 0x3B8DAF20190D460D, 0xB02D6FF9AAFA0C7, 0x15A435D19526, // XPA0 + 0xE85E3F2B4EDDAF22, 0x4824EDCA0A253CB2, 0x65C70852876C50A0, 0x917389F0D88B919, 0x93FBE011EFA068E5, 0x72703759A4651388, + 0xA266A6AEE1213EE0, 0xC496ABC50E388B6E, 0x564CB9FE0EBD72B5, 0x88B483157D3BADC8, 0x326D337A76B5317, 0x440F6F4F2D5A, // XPA1 + 0xCDD55D2646A1DE32, 0xAA056CDD8B80E53E, 0xAA87189B3A885C53, 0x9F6D9809057564A1, 0xC59794A13E1D38B8, 0x97F8ED39F3FA7DE5, + 0xFC0CAF68C8B95129, 0x393F28B240A42FFE, 0xCD99B2F9792DEF96, 0xF1036825CBF416B9, 0x877B835F0533F2AE, 0xCDFFE238E18, // XQA0 + 0xAC4EF1B17010B136, 0xEC411E1B5AD8A667, 0x7737372EDB66A1AF, 0x43593ECED672CF87, 0x1E418547C7B8A975, 0x8CC78DCB18BD469A, + 0x6C9FB93FD2EF8496, 0x8A4AC42666AB8545, 0x8A973B8387C15F1D, 0xC1657503D4BB4ADA, 0x22F49E4311D7BBF0, 0x1299B8FDA94C, // XQA1 + 0xC04B8957D3A4748F, 0xF3FB80F19063629F, 0x595434555D4EBE94, 0x8E1FEF11BFD1E0DA, 0xE31E3377248C0BB4, 0x9A05DEFF75EA51BA, + 0x398686FBB343398A, 0x20331307B470DA54, 0x964FA62AD10005C5, 0x9EA5CC4D64E5D9EE, 0xC84675CF9B96060F, 0x1DECCB78CFAC, // XRA0 + 0x6B20FF684759DDC2, 0xD50EB91730DEAFBF, 0xAA5CA048E2DAF488, 0xE29708E28654FC18, 0x542928AD1F445359, 0xA311B83D79E73FF6, + 0x850B7F5926826B22, 0x2D46731863BDB99D, 0x467A80CD8320B69D, 0xC046B12F05BFD513, 0x35D9B2FF794BDB40, 0x633276495B85 }; // XRA1 + +/* Basis for Bob on A = 6, expressed in Montgomery representation */ +const uint64_t B_gen[6*NWORDS64_FIELD] = { 0x110F4508C6634CCB, 0x31910BC05E296F4C, 0xED17AB0D6C029EA6, 0x9C863AB6172B9974, 0x5C15236CDB216F99, 0xDC025064818EC7D7, + 0xC2180F387487EBF0, 0x946B1D0F025CBC3B, 0x5AE34395A520CB46, 0xB52034F98A879F2C, 0x3D2FAE10A22AB7C7, 0x174CD090DA3D, // XPB0 + 0xC3C6A839776171F2, 0x5883AFB529C8E50A, 0xDE1622BBD192925, 0x64CCE86B1826A21, 0x441AF1ABE9F6568E, 0x3F29EEC0BC6F962D, + 0xA7845A0127159975, 0x109DCD6D92B0C3F2, 0x462438CD0100EE2E, 0xFB7869F2B1DF80EB, 0x563B0C55F0EEDC53, 0x1958C37D4721, // XPB1 + 0x110F4508C6634CCB, 0x31910BC05E296F4C, 0xED17AB0D6C029EA6, 0x9C863AB6172B9974, 0x5C15236CDB216F99, 0xDC025064818EC7D7, + 0xC2180F387487EBF0, 0x946B1D0F025CBC3B, 0x5AE34395A520CB46, 0xB52034F98A879F2C, 0x3D2FAE10A22AB7C7, 0x174CD090DA3D, // XQB0 + 0x3C3957C6889E8E0D, 0xA77C504AD6371AF5, 0xF21E9DD442E6D6DA, 0xF9B331794E7D95DE, 0xBBE50E541609A971, 0xAF86113F439069D2, + 0x3C683C8422E2DF33, 0xC9F7CDAC81470884, 0xC22A5F9AD5EAFA48, 0x89EA4B11AAD2D65C, 0xB7D78449A6CC0012, 0x568D11C4AFFA, // XQB1 + 0x31BB0964DFBDC34F, 0xFDC65CF4959AB106, 0xA3071E4B8B04D8FF, 0x9B68CFCE270DE486, 0x2339E590896E0095, 0xFC753508AD83E33E, + 0x73A274E4A6908387, 0x88D1B207BBE8E2DC, 0xA6D0583233DC71F, 0xCF7F2ECC609DE5BE, 0xB8AF0669FBD1CF01, 0x1F3EF25DD512, // XRB0 + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0 }; // XRB1 + +/* The x-coordinate of lB^(eB-1)*QB, expressed in Montgomery representation */ +const uint64_t XQB3[2*NWORDS64_FIELD] = { 0x96DCB5BD39AA8288, 0x81E7BA9AA19C1C53, 0x7021384077E4FEB6, 0xA1490C7A753E8E74, 0xA31871E13D80831C, 0x7E653AD5931BC82E, + 0x8A0C230821766ECA, 0x1CE14E07EB29B669, 0xF985F42F404E45EF, 0x44AF699D9546F9B, 0x8A8C976EE869BE6B, 0xEC5AA84C390, + 0xF16AEFC3FA025CCB, 0x205E4E1559261A6E, 0xFA6EEE97610CA4AA, 0x4B29DB4DF10E7D9, 0x83BC8A148E0FBB2, 0x1065373142BD8B81, + 0xD7C4A7221ED3E403, 0x1071E13BCEB89A2A, 0x54A18AEA86CD9D51, 0x39BF04224B598D62, 0xD4B89FF2AA465908, 0x5A0F792EB1A3 }; + +const uint64_t A_basis_zero[8 * NWORDS64_FIELD] = { 0x2584350E0C38565F, 0x51E9C29E234DC61E, 0xC6E65A7BF90ACC05, 0xB1333E2E19B3A930, 0xA4F7CA2F7F66909F, 0xF78E9E6F6704BF9E, + 0xA8972A8BE4E1FD91, 0x694D0F3DFDE63EAC, 0x48A2455F29C6089, 0x4F74628F6069C173, 0x1EDF6B38ED1A5433, 0x74AA0969CE, + 0xE85E3F2B4EDDAF22, 0x4824EDCA0A253CB2, 0x65C70852876C50A0, 0x917389F0D88B919, 0x93FBE011EFA068E5, 0x72703759A4651388, + 0xA266A6AEE1213EE0, 0xC496ABC50E388B6E, 0x564CB9FE0EBD72B5, 0x88B483157D3BADC8, 0x326D337A76B5317, 0x440F6F4F2D5A, + 0xCF298A24AB4EECC8, 0x426BE362D17B58E1, 0xDEC9E4AB0C0813E4, 0xBB213D92B1A23DEC, 0x73F9337EBF1AFB1E, 0x22A428421E3F369D, + 0x4C504FBA8D4C1F41, 0x97C03C026B64E556, 0x94524150E5242247, 0x8F397D005B7D0F3, 0x2EEEFB40C2D1D40F, 0x49FFA7880CC0, + 0xC735AE6A6D9AB879, 0x4431FCF02097BF97, 0xCD6C8982E0B17062, 0xD38791B330DBF671, 0xBBE57BF59A8D9150, 0x58F968F33F45A7D8, + 0x903068B77EC83B26, 0x7DADADD772211F21, 0x2A8DEA498D8A12BB, 0xAE73B6AE3E7657F, 0x11695A4A18565FCD, 0x303FE0D52CDB, + 0xCDD55D2646A6718C, 0xAA056CDD8B80E53E, 0xAA87189B3A885C53, 0x9F6D9809057564A1, 0xC59794A13E1D38B8, 0x9E18ED39F3FA7DE5, + 0xA65C1331377229F6, 0xC2E5830BF42799F, 0x5ED5225ED1E68BF3, 0x8A4CD0997002E967, 0xA96AA837EF598281, 0x6796479D59DC, + 0xAC4EF1B17010B136, 0xEC411E1B5AD8A667, 0x7737372EDB66A1AF, 0x43593ECED672CF87, 0x1E418547C7B8A975, 0x8CC78DCB18BD469A, + 0x6C9FB93FD2EF8496, 0x8A4AC42666AB8545, 0x8A973B8387C15F1D, 0xC1657503D4BB4ADA, 0x22F49E4311D7BBF0, 0x1299B8FDA94C, + 0xD976D6B7056D9BE, 0x269169101B22C490, 0x485B7EFC9E5BBC09, 0xD0B55BEABD8EF10, 0x985F36CD657501DD, 0x19FD14B27B195F17, + 0xF0F7E577A00E0E42, 0x1A179D4A080F58D2, 0x97603A54D8CFB3E5, 0x96E69A6743A68CE1, 0xF04C8D027EB4B382, 0xA8E741B2F5C, + 0xBBF34629BA51923B, 0x94250E3ECE841C7C, 0x56CD785FA63E19F9, 0x126F4144FC6B39F4, 0x4BB54DEE559E01E3, 0x3195B2E094E0D92, + 0x1F40204597E534A, 0x7F9B8D473586B966, 0x38281C1E6F54E744, 0x215C5889B91D5D63, 0x9CEA26343AD2B060, 0x22374E0C0255 }; + +/* Basis for Bob on A = 0, expressed in Montgomery representation */ +const uint64_t B_basis_zero[8*NWORDS64_FIELD] = { 0xF1A8C9ED7B96C4AB, 0x299429DA5178486E, 0xEF4926F20CD5C2F4, 0x683B2E2858B4716A, 0xDDA2FBCC3CAC3EEB, 0xEC055F9F3A600460, + 0xD5A5A17A58C3848B, 0x4652D836F42EAED5, 0x2F2E71ED78B3A3B3, 0xA771C057180ADD1D, 0xC780A5D2D835F512, 0x114EA3B55AC1, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x2E1EB8ED8C1C8C94, 0x6CFE456B25DBE01, 0x1EB54C3E8010F57A, 0x4B222D95FC81619D, 0xF99EBD204D501496, 0xC18348F9B629361, + 0xC29E9A16BEDE6F96, 0x3B39F30163DAD41D, 0x807D3D1ECF2AC04E, 0xE088443F222A4988, 0x61B49A7524F1EA12, 0x41BF31133104, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xE57361284693B54, 0xD66BD625AE87B791, 0x10B6D90DF32A3D0B, 0x97C4D1D7A74B8E95, 0x225D0433C353C114, 0x2AAA060C59FFB9F, + 0xE46F50AF134F41D, 0x9442C2E31FC91DA1, 0xD920267A5E3844C3, 0xDDF0F4AD44A77A2A, 0x4691EACCBF84E753, 0x5E97318C9C5A, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x2E1EB8ED8C1C8C94, 0x6CFE456B25DBE01, 0x1EB54C3E8010F57A, 0x4B222D95FC81619D, 0xF99EBD204D501496, 0xC18348F9B629361, + 0xC29E9A16BEDE6F96, 0x3B39F30163DAD41D, 0x807D3D1ECF2AC04E, 0xE088443F222A4988, 0x61B49A7524F1EA12, 0x41BF31133104 }; + +/* Full 3-torsion for Bob on A = 0, expressed in Montgomery representation */ +const uint64_t B_gen_3_tors[16 * NWORDS64_FIELD] = { 0x7BB7A4A07B0788DC, 0xDC36A3F6607B21B0, 0x4750E18EE74CF2F0, 0x464E319D0B7AB806, 0xC25AA44C04F758FF, 0x392E8521A46E0A68, + 0xFC4E76B63EFF37DF, 0x1F3566D892E67DD8, 0xF8D2EB0F73295E65, 0x457B13EBC470BCCB, 0xFDA1CC9EFEF5BE33, 0x5DBF3D92CC02, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xE7E952E9A260914, 0x92C98EDCD6E01424, 0x8F2B207221D33C50, 0xAEF2728CA22F318E, 0x5FD0E29877DC3D43, 0x1BDC7B7367E4E124, + 0xFF5BC4186BDDCAE7, 0xD20A34710EE8B44B, 0x2E0866A5B9467EBD, 0x876EFC05B732A6AD, 0x9D39159E24822ABB, 0x658F31DC0D6E, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x84485B5F84F87723, 0x23C95C099F84DE4F, 0xB8AF1E7118B30D0F, 0xB9B1CE62F48547F9, 0x3DA55BB3FB08A700, 0xB5817ADE5B91F597, + 0xE79E1FCF0AF940C9, 0xBB60344181114E9D, 0xF7BAD5863C28A11, 0x3FE7A11898419A7C, 0x1070C40098C51E33, 0x122697AF2B19, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0xE7E952E9A260914, 0x92C98EDCD6E01424, 0x8F2B207221D33C50, 0xAEF2728CA22F318E, 0x5FD0E29877DC3D43, 0x1BDC7B7367E4E124, + 0xFF5BC4186BDDCAE7, 0xD20A34710EE8B44B, 0x2E0866A5B9467EBD, 0x876EFC05B732A6AD, 0x9D39159E24822ABB, 0x658F31DC0D6E, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x6491DDA56B18F762, 0xB50239F87A977F80, 0xD061934416F37D7C, 0xD79D328C01810FEC, 0x4F4BB58557C706AF, 0xEFE0C6963007AABB, + 0x20EA47B4FDE821A5, 0xDE5144774B84AE51, 0x262E82E15B85FF1B, 0x7A0820D88294BDEE, 0xA36653F0DFF6FE6E, 0x239BB2213058, + 0xA8C40A6A4ACECF3A, 0xE988877E7DF4D938, 0xC2353D8E5C2F0BAB, 0xC4758A5B1437A358, 0xC5CEE9FD3A3B088D, 0x86B2876D6520F51, + 0xD31476314E3DAD08, 0x517E8096137AFBC9, 0xE52ADD7D2B85BB6C, 0x43A92AC98B1E5F2B, 0x4F32E4103B80C703, 0x68BCEB2391D2, + 0x573BF595B53130C5, 0x16777881820B26C7, 0x3DCAC271A3D0F454, 0x3B8A75A4EBC85CA7, 0x3A311602C5C4F772, 0xE644D78929ADF0AE, + 0x10D82053FBBACBA0, 0x89171A84007CD0AD, 0x2323BAEAAB662D0A, 0x41B98A3AD193F81C, 0xBEDFAC8F5C3A1563, 0x728EA1E6549, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x9B6E225A94E7089D, 0x4AFDC6078568807F, 0x2F9E6CBBE90C8283, 0x2862CD73FE7EF013, 0xB0B44A7AA838F950, 0xFECF3969CFF85544, + 0xC3024ED04C105702, 0xFC4456A2C8731E25, 0xE22015867B65E95A, 0xB5A942BDA1D9959, 0x6AAC3CAEB7C3DDF8, 0x4C4A2320C6C3, + 0xA8C40A6A4ACECF3A, 0xE988877E7DF4D938, 0xC2353D8E5C2F0BAB, 0xC4758A5B1437A358, 0xC5CEE9FD3A3B088D, 0x86B2876D6520F51, + 0xD31476314E3DAD08, 0x517E8096137AFBC9, 0xE52ADD7D2B85BB6C, 0x43A92AC98B1E5F2B, 0x4F32E4103B80C703, 0x68BCEB2391D2, + 0xA8C40A6A4ACECF3A, 0xE988877E7DF4D938, 0xC2353D8E5C2F0BAB, 0xC4758A5B1437A358, 0xC5CEE9FD3A3B088D, 0x86B2876D6520F51, + 0xD31476314E3DAD08, 0x517E8096137AFBC9, 0xE52ADD7D2B85BB6C, 0x43A92AC98B1E5F2B, 0x4F32E4103B80C703, 0x68BCEB2391D2 }; + +/* Pre-computed pairing ReducedTatePairing(R0,S3,lB^eB) on A = 0 */ +const uint64_t g_R_S_im[NWORDS64_FIELD] = { 0xCB6E5ADE9CD78AF1, 0x40F3DD4D50CE0E29, 0x38109C203BF27F5B, 0x50A4863D3A9F473A, 0x518C38F09EC0418E, 0xC2429D6AC98DE417, + 0x1A2DC3684817A3CB, 0xF7E83EC334E40005, 0xC560B1CA4C837125, 0xCECA2F86BEB1A124, 0x563DDE23E947A71E, 0x34BDF9FF47AA }; + +// Montgomery constant Montgomery_R2 = (2^768)^2 mod p751 +const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x233046449DAD4058, 0xDB010161A696452A, 0x5E36941472E3FD8E, 0xF40BFE2082A2E706, 0x4932CCA8904F8751 ,0x1F735F1F1EE7FC81, + 0xA24F4D80C1048E18, 0xB56C383CCDB607C5, 0x441DD47B735F9C90, 0x5673ED2C6A6AC82A, 0x06C905261132294B, 0x000041AD830F1F35 }; +// Value one in Montgomery representation +const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x00000000000249ad, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8310000000000000, + 0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2 }; + +// constant Montgomery_RB1 = (2^NBITS_ORDER)^2 mod Bob_order +const uint64_t Montgomery_RB1[NWORDS64_FIELD] = { 0x1A55482318541298,0x70A6370DFA12A03,0xCB1658E0E3823A40,0xB3B7384EB5DEF3F9,0xCBCA952F7006EA33,0x569EF8EC94864C}; + +// constant Montgomery_RB2 = (-Bob_order)^-1 mod 2^NBITS_ORDER +const uint64_t Montgomery_RB2[NWORDS64_FIELD] = { 0x48062A91D3AB563D, 0x6CE572751303C2F5, 0x5D1319F3F160EC9D, 0xE35554E8C2D5623A, 0xCA29300232BC79A5, 0x8AAD843D646D78C5}; + +// 1/3 mod p +const uint64_t threeinv[NWORDS64_FIELD] = {0x555555555556188F, 0x5555555555555555, 0x5555555555555555, 0x5555555555555555, + 0x5555555555555555, 0x8105555555555555, 0x1C6290A167C97977, 0xCDD287EA6A6FB6F0, + 0x42DF3D3B8EC96F64, 0x198C3C1346027872, 0xB0528624270642A3, 0xF1E61944CA0}; + +// Fixed parameters for isogeny tree computation +const unsigned int strat_Alice[MAX_Alice-1] = { +80, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, +1, 3, 2, 1, 1, 1, 1, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, +1, 1, 2, 1, 1, 1, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, +1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, +33, 20, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, +1, 1, 8, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, +1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 }; + +const unsigned int strat_Bob[MAX_Bob-1] = { +112, 63, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, +1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, +1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 31, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, +1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, +2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 49, 31, 16, 8, 4, 2, +1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, +15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, +1, 1, 1, 21, 12, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 3, 2, 1, 1, 1, 1, +2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1 }; + +// Fixed traversal strategies for Pohlig-Hellman discrete logs + +const unsigned int ph2_path[PLEN_2] = { // w_2 = 4 + 0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 13, 13, 13, 14, + 14, 15, 16, 17, 18, 19, 19, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, + 28, 28, 28, 28, 28, 29, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 39, 40, 40, + 40, 40, 41, 42, 42, 42, 42, 42, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, + 52, 53, 54, 55, 56, 57, 58, 59, 59, 59, 59, 59, 59, 59 +}; + +const unsigned int ph3_path[PLEN_3] = { // w_3 = 5 + 0, 0, 1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, + 17, 18, 19, 20, 20, 20, 21, 22, 23, 24, 25, 26, 26, 26, 26, 27, 28, 29, 30, + 31, 32, 33, 34, 34, 34, 34 +}; + +// Entangled bases related static tables and parameters + +// Constants u and u0 where u = u0^2 in F_{p^2} \ F_p used in entagled basis generation +// For the 2^eA-torsion basis generation: +// Two tables of 17 elements each for the values r in F_p such that v = 1/(1+ur^2) where r is already converted to Montgomery representation +// Also, 2 tables for the quadratic residues (qr) and quadratric non residues (qnr) v in F_{p^2} with 17 GF(p^2) elements each. +// For the 3^eB-torsion basis generation: +// A table of size 20 for values v = 1/(1+U*r^2) where U = 4+i + +const uint64_t u_entang[2*NWORDS64_FIELD] = { +0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, +0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, +0x000000000004935a, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0620000000000000, +0xaa4f63c86eb8d8cd, 0xd2ef2f7e7e9e49a0, 0x913b6f6558b89c5c, 0x99496873a40ed2ad, 0x21ef24d8ea258fd2, 0x00005ab64979cbc4}; + +const uint64_t u0_entang[2*NWORDS64_FIELD] = { +0x00000000000249ad, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8310000000000000, +0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2, +0x00000000000249ad, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8310000000000000, +0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2}; + +// Tables for quadratic residues and quadratic non residues v with 17 elements each. + +const uint64_t table_r_qr[][NWORDS64_FIELD] = +{{0x249AD,0x0,0x0,0x0,0x0,0x8310000000000000,0x5527B1E4375C6C66,0x697797BF3F4F24D0,0xC89DB7B2AC5C4E2E,0x4CA4B439D2076956,0x10F7926C7512C7E9,0x2D5B24BCE5E2}, +{0x926B5,0x0,0x0,0x0,0x0,0x1D90000000000000,0x70B2310B937938F1,0xCB48C3E2E944C6CA,0x1A284662DA855042,0xAD301BE2EB6B4E13,0x35CBB9123C90433E,0x4586BDB1A06C}, +{0xDBA10,0x0,0x0,0x0,0x0,0x3500000000000000,0x3714FE4EB8399915,0xC3A2584753EB43F4,0xA3151D605C520428,0xC116CF5232C7C978,0x49A84D4B8EFAF6AA,0x305731E97514}, +{0x1003BD,0x0,0x0,0x0,0x0,0xB810000000000000,0x8C3CB032EF96057B,0x2D19F006933A68C4,0x6BB2D51308AE5257,0xDBB838C04CF32CF,0x5A9FDFB8040DBE94,0x5DB256A65AF6}, +{0x124D6B,0x0,0x0,0x0,0x0,0x4C70000000000000,0xFD77CB91DCF9F939,0xBBFBECABBE91C11D,0x2C01F45DDE1EB80E,0xD4FD82C17A2444DE,0x5D84E184E165AA16,0x1B27A62149BC}, +{0x149718,0x0,0x0,0x0,0x0,0xCF80000000000000,0x529F7D761456659F,0x2573846AFDE0E5EE,0xF49FAC108A7B063D,0x21A236FB4C2BAE34,0x6E7C73F156787200,0x4882CADE2F9E}, +{0x192A73,0x0,0x0,0x0,0x0,0xE6F0000000000000,0x19024AB93916C5C3,0x1DCD18CF68876318,0x7D8C830E0C47BA23,0x3588EA6A9388299A,0x8259082AA8E3256C,0x33533F160446}, +{0x1DBDCE,0x0,0x0,0x0,0x0,0xFE60000000000000,0xDF6517FC5DD725E7,0x1626AD33D32DE041,0x6795A0B8E146E09,0x496F9DD9DAE4A500,0x96359C63FB4DD8D8,0x1E23B34DD8EE}, +{0x249AD6,0x0,0x0,0x0,0x0,0x98E0000000000000,0xFAEF9723B9F3F272,0x77F7D9577D23823B,0x5803E8BBBC3D701D,0xA9FB0582F44889BC,0xBB09C309C2CB542D,0x364F4C429378}, +{0x292E31,0x0,0x0,0x0,0x0,0xB050000000000000,0xC1526466DEB45296,0x70516DBBE7C9FF65,0xE0F0BFB93E0A2403,0xBDE1B8F23BA50521,0xCEE6574315360799,0x211FC07A6820}, +{0x2B77DE,0x0,0x0,0x0,0x0,0x3360000000000000,0x167A164B1610BEFD,0xD9C9057B27192436,0xA98E776BEA667231,0xA866D2C0DAC6E78,0xDFDDE9AF8A48CF83,0x4E7AE5374E02}, +{0x2DC18C,0x0,0x0,0x0,0x0,0xC7C0000000000000,0x87B531AA0374B2BA,0x68AB022052707C8F,0x69DD96B6BFD6D7E9,0xD1C86C6183018087,0xE2C2EB7C67A0BB05,0xBF034B23CC8}, +{0x300B39,0x0,0x0,0x0,0x0,0x4AD0000000000000,0xDCDCE38E3AD11F21,0xD22299DF91BFA15F,0x327B4E696C332617,0x1E6D209B5508E9DE,0xF3BA7DE8DCB382EF,0x394B596F22AA}, +{0x3254E6,0x0,0x0,0x0,0x0,0xCDE0000000000000,0x32049572722D8B87,0x3B9A319ED10EC630,0xFB19061C188F7446,0x6B11D4D527105334,0x4B2105551C64AD8,0x66A67E2C088D}, +{0x349E94,0x0,0x0,0x0,0x0,0x6240000000000000,0xA33FB0D15F917F45,0xCA7C2E43FC661E89,0xBB682566EDFFD9FD,0x3253D40A9C656543,0x79712222F1E365B,0x241BCDA6F753}, +{0x3B7B9C,0x0,0x0,0x0,0x0,0xFCC0000000000000,0xBECA2FF8BBAE4BCF,0x2C4D5A67A65BC083,0xCF2B4171C28DC12,0x92DF3BB3B5C94A00,0x2C6B38C7F69BB1B0,0x3C47669BB1DD}, +{0x3DC549,0x0,0x0,0x0,0x0,0x7FD0000000000000,0x13F1E1DCF30AB836,0x95C4F226E5AAE554,0xD5906BC9C8852A40,0xDF83EFED87D0B356,0x3D62CB346BAE7999,0x69A28B5897BF}}; + +const uint64_t table_r_qnr[17][NWORDS64_FIELD] = +{{0x4935A,0x0,0x0,0x0,0x0,0x620000000000000,0xAA4F63C86EB8D8CD,0xD2EF2F7E7E9E49A0,0x913B6F6558B89C5C,0x99496873A40ED2AD,0x21EF24D8EA258FD2,0x5AB64979CBC4}, +{0x6DD08,0x0,0x0,0x0,0x0,0x9A80000000000000,0x1B8A7F275C1CCC8A,0x61D12C23A9F5A1FA,0x518A8EB02E290214,0x608B67A91963E4BC,0x24D426A5C77D7B55,0x182B98F4BA8A}, +{0xB7063,0x0,0x0,0x0,0x0,0xB1F0000000000000,0xE1ED4C6A80DD2CAE,0x5A2AC088149C1F23,0xDA7765ADAFF5B5FA,0x74721B1860C06021,0x38B0BADF19E82EC1,0x2FC0D2C8F32}, +{0x16E0C6,0x0,0x0,0x0,0x0,0x63E0000000000000,0xC3DA98D501BA595D,0xB455811029383E47,0xB4EECB5B5FEB6BF4,0xE8E43630C180C043,0x716175BE33D05D82,0x5F81A591E64}, +{0x1B7420,0x0,0x0,0x0,0x0,0x6A00000000000000,0x6E29FC9D7073322A,0x8744B08EA7D687E8,0x462A3AC0B8A40851,0x822D9EA4658F92F1,0x93509A971DF5ED55,0x60AE63D2EA28}, +{0x20077B,0x0,0x0,0x0,0x0,0x8170000000000000,0x348CC9E09533924E,0x7F9E44F3127D0512,0xCF1711BE3A70BC37,0x96145213ACEC0E56,0xA72D2ED07060A0C1,0x4B7ED80ABED0}, +{0x225129,0x0,0x0,0x0,0x0,0x15D0000000000000,0xA5C7E53F8297860C,0xE8041983DD45D6B,0x8F6631090FE121EF,0x5D56514922412065,0xAA12309D4DB88C44,0x8F42785AD96}, +{0x26E483,0x0,0x0,0x0,0x0,0x1BF0000000000000,0x50174907F1505ED9,0xE16F7116BC72A70C,0x20A1A06E6899BE4B,0xF69FB9BCC64FF313,0xCC01557637DE1C16,0x63AA70FF795A}, +{0x36E841,0x0,0x0,0x0,0x0,0xE550000000000000,0xF86762B596EDEBAB,0x33F3C6033BB54359,0x8405DD199A5C282C,0x7EF888446E6CCE9A,0x188EA48EA430FE44,0x5176F263DD35}, +{0x3931EF,0x0,0x0,0x0,0x0,0x79B0000000000000,0x69A27E148451DF69,0xC2D5C2A8670C9BB3,0x4454FC646FCC8DE3,0x463A8779E3C1E0A9,0x1B73A65B8188E9C7,0xEEC41DECBFB}, +{0x400EF7,0x0,0x0,0x0,0x0,0x1430000000000000,0x852CFD3BE06EABF4,0x24A6EECC11023DAD,0x95DF8B149DF58FF8,0xA6C5EF22FD25C565,0x4047CD014906651C,0x2717DAD38685}, +{0x4258A4,0x0,0x0,0x0,0x0,0x9740000000000000,0xDA54AF2017CB185A,0x8E1E868B5051627D,0x5E7D42C74A51DE26,0xF36AA35CCF2D2EBC,0x513F5F6DBE192D05,0x5472FF906C67}, +{0x44A252,0x0,0x0,0x0,0x0,0x2BA0000000000000,0x4B8FCA7F052F0C18,0x1D0083307BA8BAD7,0x1ECC62121FC243DE,0xBAACA292448240CB,0x5424613A9B711888,0x11E84F0B5B2D}, +{0x46EBFF,0x0,0x0,0x0,0x0,0xAEB0000000000000,0xA0B77C633C8B787E,0x86781AEFBAF7DFA7,0xE76A19C4CC1E920C,0x75156CC1689AA21,0x651BF3A71083E072,0x3F4373C8410F}, +{0x4935AC,0x0,0x0,0x0,0x0,0x31C0000000000000,0xF5DF2E4773E7E4E5,0xEFEFB2AEFA470477,0xB007D177787AE03A,0x53F60B05E8911378,0x761386138596A85B,0x6C9E988526F1}, +{0x4DC907,0x0,0x0,0x0,0x0,0x4930000000000000,0xBC41FB8A98A84509,0xE849471364ED81A1,0x38F4A874FA479420,0x67DCBE752FED8EDE,0x89F01A4CD8015BC7,0x576F0CBCFB99}, +{0x525C62,0x0,0x0,0x0,0x0,0x60A0000000000000,0x82A4C8CDBD68A52D,0xE0A2DB77CF93FECB,0xC1E17F727C144806,0x7BC371E4774A0A43,0x9DCCAE862A6C0F33,0x423F80F4D041}}; + +const uint64_t table_v_qr[TABLE_V_LEN][NWORDS64_FIELD] = +{{0xCCCCCCCCCCCD41EF,0xCCCCCCCCCCCCCCCC,0xCCCCCCCCCCCCCCCC,0xCCCCCCCCCCCCCCCC,0xCCCCCCCCCCCCCCCC,0x467CCCCCCCCCCCCC,0x5CCF962F575DF8B,0x3953C2CA47D95926,0xC50BC81A120A6C9F,0xDE486C73B57C04C7,0x3C38F0BBEDB4E68A,0x35D48FD9C405}, +{0x6666666666657C21,0x6666666666666666,0x6666666666666666,0x6666666666666666,0x6666666666666666,0x61B6666666666666,0xD852A3BF5F0CB992,0x67EE158584451A2A,0x7E370833B2D70F38,0xC8D1DC1CF1BA4DB8,0x95A0AF27BC510F50,0x43CB58E6F11}, +{0xB891DB891DB8926D,0xDB891DB891DB891D,0x1DB891DB891DB891,0x91DB891DB891DB89,0x891DB891DB891DB8,0xB7A1DB891DB891DB,0x7667EA3E359A528F,0x920F68111BC2395B,0x73153DF2CE971E2C,0x16EDA0D863AC7DA5,0xBF837289A3FC18BF,0x5ADF5C37BA11}, +{0xEDC48EDC48EDB246,0x8EDC48EDC48EDC48,0x48EDC48EDC48EDC4,0xC48EDC48EDC48EDC,0xDC48EDC48EDC48ED,0x49A48EDC48EDC48E,0x590A01C2CFF1EF31,0xF144BE828EE398A4,0x7553BC320111D67F,0xAE524764F48D28A2,0x7D745F00E9774A86,0x16C21BBD6A1}, +{0x5E40E05A0E84063C,0x1F4D776F0A51A9CB,0xCB5E40E05A0E8406,0x61F4D776F0A51A9,0xA9CB5E40E05A0E84,0x72C61F4D776F0A51,0x618B216FB9C76A1E,0xE22409F266B16463,0x894A7D245553FD6B,0x4E89F364CCE00FA7,0x77A8C743F3083EC9,0x188BE18D4AC5}, +{0x7DC0E6ABEADE3F10,0x323668C519083ECD,0xCD7DC0E6ABEADE47,0x47323668C519083E,0x3ECD7DC0E6ABEADE,0xA347323668C51908,0xCFA800E85F71B1FE,0xF36E5745D988B7A,0xE7F654456F1F4116,0x3F5EDBEC2C210D61,0x39B0FEDD215C1DCA,0x1705E4626A37}, +{0x791C39AD37694088,0x40791C39AD376940,0x6940791C39AD3769,0x376940791C39AD37,0xAD376940791C39AD,0x6C2D376940791C39,0x4A463885B9946D81,0x736B37A93397FE42,0x3874F55B29BB4D54,0x5F7A8A5F8D7543C5,0x228CCBA8F76BD619,0x5096624D7492}, +{0xA331EBB0C9B54BA9,0x51A331EBB0C9B551,0xB551A331EBB0C9B5,0xC9B551A331EBB0C9,0xB0C9B551A331EBB0,0xC980C9B551A331EB,0xC7BC1BC679178B4E,0x7072B575C98A5F98,0xB10657E6A1B9DEA2,0x71773BA18E92437A,0xAD4025945D8B2AB8,0x2F2C83A4E8D6}, +{0x732233773223377C,0x3773223377322337,0x2337732233773223,0x3223377322337732,0x7732233773223377,0xC637322337732233,0x2695C5C06B69B3F6,0x2330B3C47A0D9F3,0x1FF319B45BEC27C0,0xA128906C609EE6B9,0x736A7518122E449F,0x1FCE86244E63}, +{0x6EE64466EE6441DB,0x466EE64466EE6446,0x64466EE64466EE64,0xEE64466EE64466EE,0x66EE64466EE64466,0x63D6EE64466EE644,0xA64EE10DFC0F7507,0x7E19CCA11263939B,0x39CF2CD41A04B92C,0xB2FBF371165340D9,0x53745B07D6DF8B00,0x44F4C0618554}, +{0x70E5437D550C15E9,0x514AB52CDC183AC2,0xA4D63DFA7AA6594A,0x46DAD39BC3F3F19,0x82FD5B4A38522B72,0xAD58A5AA7E8D2ECF,0x523BAAB70A135BE2,0x45782546050175F7,0xB24F33FAA2472B55,0xEBA7A14C1F8593CD,0x20600FBAB2D24E65,0x133D309F7EC7}, +{0x8EEB4AB02E5A2272,0x8EB9599CB8AAD0F4,0xB06CC77E62BB7EF8,0x32986176DFFA11C5,0x1BAC3B085C0081D9,0x69272A1BEAA860AF,0xE41E6EBFB6ED0D08,0xF255608B042DB67E,0x1279C6C0D0C40109,0x76B7BA4E30FA03B6,0xD3DDD4F6F5A7EB7,0x106A8E48CD0F}, +{0xD5120148FEAF2C06,0x255365F9DAA4C4B8,0xCC272EFC74777061,0xD9E68887C98D5C50,0x383B3424E91729B,0xE0B5120148FEAF2C,0x1BE4FA2B9F7CFD78,0xDA98A1C587680DD9,0xACC09E7217DDD41D,0xBAB5E239D699C58C,0x41FD047089438309,0x858395E2C66}, +{0x94FAC8FF3E686241,0xB72999CF503E0946,0x2F59559E717C42A,0x412EFA3785EBB9F,0xAD808B51BA81A8AC,0x4BE4FAC8FF3E6864,0x8C1AAEA7B9495845,0x94D196357B071596,0x4FBF87DA63CFBC99,0x666394A603DFBB5D,0xAA328976810C7C69,0x6AA898DF5E6A}, +{0x40E70907368FAAA3,0x2531EC3903CE9F2C,0xF8AB9BFACF708D95,0xD2DE3A9B1838859A,0x4E47B12D7C682948,0x281BDC83C4953F02,0xDE0EF99ABED7AFEA,0xB81783A3E8034AE6,0x3E73219AAC32B265,0xA6F25C569E80F4D3,0x6961E44D2E61E550,0x54AF9D7748CE}, +{0x4EF61479F650B3CA,0xE4161CB8F931D792,0xAD6C0EDA1D651114,0x96969F3A055F9963,0xA55811F1BE797DD9,0xBB36DA0672F2CEF4,0xBCD0F6F9FFB265C5,0x868F4BABA3739212,0xDA96099F90F8EC8D,0xF6B719FF6C14091F,0xEF5131B07D9BA208,0x15F75A78FB86}, +{0xB5CA528D6B5CA529,0xCA528D6B5CA528D6,0x528D6B5CA528D6B5,0x8D6B5CA528D6B5CA,0x6B5CA528D6B5CA52,0xB27528D6B5CA528D,0xD7C00A95FC590145,0x4E4610B31250410D,0x92EB9C10C371F0FC,0x71D124AD03784C6D,0xFBA87309E1A6D857,0x2DF3B0F268CD}, +{0x6B5AE52946B5AD2D,0x5AE52946B5AE5294,0xE52946B5AE52946B,0x2946B5AE52946B5A,0x46B5AE52946B5AE5,0xD0BE52946B5AE529,0x5BEAE3E345C8E7D7,0x9D2D7059D4BB6A4E,0x18F7C0F408EA159,0x4E11D89176651539,0x48671FC6C152F99C,0x530CE08D1028}, +{0xCE57AA6B0A6E427F,0x9B8F883433A0EB6A,0xBD90869A824E3109,0xD1840719519276EA,0xF601CD0A72F12455,0x8904C6A15653D646,0x72DB02908565884,0x71294DC40DC2EB13,0x361608701CEA745E,0x1279CC6C51A4F800,0xDD923715582E9EDE,0x6578E5CC44C5}, +{0xB218A10D98E7AC3C,0x3CAF3BDD50AC19A5,0x2A2B48E62A13DFAE,0xA9CE07E98542FDD0,0x4B70FD8D0D9C06C5,0x6829379D7BC99C61,0x57C3D248CC251489,0x9F1367A307C698E9,0x2CC0B2B8746361EF,0x9A6A53D6400CB8EA,0x7888C0894B30195B,0x29E026757F97}, +{0xB7B49E77DD01B05A,0xC7FCDE689EA7A30E,0x3B83E48534D253E7,0xE1F4F28B24C70D5F,0xC226AF798CDAE97,0x29592FFABA44E0BF,0x451BFFACF7902A0B,0xEF0C4136DB713262,0x7F066B8D7CD90C93,0x193C99BB6A2BD9E4,0xDCCEB7DD7547E7EE,0x1BC6242C97DB}, +{0xE49911F2B13CA178,0xF8D4BCF08B36207D,0x2605805106CF5C4D,0xBB2BF392469C496A,0xC6EE51B30BE997A4,0x3636AEDEA9BE252F,0x5962BFE5CE1E434D,0x80A1219F24FBAA71,0x9727D3F901B9FA59,0x9C7DB47FBDB8D837,0x260B21A1EA96DA92,0x58C7EC9D75A5}, +{0x11372FCC7943203A,0x5C4549B345DE13E1,0xB35E08AA984D8EEB,0x9AD22A4F3D9CF45D,0x84408FBE68108C13,0xD6F34279BA1D5079,0xFD86BCE1D485CE9C,0x7547DCC9E6A72B9A,0x82BAC6E5640D1B8,0xA0AA9060525B5FA0,0x9DF6B6008023369A,0x64534002FC0F}, +{0x338AA1050E3B47F2,0xA779AFC5AA01E0AA,0x7A24EAE40DA1607F,0x2F3BC85F75845B2F,0xB63ECCFACC4A42BC,0xB970439A64648442,0xFC7FE81D54BCBFAD,0x8F070C333697311A,0xC3F49A6F3F169CEA,0x5D4853A9EA5F7ED,0xD518DE0B200B8454,0x527415AF5FE1}, +{0x29D6C703462657AD,0xDC60DB370D32F7B9,0x7ECF292BC2C418DD,0x37B10E0D29478FC0,0x2DFAFEF9EA3B8E16,0xE9716B45FA8908A4,0x6CB32B342A6375FF,0xFD73F31AB04928C5,0xB397940272F73C0C,0x5B001264620355C2,0x5803F26169F9945B,0x5C5620099D9B}, +{0xDA0656B84FE5EB1E,0xBA4CBC548666840D,0x1A44273AF862539E,0x1FFD96A7C772BACB,0x953D86F6FED07774,0x7BBC68E6D3E03A59,0xA78131504FEA94B4,0x5FF580356C9EF9E7,0xDF4576DB17102D3C,0xCA73668DEBAABC08,0xC73232385D81A0CB,0x14DC1275B692}, +{0xE1C98F3C564A49CD,0x76847854DFFF1979,0x6DD3A9A2B019D474,0xFEB9A85944A3C836,0x4C554E80A25DEBB9,0xC247DBF7209CBA59,0xE606E4DA4D403E68,0x5AABAE35231E6C78,0x1E08F32D70B4CF5A,0x8EDD7B4A0D3949FA,0xA549CBAE571FABD6,0x345B562BB1C2}, +{0x3DDA63D9B718EF13,0xDB18FF110367AB22,0xB7A690D61E54A79F,0xD1FB6E7474B2F230,0x5D6F299A0CDCA8B4,0xBDB8418CAF5F5E57,0x87950067C9C186CF,0xF190BC388A72A53B,0x213C2BED23C24CA9,0xD23020B606F4B8B5,0xE7CFBF2E0DE63E1D,0x85488821CA3}, +{0x2E87222F0886018B,0x2006A348352327DC,0x19561FC0617F066,0x390FD49917EAD64,0xC8962E05BE5C859E,0x9098F7D823688E17,0xA367361FE7730947,0x4C6AE2F141441363,0x6012B07C3CA41E86,0xB27005C079FEB1B6,0x825B9BFC26C91F27,0x3F1183F8513F}, +{0xB584B99EC62D9D35,0xA4912F9464B54407,0x74A10C6ED11079EF,0x42C935F4B27768B1,0x355CC43459FC8F5,0x83FB4BDA9E4C1B5,0x362D54FAF7050831,0xED24CAC0D587AF78,0x520C08B595DEF623,0x9C385DB3FD4B1742,0x12B09C148B913905,0x4C96EA957BF4}, +{0xCCB2CE7886EF239D,0x47C704F6F492B661,0x63CDC17F473B3143,0xE43575F9DEDACC50,0xED36745A83436E23,0xB43E3A2A47D36381,0x6FE523A476BF9F48,0x82B1F402B3BD2A0,0xDBE6E728B539ADAE,0xA37C34807A76FF4E,0x538EE747772483FB,0xDB5A5E658A6}, +{0xEFAD9377610BEA32,0xECEDC7C4592CCB7E,0xE95A17CFCF63D4AC,0xC5A8F05F0C78F770,0x386981FAC3E25272,0xDD7CD0B4AB9A79D3,0xD9455DDAD31D0592,0x994588049EBE35C8,0x7820458445B7DF6,0x160C1A4D5730403C,0xD554560F2A51E183,0x27B420420DC7}, +{0xED6F9F18F5F91D9B,0xD0140983A4C9F4FA,0x4B28E37741FCEC6E,0x58485D7E32AF47F7,0xBFCAD3B8EF182455,0xAA683462489724D5,0x4F7F01FFFD1C1E61,0xDB4F6A13AEBB1ACA,0x40272AE951D7AD1B,0x430F04D3C2402C98,0x67C05BFAD21BAAF1,0x53D2C0CD2C47}, +{0xBA47E3D71B355EF5,0xEDE1D03F79CAC2E3,0xF12082CA2D8570E2,0x33DB874355B82195,0xAED62CBE488111EF,0x8FF5A83E933036A1,0x5FC5432547B62106,0x3675123E1B5D6362,0x187E4E847EDF9ACC,0x92E55D9773F0AB6E,0x2FB79EE22F3B6FA7,0x59F9721DDC1B}}; + +const uint64_t table_v_qnr[TABLE_V_LEN][NWORDS64_FIELD] = +{{0xE85E85E85E85F161,0x5E85E85E85E85E85,0x85E85E85E85E85E8,0xE85E85E85E85E85E,0x5E85E85E85E85E85,0x65385E85E85E85E8,0x85F916A5F6E08638,0x2609C462575E3A01,0xD55BC460BFFDB5F7,0x394FD56C08877041,0x90A4C64E64B48269,0x155B182E978E}, +{0xBD0BD0BD0BD074F6,0xBD0BD0BD0BD0BD0,0xD0BD0BD0BD0BD0BD,0xBD0BD0BD0BD0BD0B,0xBD0BD0BD0BD0BD0,0xB39D0BD0BD0BD0BD,0x981077DADCECBF8E,0x84DD13216CFDC8E1,0x65BF0DC9ADEA2134,0x4046BEA875292C81,0x96FEEECC09D1A583,0x34F2E90F31C3}, +{0x94DFB461AC813046,0x794DFB461AC812E7,0xE794DFB461AC812E,0x2E794DFB461AC812,0x12E794DFB461AC81,0x3D0E794DFB461AC8,0x70595ED790F5300A,0x8AC21DF01D745314,0x960E4F84DA8D1645,0x5B7E64183952E46B,0xF22C180908C76B1F,0x4768EB30E5C6}, +{0x88455121DEEA9B08,0x788455121DEEABB7,0xB788455121DEEABB,0xBB788455121DEEAB,0xABB788455121DEEA,0xE53B788455121DEE,0xC8CE631746684732,0x7D5D2A56DD6FBE22,0xD6AD8D86B52354AE,0xD1BD7280508807CF,0xA1C516D87EBCCC99,0x396575A76D53}, +{0xD62298ECA7759C89,0x4D62298ECA7759C4,0xC4D62298ECA7759C,0x9C4D62298ECA7759,0x59C4D62298ECA775,0x796C4D62298ECA77,0xAE6DBC543FEF825C,0xEC1F7E95B33ED029,0xCA719FAF0D52EACA,0xF0376BE32D0BF058,0xF65BA4732A06CB30,0x253E29FDA895}, +{0x2D3E21C74B076D2D,0xE2D3E21C74B0778E,0x8E2D3E21C74B0778,0x78E2D3E21C74B077,0x778E2D3E21C74B07,0x2288E2D3E21C74B0,0x114736656CB88D28,0x65C8937E512FEBC1,0x306EEB4AB789442,0xF0BAF2EB5B82DA71,0xD1557C1ADE14F33F,0x281EF5D67B92}, +{0x55A7CC22BD034BC5,0xCF664D2B55543DB8,0xAD0509637903BB29,0xCC764B6DB31CC125,0xA38DE755C3A64634,0xC5DBC1418728812C,0x54CDBEA5DAAB0EBF,0x784DA3FDEE94F653,0xACD92FABB346E2C0,0x309E575438F3301C,0xDE6DA98747E3BC84,0x78998A0688}, +{0x14E884DC556CCE17,0xF813B625562FC7FD,0xD410AA497515C755,0x4395124C11891A90,0x392344FF261926C0,0x5B0104CE685B1520,0xA32FA4F27454F2D6,0xDDED7CB7AF975B5C,0xFEA15A43C78AC218,0x89AE7B37DEB4C0E0,0x48661EEF6DCF9520,0x11ADE16CDC2E}, +{0xD2261143E5B763C9,0x7BAF0692270E1A07,0x3E5B763C797E0B76,0x2270E1A07D226114,0xC797E0B767BAF069,0x8FA2261143E5B763,0x6F563606E110ED58,0xCD1C300154910AA4,0xB61EDFD60C5C6096,0x12CADF965191532E,0xA045CA5ADE8C8CA6,0x2CDC07A09F1D}, +{0x952C939D91AFBD6C,0xDB189B941022B733,0xD91AFBF752331AB4,0x41022B733952C939,0x752331AB4DB189B9,0x91552C939D91AFBF,0x6376CA8518BA8EA,0x4C144651E91CACE2,0xE0E13E3F7AF8AC34,0x4C7E7CDE3D51F816,0x11E5E216628DA39F,0x3C9C0D30F762}, +{0xC605DAAC2686111,0x653B01B6DAB28C3B,0xC50A3A32DE5449A4,0xB6EBC1C42E96427E,0x8FEFFAE8A88084D9,0x58EA39884624C641,0x9EC005ED22C5BC45,0x1633B0FBD77D6D9D,0xA57C267B6FBA36DB,0xF94465FAC0B899A2,0x34A4BE281ED17637,0x55D1BDD26591}, +{0xC709286502B5CCB,0xFDA560011E994595,0x4856E21B8EEF3C44,0xE6FF4B98A9EA2DE2,0x9887CBBDFB34929F,0x7E47E75497B06B9B,0xE723E79ABA5D9470,0x2C05C07824B8E6E,0x5E4E45149E3C5445,0x2452AE29E3055EA4,0xEF90DE3635F81ED5,0x2811146405A3}, +{0x9807214A3A1C1CF3,0x7A0E708928E1F773,0x6B79A82BEC4DCC5F,0xE98AFBE2931E7695,0xF1BFAF7F0D6FE513,0x729355B40CC74834,0x7355193ADF5FC317,0xAABE07A1788CB696,0x22D720814DB72B6B,0x37DF09E734DE45BA,0xFD056FDA4F240CBA,0x68ABBB7B5C8E}, +{0xC3777B85DA951B35,0x729E2EE622CB06CE,0x142662CA9F3EC02B,0x79B13BB964738D59,0xD0D82AA614F52FF,0x2073598189B312EF,0x187D2FB5FF497E99,0x55FEA80CEF2A4B0E,0x6B197F79D5FAF833,0x254447C18292F844,0x60F938B568EE1543,0x71826A2ADCA}, +{0x9C02260C68B4DBCD,0xEAD5B56BFB777BE,0x3BC3BE5177278FD6,0xDAB6622B90CD39DE,0x90CC3EC6ACA6DDD0,0x6E158FF767CE5D2C,0xA8B669D3FF7489EA,0xAF133837592C7ADA,0xFBF80D62062EC026,0xC3512D9A00005FBB,0xB759F49E11D399A6,0x2B5BC9341B5D}, +{0xC32617FB97A7BA46,0xDC97C62323C3A3A3,0x100C4C10F8AD3EB2,0x303659A310A3583D,0x12DA436E2F3F2E72,0x4D50F367A011A161,0x8328C3F9F44A3084,0xF982C9DA22658656,0x5EB7238A18DD90A7,0xB9156E1D1B343898,0x57243EC083BFEF2F,0x3DE52126EF4}, +{0xBBD06880C51C680B,0x7A81A7C7078464C3,0xFDECD7041B4ECF3E,0x2C5C3D04ED2F2A03,0x5D174A6A4E7F7DB4,0x1B52D2539D1EA2E8,0xA5CC20018839AB95,0x67625D02AE4CF980,0x186074DCBD384821,0x9E5E42872A3C7A83,0x545832703A5A56B9,0x27681CF8D9FB}, +{0xD629BC89002BCCEA,0xB88D005E2C3A8F32,0x56386D851D5B66D8,0x60ED69D4ABC2EE09,0x1731219EC24A5538,0x966D87BCF622EA5D,0x62A6B07E4C8B3CEF,0x6EA16F4B509B81A3,0x7A97D35B5CDE162D,0xE25FB4ACF2AF1E4F,0xC48E64140BD3474E,0x21FDD6C8FB82}, +{0x9288477180A6C951,0xB2D2DE965A033D61,0x3BA1694AB827311A,0x70A5B57FC1C70CDC,0xBFD11385625A2E5B,0x2DDDAFB04A38853F,0xF21823FF1B225FDC,0x5F007A2E1641AEB8,0xC3E5684AC220ECAA,0x78179AF27DD10F63,0x96DC98F67C36644F,0x7D6D89BB770}, +{0x829327C9D19D0226,0xD65D25DC7C2E4992,0xD5DBE128D0A23BA2,0xF6DFC62FD21334A4,0x651EAEB5C3A9A583,0x180C253598055EB9,0x3F73FA2EEF9168FA,0x4318BBEE307725D0,0x54DD26A9FC5450F7,0x76ABA5758680DBA0,0x353ED351A6A5F735,0x2FF3A6573DE4}, +{0xB9993936AA2301F8,0x7B319EACE5E9B127,0x12E616BD697BA4E,0x811B1F35F96913B0,0x474DB18B6AB00C82,0xC1FFF493FE2C0901,0x796424D7A11AEDE9,0x61076638D85C4C48,0x64774660A3BE93D0,0x43FA3F433B9D067D,0x47A0B426F92F7600,0xA280AE8D170}, +{0x3581912DE993F071,0x70141CFFC8A2ECAF,0xC3EB4B7D9EAADF4D,0x39E0D5685C6769F8,0x44208A1289B360A9,0x1495F58B3248D82B,0xCBC66BB98CDA2E99,0xCC3F8763F217FA81,0x495812161E7D7E11,0x255FA1A2A5D70135,0x240F5A6F7EAE5BA4,0x4C1F4DD638F5}, +{0x5B9845DD9A79003D,0xEF65F03C8F56ECBD,0x30F64FF52B455D62,0xD45579863FAD5D92,0xC798CD9C72EB564D,0xDD15C4F63ED0D645,0x9F35EC5BCF419520,0x2759D2CB3306DFB3,0x6A4CEE0C84723002,0x62AE428E1405808C,0xA93787CE06A12315,0x4885205A0A7F}, +{0x3184F5FF10FC6AF3,0x143B921A36E08BDC,0x4DA6A729B2406BF7,0xE6678BF19EEF357A,0x96091214F1C2F4A2,0x9F07E61747E02986,0x48FA86D281046604,0xFF69050DD5E29481,0xF97F744AB920445E,0x16B828177FE35D68,0x2A44107C12A0C668,0x65CD488721CA}, +{0x4E5420F1827B439D,0xF487A4ED360B1C4D,0xC55EFC7F8D8112D0,0xED67A91DBC5910C6,0x9E9A78EFA44FC34F,0xD40F65D4211D8623,0x5C21F3F0FE48DBC9,0x9CEA4A83954032F,0x68A443A160CCF02,0xBA2D35302646DABE,0xB27CC0AAD03BA372,0x2E3F49905A08}, +{0x40785DE28D4C9530,0xA6405C1C01E10071,0x3C209F250C73B2C8,0xBF22E6EBADC20A64,0xD1DDAB04AF2AB602,0xA33C04772868D58C,0x98DA3CE309D547DA,0x4DD504F6F173D486,0x283B355D938C1316,0x99001A20441BA13A,0xE8C99EC8D3BB4B46,0x6F688BD1C61}, +{0x459A64577F98DD28,0x3FD6890B60AA7022,0x32B84AB229B33D20,0x7CA6E1524F6EBF03,0x4F0242DD469A4D8B,0x53EAA4C1EBC77C19,0x62C19F1C435AC30D,0xF230AE4E1F1BF94B,0xCF7E083E29C16D7E,0xCA42C2833B78234E,0xD01EFFD11DB566A8,0x224E1F2FFD2E}, +{0x6EDAA71406539762,0xB74F189440621EB1,0x345F3262EC4F13E0,0x23185407A289E9FD,0xD105FEB3ED85CEC2,0x11F70813D04E49FC,0xD99654FECB39AB46,0x734ECF9475139205,0x54E95C9BD579AED5,0xE044D2C9270C1251,0xE60CAFCEA4BB3508,0x552B57BCA931}, +{0xD91B6C9B924D91B6,0x9B924D91B6C9B924,0x91B6C9B924D91B6C,0xB924D91B6C9B924D,0x1B6C9B924D91B6C9,0x312D91B6C9B924D9,0x17D193651E9DCA60,0x8DF224D4272EC01E,0xCBD2BC92A7A778F6,0xA59CF2B6356CD90E,0x9C712EB8F35468FD,0x5C2C61931F7C}, +{0x249B236D93724969,0x6D937249B236D937,0x49B236D937249B23,0xD937249B236D9372,0x9B236D937249B236,0x7D4249B236D93724,0x6F78BF6586101FB3,0xDEBA77A01FF372B9,0x2809BF0C10D132CA,0x15E12E137474B550,0x32E144163D1A7A6C,0x83BCB784FD}, +{0xA014E250439995F,0x45FC65F1FFF85333,0x6BCB9B2F717EC6B4,0xE17F29C4A3AAB256,0x84007F11103DBAF3,0x8F00A6A9F3A093F6,0x9726358A43891D51,0x897A6562E06B392,0x9C43741CF4F314B9,0xF134466DE6EFE2AB,0xF564982D2C7FD077,0x1314C36F69C9}, +{0xA43641B1D7CEDC7D,0xF0874E7045509B0D,0x792E7B86FF0D73E7,0x7B8EC819E2656382,0xDB846DE5527F9573,0xCBAED11FBDC7B5A7,0x9CF8B6F734116414,0xAB4016ED22D2B78C,0x901482B46AAC884D,0x6F313D2D60B58E49,0x8226CE453AFF56F5,0x541B0694E059}, +{0xE39251FB5F896DD7,0x861156ADC66BF25B,0xD3B6E410C9EB77F6,0x149A5B2E22C5FF6,0x39BF19B234BC83FE,0x6FC6DDCDE9500C15,0x33D635192E7CA410,0xF40BB7C04811EFE5,0xB95BDBAD0678F5E3,0xFFEE8DDD2907E2DA,0x71BB095C5885E70A,0x3006B1C7034E}, +{0xD681EED8B087DAC7,0x90726086FB0A1D9F,0x643AD6038FE15FF2,0xF6524CCDFEB45CE0,0x511BD3AA0B479432,0xFDAA3B25B585A917,0x16C0CA87EB477009,0x5DCAD9871ABB0038,0x5BA46393DEEC08B5,0x9AC8A0B793849197,0xA8F7FEDA5FA4EA5A,0x3A742CC9DEB9}}; + + +const uint64_t v_3_torsion[20][2 * NWORDS64_FIELD] = +{{0xD89D89D89D8A493E,0x9D89D89D89D89D89,0x89D89D89D89D89D8,0xD89D89D89D89D89D,0x9D89D89D89D89D89,0x8B389D89D89D89D8,0xB4C6B9529F01D8C3,0x1399AE2626262260,0xDE85321D9D8185DF,0x8451DC3FDF91784A,0xFAEFD5E487381389,0x6319EE6373CB,0x3B13B13B13B1248D,0x13B13B13B13B13B1,0xB13B13B13B13B13B,0x3B13B13B13B13B13,0x13B13B13B13B13B1,0x7A4B13B13B13B13B,0xA30792A3BBCAECC7,0x8E3262972F905537,0x6EC1E1420B7BAD51,0x3369C4F4190692FF,0x9D6D588BD01A282C,0x28F2E2C80A9}, +{0x673D45AA630B09FB,0x5673D45AA630AE95,0x95673D45AA630AE9,0xE95673D45AA630AE,0xAE95673D45AA630A,0xD4595673D45AA630,0x6D7B45385F91ACC,0x7FDE0F3B044702EF,0xF1BFC4766FC2E18A,0xD67138B8790E3167,0x9EF75C6F0552A406,0x2C5A25459904,0xF6C4681424EE5801,0xAF6C4681424EE5FA,0xFAF6C4681424EE5F,0x5FAF6C4681424EE5,0xE5FAF6C4681424EE,0x7FAFAF6C4681424E,0x71E7F021FC96E1CF,0xBD317223E4665091,0x4D1B06EED834E4E,0xF423F47B02EEF4B8,0xA418B4D55C23C88,0x94F95559E31}, +{0xBC8EA75EFC1DB814,0xDC562840F895B742,0xEA75EFC1DA922F50,0x62840F895B742BC8,0x5EFC1DA922F50DC5,0x1B3895B742BC8EA7,0xEF4E35288013377,0x7034C1EDC7954F9D,0x404E07FFDCD9C4B4,0x6C0D3C3112E9FC8B,0xE93593735AD57C40,0x5E74FB7D527D,0x5C835ABF61CF41ED,0xDF2950278C2E9C12,0x35ABF61CF458FB68,0x950278C2E9C125C8,0xBF61CF458FB68DF2,0x7E9C2E9C125C835A,0xCA8064284EDAE000,0xB011CE81CE7860C5,0xF2D3F4033A9B8AE2,0x2FF7880A1DE06DD0,0x7182DD9DC3FCB499,0xA4A77D973AB}, +{0x8AE21EF6EA938B09,0x37966C6ED5186501,0x69DCB18F74253FB3,0x3188241B31A56443,0x9156C7D752C811D,0x9CFAE79AFE751DE1,0x8BF44341193A82F9,0x34DAFBE7EE16D274,0x272F0852BA272D8,0xA0F247E8810D0FE5,0x48E124BE4CC4D188,0x4FDE2C9A5389,0x44369DCB18F7403C,0x11D3188241B31A56,0xDE109156C7D752C8,0x993912AE79AFE751,0x34E708BDAC04CC86,0x8C7E4CE5A9BBC962,0xF269836E4C98DDD3,0x45188E7965A38A0,0xDAB83EB832EB62A0,0xCCEFE1931E93559A,0x775966B73B29F6D5,0x45DBC312B900}, +{0xB71EE1F7F5C9327,0x8A5569830CE94076,0x12961C17A5932157,0xDD79C7E8EBB6086B,0x2BEF8AB644F43951,0x37277CB68D98CE33,0xDE633F0A815B7506,0x61740E19C3F2EFA4,0x61B1E49FB5E4EABE,0xA015247782FF386E,0xE25E2C7B9F068D08,0x5A5611C2C7A3,0xD213F53791E68D00,0x2EDE2F635D1EFA2E,0xDA72EC5F8871204D,0xDAEBFEACFFF3E491,0x5F948C8E72BBF1CF,0x4A440214B6EE743F,0xD224FC96C70931D9,0xEA00C3F488138831,0x9D46231784C01FDC,0xB12AA781AEC3B474,0xE312A59BD123CE5A,0x1FED35710EB4}, +{0x72F7284A69378371,0x3D4A5A89547E058,0xB12975E3DAE2E152,0x599E71CBADA705F9,0x4ACD0B0B6F42CE9A,0xE5285A0245577966,0x6C038D909BB02FA1,0x124374A6F770AF89,0x99103DFE37CA79AF,0x147E8A248FDBCAAE,0xEB9B0A578010CFB9,0x37F0B3678B6F,0x5D470CF2D274DD99,0xC8516258CB0C2B2B,0xB43C53B94E11D2A6,0x5ABE2DE626199F2D,0x29D6C7C473EDC98,0xE0376A892583E1DC,0xC0CAA571F277C6A0,0xD4F6AD7F88406328,0xC9A2779B2F2431FD,0xD7757D28491C9C9C,0x3710D688A0ED993D,0x4ADB9FE768DE}, +{0x81F1C30C09FD33FC,0xDBF51DCE3A9149C9,0xE9CF78A0524C35B8,0xC02099DC646FDE01,0xB0594156B5517D78,0xCDF2CD6BD4510E26,0xA62E43C6D4ABA685,0x6282F81A9AB8658,0xD6D76B986C3AFC2D,0x82003479185AC489,0x68A227ED5A5D8D62,0x4CB44C725522,0x248D49A3572E2D8B,0xD7958CBA82F9C02A,0x8CAA9BD2ECD45A98,0xD568F26B9E3F23BE,0x6C2D5F812C90C433,0xF1565E72D2FCBB81,0x27E816D21960503D,0xC557356BF112F986,0x4C0F35DCE29E0B8B,0xB5D66BBE22866AEA,0xA93F73DFFDAB2E0A,0x615CF5C957D3}, +{0x516EE2A1BE021E2A,0xF602D6E151658AD7,0x26B24FB3189298B0,0xD965FAF4CE85C95,0xEFEF3DB9B3A4B775,0xD851DD3FA8E08D31,0x2DA32E186C78CE68,0x143617DD482EE422,0x667237E94436FC75,0x1AC3465D96DCFDBB,0x56D74ABF63E8D5D3,0x5D7C60C0D2E4,0xA30146117F0077FD,0x9BE366E0CADBC188,0xEF64080B2EACAD26,0xA8FD83BF0D513C6,0x877CB3DDB56170B2,0xB35C3C73A225B6FC,0xBF79CBB465569B88,0x498384E224080C8B,0xB2F0B94988649443,0xB3DCD435A017EB4F,0xE9941938991157FB,0x21C1C22E5E5B}, +{0xD40E007BD838CEA,0xA6EFBD2F6C46FEC8,0xDC1072B787D7CD36,0x7204C616DD691C29,0xF3C600AA941422BD,0xB810967F5BD8F3A2,0x53CCFBAE4D3DD147,0xCC071945DE01CFF7,0x6DD53CCD52E214A3,0xB2C2FB56192E2E38,0xD2B99B61C093CFD5,0x51BE0034F0EA,0x8107763EA961F872,0x74B86F2CE50392D0,0xDB4527F030D9F82D,0xEC3F66A797FB122F,0xF4DE67CF2F609807,0xEFC422F586A5B1F2,0xB765C11D7152D2E1,0xB0A5BFC4FD2AC62B,0x589DF808D4BB351A,0x1165BA9E7035FA93,0xE9B487C366AEC785,0x586D2918F33C}, +{0x6E3302C6FE0C0C01,0xDFAC66DC6CEDA28C,0xDED64C5EF280083F,0x8B39B4C197F785CD,0x11B93A8C64FD9206,0x9AC84CC06813FCFF,0xCF85682DC9D9B864,0xC23496D96970C301,0x5194BE86F6E26D90,0x4DB579722DE163E0,0x66DAEB4660E533AE,0x15B525F2A541,0x7C758374FFD93EC3,0x2C7354CAF23E0942,0xBD93A801DBC916D7,0x47E4D764786D5DAC,0x712497FC82C0471,0x87311F4B3AF3FE32,0xEFAEC8155C91650E,0xE2169C5AD02053FE,0xC96489E29375ADEB,0x5E7D1381050F03CE,0xB88C1A56DDD05F31,0x6070D9E2F41}, +{0x9ED7073D4D892D5E,0x7A8ACF5D59CC31D7,0x149DB0BEB6B3A2E1,0xC059D51CC46D3357,0xEE43544B33B041DD,0x5CC5EB8BC024538F,0x4B759EA5B9EAB631,0xA335C8BC0AEEAFBC,0xB03F67E326524765,0x2C790108FA72A4B0,0x789B5DA805C4192F,0x64DEC5C9AB82,0x36DAB776C6A6E1AD,0x70788D740F12BB16,0x678109B1BC9AEB8,0x6CC747669CD9ABEF,0xCBF25E90DDFDB9BA,0x9186ABE61B8B423E,0x29E06834AA38279D,0x45176543D221EEC1,0x761F084D3249B19E,0xB968904364D0E464,0x5DB85DA70B052289,0x521E2DDB50A5}, +{0x395783F790D29774,0x112CEC9A5FB0FD8E,0x2286B13D7C636B50,0x3BB1C1FAABC848AE,0xCEBD9A801EAB03DC,0xD0D0F3042DC47BD3,0xBA7CC91C76FBFC6F,0x7E4B81D9BC252CC4,0x791DA3C97B45B52E,0x76E4B2A8663A7CDB,0xB18F9D7CDF16DE77,0x6738B89E9A90,0xC5C400C8DEF67ACF,0x7DB5C96374C369C2,0x4DE65F1497C0251B,0x3D6A0B0AA5A7DC1D,0xCFF42CDA41FF0694,0x13585BF9A20DF747,0x29F5EA2387657EA2,0x85F982D144BC9D02,0x70BA26172B51F920,0x7CDC5B7AD3069E68,0xDA452B30229CE4DE,0x5308C36EA06B}, +{0xAC4F402D28A1B7D9,0x1F9692D5D204DA19,0x7B09C49F36556C65,0x74E03DD0CC93BAA4,0x2857AF2E2C697F78,0xB5B97969D9A74314,0x9B0B4C1B8B9C5804,0x12FE23955636F0E,0xB8E8FEC4456834F9,0xF6E7C5B893C1F2AC,0x5A45A12C0CF9B64,0x4242B7D98CD1,0x895BC47E5E99FE58,0xCFD306BF78ED7A,0x43394EBA61FCD38C,0x83E94C74E7C77585,0x9E944616E2627346,0x9BA6856CF3432676,0x2185C6AFF5533077,0x67F7CB233436A703,0x52D795D168AD54FF,0xBB7BF59763DC0670,0x79561A9B5335EFFB,0x6F8E14E2EA1D}, +{0x52170E4682673A4B,0xAD4577028668C00,0x105830C4E5B35043,0xE44B518DCE2097C,0x1DC57628AFA086C9,0x7017D10868A9652D,0xF52DAC7D308B4DED,0xE5F8D6B44798B8A4,0x860E5513916A8B0B,0xEF1A2AE69403037,0xFD7E1676F8DB8D34,0x1DA40260AF34,0x438DF92CAED981E9,0xE0EC927187AF9BD2,0x2C47A2EB752165A,0x10A814019E74674B,0xAD43DCF5C2393FE,0x9EF40A6C20918C14,0x827A35EE6A2A622C,0xC5367CAADECCABBA,0xDEC9E5F60CC017A0,0x89393E2776CC5F44,0x7AD261CF40C946E0,0x69EC298FC2C5}, +{0xE370D28A643127FE,0x6484E527E4F15551,0x3F59642BD5A34627,0x85A03E71ECC4BDC1,0x7B2E731CBACBC6B9,0x70F5FDBD8FDA90B6,0x24E12F3C9683795B,0x35FAA7C6879A3C7C,0xFF53C1E88A24C6E7,0xE5DD61BDDC562FD5,0xE68B1C39660B3261,0x6259E2A86D74,0x2982F0136CCDEF7A,0x8848824CB25EDE31,0x7BF8BC5D9CE7B4CD,0x5A3A0205A555D497,0x9240434A161CAB24,0xFDB3CBB75FE9869F,0xC97131D9A60D18C9,0x9DB915412B8CB0B8,0x5B7E4834AD58F24F,0xDF6E9178CA871824,0xF1259454624AC092,0x1327C8999EB4}, +{0x666280546751F204,0x3124828432952042,0x628126D710FA6B0A,0x1D3B96F1B28EB258,0xA3E698E6B79C0621,0x5CFD4588D9A09890,0x43A7B8C256D49EBA,0xE2F94301C0032B74,0x8953956AC6CA7C77,0x7F8015DC765F106C,0x82E4DDDD36ED8083,0x133AE4EA2F71,0xDBF063D1F1AF17B9,0xCEC32E934E871629,0xE2671C831AFAA693,0x960B975DBBED5813,0x203E4A33C527B48A,0x423CD368EF5C02DB,0x361633B23B9CEB74,0x5F11CA4E0B5ECBDD,0xAD9328EC4662A397,0xEA2509539AEEDDBA,0x15BB2346F14D8146,0x2F2B9A05EEE}, +{0x795D912BDEF015D7,0x65E6C0F35599987E,0x8BE785422F397093,0xCD93F70F07BAA7DB,0xF1A8945586B3C277,0x26353E447C9BF58B,0x4CD879A487B985CA,0x9E680A1F08FF3F3F,0xEA67CD5F51356E12,0x501DDEE09936B7D1,0x559A868F99683C3A,0x23FA0B67D681,0xEDDAB05F06B5A605,0xC6E7FE44E0E20ACE,0xDA2D7FCAF5C0C0EB,0x7507BC508BE5F429,0x7516F14BC559D8F0,0x55DB0692A07CC717,0x12F7611288A3B08B,0x34ED3DD86C14B639,0x2BCFE7EA6234CAAA,0xA20E37F49CD7B313,0xED785E90CA869C5F,0x524FB4A9B68D}, +{0xB24323DEA264A910,0xFBB77EB1969BA34D,0x6DFE6BD2DF0E62D,0x4BA1D9212AAC1737,0x6604456CC168CE0D,0x1F045C2902E70B1A,0xC30F3CF005747BBB,0xD0808A1E60231D09,0x616E5202B8B68AB9,0x91279DE1E1F59C61,0x17039A54DE74E351,0x483F7B722965,0xCA63AE6778B0F84E,0x3920204D38EBDF19,0xFB1FE6BAD523F1EC,0x8B34EDE136AC2733,0x7409325BA76B71BB,0x987FACF98158EF9B,0x3EBAB81D7CC6988B,0x518A2D688F371575,0xC77B4766A9D72BCA,0xAF7343FE6E77A7C4,0x54516072DE9FE449,0x52E493B8BEDC}, +{0x95B9273E98BEE101,0x6CF2C2CC7C2F0D29,0xEFE3B76E594AA11B,0x3DDEDCDD1FE42241,0xF7E15F986E39CC89,0x3CF9E152B6FD333B,0xE7F2CF0844AD69DD,0xB792DFF3C762D02E,0x3888F4A332FD9030,0x8A4CC0E4C437575A,0x833E2BA7BAF41403,0x135FE5EBD4BB,0x657D9769E52DAD91,0x84951CC10B514173,0x7678CDEC0CC5511B,0xD4E7DB99FC763848,0xC6ADD473DF8087CE,0x842DE2D06829FA76,0xD086DB2A4651BE48,0xD0399255E5DAD344,0x6B2EAEB21B8BB524,0xF6DE9148F0694AEF,0x5A85093194755805,0x2570D86C9FCF}, +{0xD665CD614A703CBD,0x7251A4FFE04E2B30,0x8AD6A13EAA0B07BC,0x2AB5112D91260BE2,0xF31D78441E75FDE5,0x981D1D465A8768E6,0x7AD08CCEE352CCDD,0x31C6C60ACD409AC7,0xDFC10AD642C330AA,0x16DA3C495AE40C44,0x89AB4B294D700C6D,0x13081265A555,0xB649623190FAD2EC,0x9E0A9F4A626C11FD,0xEF8A6A8092D66371,0xEB9370EA38CC1EED,0x74BF8D8667FFF12C,0xF931EE21E90FE5CA,0x5E180EC10EC59AE0,0xBA6729A7EF221E52,0xAEAB0D0AC6ED85F9,0x2401EAF62859B015,0xD309B49CD60C1B34,0x2CBA9B452CC8}}; + +// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions +#define fpcopy fpcopy751 +#define fpzero fpzero751 +#define fpadd fpadd751 +#define fpsub fpsub751 +#define fpneg fpneg751 +#define fpdiv2 fpdiv2_751 +#define fpcorrection fpcorrection751 +#define fpmul_mont fpmul751_mont +#define fpsqr_mont fpsqr751_mont +#define fpinv_mont fpinv751_mont +#define fpinv_chain_mont fpinv751_chain_mont +#define fpinv_mont_bingcd fpinv751_mont_bingcd +#define fp2copy fp2copy751 +#define fp2zero fp2zero751 +#define fp2add fp2add751 +#define fp2sub fp2sub751 +#define fp2neg fp2neg751 +#define fp2div2 fp2div2_751 +#define fp2correction fp2correction751 +#define fp2mul_mont fp2mul751_mont +#define fp2sqr_mont fp2sqr751_mont +#define fp2inv_mont fp2inv751_mont +#define fp2inv_mont_bingcd fp2inv751_mont_bingcd +#define fpequal_non_constant_time fpequal751_non_constant_time +#define mp_add_asm mp_add751_asm +#define mp_subaddx2_asm mp_subadd751x2_asm +#define mp_dblsubx2_asm mp_dblsub751x2_asm +#define random_mod_order_A random_mod_order_A_SIDHp751 +#define random_mod_order_B random_mod_order_B_SIDHp751 +#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp751_Compressed +#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp751_Compressed +#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp751_Compressed +#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp751_Compressed +#define crypto_kem_keypair crypto_kem_keypair_SIKEp751_compressed +#define crypto_kem_enc crypto_kem_enc_SIKEp751_compressed +#define crypto_kem_dec crypto_kem_dec_SIKEp751_compressed + + +#include "../fpx.c" +#include "../ec_isogeny.c" +#include "../compression/torsion_basis.c" +#include "P751_compressed_pair_tables.c" +#include "../compression/pairing.c" +#include "P751_compressed_dlog_tables.c" +#include "../compression/dlog.c" +#include "../compression/sidh_compressed.c" +#include "../compression/sike_compressed.c" \ No newline at end of file diff --git a/src/P751/P751_compressed_api.h b/src/P751/P751_compressed_api.h new file mode 100644 index 0000000..8a910de --- /dev/null +++ b/src/P751/P751_compressed_api.h @@ -0,0 +1,109 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: API header file for P751 using compression +*********************************************************************************************/ + +#ifndef P751_COMPRESSED_API_H +#define P751_COMPRESSED_API_H + + +/*********************** Key encapsulation mechanism API ***********************/ + +#define CRYPTO_SECRETKEYBYTES 413 // MSG_BYTES + SECRETKEY_A_BYTES + CRYPTO_PUBLICKEYBYTES bytes +#define CRYPTO_PUBLICKEYBYTES 334 // 3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES + 2 bytes for shared elligator +#define CRYPTO_BYTES 32 +#define CRYPTO_CIPHERTEXTBYTES 363 // COMPRESSED_CHUNK_CT + MSG_BYTES bytes + +// Algorithm name +#define CRYPTO_ALGNAME "SIKEp751_compressed" + +// SIKE's key generation +// It produces a private key sk and computes the public key pk. +// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 413 bytes) +// public key pk (CRYPTO_PUBLICKEYBYTES = 334 bytes) +int crypto_kem_keypair_SIKEp751_compressed(unsigned char *pk, unsigned char *sk); + +// SIKE's encapsulation +// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 334 bytes) +// Outputs: shared secret ss (CRYPTO_BYTES = 32 bytes) +// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 363 bytes) +int crypto_kem_enc_SIKEp751_compressed(unsigned char *ct, unsigned char *ss, const unsigned char *pk); + +// SIKE's decapsulation +// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 413 bytes) +// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 363 bytes) +// Outputs: shared secret ss (CRYPTO_BYTES = 32 bytes) +int crypto_kem_dec_SIKEp751_compressed(unsigned char *ss, const unsigned char *ct, const unsigned char *sk); + + +// Encoding of keys for KEM-based isogeny system "SIKEp751" (wire format): +// ---------------------------------------------------------------------- +// Elements over GF(p751) are encoded in 94 octets in little endian format (i.e., the least significant octet is located in the lowest memory address). +// Elements (a+b*i) over GF(p751^2), where a and b are defined over GF(p751), are encoded as {a, b}, with a in the lowest memory portion. +// +// Private keys sk consist of the concatenation of a 32-byte random value, a value in the range [0, 2^372-1] and the public key pk. In the SIKE API, +// private keys are encoded in 413 octets in little endian format. +// Public keys pk consist of 3 values of length OBOB_BITS, one element in GF(p751^2) and 2 bytes. In the SIKE API, pk is encoded in 334 octets. +// Ciphertexts ct consist of the concatenation of 3 values of length OALICE_BITS, one element in GF(p751^2), 2 bytes and a 32-byte value. In the SIKE API, +// ct is encoded in 3*47 + 188 + 2 + 32 = 363 octets. +// Shared keys ss consist of a value of 32 octets. + + +/*********************** Ephemeral key exchange API ***********************/ + +#define SIDH_SECRETKEYBYTES_A 47 +#define SIDH_SECRETKEYBYTES_B 48 +#define SIDH_PUBLICKEYBYTES 334 +#define SIDH_BYTES 188 + +// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys. +// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016. +// Extended version available at: http://eprint.iacr.org/2016/859 + +// Generation of Alice's secret key +// Outputs random even value in [0, 2^372 - 1] to be used as Alice's private key +void random_mod_order_A_SIDHp751(unsigned char* random_digits); + +// Generation of Bob's secret key +// Outputs random value multiple of 3 in [0, 2^Floor(Log(2,3^239)) - 1] to be used as Bob's private key +void random_mod_order_B_SIDHp751(unsigned char* random_digits); + +// Alice's ephemeral public key generation +// Input: a private key PrivateKeyA in the range [0, 2^372 - 1], stored in 47 bytes. +// Output: the public key PublicKeyA consisting of 3 GF(p751^2) elements encoded in 334 bytes. +int EphemeralKeyGeneration_A_SIDHp751_Compressed(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA); + +// Bob's ephemeral key-pair generation +// It produces a private key PrivateKeyB and computes the public key PublicKeyB. +// The private key is an integer in the range [0, 2^Floor(Log(2,3^239)) - 1], stored in 48 bytes. +// The public key consists of 3 GF(p751^2) elements encoded in 334 bytes. +int EphemeralKeyGeneration_B_SIDHp751_Compressed(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB); + +// Alice's ephemeral shared secret computation +// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB +// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^372 - 1], stored in 47 bytes. +// Bob's PublicKeyB consists of 3 GF(p751^2) elements encoded in 334 bytes. +// Output: a shared secret SharedSecretA that consists of one element in GF(p751^2) encoded in 188 bytes. +int EphemeralSecretAgreement_A_SIDHp751_Compressed(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA); + +// Bob's ephemeral shared secret computation +// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA +// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^239)) - 1], stored in 48 bytes. +// Alice's PublicKeyA consists of 3 GF(p751^2) elements encoded in 334 bytes. +// Output: a shared secret SharedSecretB that consists of one element in GF(p751^2) encoded in 188 bytes. +int EphemeralSecretAgreement_B_SIDHp751_Compressed(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB); + + +// Encoding of keys for KEX-based isogeny system "SIDHp751" (wire format): +// ---------------------------------------------------------------------- +// Elements over GF(p751) are encoded in 94 octets in little endian format (i.e., the least significant octet is located in the lowest memory address). +// Elements (a+b*i) over GF(p751^2), where a and b are defined over GF(p751), are encoded as {a, b}, with a in the lowest memory portion. +// +// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^372-1] adn [0, 2^Floor(Log(2,3^239)) - 1], resp. In the SIDH API, +// Alice's and Bob's private keys are encoded in 47 and 48 octets, resp., in little endian format. +// Public keys pk consist of 3 values of length OBOB_BITS, one element in GF(p751^2) and 2 bytes. In the SIKE API, pk is encoded in 334 octets. +// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p751^2). In the SIDH API, they are encoded in 188 octets. + + +#endif diff --git a/src/P751/P751_compressed_dlog_tables.c b/src/P751/P751_compressed_dlog_tables.c new file mode 100644 index 0000000..9be4580 --- /dev/null +++ b/src/P751/P751_compressed_dlog_tables.c @@ -0,0 +1,49654 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: precomputed tables for Pohlig-Hellman when using compression +*********************************************************************************************/ + + +const uint64_t ph2_T[DLEN_2*ELL2_W*2*NWORDS64_FIELD] = { +0x249AD,0x0,0x0,0x0,0x0,0x8310000000000000,0x5527B1E4375C6C66,0x697797BF3F4F24D0,0xC89DB7B2AC5C4E2E,0x4CA4B439D2076956,0x10F7926C7512C7E9,0x2D5B24BCE5E2, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x3156AAF9F437A3FC,0x36ADB2EFCCDC4BAA,0x5618FDD1B2675B29,0x7BA8B8749BAB61A9,0x66D494A30F7AC727,0xA5E1D5DBA320CE37,0x5B0FF9C6B93B3734,0x6D518D4F8AABBB36,0xF228F7553E4C4D71,0x67A8F419774A331B,0x45EEBD2B27D6B62C,0x1B752993D57F, +0x6FE4CC143684AEA5,0xFD55BE8433DA905E,0x31BC0BCB6E641755,0x2AFE733B9A86B029,0x91F740635E5D3E88,0x4F84211BFCBF0381,0x3A0AD6489F0F87D,0xCEA95458DED6266,0xC40D3986226619E2,0x5A2521420D6B64B6,0x39C5955269D225F1,0x1039A3BC03E5, +0xE826363CF9124DB3,0x3952D58B1916BCB2,0xEEAEA21ED676496D,0xE0927DE124EA9B40,0x86761313D7C396F8,0x7DABA686AA776113,0x6A8F416AA5896C10,0xFB466E1C9471DFEC,0x849C50CCDDF761AC,0x9ADE9058FC402892,0x6DC8F418F8FB3025,0x22A9055B9EC7, +0x19C41A93A43C9F29,0xB3F3E8059F007ABD,0x573DC20273467DD0,0xE487CE81FE1CB6E3,0xBEF7627C2736D07E,0xB55101C5C73A1781,0x3E91878DDEE10DC5,0x57E9613142344FB9,0x8BDB15B2D4515043,0x4CB1D70C45484A76,0x747ED5C01262FA62,0x5416484A457A, +0x7DEB51751637A9EB,0x49A95525C11B33C8,0xAD16A8ACE107A7DA,0xCE797DDD5C4C459F,0xC0D901341C334556,0x370D2570227E7158,0x54568B5AC2E2C6BB,0x2472074D84F5AC34,0x647116E3734D402A,0x881C90D74347FEA7,0x25E96DE21812FC2D,0x30B072E1FC5C, +0xAE7C1E6B93616A84,0xC1C80068DF41DEB1,0x422CC5C095AE77B3,0x16C26C47141357B5,0xE4F0146DB9EA8A2,0xC8388463CC5653C,0x494C0877DCEAAD3C,0xFA2E1BA988DA8B6A,0xF96DBDD53B344E3A,0x52AF3C05A1A0DD72,0xBFCF60C8FF0F305A,0x22B83242E90E, +0xA8F9370AB1BE0CB0,0xC736863BF34ED56E,0xAE9D1830B3D36A9A,0x635151D1599A2290,0x5D6ED4D4942DA036,0xCEE349C0289F34B9,0x386633C515D09A6B,0x6D81056DE922E4E9,0x642EEBE7896348E3,0x7B64A764C32EBA84,0x1B2F7F945368566A,0x233E3F2925E8, +0x86944FC647E71EE8,0x3BB41B1D4E95D2A6,0x5D7F1E4BE4254DBA,0x9D03A2C2F0341BA0,0x966344A3B6009509,0x286F9711AE1A21BC,0x9600D5119AC0D71E,0xC3CEACA8514865B0,0xA5754F75C5DE8A9F,0xD11B2E09ABB9C05D,0xE435788A97B4ED85,0x35332CF89FA3, 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+0xCABF5D6A44FB3E37,0x4A463EE81BE2326A,0x292B1371F2D49BC1,0xB467A4E46981CC0,0x81E9E78ACD0246D5,0x9B1A02772D0BC5E4,0x99272F66C368B766,0x123A861FAC0784AA,0x2F590470894DA4CA,0x81C5DF3CDA17A448,0x52FB592E19D1B364,0x61AB25B7DB60, +0x4DCA3B50388E0559,0xFAE384D32990D875,0x40E3A57393025DC9,0xD45F07643DE98C8A,0x8FFF53F8943844B6,0xD52AD9579C28B585,0x659B203F4B477768,0xB330E8F6D1009643,0xDA73A996FE44DA14,0x4D9117A401E123B1,0xDC7899528B71B286,0x1A882CA55E85, +0xC6A5EE3731B53259,0x80833F1AF7089334,0x1DC50C606BD6C08A,0xF0E458C36A4D6C55,0xF53E3C70964473B,0xE24DA352CEED8B82,0xBC15BA90BCC55682,0x382F1913547AAC13,0x9B6A71F2FF923FB8,0x1E6B152C3F7F55FC,0x8AD2E9910F9A6AF,0x50A702A11CAF +}; + + +const uint64_t *ph2_T1 = {0}; +const uint64_t *ph2_T2 = {0}; +// Assume W_3 = 5 therefore only using ph3_T1 and ph3_T2 +const uint64_t *ph3_T = {0}; + +const uint64_t ph3_T1[DLEN_3*ELL3_W*2*NWORDS64_FIELD] = { +0x249AD,0x0,0x0,0x0,0x0,0x8310000000000000,0x5527B1E4375C6C66,0x697797BF3F4F24D0,0xC89DB7B2AC5C4E2E,0x4CA4B439D2076956,0x10F7926C7512C7E9,0x2D5B24BCE5E2, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x61F2C46235355981,0xB14A772CB29B82A6,0xD42C0B8FC04184DF,0xFCA910510D39E137,0x7C362C336F08DC04,0x5AD83F13B81712F6,0x4F3DBBC2A96F63FA,0xA57610E390A5607,0x14C5DAF1A1626E5C,0x9E44E107664A2F4E,0x8DAAED26BBFDB0E3,0x2D6B4A339DF9, +0x3E26404B0AF5D1CC,0x500F8B5016019FE4,0x783C57F59330D4AE,0x9A63B0E9FEC0B16A,0x60C2C9156C323CB1,0x7FDE85AB8348E8BE,0xD948E42F685D4A6,0xD2620E19066F726,0xE0F7B959E1E34CC4,0xDA22A41492CA4FB4,0x45FC1205CD9A9FF3,0x647A168C97DD, +0xA3E1E0F284119083,0x54A1675AD5FCE7F0,0x367178870AE5931,0x1DDF75E74BF11C01,0xD575FEF284B33B38,0xCE98D0BD1FFEC121,0x38F63CFB654FABE3,0xE6787C23FEE5167E,0x673649AFC7CD4016,0xE94DB8301F0C3EE7,0x673E019BECC49377,0xD2F6E941025, +0x380DD270B4E38753,0x3887493104C70199,0xACB249A68C2C8A2C,0x2AF58A3740A4DC72,0xEB9FDADA18EA7B81,0xDF2B51EB589F2BBB,0x2B5D7B01DA7B98F4,0xD29718C86EF95744,0x45BE21485F9B5841,0x359BA73A6AF7D10B,0xE9A780CED50BB85B,0x5962C56E14AE, +0x6D528C376AE2568A,0xF5E98924F27E28F2,0x83BBFCC7C51C11ED,0xDF8E1157C0B2104,0x9EAC3B579A1FB0F,0x1D8A1308F31C3293,0x4F39128DBCCCF72,0x84757DC1D6865E0D,0x9077B3C839D63CAA,0x9885B3F80F35DEF5,0x5D2A7A7F119311D8,0x5E9573EBA6E, +0xEEB80519CE828003,0x5FAA4F091FFA4B3C,0x180F1C0D7A185086,0x4E39DB5A8788A014,0x92ECBDA3B525C47B,0xACBCA986C588FBA,0xB79A38862540BF6A,0x475048369F46FBCB,0x3DEA309CD1624773,0xF1C9CFC0B8AF783C,0xC976322CE2C8C02B,0x239CFFAD4B79, +0xA433E0DD4C33DD9D,0x1DB3C40D971FBC98,0x7148DFCB642ADD87,0xA90DF39D90FEB5B1,0xC30D9D6BD4D03BDB,0xFC9B4AC25D560D3E,0x655F6EB70FE2464B,0xDFB7E778CC4C60E3,0xE19C560DC64269C9,0xC31206407A0FEBFE,0x80218BA788FB306,0x1B23221F863B, +0x8C3EEBB6C18E2751,0x6D8DA6F801331A10,0x203945342960FC09,0xC21DD47346BA5B4B,0x801E1D5637E8BFB3,0x30D207D58C2883C1,0x3F0FF731C15A5372,0xA8948F3D9D05CA82,0x5699F3E728A4995A,0x978DCFFC7D1FCBE,0xB18D4EE97DB42F2F,0x50F2EC7B0BAF, +0xA78927CF314B8C94,0xCD8550A2160099E2,0x43A5069BD3B2FE47,0x61CF5B9C1CFFE0BD,0xF9075CB076B7BCFE,0x7E26934BE2ACD14A,0x8FD4EBC9B50A43FD,0xF9C0B9D603608F11,0xB8BAD7BAB7E7B8B4,0xC99B88E620745263,0x7AA683F3112BD1D6,0x7726CA73D, +0x8027986681D32884,0xDC639598DE6C7D0B,0x1331F490E5D4111C,0x96DE70470A45E502,0x4FC409BF13B910ED,0x78BA2F3829ACD860,0xE8653E219B87EA16,0x8E98824746BD30D8,0xE04A044C5AC1E23E,0x894A19390A89078A,0x4C2E506BB1950536,0x4B2B337B7465, +0x6B2E15CA156FC79C,0x77188A6E2E7D8B91,0x6CD043B43052F252,0xE1BEC7AE9D6EDDB8,0xDDA346E92E996B4A,0x2295EA20B1340163,0x1B7E59C08B6A510B,0x154984C4076E74C,0x4A41430F237B4005,0xA7AFA207DB760555,0xE1CA6D12AE3A29E7,0x5DCDDFAC4320, +0x7AED6895B0CE7BD,0xE2592AE7447D965,0x492AEEC10F601D46,0xE59AEEE4A025E80C,0xB61660758F5660A3,0xE97E78C2288FADA3,0x9CB16533AF75E84,0x5A41C21412E81810,0x20C679A70AB34175,0xED569B6A5612B192,0x56532D50825658C3,0x2623A5E90691, +0x30FD5A3045EACC1D,0x1FBDBC13BDA82DE5,0x3A3EC2934A322064,0xDBA996F38E453D23,0xA11BE6A70BEDD90E,0x45C19065005CB33A,0x4426AEED0619061E,0x76FA12F869ECC7CC,0xDA55C31FF849950A,0x1E0029A16B1228C4,0xCD59A6AD63FD8447,0x5A55677BB501, +0xFCF27604F4B08E92,0x62769B284268C25C,0xBA0CD67CD35E982A,0xB2194B734F471A50,0x9B500EBEDE8AF10A,0x863BE756685D164B,0x877A32C1F62857F,0x40FB1CE4819CCEAB,0xD5EC1C7578B6541F,0x8D692C11E1253C2B,0xC5091ED42C8BF666,0x7C6532A5A14, +0xF42F6A14628B8F21,0x8EA82569519644B8,0x4F80AE531AE0EFD6,0x3FFC70361727D330,0x734D3549A86D3032,0x5EED94A9536AEDBD,0x5D2CA5FCCB6A5C99,0x2A70FFD43D8E2A2A,0xB6D672F5F67B5750,0x3422F460E4781E65,0xE3A8FB856ECAC907,0x5CA66BCE5A32, +0x150AC998C143A5F6,0x46102EB917878DD8,0xD2C9150AEFFE6D74,0x694DE55C6265A7AC,0xCE58ABD3FA7799F7,0x1A829B6BFC595EEC,0xF45A23838B981AF5,0x6D3017F6D0E11F2D,0xFB554B978A50ECF3,0x39348E2DAFA0776,0x303B29BCD086DF41,0x43931162ACCD, +0xB43A5B7EC264A484,0xCC91FD3A4AF8C866,0xA09A12C3A46CA8F6,0x886A77C6ABEA7A11,0x9A953AA6BD9A1871,0xCA47A5D6533BE74A,0x7FBE28A88A394C8F,0xDEBFDC4033F480A0,0x96826AFAB216C488,0x2F6CBF18A8723C12,0x3F637ABBBD64520D,0x202B45A4CBE0, +0xBC28A0F4EFEF59BA,0xC5FCDD4CB236024D,0xA7F8FA7F004B2462,0xE45DF3A3A2317475,0x403B8B831862F2C7,0xB387AD1E0D9C4361,0xF88E048E2A030F39,0x6DD9A98FF681C183,0xA9A5644A4B061A4D,0x88A9191C14DCC723,0xB441BD1A86F5191,0x6D19455EDAF3, +0xD2C974E28703A95,0x175559ECB942C34C,0x7CD732A9A37F2676,0xF2FA7524199AE520,0xD16E612286D2EE3C,0xB755DB85BF9CF7D1,0x32AB8DE6D35C9B0C,0x9BC090F62B4CD17F,0xBA40606F3E7AA0D1,0xE203E9B3174F5F66,0x2F13B46444F735CD,0x653531FB68C9, +0xDA48FD257901590C,0x534CFEF849AC6CD2,0x81635EECE6895A6B,0x7A5EEEA3B37CE63B,0xA3382AE6B52A52DD,0x7CA88A5FA81D0C99,0xBFCA0451505AA86,0xBB38A5EB1964C3FE,0x698C82FD96357312,0x77F5C131F6E5F82,0x98ED1D2461C693E,0x1DB8AC87CF5F, +0xE6570173DDCBDDFD,0x4F5401BF473E8433,0xF95D519665F12BC0,0x9EE519F3F4E39C8D,0xBA1C60BBB24FADE0,0xF8C6F9E575CB937C,0x5840112F5A529F33,0xD4118A42AEA1B0ED,0xB67D3908E1419945,0x8CBB35343C590AF7,0x2CB9B99D9FC6950B,0x212A4B33D257, +0x24011EE9F6E74861,0x37DB9AD9F53BFC99,0x4E1A0877A39771DF,0x5B89DA750C844A12,0x99674C0EB0BE3A85,0xD8E85B87645E10A6,0x2D4B4BF6CC5BB090,0xDF40EF7E5D94937B,0xF8108D6EDA17256B,0x7339FCFCF73F5495,0x74FD2B4410839642,0x34E57C46D50B, +0xBCEB409B401223CB,0x97803C03A2190A51,0x3BE6A9D77A4B823E,0xB7686663E7CA86C9,0x4C2E034714E5F721,0x64428B94E70B0D4B,0xC562BECF74BFFFCB,0x7B89522C69D71ADE,0xDD68D30FF08EE555,0x820F9F35E2B8FF3F,0x4FF92D89D2BD54B5,0x68BE2983BA5F, +0x722A6DEF84D2A077,0x3226ECD43774B9DF,0x905FD3C9B1D5D888,0x6AD3CE3D7053313C,0x4004EF0D83712C08,0x601DCD6E2BBB8C7,0x782C7E9184C522AC,0xE9FEA5363B4720A8,0xEBB8649C8FF39264,0x1CFCFB9370084C1F,0xEB847AF675C0AF4A,0x6EBB36983E1, +0x81CF5DC5BE123C64,0xF75EFF5DC1850BDA,0x286AB6E7CD68399F,0xDAF45719B6E3CA5D,0x86F92B4297721168,0x3A5690E6F3BE9794,0x4A80C1CFBE34E306,0xCAD698244676F53D,0x367B4D2056B09EEA,0xA5CDDEF2EF51838E,0xFED1FFF910F75272,0xE0C28703833, +0x7D9E374864DC1729,0xB76D13AD977F4351,0xF57C91CB9BF62AA1,0x2DD6FF89B9E016E,0xB38148BFBA93F989,0xB9CB8D05032D2BE1,0x9869628E1DD4C118,0xC41FD6606CF8E64E,0xB79ADF470C090C66,0x54B7D64AD46D23F2,0x6FE6671ABCDD4A43,0x2A4C465FEA5, +0x47006F497EBA7DC2,0xCBFDCA53EED2F279,0x42EB246AC950F61B,0x68B7199113B6A159,0x45B9D2B2B9B7C7EA,0x3E7699ADEBC63231,0x3F4BA7472D6CE870,0xDDFA98B6D9AA38FE,0x42D9E26F622E4B59,0xC89A36DD10B5BD39,0xC324B7E035D9FF4D,0x6CBB2A8D2CFA, +0x44C4196FC5C17B30,0xB686657884D359F0,0x2D483B0B6357E8BF,0x1FE9A617595D2793,0x9966662A48A79,0x1FD1325058EF29BA,0x5D3DF960DC2B25D1,0x72864817B99AA737,0xA27A20DF28F55038,0x5F0DFFD131B23B3F,0xD3C39E06E366D8DD,0x1535CD95B28, +0xF52A61AC098EE59,0xA8163DA5BF15747D,0x3930FD16A113710C,0x7EB6AE2BD6BC4630,0x19AC43769B981082,0x414A79CB3C2EA22C,0x6849EB5257827765,0xD6A1CA58922BEC17,0x390BAF7DC1F81623,0xC2441B38FB750B89,0x78198FDC770A6BA4,0xAC4008A5565, +0xB4F7F71026CDFC05,0x9F23F7DBFBC17762,0xE6137C945D2BBA39,0x49459FDC7881630D,0x4026C5ACBD05EB17,0x9F4B5FEE26CE5CB7,0x8694C943FEA6AF89,0x135AA091A884AA53,0x9B74F3942952B44D,0xD2F5C34529DF13FA,0x984A4BC277878995,0x1F9A9190222, +0xF8FD9DDDE757708,0x71848F18EACA134A,0xD1599D7871250946,0x23B2F4AFB531C47D,0xFC96493C6B15FFE1,0xA0E2362EA5F7A307,0xF0808D736EA6EF5E,0x969A56A2CF71C309,0xB1F8F5FDEE8FD75D,0x9421AA13D75C8436,0x9FE6E6517BA387C9,0x533819CCD0FA, 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+0xD163EEEC1BAFCA52,0x226BDC5A477ECADE,0x40AC4CA80EC286DA,0xEB9013919BE65D37,0x233B5E7D9B2F69FE,0x341204A3134E7D6F,0x1363DF8394C6DCCE,0xCECDFE19C4E3E67,0x28E14E96AD97AFE0,0x18F93ED78262F82C,0x9304F5E4678E0988,0x67C157C7D0EF, +0x30618A859BEE98C5,0xF5CF65EF8211C35F,0x4035312FAB88F32D,0x2E44AD546D5384D2,0x7337EFC1A1304DFD,0x9DF6E7ADCB6D2B40,0x12D3F35C8D8DA3B0,0x68EB1FED0F3BC969,0x68CD511E278903B2,0x43A934813220F845,0xFB01BEC2C37EE906,0xEEE5B66AE64, +0x9C44ABD779E15A56,0x11EA1087FBEE0EDA,0x7FCDC28C4FAFC8A3,0xCB428C68CAFFB9EA,0xD0D9CC4A0976D530,0x2610F45ECE96D02,0x5D881AEF738F051,0xDF71B282874965CD,0x3C716E8549ACEF54,0x5AC39E0D4D5596FB,0x395D140F80D9A004,0x4B708019F2EB, +0xA7B544FDA5EA5F08,0xA8C38B5A8249E5A8,0x19CE471AF724B171,0x37A37E09CA748D0E,0x40AEC9F822B96607,0x3721FB72B8726DCC,0x50E05A716E7A018C,0x19A764BD22BE49D3,0xE405020FD6C75552,0xC6D510EC542924A2,0x4DACF6F5734FF2D0,0x2117EA4E908D, +0xCEBB566A37B60E1C,0x36A1BE9F5CD46BC9,0x7DFB845E80F2B300,0xECF1F85FE7D937FF,0xA39788890E0C2161,0x991192474C8CAEAE,0xA480840F27065516,0x4E9A6E91BA4B5B5,0x617C567224C17A8,0x5C5BC36A13E90830,0x8B94B2F174578E50,0x169B81A0518F, +0x38B9EBECEA381D99,0x914649F6D23D0F6C,0x2C6E47462CFFD5CE,0xD62C3048E5F23148,0x755736CAADAE82D5,0x2D586D665609D6C7,0xF817A00C919BAFB6,0x4DC4C56BECA1BCFF,0x65D74722C1A69C0F,0x2B96CB4C4B9E7EA8,0xCC56ACCCB300FEC1,0x545FDE55CFBE +}; + + +const uint64_t ph3_T2[DLEN_3*ELL3_W*2*NWORDS64_FIELD] = { +0x249AD,0x0,0x0,0x0,0x0,0x8310000000000000,0x5527B1E4375C6C66,0x697797BF3F4F24D0,0xC89DB7B2AC5C4E2E,0x4CA4B439D2076956,0x10F7926C7512C7E9,0x2D5B24BCE5E2, +0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0, +0x61F2C46235355981,0xB14A772CB29B82A6,0xD42C0B8FC04184DF,0xFCA910510D39E137,0x7C362C336F08DC04,0x5AD83F13B81712F6,0x4F3DBBC2A96F63FA,0xA57610E390A5607,0x14C5DAF1A1626E5C,0x9E44E107664A2F4E,0x8DAAED26BBFDB0E3,0x2D6B4A339DF9, +0x3E26404B0AF5D1CC,0x500F8B5016019FE4,0x783C57F59330D4AE,0x9A63B0E9FEC0B16A,0x60C2C9156C323CB1,0x7FDE85AB8348E8BE,0xD948E42F685D4A6,0xD2620E19066F726,0xE0F7B959E1E34CC4,0xDA22A41492CA4FB4,0x45FC1205CD9A9FF3,0x647A168C97DD, +0xA3E1E0F284119083,0x54A1675AD5FCE7F0,0x367178870AE5931,0x1DDF75E74BF11C01,0xD575FEF284B33B38,0xCE98D0BD1FFEC121,0x38F63CFB654FABE3,0xE6787C23FEE5167E,0x673649AFC7CD4016,0xE94DB8301F0C3EE7,0x673E019BECC49377,0xD2F6E941025, +0x380DD270B4E38753,0x3887493104C70199,0xACB249A68C2C8A2C,0x2AF58A3740A4DC72,0xEB9FDADA18EA7B81,0xDF2B51EB589F2BBB,0x2B5D7B01DA7B98F4,0xD29718C86EF95744,0x45BE21485F9B5841,0x359BA73A6AF7D10B,0xE9A780CED50BB85B,0x5962C56E14AE, +0x6D528C376AE2568A,0xF5E98924F27E28F2,0x83BBFCC7C51C11ED,0xDF8E1157C0B2104,0x9EAC3B579A1FB0F,0x1D8A1308F31C3293,0x4F39128DBCCCF72,0x84757DC1D6865E0D,0x9077B3C839D63CAA,0x9885B3F80F35DEF5,0x5D2A7A7F119311D8,0x5E9573EBA6E, +0xEEB80519CE828003,0x5FAA4F091FFA4B3C,0x180F1C0D7A185086,0x4E39DB5A8788A014,0x92ECBDA3B525C47B,0xACBCA986C588FBA,0xB79A38862540BF6A,0x475048369F46FBCB,0x3DEA309CD1624773,0xF1C9CFC0B8AF783C,0xC976322CE2C8C02B,0x239CFFAD4B79, +0xA433E0DD4C33DD9D,0x1DB3C40D971FBC98,0x7148DFCB642ADD87,0xA90DF39D90FEB5B1,0xC30D9D6BD4D03BDB,0xFC9B4AC25D560D3E,0x655F6EB70FE2464B,0xDFB7E778CC4C60E3,0xE19C560DC64269C9,0xC31206407A0FEBFE,0x80218BA788FB306,0x1B23221F863B, +0x8C3EEBB6C18E2751,0x6D8DA6F801331A10,0x203945342960FC09,0xC21DD47346BA5B4B,0x801E1D5637E8BFB3,0x30D207D58C2883C1,0x3F0FF731C15A5372,0xA8948F3D9D05CA82,0x5699F3E728A4995A,0x978DCFFC7D1FCBE,0xB18D4EE97DB42F2F,0x50F2EC7B0BAF, +0xA78927CF314B8C94,0xCD8550A2160099E2,0x43A5069BD3B2FE47,0x61CF5B9C1CFFE0BD,0xF9075CB076B7BCFE,0x7E26934BE2ACD14A,0x8FD4EBC9B50A43FD,0xF9C0B9D603608F11,0xB8BAD7BAB7E7B8B4,0xC99B88E620745263,0x7AA683F3112BD1D6,0x7726CA73D, +0x8027986681D32884,0xDC639598DE6C7D0B,0x1331F490E5D4111C,0x96DE70470A45E502,0x4FC409BF13B910ED,0x78BA2F3829ACD860,0xE8653E219B87EA16,0x8E98824746BD30D8,0xE04A044C5AC1E23E,0x894A19390A89078A,0x4C2E506BB1950536,0x4B2B337B7465, +0x6B2E15CA156FC79C,0x77188A6E2E7D8B91,0x6CD043B43052F252,0xE1BEC7AE9D6EDDB8,0xDDA346E92E996B4A,0x2295EA20B1340163,0x1B7E59C08B6A510B,0x154984C4076E74C,0x4A41430F237B4005,0xA7AFA207DB760555,0xE1CA6D12AE3A29E7,0x5DCDDFAC4320, +0x7AED6895B0CE7BD,0xE2592AE7447D965,0x492AEEC10F601D46,0xE59AEEE4A025E80C,0xB61660758F5660A3,0xE97E78C2288FADA3,0x9CB16533AF75E84,0x5A41C21412E81810,0x20C679A70AB34175,0xED569B6A5612B192,0x56532D50825658C3,0x2623A5E90691, +0x30FD5A3045EACC1D,0x1FBDBC13BDA82DE5,0x3A3EC2934A322064,0xDBA996F38E453D23,0xA11BE6A70BEDD90E,0x45C19065005CB33A,0x4426AEED0619061E,0x76FA12F869ECC7CC,0xDA55C31FF849950A,0x1E0029A16B1228C4,0xCD59A6AD63FD8447,0x5A55677BB501, +0xFCF27604F4B08E92,0x62769B284268C25C,0xBA0CD67CD35E982A,0xB2194B734F471A50,0x9B500EBEDE8AF10A,0x863BE756685D164B,0x877A32C1F62857F,0x40FB1CE4819CCEAB,0xD5EC1C7578B6541F,0x8D692C11E1253C2B,0xC5091ED42C8BF666,0x7C6532A5A14, +0xF42F6A14628B8F21,0x8EA82569519644B8,0x4F80AE531AE0EFD6,0x3FFC70361727D330,0x734D3549A86D3032,0x5EED94A9536AEDBD,0x5D2CA5FCCB6A5C99,0x2A70FFD43D8E2A2A,0xB6D672F5F67B5750,0x3422F460E4781E65,0xE3A8FB856ECAC907,0x5CA66BCE5A32, +0x150AC998C143A5F6,0x46102EB917878DD8,0xD2C9150AEFFE6D74,0x694DE55C6265A7AC,0xCE58ABD3FA7799F7,0x1A829B6BFC595EEC,0xF45A23838B981AF5,0x6D3017F6D0E11F2D,0xFB554B978A50ECF3,0x39348E2DAFA0776,0x303B29BCD086DF41,0x43931162ACCD, +0xB43A5B7EC264A484,0xCC91FD3A4AF8C866,0xA09A12C3A46CA8F6,0x886A77C6ABEA7A11,0x9A953AA6BD9A1871,0xCA47A5D6533BE74A,0x7FBE28A88A394C8F,0xDEBFDC4033F480A0,0x96826AFAB216C488,0x2F6CBF18A8723C12,0x3F637ABBBD64520D,0x202B45A4CBE0, +0xBC28A0F4EFEF59BA,0xC5FCDD4CB236024D,0xA7F8FA7F004B2462,0xE45DF3A3A2317475,0x403B8B831862F2C7,0xB387AD1E0D9C4361,0xF88E048E2A030F39,0x6DD9A98FF681C183,0xA9A5644A4B061A4D,0x88A9191C14DCC723,0xB441BD1A86F5191,0x6D19455EDAF3, +0xD2C974E28703A95,0x175559ECB942C34C,0x7CD732A9A37F2676,0xF2FA7524199AE520,0xD16E612286D2EE3C,0xB755DB85BF9CF7D1,0x32AB8DE6D35C9B0C,0x9BC090F62B4CD17F,0xBA40606F3E7AA0D1,0xE203E9B3174F5F66,0x2F13B46444F735CD,0x653531FB68C9, +0xDA48FD257901590C,0x534CFEF849AC6CD2,0x81635EECE6895A6B,0x7A5EEEA3B37CE63B,0xA3382AE6B52A52DD,0x7CA88A5FA81D0C99,0xBFCA0451505AA86,0xBB38A5EB1964C3FE,0x698C82FD96357312,0x77F5C131F6E5F82,0x98ED1D2461C693E,0x1DB8AC87CF5F, +0xE6570173DDCBDDFD,0x4F5401BF473E8433,0xF95D519665F12BC0,0x9EE519F3F4E39C8D,0xBA1C60BBB24FADE0,0xF8C6F9E575CB937C,0x5840112F5A529F33,0xD4118A42AEA1B0ED,0xB67D3908E1419945,0x8CBB35343C590AF7,0x2CB9B99D9FC6950B,0x212A4B33D257, +0x24011EE9F6E74861,0x37DB9AD9F53BFC99,0x4E1A0877A39771DF,0x5B89DA750C844A12,0x99674C0EB0BE3A85,0xD8E85B87645E10A6,0x2D4B4BF6CC5BB090,0xDF40EF7E5D94937B,0xF8108D6EDA17256B,0x7339FCFCF73F5495,0x74FD2B4410839642,0x34E57C46D50B, +0xBCEB409B401223CB,0x97803C03A2190A51,0x3BE6A9D77A4B823E,0xB7686663E7CA86C9,0x4C2E034714E5F721,0x64428B94E70B0D4B,0xC562BECF74BFFFCB,0x7B89522C69D71ADE,0xDD68D30FF08EE555,0x820F9F35E2B8FF3F,0x4FF92D89D2BD54B5,0x68BE2983BA5F, +0x722A6DEF84D2A077,0x3226ECD43774B9DF,0x905FD3C9B1D5D888,0x6AD3CE3D7053313C,0x4004EF0D83712C08,0x601DCD6E2BBB8C7,0x782C7E9184C522AC,0xE9FEA5363B4720A8,0xEBB8649C8FF39264,0x1CFCFB9370084C1F,0xEB847AF675C0AF4A,0x6EBB36983E1, +0x81CF5DC5BE123C64,0xF75EFF5DC1850BDA,0x286AB6E7CD68399F,0xDAF45719B6E3CA5D,0x86F92B4297721168,0x3A5690E6F3BE9794,0x4A80C1CFBE34E306,0xCAD698244676F53D,0x367B4D2056B09EEA,0xA5CDDEF2EF51838E,0xFED1FFF910F75272,0xE0C28703833, +0x7D9E374864DC1729,0xB76D13AD977F4351,0xF57C91CB9BF62AA1,0x2DD6FF89B9E016E,0xB38148BFBA93F989,0xB9CB8D05032D2BE1,0x9869628E1DD4C118,0xC41FD6606CF8E64E,0xB79ADF470C090C66,0x54B7D64AD46D23F2,0x6FE6671ABCDD4A43,0x2A4C465FEA5, +0x47006F497EBA7DC2,0xCBFDCA53EED2F279,0x42EB246AC950F61B,0x68B7199113B6A159,0x45B9D2B2B9B7C7EA,0x3E7699ADEBC63231,0x3F4BA7472D6CE870,0xDDFA98B6D9AA38FE,0x42D9E26F622E4B59,0xC89A36DD10B5BD39,0xC324B7E035D9FF4D,0x6CBB2A8D2CFA, +0x44C4196FC5C17B30,0xB686657884D359F0,0x2D483B0B6357E8BF,0x1FE9A617595D2793,0x9966662A48A79,0x1FD1325058EF29BA,0x5D3DF960DC2B25D1,0x72864817B99AA737,0xA27A20DF28F55038,0x5F0DFFD131B23B3F,0xD3C39E06E366D8DD,0x1535CD95B28, +0xF52A61AC098EE59,0xA8163DA5BF15747D,0x3930FD16A113710C,0x7EB6AE2BD6BC4630,0x19AC43769B981082,0x414A79CB3C2EA22C,0x6849EB5257827765,0xD6A1CA58922BEC17,0x390BAF7DC1F81623,0xC2441B38FB750B89,0x78198FDC770A6BA4,0xAC4008A5565, 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+0xA7C32866A3CA9184,0x5182E0016B4BD5B0,0xDAB4C2039EC1C8D0,0x961F52A85ACE91DC,0x56EB3ADAD1A29D70,0x66A79D915229590C,0x3FA3654C1DCF439A,0x734BB6297043A009,0x134EF8C2B0234D50,0x372A03E5A05B21CC,0x36DE816541AFB17A,0x1D59B6BF184E, +0x908FD2146DD4A608,0x8ED2FD151F6541E6,0x18D852207393315,0xBC343FA9851267D5,0x2A7994C2AE5FAF88,0x62440CADE5B04D98,0x578CD669922393F1,0xFF570620D1C36D67,0xCF2392601E37EEE6,0x498B94C60E8C153,0x4FCE3BD0B18CD265,0x2A8D203C9EF3, +0x6CF4FCA7507CEAA,0xE70DEFEFDBD2D640,0xD22B03EAEF8DE729,0x22721260E8046D82,0xBFC5C096F141B6E,0xA7501AE062B57F1C,0x64D81F43E11C61E3,0x8D829DDC3AB747F,0x951C28BC9CFEE07C,0x70602ACB064C366,0x19630B43C42F7B54,0x6C29FBE9A80, +0x7688492D4D9A154,0xF6612698545D6D3F,0xFD8F17BACB6862D6,0xB4B7CA90E51030B8,0xF26BCA1B94A8F017,0x73617832BB7A1D27,0xC3FB18762891A59,0x6E5C1D3B4EB7AC68,0x39DC0AA98E5412B8,0x290ACBFD72A4FE1F,0xAA065999F37B9C76,0x3FE8B7E9F69C, +0xCEBB566A37B60E1C,0x36A1BE9F5CD46BC9,0x7DFB845E80F2B300,0xECF1F85FE7D937FF,0xA39788890E0C2161,0x991192474C8CAEAE,0xA480840F27065516,0x4E9A6E91BA4B5B5,0x617C567224C17A8,0x5C5BC36A13E90830,0x8B94B2F174578E50,0x169B81A0518F, +0x38B9EBECEA381D99,0x914649F6D23D0F6C,0x2C6E47462CFFD5CE,0xD62C3048E5F23148,0x755736CAADAE82D5,0x2D586D665609D6C7,0xF817A00C919BAFB6,0x4DC4C56BECA1BCFF,0x65D74722C1A69C0F,0x2B96CB4C4B9E7EA8,0xCC56ACCCB300FEC1,0x545FDE55CFBE, +0x96FAFBE5FEACB5B9,0x8ED4706293642332,0xE68A928EF4A51381,0xAFF7849D6EAF9DD8,0xFF3E2FDD9BFE5384,0x66935A59D28F28D1,0x23E95524C79B443B,0x9402619CCCC69DE,0x32E20981CEDA9020,0xE1083952A4FD604F,0xA52D96C4C04486F6,0xFD12D8DD918, +0x3F2193B007F94451,0x218BA0142B762379,0xE0AC89829AD36EAA,0x99176AE5E65871E9,0xF933DD5B19F45071,0x52924C1CCF9F7CDB,0x43F0A62E14BDFB67,0xB0ED716F9D8F438,0xF7FF0107A43721CF,0x6A9549265770C178,0xFAF3F28224E910B5,0x480EC0AA2924, +0x9229A6C4682E4E40,0x6F470794BA7DBB44,0x103B84AB358E7047,0xACF1C9BE01916015,0xD192FE463BB984CC,0xA139C55CB77A7C68,0x59BCF21EE52C20FC,0xA3F6144E232117D2,0x23E3B638EC423A24,0x3ABB650B709E69C1,0x6CBD173D5C55A2C8,0x62523C7071E3, +0x2490688EF6641F64,0xD2886BB71C7217A9,0xD55C2CB472835AD7,0xF27C5D0CE9033912,0x2106FCABBC698F4,0xDFFC413F5240BA47,0x8CAB7B71E921E8DD,0x6E050F585E76831C,0xF3B4E5499D3DFB4D,0xA9F851E0609B877B,0x2D4A93E8629764C5,0x6729A2B1C35C +}; \ No newline at end of file diff --git a/src/P751/P751_compressed_pair_tables.c b/src/P751/P751_compressed_pair_tables.c new file mode 100644 index 0000000..d70e224 --- /dev/null +++ b/src/P751/P751_compressed_pair_tables.c @@ -0,0 +1,11018 @@ +/************************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: precomputed tables for pairing computation on E0: y^2 = x^3 + x when using compression +***************************************************************************************************/ + + +// T_tate3 contains 6*(eB-1)+4 elements from Fp. There are (eB-1) 6-tuples (l1,l2,n1,n2,x23,x2p3), each corresponding to a single step in the Miller loop. +// The values l1 and l2 are the slopes of the doubling and point addition to compute the tripling, n1 and n2 are coefficients of the corresponding lines and +// x23 and x2p3 are the product and sum of the x-coordinates of the intermediate double and the tripled point. The last Miller iteration only needs four +// precomputed values. + +const uint64_t T_tate3[(6 * (OBOB_EXPON - 1) + 4) * NWORDS64_FIELD] = { +0x27DD15B8A940103C, 0x698445579C6FC8AF, 0xEF0662EE3F8DA506, 0x93D4F81B06781F60, +0xC74371742E7C108A, 0x3101E9FA3DF1F2D, 0xF5326D30834BAB52, 0xCC65719BBE7A0F07, +0xDDE26695C63C52A9, 0x5EF3096F1CC1375B, 0xC294077DF435C984, 0x82F3986076B, +0x3473C9FA7E5404DB, 0x4F95A1FB1D629EA5, 0x712BEDC72A682C10, 0x1DD108940590DB2D, +0x88BFC71946DE8BEF, 0xE41ADDF572557D71, 0x7552B158479D3FFF, 0x99E1BB53518B911B, +0xAA15601D2EA66BDF, 0x3BB21CBAC6C72B06, 0x5AFDB90E6F37C129, 0xAD8B9D22E50, +0x1D03B8B14750F050, 0x1545B963A3FBD292, 0xABF9110C1B06DEDE, 0x3FDFF9C8BD2736B6, +0x98C7049844B874A5, 0xAE5AB4D180ACDFF2, 0xB2B03879747E80D1, 0x466061A914E71020, +0xEF39255AB2765772, 0xF44DAF12BF260DAA, 0x63A33411506608DD, 0x35F8D0942C29, +0x4C41EF1D22E3730F, 0x68090B20EA18192E, 0x935C391908CFEB88, 0x907417F890C3D4A7, +0x62730A7D330A3A4, 0xA7E28590A7B8CC24, 0xF119C30CAEEE2222, 0x9F57B7D3E735D202, +0xE96A09A47460C945, 0xCDE908B9508F202F, 0x2A5610F61338D28C, 0x62D46F8CD535, +0xF506C72790301F65, 0x81BDE514D427C37D, 0x73EB4DE892519A96, 0x36AFF40874618466, +0x5D53626AF47DD1DF, 0x8C694A59134848A6, 0x87DECA426BB0D72, 0x5B9B923DE58AC167, +0x6B73AE4AAF31F30, 0x2202F66A5F525580, 0xCD5448A1EA96723B, 0x6EB824809EF0, +0xC195DE8689A2FD6C, 0xA109A88AE0397829, 0x9A0215273010AC45, 0xAEE291C7219346BA, +0xBA84BFF92BA1FA28, 0x8E97DEA0B08DBD63, 0x582399FC4165E40E, 0xB33116A920516714, +0x18BBC373DBA7F1D8, 0xCDB31D989C06D0C, 0xF9C8FBCC8D34E576, 0x6C6114FAA9A4, +0x48C137EE4E478CAB, 0x44E62599FAAF4E06, 0xF05611486EBB7304, 0x501FF325BA0B6ED, +0x611F4852609A1831, 0x6C6AF3F43FBAAC0E, 0xCDD201ADF7CCF097, 0xA7407BF8B95DCBC3, +0x1D2C7DCDECF6EF56, 0x189A58984ABD279A, 0xCF741A50B523FF00, 0x470A2BBBBEB6, +0x1CDAE85F214D6C32, 0x749F9F77D1BF2C46, 0xD9945F9BAD81FC58, 0xAAD1FD641B6DF6B, +0xBF3AECABB7688DF7, 0xC7F088F8A1AE546E, 0x7ECC318544EEAE08, 0x1EC797D23BC3BDF3, +0xB78BA5063DADD7E, 0x472A6CB0E73F8649, 0xF1EFDE3F8C775A21, 0x3D3C79A41BA3, +0x654890F70F254EE2, 0x46FCF3F802DC1863, 0xBC2ACA8732057A49, 0x4793578578918662, +0x13F9D2A8055FC5B6, 0x95134A341F47A377, 0xB02678E2FFC3F9A7, 0xB15EEDA559408FD3, +0xDF5928147B9874AD, 0x5AF25AFCA56C562, 0x5AAF5F2A26F70AD2, 0x2999090B0934, +0x24AFE67E904D1E7B, 0x70A4296D4480E374, 0x7D47CEBFCE196041, 0xDBC6EB8FD8C2AD30, +0xA2715D74F3DE2FEF, 0x65E9AE1945DA8895, 0xA304C3917064E243, 0x68EDE55B09294838, +0xEC2B4DEC447F24FD, 0x7B8D6910FF878D1C, 0x7ED7122B09453E64, 0x4C1E3D9693BB, +0xB6F7D6D95CBB4A5, 0xF77208B181FAA21B, 0x837E9B2C63489521, 0x5C3B23B45DDC65A2, +0x40E8385F8AA6531D, 0xD4979ED3226C8D19, 0x5CE67536708B4C93, 0x7FD383B8B5A7AD28, +0x7CA14C29E46E05CC, 0x47C5AA8788B93085, 0x5E1AD8ACE0854B42, 0x4D9D3D953582, +0xB7B6435234F3E181, 0xE0D2D28F51DB59A9, 0x1247DCA8EC56E66, 0x35DED45949912A31, +0xC1864744A027371B, 0x5808F8ADB370D498, 0x5F67E3655A0AC3D2, 0xCB39B4CFD962C12F, +0x9BEC506F8F1D0B12, 0xE7175121352F092A, 0x5490EF8254BD37C6, 0x4B8A61AF6106, +0xAC349D1FF4D13AF1, 0x106F79E101351FF3, 0x877CAA38D78128A6, 0x6B9A534E6A0F9DFE, +0xC2A783F3AE8594C9, 0xBD4CC798AE2F6E58, 0x2EE9F13CAA22059C, 0xA457F0F9FBAB66C8, +0x79657BEC936CA9E6, 0x8D5BA16E8C374059, 0xAFAC28183088CA3A, 0x69A201357D0D, +0xED04AC1653CA8AF8, 0xA80878C3C3A2EC1D, 0xD1EA429583D566AF, 0x9271AE45BAF46187, +0x1DE359199DA053A2, 0x8D86898DC3A9978, 0x1CFF69D03680A86C, 0xA2C1C9F40713AD4E, +0x63FF6C657242F3C5, 0x40D3A82B83777930, 0x6A516DC1B80F7710, 0x378A446595C2, +0xC8C8AE7E5672FAEF, 0x80A2BA4299C33A15, 0x853896A3C8583D3B, 0x6EC191226EA30988, +0x47E271D3D9C1170F, 0x9511548DA4C7B80C, 0x84B50C649C598D1D, 0xA2369DE7C229779D, +0x856EB3DB68C61F41, 0x4A6C91708809DA6F, 0x970E45E9AFAE435, 0x208F25F4E4CB, +0x47DB16A45D143655, 0x9EAFFAC87CCC30A6, 0xA161771EC1CB1744, 0x5F37A551302E97AF, +0xB339508C6DA1022D, 0xCA7D139BDEB79F5D, 0x11030EFD06466CDB, 0x948B13D5806C8D94, +0xD95D27B24AF17C40, 0x83FDF65F891DC33A, 0xE441CA7ACBD588D7, 0x269BC8FC9DD2, +0xFE228564FDF4EF1C, 0x8C949CFEA47F9942, 0x77A75FE6BE359434, 0xFA22B6F8523DE1F1, +0x420B7C9B2B0A0DDE, 0xB9D6D9C4E1D20A20, 0xC3C341C47A8635D2, 0xF9A76E97B05E321B, +0x54FB524CCA4FDE38, 0x3BE8E5DB94358FB, 0x20ED2FDFC8CBAF60, 0xDABCE633FB4, +0xEA9C32970A9B8B5, 0x35681AFA2347A2E2, 0x9C4FC5C401B191DC, 0x828FA2ADED7A2ED2, +0xA6103BCA059925B4, 0x64945E98A706218E, 0x72DD13BF9BB6EE98, 0x81DDED0E81E39B57, +0x7B407F083BA79458, 0x8AE8B5D83EE8C976, 0x260887045E98D20B, 0x67878FC0F05E, +0xE25C55A99945618F, 0x6A2AD616786FC92B, 0x2A73072F3B4A43A9, 0xF1C4FFCFA82A00E2, +0x576E1E868C3889EB, 0xE655C9AEAE0D7A3A, 0x55CFF76DB1B5DBA8, 0x3E7F1679B83FBC2C, +0x152AE6198CA610DC, 0xC14EF0497313D1D2, 0xAE9BA246913C7355, 0xE7DFAFFD70, +0x9674F55496D1DFB3, 0x7004C6D79B3A8497, 0xFEB3FC07FAAAA026, 0xB34968F053876B2B, +0x62DE0C3FFFF1BC77, 0x8629B80CFB5D3143, 0x1498A8BAC617E694, 0x6B543C3E2C98415D, +0xCA9E36A9BF66112D, 0x2D0D7C15DC485C7A, 0x1A3112A026AAD4E, 0x398BFE09B, +0xDBB77D7DA7DF767A, 0xD594D4FD412F95B0, 0xA9F5D84FF021EBE8, 0x3D78BE5CA9727EFC, +0x85076F15E9824C73, 0xA05598C1A3E8D5F, 0xB66FF100E28DE4C2, 0xE27187F3CE2AF4EA, +0x556EB1F8DF44EE32, 0x3A21C08AAD6169FC, 0xE6F76B7A13B795DD, 0x1BBB94C87EE3, +0xECDAB5BA1B165D15, 0xCAB602B7DDE22388, 0xB41892CF77242694, 0xBB672311D503EF7B, +0x128037FD702B97D4, 0xDAB844A0A56E9E52, 0x67ABDC0A3DB2FBC2, 0x4732C6D17373D3E3, +0x5D6EA883C4DA2E1E, 0xAD180ED09AD8FB52, 0xB8C5079048AA54, 0xE7E87AB8651, +0xE781228F72419840, 0xC51481F3C47F0B6A, 0x4CDFDF0B613C4430, 0x13EA7A47D47FD86F, +0xA024404100BFFD8, 0xE9B9499124064C9E, 0xAB2C978DB8186B0D, 0x6B6AD7225ED4C3F3, +0x154ECC643AC67650, 0x9E05A829E4BF69E1, 0x26082BB007CF1FB1, 0x6828C0A86A4C, +0xA6FED9510B44DBE9, 0x9D79F771023F2DC6, 0xAE4F73C196CDFFBB, 0x379046A26A342B1D, +0x44F023F3E05C312B, 0xA5DE3DB75A486BC1, 0x86371784CC327395, 0xF0CAF621E8628D7B, +0x368586F1A0000799, 0xDE3A07F4189C0502, 0x61B02BA6D5BF3122, 0x10BFF23BDEB8, +0x108F3B472021BE40, 0x1E49DE9A1F923FA2, 0x4D96A0CA68577C45, 0xCD21F175B51728A7, +0xFD4A6C7ABE6C7CF5, 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0xAE2A8248E6A96603, 0x89DC8751BB87AD59, 0x69594717F588D730, +0xB1676A4FE6359901, 0x5B458B60706C4F8E, 0xE30F6D6AC1430FAF, 0x716CD773F0E3BE0, +0x4D5504838FD61D05, 0x2F17D6546EBB81E1, 0x4EEBD1D6645F6F6C, 0x1A98BB8810D8, +0xFAF84DD265BFCF47, 0x2994E377DAD4E8ED, 0x3A002F0D0A1866A0, 0x2995F03FCAF9DBF0, +0x41A38DE91D61F658, 0xDCC6D75D6B55BEE0, 0x86C9405F1A96EFB2, 0x3034B72904386C0B, +0xB0A6B51563ABAC62, 0x990C6E7FB69880FA, 0xBD760D13300FF5E3, 0x122CC60DDC9A, +0x56E8A60558E199B6, 0x274948419BBBF650, 0x8C1F74719A898ED4, 0x607978458D264C38, +0xC947FE83D89557C5, 0x39152089B89B40EC, 0xB20E8171081D128A, 0x51FEFEEF8000BC08, +0xE8CD09BA9B329784, 0x7885B3E983D9EDDC, 0xFA5CED75B525F0BC, 0x20C90E71CC8D, +0xBF1DBEFACE905B5C, 0xAAF8E22B65B3C1AF, 0x5ABE5066A7A0080, 0x4918B53D45C71A12, +0x2A0B82E18F9FA131, 0xDBEB35BE2BE653D5, 0x501811FF6C6CE486, 0xAB038B187A1BF7CB, +0x85ADD4B0FB003B9C, 0x26610FF3EDA2FD, 0xADC131B9B96CB638, 0x5FF7CBCD82F6, +0xA872907E10C48950, 0xFD3CD1E53B8BEE4D, 0xB9782EFE81B7D169, 0x106C8B08F55CD6B, +0xAC8AFD00A4BF95F2, 0xBAA05D060A5446, 0xC30829C3B40B8F7D, 0x970104C092394F62, +0x59EDC1BE4011336D, 0x84A1A72482A2D3A2, 0x5B49C9C509C083DD, 0x207FEFB3893A, +0x473A2E91E160E3A7, 0x569E9C68D53A22C0, 0x58699AE6E8AEEA5E, 0x49195CBD673B727D, +0x46B994FB372EA416, 0x2D6B25B8D039E01D, 0x675B03BEE62E325B, 0xAA74C1B5DDF48A61, +0x562621BEDE69A3E, 0xE0330EC256D773F5, 0x417F4C28FBA46F57, 0x4099C579D87, +0xB32E0041134A34F0, 0x3370A43D85D059C1, 0x52EF725DE7A5E9D2, 0x5BE40C0E283F8515, +0xE2AA999A0AEE122F, 0x1F08BCB36AD80CB6, 0x1268729561AB734D, 0x9FA6D96317077000, +0x9F50AD897B9E0920, 0x849CF72ABCC93B5E, 0x2D2AB79102F8DA25, 0x3BB804BA4E11, +0xEBD8AF2ABDF0B2CB, 0x28B9EEC89B69215E, 0x813647CE1D8D931E, 0xD6B11907CD6C37E5, +0x7DA2297D2D4B528B, 0x2B9C3CFA6B638921, 0xA21CD5B24A6DDA41, 0xAC5DC5661635DA5B, +0x33360CB7820837CB, 0x92F86D1AABDC5CB4, 0x4B1C48B68D2E90AD, 0x297BDE937B92, +0x5592B04EA0F4DCD1, 0xCAE00288CC5C79AF, 0xEF28822A7FE1300E, 0x49804F824D14B71A, +0x2E477E78C3D6910B, 0xA22BCE94F6551602, 0x60A9820856FBF693, 0x7E42733A6F6618A9, +0x29406576E06A6DF9, 0x2CBF4465F9439B6C, 0xE37B541FAB689300, 0x5D616B5F1649, +0x82AFD7F2ACEF3318, 0xECA7A6EF2B1F55A6, 0x3E7571E9CDDF810C, 0x27BF287819E444C2, +0x3E9B3848807FC0BC, 0xE8CFD9EBD6009415, 0x159667488F81E676, 0x5041FE39046FC7B3, +0x82DC2577E5C91F4C, 0x4198FA83F6796F58, 0x2AC5A4F96E5FCE24, 0x3CE66C899C43, +0x1C9F6A5718262FF0, 0x75E02A7A0A7E8B33, 0x9BB4233B518F13BE, 0x99CFB686A44F94EC, +0x8AA07F104A7AFBFC, 0x1E13D49D1B0DDC7E, 0xEA371165C5328D48, 0xEC5C0CB7FD9A3579, +0x21D9030F216BF8AA, 0xBC9BD83626BF8EBB, 0x644C9F03387ED80D, 0x3D5B98F6B919, +0xAD873DD76971F844, 0x148EFE7DA6353006, 0x565798EC192823E0, 0x9D669126755B4F09, +0x8446536EDF0EAED6, 0x2A9BD249A44097BE, 0xB1C62F93F3A314E1, 0xC893597285E6FDD7, +0x24065586B095F5C9, 0x1BD57515721D32E4, 0x59CD981D14024E73, 0x5AC153EB18A2, +0xEF4807553309D43E, 0x97442BCFA652CA0B, 0x591E9AFB714626F, 0xF0F3529150D265A, +0xE1193266710B8FD8, 0xD68DCC81638F18AF, 0x137D13D195E681A5, 0xF28D9270C9810A7B, +0x7EAD684D345A7B02, 0x4001EDD6F14A4924, 0xE2E53FC05F7A9C29, 0x16567231518E, +0x4A9E9037F98AF45E, 0xA65FFA9888CE9458, 0x6F4162FA5A1B8306, 0xE150308D8C319661, +0x2921D73E3A8C2002, 0xC40A192BD44C7618, 0xCD4F2E2DDAA764F7, 0xCFC68584BBB3F358, +0x4DB2A104FD8839E7, 0xC2F226ECBBC1FD40, 0x5243EAD493E93AE0, 0x3B777BBE4D73, +0xDD27B65148F58B21, 0x99CE55CFAE7BD55, 0x41C27D52B8DD1B04, 0xD605F6A781D905A7, +0xFC8427F430961DC0, 0xF28A560DBCA10016, 0x8BE20C0F0AB9A17, 0x91C6975B9C8E13FE, +0xEEEB1BE1CE213D7D, 0x81682DE0B068DE83, 0x74F8772F011ADF8C, 0x3C832A035C75, +0x5C46243F2505F67C, 0xBE8E2558543ACDD9, 0x1819A7C1A984144, 0xA7AF17A10D68C153, +0xAFD8E0168E603A4A, 0x67EE073C47F3E727, 0xBCAC6F31E6A18C5F, 0xE6A3D1EADDCF785B, +0x9384CF80965085F5, 0xF0B5DA198A9022F3, 0x2EDCACA691C05E6E, 0x2CA9FE826708, +0xB87C1B0CAD255101, 0xE403B3BD778C2AE8, 0x8202C15FF7121651, 0x9DFEFAE27853AEE7, +0x808E1B258BC1BB28, 0x4574F026DA7C21CD, 0x637491F38E090941, 0x71519947250FA1D, +0xE7ABC8AB4229EB1E, 0x861D099B45513766, 0xE6C7852EA7745969, 0x2C67D7E28815, +0xE594A044472E24D6, 0x8EA82E65887346C2, 0x6580EE2CD94C2759, 0xD51ACA3DD30329D2, +0xCC2F8A6377BBA702, 0xA135FC550A145E20, 0xD9FCFB2FD152D5DC, 0xBAFD5EC5D2E68C48, +0x8294929F99552F90, 0xF62D08DD945A7C0F, 0x8DB4C7CDCD164F35, 0x271550F58E9B, +0x72DE58B51ED072AC, 0x916444EDA54D70D8, 0x337CABB249A2D78, 0x3EF5C8E3A95898AD, +0xBB86C8FFBB410F1B, 0xE35066B5FD75AF82, 0xEDE93498E0AEA548, 0x649AD826C683EDAF, +0x8B863FBB760DD697, 0x9E9BF2112C93F1, 0xC1F9A5D9A3C6A744, 0x49072A18B861, +0x21D4645EC2479699, 0x98E50C29BA3BFF08, 0xFEDCFD89C45CB3D0, 0x72622C801771915C, +0x12F906626AC5F963, 0xCB0523C3EA33B6AF, 0x88861D2DC63B38BC, 0xBD8C32B332CEE45E, +0xC778D05DC9BE3502, 0x17507D845ED2A340, 0xDE16DC52FBB15FC4, 0x41155D6C7FE0, +0xC48514EDC6A1DB39, 0x75FDA2BC43BA3AF1, 0xB69DFCD14002FB88, 0xBF06B1DE5B9B5BA4, +0xFEA60A69D7EFC099, 0xAF900413A8196390, 0xBCE92944AB61FD9B, 0x2A7AE6FAA73A0401, +0x3C55C81A8E9B3DDB, 0x36B6DB77F7FC0B53, 0x38BA8EDC06925BB2, 0x8FF1A28B409, +0xE7B6EAD96D22C10D, 0xC023ED73C9F17531, 0x882CDAF7006E2CF2, 0xAAC7917E8C0BEFCC, +0x1B58887427AEC615, 0x2C5688CC702ABF38, 0x558FF8322E7C4FC3, 0xC1B78E732B8CFCA8, +0xB980C6939B6A645A, 0x291F2D3214D6B5E6, 0xF3433BCE1682F401, 0x5167C5D46E82, +0x538D960CF5692731, 0x7D429FFA46F16921, 0x4B6BDEFE408ABF4F, 0x8A40B431585CBB16, +0x5D5E212DA0D27521, 0x9E20450523E93FF0, 0xFD2853410F769E14, 0x3465805DD153DF6A, +0x86B63EC6DF75B976, 0x9CD9D6BC2B705E6E, 0xDA9AF6207873B0B2, 0x2CDDF260F89, +0xA6D91EED026C59AD, 0xC991BBC99292FF6, 0x30602CA7CFA46BFD, 0xBD1D5D8D8DEAB6D4, +0x37FFF673774F5043, 0x5530C32732D10C72, 0x2BA4CC06F348C855, 0x4E37F63D39A347ED, +0x35CE6FE190234E18, 0x5F67EE7929273252, 0x43901A1F9205540D, 0xFCC4249E0F2, +0xAD8C2816A5543E4A, 0xF866DFF2B44C08AF, 0x6CBCED1351585705, 0x9FF95050A6F9767F, +0x482A222772C3614E, 0x9A0B41583E16DBBF, 0x41ABC0FB4F7F7656, 0xF037BCD40D1DE9FE, +0x8C7D24E106EC5482, 0x6EA87BF9D6CBEA03, 0xC0686582F37F606B, 0x3C77AD8A76CB, +0xFD243F6D77815D12, 0xBAC5D551A15B3BBE, 0x33D1313AD315B317, 0xF2AB507E47305EA3, +0xE75F065D5A6EDC6, 0x243554E664E66330, 0x85D19215A81972B3, 0xF5D41CAE76255AD1, +0xD5DB6C54CCC93376, 0x4D0EBF032182CDE0, 0x870E0A5857B790E8, 0x296654761D15, +0xAC803BCC634B0BF3, 0x900831CCCBD9988D, 0x33FF3001884BDCE2, 0xA8B96C556F2CABCE, +0x80C4CA0A3A8AF393, 0x3D921F229120EB0A, 0x52C1A3C49A8957A1, 0x7F3B5DFF658BACE7, +0x451BC28C6E0C867C, 0x3DBA60A7FD58A5A1, 0xE756D3273E07FD02, 0x69F9567C54D7, +0xD495D8FC5839BF37, 0x9A785D9FC13B8EAE, 0x1DA50AC60F0D1254, 0xB1CB49C1D73A6A51, +0x4F2B7809A6C4A1E5, 0x659D48652B33FADC, 0x80CD6D2820478944, 0xFD926CBFE82B90FF, +0x95A1D0A77CD72C5E, 0xC7D3667659B83E41, 0xD343852972887C37, 0x6C5B9322CA29, +0x3C06B9FD1EB59EB0, 0x8C564E07BFA9DDD0, 0xBEB9EFA42F10B0DC, 0x1AEA14E3E2E72309, +0x72523D009332E87D, 0x42951E0B2F9BDDFC, 0x112BF989D65F8A51, 0x2421443DF7B4D8AB, +0x9EBCA97A8F2A9791, 0xA3DEBD29B9329962, 0x7046B0DF5D35650C, 0x6EB5DAA5B102, +0xF6C5C005BEA71D9D, 0xDE5D1178508F89CA, 0x28287223D20DEBD4, 0x7FD4A49738B33552, +0x5E736A0F4C79F74F, 0x9D13FDBDF827B939, 0x1A58CB00918525EF, 0xB91963EE3EC1E364, +0x3A85101A1E624E3A, 0x97268A9459FF7105, 0x3450C9EB02B50ECE, 0x4EC30888784D, +0x4D592F8247769FA7, 0xD17CBA765F287921, 0x9446269E8D71CAD2, 0x2E4677954CF006C7, +0x7C4FB4BA5FEC0F87, 0xBC35924F67C4959E, 0x933BB6614A569C91, 0x27D696D000EE646F, +0x28E458D5821312CB, 0x6EB36AF7A660C39F, 0xB2278225246637DF, 0x3E1CBB0D6DA4, +0xC879BFB23DE4EFE, 0xCB595BE837459E02, 0x7A4BE19C0640FBB5, 0xA31B2D25D1887EC4, +0xBF43B4F8E2C560FA, 0x3410900F232FAEB1, 0x5424E0472FC29A9D, 0xD8086249385C355B, +0x7BE33589DC03FD95, 0x7A2E2BC6453DF00F, 0x20A139DFBD02D0D9, 0x3FFBF7D81C34, +0x3671CF959D17BDD2, 0x617495F4A2827043, 0xAE6FBE6125C74794, 0x18285ABDC0AC2FE7, +0x90F8E6CAC9196102, 0x4AA0F8EB6B643842, 0x41B40701F42189D6, 0x40C469044E0A6A32, +0x7867859157B3C889, 0x641694A79C2AED15, 0xB1EC1A94DD1559B, 0x5383AF7F3A84, +0xC8D14F7DE9415F67, 0xC4A1F316F3D2CFCB, 0x839C06181F43748B, 0x49B7B5997E0EAE31, +0x542F103F7220FFE5, 0x30288AEA1E3BB12C, 0x9D600C7DC228CD58, 0x626C146D30C32715, +0xBE92D57BCFEEB7CC, 0xD67CEF2432C59411, 0xED1998F0C906BBD9, 0x38B52C02F086, +0x87C903A66963CE20, 0xC2A87DD243FC033B, 0x52AC0C317BB34595, 0x75C0FD2B9B02B533, +0x8D4264F2C28DD80C, 0x14980EFDFA973051, 0xB0F522402E01CC80, 0x733211B7A1C8CD56, +0xFDF83A9C38AFD944, 0xA22ACB4AEABE37C5, 0x347CFE3DDC849B1C, 0x9D6299327E7, +0xFE0EAEE30D1AC6C3, 0x8DA0C89E619C0B24, 0x955933012F1D54AF, 0x1CF562B46275815A, +0xAB998BA36B829A66, 0x81A93C1F2263A5FB, 0x888320AA5244EA57, 0x5616B1B352CD8D74, +0x6F4B9D7CE3286A42, 0x5AA8A439C008D381, 0x92E92F9035C2A33A, 0x5E63ADA7A3, +0xBB02362E62A4EBB, 0xCEA27DC681271FDA, 0xB5D778DE27497277, 0xA0122BA7A1D2226, +0xB56F84EACA6C3CC9, 0xC4D7EE543A4DDB09, 0x66968323B3AD791, 0xE2ACECAB4626FFE1, +0x962AE4D6DDDC18D8, 0x54E1999E854791B5, 0x630BAB553B46BF2A, 0x271EE333D10, +0x7BB7A4A07B0788DC, 0xDC36A3F6607B21B0, 0x4750E18EE74CF2F0, 0x464E319D0B7AB806, +0xC25AA44C04F758FF, 0x392E8521A46E0A68, 0xFC4E76B63EFF37DF, 0x1F3566D892E67DD8, +0xF8D2EB0F73295E65, 0x457B13EBC470BCCB, 0xFDA1CC9EFEF5BE33, 0x5DBF3D92CC02, +0xE7E952E9A260914, 0x92C98EDCD6E01424, 0x8F2B207221D33C50, 0xAEF2728CA22F318E, +0x5FD0E29877DC3D43, 0x1BDC7B7367E4E124, 0xFF5BC4186BDDCAE7, 0xD20A34710EE8B44B, +0x2E0866A5B9467EBD, 0x876EFC05B732A6AD, 0x9D39159E24822ABB, 0x658F31DC0D6E, +0x73E75CE4A532CE4E, 0x8A9CFA6FD7C7D8D7, 0x5C32241579AB4D31, 0xC3B150BD8F701620, +0x3490B85EA3AECEC0, 0x95A369A8DFFA3A5D, 0x4FD3E2058B184D09, 0xEA9B75C9C036EB14, +0x4E0764498F8C479C, 0xB292905A05D75662, 0x31CAFF3E38483EA8, 0x5D55ADDEE14F, +0x7BB7A4A07B0788DC, 0xDC36A3F6607B21B0, 0x4750E18EE74CF2F0, 0x464E319D0B7AB806, +0xC25AA44C04F758FF, 0x392E8521A46E0A68, 0xFC4E76B63EFF37DF, 0x1F3566D892E67DD8, +0xF8D2EB0F73295E65, 0x457B13EBC470BCCB, 0xFDA1CC9EFEF5BE33, 0x5DBF3D92CC02 +}; + + +// Precomputed values for the first Miller iteration of the Tate pairing on the +// 2^eA-torsion of E0: y^2 = x^3 + x. Contains a triple (x,y,l1), there the +// coordinates x and y of the double of P are in Fp, the slope l1 is in Fp2. + +const uint64_t T_tate2_firststep_P[4 * NWORDS64_FIELD] = { +0xD25C46609D011910, 0x135AF5A98C28ADCB, 0x1FBBAA32F245FF2F, 0xAFD791F380D906A5, +0xA7A53C388793D95A, 0xFBD17414C81EC903, 0xEB07E1336AF105F8, 0xAC3EA4E2E4FE53F6, +0xB6256871166682DF, 0x53E7689F74C06845, 0x23F839F6531DDBCC, 0x6BC870E1A52, +0xBD5F83502C76EB7, 0x4EC78E2DD52CAB67, 0xF9BDA9CCE6539EBA, 0xB97FD14D7E4109C1, +0xF486C305000BC492, 0x138E2273FD8FA40B, 0x22A1D7254ABCCD27, 0x9040445BBBAC4D22, +0xC5F6A6E6E30F03DC, 0xDCD17AA07985BD11, 0x4DA3C9A422AC99FC, 0x3BB8A508D510, +0xD40A45531EB0EDC2, 0xC2299904BAE9675D, 0x1FC9934035AE1105, 0xA657E853BA42593, +0x9AEA7A9998765F91, 0xC971E696D54D7F4D, 0xF0BBEFBC42CA0BFC, 0xA1B703139AFBBA4, +0x1449BEEDD33383E2, 0xD56E2ADA01E1CE44, 0x123F51487ABD92C1, 0x2AEC11AF4E3, +0xA705DECD67BB154E, 0x3671355CABABE5F6, 0x92D2CA2173DF3764, 0x9287F2C3C3ACC70D, +0x22553D769BF6FA4C, 0x1A02C98F8E9FF24C, 0xA1F4FF3CB5A2879A, 0x786B1F479BB26317, +0x6C788B0D7262433E, 0x5C08F513D0B359E6, 0xDF77EE49CF2DDDB, 0x2BE7A0285CE3 +}; + + +// From here on all values are in Fp. The table contains eA-2 triples (x,y,l1). + +const uint64_t T_tate2_P[3 * (OALICE_BITS - 2) * NWORDS64_FIELD] = { +0x5CBA3D258C4DB901, 0xC93BEDE745B295DE, 0xBACDF727F64CA987, 0x83ECDF3588EB0EEF, +0xCD2BAC5AB77E0E4, 0x1D56430F8D7803B2, 0xEA6FD88513503E97, 0x92589961E52EBA47, +0x915B0E001AEFB2F2, 0x85FE3AD27CF8A2C7, 0xA2A5879C170ABF08, 0x6756AABEF4A2, +0x6958EE2BDB497F9B, 0xDB206E7ACB9FCE8, 0x67969F38A0162224, 0x22C73FE0E1C96671, +0x2A145539A0E9EDFC, 0xDDDE81220226093F, 0x5AEF2EF0589015C, 0xB2D79977770478D4, +0x92E804AE163BC6A2, 0x607A5C228D62FBAA, 0x9EA104FCAA562E01, 0xAC521235AF0, +0x1DFA0D28D1939568, 0xBF57BE62BC3BDA6, 0xA044A0DB9CB3D35A, 0x1A05ADF0635ED21B, +0xD194D18A476E296, 0x1FC7E5835179FF39, 0xE69F2A9DE5CE4A0, 0x1361BEA4591991EF, +0x8CE96F83FC3CEC3, 0x22381B2E2D28978D, 0xD709B6C6CD68C642, 0x6518ECE8D749, +0x8E8E1E64DDFDF364, 0x7A7D339CB2539473, 0x601E8F3CE5CA7C4E, 0xD94528B30DC5C326, +0x8A428DB8B5F6A148, 0xAE14E31B05C912CF, 0xEA3E94DE2C6163FA, 0xAACB9CCC709F9492, +0x2F6F88D6C13D722B, 0x1F0517DCCFB44B27, 0xE000AA61246E6DBD, 0x3D98D655AEBC, +0x511E94EB02FEFED3, 0xE7D839A4F7ABD9EC, 0xE505B5461C5D8D99, 0x83540DFA28217FFC, +0xE647DC67A73BED9B, 0xCC433B88615C8DF1, 0xB0F928600AD8DAD9, 0x7062211A58F6C440, +0x6D55864BD21E37BB, 0x97F47967D7A0A780, 0xF83294597DDAF9F0, 0x60C4D23B7EAD, +0x80059A4DD85AA23B, 0x7C5B5A29CC77FA47, 0xDAA8AF0AF6697D0B, 0xFFF54D8372626502, +0xC745F543DC3C19AC, 0xF76B389DF4A1DB76, 0xA8CE3A39463C476, 0x28A8939ECA08C223, +0xF51F040970CBEA9C, 0xFE97C69A195B7F09, 0x1E1D163A38DBEA2E, 0x56DD83D2C142, +0x21BC23E97B1C7B97, 0xA0997FD85A8F9B45, 0x6A727E0402B0DDC4, 0xE874CC2199F9882E, +0xC78E3C135436E8A5, 0xAA7D317588E787E6, 0x9A42E70C91B21B1C, 0xE9FC183C27F7E021, +0x31D3AF2F13D804D9, 0x8C05C0395551A380, 0x74B3B5BBB15EF970, 0x4779B71B0005, +0x157F0DA1088D3B9E, 0x9DB2C0ADF97DC9F5, 0x6A98D257AFB571EF, 0x32E96D0346445618, +0x6CB8469D7B62E2EF, 0xCC0491868B121142, 0x67F88CB845DC74AB, 0xB8778DE9D7C7432A, +0x148171F3A97AD64E, 0x917718DCBB09E79E, 0x96E83D4A274E6FB0, 0x20182B229ADE, +0x5FA5C292FC75CCB9, 0x37DA3EE82B12DEA0, 0xF6C8A8FE3DCE6BA1, 0xCBD544A976C5741F, +0x14EBC6847C58126, 0xBCBCAD6E1B25AEDF, 0x80CB31C6F315851C, 0x4D92B6C1C9E51A19, +0x7341B0B9927CFD37, 0xF858A9A191EEA266, 0xA8A6A4F2ADEE9940, 0x59D251005B93, +0x97F8276F285F23D0, 0x74BFEBA2BFF06B30, 0xECB37C5724D93B7, 0xB428830038FA655F, +0x621BDC14CF2EBCA7, 0x2AC5988F5C03570B, 0xEC63CE172DE253DC, 0xAB853C36B89FB08B, +0x6AE0B9362B60555D, 0x821B834612261F22, 0xFFD9892A3BB0D1DE, 0x20FF757CDD24, +0xB3CC96053606DB8E, 0xBB6F66FD1811D1B9, 0x3DDCFF4CBA448531, 0x15F921BEF2FE0EE0, +0xEBE20A463D1B918C, 0x81898EFFD5E2CBA7, 0x6365264C10FE4400, 0xCFF74664FA761D97, +0xB601B512F2DC0DA4, 0x965C72D8A1EBF74E, 0xB4A225CD1421351A, 0x4D0C08F4CFB2, +0x3D6820D24ADF83AB, 0x7E22241B437094E4, 0x2835524C8809AD2F, 0x5CB80B3D13478B06, +0x5E9C772CEB8FDB75, 0xFBBE0407E9C7BCF, 0x9FB164E6E97798CF, 0xEF2BDA583BDD09EA, +0x945822D3F7FA6B6B, 0x22C72B0E217BACD2, 0xB19C22156612DDBF, 0x4646BA37E3D9, +0x1528926005935DF8, 0x47177C66840F357E, 0x360EF7FC3B79C99B, 0x558F3B2C453BE8C3, +0x7893E58AA524D581, 0x40759484EC40CBE5, 0x8C077635B826CE30, 0x8CD6B8338E439E3E, +0xE54AFE880266770D, 0xF14FBE1CAF5E102B, 0x2E633C12D04E905C, 0x5C31AE074815, +0x18E7E91AF372066C, 0x2FC235FF6A7B0D9F, 0xA588D6FC403871FC, 0x44F9248FA75082A9, +0xD6012014658D0AEA, 0x559D683C9C5369C8, 0x62761914883D677C, 0x89DA613889806CC2, +0x203455F3EB39BD1C, 0x7523EA22C34CCA50, 0x100211A596651283, 0x227DA670A0EE, +0xAA211663BF26A0DA, 0xD68340FA36F1782F, 0x1F8096ABFA533427, 0xE422F82A58B813EF, +0x7349F71DEC318042, 0xB88A9B54193F5162, 0x652EF038E4A7753F, 0x25899E70AEAD37A4, +0x1AFFA684C58BBD42, 0x96C251CBF0FF147D, 0xCE368E97691D3B2F, 0x68575308EA86, +0x2E889154842FBBD7, 0xC3D444D331CC5830, 0x7A11F55998B74F6B, 0x923AB01B0A568215, +0x465F390DC2EAB449, 0x1B16D976D7C3F527, 0xF8635AC7BA92EA77, 0x76C2994383401758, +0x48E84B960E5C431E, 0x915627D09C705E21, 0x7DA30EDCF64C0526, 0x4ACF5D342AF2, +0xE2CE2864B31F854, 0xB334DFB6EFDEA11A, 0x8E8D235C6F622A0B, 0x696C058ADBE58A51, +0xDFF7A7F1C8042792, 0xDE0158CBC432F386, 0x694E5764877BF8AE, 0xB8C0AF407FAD626F, +0xE0174B31F9DBDC2F, 0x37604D38476031C6, 0x13638B9011F63BA8, 0x2789E3D82D8A, +0xE847C382CAE8E73A, 0x3F71405F0C894063, 0xD48AA86DD161AB69, 0xD866A387D95E2402, +0x5F65D9E290549A0E, 0xDFEEAD352A939C9B, 0x2FEB2E81E748FADC, 0x27E10E8AB865B35B, +0xD72F7F009385ED20, 0xD203BF970FD947FF, 0x6047B015BAD7BC20, 0x4F739EA1278A, +0xFDD2EE96DE27FBD9, 0xB55C39FAC37DD274, 0xD6C6AFA29ACCB9BD, 0x207B9B4CD82C8300, +0xF6A8C029CFFD5BE3, 0x3926C29655BD2E5E, 0x9FB1884F9FCE6721, 0xA504F780822946AC, +0x4DF965791CA48528, 0x64F66606FAEB46AA, 0x72B0E9549D782D46, 0x4E241838E0D4, +0xE5AFFD63A5A01D7A, 0xDFACB8D01FAE4C86, 0x86F5FC9C11AF1E34, 0x83DFF2415FFA6638, +0x3D30E56FBDF2409, 0xAAF6B44C8ADA2FA2, 0x1D2D9917EA040D74, 0x3EDA7ECC9152F949, +0x1594F595C725C60, 0x32F77925526F70BF, 0xA6D31E12DF98F937, 0xFD6568BB39E, +0xE7E10782E0939000, 0x51CC1CEC8B970616, 0x5E4DAFFE99AAABAD, 0x28B8274220EB051, +0x4EC720E0B1157EF6, 0x2EC0FA75F0E9B7E0, 0x15F2AC3FBDC86011, 0xFA0473CF7E13401C, +0x4FA72110D8E7C0B, 0x95E24A3613327DF0, 0xE5E621B5A6A3C58F, 0x2DF1B098DBDC, +0xA3895071D8A40F47, 0x223A862093A028B0, 0x6706AF2B0277DBEA, 0x2785CFE85513F89B, +0x2F2A1DF3FEA5A0E9, 0xED7019D13CA2FEB7, 0x9AAED87445D0EE0F, 0x1C08981A646AB5D1, +0xE5BF74DFCE52CB8A, 0x6DC18BA62068335C, 0x5C6C2774F382BD6B, 0x60C113164B4F, +0xE8A3BDCFC1B1211B, 0x1EF2D18FE3EF92C2, 0xF4B209A1B55B997C, 0xE61F94D43AA5B5A1, +0xF5792FA187BEA099, 0xBE5779F1878B6D86, 0xB9B53B36F23F8519, 0x536239ADD745A207, +0x46BFFD688C7785FD, 0x10DDC2DE07F59822, 0xA933C8145C093A47, 0x3BBA4D8DA213, +0x7D9AE9767A12C6D1, 0xD0C72701AFDFD84C, 0x82FD4C3AC7A57466, 0xD5E90F19BFBB48B0, +0x5C9D0A35AE541D9A, 0x38860009532762E5, 0x7809641F3A07C1BF, 0x189D2BD8D3AAA854, +0x306E41668A35AD75, 0x61FFC0F572231E49, 0x4E4055AAD90A1B6A, 0x3432BCE941BC, +0x4CF2FAFE5435C1E1, 0xA1C6B2319150C0FC, 0x1B156DA8A019B27D, 0x9CF84674521A0605, +0xF1AB517F13BCA3BB, 0x10F1D76570F449A, 0xCA9CDBEF134CC872, 0x4B1D481D7F9E4BAA, +0xE6CCD3380ECA732F, 0xFA5D0CF663BBB182, 0x51A4556EB5356C77, 0x1BBEFB926A0F, +0x2D60A1FF932D563, 0xE30A677AF09DA717, 0xCE46A75A0C997B55, 0xE32E77BDC80520C4, +0x33D446BA879DA878, 0xD1EBEFD3868D23DA, 0x2C5325C8B57E4A74, 0x762651C02C4804B9, +0xD107802DA5F9C096, 0xD7D7D855202ABF06, 0xE0DB99C066F47426, 0x65CDEBD7B009, +0x832AC3AD8DC6CD68, 0xBA29CBBD0464CA09, 0x468A993209994C0D, 0xD4F5E0C12A47B9E7, +0xD94F9FFC9B7D72A9, 0x2E4E3370D80CE2E8, 0xB78E9F94771787D3, 0xCE1D7D416A8B02E7, +0xCE1E8E808501E697, 0x7F6976CF60C41BF1, 0xA6D13EE55001B1DD, 0xFF3D189024E, +0x2A038EFB6524390, 0xA91B92F129350589, 0x6D9652A0FD20EE32, 0x2FDD5B9CB673F28, +0xBED536807A7BB51C, 0x7F3CA6737577A4AD, 0xF9A4834D559973B6, 0xEE1E54D8DE63CD6C, +0x228AB67D384A117E, 0x303E38F3678579CA, 0xA35FC4539C009EA4, 0x4DC489310E29, +0xF54B16115A969658, 0xB5EED2582C55B776, 0x292E95F3FE25D951, 0xF3EE707A7DE0FD70, +0xA4C7C57F13D6F285, 0x2F35D8E73C42A63, 0xD7ED3A9C4B6F6A0, 0x4391CE88B005976D, +0x5470E01FE61AD8C7, 0x3F6B312FDBC6A2BD, 0xB614ECB48784A9FC, 0x219F0C24C58, +0x80F7A8BC66EA5ED, 0x99A4996F19CF23F, 0x634E892A0FBCA564, 0x70E0F734BB9DC55A, +0xE540BDC568041922, 0x52CA58080DF9FE46, 0x6A4FDC548C380C67, 0xA0B7F54A08612419, +0x42CA4E5B04627BA4, 0x95E82F45A4B3A07C, 0xCB69A1B827441646, 0x62E9A37AE93, +0x8BF3F8CE2159D735, 0x2A2F10F5FE0764E4, 0x74E33C9EAE8164BC, 0xE9964C5C578CF675, +0x739648B3BF9A5516, 0x2EB28FE4C5A8A9B7, 0xC544882008B0954D, 0x2B645703CFB3F4A4, +0x8B7D7CC7A96BED8F, 0xA836D7F8519FF12B, 0xDCD83DF734BB00E5, 0x3522B042BFB2, +0x1AEB3929627FB774, 0x2C943ADA0996AFB, 0x60AFF98AE7CD526C, 0x6226BF64CA64F717, +0x8AA151F57582F546, 0x6A26D73BE76E48F0, 0x411F85A23C13051C, 0x9938464F96262C80, +0xB203B869951070D, 0xBB7E94B8B4CDB5BF, 0x21AA8C2CF15C4BC5, 0x166C41FD4896, +0xBE6119B114DF7800, 0xB89918A851AF141D, 0x2908FC0ECF1C68DD, 0x44D0649947CBEB2C, +0xF6A8D53D74C7E8E, 0x583CD18B906AF16E, 0x4739A05CD0877213, 0x3BEFC67DF16EEA55, +0x14B47F2E28079D5A, 0xE86CAFC132EAEE1D, 0x7AD2DCC5893DBCF, 0xEB054F6E35F, +0x14C4D81E47993159, 0x6EF5A4D78FCF6718, 0xCE27020FF4FD513E, 0x60440CB6A5120988, +0x4E7728C4DA1603D6, 0x88EE6B817800F286, 0x45903C2945EC4C86, 0xA8EA0F5F9321F4E9, +0x4C0043CA8F016E17, 0xA28F83135B194482, 0xEE8C871CB3364291, 0x2B180ECB1584, +0x2053F02CEA651A06, 0xC7BECF674E947C66, 0xFFD638A35D757DA7, 0xE6271C319C1371AE, +0x38FDFE0A8C6E921D, 0x65DAE7059782ED5B, 0x85E86618764F68B7, 0xF4C4D2294CCC2D3E, +0x5104B360F302C231, 0x557CDC90E7A17C75, 0xBBDC3B0AFD71F151, 0x2B9652E409A, +0xDD429BA06F75A5B7, 0x722BC7DA609AEC4B, 0x27AE1B6692CB08DE, 0x460B1EBF4FF76939, +0xFA570BFFF9A27895, 0xAD12503F7568D9A6, 0x46969ABF8AC3A78D, 0x1FED6E47BB4E3A1B, +0x403E32854BA1FA7B, 0xD4A6A0AB0B0A181A, 0x7806AA7123F43CA, 0x597F5D7BC9B8, +0x4C554FD58C1C2C7F, 0x8DF98378847C13DE, 0x3A8B3D223CC796B0, 0x2DEF2DEF83AD72A9, +0x83C7AC1C78DC243B, 0x6904B9772743A207, 0xE2F7AC6DD8063326, 0x7AA6BEB0E91BFF00, +0xFFF091EA0436F977, 0x781DF8B85120E82E, 0xFC718537BDC20CF1, 0x3C8EB54237EB, 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0xDC0F0E058A7DF232, 0xA53FF227CB669A58, +0xD461ED920FD0F6CF, 0xEA8EF1B6C4C60944, 0xC2FAA503DE6DE379, 0xBD3D85414FAFCA2C, +0x547D88301AB2A6F4, 0x4897DEEBAC29A8EE, 0xC60CC189E53C8CC0, 0x6E2860B7707E, +0x654E9846AFC25E9A, 0x4A6C432422955BFF, 0xD479E57E806F9B0F, 0x1EACD5D1A40DC6F0, +0x70FD51940A72BB3D, 0x2B499D5DA9816A74, 0x63ED68212A582278, 0x9D4B642D67609ECF, +0xABF524D84CE99BC8, 0x63AE535EB130B68E, 0x65E0253DC3A85458, 0x6D47B642A56E, +0xC148AA51E055872D, 0x8E324779D168CB32, 0x891E7AAFBD89EB9, 0xC3E1643D34637450, +0x5B5273147B55B0A9, 0x62634F4A463054BF, 0xB69903B5848C2A2B, 0x9F6835277A93746F, +0xD4A57101565060CC, 0x5094121E7DA475F0, 0xA2B17E38720483E9, 0x6633D1D9E422, +0x2C3AFD6A626BFF3B, 0xEBB37E2E90DCC6E3, 0x290A635C48DFC0, 0xDF782D3BE2215C59, +0xD9A7581D83897148, 0x5CD75ECFAC32FD4B, 0xFC0FF366696F1A4C, 0xA338F112E6DB6B0A, +0x41C619904A1E03D8, 0xD11741151EC068FF, 0x203F87AF5A6D83F5, 0x54D4D78EF693, +0xDAA80E5946D290FB, 0xDE9C468FBFE9C640, 0x4F559021BD23FB51, 0x24D5600AD58D0C25, +0x1DF90AE480489E42, 0xFF6251166692978C, 0xE0EA3360C57F5709, 0xDE8B69EDB05B1B93, +0xFC70ECF9E211EE21, 0xEE02D7938525232F, 0xE622144C11C3D092, 0x3B0932F76379, +0x9BDF866D1147823B, 0x104D74DA09064739, 0x5B94D16FD75726B9, 0x6C343944F80E8E19, +0x758E60EDCF612E30, 0x837DE24F34AB3C31, 0x680BF134F7C6164E, 0x89BC2F951349F1B2, +0xCC438F34E9B0C6F0, 0x236730025E17A5E8, 0x669FA5603276CA90, 0x14B3BFD5492A, +0xF87760364D3E22B6, 0xCF83C285E6752BB4, 0xDC87C4B39FBBE9B1, 0x2ED1CED5E33E0243, +0x434C81D3A3D8A287, 0xB98369664933A519, 0x77E6490F5A9E83DE, 0xB37D59DED37F4567, +0xE0089A234E212CED, 0xD6F66911726BFA14, 0xF3521D0AACE36C1C, 0x5E11BCA91494, +0xB5A5B96B4D50BEAF, 0x30F8583B1D425025, 0x69E0DFE39938F0BC, 0xCCA27FBCECF0CED3, +0xC1AD89123AFCFCE6, 0x9C78C6AC544F0BC1, 0x5E24F1B8AC9ECFAF, 0xA6105380F684EA70, +0x6AEF590A84354364, 0x777EA6DDD519D373, 0x80A976D133253645, 0xA980C30AC03, +0xE713DA860A6C9175, 0x1CA7DAC141BD05A9, 0x91FAA9E95898D639, 0x856B4E2957E91474, +0x31A857939E84D300, 0xC95ABB1C66751A15, 0xEC6433F7D3077F2A, 0xB80846FD1E347D0D, +0x452A57EEA40938F9, 0x80F5200815EBC71B, 0xB7352EA0187C2767, 0x5B2179724725, +0xA42B14F2CCFD7353, 0x938429792DAEEB1F, 0x18A1E4FE05346B24, 0x2949888B18A67FC4, +0x129F39451EAD6158, 0xF1FB8B67684516A4, 0xF46838270512AB54, 0x29A1238626856648, +0xF52E093367AD6A9, 0x9145DCC843E9805F, 0x502F51925D667B5A, 0x16027E348AC3, +0x56029B7F24B6F996, 0xDCA93CF3C9A7E23B, 0x4E795C2EACC539E6, 0x2E91272018C5A9A0, +0x479DCCECA9CE310C, 0x27FFCEB3D6416015, 0x37F093951665FB7, 0x78099BCB0491C2EE, +0x7084E73DAD3355A0, 0x1FEE7C5F8D8FA80A, 0x86B5AAB7985B1FD7, 0xBCEBBC9887F, +0xDD11D8BA0FAB4584, 0xA3DA540DB2F5FB2F, 0x5D4988539F0364A7, 0x528549CA1DE048EF, +0x3D648E69CFF07D2A, 0x8487D6E1488ADD58, 0xB54169B637A312B3, 0x94225BB6AEEBCF7D, +0x4C961390BCD60B1D, 0xC2DC536C217687C4, 0x71AA70BEB74D187D, 0x1F2ADCB69D0A, +0x9C60DF292D2E5157, 0xECBEBCB3739F9DD2, 0x59CA5D70108E0AA, 0xC0AE2AF3789C9F62, +0x2CBE6751F8D1C691, 0x110EEDFD39BD6251, 0x2C423AA000993DF0, 0x3E8D828BC06F7E6F, +0xE777C5E5E6E43B4B, 0x481DC24EAE2A9EE7, 0x3BEE29138D9D73B6, 0x596C658E18BD, +0x316BE2C2CE7E5524, 0xF58F3C67FD0C1659, 0xF464D82AB7CA2932, 0x8DAA582BD122075E, +0xCB32C9DC801CD1BB, 0xCF27C633BD6FE0DC, 0x6645AC35A0DB1E3A, 0x8E138D15B7ACB273, +0x568590D47F583116, 0x6856DA094446B253, 0x785456311CD10602, 0x383A7B486122, +0x2563EB719E1FADD4, 0x8C93D422C4046EB3, 0x8AD7C054874A9810, 0xD839B76D51609649, +0xD51D6BC971D47E51, 0x38D1A1E875EF67C6, 0x103D21F8275E1146, 0xD819B41373F9D3A5, +0xBC77BFDEBD61CFE9, 0x274E8926C5501C4E, 0x7A733C0C4C54B41A, 0x3F4F73084CFA, +0xABAE8ED5F82B0680, 0xA8B95E8FFC14C455, 0xE8DF83AF192B0E60, 0x443E3E9D6EFF0AC7, +0xC2968B0B05185376, 0xA0318260D0FFB041, 0xB301D40052AF3974, 0xCBFC8C9902395B70, +0xCB73A3F056D236F2, 0x8A9B5A07952AEBCD, 0x2E69A9F30C7BF42F, 0x1C5605D5F420, +0x4C878FFAAA9ECCE6, 0x1B2C694DE4260D9E, 0x5A0A4CB41EB8EEC, 0x3ACF6C2F63464FF6, +0x42567F0B56F4028D, 0xDE50491DC2F9AB7E, 0xF9E51488C2415BF7, 0x3BE1E4A6A29B1604, +0xFB89A33E46458437, 0x5E1AD924C5C5C591, 0x52F7C4ED87467A0E, 0x241D0FA8D867, +0xA318D35E61FF1D2A, 0xA86374B5DB18E65B, 0x24665617C93A0302, 0xF352BFDAC6E91976, +0x2CE390C4CE72C94D, 0xC15F676EC7A4833B, 0xE0F48CB3A408C094, 0xF687729CFFEDFAD7, +0xD41EFB97AC9AEF62, 0xF335022BBDC16504, 0xB256E9C6792619E6, 0x3D4FE8E415E3, +0xE1A5835DDF9BD2B5, 0x83820FF55CD6CC91, 0x2E277EF4CEBE3F0A, 0x606AF9094C7573E, +0xFDA337D6F286F9E2, 0xA09B73C3F6C801E8, 0x4ED6373886C9C69C, 0x3D2267728F1DFDFD, +0x814B1AFC84F2DED9, 0x523221864838CEB8, 0x6F6A67284AA5690B, 0x203678E31369, +0xCD990FD29CBBA6A, 0x10DD70E58E4FC1D8, 0x5A0A484E2ED4A97A, 0xEB065FA9EFAEC597, +0x7C4F975D6DF62DF1, 0x9C3D997DEEFC8F09, 0x452F29259FADD5D, 0x5AB97EF4DE91ABFD, +0xAB0417105EB48F1B, 0x52032E8055EB77E, 0xCB3F9A8EE503D31B, 0x500B9DF19724, +0xFB4DA608FA4DE382, 0x879387A075F9D038, 0x9B150061FD42877D, 0xA08509EFCFE0DACE, +0x3C33F9569CB4F440, 0xB1BA9DC0B468EE8A, 0x9BF6D57D6532E38F, 0x59DF991D3DE05E54, +0x790CAFA3A42A78A4, 0x74E04FFF8C3252C2, 0xCE62447A8CE813AB, 0x6A572522F7D8, +0x6F57D302B4F0A306, 0x11D83460D4B6AE1F, 0x5D5B2546A4811604, 0xC0A3BC5D1DD684CF, +0xC2A4853DA4E968A8, 0x635972C32C5EB4C0, 0xABE746E322DB98FF, 0xB01C003EAF944159, +0xA62BB9039E2E2453, 0x8F28ACFAC37B1519, 0x43CA6505F0B6B680, 0x6A5B2FB8BEE, +0xCF98FC8D4DB72D6D, 0xFA299B2F12FE18AE, 0xD8F9DAEF5DF603A4, 0x196C1C9C9A42C16C, +0xD9D68A67337AD105, 0x9F379FB4FFA867B8, 0x25F2C87A7DC7683F, 0x8D38E25CFCD9AFF9, +0xCA6BA1D4CC87BCD5, 0x20EA88AA2927E1F5, 0x3192D1AC8823BBB1, 0x335934C06E7, +0x1E4E694750482E74, 0x27C44FBE959777A5, 0x8A69286337CFB532, 0x27238BD5D5A13CFC, +0x602CC397F8A8251D, 0x11A53FEEAB36DF92, 0xEE86995C513FF3EB, 0x657145D5EE3E3DE3, +0xF33D20F962FF22C0, 0xFBBA16ECF96E7D41, 0x16078163ABFBDF5E, 0x5526B87B3C75, +0xFCFC86F34C10EA8, 0x7ADC161B7D5659AD, 0xAA54DD47DCEC68BC, 0x2C49A54AD9B73D2D, +0xE2E8D7EB9F2B403B, 0xD0011EE5601CD1A1, 0x32DB9B2D6DB5229B, 0x7900FAC1002F6DAC, +0x96501A73567958F3, 0x58467DFFAF695E49, 0x8811FBBA0981F699, 0xC1814051FD1, +0x4682E304660321B6, 0x8BC18F35407668E1, 0xEC7B89D2AD766860, 0xDE8E78EAAD8F0CD3, +0xAA2DDF58A68525B8, 0xD7876BE71D4953E3, 0xFF0C9CF0FD1784D9, 0xC054DD85CC3046F9, +0xA0BC58FF88C362B, 0x9C2635FD37EF9DD1, 0xD377F026FDBD298F, 0x34E60BCA8254, +0xD729F0553670CC26, 0xEE22A18F707CDF19, 0x2AA8AF841FFE1718, 0x759CA8CE49B347B4, +0x300D603C33A03DD7, 0xD00AB13C8EEF33D1, 0x2D3A4F5A38A9A997, 0xD07FF6342CC4563F, +0xCF6CF28222E1DD4F, 0x44C70D3FEE8A7DCB, 0xD6E124C173310D67, 0x544493FB8B7, +0x40A7D1856D22BAE5, 0x53341FDF697712, 0x9E1128EB9EA7B8B1, 0x13004D0E16A3A565, +0x1499C27283C54280, 0x5DF74E52AC1DB078, 0x554D75601666CFBD, 0x698DA097DE804F8F, +0x9784260784D05F8C, 0xEFE442475ADEF241, 0xD94EF62C70168327, 0x58C7D121B012, +0x1A4E0B9F6922EFE8, 0xE54AC9015212B9E6, 0x7C97681644C79CC5, 0x21300E9B8F3B4ACC, +0xB1EEE821CCA17C39, 0xE9F099FC2AB08647, 0xB04A4AFA72BC2C, 0xFC48417CFC744D26, +0xEF926794B84487DB, 0x81D73CF0C3484945, 0xA5E493E5107203F2, 0x5F92ED8F1572, +0x1CF833FB81C0FC38, 0xAC122EBFA52C4E53, 0x1E0E736DF937C190, 0x699828C377295402, +0xE71AECEB3186B26A, 0x329FDE3DAF6FD136, 0x1563F5261CBD7D09, 0x94FDFD0CF55A46DE, +0xE4ED5DE048F893B0, 0x58783687578ADCB4, 0x952CB79A971023F, 0x5B5EA7F7EC29, +0xCFE36EB77874D6DD, 0xDFE43FC1B9D4BA9, 0xB1EE80E707C5D4EA, 0x56165D8241BBB013, +0x4B860EFC4F18E7AD, 0x4096EFDD36F94068, 0x9C23E696579C1F90, 0xD683932679F8E4E8, +0x79C46F4AE2E2D0BE, 0xE58BDAF4120C6177, 0xB9F500CA9112B9B, 0x614694BECDC, +0xDC994CF4EFDEEE59, 0x334DFCC3C1CC2D1C, 0xE1340F14E89870FC, 0xA0E70242C96BCE66, +0x4CF45D6C903CE261, 0xADE78B9DC499EC01, 0xB3863176DBF79FD8, 0x7FDA014645EFDE2D, +0xAD923CB6697676F, 0x7AB36F49A4258290, 0x640FC6876A6DD6A2, 0x242A7A5219A1, +0xB4C76DFCB65CB814, 0xB1266C9E547E737E, 0x3B2D99CEE4586821, 0xE45A28BC0EBB7F1C, +0x67FFC7FB4E7CE8A8, 0x5FB0BCEBD1B893C1, 0xA35754C6924F30FF, 0xAADB6EE4DE6752EA, +0xFBC046FB01C8C624, 0xA473CE053FEAF8A7, 0xE01AF15964BAD891, 0x5AC94533E01, +0xE89956A2B0687473, 0x109943DAF24F463E, 0x41BCF3D13CC8F751, 0x123C0F6988CC8C8A, +0xF30DDE340AD57366, 0x694FBF7ADB6A5D13, 0xBED99691C28D64F5, 0xB046B0D2B23BA509, +0xB4B723608EFA8228, 0x854CF7198876EADC, 0x6F58DF21B276D1E3, 0x19944039B184, +0x5DFDC8B7D9F81AA, 0xBDD48CB4EA61721E, 0x5606459606ED1A6, 0x2359DDF6DF32D627, +0x3D7F20E561CD1969, 0x56C78828E1311797, 0xFBDEE1F03527A740, 0x132DCBB1DD39604E, +0x40FF93F18AF74653, 0x823539DBEFF623F6, 0x4F7CBF2E3B9E8975, 0x2B81B37B4A8C, +0x15AF84BABBF928BC, 0x5E37FF797E9203F8, 0x5E3E7E57993F6830, 0x6582EEB3BC579A5E, +0x72CE778A049C485D, 0x86E48F405E8A5BF5, 0xDD13B0CE992E7D76, 0x9E215E87CB442693, +0x9FEFA65326C2E387, 0xF5B7396C04134EBB, 0x4510C822D1A09F33, 0x6E15D9E3A500, +0xA01ADC1C0EC799C0, 0xB45A5334E7FFD166, 0x86E9E4A86E04F95E, 0xA1C792C9707E830D, +0x4CA3DBA6E41A6361, 0xF03E01E8AD5EDC18, 0xAE700AB654CDE377, 0xBB59E289496B277C, +0xC819ADA4D08393C1, 0x575384FC5579A298, 0x27E4FE587CDDC0AF, 0x4EF63D2A12CB, +0x9B65683423EC1582, 0xC79906D016DD5316, 0x5FCE805ACC216D3F, 0x36995684490D2DDA, +0xA972DB53D88BEBAF, 0xF6552140F29EDE4D, 0xD1417284701A24EF, 0x257DED2988B56A3B, +0x413826B173DFA38C, 0x422473C6F652151A, 0x8108904E9AAE89EE, 0x2DBDFB3858B8, +0x36F5DC3F953669EE, 0x8B64F0AEEF395B96, 0x6E503110176BFF74, 0x775CE16CFB177855, +0xEBA50FB703A8A3E4, 0x271EA63B2192F558, 0xB29F156B65C0584A, 0xFF2AD136205FFD0B, +0xF966C93FEEA58DE2, 0x839850AFC45BDAF, 0x8987EA1044736087, 0x628C4B13D9B8, +0x2A57B49142F35374, 0xFB276F837F997D93, 0x17F2D22DE2B7D391, 0x43B9BA09DE22286F, +0x434D35F807E8345D, 0x31E6667C401C250, 0xB5D5C6069DE43F8C, 0xD660251FADFC0196, +0x31CF9A7EC8E4266F, 0xA249ACD67DF6BA1E, 0x4EB8AEE9D87AD511, 0xFE63AB18ACD, +0x12D14205D2F9D943, 0x44CD80A0C20B4B5, 0xEF605D4B365F5F6, 0x3F2D12CE69365073, +0xFA3D3A9A8BBDFC91, 0x825551B27ED6071C, 0x83FE0947718D85A0, 0x1854946BAA2BDBFE, +0x9407222329D73623, 0x51D7392B9AD0E843, 0xED4646AEF1940EE8, 0x1A44A00C61AD, +0x2AFD75A913EAAF32, 0x2918FBA06F88C9AB, 0xA4AC4DC7CB526F05, 0x2D19E9391A607300, +0x7A79E2B34091B54, 0x1D4809DCB42F1792, 0x63AF4826F85D0739, 0x4FB1AF7134E78875, +0xDBDA90D7F4168B95, 0x2A4AA9AC804021F1, 0x10BE206D2B037075, 0x99FF25CA24B, 0x0, +0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x51EAB6E6A2886C69, +0x78EA0BF5D8EB2B3C, 0x8DA896F199890C2B, 0x6B8CEBCC75237144, 0x6FD6E59F9A9B7A3E, +0x9D051EDFDAF36367, 0x64D34667DA122A73, 0x56AA4F7AD9E72FF8, 0x782B768DAE2A0A38, +0x9D47C529A5AE770, 0x1A5048049D1FA98E, 0x111FFD261D4F +}; + + +// Precomputed values for the first Miller iteration of the Tate pairing on the +// 2^eA-torsion of E0: y^2 = x^3 + x. Contains a triple (x,y,l1), there the +// coordinates x and y of the double of Q are in Fp, the slope l1 is in Fp2. + +const uint64_t T_tate2_firststep_Q[4 * NWORDS64_FIELD] = { +0xAC2B2D74F888733E, 0xDA9B5D82CAA27D78, 0xF8656EBC40D57F4C, 0x5E1CD5BDBF041897, +0x1A30C6A718D110C8, 0x42ADEF0DC70D6806, 0x3BFA8FF5013BB159, 0x5E5A1D50DBB0E0C1, +0x3BCE4C7EDB3B6E6A, 0xA2C0219900C16A99, 0x18C7D034FA944E4C, 0x6715FAF4D0DA, +0xD5592BABBCC2584E, 0xE0547C84CD5E0C1, 0xFBE528CB2D17B51B, 0x2168CC83A03036BC, +0x46149EA13591E9E3, 0xFF230F71ABE6A6E0, 0xD4A9A33BEEBB78FA, 0x63627D7CDDA2D559, +0x601FCFC408949785, 0xCDE4532F5618BCF6, 0xBC83162A741E1D9B, 0x6F443172FD95, +0xF15CCA64ECAF5A88, 0x952ED60EBC735272, 0x2C5E9BA5561DAE61, 0x948952AD32E5CA87, +0x31D2F32D2C887D6C, 0x580EF5FDC2D40B61, 0xDB49D392D81A2D21, 0x8B011B5F9336CBDE, +0x3B4C85B0A54AB1E1, 0x71544DD7454B3E41, 0xC6D6334162EDD2AC, 0x224A7B1CCFCB, +0x38E59BA0C402905B, 0x662836C27434DBA5, 0xCF76292E8B52FE60, 0xC8DB8AAFAFB4CE6D, +0x2FEA96B083869ADA, 0x60347DA847067588, 0xBC88696946B32293, 0x17B2DF2CBFD97F3C, +0x9B56940153EFAA92, 0xB10099C181CFD23D, 0xD3DD0D847F870C47, 0x21D326FF0152 +}; + + +// From here on all values are in Fp. The table contains eA-2 triples (x,y,l1). + +const uint64_t T_tate2_Q[3 * (OALICE_BITS - 2) * NWORDS64_FIELD] = { +0x41FEAA3F231C32B5, 0x97F8BC8686891429, 0x56686BC64B25B1FF, 0x2CC4DECC8CA1D20E, +0x6AD16AF6F21BD80F, 0x38CBFDB8AC2567EE, 0x59A5A6E1701EE606, 0x7A6492F0D852FE48, +0x26EE6C4CC625968F, 0x76632520C7F63518, 0x7855AF0F7D287025, 0x245A1BD67EFB, +0x35C31F2D08EF9B83, 0xB0D74D62EDBBA7F7, 0x3C45BCC1AA3C6485, 0xCA936D3A1B4CAA12, +0xCF0DD083AA764971, 0x798D508D343AC629, 0x5FDBC47651C5B462, 0x73D37E0F79F94264, +0x8C40D219DA4C1F87, 0x8E9AAC7FE49A4C49, 0xC63AB2AE378C3902, 0x359FE5848718, +0x228B45E4774FB918, 0x50E5D9D6958BC5B9, 0xF8FB73BC851DB391, 0x3E55CF2C83D672E6, +0xB08ABFD29A6D6581, 0xE35C7DA6A08D1581, 0xF31632D4022C4140, 0xB1AD8EA4ACA36529, +0xF8D4B59A749825C, 0x534D0CE6433A7537, 0x6A2A7D60DCF9A2E8, 0x5FE0AEEE043, +0x1896832C8E469E4D, 0x201684DF9A73CD95, 0x5B8BD5CCFA47E7DB, 0xB9C637B9DDB78EA9, +0xB6FA06910C4576EA, 0xDD0FBB74B0F51F6C, 0x2B6D944304F25530, 0x22DBF0CDC51CEBD2, +0x2673ABADD331CB06, 0xAE697CEA61882AE3, 0xC08F5C7C8AA9090B, 0x34C2708E230D, +0x1F25DF4484B6AFA3, 0x20C3A3554A4F1176, 0x99046B5E2CAAA455, 0xEF6AC79E0DEA76D4, +0x2CC0030FCFF889F9, 0x610CEE38BB3C5C39, 0x58B64535FEF64886, 0xFB9373E0AEDF3891, +0xAD3671028CF3C62F, 0x89400131E9B5D09, 0xE1F72DFB029507BE, 0x154A16B9337B, +0x1C58A2F1CAD3D47A, 0xED548D4CAC22437A, 0xD150700AE4CCC30A, 0xF56FFFBD67CA41CC, +0x7D70EAE58BCDB818, 0x898FD54A626B32C2, 0xA18C38AD14E0CE6B, 0xDBFEF4576BC271AB, +0x106F1C06124BD417, 0x18B8621A7EFB024D, 0xE82DFBF24FD09313, 0x6081C5A62381, +0x2497081E98D74D97, 0x984E40412694B161, 0x93BB72B5CCB1484D, 0xC195C4D32240423A, +0x382B0072EE919E37, 0x7C0D8D479807ED4C, 0x1CA0EF95CF5F73F2, 0xC043B16F43924A1C, +0x5396BE7C87D6D702, 0x33A11E4D031187E6, 0x8EF0EA15468B2701, 0x47A070A25281, +0x2F32839488886B3F, 0x1E9BA6C63C254349, 0x29CCE943F08B0D8C, 0x24DC7F4B41545FFC, +0xC4C473382393C68F, 0x81D55D0FE82C03A5, 0xBFE4997900BDC79C, 0x4D034AFB23682136, +0x75165D4B11A833A, 0x861F70D5074E9D3A, 0xF86DE258AAE06315, 0x5311F6256DC6, +0x4322ED2B2AFC377B, 0xD974042DDE883E8B, 0x84C4ADE79F910F21, 0xD549934B815C93C2, +0xB839AA00ABA5945A, 0xDB2D3FF6A7ECFA41, 0xBCD67E395C628955, 0xDD98F7CB5D609AB7, +0xB1F16EAA780195BA, 0x3DE4B0DAEF9F92C, 0xA132760C88C7BE41, 0x28C895111871, +0x7DE89EB39CC23B63, 0x106C387265B69E3A, 0x8CF3A280D95F3FEC, 0xA76317D104A9C84D, +0x7BFDD754FE07719C, 0x3CCC0F6D3528D7A0, 0x727ED0306A5F5A99, 0x4E5CFC0EF64086A, +0xC8451E351AC0055B, 0xD0D6C802E9F24B7B, 0xC9D65D953611F4BC, 0x48A2C9D6A652, +0x85B3C8A3C07680C6, 0x2FEEBEDFDA6DC4FB, 0xC7DD0B54000B53BD, 0x286BD398D8CD97DA, +0xDD7EF32341078D3D, 0xFACA5DB4EAC9710C, 0x4642104FC79F8508, 0x7FEE5C63D6E8CBC6, +0x139B51F90DF11EE8, 0x2D83CEF979808974, 0x5AE055D8AE5CCF9, 0x750D6D9B980, +0xF05FB27861EA2DC3, 0x6F9A9263C676A000, 0x85586BF4B1C51750, 0xEA114FE37A3622FF, +0xF29F02D34A019A69, 0x6531978C8492037B, 0x838572E6E1E84CF6, 0x392E2C5CC41FADF5, +0xCDCA4395E2BD4B78, 0x6F21CC1CCC3325C2, 0xC87AB58B148F8A7E, 0x32999B8FC8AF, +0x18C5CB26C85C36AA, 0xCEBE765747D8ABA0, 0xDE857021D0BC3BC0, 0xFAEFC794723E74A4, +0x9FAE9057F8A57AB4, 0x7C23DBB3F9216329, 0x2A7A9C1C428D7B5D, 0x15DE406E0B2B09B9, +0xBE2BB184084C491E, 0xEAC5809D3E474A72, 0xBC6D37913710131, 0x4AF8CB65AA4D, +0xEB257B1EBDAC13F8, 0x8FF771C60F3D1473, 0x27B57486C49D823E, 0xE9D9CDB05EF83ED7, +0xE79FFA6C4484A7E, 0xD06FDC98B0AEF475, 0xD89C600530F0111D, 0xFFD5E4982A100391, +0xBB8AFCB5B3E7A1, 0x24D2B05FFA34F225, 0x6BFC87BC84941B00, 0x62DE743A18BD, +0x3D40CBD27640A6F7, 0xA542619129C8921C, 0xDA9CEB9BF4AF292D, 0xF46A0865877321B5, +0x78FB29FD75A4A866, 0x5A56206E332EE69C, 0xE3BFF679508EBFCB, 0x8BE80DA15C5A18BA, +0xFA3A21459D776E46, 0xF8373D1FAE8D7BF6, 0x2742C2D81C344BE9, 0x12733B2921D6, +0xF7BBF940DB253223, 0xF508512B81BAA047, 0x3604A37B3C0F7250, 0x1A5AAC257B46434, +0xE9A7DCD97783105D, 0x5F3CAB56484A3AE9, 0xC055AEC63AA95FF0, 0xEC3FBA19501A99B7, +0x9E7AF8E1B398D603, 0xED1DC8A4EE361FF3, 0x40EB0D43C0A44B13, 0x36CDFCF866A9, +0x4D8FFA39D021E487, 0x5D887C92C3C8F31, 0x9F4CF9D71F276CB2, 0xD5873F38ACD5AE9A, +0xB62F548F2AC02EC, 0x7670AAAADF81358E, 0x32BC40445BD82BB1, 0xC52BCCB897E5763B, +0xDC03C8C56CCBE91F, 0xB25F75795534CCB, 0x1FC17783F20DF749, 0x370729149250, +0x8E3307D0FF3B094D, 0xBEC6858D31CB842C, 0x18A8720CF8A3E3C2, 0x8FE64B235E6004D9, +0x8202926B7E4117B3, 0x328207E18BD03EF6, 0x3DACEBBB2A6E30A1, 0xCB7DE4EAC4425ACA, +0x4D51959B5449E6EA, 0xDB3ED00AE5E84D0D, 0x7D7313A2D1497577, 0x29CF10A332B6, +0xF69CB74F4B2312A7, 0xFE2141EC83DB9093, 0xC737A8013581358C, 0xEA1B48DD7839A2B9, +0xE6C3BA0539731E55, 0x4FE8934AFCB2DBA2, 0xD43C9C3F683EB974, 0xDC4B387E3B881758, +0xACDE8CF447B4667A, 0xE3C6D891BE3F6F8A, 0x2F4F1B2FED420A5, 0x4AF4A04F7EDA, +0x4CDDB1050FF54A9D, 0xF52C072234A751BC, 0x7EF2C3B0D4F0FB9C, 0x26E3E48F3F75B53F, +0xFC93F7EFD3101B26, 0x3F777590510AED37, 0x37EE1A1732F029A3, 0xAC2703036C959234, +0xB1613D5B238EEFC0, 0x14BEF779A3272D96, 0xFFA5D9936C6F57AF, 0x48145DDE5D84, +0x7930B4D3AFF7623C, 0xF579D82ACA0EB325, 0x7CAE78FCEF56CD16, 0xD54874E796A5AF24, +0xFF0928F57C5BD203, 0x1ADCC7CFA1C533A3, 0xBA14EA874674D3D4, 0x65CD865C41EC0246, +0xD564F88596889248, 0x7B65445DF0291D00, 0x4FFDE34C11FBD732, 0x202E78EB43E1, +0xE55BE122B67AFE2D, 0xE45AE41FD3CC1390, 0xBC667DFA66539555, 0xD85470081E324755, +0x678E52FB7559B94D, 0x4B83A7C24B6A3824, 0x3DF099DF7025B8D, 0x85043A9B1F72F6DE, +0xF9AD22B317560A91, 0x691AD1A859A290EC, 0x6EC3B345674A072E, 0x6DB6E9866087, +0x3B6774ED233ED497, 0x7DFDBFF0B8C33FBD, 0x1A6FF897BD3AF7F, 0xF6C8663010B605BB, +0xAF82A409B891C427, 0x93647FA1C36D6BCC, 0x297153BFDE90B93A, 0xA008B10A0D0502C1, +0xA317DAEEFB021D41, 0x7B3467F72423A93F, 0x4724FAE9816E19E0, 0xE4B0D1E692D, +0x3F3AD94B8CFC8908, 0xAE39264BADAC6B3E, 0x34DDF5849F69666, 0x15B26B312BF7D825, +0xA98481F96E75CF29, 0x63A564E31003DB6C, 0x169D2009CE8F6D2F, 0x6A1DFABF806A9D0B, +0xEF529AD1F1B16F94, 0xCFA27EB2F415DF7C, 0x12A28DCAD099F7EB, 0x3F1D04D6B540, +0xD5EF67D17501920E, 0xEC581EE34206DE9D, 0xC0A40DF96BAE4C15, 0xAB5797EC29219B32, +0xE37FF347DC996140, 0x7845D81C58B1F068, 0x32CBCCB7D206AB07, 0x47AE6786EACDF058, +0xE307D29DCE92BA2A, 0x14E895B8F9F6AD8E, 0xBCA43646758320B0, 0x1524A09074BF, +0x777774041B0CE1F8, 0xEE4E9A95DF96B2FA, 0xAB79D65A4251114C, 0x9B8D054F5487E829, +0x746354637DF490E7, 0x74623B2D676D29BE, 0xC56CB27124264B7A, 0xAB78F4A7BBE5D610, +0xC97AA31A9488372C, 0xD1065224267A0F6A, 0x5AF06E5CF449B916, 0xF50AE676A6E, +0x50E62E54B2E87301, 0xBF0A643FA8B4DDDE, 0x7CFCF55BE5416988, 0x3F52CD98FD999820, +0x8A521DA6C3E6E21C, 0x54FFDD969802C059, 0x5780676B3BEDCB0F, 0x4D0E5EB6CD677A43, +0x9D9A3AF09C5E8DB4, 0xC03376BE331D0876, 0xCBDCF7C3C349A0D8, 0x49A3DC9874AD, +0xA05EAAB8C9BDE361, 0xBBACD4C2509610B8, 0x1BD0354BA8EE1C41, 0xB63DE836D1CF448D, +0x2C3D81D0D6001430, 0x8EE5F1599B51142, 0x3AFC5F93A2094C5A, 0xAD9F00F33C7BCC36, +0xCC53DECF2C70C0E1, 0x75A6BE224961CB24, 0xA5FFD47CE0201406, 0x260334B0E8AC, +0x947BE05B275FF3BC, 0xBEF35F81BDE60736, 0x6BB16108963EB92B, 0x260CDC5CFE9FCA2D, +0xB64D81EE29F0422E, 0xE9A96B78E03D317E, 0xDBBFF8525B0B9D08, 0x489961EDE56D5F05, +0x8486CFB4FAD913E5, 0x201AB18D2E9C35F1, 0xAB4C544E4189EBFC, 0x52F60D390FF5, +0xCF7F647818703378, 0xCA8D6E5CC199509C, 0x6508F68F7BDCBE0, 0xC868FFF8C3FBB311, +0x61DFCBAA7C9965AF, 0x4763D41CBF6A65D6, 0xFF9EA78F40574CFF, 0x1B0981E2E182B85D, +0x8F39686AB54CAD5F, 0x8F79D205DCA1C13D, 0xF491AC44B180924B, 0x68215502D936, +0xAD41F9E45A7AE4C2, 0x52FB46556B4C4239, 0x5B393866A3DC800, 0xF6FB9729D903C714, +0x525846399056D232, 0x7C04FFB8CEEA4336, 0x8A7AE6EDACC8D150, 0x567436CAE3D48C37, +0x2019114B0928DA77, 0xD8087C1798C68A66, 0xAED0EEE7E4A67A6, 0xA8BA7BFFAB2, +0x12E49DFD3495F0DF, 0x97C7690271F02A94, 0x89BEE6C3145D0CE9, 0x3DA863DC8C497AED, +0xA09902C19E2D5EC8, 0xD5877B4B793BE359, 0x682CF667DEAEB22C, 0x7C71EF563762AB50, +0xF25C27EA0A72AD0B, 0x166B2BB7ABAABE90, 0x1E6F57A164F6485D, 0x376F983A1111, +0x4D713026D898E1FE, 0xA80B1B9E52AD4565, 0xD08097D212BD8533, 0x5C4CC160EF4A1EE5, +0x1B3FB4D6C031BD9B, 0xE727AB389C0BE2A4, 0x52E057D21775A2BA, 0x408A5A31061074CA, +0x256192F282DC2F64, 0x29AA8B5DE742221C, 0x1785490F4F4A27EA, 0x4DFD6EBFF14B, +0xC1FF64E6AD802C0B, 0x68CF36453DAAE4DF, 0x387ADFB2F5305825, 0x80731715ED3D5891, +0x22AD8F352BB7391F, 0x75505D7556AF5DAF, 0xB3809032AFAE94E9, 0x2920EB485F566FC9, +0xF3533032C7109CE1, 0xA42C31AD0C38DEE7, 0xA7D0B1B4011BB483, 0x56597954D087, +0x37DF8020E63601A9, 0x61FF8EFD4CCB7FCC, 0xE05E27C19AE72C7A, 0xA0AFC6B2C7788BFB, +0xD44F084AA4DC1F2C, 0xB0013C8613446BA6, 0xBC57E796306F0791, 0x1FBB4FB326418CCF, +0x4C31005C8AD3016A, 0x6433506F86D56B8E, 0x7661AA230C749889, 0x3A9AD6628533, +0x7D5F07406B78DC66, 0xD0C1A2C72EBA5032, 0xF991E71EB5C9313C, 0xF9236EA7575E0B42, +0x88B52B8041839A28, 0x36FC6A483E43B526, 0xF4E7AC46096E0C1E, 0xD7FAC39B0B63695E, +0x810F75D31A3616A0, 0xC1EE6CFED4A37636, 0x2EFEE4561AE7A50F, 0x6750799873B7, +0x609599110A5F3D67, 0x3BD789C721897187, 0x50D3EF6A13105673, 0x9E5E02B09FEECC22, +0x2704C3833EF70F47, 0x9C99277154B8E684, 0xE0FF03EB99F94612, 0x77F9FE62CC9613E5, +0xB12C320176A87E77, 0x5E191289C4ABFC53, 0xB060F409121F1699, 0x62D6408A987, +0x39BB70FF237110F5, 0xE90E3B03EF738F74, 0x8907FEB153DFD12C, 0x988CAF0B4DD52F6, +0x9C1D16A181A4A4D8, 0xFD4B966FBA7520CA, 0x4C77C87DFD898E7F, 0xAD25306D911111D8, +0x79A07CB257064DBB, 0x751322A905EA0DF9, 0xB81071DB113BF999, 0x16B29A8AC59A, +0x2FCBDC23682572D1, 0x59894B9332AF87E3, 0xA7F8A5D3C6B1538D, 0xEC4BF918405E20CE, +0xB34D6419CF8DFDE2, 0x803DEB7DFC02DC32, 0xBA3C7D057AF27DA0, 0x2BEB5CAF9C9747E7, +0x319F85023D7B10B8, 0x9648E2061A2108DC, 0xF6276BE3FA8BC7DC, 0x473C8BA0459B, +0x99C76C144C052E8D, 0x334DC40BBB3996AD, 0xBEAFD2D89C78248A, 0xFE7EB7CD75CEFA17, +0xA0D2442A24979501, 0x93A8E9DA87B24482, 0x4CFC19DF3EC6B24C, 0xBBD8494110F430, +0xA6065FBC65A2A388, 0x2583F9E9F247E9E8, 0x1A2128710E3E9B16, 0x60D254FFB63D, +0x730F66F21A098041, 0x7F4F2CC18EFF73F8, 0x2A2D35794612F0D6, 0x724694BC44ED8711, +0xDB530CF8665161CB, 0xF3A006C94F83E678, 0xAD90914CAEBF9796, 0xB15A239C918AFFB8, +0x49427633FBBCBF63, 0x711B5F96040BD253, 0x37A1C953F9D7137F, 0x2188556CDE16, +0x8FCDE842080679D, 0xD3877D6C2685608D, 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0xCEED86A0106D1D00, 0x17C0AF6653F02438, +0x841A62A6D28D50E8, 0xC80A6C2FB70778C7, 0x66FDDD651F679059, 0xB4CD1ADEFD25464F, +0x2F549A758C64E4D4, 0xFF959796F158E5DE, 0x5E5D23DF2A3B20D6, 0x30530AC15334, +0x7D9164ED3F513D5F, 0xD7E7370890A80C1F, 0x32345AA52CCD2BAD, 0xD237083AF464F428, +0xBC1C2D9476B07EC1, 0xDF335D4986270DA8, 0x9CC36315CEB4EB24, 0x94F04B88189C2E62, +0xEA173E9289BE5CC3, 0x8ABF429DD2CBCE73, 0x271F8587907751FA, 0x26BBEAD6D08F, +0xFD42D9F8DFAF2B54, 0x27E4B9E261EBD9BB, 0x12E53F1A1788902D, 0x614BF3AB893EF060, +0x9284168A1F4C33BA, 0x24B27D6CD1C82F80, 0xA3506BDD8B226323, 0x2C7D14731CC482AE, +0xE27C2ABD813ADFAB, 0xCDD799D88281A24F, 0x57B25E547F30C74E, 0x5BF31EE7CC40, +0xC72C063D2AAE5D93, 0xE9437F48D532F889, 0xB61CE08BC13CCF95, 0x68B3BCE23B0A4474, +0x9EFF4E662EDBC49A, 0x3C66BF33897184AC, 0x24E32F3C35C3AB9E, 0x2FD449E12CFE5AA5, +0xBC884D9DBF6CE7C7, 0xAAFE16ECCAF72E6E, 0x257E67D596CA8E85, 0x55F611CDC981, +0x7056887E5883EABA, 0xEA77C44A48F7D2AE, 0xBFC783D6BB39575E, 0x1C554FC0F325341E, +0xE23EEE560F1B5112, 0x5AC70D75BCC215C, 0x74151B32FFBDD90A, 0xB5372C5CA5CD10F3, +0xD91C766FC61C3289, 0xCD58BFB5D5CD11ED, 0xEC5E0A60B4E32998, 0x6EC753D510D3, +0x58B22947490B8887, 0x4B10647E1F376725, 0x471EDF1C9A4E284E, 0xA726244CC3876322, +0x72FD1A14B2CD6FD2, 0xF9EF896D3DEE2725, 0x9A28D904283ADE94, 0x1AFEBB9539505717, +0x1C0E04EA188A6589, 0x89B27E66D3CA8E14, 0x68B5408318DF6EAD, 0x15F1376D91B, +0x6B63F896DE29FC8B, 0xF53306D24B39A502, 0xD5687AEFD069C6DE, 0x4550D0DA397F756A, +0x82D063B3AE27AE45, 0x878EABA0F39CD296, 0x91461C5912F24CC9, 0xEDCE4E214AD17E97, +0xBE39C3E01CC36303, 0x7093ACBAF7D5A4BB, 0xF74FFD24B80E1716, 0x5F23A42DF1C9, +0xA2F509ACA849FA9B, 0xAE350A201C9CC29B, 0xC37C41E8CB32B00, 0x3DE946804C2F5BA2, +0x1E408D035D1F66DC, 0xE9B2D09E91A5EBC5, 0x30ED4AEB468E23, 0xE992D740E5A4DAD8, +0xA4DA8E6EACFC1DF9, 0x4717E55C565BD942, 0x7E008535D2D324FE, 0x53479F387512, +0x706324FC10980020, 0xB323960F621EEFDC, 0xA45A0C708DD07CE3, 0x2BE4297B3C3599BD, +0xB671A6B69F3AAF6E, 0xBEB5CF5180B1E19, 0x7CFFACA60915754B, 0x304BB79DD1E863AA, +0x5EF1F5B6A85C4C6A, 0x7FA5D5AD06AC0862, 0x76751FDCA472F889, 0x3DFDAA509735, +0x87D29CD1326B7E33, 0x750AEEAC58103933, 0x71DE8581358E63A5, 0xED90B578A58E60F7, +0x2E56F945FB6D3987, 0xFAAB25859CCEF21C, 0x25D6CD62C8B2FD49, 0x43F9B11C075BB3DB, +0xF8E8BFD74B64494, 0x81BA570CD6F32C8E, 0x9CA5E1062D425358, 0xCFBE588C01, +0x1B39C646FB91632D, 0xFDC30365B1C4CF12, 0x57BB56A60975D4B2, 0x9DC66467CB466B8C, +0xFEF903A3871C4EC, 0xE269852E52B546AA, 0x609779856A33FD32, 0x5C84AFFEAC71EE60, +0xB96B46A956FBA3BB, 0x60BCDBE69195EFC, 0x7C0EED6A797FE3D7, 0x5808F582BBEC, +0xC60103FF55334D85, 0x986966A33D6517FF, 0x84EAF8A60493A34C, 0xFA9E8D8E03B9A1D0, +0x654E25A495BEA1FC, 0x4BCD540BFD46B575, 0x5D2338DA4A2BBD5B, 0x7AF5AC8694381272, +0x3C8DDC5C7962CD35, 0x88F4301650D79C4E, 0xDA918DD29E46B90D, 0x3305DA26356D, +0xA197F1B9D7577089, 0x23389CABE1A02A64, 0xCE0C1505D8D3A36E, 0x3EF64D892396A6E2, +0x7F04CD4A24F1381F, 0x517D72779F1E975B, 0x592506E5AFD115EA, 0xCA60198D3538B967, +0xF306D5876B2EBE70, 0xD1E91248F4B0B2EA, 0x2CBD02D7E3AD393A, 0x5EA6A48D927B, +0x23349556C131FB73, 0x1AA7552B421FF020, 0xEE0EBB7C76DBE482, 0x6A5127F710DE980B, +0xB96FC57DDF912668, 0xD89D31D50A99797A, 0x484067673650D761, 0xDE33896724DEF1F1, +0xA5D31C6E0431D492, 0x4835A3305DDB74A4, 0xD0BB1E1070CB52D5, 0x21EAD8AE4F41, +0xE086C97DF529E919, 0x1C1C275E695F00ED, 0x456E26CF17BCDD9B, 0x204C75673CE8ABE8, +0x77FF4D6235CD70E4, 0x3F5230C0ED2FBC55, 0xFDBF5A76046356A7, 0xE8D3F42EC462B653, +0x65FC5B72A26BFE01, 0x58EE51C24D09340B, 0x51296B33808A3F31, 0x3AC386DAB60C, +0xAE43D55F7B0580BD, 0x6BA5EE2ECB7A2ECB, 0xAD8839E567BDC982, 0x2F0B8998E0405E9E, +0x75BF8BBAD2336080, 0x95B794166AEAB45F, 0x8D72D18874ACDB7C, 0x71BE5C46E5E9A0AD, +0x7441AFE4D0D5F48E, 0x922468E87BCFDE94, 0xD3FFB3C46172436, 0x5F92280E6A37, +0xF414D56B0EDC4747, 0x64916AC4660261FC, 0x9EBEB33906AD8953, 0xEDBE52E0DA53D198, +0xB62B69D7CBDE1144, 0x68BC69F9383ED43A, 0x72C618308BEB1FC1, 0x89FF71486F43C437, +0x7955B6B132A4DB30, 0xBC2CA9E22893BE1A, 0xCCF5F3154781007F, 0x4E046F5B8EEB, +0x4659FB28151C8DE4, 0x39A7FA767E6FA3C5, 0x1F333A51A592861C, 0xC24D9F7725CFBC89, +0x5EDD8B4B0BFE8E08, 0x1925C4979A2E9A19, 0x7704E8814E14747B, 0x1586A214C0E2520A, +0x55A3297B1B6C93AB, 0xCEDE2C89ED91492C, 0xB3700269D73171A5, 0x517B6BB3E04D, +0xC2048946D8DDF9FD, 0x136B7B77C757F782, 0xECC50261633088D9, 0xB680BA279C8F1B07, +0xB28548AB84F5D6F7, 0xB5E6690E0B0D2958, 0xE1C114A3020F3B42, 0x8ADF56025A3C83C6, +0xD9F2F147C6909FD5, 0x5EC60774F45705CA, 0x491F08403B362879, 0x4BCBF3C05E0E, +0x886265A7E4CEBBB6, 0xC2AE750591294A7A, 0x2DCA149D7CAFD814, 0x506102192C27BEEC, +0x7F35EDBCB3B01615, 0xE92AC980D416B428, 0xB7EF9622FC844ED1, 0x259581F38AC3769, +0xC108F44159EE5034, 0x9A71A67221103434, 0x8FE3849C196E878F, 0x75626D6A7DC, +0x1E0A16D78C626344, 0x226AB76C19AE111D, 0x21CBAD5C4FA21FBA, 0x1526DA66F753BEC2, +0x3E40CFBA1578A898, 0x9A682A0058EC6166, 0xE8A0433E1358EFA8, 0xF240856F0B497F7F, +0xCFAD5125225D3BFF, 0xC691B4FB463DE7E6, 0x90C2DEBF41DC6D5F, 0x11FCEAC513DE, +0xBA5C6C2911F980BC, 0x9C35A5DFD47773CD, 0xADB2548101BDF4E6, 0xE54D9F6E60667FC3, +0x435700CE7A378055, 0xB5C9EE54DA5FF464, 0x70A148C198BACDC0, 0x2BE4444A6AA87B57, +0x33B2EAFCD62AA4E2, 0x2BD60156072C9955, 0x4D909F98BA33B407, 0x40B14FFCB239, +0x66519FEE56007A3, 0xBF9E0087BBB7830E, 0xF7747552E4010EC9, 0x47AC410A15692AB5, +0x1DCA01780E007C33, 0x9C7C599F0E063BB6, 0xB41A3DCC200CF2F7, 0x888F63DC314609EC, +0xFF7718AA36AF9B93, 0x7DABBE90849B80B0, 0xBC6F5AD58FBE9F47, 0x3EA591DE227F, +0xF87B3774C50FDDE, 0xCC673CFE8F68D09E, 0x1C20CCB31926F562, 0xB5C1C7542B1A7ED4, +0x15B5CEC813F1C297, 0xC101D5B76AD0F30D, 0xDC5ACB9F20A914C9, 0x600E05863330862A, +0xA22340AC35E9B70A, 0xF8F425BCF901E6E2, 0x790452E8484D4376, 0x6D539A740DA5, +0x6237F4ED1ED274CC, 0x7B992E6D1876B6D7, 0x7912B44F1E12B6AA, 0x8400003624A71447, +0x1C1F41B6930631D, 0x404A73C2A7ED8AE0, 0x4A91BD587C4C2FC1, 0x19BF0A548B1B76CF, +0xC78006129BE1AAB2, 0xEBE771AD7D7B353C, 0xA9B37F23C5805620, 0x25214E5E7866, +0x457BF00CF9C66311, 0xE70F9C9D451F6CDE, 0x9073C55282756066, 0x8AC30E6D1956FE22, +0x60C68FB2AB2CD96B, 0xCB6F6B64BDEB70F2, 0x245ABF0C5B475FFC, 0x8DE20C6B0151F862, +0x35ED831720063B28, 0x70BC87CAAF983119, 0x68C8FC39D67A971E, 0x2BD694ABDD9, +0x5F36AF1C6F0E9A5B, 0xD9EB532CA7C44C4C, 0xBE00EF63820E3FE9, 0x3228406BD0EE879E, +0x65086D9937814A91, 0x6D50C2B2BB985EC8, 0x99121655EACC8D30, 0x682874872952D9DF, +0x9EF725300D0DD7C3, 0x43C05F5486B1D386, 0xA99DE4C6D79F3519, 0x63F8D92A7571, +0xCB95C30FC3174D35, 0xEB2D804ECC6FCD08, 0x6F64D7C1DC92882, 0x632F8C3CDA3D32E6, +0x4B810F8D093F0DA2, 0x73E4FE3AD967E64A, 0xBAA3DC15787BE9E6, 0xA3EE912C5EBBD4D7, +0xDB27AB863331109B, 0xFD2F7D2AF3DD92B8, 0x2C1B1850368F487D, 0x4A22D98E9F68, +0x24F87291E2A07F12, 0xDA6A9231AAF6BD64, 0x8CD2BCD6F3A7A617, 0x55DCC041BB1C18D1, +0x74E836F38891757D, 0x6EF32A847FF5488, 0xBCCC16A32572A83F, 0xFC131A8BE7D5591D, +0x5F01911C8F0BDC7D, 0xE357CC673FC652F3, 0xE5911670A82801BE, 0x46CE1687F71E, +0x1514525367BCD0E5, 0x2B22BAB04D11B869, 0xA68B5BA67A2C0227, 0x12928C65959A6E72, +0x6D75FF5512A6FDE5, 0x2A3F9D2021AEE65B, 0x8D5AEDC8F8125590, 0xC4D958DCDDF7DB06, +0xE39351EA9592245E, 0x1EE0ABCF0FD05085, 0x7579DE7B721F8D3F, 0x4E2801128E4, +0x17B0959467EC8E27, 0x295DBAC9D48B1B26, 0x114120B6CDEF3FE6, 0x4D5C26171008794A, +0x2353914B84B8B55D, 0xA30DC896A6DD004D, 0xF7606531B244E8B3, 0xB8075F8DD844102D, +0x8F0A1EBEC1E3801, 0x4340C408EAE9DF0A, 0xD73EBC3AE19A6404, 0x506C451132E1, +0x4055AC928B226585, 0x3E08FD03DA5062CF, 0x53D79EED1399D30E, 0xB3D37032CC4D489E, +0xB771F96700F79F9D, 0xA11CE98855CD5AEF, 0x5873EE54DEBD52E2, 0xC62EC293E8BFD596, +0xF71CD796793DEE39, 0xF8B0C45C51C78C91, 0x1CB88C7BD8767DA0, 0x578543F8D455, +0xC3E0C2B6BAB78CB7, 0xB903667D4558326B, 0x54E4AE2B85F23911, 0x5649D99D06BB61FF, +0xD09785C64F1B4029, 0x8BB26D1292D78CAB, 0xBCCA9514540915D7, 0x76BE7E9FF4C3DE3F, +0x72E4AD6F7BE0004B, 0xF2E439AE536E2E, 0xBFC66F367F87E558, 0x4894C93B1B03, +0x867BBFC0E08A6D07, 0x3B5E68AD7EFA1083, 0x17D461189A4B3FA9, 0xB833EA51082E6C15, +0x37A67B06B1465753, 0xD8EF3548E2D08CE8, 0xEBAE029CEEE344E3, 0x5BD9E8AB7E4D077B, +0x332CF5ACF9DD15C6, 0xC34BE7AFAAA087D7, 0x2D7698A34F912614, 0x34452A442EA5, +0x84BC9927764FF643, 0x2F3FF1E0A9458E3C, 0x3C56A96BCC54530B, 0xE052EEC6BEEB6EF4, +0x1C5A198D9FEB8C8C, 0x21EEFEC6B6392FC5, 0x744365BC036E4C06, 0xB1A87629DB585882, +0x67025185091206E0, 0xE2609BBF520CE6C0, 0x3B3C52B3C164DE7B, 0x5B7196743997, +0x9DD99D1609E1CEC3, 0xEB58F112EA33D47F, 0x57C51C69E8A419D2, 0x8169F935EDF95AD6, +0xB85B11F27B15D1D0, 0x82DC90C4DB2E1257, 0x9420312993366C99, 0x910F774C19AC3494, +0x53E0D099427A90EB, 0xBE1D153B78FC793C, 0xAD612FC1291631AA, 0x56DB79C9A67D, +0xC646415B40C651B4, 0x10C2384F19971F2F, 0x65DBF9F71C0B3F2E, 0xC7856509C94819D3, +0x54A80DC50F93355A, 0xABE5293E42DA5556, 0x2939A8601913CD3, 0xEAE995FA8DF4A95D, +0x97F2C96AD632F013, 0x587DCA665B14D3FC, 0x205BF123277E84AC, 0x5BAA0A8F34C0, +0xD4DF793521E66053, 0xDBFF6F5D95305442, 0x73C399CE95AF8A1C, 0x81FB12A972AC7321, +0x6DAA1AF4CA30A820, 0xA4E6931E8150498, 0x954969150AA962C4, 0x6C9AA122565C9A66, +0x7CB81205ADF37420, 0x5AAA4E6E2849B52B, 0x297B9337817F4C75, 0x5AE710F672FD, +0x6DD08, 0x0, 0x0, 0x0, 0x0, 0x9A80000000000000, 0x1B8A7F275C1CCC8A, +0x61D12C23A9F5A1FA, 0x518A8EB02E290214, 0x608B67A91963E4BC, 0x24D426A5C77D7B55, +0x182B98F4BA8A, 0x2AFD75A913ECF8DF, 0x2918FBA06F88C9AB, 0xA4AC4DC7CB526F05, +0x2D19E9391A607300, 0x7A79E2B34091B54, 0xA05809DCB42F1792, 0xB8D6FA0B2FB9739F, +0xB92947307436AD45, 0xA478488AA072D9C3, 0x76EF5DE652478B48, 0x21B5B2D9A016385E, +0x36FB1719882D, 0x3728ED40E235CBB7, 0xEB8E134CA64361D5, 0x38E95CE4C097727, +0x517C1D90F7A63229, 0x3FFD4FE250E112DB, 0xD19B655E70A2D616, 0x4144CF18F5C1713C, +0x634C0C1C04B3343D, 0xA130EEA94CB71A24, 0xE99FAA56357D2570, 0x60EAD2DDB8B4022F, +0x3CC58DD89435, +0x4935A, 0x0, 0x0, 0x0, 0x0, 0x620000000000000, 0xAA4F63C86EB8D8CD, +0xD2EF2F7E7E9E49A0, 0x913B6F6558B89C5C, 0x99496873A40ED2AD, 0x21EF24D8EA258FD2, +0x5AB64979CBC4, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, +0x2AFD75A913ECF8DF, 0x2918FBA06F88C9AB, 0xA4AC4DC7CB526F05, 0x2D19E9391A607300, +0x7A79E2B34091B54, 0xA05809DCB42F1792, 0xB8D6FA0B2FB9739F, 0xB92947307436AD45, +0xA478488AA072D9C3, 0x76EF5DE652478B48, 0x21B5B2D9A016385E, 0x36FB1719882D +}; + diff --git a/src/P751/P751_internal.h b/src/P751/P751_internal.h index 4bc7d6f..f29182f 100644 --- a/src/P751/P751_internal.h +++ b/src/P751/P751_internal.h @@ -55,6 +55,35 @@ #define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8) #define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8) +#ifdef COMPRESS + #define MASK2_BOB 0x00 + #define MASK3_BOB 0xFF + #define ORDER_A_ENCODED_BYTES SECRETKEY_A_BYTES + #define ORDER_B_ENCODED_BYTES SECRETKEY_B_BYTES + #define COMPRESSED_CHUNK_CT (3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES + 2) + #define UNCOMPRESSEDPK_BYTES 564 + // Table sizes used by the Entangled basis generation + #define TABLE_R_LEN 17 + #define TABLE_V_LEN 34 + // Parameters for discrete log computations + // Binary Pohlig-Hellman reduced to smaller logs of order ell^W + #define W_2 4 + #define W_3 5 + // ell^w + #define ELL2_W (1 << W_2) + #define ELL3_W 243 // W_3 = 5 + // ell^(e mod w) + #define ELL2_EMODW (1 << (OALICE_BITS % W_2)) + #define ELL3_EMODW 81 + // # of digits in the discrete log + #define DLEN_2 93 // ceil(eA/W_2) + #define DLEN_3 48 // ceil(eB/W_3) + // Length of the optimal strategy path for Pohlig-Hellman + #define PLEN_2 94 + #define PLEN_3 49 +#endif + + // SIDH's basic element definitions and point representations typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 751-bit field elements (768-bit max.) @@ -64,6 +93,16 @@ typedef felm_t f2elm_t[2]; // Datatyp typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates. typedef point_proj point_proj_t[1]; +#ifdef COMPRESS + typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates + typedef point_full_proj point_full_proj_t[1]; + + typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates. + typedef point_affine point_t[1]; + + typedef f2elm_t publickey_t[3]; +#endif + /**************** Function prototypes ****************/ @@ -81,7 +120,10 @@ void mp_add751_asm(const digit_t* a, const digit_t* b, digit_t* c); // Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit unsigned int mp_sub(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords); -digit_t mp_sub751x2_asm(const digit_t* a, const digit_t* b, digit_t* c); + +// 2x751-bit multiprecision subtraction followed by addition with p751*2^768, c = a-b+(p751*2^768) if a-b < 0, otherwise c=a-b +void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c); +void mp_subadd751x2_asm(const digit_t* a, const digit_t* b, digit_t* c); // Double 2x751-bit multiprecision subtraction, c = c-a-b, where c > a and c > b void mp_dblsub751x2_asm(const digit_t* a, const digit_t* b, digit_t* c); diff --git a/src/compression/dlog.c b/src/compression/dlog.c new file mode 100644 index 0000000..533581b --- /dev/null +++ b/src/compression/dlog.c @@ -0,0 +1,182 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: Pohlig-Hellman with optimal strategy +*********************************************************************************************/ + + +void from_base(int *D, digit_t *r, int Dlen, int base) +{ // Convert a number in base "base": (D[k-1]D[k-2]...D[1]D[0])_base < 2^(NWORDS_ORDER*RADIX)into decimal + // Output: r = D[k-1]*base^(k-1) + ... + D[1]*base + D[0] + digit_t ell[NWORDS_ORDER] = {0}, digit[NWORDS_ORDER] = {0}, temp[NWORDS_ORDER] = {0}; + int ellw; + + ell[0] = base; + r[0] = D[Dlen-1]*ell[0]; + for (int i = Dlen-2; i >= 1; i--) { + ellw = base; + digit[0] = (digit_t)D[i]; + mp_add(r, digit, r, NWORDS_ORDER); + if ((base & (int)0x1) == 0x0) { + while (ellw > 1) { + mp_add(r, r, r, NWORDS_ORDER); + ellw /= 2; + } + } else { + while (ellw > 1) { + mp_add(r, r, temp, NWORDS_ORDER); + mp_add(r, temp, r, NWORDS_ORDER); + ellw /= 3; + } + } + } + digit[0] = (digit_t)D[0]; + mp_add(r, digit, r, NWORDS_ORDER); +} + + +void Traverse_w_div_e(const f2elm_t r, int j, int k, int z, const unsigned int *P, const f2elm_t *T, int *D, int Dlen, int ell, int w) +{// Traverse a Pohlig-Hellman optimal strategy to solve a discrete log in a group of order ell^e + // The leaves of the tree will be used to recover the digits which are numbers from 0 to ell^w-1 + // Assume the integer w divides the exponent e + f2elm_t rp = {0}; + + if (z > 1) { + int t = P[z]; + fp2copy(r, rp); + for (int i = 0; i < z-t; i++) { + if ((ell & 1) == 0) { + for (int ii = 0; ii < w; ii++) + sqr_Fp2_cycl(rp, (digit_t*)&Montgomery_one); + } else { + for (int ii = 0; ii < w; ii++) + cube_Fp2_cycl(rp, (digit_t*)&Montgomery_one); + } + } + Traverse_w_div_e(rp, j + (z - t), k, t, P, T, D, Dlen, ell, w); + + fp2copy(r, rp); + for (int h = k; h < k + t; h++) { + fp2mul_mont(rp, (const felm_t *)&T[(j + h)*ell][2*D[h]], rp); + } + Traverse_w_div_e(rp, j, k + t, z - t, P, T, D, Dlen, ell, w); + } else { + fp2_conj(r, rp); + fp2correction(rp); + for (int t = 0; t < ell; t++) { + if (memcmp((unsigned char*)&T[(Dlen - 1)*ell][2*t], rp, 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + D[k] = t; + break; + } + } + } +} + + +void Traverse_w_notdiv_e(const f2elm_t r, int j, int k, int z, const unsigned int *P, const f2elm_t *T1, const f2elm_t *T2, int *D, int Dlen, int ell, int ellw, int ell_emodw, int w, int e) +{// Traverse a Pohlig-Hellman optimal strategy to solve a discrete log in a group of order ell^e + // Leaves are used to recover the digits which are numbers from 0 to ell^w-1 except by the last leaf that gives a digit between 0 and ell^(e mod w) + // Assume w does not divide the exponent e + f2elm_t rp = {0}; + + if (z > 1) { + int t = P[z], goleft; + fp2copy(r, rp); + + goleft = (j > 0) ? w*(z-t) : (e % w) + w*(z-t-1); + for (int i = 0; i < goleft; i++) { + if ((ell & 1) == 0) + sqr_Fp2_cycl(rp, (digit_t*)&Montgomery_one); + else + cube_Fp2_cycl(rp, (digit_t*)&Montgomery_one); + } + + Traverse_w_notdiv_e(rp, j + (z - t), k, t, P, T1, T2, D, Dlen, ell, ellw, ell_emodw, w, e); + + fp2copy(r, rp); + for (int h = k; h < k + t; h++) { + if (j > 0) + fp2mul_mont(rp, (const felm_t *)&T2[ellw*(j + h)][2*D[h]], rp); + else + fp2mul_mont(rp, (const felm_t *)&T1[ellw*(j + h)][2*D[h]], rp); + } + + Traverse_w_notdiv_e(rp, j, k + t, z - t, P, T1, T2, D, Dlen, ell, ellw, ell_emodw, w, e); + } else { + fp2_conj(r, rp); + fp2correction(rp); + if (!(j == 0 && k == Dlen - 1)) { + for (int t = 0; t < ellw; t++) { + if (memcmp((unsigned char*)&T2[ellw*(Dlen-1)][2*t], rp, 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + D[k] = t; + break; + } + } + } else { + for (int t = 0; t < ell_emodw; t++) { + if (memcmp((unsigned char*)&T1[ellw*(Dlen - 1)][2*t], rp, 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + D[k] = t; + break; + } + } + } + } +} + + +void solve_dlog(const f2elm_t r, int *D, digit_t* d, int ell) +{ // Computes the discrete log of input r = g^d where g = e(P,Q)^ell^e, and P,Q are torsion generators in the initial curve + // Return the integer d + if (ell == 2) { +#if (OALICE_BITS % W_2 == 0) + Traverse_w_div_e(r, 0, 0, PLEN_2 - 1, ph2_path, (const f2elm_t *)&ph2_T, D, DLEN_2, ELL2_W, W_2); +#else + Traverse_w_notdiv_e(r, 0, 0, PLEN_2 - 1, ph2_path, (const f2elm_t *)&ph2_T1, (const f2elm_t *)&ph2_T2, D, DLEN_2, ell, ELL2_W, ELL2_EMODW, W_2, OALICE_BITS); +#endif + from_base(D, d, DLEN_2, ELL2_W); + } else if (ell == 3) { +#if (OBOB_EXPON % W_3 == 0) + Traverse_w_div_e(r, 0, 0, PLEN_3 - 1, ph3_path, (const f2elm_t *)&ph3_T, D, DLEN_3, ELL3_W, W_3); +#else + Traverse_w_notdiv_e(r, 0, 0, PLEN_3 - 1, ph3_path, (const f2elm_t *)&ph3_T1, (const f2elm_t *)&ph3_T2, D, DLEN_3, ell, ELL3_W, ELL3_EMODW, W_3, OBOB_EXPON); +#endif + from_base(D, d, DLEN_3, ELL3_W); + } +} + + + +void ph2(const point_full_proj_t phiP, const point_full_proj_t phiQ, const point_t PS, const point_t QS, const f2elm_t A, digit_t* c0, digit_t* d0, digit_t* c1, digit_t* d1) +{ // Computes the 4 coefficients of the change of basis matrix between the bases {phiP,phiQ} and {PS, QS} + // Assume both bases generate the full 2^eA torsion + f2elm_t n[4] = {0}; + int D[DLEN_2]; + + // Compute the four pairings + Tate_4_pairings_2_torsion(phiP, phiQ, PS, QS, A, n); + + solve_dlog(n[0], D, d0, 2); + solve_dlog(n[2], D, c0, 2); + mp_sub((digit_t*)Alice_order, c0, c0, NWORDS_ORDER); + solve_dlog(n[1], D, d1, 2); + solve_dlog(n[3], D, c1, 2); + mp_sub((digit_t*)Alice_order, c1, c1, NWORDS_ORDER); +} + + +void ph3(point_full_proj_t phiP, point_full_proj_t phiQ, point_full_proj_t PS, point_full_proj_t QS, f2elm_t A, digit_t* c0, digit_t* d0, digit_t* c1, digit_t* d1) +{ // Computes the 4 coefficients of the change of basis matrix between the bases {phiP,phiQ} and {PS, QS} + // Assume both bases generate the full 3^eA torsion + f2elm_t n[4] = {0}; + int D[DLEN_3]; + + // Compute the four pairings + Tate_4_pairings_3_torsion(phiP, phiQ, PS, QS, A, n); + + solve_dlog(n[0], D, d0, 3); + solve_dlog(n[2], D, c0, 3); + mp_sub((digit_t*)Bob_order, c0, c0, NWORDS_ORDER); + solve_dlog(n[1], D, d1, 3); + solve_dlog(n[3], D, c1, 3); + mp_sub((digit_t*)Bob_order, c1, c1, NWORDS_ORDER); +} \ No newline at end of file diff --git a/src/compression/pairing.c b/src/compression/pairing.c new file mode 100644 index 0000000..efe8340 --- /dev/null +++ b/src/compression/pairing.c @@ -0,0 +1,644 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: pairing computation for compression +*********************************************************************************************/ + + +#define t_points 2 + +void get_A_compression(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xR, f2elm_t A) +{ // Given the x-coordinates of P, Q, and R, returns the value A corresponding to the Montgomery curve E_A: y^2=x^3+A*x^2+x such that R=Q-P on E_A. + // Input: the x-coordinates xP, xQ, and xR of the points P, Q and R. + // Output: the coefficient A corresponding to the curve E_A: y^2=x^3+A*x^2+x. + f2elm_t t0, t1, one = {0}; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + fp2add(xP, xQ, t1); // t1 = xP+xQ + fp2mul_mont(xP, xQ, t0); // t0 = xP*xQ + fp2mul_mont(xR, t1, A); // A = xR*t1 + fp2add(t0, A, A); // A = A+t0 + fp2mul_mont(t0, xR, t0); // t0 = t0*xR + fp2sub(A, one, A); // A = A-1 + fp2add(t0, t0, t0); // t0 = t0+t0 + fp2add(t1, xR, t1); // t1 = t1+xR + fp2add(t0, t0, t0); // t0 = t0+t0 + fp2sqr_mont(A, A); // A = A^2 + fp2inv_mont_bingcd(t0); // t0 = 1/t0 + fp2mul_mont(A, t0, A); // A = A*t0 + fp2sub(A, t1, A); // Afinal = A-t1 +} + + +void recover_y(const publickey_t PK, point_full_proj_t phiP, point_full_proj_t phiQ, point_full_proj_t phiX, f2elm_t A) +{ // Recover the y-coordinates of the public key + // The three resulting points are (simultaneously) correct up to sign + f2elm_t tmp, phiXY, one = {0}; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + get_A_compression(PK[0], PK[1], PK[2], A); // NOTE: don't have to compress this, can output in keygen + + fp2add(PK[2], A, tmp); + fp2mul_mont(PK[2], tmp, tmp); + fp2add(tmp, one, tmp); + fp2mul_mont(PK[2], tmp, tmp); // tmp = PK[2]^3+A*PK[2]^2+PK[2]; + sqrt_Fp2(tmp, phiXY); + fp2copy(PK[2], phiX->X); + fp2copy(phiXY, phiX->Y); + fp2copy(one, phiX->Z); // phiX = [PK[2],phiXY,1]; + + recover_os(PK[1], one, PK[0], one, PK[2], phiXY, A, phiQ->X, phiQ->Y, phiQ->Z); + fp2neg(phiXY); + recover_os(PK[0], one, PK[1], one, PK[2], phiXY, A, phiP->X, phiP->Y, phiP->Z); +} + + +static void final_exponentiation_2_torsion(f2elm_t f, const f2elm_t finv, f2elm_t fout) +{ // The final exponentiation for pairings in the 2^eA-torsion group. Raising the value f to the power (p^2-1)/2^eA. + felm_t one = {0}; + f2elm_t temp = {0}; + unsigned int i; + + fpcopy((digit_t*)&Montgomery_one, one); + + // f = f^p + fp2_conj(f, temp); + fp2mul_mont(temp, finv, temp); // temp = f^(p-1) + + for (i = 0; i < OBOB_EXPON; i++) { + cube_Fp2_cycl(temp, one); + } + fp2copy(temp, fout); +} + + +void Tate_pairings_2_torsion(const point_full_proj_t P, point_full_proj_t *Qj, f2elm_t a, f2elm_t* n) +{ // Compute the reduced Tate pairings e_{2^m}(P, Q_j) for the curve y^2 = x^3 + a*x + b: + f2elm_t h[t_points], one = {0}; + f2elm_t X, Y, Z, X2, Y2, Y4, M, S, T, temp; + f2elm_t Xp, Yp, Zp, Tp; + f2elm_t L, W, g; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + fp2copy(P->X, X); + fp2copy(P->Y, Y); + fp2copy(P->Z, Z); + fp2sqr_mont(Z, T); + + for (int j = 0; j < t_points; j++) { + fp2copy(one, n[j]); + fp2mul_mont(T, Qj[j]->X, temp); + fp2sub(temp, X, h[j]); + } + + for (int k = 0; k < OALICE_BITS; k++) { + // Point doubling and line function construction: + fp2sqr_mont(X, X2); + fp2sqr_mont(Y, Y2); + fp2sqr_mont(Y2, Y4); + fp2sqr_mont(T, temp); + fp2mul_mont(a, temp, temp); + fp2add(X2, X2, M); + fp2add(M, X2, M); + fp2add(M, temp, M); // M = 3*X_2 + a*T^2 + fp2add(X, Y2, S); + fp2sqr_mont(S, S); + fp2sub(S, X2, S); + fp2sub(S, Y4, S); + fp2add(S, S, S); // S = 2*((X + Y2)^2 - X2 - Y4) + fp2sqr_mont(M, temp); + fp2add(S, S, Xp); + fp2sub(temp, Xp, Xp); // Xp = M^2 - 2*S + fp2sub(S, Xp, temp); + fp2mul_mont(M, temp, temp); + fp2shl(Y4, 3, Yp); + fp2sub(temp, Yp, Yp); // Yp = M*(S - Xp) - 8*Y4 + fp2add(Y, Z, temp); + fp2sqr_mont(temp, temp); + fp2sub(temp, Y2, temp); + fp2sub(temp, T, Zp); // Zp = (Y + Z)^2 - Y2 - T + fp2sqr_mont(Zp, Tp); // Tp = Zp^2 + fp2mul_mont(Zp, T, L); // L = Zp*T + fp2add(Y2, Y2, W); // W = 2*Y2 + + fp2correction(Zp); + if (is_felm_zero(Zp[0]) && is_felm_zero(Zp[1])) { // Doubling exception for points in 2*E + fp2copy(one, Xp); + fp2copy(one, Yp); + } + + // Line function evaluation and accumulation: + for (int j = 0; j < t_points; j++) { + if (!is_felm_zero(Zp[0]) || !is_felm_zero(Zp[1])) { + fp2mul_mont(M, h[j], temp); + fp2add(temp, W, temp); + fp2mul_mont(L, Qj[j]->Y, g); + fp2sub(temp, g, g); // g = M*hj + W - L*Y_{Qj} + fp2mul_mont(Tp, Qj[j]->X, temp); + fp2sub(temp, Xp, h[j]); // hj = Tp*X_{Qj} - Xp + fp2_conj(h[j], temp); + fp2mul_mont(temp, g, g); // g = g*hj^* + } else { + fp2copy(h[j], g); + } + fp2sqr_mont(n[j], n[j]); + fp2mul_mont(n[j], g, n[j]); + } + fp2copy(Xp, X); + fp2copy(Yp, Y); + fp2copy(Zp, Z); + fp2copy(Tp, T); + } + + // Final exponentiation: + mont_n_way_inv(n, t_points, h); + for (int j = 0; j < t_points; j++) { + fp2correction(Qj[j]->Z); + if (is_felm_zero(Qj[j]->Z[0]) && is_felm_zero(Qj[j]->Z[1])) + fp2copy(one, n[j]); + else { + final_exponentiation_2_torsion(n[j], h[j], n[j]); + } + } +} + + +void Monty2Weier(const f2elm_t A, f2elm_t a, f2elm_t b) +{ // Convert a Montgomery curve EM: y^2 = x^3 + A*x^2 + x into its short Weierstrass form EW: v^2 = u^3 + a*u + b. + f2elm_t one = {0}, temp, A2, AA; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + // a = 1 - A^2/3 + fp2sqr_mont(A, A2); + fpmul_mont(A2[0], (digit_t*)threeinv, temp[0]); + fpmul_mont(A2[1], (digit_t*)threeinv, temp[1]); + fp2sub(one, temp, a); + + // b = (2*A^3 - 9*A)/27 + fp2add(A, A, AA); // AA = 2*A + fp2mul_mont(AA, A2, temp); // temp = 2A^3 + fp2add(AA, AA, A2); // A2 = 4*A + fp2add(A2, A2, A2); // A2 = 8*A + fp2add(A2, A, A2); // A2 = 9*A + fp2sub(temp, A2, b); // b = 2A^3 - 9*A + fpmul_mont((digit_t*)threeinv, (digit_t*)threeinv, temp[0]); + fpmul_mont(temp[0], (digit_t*)threeinv, temp[0]); + fpmul_mont(temp[0], b[0], b[0]); + fpmul_mont(temp[0], b[1], b[1]); +} + + +void PointMonty2Weier(const point_full_proj_t PM, point_full_proj_t PW, const f2elm_t A) +{ // Convert a point PM on a Montgomery curve y^2 = x^3 + A*x^2 + x into the corresponding point on its short Weierstrass form EW. + f2elm_t zero = {0}, one = {0}, temp; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + + if (is_felm_zero(PM->Z[0]) && is_felm_zero(PM->Z[1])) { + fp2copy(zero,PW->X); + fp2copy(one, PW->Y); + fp2copy(zero,PW->Z); + return; + } + fpmul_mont((digit_t*)threeinv, A[0], temp[0]); + fpmul_mont((digit_t*)threeinv, A[1], temp[1]); + + // PW = EW(PM->X + A/3, PM->Y, 1) + fp2add(temp, PM->X, PW->X); + fp2copy(PM->Y, PW->Y); + fp2copy(one, PW->Z); +} + + +void Tate_4_pairings_2_torsion(const point_full_proj_t P, const point_full_proj_t Q, const point_t S1, const point_t S2, const f2elm_t A, f2elm_t* n) +{ // The doubling only 2-torsion Tate pairing of order 2^eA, consisting of the doubling only Miller loop and the final exponentiation.] + // Computes 4 pairings at once: e(P, S1), e(P, S2), e(Q, S1), e(Q, S2). + point_full_proj_t Qj[2], PW, QW, QjW[2]; + f2elm_t a, b, one = {0}; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + Monty2Weier(A, a, b); + + // Assume S1 and S2 are normalized + fp2copy(S1->x, Qj[0]->X); + fp2copy(S1->y, Qj[0]->Y); + fp2copy(one, Qj[0]->Z); + fp2copy(S2->x, Qj[1]->X); + fp2copy(S2->y, Qj[1]->Y); + fp2copy(one, Qj[1]->Z); + + PointMonty2Weier(P, PW, A); + PointMonty2Weier(Q, QW, A); + PointMonty2Weier(Qj[0], QjW[0], A); + PointMonty2Weier(Qj[1], QjW[1], A); + + Tate_pairings_2_torsion(PW, QjW, a, n); + Tate_pairings_2_torsion(QW, QjW, a, n + 2); +} + + +static void final_exponentiation_3_torsion(f2elm_t f, const f2elm_t finv, f2elm_t fout) +{ // The final exponentiation for pairings in the 3-torsion group. Raising the value f to the power (p^2-1)/3^eB. + felm_t one = {0}; + f2elm_t temp; + unsigned int i; + + fpcopy((digit_t*)&Montgomery_one, one); + + // f = f^p + fp2_conj(f, temp); + fp2mul_mont(temp, finv, temp); // temp = f^(p-1) + + for (i = 0; i < OALICE_BITS; i++) { + sqr_Fp2_cycl(temp, one); + } + fp2copy(temp, fout); +} + + +void Tate_pairings_3_torsion(const point_full_proj_t P, point_full_proj_t *Qj, f2elm_t a, f2elm_t* n) +{ // The tripling only 3-torsion Tate pairing of order 3^eB, consisting of the tripling only Miller loop and the final exponentiation. + // Computes 4 pairings at once: e(P, R1), e(P, R2), e(Q, R1), e(Q, R2). + f2elm_t h[t_points], one = {0}; + f2elm_t X, Y, Z, X2, Y2, Y4, M, S, T; + f2elm_t Xp, Yp, Zp, Tp, D, U, Up, Fp; + f2elm_t L, W, Wp, g, T2, M2, F, F2, d; + f2elm_t temp, temp1; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + fp2copy(P->X, X); + fp2copy(P->Y, Y); + fp2copy(P->Z, Z); + fp2sqr_mont(Z, T); + + for (int j = 0; j < t_points; j++) { + fp2copy(one, n[j]); + fp2mul_mont(T, Qj[j]->X, temp); + fp2sub(temp, X, h[j]); + } + + for (int k = 0; k < OBOB_EXPON; k++) { + // Point tripling and parabola function construction: + fp2sqr_mont(X, X2); + fp2sqr_mont(Y, Y2); + fp2sqr_mont(Y2, Y4); + fp2sqr_mont(T, T2); + fp2add(X2, X2, temp); + fp2add(temp, X2, temp); + fp2mul_mont(a, T2, M); + fp2add(temp, M, M); // M = 3*X2 + a*T2 + fp2sqr_mont(M, M2); + fp2add(X, Y2, temp); + fp2sqr_mont(temp, temp); + fp2sub(temp, X2, temp); + fp2sub(temp, Y4, D); // D = (X + Y2)^2 - X2 - Y4 + fp2add(D, D, temp); + fp2add(temp, D, temp); + fp2add(temp, temp, temp); + fp2sub(temp, M2, F); // F = 6*D - M2 + fp2sqr_mont(F, F2); + fp2add(Y2, Y2, W); + fp2add(W, W, Wp); + fp2shl(Y4, 4, S); + fp2add(M, F, temp); + fp2sqr_mont(temp, temp); + fp2sub(temp, M2, temp); + fp2sub(temp, F2, temp); + fp2sub(temp, S, U); // U = (M + F)^2 - M2 - F2 - S + fp2sub(S, U, Up); + fp2mul_mont(X, F2, temp); + fp2mul_mont(Wp, U, Xp); + fp2sub(temp, Xp, Xp); + fp2shl(Xp, 2, Xp); // Xp = 4*(X*F2 - Wp*U) + fp2mul_mont(U, Up, temp); + fp2mul_mont(F, F2, Yp); + fp2sub(temp, Yp, Yp); + fp2mul_mont(Y, Yp, Yp); + fp2shl(Yp, 3, Yp); // Yp = 8*Y*(U*Up - F*F2) + fp2add(Z, F, temp); + fp2sqr_mont(temp, temp); + fp2sub(temp, T, temp); + fp2sub(temp, F2, Zp); // Zp = (Z + F)^2 - T - F2 + fp2sqr_mont(Zp, Tp); + fp2add(Y, Z, temp); + fp2sqr_mont(temp, temp); + fp2sub(temp, Y2, temp); + fp2sub(temp, T, temp); + fp2mul_mont(temp, T, L); + fp2add(F, F, Fp); + + fp2correction(Zp); + if (is_felm_zero(Zp[0]) && is_felm_zero(Zp[1])) { + fp2copy(one, Xp); + fp2copy(one, Yp); + } + + // Parabola function evaluation and accumulation + for (int j = 0; j < t_points; j++) { + fp2mul_mont(L, Qj[j]->Y, temp); + fp2sub(W, temp, d); + if (!is_felm_zero(Zp[0]) || !is_felm_zero(Zp[1])) { + fp2mul_mont(M, h[j], temp); + fp2add(d, temp, g); // g = (M*h + d) + fp2mul_mont(Up, h[j], temp); + fp2mul_mont(Fp, d, temp1); + fp2add(temp, temp1, temp1); + fp2mul_mont(temp1, g, g); // g = (M*h + d)*(Up*h + Fp*d) + fp2mul_mont(Wp, h[j], temp); + fp2add(F, temp, temp); + fp2_conj(temp, temp); + fp2mul_mont(temp, g, g); // g = (M*h + d)*(Up*h + Fp*d)*(Wp*h + F)^* + fp2mul_mont(Tp, Qj[j]->X, temp); + fp2sub(temp, Xp, h[j]); // h = Tp*X_{Qj} - Xp + fp2_conj(h[j], temp); + fp2mul_mont(temp, g, g); + } else { + fp2mul_mont(M, h[j], temp); + fp2add(temp, d, g); + } + fp2sqr_mont(n[j], temp); + fp2mul_mont(temp, n[j], n[j]); + fp2mul_mont(g, n[j], n[j]); + } + fp2copy(Xp, X); + fp2copy(Yp, Y); + fp2copy(Zp, Z); + fp2copy(Tp, T); + } + + // Final exponentiation: + mont_n_way_inv(n, t_points, h); + for (int j = 0; j < t_points; j++) { + fp2correction(Qj[j]->Z); + if (is_felm_zero(Qj[j]->Z[0]) && is_felm_zero(Qj[j]->Z[1])) + fp2copy(one, n[j]); + else { + final_exponentiation_3_torsion(n[j], h[j], n[j]); + } + } +} + + +void Tate_4_pairings_3_torsion(const point_full_proj_t P, const point_full_proj_t Q, const point_full_proj_t R1, const point_full_proj_t R2, const f2elm_t A, f2elm_t* n) +{ // The tripling only 3-torsion Tate pairing of order 3^eB, consisting of the tripling only Miller loop and the final exponentiation. + // Computes 4 pairings at once: e(P, S1), e(P, S2), e(Q, S1), e(Q,S2). + point_full_proj_t Qj[2] = {0}, PW, QW, QjW[2] = {0}; + f2elm_t a, b; + + Monty2Weier(A, a, b); + fp2copy(R1->X, Qj[0]->X); + fp2copy(R1->Y, Qj[0]->Y); + fp2copy(R1->Z, Qj[0]->Z); + fp2copy(R2->X, Qj[1]->X); + fp2copy(R2->Y, Qj[1]->Y); + fp2copy(R2->Z, Qj[1]->Z); + + PointMonty2Weier(P, PW, A); + PointMonty2Weier(Q, QW, A); + PointMonty2Weier(Qj[0], QjW[0], A); + PointMonty2Weier(Qj[1], QjW[1], A); + Tate_pairings_3_torsion(PW, QjW, a, n); + Tate_pairings_3_torsion(QW, QjW, a, n + 2); +} + + +void Tate3_pairings(point_full_proj_t *Qj, f2elm_t* f) +{ + felm_t *x, *y, *l1, *l2, *n1, *n2, *x2, *x23, *x2p3; + f2elm_t xQ2s[t_points], finv[2*t_points], one = {0}; + f2elm_t t0, t1, t2, t3, t4, t5, g, h, tf; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + + for (int j = 0; j < t_points; j++) { + fp2copy(one, f[j]); + fp2copy(one, f[j+t_points]); + fp2sqr_mont(Qj[j]->X, xQ2s[j]); + } + + for (int k = 0; k < OBOB_EXPON - 1; k++) { + l1 = (felm_t*)T_tate3 + 6*k + 0; + l2 = (felm_t*)T_tate3 + 6*k + 1; + n1 = (felm_t*)T_tate3 + 6*k + 2; + n2 = (felm_t*)T_tate3 + 6*k + 3; + x23 = (felm_t*)T_tate3 + 6*k + 4; + x2p3 = (felm_t*)T_tate3 + 6*k + 5; + for (int j = 0; j < t_points; j++) { + fpmul_mont(Qj[j]->X[0], *l1, t0[0]); + fpmul_mont(Qj[j]->X[1], *l1, t0[1]); + fpmul_mont(Qj[j]->X[0], *l2, t2[0]); + fpmul_mont(Qj[j]->X[1], *l2, t2[1]); + fpadd(xQ2s[j][0], *x23, t4[0]); + fpcopy(xQ2s[j][1], t4[1]); + fpmul_mont(Qj[j]->X[0], *x2p3, t5[0]); + fpmul_mont(Qj[j]->X[1], *x2p3, t5[1]); + + fp2sub(t0, Qj[j]->Y, t1); + fpadd(t1[0], *n1, t1[0]); + fp2sub(t2, Qj[j]->Y, t3); + fpadd(t3[0], *n2, t3[0]); + fp2mul_mont(t1, t3, g); + fp2sub(t4, t5, h); + fp2_conj(h, h); + fp2mul_mont(g, h, g); + + fp2sqr_mont(f[j], tf); + fp2mul_mont(f[j], tf, f[j]); + fp2mul_mont(f[j], g, f[j]); + + fpsub(t0[1], Qj[j]->Y[0], t1[0]); + fpadd(t0[0], Qj[j]->Y[1], t1[1]); + fpneg(t1[1]); + fpadd(t1[1], *n1, t1[1]); + fpsub(t2[1], Qj[j]->Y[0], t3[0]); + fpadd(t2[0], Qj[j]->Y[1], t3[1]); + fpneg(t3[1]); + fpadd(t3[1], *n2, t3[1]); + + fp2mul_mont(t1, t3, g); + fp2add(t4, t5, h); + fp2_conj(h, h); + fp2mul_mont(g, h, g); + + fp2sqr_mont(f[j+t_points], tf); + fp2mul_mont(f[j+t_points], tf, f[j+t_points]); + fp2mul_mont(f[j+t_points], g, f[j+t_points]); + } + } + for (int j = 0; j < t_points; j++) { + x = (felm_t*)T_tate3 + 6*(OBOB_EXPON-1) + 0; + y = (felm_t*)T_tate3 + 6*(OBOB_EXPON-1) + 1; + l1 = (felm_t*)T_tate3 + 6*(OBOB_EXPON-1) + 2; + x2 = (felm_t*)T_tate3 + 6*(OBOB_EXPON-1) + 3; + + fpsub(Qj[j]->X[0], *x, t0[0]); + fpcopy(Qj[j]->X[1], t0[1]); + fpmul_mont(*l1, t0[0], t1[0]); + fpmul_mont(*l1, t0[1], t1[1]); + fp2sub(t1, Qj[j]->Y, t2); + fpadd(t2[0], *y, t2[0]); + fp2mul_mont(t0, t2, g); + fpsub(Qj[j]->X[0], *x2, h[0]); + fpcopy(Qj[j]->X[1], h[1]); + fpneg(h[1]); + fp2mul_mont(g, h, g); + + fp2sqr_mont(f[j], tf); + fp2mul_mont(f[j], tf, f[j]); + fp2mul_mont(f[j], g, f[j]); + + fpadd(Qj[j]->X[0], *x, t0[0]); + fpmul_mont(*l1, t0[0], t1[0]); + fpsub(Qj[j]->Y[0], t1[1], t2[0]); + fpadd(Qj[j]->Y[1], t1[0], t2[1]); + fpsub(t2[1], *y, t2[1]); + fp2mul_mont(t0, t2, g); + fpadd(Qj[j]->X[0], *x2, h[0]); + fp2mul_mont(g, h, g); + + fp2sqr_mont(f[j+t_points], tf); + fp2mul_mont(f[j+t_points], tf, f[j+t_points]); + fp2mul_mont(f[j+t_points], g, f[j+t_points]); + } + + // Final exponentiation: + mont_n_way_inv(f, 2*t_points, finv); + for (int j = 0; j < 2*t_points; j++) { + final_exponentiation_3_torsion(f[j], finv[j], f[j]); + } +} + + +void Tate2_pairings(const point_t P, const point_t Q, point_full_proj_t *Qj, f2elm_t* f) +{ + felm_t *x, *y, *x_, *y_, *l1; + f2elm_t finv[2*t_points], one = {0}; + f2elm_t *x_first, *y_first, l1_first, t0, t1, g, h; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + + for (int j = 0; j < t_points; j++) { + fp2copy(one, f[j]); + fp2copy(one, f[j+t_points]); + } + + // Pairings with P + x_first = (f2elm_t*)P->x; + y_first = (f2elm_t*)P->y; + + x_ = (felm_t*)T_tate2_firststep_P + 0; + y_ = (felm_t*)T_tate2_firststep_P + 1; + fpcopy((digit_t*)T_tate2_firststep_P + 2*NWORDS_FIELD, l1_first[0]); + fpcopy((digit_t*)T_tate2_firststep_P + 3*NWORDS_FIELD, l1_first[1]); + + for (int j = 0; j < t_points; j++) { + fp2sub(Qj[j]->X, *x_first, t0); + fp2sub(Qj[j]->Y, *y_first, t1); + fp2mul_mont(l1_first, t0, t0); + fp2sub(t0, t1, g); + + fpsub(Qj[j]->X[0], *x_, h[0]); + fpcopy(Qj[j]->X[1], h[1]); + fpneg(h[1]); + fp2mul_mont(g, h, g); + + fp2sqr_mont(f[j], f[j]); + fp2mul_mont(f[j], g, f[j]); + } + x = x_; + y = y_; + + for (int k = 0; k < OALICE_BITS - 2; k++) { + x_ = (felm_t*)T_tate2_P + 3 * k + 0; + y_ = (felm_t*)T_tate2_P + 3 * k + 1; + l1 = (felm_t*)T_tate2_P + 3 * k + 2; + for (int j = 0; j < t_points; j++) { + fpsub(*x, Qj[j]->X[0], t0[1]); + fpmul_mont(*l1, t0[1], t0[1]); + fpmul_mont(*l1, Qj[j]->X[1], t0[0]); + fpsub(Qj[j]->Y[1], *y, t1[1]); + fpsub(t0[1], t1[1], g[1]); + fpsub(t0[0], Qj[j]->Y[0], g[0]); + + fpsub(Qj[j]->X[0], *x_, h[0]); + fpcopy(Qj[j]->X[1], h[1]); + fpneg(h[1]); + fp2mul_mont(g, h, g); + + fp2sqr_mont(f[j], f[j]); + fp2mul_mont(f[j], g, f[j]); + } + x = x_; + y = y_; + } + for (int j = 0; j < t_points; j++) { + fpsub(Qj[j]->X[0], *x, g[0]); + fpcopy(Qj[j]->X[1], g[1]); + fp2sqr_mont(f[j], f[j]); + fp2mul_mont(f[j], g, f[j]); + } + + // Pairings with Q + x_first = (f2elm_t*)Q->x; + y_first = (f2elm_t*)Q->y; + x_ = (felm_t*)T_tate2_firststep_Q + 0; + y_ = (felm_t*)T_tate2_firststep_Q + 1; + fpcopy(((felm_t*)T_tate2_firststep_Q)[2], l1_first[0]); + fpcopy(((felm_t*)T_tate2_firststep_Q)[3], l1_first[1]); + + for (int j = 0; j < t_points; j++) { + fp2sub(Qj[j]->X, *x_first, t0); + fp2sub(Qj[j]->Y, *y_first, t1); + fp2mul_mont(l1_first, t0, t0); + fp2sub(t0, t1, g); + + fpsub(Qj[j]->X[0], *x_, h[0]); + fpcopy(Qj[j]->X[1], h[1]); + fpneg(h[1]); + fp2mul_mont(g, h, g); + + fp2sqr_mont(f[j+t_points], f[j+t_points]); + fp2mul_mont(f[j+t_points], g, f[j+t_points]); + } + x = x_; + y = y_; + + for (int k = 0; k < OALICE_BITS - 2; k++) { + x_ = (felm_t*)T_tate2_Q + 3*k + 0; + y_ = (felm_t*)T_tate2_Q + 3*k + 1; + l1 = (felm_t*)T_tate2_Q + 3*k + 2; + for (int j = 0; j < t_points; j++) { + fpsub(Qj[j]->X[0], *x, t0[0]); + fpmul_mont(*l1, t0[0], t0[0]); + fpmul_mont(*l1, Qj[j]->X[1], t0[1]); + fpsub(Qj[j]->Y[0], *y, t1[0]); + fpsub(t0[0], t1[0], g[0]); + fpsub(t0[1], Qj[j]->Y[1], g[1]); + + fpsub(Qj[j]->X[0], *x_, h[0]); + fpcopy(Qj[j]->X[1], h[1]); + fpneg(h[1]); + fp2mul_mont(g, h, g); + + fp2sqr_mont(f[j+t_points], f[j+t_points]); + fp2mul_mont(f[j+t_points], g, f[j+t_points]); + } + x = x_; + y = y_; + } + // Last iteration + for (int j = 0; j < t_points; j++) { + fpsub(Qj[j]->X[0], *x, g[0]); + fpcopy(Qj[j]->X[1], g[1]); + + fp2sqr_mont(f[j+t_points], f[j+t_points]); + fp2mul_mont(f[j+t_points], g, f[j+t_points]); + } + + // Final exponentiation: + mont_n_way_inv(f, 2*t_points, finv); + for (int j = 0; j < 2*t_points; j++) { + final_exponentiation_2_torsion(f[j], finv[j], f[j]); + } +} + diff --git a/src/compression/sidh_compressed.c b/src/compression/sidh_compressed.c new file mode 100644 index 0000000..0d7eb64 --- /dev/null +++ b/src/compression/sidh_compressed.c @@ -0,0 +1,1219 @@ +/************************************************************************************************* +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: ephemeral supersingular isogeny Diffie-Hellman key exchange (SIDH) using compression +**************************************************************************************************/ + +#include "../random/random.h" + + +static void init_basis(digit_t *gen, f2elm_t XP, f2elm_t XQ, f2elm_t XR) +{ // Initialization of basis points + + fpcopy(gen, XP[0]); + fpcopy(gen + NWORDS_FIELD, XP[1]); + fpcopy(gen + 2*NWORDS_FIELD, XQ[0]); + fpcopy(gen + 3*NWORDS_FIELD, XQ[1]); + fpcopy(gen + 4*NWORDS_FIELD, XR[0]); + fpcopy(gen + 5*NWORDS_FIELD, XR[1]); +} + + +void FormatPrivKey_B(unsigned char *skB) +{ + skB[SECRETKEY_B_BYTES-2] &= MASK3_BOB; + skB[SECRETKEY_B_BYTES-1] &= MASK2_BOB; // Clear necessary bits so that 3*ephemeralsk is still less than Bob_order + mul3(skB); // Multiply ephemeralsk by 3 +} + + +void random_mod_order_A(unsigned char* random_digits) +{ // Generation of Alice's secret key + // Outputs random value in [0, 2^eA - 1] + + memset(random_digits, 0, SECRETKEY_A_BYTES); + randombytes(random_digits, SECRETKEY_A_BYTES); + random_digits[0] &= 0xFE; // Make private scalar even + random_digits[SECRETKEY_A_BYTES-1] &= MASK_ALICE; // Masking last byte +} + + +void random_mod_order_B(unsigned char* random_digits) +{ // Generation of Bob's secret key + // Outputs random value in [0, 2^Floor(Log(2, oB)) - 1] + + randombytes(random_digits, SECRETKEY_B_BYTES); + FormatPrivKey_B(random_digits); +} + + +static void Ladder3pt_dual(const point_proj_t *Rs, const digit_t* m, const unsigned int AliceOrBob, point_proj_t R, const f2elm_t A24) +{ // Project 3-point ladder + point_proj_t R0 = {0}, R2 = {0}; + digit_t mask; + int i, nbits, bit, swap, prevbit = 0; + + if (AliceOrBob == ALICE) { + nbits = OALICE_BITS; + } else { + nbits = OBOB_BITS; + } + + fp2copy(Rs[1]->X, R0->X); + fp2copy(Rs[1]->Z, R0->Z); + fp2copy(Rs[2]->X, R2->X); + fp2copy(Rs[2]->Z, R2->Z); + fp2copy(Rs[0]->X, R->X); + fp2copy(Rs[0]->Z, R->Z); + + // Main loop + for (i = 0; i < nbits; i++) { + bit = (m[i >> LOG2RADIX] >> (i & (RADIX-1))) & 1; + swap = bit ^ prevbit; + prevbit = bit; + mask = 0 - (digit_t)swap; + + swap_points(R, R2, mask); + xDBLADD(R0, R2, R->X, A24); + fp2mul_mont(R2->X, R->Z, R2->X); + } + swap = 0 ^ prevbit; + mask = 0 - (digit_t)swap; + swap_points(R, R2, mask); +} + + +static void Elligator2(const f2elm_t a24, const unsigned int r, f2elm_t x) +{ // Generate an x-coordinate of a point on curve with (affine) coefficient a24 + // Use the counter r + int i; + felm_t one_fp, a2, b2, N, temp0, temp1; + f2elm_t A, y2, *t_ptr; + + fpcopy((digit_t*)&Montgomery_one, one_fp); + fp2add(a24, a24, A); + fpsub(A[0], one_fp, A[0]); + fp2add(A, A, A); // A = 4*a24-2 + + // Elligator computation + t_ptr = (f2elm_t *)&v_3_torsion[r]; + fp2mul_mont(A, (felm_t*)t_ptr, x); // x = A*v; v := 1/(1 + U*r^2) table lookup + fp2neg(x); // x = -A*v; + fp2add(A, x, y2); // y2 = x + A + fp2mul_mont(y2, x, y2); // y2 = x*(x + A) + fpadd(y2[0], one_fp, y2[0]); // y2 = x(x + A) + 1 + fp2mul_mont(x, y2, y2); // y2 = x*(x^2 + Ax + 1); + fpsqr_mont(y2[0], a2); + fpsqr_mont(y2[1], b2); + fpadd(a2, b2, N); // N := norm(y2); + + fpcopy(N, temp0); + for (i = 0; i < OALICE_BITS - 2; i++) { + fpsqr_mont(temp0, temp0); + } + for (i = 0; i < OBOB_EXPON; i++) { + fpsqr_mont(temp0, temp1); + fpmul_mont(temp0, temp1, temp0); + } + fpsqr_mont(temp0, temp1); // z = N^((p + 1) div 4); + fpcorrection(temp1); + fpcorrection(N); + if (memcmp(temp1, N, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fp2neg(x); + fp2sub(x, A, x); // x = -x - A; + } +} + + +static void make_positive(f2elm_t x) +{ + unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); + felm_t zero = {0}; + + from_fp2mont(x, x); + if (memcmp(x[0], zero, (size_t)nbytes) != 0) { + if ((x[0][0] & 1) == 1) + fp2neg(x); + } else { + if ((x[1][0] & 1) == 1) + fp2neg(x); + } + to_fp2mont(x, x); +} + + +static void BiQuad_affine(const f2elm_t a24, const f2elm_t x0, const f2elm_t x1, point_proj_t R) +{ + f2elm_t Ap2, aa, bb, cc, t0, t1; + + fp2add(a24, a24, Ap2); + fp2add(Ap2, Ap2, Ap2); // Ap2 = a+2 = 4*a24 + + fp2sub(x0, x1, aa); + fp2sqr_mont(aa, aa); + + fp2mul_mont(x0, x1, cc); + fpsub(cc[0], (digit_t*)Montgomery_one, cc[0]); + fp2sqr_mont(cc, cc); + + fpsub(x0[0], (digit_t*)Montgomery_one, bb[0]); + fpcopy(x0[1], bb[1]); + fp2sqr_mont(bb, bb); + fp2mul_mont(Ap2, x0, t0); + fp2add(bb, t0, bb); + fp2mul_mont(x1, bb, bb); + fpsub(x1[0], (digit_t*)Montgomery_one, t0[0]); + fpcopy(x1[1], t0[1]); + fp2sqr_mont(t0, t0); + fp2mul_mont(Ap2, x1, t1); + fp2add(t0, t1, t0); + fp2mul_mont(x0, t0, t0); + fp2add(bb, t0, bb); + fp2add(bb, bb, bb); + + fp2sqr_mont(bb, t0); + fp2mul_mont(aa, cc, t1); + fp2add(t1, t1, t1); + fp2add(t1, t1, t1); + fp2sub(t0, t1, t0); + sqrt_Fp2(t0, t0); + make_positive(t0); // Make the sqrt "positive" + fp2add(bb, t0, R->X); + fp2add(aa, aa, R->Z); +} + + +static void get_4_isog_dual(const point_proj_t P, f2elm_t A24, f2elm_t C24, f2elm_t* coeff) +{ + fp2sub(P->X, P->Z, coeff[1]); + fp2add(P->X, P->Z, coeff[2]); + fp2sqr_mont(P->Z, coeff[4]); + fp2add(coeff[4], coeff[4], coeff[0]); + fp2sqr_mont(coeff[0], C24); + fp2add(coeff[0], coeff[0], coeff[0]); + fp2sqr_mont(P->X, coeff[3]); + fp2add(coeff[3], coeff[3], A24); + fp2sqr_mont(A24, A24); +} + +#if (OALICE_BITS % 2 == 1) + +static void eval_dual_2_isog(const f2elm_t X2, const f2elm_t Z2, point_proj_t P) +{ + f2elm_t t0; + + fp2add(P->X, P->Z, t0); + fp2sub(P->X, P->Z, P->Z); + fp2sqr_mont(t0, t0); + fp2sqr_mont(P->Z, P->Z); + fp2sub(t0, P->Z, P->Z); + fp2mul_mont(X2, P->Z, P->Z); + fp2mul_mont(Z2, t0, P->X); +} + +#endif + +static void eval_final_dual_2_isog(point_proj_t P) +{ + f2elm_t t0, t1; + felm_t t2; + + fp2add(P->X, P->Z, t0); + fp2mul_mont(P->X, P->Z, t1); + fp2sqr_mont(t0, P->X); + fpcopy((P->X)[0], t2); + fpcopy((P->X)[1], (P->X)[0]); + fpcopy(t2, (P->X)[1]); + fpneg((P->X)[1]); + fp2add(t1, t1, P->Z); + fp2add(P->Z, P->Z, P->Z); +} + + +static void eval_dual_4_isog_shared(const f2elm_t X4pZ4, const f2elm_t X42, const f2elm_t Z42, f2elm_t* coeff) +{ + fp2sub(X42, Z42, coeff[0]); + fp2add(X42, Z42, coeff[1]); + fp2sqr_mont(X4pZ4, coeff[2]); + fp2sub(coeff[2], coeff[1], coeff[2]); +} + + +static void eval_dual_4_isog(const f2elm_t A24, const f2elm_t C24, const f2elm_t* coeff, point_proj_t P) +{ + f2elm_t t0, t1, t2, t3; + + fp2add(P->X, P->Z, t0); + fp2sub(P->X, P->Z, t1); + fp2sqr_mont(t0, t0); + fp2sqr_mont(t1, t1); + fp2sub(t0, t1, t2); + fp2sub(C24, A24, t3); + fp2mul_mont(t2, t3, t3); + fp2mul_mont(C24, t0, t2); + fp2sub(t2, t3, t2); + fp2mul_mont(t2, t0, P->X); + fp2mul_mont(t3, t1, P->Z); + fp2mul_mont(coeff[0], P->X, P->X); + fp2mul_mont(coeff[1], P->Z, t0); + fp2add(P->X, t0, P->X); + fp2mul_mont(coeff[2], P->Z, P->Z); +} + + +static void eval_full_dual_4_isog(const f2elm_t As[][5], point_proj_t P) +{ + // First all 4-isogenies + for(unsigned int i = 0; i < MAX_Alice; i++) { + eval_dual_4_isog(As[MAX_Alice-i][0], As[MAX_Alice-i][1], *(As+MAX_Alice-i-1)+2, P); + } +#if (OALICE_BITS % 2 == 1) + eval_dual_2_isog(As[MAX_Alice][2], As[MAX_Alice][3], P); +#endif + eval_final_dual_2_isog(P); // to A = 0 +} + + +static void CompletePoint(const point_proj_t P, point_full_proj_t R) +{ // Complete point on A = 0 curve + f2elm_t xz, s2, r2, yz, invz, t0, t1, one = {0}; + fpcopy((digit_t*)&Montgomery_one, one[0]); + + fp2mul_mont(P->X, P->Z, xz); + fpsub(P->X[0], P->Z[1], t0[0]); + fpadd(P->X[1], P->Z[0], t0[1]); + fpadd(P->X[0], P->Z[1], t1[0]); + fpsub(P->X[1], P->Z[0], t1[1]); + fp2mul_mont(t0, t1, s2); + fp2mul_mont(xz, s2, r2); + sqrtinv2(r2, P->Z, yz, invz); + fp2mul_mont(P->X, invz, R->X); + fp2sqr_mont(invz, t0); + fp2mul_mont(yz, t0, R->Y); + fp2copy(one, R->Z); +} + + +static void TripleAndParabola_proj(const point_full_proj_t R, f2elm_t l1x, f2elm_t l1z) +{ + fp2sqr_mont(R->X, l1z); + fp2add(l1z, l1z, l1x); + fp2add(l1x, l1z, l1x); + fpadd(l1x[0], (digit_t*)&Montgomery_one, l1x[0]); + fp2add(R->Y, R->Y, l1z); +} + + +static void Tate3_proj(const point_full_proj_t P, const point_full_proj_t Q, f2elm_t gX, f2elm_t gZ) +{ + f2elm_t t0, l1x; + + TripleAndParabola_proj(P, l1x, gZ); + fp2sub(Q->X, P->X, gX); + fp2mul_mont(l1x, gX, gX); + fp2sub(P->Y, Q->Y, t0); + fp2mul_mont(gZ, t0, t0); + fp2add(gX, t0, gX); +} + + +static void FinalExpo3(f2elm_t gX, f2elm_t gZ) +{ + unsigned int i; + f2elm_t f_; + + fp2copy(gZ, f_); + fpneg(f_[1]); + fp2mul_mont(gX, f_, f_); + fp2inv_mont(f_); // TODO: Make non-constant time... + fpneg(gX[1]); + fp2mul_mont(gX,gZ, gX); + fp2mul_mont(gX,f_, gX); + for(i = 0; i < OALICE_BITS; i++) + fp2sqr_mont(gX, gX); + for(i = 0; i < OBOB_EXPON-1; i++) + cube_Fp2_cycl(gX, (digit_t*)Montgomery_one); +} + + +static void FinalExpo3_2way(f2elm_t *gX, f2elm_t *gZ) +{ + unsigned int i, j; + f2elm_t f_[2], finv[2]; + + for(i = 0; i < 2; i++) { + fp2copy(gZ[i], f_[i]); + fpneg(f_[i][1]); // Conjugate + fp2mul_mont(gX[i], f_[i], f_[i]); + } + mont_n_way_inv(f_,2,finv); + for(i = 0; i < 2; i++) { + fpneg(gX[i][1]); + fp2mul_mont(gX[i], gZ[i], gX[i]); + fp2mul_mont(gX[i], finv[i], gX[i]); + for(j = 0; j < OALICE_BITS; j++) + fp2sqr_mont(gX[i], gX[i]); + for(j = 0; j < OBOB_EXPON-1; j++) + cube_Fp2_cycl(gX[i], (digit_t*)&Montgomery_one); + } +} + + +static bool FirstPoint_dual(const point_proj_t P, point_full_proj_t R, unsigned char *ind) +{ + point_full_proj_t R3,S3; + f2elm_t gX[2],gZ[2]; + felm_t zero = {0}; + unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); + unsigned char alpha,beta; + + fpcopy((digit_t*)B_gen_3_tors + 0*NWORDS_FIELD, (R3->X)[0]); + fpcopy((digit_t*)B_gen_3_tors + 1*NWORDS_FIELD, (R3->X)[1]); + fpcopy((digit_t*)B_gen_3_tors + 2*NWORDS_FIELD, (R3->Y)[0]); + fpcopy((digit_t*)B_gen_3_tors + 3*NWORDS_FIELD, (R3->Y)[1]); + fpcopy((digit_t*)B_gen_3_tors + 4*NWORDS_FIELD, (S3->X)[0]); + fpcopy((digit_t*)B_gen_3_tors + 5*NWORDS_FIELD, (S3->X)[1]); + fpcopy((digit_t*)B_gen_3_tors + 6*NWORDS_FIELD, (S3->Y)[0]); + fpcopy((digit_t*)B_gen_3_tors + 7*NWORDS_FIELD, (S3->Y)[1]); + + CompletePoint(P,R); + Tate3_proj(R3,R,gX[0],gZ[0]); + Tate3_proj(S3,R,gX[1],gZ[1]); + FinalExpo3_2way(gX,gZ); + + // Do small DLog with respect to g_R3_S3 + fp2correction(gX[0]); + fp2correction(gX[1]); + if (memcmp(gX[0][1], zero, (size_t)nbytes) == 0) // = 1 + alpha = 0; + else if (memcmp(gX[0][1], (digit_t*)g_R_S_im, (size_t)nbytes) == 0) // = g_R3_S3 + alpha = 1; + else // = g_R3_S3^2 + alpha = 2; + + if (memcmp(gX[1][1], zero, (size_t)nbytes) == 0) // = 1 + beta = 0; + else if (memcmp(gX[1][1], (digit_t*)g_R_S_im, (size_t)nbytes) == 0) // = g_R3_S3 + beta = 1; + else // = g_R3_S3^2 + beta = 2; + + if (alpha == 0 && beta == 0) // Not full order + return false; + + // Return the 3-torsion point that R lies above + if (alpha == 0) // Lies above R3 + *ind = 0; + else if (beta == 0) // Lies above S3 + *ind = 1; + else if (alpha + beta == 3) // Lies above R3+S3 + *ind = 3; + else // Lies above R3-S3 + *ind = 2; + + return true; +} + + +static bool SecondPoint_dual(const point_proj_t P, point_full_proj_t R, unsigned char ind) +{ + point_full_proj_t RS3; + f2elm_t gX, gZ; + felm_t zero = {0}; + unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); + + // Pair with 3-torsion point determined by first point + fpcopy((digit_t*)B_gen_3_tors + (4*ind + 0)*NWORDS_FIELD, (RS3->X)[0]); + fpcopy((digit_t*)B_gen_3_tors + (4*ind + 1)*NWORDS_FIELD, (RS3->X)[1]); + fpcopy((digit_t*)B_gen_3_tors + (4*ind + 2)*NWORDS_FIELD, (RS3->Y)[0]); + fpcopy((digit_t*)B_gen_3_tors + (4*ind + 3)*NWORDS_FIELD, (RS3->Y)[1]); + + CompletePoint(P, R); + Tate3_proj(RS3, R, gX, gZ); + FinalExpo3(gX, gZ); + + fp2correction(gX); + if (memcmp(gX[1], zero, (size_t)nbytes) != 0) // Not equal to 1 + return true; + else + return false; +} + + +static void FirstPoint3n(const f2elm_t a24, const f2elm_t As[][5], f2elm_t x, point_full_proj_t R, unsigned int *r, unsigned char *ind) +{ + bool b = false; + point_proj_t P; + felm_t zero = {0}; + *r = 0; + + while (!b) { + Elligator2(a24, *r, x); // Get x-coordinate on curve a24 + + fp2copy(x, P->X); + fpcopy((digit_t*)&Montgomery_one, (P->Z)[0]); + fpcopy(zero, (P->Z)[1]); + eval_full_dual_4_isog(As, P); // Move x over to A = 0 + + b = FirstPoint_dual(P, R, ind); // Compute DLog with 3-torsion points + *r = *r + 1; + } +} + + +static void SecondPoint3n(const f2elm_t a24, const f2elm_t As[][5], f2elm_t x, point_full_proj_t R, unsigned int *r, unsigned char ind) +{ + bool b = false; + point_proj_t P; + felm_t zero = {0}; + + while (!b) { + Elligator2(a24, *r, x); + + fp2copy(x, P->X); + fpcopy((digit_t*)&Montgomery_one, (P->Z)[0]); + fpcopy(zero, (P->Z)[1]); + eval_full_dual_4_isog(As, P); // Move x over to A = 0 + + b = SecondPoint_dual(P, R, ind); + *r = *r + 1; + } +} + + +static void makeDiff(const point_full_proj_t R, point_full_proj_t S, const point_proj_t D) +{ + f2elm_t t0, t1, t2; + unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); + + fp2sub(R->X, S->X, t0); + fp2sub(R->Y, S->Y, t1); + fp2sqr_mont(t0, t0); + fp2sqr_mont(t1, t1); + fp2add(R->X, S->X, t2); + fp2mul_mont(t0, t2, t2); + fp2sub(t1, t2, t1); + fp2mul_mont(D->Z, t1, t1); + fp2mul_mont(D->X, t0, t0); + fp2correction(t0); + fp2correction(t1); + if (memcmp(t0[0], t1[0], (size_t)nbytes) == 0 && memcmp(t0[1], t1[1], (size_t)nbytes) == 0) + fp2neg(S->Y); +} + + +static void BuildOrdinary3nBasis_dual(const f2elm_t a24, const f2elm_t As[][5], point_full_proj_t *R, unsigned int *r) +{ + point_proj_t D; + f2elm_t xs[2]; + unsigned char ind; + + FirstPoint3n(a24, As, xs[0], R[0], r, &ind); + *(r+1) = *r; + SecondPoint3n(a24, As, xs[1], R[1], r+1, ind); + + // Get x-coordinate of difference + BiQuad_affine(a24, xs[0], xs[1], D); + eval_full_dual_4_isog(As, D); // Move x over to A = 0 + makeDiff(R[0], R[1], D); +} + + +static void FullIsogeny_A_dual(const unsigned char* PrivateKeyA, f2elm_t As[][5], f2elm_t a24) +{ + // Input: a private key PrivateKeyA in the range [0, 2^eA - 1]. + // Output: the public key PublicKeyA consisting of 3 elements in GF(p^2) which are encoded by removing leading 0 bytes. + point_proj_t R, pts[MAX_INT_POINTS_ALICE]; + f2elm_t XPA, XQA, XRA, coeff[5], A24 = {0}, C24 = {0}, A = {0}; + unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_ALICE], npts = 0, ii = 0; + + // Initialize basis points + init_basis((digit_t*)A_gen, XPA, XQA, XRA); + + // Initialize constants: A24 = A+2C, C24 = 4C, where A=6, C=1 + fpcopy((digit_t*)&Montgomery_one, A24[0]); + fp2add(A24, A24, A24); + fp2add(A24, A24, C24); + fp2add(A24, C24, A); + fp2add(C24, C24, A24); + + // Retrieve kernel point + LADDER3PT(XPA, XQA, XRA, (digit_t*)PrivateKeyA, ALICE, R, A); + +#if (OALICE_BITS % 2 == 1) + point_proj_t S; + + xDBLe(R, S, A24, C24, (int)(OALICE_BITS-1)); + get_2_isog(S, A24, C24); + eval_2_isog(R, S); + fp2copy(S->X, As[MAX_Alice][2]); // These 2 are unused anyway + fp2copy(S->Z, As[MAX_Alice][3]); +#endif + + // Traverse tree + index = 0; + for (row = 1; row < MAX_Alice; row++) { + while (index < MAX_Alice-row) { + fp2copy(R->X, pts[npts]->X); + fp2copy(R->Z, pts[npts]->Z); + pts_index[npts++] = index; + m = strat_Alice[ii++]; + xDBLe(R, R, A24, C24, (int)(2*m)); + index += m; + } + + fp2copy(A24, As[row-1][0]); + fp2copy(C24, As[row-1][1]); + get_4_isog_dual(R, A24, C24, coeff); + for (i = 0; i < npts; i++) { + eval_4_isog(pts[i], coeff); + } + eval_dual_4_isog_shared(coeff[2], coeff[3], coeff[4], *(As+row-1)+2); + + fp2copy(pts[npts-1]->X, R->X); + fp2copy(pts[npts-1]->Z, R->Z); + index = pts_index[npts-1]; + npts -= 1; + } + + fp2copy(A24, As[MAX_Alice-1][0]); + fp2copy(C24, As[MAX_Alice-1][1]); + get_4_isog_dual(R, A24, C24, coeff); + eval_dual_4_isog_shared(coeff[2], coeff[3], coeff[4], *(As+MAX_Alice-1)+2); + fp2copy(A24, As[MAX_Alice][0]); + fp2copy(C24, As[MAX_Alice][1]); + fp2inv_mont(C24); + fp2mul_mont(A24,C24,a24); +} + + +static void Dlogs3_dual(const f2elm_t *f, int *D, digit_t *d0, digit_t *c0, digit_t *d1, digit_t *c1) +{ + solve_dlog(f[0], D, d0, 3); + solve_dlog(f[2], D, c0, 3); + solve_dlog(f[1], D, d1, 3); + solve_dlog(f[3], D, c1, 3); + mp_sub((digit_t*)Bob_order, c0, c0, NWORDS_ORDER); + mp_sub((digit_t*)Bob_order, c1, c1, NWORDS_ORDER); +} + +// TODO: Optimize.. +static void BuildOrdinary3nBasis_Decomp_dual(const f2elm_t A24, point_proj_t *Rs, unsigned char *r) +{ + // Elligator2 both x-coordinates + Elligator2(A24, r[0]-1, Rs[0]->X); + Elligator2(A24, r[1]-1, Rs[1]->X); + // Get x-coordinate of difference + BiQuad_affine(A24, Rs[0]->X, Rs[1]->X, Rs[2]); +} + + +static void PKADecompression_dual(const unsigned char* SecretKeyB, const unsigned char* CompressedPKA, point_proj_t R, f2elm_t A) +{ + unsigned char bit, rs[2]; + f2elm_t A24; + point_proj_t Rs[3] = {0}; + digit_t t1[NWORDS_ORDER] = {0}, t2[NWORDS_ORDER] = {0}, t3[NWORDS_ORDER] = {0}, t4[NWORDS_ORDER] = {0}; + digit_t vone[NWORDS_ORDER] = {0}, temp[NWORDS_ORDER] = {0}, SKin[NWORDS_ORDER] = {0}; + + fp2_decode(&CompressedPKA[3*ORDER_B_ENCODED_BYTES], A); + vone[0] = 1; + to_Montgomery_mod_order(vone, vone, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); // Converting to Montgomery representation + + bit = CompressedPKA[3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES] >> 7; + memcpy(rs, &CompressedPKA[3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES], 2); + rs[0] &= 0x7F; + + fpadd(A[0], (digit_t*)Montgomery_one, A24[0]); + fpcopy(A[1], A24[1]); + fpadd(A24[0], (digit_t*)Montgomery_one, A24[0]); + fp2div2(A24, A24); + fp2div2(A24, A24); + + BuildOrdinary3nBasis_Decomp_dual(A24, Rs, rs); + fpcopy((digit_t*)Montgomery_one, (Rs[0]->Z)[0]); + fpcopy((digit_t*)Montgomery_one, (Rs[1]->Z)[0]); + + swap_points(Rs[0], Rs[1], 0-(digit_t)bit); + memcpy((unsigned char*)SKin, SecretKeyB, SECRETKEY_B_BYTES); + to_Montgomery_mod_order(SKin, t1, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); // Converting to Montgomery representation + memcpy((unsigned char*)&temp, &CompressedPKA[0], ORDER_B_ENCODED_BYTES); + to_Montgomery_mod_order(temp, t2, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + memcpy((unsigned char*)&temp, &CompressedPKA[ORDER_B_ENCODED_BYTES], ORDER_B_ENCODED_BYTES); + to_Montgomery_mod_order(temp, t3, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + memcpy((unsigned char*)&temp, &CompressedPKA[2*ORDER_B_ENCODED_BYTES], ORDER_B_ENCODED_BYTES); + to_Montgomery_mod_order(temp, t4, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + if (bit == 0) { + Montgomery_multiply_mod_order(t1, t3, t3, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + mp_add(t3, vone, t3, NWORDS_ORDER); + Montgomery_inversion_mod_order_bingcd(t3, t3, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + Montgomery_multiply_mod_order(t1, t4, t4, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + mp_add(t2, t4, t4, NWORDS_ORDER); + Montgomery_multiply_mod_order(t3, t4, t3, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + from_Montgomery_mod_order(t3, t3, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); // Converting back from Montgomery representation + Ladder3pt_dual(Rs,t3,BOB,R,A24); + } else { + Montgomery_multiply_mod_order(t1, t4, t4, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + mp_add(t4, vone, t4, NWORDS_ORDER); + Montgomery_inversion_mod_order_bingcd(t4, t4, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + Montgomery_multiply_mod_order(t1, t3, t3, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + mp_add(t2, t3, t3, NWORDS_ORDER); + Montgomery_multiply_mod_order(t3, t4, t3, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + from_Montgomery_mod_order(t3, t3, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); // Converting back from Montgomery representation + Ladder3pt_dual(Rs,t3,BOB,R,A24); + } + + Double(R, R, A24, OALICE_BITS); // x, z := Double(A24, x, 1, eA); +} + + +static void Compress_PKA_dual(digit_t *d0, digit_t *c0, digit_t *d1, digit_t *c1, f2elm_t a24, unsigned int *rs, unsigned char *CompressedPKA) +{ + unsigned int bit; + digit_t temp[NWORDS_ORDER] = {0}, inv[NWORDS_ORDER]; + unsigned char mask = (unsigned char)-1; + f2elm_t A; + + fp2add(a24,a24,A); + fp2add(A,A,A); + fpsub(A[0],(digit_t*)Montgomery_one,A[0]); + fpsub(A[0],(digit_t*)Montgomery_one,A[0]); // 4*a24-2 + + bit = mod3(d1); + to_Montgomery_mod_order(c0, c0, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); // Converting to Montgomery representation + to_Montgomery_mod_order(c1, c1, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + to_Montgomery_mod_order(d0, d0, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + to_Montgomery_mod_order(d1, d1, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + + if (bit != 0) { // Storing [d1*c0inv, c1*c0inv, d0*c0inv] and setting bit "NBITS_ORDER" to 0 + Montgomery_inversion_mod_order_bingcd(d1, inv, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + Montgomery_neg(d0, (digit_t*)&Bob_order); + Montgomery_multiply_mod_order(d0, inv, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + from_Montgomery_mod_order(temp, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); // Converting back from Montgomery representation + memcpy(&CompressedPKA[0], temp, ORDER_B_ENCODED_BYTES); + CompressedPKA[ORDER_B_ENCODED_BYTES-1] &= mask; + Montgomery_neg(c1, (digit_t*)&Bob_order); + Montgomery_multiply_mod_order(c1, inv, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + from_Montgomery_mod_order(temp, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + memcpy(&CompressedPKA[ORDER_B_ENCODED_BYTES], temp, ORDER_B_ENCODED_BYTES); + CompressedPKA[2*ORDER_B_ENCODED_BYTES-1] &= mask; + Montgomery_multiply_mod_order(c0, inv, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + from_Montgomery_mod_order(temp, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + memcpy(&CompressedPKA[2*ORDER_B_ENCODED_BYTES], temp, ORDER_B_ENCODED_BYTES); + CompressedPKA[3*ORDER_B_ENCODED_BYTES-1] &= mask; + CompressedPKA[3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES] = 0x00; + } else { // Storing [d1*d0inv, c1*d0inv, c0*d0inv] and setting bit "NBITS_ORDER" to 1 + Montgomery_inversion_mod_order_bingcd(d0, inv, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2, (digit_t*)&Montgomery_RB1); + Montgomery_neg(d1, (digit_t*)&Bob_order); + Montgomery_multiply_mod_order(d1, inv, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + from_Montgomery_mod_order(temp, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); // Converting back from Montgomery representation + memcpy(&CompressedPKA[0], temp, ORDER_B_ENCODED_BYTES); + CompressedPKA[ORDER_B_ENCODED_BYTES-1] &= mask; + Montgomery_multiply_mod_order(c1, inv, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + from_Montgomery_mod_order(temp, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + memcpy(&CompressedPKA[ORDER_B_ENCODED_BYTES], temp, ORDER_B_ENCODED_BYTES); + CompressedPKA[2*ORDER_B_ENCODED_BYTES-1] &= mask; + Montgomery_neg(c0, (digit_t*)&Bob_order); + Montgomery_multiply_mod_order(c0, inv, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + from_Montgomery_mod_order(temp, temp, (digit_t*)Bob_order, (digit_t*)&Montgomery_RB2); + memcpy(&CompressedPKA[2*ORDER_B_ENCODED_BYTES], temp, ORDER_B_ENCODED_BYTES); + CompressedPKA[3*ORDER_B_ENCODED_BYTES-1] &= mask; + CompressedPKA[3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES] = 0x80; + } + + fp2_encode(A, &CompressedPKA[3*ORDER_B_ENCODED_BYTES]); + CompressedPKA[3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES] |= (unsigned char)rs[0]; + CompressedPKA[3*ORDER_B_ENCODED_BYTES + FP2_ENCODED_BYTES + 1] = (unsigned char)rs[1]; +} + + +int EphemeralKeyGeneration_A(const unsigned char* PrivateKeyA, unsigned char* CompressedPKA) +{ // Alice's ephemeral public key generation using compression + unsigned int rs[2]; + int D[DLEN_3]; + f2elm_t a24, As[MAX_Alice+1][5], f[4]; + digit_t c0[NWORDS_ORDER] = {0}, d0[NWORDS_ORDER] = {0}, c1[NWORDS_ORDER] = {0}, d1[NWORDS_ORDER] = {0}; + point_full_proj_t Rs[2]; + + FullIsogeny_A_dual(PrivateKeyA, As, a24); + BuildOrdinary3nBasis_dual(a24, As, Rs, rs); + Tate3_pairings(Rs, f); + Dlogs3_dual(f, D, d0, c0, d1, c1); + Compress_PKA_dual(d0, c0, d1, c1, a24, rs, CompressedPKA); + + return 0; +} + + +int EphemeralSecretAgreement_B(const unsigned char* PrivateKeyB, const unsigned char* PKA, unsigned char* SharedSecretB) +{ // Bob's ephemeral shared secret computation using compression + // It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's decompressed data point_R and param_A + // Inputs: Bob's PrivateKeyB is an integer in the range [1, oB-1], where oB = 3^OBOB_EXP. + // Alice's decompressed data consists of point_R in (X:Z) coordinates and the curve parameter param_A in GF(p^2). + // Output: a shared secret SharedSecretB that consists of one element in GF(p^2). + unsigned int i, ii = 0, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0; + f2elm_t A24plus = {0}, A24minus = {0}; + point_proj_t R, pts[MAX_INT_POINTS_BOB]; + f2elm_t jinv, A, coeff[3]; + f2elm_t param_A = {0}; + + PKADecompression_dual(PrivateKeyB, PKA, R, param_A); + + fp2copy((felm_t*)param_A, A); + fpadd((digit_t*)&Montgomery_one, (digit_t*)&Montgomery_one, A24minus[0]); + fp2add(A, A24minus, A24plus); + fp2sub(A, A24minus, A24minus); + + // Traverse tree + index = 0; + for (row = 1; row < MAX_Bob; row++) { + while (index < MAX_Bob-row) { + fp2copy(R->X, pts[npts]->X); + fp2copy(R->Z, pts[npts]->Z); + pts_index[npts++] = index; + m = strat_Bob[ii++]; + xTPLe(R, R, A24minus, A24plus, (int)m); + index += m; + } + get_3_isog(R, A24minus, A24plus, coeff); + + for (i = 0; i < npts; i++) { + eval_3_isog(pts[i], coeff); + } + + fp2copy(pts[npts-1]->X, R->X); + fp2copy(pts[npts-1]->Z, R->Z); + index = pts_index[npts-1]; + npts -= 1; + } + + get_3_isog(R, A24minus, A24plus, coeff); + fp2add(A24plus, A24minus, A); + fp2add(A, A, A); + fp2sub(A24plus, A24minus, A24plus); + j_inv(A, A24plus, jinv); + fp2_encode(jinv, SharedSecretB); // Format shared secret + + return 0; +} + + +static void BuildEntangledXonly(const f2elm_t A, point_proj_t *R, unsigned char *qnr, unsigned char *ind) +{ + felm_t s; + f2elm_t *t_ptr, r, t; + + // Select the correct table + if (is_sqr_fp2(A, s)) { + t_ptr = (f2elm_t *)table_v_qnr; + *qnr = 1; + } else { + t_ptr = (f2elm_t *)table_v_qr; + *qnr = 0; + } + + // Get x0 + *ind = 0; + do { + fp2mul_mont(A, (felm_t *)*t_ptr++, R[0]->X); // R[0]->X = A*v + fp2neg(R[0]->X); // R[0]->X = -A*v + fp2add(R[0]->X, A, t); + fp2mul_mont(R[0]->X, t, t); + fpadd(t[0], (digit_t*)Montgomery_one, t[0]); + fp2mul_mont(R[0]->X, t, t); // t = R[0]->X^3 + A*R[0]->X^2 + R[0]->X + *ind += 1; + } while (!is_sqr_fp2(t, s)); + *ind -= 1; + + if (*qnr) + fpcopy((digit_t*)table_r_qnr[*ind], r[0]); + else + fpcopy((digit_t*)table_r_qr[*ind], r[0]); + + // Get x1 + fp2add(R[0]->X, A, R[1]->X); + fp2neg(R[1]->X); // R[1]->X = -R[0]->X-A + + // Get difference x2, z2 + fp2sub(R[0]->X, R[1]->X, R[2]->Z); + fp2sqr_mont(R[2]->Z, R[2]->Z); + + fpcopy(r[0], r[1]); // (1+i)*ind + fpadd((digit_t*)Montgomery_one, r[0], r[0]); + fp2sqr_mont(r, r); + fp2mul_mont(t, r, R[2]->X); +} + + +static void RecoverY(const f2elm_t A, const point_proj_t *xs, point_full_proj_t *Rs) +{ + f2elm_t t0, t1, t2, t3, t4; + + fp2mul_mont(xs[2]->X, xs[1]->Z, t0); + fp2mul_mont(xs[1]->X, xs[2]->Z, t1); + fp2mul_mont(xs[1]->X, xs[2]->X, t2); + fp2mul_mont(xs[1]->Z, xs[2]->Z, t3); + fp2sqr_mont(xs[1]->X, t4); + fp2sqr_mont(xs[1]->Z, Rs[1]->X); + fp2sub(t2, t3, Rs[1]->Y); + fp2mul_mont(xs[1]->X, Rs[1]->Y, Rs[1]->Y); + fp2add(t4, Rs[1]->X, t4); + fp2mul_mont(xs[2]->Z, t4, t4); + fp2mul_mont(A, t1, Rs[1]->X); + fp2sub(t0, t1, Rs[1]->Z); + + fp2mul_mont(Rs[0]->X, Rs[1]->Z, t0); + fp2add(t2, Rs[1]->X, t1); + fp2add(t1, t1, t1); + fp2sub(t0, t1, t0); + fp2mul_mont(xs[1]->Z, t0, t0); + fp2sub(t0, t4, t0); + fp2mul_mont(Rs[0]->X, t0, t0); + fp2add(t0, Rs[1]->Y, Rs[1]->Y); + fp2mul_mont(Rs[0]->Y, t3, t0); + fp2mul_mont(xs[1]->X, t0, Rs[1]->X); + fp2add(Rs[1]->X, Rs[1]->X, Rs[1]->X); + fp2mul_mont(xs[1]->Z, t0, Rs[1]->Z); + fp2add(Rs[1]->Z, Rs[1]->Z, Rs[1]->Z); + + fp2inv_mont(Rs[1]->Z); // TODO: Make non constant-time.. + fp2mul_mont(Rs[1]->X, Rs[1]->Z, Rs[1]->X); + fp2mul_mont(Rs[1]->Y, Rs[1]->Z, Rs[1]->Y); +} + + +static void BuildOrdinary2nBasis_dual(const f2elm_t A, const f2elm_t Ds[][2], point_full_proj_t *Rs, unsigned char *qnr, unsigned char *ind) +{ + unsigned int i; + felm_t t0; + f2elm_t A6 = {0}; + point_proj_t xs[3] = {0}; + + // Generate x-only entangled basis + BuildEntangledXonly(A, xs, qnr, ind); + fpcopy((digit_t*)Montgomery_one, (xs[0]->Z)[0]); + fpcopy((digit_t*)Montgomery_one, (xs[1]->Z)[0]); + + // Move them back to A = 6 + for(i = 0; i < MAX_Bob; i++) { + eval_3_isog(xs[0], Ds[MAX_Bob-1-i]); + eval_3_isog(xs[1], Ds[MAX_Bob-1-i]); + eval_3_isog(xs[2], Ds[MAX_Bob-1-i]); + } + + // Recover y-coordinates with a single sqrt on A = 6 + fpcopy((digit_t*)Montgomery_one, A6[0]); + fpadd(A6[0], A6[0], t0); + fpadd(t0, t0, A6[0]); + fpadd(A6[0], t0, A6[0]); // A6 = 6 + + CompleteMPoint(A6, xs[0], Rs[0]); + RecoverY(A6, xs, Rs); +} + + +static void FullIsogeny_B_dual(const unsigned char* PrivateKeyB, f2elm_t Ds[][2], f2elm_t A) +{ // Bob's ephemeral public key generation + // Input: a private key PrivateKeyB in the range [0, 2^Floor(Log(2,oB)) - 1]. + // Output: the public key PublicKeyB consisting of 3 elements in GF(p^2) which are encoded by removing leading 0 bytes. + point_proj_t R, Q3 = {0}, pts[MAX_INT_POINTS_BOB]; + f2elm_t XPB, XQB, XRB, coeff[3], A24plus = {0}, A24minus = {0}; + unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0; + + // Initialize basis points + init_basis((digit_t*)B_gen, XPB, XQB, XRB); + fpcopy((digit_t*)XQB3, (Q3->X)[0]); + fpcopy((digit_t*)XQB3 + NWORDS_FIELD, (Q3->X)[1]); + fpcopy((digit_t*)Montgomery_one, (Q3->Z)[0]); + + // Initialize constants: A24minus = A-2C, A24plus = A+2C, where A=6, C=1 + fpcopy((digit_t*)&Montgomery_one, A24plus[0]); + fp2add(A24plus, A24plus, A24plus); + fp2add(A24plus, A24plus, A24minus); + fp2add(A24plus, A24minus, A); + fp2add(A24minus, A24minus, A24plus); + + // Retrieve kernel point + LADDER3PT(XPB, XQB, XRB, (digit_t*)PrivateKeyB, BOB, R, A); + + // Traverse tree + index = 0; + for (row = 1; row < MAX_Bob; row++) { + while (index < MAX_Bob-row) { + fp2copy(R->X, pts[npts]->X); + fp2copy(R->Z, pts[npts]->Z); + pts_index[npts++] = index; + m = strat_Bob[ii++]; + xTPLe(R, R, A24minus, A24plus, (int)m); + index += m; + } + get_3_isog(R, A24minus, A24plus, coeff); + for (i = 0; i < npts; i++) { + eval_3_isog(pts[i], coeff); + } + eval_3_isog(Q3, coeff); // Kernel of dual + fp2sub(Q3->X,Q3->Z,Ds[row-1][0]); + fp2add(Q3->X,Q3->Z,Ds[row-1][1]); + + fp2copy(pts[npts-1]->X, R->X); + fp2copy(pts[npts-1]->Z, R->Z); + index = pts_index[npts-1]; + npts -= 1; + } + get_3_isog(R, A24minus, A24plus, coeff); + eval_3_isog(Q3, coeff); // Kernel of dual + fp2sub(Q3->X, Q3->Z, Ds[MAX_Bob-1][0]); + fp2add(Q3->X, Q3->Z, Ds[MAX_Bob-1][1]); + + fp2add(A24plus, A24minus, A); + fp2sub(A24plus, A24minus, A24plus); + fp2inv_mont(A24plus); + fp2mul_mont(A24plus, A, A); + fp2add(A, A, A); // A = 2*(A24plus+A24mins)/(A24plus-A24minus) +} + + +static void Dlogs2_dual(const f2elm_t *f, int *D, digit_t *d0, digit_t *c0, digit_t *d1, digit_t *c1) +{ + solve_dlog(f[0], D, d0, 2); + solve_dlog(f[2], D, c0, 2); + solve_dlog(f[1], D, d1, 2); + solve_dlog(f[3], D, c1, 2); + mp_sub((digit_t*)Alice_order, c0, c0, NWORDS_ORDER); + mp_sub((digit_t*)Alice_order, c1, c1, NWORDS_ORDER); +} + + +static void BuildEntangledXonly_Decomp(const f2elm_t A, point_proj_t *R, unsigned char qnr, unsigned char ind) +{ + f2elm_t *t_ptr, r, t; + + // Select the correct table + if ( qnr == 1 ) + t_ptr = (f2elm_t *)table_v_qnr; + else + t_ptr = (f2elm_t *)table_v_qr; + + // Get x0 + fp2mul_mont(A, t_ptr[ind], R[0]->X); // x1 = A*v + fp2neg(R[0]->X); // R[0]->X = -A*v + fp2add(R[0]->X, A, t); + fp2mul_mont(R[0]->X, t, t); + fpadd(t[0], (digit_t*)Montgomery_one, t[0]); + fp2mul_mont(R[0]->X, t, t); // t = R[0]->X^3 + A*R[0]->X^2 + R[0]->X + + if (qnr == 1) + fpcopy((digit_t*)table_r_qnr[ind], r[0]); + else + fpcopy((digit_t*)table_r_qr[ind], r[0]); + + // Get x1 + fp2add(R[0]->X, A, R[1]->X); + fp2neg(R[1]->X); // R[1]->X = -R[0]->X-A + + // Get difference x2,z2 + fp2sub(R[0]->X, R[1]->X, R[2]->Z); + fp2sqr_mont(R[2]->Z, R[2]->Z); + + fpcopy(r[0],r[1]); // (1+i)*ind + fpadd((digit_t*)Montgomery_one, r[0], r[0]); + fp2sqr_mont(r, r); + fp2mul_mont(t, r, R[2]->X); +} + + +static void PKBDecompression_dual(const unsigned char* SecretKeyA, const unsigned char* CompressedPKB, point_proj_t R, f2elm_t A) +{ + uint64_t mask = (digit_t)(-1); + unsigned char bit,qnr,ind; + f2elm_t A24; + digit_t tmp1[2*NWORDS_ORDER] = {0}, tmp2[2*NWORDS_ORDER] = {0}, vone[2*NWORDS_ORDER] = {0}; + digit_t SKin[NWORDS_ORDER] = {0}, comp_temp[NWORDS_ORDER] = {0}; + point_proj_t Rs[3] = {0}; + + mask >>= (MAXBITS_ORDER - OALICE_BITS); + vone[0] = 1; + + fp2_decode(&CompressedPKB[3*ORDER_A_ENCODED_BYTES], A); + bit = CompressedPKB[3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES] >> 7; + qnr = CompressedPKB[3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES] & 0x1; + ind = CompressedPKB[3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES + 1]; + + // Rebuild the basis + BuildEntangledXonly_Decomp(A,Rs,qnr,ind); + fpcopy((digit_t*)Montgomery_one, (Rs[0]->Z)[0]); + fpcopy((digit_t*)Montgomery_one, (Rs[1]->Z)[0]); + + fpadd(A[0], (digit_t*)Montgomery_one, A24[0]); + fpcopy(A[1], A24[1]); + fpadd(A24[0], (digit_t*)Montgomery_one, A24[0]); + fp2div2(A24, A24); + fp2div2(A24, A24); + + memcpy((unsigned char*)SKin, SecretKeyA, SECRETKEY_A_BYTES); + swap_points(Rs[0], Rs[1], 0-(digit_t)bit); + if (bit == 0) { + memcpy((unsigned char*)&comp_temp, &CompressedPKB[ORDER_A_ENCODED_BYTES], ORDER_A_ENCODED_BYTES); + multiply((digit_t*)SKin, comp_temp, tmp1, NWORDS_ORDER); + mp_add(tmp1, vone, tmp1, NWORDS_ORDER); + tmp1[NWORDS_ORDER-1] &= (digit_t)mask; + inv_mod_orderA(tmp1, tmp2); + memcpy((unsigned char*)&comp_temp, &CompressedPKB[2*ORDER_A_ENCODED_BYTES], ORDER_A_ENCODED_BYTES); + multiply((digit_t*)SKin, comp_temp, tmp1, NWORDS_ORDER); + memcpy((unsigned char*)&comp_temp, &CompressedPKB[0], ORDER_A_ENCODED_BYTES); + mp_add(&comp_temp[0], tmp1, tmp1, NWORDS_ORDER); + multiply(tmp1, tmp2, vone, NWORDS_ORDER); + vone[NWORDS_ORDER-1] &= (digit_t)mask; + Ladder3pt_dual(Rs,vone,ALICE,R,A24); + } else { + memcpy((unsigned char*)&comp_temp, &CompressedPKB[2*ORDER_A_ENCODED_BYTES], ORDER_A_ENCODED_BYTES); + multiply((digit_t*)SKin, comp_temp, tmp1, NWORDS_ORDER); + mp_add(tmp1, vone, tmp1, NWORDS_ORDER); + tmp1[NWORDS_ORDER-1] &= (digit_t)mask; + inv_mod_orderA(tmp1, tmp2); + memcpy((unsigned char*)&comp_temp, &CompressedPKB[ORDER_A_ENCODED_BYTES], ORDER_A_ENCODED_BYTES); + multiply((digit_t*)SKin, comp_temp, tmp1, NWORDS_ORDER); + memcpy((unsigned char*)&comp_temp, &CompressedPKB[0], ORDER_A_ENCODED_BYTES); + mp_add(&comp_temp[0], tmp1, tmp1, NWORDS_ORDER); + multiply(tmp1, tmp2, vone, NWORDS_ORDER); + vone[NWORDS_ORDER-1] &= (digit_t)mask; + Ladder3pt_dual(Rs,vone,ALICE,R,A24); + } + fp2div2(A,A24); + xTPLe_fast(R, R, A24, OBOB_EXPON); +} + + +static void Compress_PKB_dual(digit_t *d0, digit_t *c0, digit_t *d1, digit_t *c1, f2elm_t A, unsigned char qnr, unsigned char ind, unsigned char *CompressedPKB) +{ + digit_t tmp[2*NWORDS_ORDER], inv[NWORDS_ORDER]; + if ((d1[0] & 1) == 1) { // Storing [-d0*d1^-1 = b1*a0^-1, -c1*d1^-1 = a1*a0^-1, c0*d1^-1 = b0*a0^-1] and setting bit384 to 0 + inv_mod_orderA(d1, inv); + Montgomery_neg(d0, (digit_t*)Alice_order); + multiply(d0, inv, tmp, NWORDS_ORDER); + memcpy(&CompressedPKB[0], (unsigned char *)&tmp, ORDER_A_ENCODED_BYTES); + CompressedPKB[ORDER_A_ENCODED_BYTES-1] &= MASK_ALICE; + Montgomery_neg(c1, (digit_t*)Alice_order); + multiply(c1, inv, tmp, NWORDS_ORDER); + memcpy(&CompressedPKB[ORDER_A_ENCODED_BYTES], (unsigned char *)&tmp, ORDER_A_ENCODED_BYTES); + CompressedPKB[2*ORDER_A_ENCODED_BYTES-1] &= MASK_ALICE; + multiply(c0, inv, tmp, NWORDS_ORDER); + memcpy(&CompressedPKB[2*ORDER_A_ENCODED_BYTES], (unsigned char *)&tmp, ORDER_A_ENCODED_BYTES); + CompressedPKB[3*ORDER_A_ENCODED_BYTES-1] &= MASK_ALICE; + CompressedPKB[3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES] = 0x00; + } else { // Storing [ -d1*d0^-1 = b1*b0inv, c1*d0^-1 = a1*b0inv, -c0*d0^-1 = a0*b0inv] and setting bit384 to 1 + inv_mod_orderA(d0, inv); + Montgomery_neg(d1, (digit_t*)Alice_order); + multiply(d1, inv, tmp, NWORDS_ORDER); + memcpy(&CompressedPKB[0], (unsigned char *)&tmp, ORDER_A_ENCODED_BYTES); + CompressedPKB[ORDER_A_ENCODED_BYTES - 1] &= MASK_ALICE; + multiply(c1, inv, tmp, NWORDS_ORDER); + memcpy(&CompressedPKB[ORDER_A_ENCODED_BYTES], (unsigned char *)&tmp, ORDER_A_ENCODED_BYTES); + CompressedPKB[2*ORDER_A_ENCODED_BYTES-1] &= MASK_ALICE; + Montgomery_neg(c0, (digit_t*)Alice_order); + multiply(c0, inv, tmp, NWORDS_ORDER); + memcpy(&CompressedPKB[2*ORDER_A_ENCODED_BYTES], (unsigned char *)&tmp, ORDER_A_ENCODED_BYTES); + CompressedPKB[3*ORDER_A_ENCODED_BYTES-1] &= MASK_ALICE; + CompressedPKB[3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES] = 0x80; + } + + fp2_encode(A, &CompressedPKB[3*ORDER_A_ENCODED_BYTES]); + CompressedPKB[3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES] |= qnr; + CompressedPKB[3*ORDER_A_ENCODED_BYTES + FP2_ENCODED_BYTES + 1] = ind; +} + + +int EphemeralKeyGeneration_B(const unsigned char* PrivateKeyB, unsigned char* CompressedPKB) +{ // Bob's ephemeral public key generation using compression + unsigned char qnr,ind; + int D[DLEN_2]; + digit_t c0[NWORDS_ORDER] = {0}, d0[NWORDS_ORDER] = {0}, + c1[NWORDS_ORDER] = {0}, d1[NWORDS_ORDER] = {0}; + f2elm_t Ds[MAX_Bob][2], f[4], A = {0}; + point_full_proj_t Rs[2]; + point_t Pw, Qw; + + FullIsogeny_B_dual(PrivateKeyB, Ds, A); + BuildOrdinary2nBasis_dual(A, Ds, Rs, &qnr, &ind); + + fpadd((digit_t*)Montgomery_one, (Rs[0]->X)[0], (Rs[0]->X)[0]); + fpadd((digit_t*)Montgomery_one, (Rs[0]->X)[0], (Rs[0]->X)[0]); // Weierstrass form + fpadd((digit_t*)Montgomery_one, (Rs[1]->X)[0], (Rs[1]->X)[0]); + fpadd((digit_t*)Montgomery_one, (Rs[1]->X)[0], (Rs[1]->X)[0]); // Weierstrass form + + fpcopy((digit_t*)A_basis_zero + 0*NWORDS_FIELD, Pw->x[0]); + fpcopy((digit_t*)A_basis_zero + 1*NWORDS_FIELD, Pw->x[1]); + fpcopy((digit_t*)A_basis_zero + 2*NWORDS_FIELD, Pw->y[0]); + fpcopy((digit_t*)A_basis_zero + 3*NWORDS_FIELD, Pw->y[1]); + fpcopy((digit_t*)A_basis_zero + 4*NWORDS_FIELD, Qw->x[0]); + fpcopy((digit_t*)A_basis_zero + 5*NWORDS_FIELD, Qw->x[1]); + fpcopy((digit_t*)A_basis_zero + 6*NWORDS_FIELD, Qw->y[0]); + fpcopy((digit_t*)A_basis_zero + 7*NWORDS_FIELD, Qw->y[1]); + Tate2_pairings(Pw, Qw, Rs, f); + + Dlogs2_dual(f, D, d0, c0, d1, c1); + Compress_PKB_dual(d0, c0, d1, c1, A, qnr, ind, CompressedPKB); + + return 0; +} + + +int EphemeralSecretAgreement_A(const unsigned char* PrivateKeyA, const unsigned char* PKB, unsigned char* SharedSecretA) +{ // Alice's ephemeral shared secret computation using compression + // It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's decompressed data point_R and param_A + // Inputs: Alice's PrivateKeyA is an even integer in the range [2, oA-2], where oA = 2^OALICE_BITS. + // Bob's decompressed data consists of point_R in (X:Z) coordinates and the curve parameter param_A in GF(p^2). + // Output: a shared secret SharedSecretA that consists of one element in GF(p^2). + unsigned int i, ii = 0, row, m, index = 0, pts_index[MAX_INT_POINTS_ALICE], npts = 0; + f2elm_t A24plus = {0}, C24 = {0}; + point_proj_t R, pts[MAX_INT_POINTS_ALICE]; + f2elm_t jinv, coeff[5], A; + f2elm_t param_A = {0}; + + PKBDecompression_dual(PrivateKeyA, PKB, R, param_A); + + fp2copy(param_A, A); + fpadd((digit_t*)&Montgomery_one, (digit_t*)&Montgomery_one, C24[0]); + fp2add(A, C24, A24plus); + fpadd(C24[0], C24[0], C24[0]); + +#if (OALICE_BITS % 2 == 1) + point_proj_t S; + + xDBLe(R, S, A24plus, C24, (int)(OALICE_BITS-1)); + get_2_isog(S, A24plus, C24); + eval_2_isog(R, S); +#endif + + // Traverse tree + index = 0; + for (row = 1; row < MAX_Alice; row++) { + while (index < MAX_Alice-row) { + fp2copy(R->X, pts[npts]->X); + fp2copy(R->Z, pts[npts]->Z); + pts_index[npts++] = index; + m = strat_Alice[ii++]; + xDBLe(R, R, A24plus, C24, (int)(2*m)); + index += m; + } + get_4_isog(R, A24plus, C24, coeff); + + for (i = 0; i < npts; i++) { + eval_4_isog(pts[i], coeff); + } + + fp2copy(pts[npts-1]->X, R->X); + fp2copy(pts[npts-1]->Z, R->Z); + index = pts_index[npts-1]; + npts -= 1; + } + + get_4_isog(R, A24plus, C24, coeff); + fp2add(A24plus, A24plus, A24plus); + fp2sub(A24plus, C24, A24plus); + fp2add(A24plus, A24plus, A24plus); + j_inv(A24plus, C24, jinv); + fp2_encode(jinv, SharedSecretA); // Format shared secret + + return 0; +} diff --git a/src/compression/sike_compressed.c b/src/compression/sike_compressed.c new file mode 100644 index 0000000..6467966 --- /dev/null +++ b/src/compression/sike_compressed.c @@ -0,0 +1,96 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: supersingular isogeny key encapsulation (SIKE) protocol using compression +*********************************************************************************************/ + +#include +#include "../sha3/fips202.h" + + +int crypto_kem_keypair(unsigned char *pk, unsigned char *sk) +{ // SIKE's key generation using compression + // Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = MSG_BYTES + SECRETKEY_A_BYTES + CRYPTO_PUBLICKEYBYTES bytes) + // public key pk_comp (CRYPTO_PUBLICKEYBYTES bytes) + + // Generate lower portion of secret key sk <- s||SK + randombytes(sk, MSG_BYTES); + random_mod_order_A(sk + MSG_BYTES); // Even random number + + // Generate public key pk + EphemeralKeyGeneration_A(sk + MSG_BYTES, pk); + + // Append public key pk to secret key sk + memcpy(&sk[MSG_BYTES + SECRETKEY_A_BYTES], pk, CRYPTO_PUBLICKEYBYTES); + + return 0; +} + + +int crypto_kem_enc(unsigned char *ct, unsigned char *ss, const unsigned char *pk) +{ // SIKE's encapsulation using compression + // Input: public key pk (CRYPTO_PUBLICKEYBYTES bytes) + // Outputs: shared secret ss (CRYPTO_BYTES bytes) + // ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = COMPRESSED_CHUNK_CT + MSG_BYTES bytes) + unsigned char ephemeralsk[SECRETKEY_B_BYTES] = {0}; + unsigned char jinvariant[FP2_ENCODED_BYTES] = {0}; + unsigned char h[MSG_BYTES]; + unsigned char temp[CRYPTO_CIPHERTEXTBYTES + MSG_BYTES] = {0}; + + // Generate ephemeralsk <- G(m||pk) mod oB + randombytes(temp, MSG_BYTES); + memcpy(&temp[MSG_BYTES], pk, CRYPTO_PUBLICKEYBYTES); + shake256(ephemeralsk, SECRETKEY_B_BYTES, temp, MSG_BYTES + CRYPTO_PUBLICKEYBYTES); + FormatPrivKey_B(ephemeralsk); + + // Encrypt + EphemeralKeyGeneration_B(ephemeralsk, ct); + EphemeralSecretAgreement_B(ephemeralsk, pk, jinvariant); + shake256(h, MSG_BYTES, jinvariant, FP2_ENCODED_BYTES); + for (int i = 0; i < MSG_BYTES; i++) { + ct[i + COMPRESSED_CHUNK_CT] = temp[i] ^ h[i]; + } + + // Generate shared secret ss <- H(m||ct) + memcpy(&temp[MSG_BYTES], ct, CRYPTO_CIPHERTEXTBYTES); + shake256(ss, CRYPTO_BYTES, temp, CRYPTO_CIPHERTEXTBYTES + MSG_BYTES); + + return 0; +} + + +int crypto_kem_dec(unsigned char *ss, const unsigned char *ct, const unsigned char *sk) +{ // SIKE's decapsulation using compression + // Input: secret key sk (CRYPTO_SECRETKEYBYTES = MSG_BYTES + SECRETKEY_A_BYTES + CRYPTO_PUBLICKEYBYTES bytes) + // compressed ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = COMPRESSED_CHUNK_CT + MSG_BYTES bytes) + // Outputs: shared secret ss (CRYPTO_BYTES bytes) + unsigned char ephemeralsk_[SECRETKEY_B_BYTES] = {0}; + unsigned char jinvariant_[FP2_ENCODED_BYTES] = {0}, h_[MSG_BYTES]; + unsigned char c0_comp_[COMPRESSED_CHUNK_CT] = {0}; + unsigned char temp[CRYPTO_CIPHERTEXTBYTES + MSG_BYTES] = {0}; + + // Decrypt + EphemeralSecretAgreement_A(sk + MSG_BYTES, ct, jinvariant_); + shake256(h_, MSG_BYTES, jinvariant_, FP2_ENCODED_BYTES); + + for (int i = 0; i < MSG_BYTES; i++) { + temp[i] = ct[i + COMPRESSED_CHUNK_CT] ^ h_[i]; + } + + // Generate ephemeralsk_ <- G(m||pk) mod oB + memcpy(&temp[MSG_BYTES], &sk[MSG_BYTES + SECRETKEY_A_BYTES], CRYPTO_PUBLICKEYBYTES); + shake256(ephemeralsk_, SECRETKEY_B_BYTES, temp, MSG_BYTES + CRYPTO_PUBLICKEYBYTES); + FormatPrivKey_B(ephemeralsk_); + + // Generate shared secret ss <- H(m||ct) or output ss <- H(s||ct) + EphemeralKeyGeneration_B(ephemeralsk_, c0_comp_); + + if (memcmp(c0_comp_, ct, COMPRESSED_CHUNK_CT) != 0) { + memcpy(temp, sk, MSG_BYTES); + } + + memcpy(&temp[MSG_BYTES], ct, CRYPTO_CIPHERTEXTBYTES); + shake256(ss, CRYPTO_BYTES, temp, CRYPTO_CIPHERTEXTBYTES + MSG_BYTES); + + return 0; +} \ No newline at end of file diff --git a/src/compression/torsion_basis.c b/src/compression/torsion_basis.c new file mode 100644 index 0000000..9a00e8f --- /dev/null +++ b/src/compression/torsion_basis.c @@ -0,0 +1,433 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: Torsion basis generation for compression +*********************************************************************************************/ + + +void get_2_torsion_entangled_basis_compression(const f2elm_t A, point_t S1, point_t S2, unsigned char *bit, unsigned char *entry) +{ // Build an entangled basis for E[2^m]. + // At first glance this is similar to the Elligator 2 technique, but the field element u is a *square* here, not a non-square. + unsigned int i, index, isSqrA = 0; + felm_t r = {0}, s, z, alpha, twoalphainv, beta; + f2elm_t t, u, u0, one = {0}, *t_ptr; + felm_t *x1 = (felm_t*) S1->x, *y1 = (felm_t*) S1->y, *x2 = (felm_t*) S2->x, *y2 = (felm_t*) S2->y; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + copy_words((const digit_t *)u0_entang, u0[0], 2*NWORDS_FIELD); + copy_words((const digit_t *)u_entang, u[0], 2*NWORDS_FIELD); + + // Select the correct table + if (is_sqr_fp2(A, s)) { + t_ptr = (f2elm_t *)table_v_qnr; + isSqrA = 1; + } else { + t_ptr = (f2elm_t *)table_v_qr; + } + *bit = (unsigned char)isSqrA; // This bit is transmitted along with the PK to speedup decompression + + index = 0; + do { + fp2mul_mont(A, (felm_t *)*t_ptr++, x1); // x1 = A*v + fp2neg(x1); // x1 = -A*v + fp2add(x1, A, t); + fp2mul_mont(x1, t, t); + fpadd(t[0], one[0], t[0]); + fp2mul_mont(x1, t, t); // t = x1^3 + A*x1^2 + x1 = x1(x1(x1 + A) + 1) + index += 2; + } while (!is_sqr_fp2(t, s)); + *entry = ((unsigned char)index - 2)/2; // This table entry will also be transmitted along with the PubKey to speedup decompression + + if (isSqrA) + copy_words((const digit_t *)table_r_qnr[(index-2)/2], r, NWORDS_FIELD); + else + copy_words((const digit_t *)table_r_qr[(index-2)/2], r, NWORDS_FIELD); + + // Finish sqrt computation for y1 = sqrt(x1^3+A*x1^2+x1) + fpadd(t[0],s,z); + fpdiv2(z,z); + fpcopy(z,alpha); + for (i = 0; i < OALICE_BITS - 2; i++) { + fpsqr_mont(alpha, alpha); + } + for (i = 0; i < OBOB_EXPON; i++) { + fpsqr_mont(alpha, s); + fpmul_mont(alpha, s, alpha); // alpha = z^((p+1)/4) + } + + fpadd(alpha,alpha,twoalphainv); + fpinv_mont_bingcd(twoalphainv); + fpmul_mont(t[1],twoalphainv,beta); + fpsqr_mont(alpha, twoalphainv); + fpcorrection(twoalphainv); + fpcorrection(z); + if (memcmp(twoalphainv, z, NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + fpcopy(alpha,y1[0]); + fpcopy(beta,y1[1]); + } else { + fpneg(beta); + fpcopy(beta,y1[0]); + fpneg(alpha); + fpcopy(alpha,y1[1]); + } + fp2add(x1, A, x2); + fp2neg(x2); // x2 = A*v - A + fp2mul_mont(u0,y1,y2); + fpmul_mont(r,y2[0],y2[0]); + fpmul_mont(r,y2[1],y2[1]); // y2 = u0*r*y1 +} + + +void get_2_torsion_entangled_basis_decompression(const f2elm_t A, point_t S1, point_t S2, unsigned char isASqr, unsigned char entry) +{ // Build an entangled basis for E[2^m] during decompression using the the entry and table already computed during compression + unsigned int i; + felm_t r = {0}, s, z, alpha, twoalphainv, beta; + f2elm_t t, u, u0, one = {0}, *t_ptr; + felm_t *x1 = (felm_t*) S1->x, *y1 = (felm_t*) S1->y, *x2 = (felm_t*) S2->x, *y2 = (felm_t*) S2->y; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + + copy_words((const digit_t *)u0_entang, u0[0], 2*NWORDS_FIELD); + copy_words((const digit_t *)u_entang, u[0], 2*NWORDS_FIELD); + + // Select the table + t_ptr = isASqr ? (f2elm_t *)table_v_qnr : (f2elm_t *)table_v_qr; + + fp2mul_mont(A, t_ptr[entry], x1); // x1 = A*v + fp2neg(x1); // x1 = -A*v + fp2add(x1, A, t); + fp2mul_mont(x1, t, t); + fpadd(t[0], one[0], t[0]); + fp2mul_mont(x1, t, t); // t = x1^3 + A*x1^2 + x1 = x1(x1(x1 + A) + 1) + is_sqr_fp2(t, s); + + if (isASqr) + copy_words((const digit_t *)table_r_qnr[entry], r, NWORDS_FIELD); + else + copy_words((const digit_t *)table_r_qr[entry], r, NWORDS_FIELD); + + // Finish sqrt computation for y1 = sqrt(x1^3+A*x1^2+x1) + fpadd(t[0],s,z); + fpdiv2(z,z); + fpcopy(z,alpha); + for (i = 0; i < OALICE_BITS - 2; i++) { + fpsqr_mont(alpha, alpha); + } + for (i = 0; i < OBOB_EXPON; i++) { + fpsqr_mont(alpha, s); + fpmul_mont(alpha, s, alpha); // alpha = z^((p+1)/4) + } + + fpadd(alpha,alpha,twoalphainv); + fpinv_mont_bingcd(twoalphainv); + fpmul_mont(t[1],twoalphainv,beta); + fpsqr_mont(alpha, twoalphainv); + fpcorrection(twoalphainv); + fpcorrection(z); + if (memcmp((unsigned char*)twoalphainv, (unsigned char*)z, NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + fpcopy(alpha,y1[0]); + fpcopy(beta,y1[1]); + } else { + fpneg(beta); + fpcopy(beta,y1[0]); + fpneg(alpha); + fpcopy(alpha,y1[1]); + } + fp2add(x1, A, x2); + fp2neg(x2); // x2 = A*v - A + fp2mul_mont(u0,y1,y2); + fpmul_mont(r,y2[0],y2[0]); + fpmul_mont(r,y2[1],y2[1]); // y2 = u0*r*y1 +} + + +void sqrtinv2(const f2elm_t v, const f2elm_t z, f2elm_t s, f2elm_t invz) +{ // Compute the square root of a field element v in F_{p^2} and invert a field element z. + int j; + felm_t az, bz, av, bv, Nz, Nv, av2, bv2, r, t, x, y, kk; + f2elm_t conjz, zero = {0}; + + fpsqr_mont(z[0],az); + fpsqr_mont(z[1],bz); + fpadd(az,bz,Nz); + fpcopy(v[0],av); + fpcopy(v[1],bv); + + if (memcmp(bv,zero[0],NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fpsqr_mont(av,av2); + fpsqr_mont(bv,bv2); + fpadd(av2,bv2,Nv); + + fpcopy(Nv,r); + for (j = 0; j < OALICE_BITS - 2; j++) + fpsqr_mont(r,r); + for (j = 0; j < OBOB_EXPON; j++) { + fpsqr_mont(r,t); + fpmul_mont(r,t,r); + } + fpsqr_mont(r,t); + fpcorrection(t); + fpcorrection(Nv); + if (memcmp(t,Nv,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + mp_add(av,r,r,NWORDS_FIELD); + + if ((r[0] & 0x01) != 0) + mp_add(r,(digit_t*)&PRIME,r,NWORDS_FIELD); + + mp_shiftr1(r,NWORDS_FIELD); + + fpcopy(r,x); + for (j = 0; j < OALICE_BITS - 2; j++) + fpsqr_mont(x,x); + for (j = 0; j < OBOB_EXPON; j++) { + fpsqr_mont(x,t); + fpmul_mont(x,t,x); + } + + if (memcmp(Nz,zero[0],NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fpmul_mont(x,Nz,t); + fpadd(t,t,t); + fpinv_mont_bingcd(t); + fpcopy(t,kk); + fpmul_mont(bv,Nz,y); + fpmul_mont(y,kk,y); + + fpsqr_mont(x,t); + fpcorrection(t); + fpcorrection(r); + if (memcmp(t,r,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + fpcopy(x,s[0]); + fpcopy(y,s[1]); + } else { + fpcopy(y,s[0]); + fpcopy(x,s[1]); + } + fp2_conj(z,conjz); + fpmul_mont(x,kk,t); + fpadd(t,t,t); + fpmul_mont(t,conjz[0],invz[0]); + fpmul_mont(t,conjz[1],invz[1]); + } else { + fpadd(x,x,t); + fpinv_mont_bingcd(t); + fpmul_mont(bv,t,y); + fpsqr_mont(x,t); + if (memcmp(t,r,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + fpcopy(x,s[0]); + fpcopy(y,s[1]); + } else { + fpcopy(y,s[0]); + fpcopy(x,s[1]); + } + fp2copy(zero,invz); + } + + } else { + fp2copy(zero,s); + if (memcmp(Nz,zero[0],NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fpinv_mont_bingcd(Nz); + fp2_conj(z,conjz); + fpmul_mont(Nz,conjz[0],invz[0]); + fpmul_mont(Nz,conjz[1],invz[1]); + } else { + fp2copy(zero,invz); + } + } + } else { + fpcopy(av,r); + for (j = 0; j < OALICE_BITS - 2; j++) + fpsqr_mont(r,r); + for (j = 0; j < OBOB_EXPON; j++) { + fpsqr_mont(r,t); + fpmul_mont(r,t,r); + } + fpsqr_mont(r,t); + if (memcmp(t,av,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + fpcopy(r,s[0]); + fpcopy(zero[0],s[1]); + } else { + fpcopy(zero[0],s[0]); + fpcopy(r,s[1]); + } + + if (memcmp(Nz,zero[0],NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fp2_conj(z,conjz); + fpinv_mont_bingcd(Nz); + fpmul_mont(Nz,conjz[0],invz[0]); + fpmul_mont(Nz,conjz[1],invz[1]); + } else { + fp2copy(zero,invz); + } + } +} + + +void CompleteMPoint(const f2elm_t A, point_proj_t P, point_full_proj_t R) +{ // Given an xz-only representation on a montgomery curve, compute its affine representation + f2elm_t zero = {0}, one = {0}, xz, yz, s2, r2, invz, temp0, temp1; + fpcopy((digit_t*)&Montgomery_one,one[0]); + + if (memcmp(P->Z[0],zero,NBITS_TO_NBYTES(NBITS_FIELD)) != 0 || memcmp(P->Z[1],zero,NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fp2mul_mont(P->X,P->Z,xz); // xz = x*z; + fpsub(P->X[0],P->Z[1],temp0[0]); + fpadd(P->X[1],P->Z[0],temp0[1]); + fpadd(P->X[0],P->Z[1],temp1[0]); + fpsub(P->X[1],P->Z[0],temp1[1]); + fp2mul_mont(temp0,temp1,s2); // s2 = (x + i*z)*(x - i*z); + fp2mul_mont(A,xz,temp0); + fp2add(temp0,s2,temp1); + fp2mul_mont(xz,temp1,r2); // r2 = xz*(A*xz + s2); + sqrtinv2(r2,P->Z,yz,invz); + fp2mul_mont(P->X,invz,R->X); + fp2sqr_mont(invz,temp0); + fp2mul_mont(yz,temp0,R->Y); // R = EM![x*invz, yz*invz^2]; + fp2copy(one,R->Z); + } else { + fp2copy(zero,R->X); + fp2copy(one,R->Y); + fp2copy(zero,R->Z); // R = EM!0; + } +} + + +void BasePoint3n(f2elm_t A, unsigned int *r, point_proj_t P, point_proj_t Q) +{ // xz-only construction of a point of order 3^n in the Montgomery curve y^2 = x^3 + A*x^2 + x from base counter r. + // This is essentially the Elligator 2 technique coupled with cofactor multiplication and LI checking. + int i; + felm_t a2, b2, N, temp0, temp1; + f2elm_t A2, A24, two = {0}, x, y2, one_fp2 = {0}, *t_ptr; + point_proj_t S; + + fpcopy((digit_t*)&Montgomery_one, one_fp2[0]); + fp2div2(A,A2); + fpcopy(one_fp2[0],two[0]); + fpadd(two[0], two[0], two[0]); + fp2add(A,two,A24); + fp2div2(A24,A24); + fp2div2(A24,A24); + + t_ptr = (f2elm_t *)&v_3_torsion[*r]; + do { + *r += 1; + fp2mul_mont(A,(felm_t*)t_ptr++,x); // x = A*v; v := 1/(1 + U*r^2) table lookup + fp2neg(x); // x = -A*v; + fp2add(A,x,y2); // y2 = x + A + fp2mul_mont(y2, x, y2); // y2 = x*(x + A) + fpadd(y2[0], one_fp2[0], y2[0]); // y2 = x(x + A) + 1 + fp2mul_mont(x,y2,y2); // y2 = x*(x^2 + Ax + 1); + fpsqr_mont(y2[0],a2); + fpsqr_mont(y2[1],b2); + fpadd(a2,b2,N); // N := norm(y2); + + fpcopy(N,temp0); + for (i = 0; i < OALICE_BITS - 2; i++) { + fpsqr_mont(temp0, temp0); + } + for (i = 0; i < OBOB_EXPON; i++) { + fpsqr_mont(temp0, temp1); + fpmul_mont(temp0, temp1, temp0); + } + fpsqr_mont(temp0,temp1); // z = N^((p + 1) div 4); + fpcorrection(temp1); + fpcorrection(N); + if (memcmp(temp1,N,NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fp2neg(x); + fp2sub(x,A,x); // x = -x - A; + } + fp2copy(x,S->X); + fp2copy(one_fp2,S->Z); + Double(S,P,A24,OALICE_BITS); // x, z := Double(A24, x, 1, eA); + xTPLe_fast(P,Q,A2,OBOB_EXPON-1); // t, w := Triple(A_2, x, z, eB-1); + fp2correction(Q->X); + fp2correction(Q->Z); + } while (is_felm_zero(Q->Z[0]) && is_felm_zero(Q->Z[1])); +} + + +void BasePoint3n_decompression(f2elm_t A, const unsigned char r, point_proj_t P) +{ // Deterministic xz-only construction of a point of order 3^n in the Montgomery curve y^2 = x^3 + A*x^2 + x from counter r1. + // Notice that the Elligator 2 counter r was generated beforehand during key compression without linear independence testing + int i; + felm_t a2, b2, N, temp0, temp1; + f2elm_t A2, A24, two = {0}, x, y2, one_fp2 = {0}; + point_proj_t S; + + fpcopy((digit_t*)&Montgomery_one, one_fp2[0]); + fp2div2(A,A2); + fpcopy((digit_t*)&Montgomery_one,two[0]); + fpadd(two[0], two[0], two[0]); + fp2add(A,two,A24); + fp2div2(A24,A24); + fp2div2(A24,A24); + + fp2mul_mont(A, (felm_t*)&v_3_torsion[r-1], x); // x = A*v; + fp2neg(x); // x = -A*v; + fp2add(x,A,y2); // y2 = x + A + fp2mul_mont(x,y2,y2); // y2 = x*(x + A) + fpadd(y2[0], one_fp2[0], y2[0]); // y2 = x(x + A) + 1 + fp2mul_mont(x, y2, y2); // y2 = x*(x^2 + A*x + 1); + fpsqr_mont(y2[0],a2); + fpsqr_mont(y2[1],b2); + fpadd(a2,b2,N); // N := Fp!norm(y2); + + fpcopy(N,temp0); + for (i = 0; i < OALICE_BITS - 2; i++) { + fpsqr_mont(temp0, temp0); + } + for (i = 0; i < OBOB_EXPON; i++) { + fpsqr_mont(temp0, temp1); + fpmul_mont(temp0, temp1, temp0); + } + fpsqr_mont(temp0,temp1); // z = N^((p + 1) div 4); + fpcorrection(temp1); + fpcorrection(N); + if (memcmp(temp1,N,NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fp2neg(x); + fp2sub(x,A,x); // x = -x - A; + } + fp2copy(x,S->X); + fp2copy(one_fp2,S->Z); + Double(S,P,A24,OALICE_BITS); // x, z := Double(A24, x, 1, eA); +} + + +void BuildOrdinaryE3nBasis(f2elm_t A, point_full_proj_t R1, point_full_proj_t R2, unsigned int rs[2]) +{ // Generate a basis for the 3^eB torsion + unsigned int r = 0; + f2elm_t t2w1, t1w2; + point_proj_t P, Q, R, S; + + // 1st basis point: + BasePoint3n(A,&r,P,Q); + rs[0] = r; + + // 2nd basis point: + do { + BasePoint3n(A,&r,R,S); + fp2mul_mont(S->X,Q->Z,t2w1); + fp2mul_mont(Q->X,S->Z,t1w2); + fp2correction(t2w1); + fp2correction(t1w2); + } while (memcmp(t2w1[0],t1w2[0],NBITS_TO_NBYTES(NBITS_FIELD)) == 0 && memcmp(t2w1[1],t1w2[1],NBITS_TO_NBYTES(NBITS_FIELD)) == 0); // Pr[t2/w2 == t1/w1] = 1/4: E[loop length] = 4/3 + rs[1] = r; + + // NB: ideally the following point completions could share one inversion at the cost of 3 products, but this is not implemented here. + CompleteMPoint(A,P,R1); + CompleteMPoint(A,R,R2); +} + + +void BuildOrdinaryE3nBasis_decompression(f2elm_t A, point_full_proj_t R1, point_full_proj_t R2, const unsigned char r1, const unsigned char r2) +{ // Generate a basis for the 3^eB torsion using shared information + point_proj_t P, R; + + // 1st basis point: + BasePoint3n_decompression(A,r1,P); + // 2nd basis point: + BasePoint3n_decompression(A,r2,R); + + // NB: ideally the following point completions could share one inversion at the cost of 3 products, but this is not implemented here. + CompleteMPoint(A,P,R1); + CompleteMPoint(A,R,R2); +} + diff --git a/src/config.h b/src/config.h index d130c24..5cbdcd5 100644 --- a/src/config.h +++ b/src/config.h @@ -55,21 +55,25 @@ #define RADIX 64 #define LOG2RADIX 6 typedef uint64_t digit_t; // Unsigned 64-bit digit + typedef uint32_t hdigit_t; // Unsigned 32-bit digit #elif defined(_X86_) #define TARGET TARGET_x86 #define RADIX 32 #define LOG2RADIX 5 typedef uint32_t digit_t; // Unsigned 32-bit digit + typedef uint16_t hdigit_t; // Unsigned 16-bit digit #elif defined(_ARM_) #define TARGET TARGET_ARM #define RADIX 32 #define LOG2RADIX 5 typedef uint32_t digit_t; // Unsigned 32-bit digit + typedef uint16_t hdigit_t; // Unsigned 16-bit digit #elif defined(_ARM64_) #define TARGET TARGET_ARM64 #define RADIX 64 #define LOG2RADIX 6 typedef uint64_t digit_t; // Unsigned 64-bit digit + typedef uint32_t hdigit_t; // Unsigned 32-bit digit #else #error -- "Unsupported ARCHITECTURE" #endif @@ -87,20 +91,15 @@ // Extended datatype support - + #if defined(GENERIC_IMPLEMENTATION) typedef uint64_t uint128_t[2]; #elif (TARGET == TARGET_AMD64 && OS_TARGET == OS_LINUX) && (COMPILER == COMPILER_GCC || COMPILER == COMPILER_CLANG) - #define UINT128_SUPPORT typedef unsigned uint128_t __attribute__((mode(TI))); #elif (TARGET == TARGET_ARM64 && OS_TARGET == OS_LINUX) && (COMPILER == COMPILER_GCC || COMPILER == COMPILER_CLANG) - #define UINT128_SUPPORT typedef unsigned uint128_t __attribute__((mode(TI))); #elif (TARGET == TARGET_AMD64) && (OS_TARGET == OS_WIN && COMPILER == COMPILER_VC) - #define SCALAR_INTRIN_SUPPORT typedef uint64_t uint128_t[2]; -#else - #error -- "Unsupported configuration" #endif @@ -136,7 +135,7 @@ static __inline unsigned int is_digit_lessthan_ct(digit_t x, digit_t y) /********************** Macros for platform-dependent operations **********************/ -#if defined(GENERIC_IMPLEMENTATION) +#if defined(GENERIC_IMPLEMENTATION) || (TARGET == TARGET_ARM) // Digit multiplication #define MUL(multiplier, multiplicand, hi, lo) \ @@ -163,18 +162,6 @@ static __inline unsigned int is_digit_lessthan_ct(digit_t x, digit_t y) #define SHIFTL(highIn, lowIn, shift, shiftOut, DigitSize) \ (shiftOut) = ((highIn) << (shift)) ^ ((lowIn) >> (DigitSize - (shift))); -// 64x64-bit multiplication -#define MUL128(multiplier, multiplicand, product) \ - mp_mul((digit_t*)&(multiplier), (digit_t*)&(multiplicand), (digit_t*)&(product), NWORDS_FIELD/2); - -// 128-bit addition, inputs < 2^127 -#define ADD128(addend1, addend2, addition) \ - mp_add((digit_t*)(addend1), (digit_t*)(addend2), (digit_t*)(addition), NWORDS_FIELD); - -// 128-bit addition with output carry -#define ADC128(addend1, addend2, carry, addition) \ - (carry) = mp_add((digit_t*)(addend1), (digit_t*)(addend2), (digit_t*)(addition), NWORDS_FIELD); - #elif (TARGET == TARGET_AMD64 && OS_TARGET == OS_WIN) // Digit multiplication @@ -201,35 +188,15 @@ static __inline unsigned int is_digit_lessthan_ct(digit_t x, digit_t y) #define MUL128(multiplier, multiplicand, product) \ (product)[0] = _umul128((multiplier), (multiplicand), &(product)[1]); -// 128-bit addition, inputs < 2^127 -#define ADD128(addend1, addend2, addition) \ - { unsigned char carry = _addcarry_u64(0, (addend1)[0], (addend2)[0], &(addition)[0]); \ - _addcarry_u64(carry, (addend1)[1], (addend2)[1], &(addition)[1]); } - // 128-bit addition with output carry #define ADC128(addend1, addend2, carry, addition) \ (carry) = _addcarry_u64(0, (addend1)[0], (addend2)[0], &(addition)[0]); \ (carry) = _addcarry_u64((carry), (addend1)[1], (addend2)[1], &(addition)[1]); -// 128-bit subtraction, subtrahend < 2^127 -#define SUB128(minuend, subtrahend, difference) \ - { unsigned char borrow = _subborrow_u64(0, (minuend)[0], (subtrahend)[0], &(difference)[0]); \ - _subborrow_u64(borrow, (minuend)[1], (subtrahend)[1], &(difference)[1]); } - -// 128-bit right shift, max. shift value is 64 -#define SHIFTR128(Input, shift, shiftOut) \ - (shiftOut)[0] = __shiftright128((Input)[0], (Input)[1], (shift)); \ - (shiftOut)[1] = (Input)[1] >> (shift); - -// 128-bit left shift, max. shift value is 64 -#define SHIFTL128(Input, shift, shiftOut) \ - (shiftOut)[1] = __shiftleft128((Input)[0], (Input)[1], (shift)); \ - (shiftOut)[0] = (Input)[0] << (shift); - -#define MULADD128(multiplier, multiplicand, addend, carry, result); \ - { uint128_t product; \ - MUL128(multiplier, multiplicand, product); \ - ADC128(addend, product, carry, result); } +#define MULADD128(multiplier, multiplicand, addend, carry, result); \ + { uint128_t product; \ + MUL128(multiplier, multiplicand, product); \ + ADC128(addend, product, carry, result); } #elif ((TARGET == TARGET_AMD64 || TARGET == TARGET_ARM64) && OS_TARGET == OS_LINUX) diff --git a/src/ec_isogeny.c b/src/ec_isogeny.c index de91dc7..8e318e8 100644 --- a/src/ec_isogeny.c +++ b/src/ec_isogeny.c @@ -363,4 +363,175 @@ static void LADDER3PT(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xPQ, con swap = 0 ^ prevbit; mask = 0 - (digit_t)swap; swap_points(R, R2, mask); -} \ No newline at end of file +} + +#ifdef COMPRESS + +void Double(point_proj_t P, point_proj_t Q, f2elm_t A24, const int k) +{ // Doubling of a Montgomery point in projective coordinates (X:Z) over affine curve coefficient A. + // Input: projective Montgomery x-coordinates P = (X1:Z1), where x1=X1/Z1 and Montgomery curve constants (A+2)/4. + // Output: projective Montgomery x-coordinates Q = 2*P = (X2:Z2). + f2elm_t temp, a, b, c, aa, bb; + + fp2copy(P->X, Q->X); + fp2copy(P->Z, Q->Z); + + for (int j = 0; j < k; j++) { + fp2add(Q->X, Q->Z, a); + fp2sub(Q->X, Q->Z, b); + fp2sqr_mont(a, aa); + fp2sqr_mont(b, bb); + fp2sub(aa, bb, c); + fp2mul_mont(aa, bb, Q->X); + fp2mul_mont(A24, c, temp); + fp2add(temp, bb, temp); + fp2mul_mont(c, temp, Q->Z); + } +} + + +void xTPL_fast(const point_proj_t P, point_proj_t Q, const f2elm_t A2) +{ // Montgomery curve (E: y^2 = x^3 + A*x^2 + x) x-only tripling at a cost 5M + 6S + 9A = 27p + 61a. + // Input : projective Montgomery x-coordinates P = (X:Z), where x=X/Z and Montgomery curve constant A/2. + // Output: projective Montgomery x-coordinates Q = 3*P = (X3:Z3). + f2elm_t t1, t2, t3, t4; + + fp2sqr_mont(P->X, t1); // t1 = x^2 + fp2sqr_mont(P->Z, t2); // t2 = z^2 + fp2add(t1, t2, t3); // t3 = t1 + t2 + fp2add(P->X, P->Z, t4); // t4 = x + z + fp2sqr_mont(t4, t4); // t4 = t4^2 + fp2sub(t4, t3, t4); // t4 = t4 - t3 + fp2mul_mont(A2, t4, t4); // t4 = t4*A2 + fp2add(t3, t4, t4); // t4 = t4 + t3 + fp2sub(t1, t2, t3); // t3 = t1 - t2 + fp2sqr_mont(t3, t3); // t3 = t3^2 + fp2mul_mont(t1, t4, t1); // t1 = t1*t4 + fp2shl(t1, 2, t1); // t1 = 4*t1 + fp2sub(t1, t3, t1); // t1 = t1 - t3 + fp2sqr_mont(t1, t1); // t1 = t1^2 + fp2mul_mont(t2, t4, t2); // t2 = t2*t4 + fp2shl(t2, 2, t2); // t2 = 4*t2 + fp2sub(t2, t3, t2); // t2 = t2 - t3 + fp2sqr_mont(t2, t2); // t2 = t2^2 + fp2mul_mont(P->X, t2, Q->X); // x = x*t2 + fp2mul_mont(P->Z, t1, Q->Z); // z = z*t1 +} + + +void xTPLe_fast(point_proj_t P, point_proj_t Q, const f2elm_t A2, int e) +{ // Computes [3^e](X:Z) on Montgomery curve with projective constant via e repeated triplings. e triplings in E costs k*(5M + 6S + 9A) + // Input: projective Montgomery x-coordinates P = (X:Z), where x=X/Z, Montgomery curve constant A2 = A/2 and the number of triplings e. + // Output: projective Montgomery x-coordinates Q <- [3^e]P. + point_proj_t T; + copy_words((digit_t*)P, (digit_t*)T, 2*2*NWORDS_FIELD); + + for (int j = 0; j < e; j++) { + xTPL_fast(T, T, A2); + } + copy_words((digit_t*)T, (digit_t*)Q, 2*2*NWORDS_FIELD); +} + + +void ADD(const point_full_proj_t P, const f2elm_t QX, const f2elm_t QY, const f2elm_t QZ, const f2elm_t A, point_full_proj_t R) +{ // General addition. + // Input: projective Montgomery points P=(XP:YP:ZP) and Q=(XQ:YQ:ZQ). + // Output: projective Montgomery point R <- P+Q = (XQP:YQP:ZQP). + f2elm_t t0 = {0}, t1 = {0}, t2 = {0}, t3 = {0}, t4 = {0}, t5 = {0}, t6 = {0}, t7 = {0}; + + fp2mul_mont(QX, P->Z, t0); // t0 = x2*Z1 + fp2mul_mont(P->X, QZ, t1); // t1 = X1*z2 + fp2add(t0, t1, t2); // t2 = t0 + t1 + fp2sub(t1, t0, t3); // t3 = t1 - t0 + fp2mul_mont(QX, P->X, t0); // t0 = x2*X1 + fp2mul_mont(P->Z, QZ, t1); // t1 = Z1*z2 + fp2add(t0, t1, t4); // t4 = t0 + t1 + fp2mul_mont(t0, A, t0); // t0 = t0*A + fp2mul_mont(QY, P->Y, t5); // t5 = y2*Y1 + fp2sub(t0, t5, t0); // t0 = t0 - t5 + fp2mul_mont(t0, t1, t0); // t0 = t0*t1 + fp2add(t0, t0, t0); // t0 = t0 + t0 + fp2mul_mont(t2, t4, t5); // t5 = t2*t4 + fp2add(t5, t0, t5); // t5 = t5 + t0 + fp2sqr_mont(P->X, t0); // t0 = X1 ^ 2 + fp2sqr_mont(P->Z, t6); // t6 = Z1 ^ 2 + fp2add(t0, t6, t0); // t0 = t0 + t6 + fp2add(t1, t1, t1); // t1 = t1 + t1 + fp2mul_mont(QY, P->X, t7); // t7 = y2*X1 + fp2mul_mont(QX, P->Y, t6); // t6 = x2*Y1 + fp2sub(t7, t6, t7); // t7 = t7 - t6 + fp2mul_mont(t1, t7, t1); // t1 = t1*t7 + fp2mul_mont(A, t2, t7); // t7 = A*t2 + fp2add(t7, t4, t4); // t4 = t4 + t7 + fp2mul_mont(t1, t4, t4); // t4 = t1*t4 + fp2mul_mont(QY, QZ, t1); // t1 = y2*z2 + fp2mul_mont(t0, t1, t0); // t0 = t0*t1 + fp2sqr_mont(QZ, t1); // t1 = z2 ^ 2 + fp2sqr_mont(QX, t6); // t6 = x2 ^ 2 + fp2add(t1, t6, t1); // t1 = t1 + t6 + fp2mul_mont(P->Z, P->Y, t6); // t6 = Z1*Y1 + fp2mul_mont(t1, t6, t1); // t1 = t1*t6 + fp2sub(t0, t1, t0); // t0 = t0 - t1 + fp2mul_mont(t2, t0, t0); // t0 = t2*t0 + fp2mul_mont(t5, t3, R->X); // X3 = t5*t3 + fp2add(t4, t0, R->Y); // Y3 = t4 + t0 + fp2sqr_mont(t3, t0); // t0 = t3 ^ 2 + fp2mul_mont(t3, t0, R->Z); // Z3 = t3*t0 +} + + +void Mont_ladder(const f2elm_t x, const digit_t* m, point_proj_t P, point_proj_t Q, const f2elm_t A24, const unsigned int order_bits, const unsigned int order_fullbits) +{ // The Montgomery ladder + // Inputs: the affine x-coordinate of a point P on E: B*y^2=x^3+A*x^2+x, + // scalar m + // curve constant A24 = (A+2)/4 + // order_bits = subgroup order bitlength + // order_fullbits = smallest multiple of 32 larger than the order bitlength + // Output: P = m*(x:1) + unsigned int bit = 0, owords = NBITS_TO_NWORDS(order_fullbits); + digit_t mask, scalar[NWORDS_ORDER]; + int i; + + // Initializing with the points (1:0) and (x:1) + fpcopy((digit_t*)&Montgomery_one, (digit_t*)P->X[0]); + fpzero(P->X[1]); + fp2zero(P->Z); + + fp2copy(x, Q->X); + fpcopy((digit_t*)&Montgomery_one, (digit_t*)Q->Z[0]); + fpzero(Q->Z[1]); + + for (i = NWORDS_ORDER-1; i >= 0; i--) { + scalar[i] = m[i]; + } + + for (i = order_fullbits-order_bits; i > 0; i--) { + mp_shiftl1(scalar, owords); + } + + for (i = order_bits; i > 0; i--) { + bit = (unsigned int)(scalar[owords-1] >> (RADIX-1)); + mp_shiftl1(scalar, owords); + mask = 0-(digit_t)bit; + + swap_points(P, Q, mask); + xDBLADD(P, Q, x, A24); // If bit=0 then P <- 2*P and Q <- P+Q, + swap_points(P, Q, mask); // else if bit=1 then Q <- 2*Q and P <- P+Q + } +} + + +void mont_twodim_scalarmult(digit_t* a, const point_t R, const point_t S, const f2elm_t A, const f2elm_t A24, point_full_proj_t P, const unsigned int order_bits) +{ // Computes P = R + [a]S + point_proj_t P0 = {0}, P1 = {0}; + point_full_proj_t P2 = {0}; + f2elm_t one = {0}; + + fpcopy((digit_t*)&Montgomery_one, one[0]); + + Mont_ladder(S->x, a, P0, P1, A24, order_bits, MAXBITS_ORDER); + recover_os(P0->X, P0->Z, P1->X, P1->Z, S->x, S->y, A, P2->X, P2->Y, P2->Z); + ADD(P2, R->x, R->y, one, A, P); +} + +#endif \ No newline at end of file diff --git a/src/fpx.c b/src/fpx.c index 2e1b70e..cb8aab8 100644 --- a/src/fpx.c +++ b/src/fpx.c @@ -5,6 +5,44 @@ *********************************************************************************************/ +void clear_words(void* mem, digit_t nwords) +{ // Clear digits from memory. "nwords" indicates the number of digits to be zeroed. + // This function uses the volatile type qualifier to inform the compiler not to optimize out the memory clearing. + unsigned int i; + volatile digit_t *v = mem; + + for (i = 0; i < nwords; i++) { + v[i] = 0; + } +} + + +static void fp2_encode(const f2elm_t x, unsigned char *enc) +{ // Conversion of GF(p^2) element from Montgomery to standard representation, and encoding by removing leading 0 bytes + unsigned int i; + f2elm_t t; + + from_fp2mont(x, t); + for (i = 0; i < FP2_ENCODED_BYTES / 2; i++) { + enc[i] = ((unsigned char*)t)[i]; + enc[i + FP2_ENCODED_BYTES / 2] = ((unsigned char*)t)[i + MAXBITS_FIELD / 8]; + } +} + + +static void fp2_decode(const unsigned char *enc, f2elm_t x) +{ // Parse byte sequence back into GF(p^2) element, and conversion to Montgomery representation + unsigned int i; + + for (i = 0; i < 2*(MAXBITS_FIELD / 8); i++) ((unsigned char *)x)[i] = 0; + for (i = 0; i < FP2_ENCODED_BYTES / 2; i++) { + ((unsigned char*)x)[i] = enc[i]; + ((unsigned char*)x)[i + MAXBITS_FIELD / 8] = enc[i + FP2_ENCODED_BYTES / 2]; + } + to_fp2mont(x, x); +} + + __inline void fpcopy(const felm_t a, felm_t c) { // Copy a field element, c = a. unsigned int i; @@ -47,9 +85,8 @@ void copy_words(const digit_t* a, digit_t* c, const unsigned int nwords) { // Copy wordsize digits, c = a, where lng(a) = nwords. unsigned int i; - for (i = 0; i < nwords; i++) { + for (i = 0; i < nwords; i++) c[i] = a[i]; - } } @@ -164,32 +201,33 @@ __inline unsigned int mp_sub(const digit_t* a, const digit_t* b, digit_t* c, con { // Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit. unsigned int i, borrow = 0; - for (i = 0; i < nwords; i++) { + for (i = 0; i < nwords; i++) SUBC(borrow, a[i], b[i], borrow, c[i]); - } return borrow; } -__inline static digit_t mp_subfast(const digit_t* a, const digit_t* b, digit_t* c) -{ // Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = 2*NWORDS_FIELD. - // If c < 0 then returns mask = 0xFF..F, else mask = 0x00..0 +__inline static void mp_subaddfast(const digit_t* a, const digit_t* b, digit_t* c) +{ // Multiprecision subtraction followed by addition with p*2^MAXBITS_FIELD, c = a-b+(p*2^MAXBITS_FIELD) if a-b < 0, otherwise c=a-b. #if (OS_TARGET == OS_WIN) || defined(GENERIC_IMPLEMENTATION) || (TARGET == TARGET_ARM) || (TARGET == TARGET_ARM64 && (NBITS_FIELD == 434 || NBITS_FIELD == 610)) + felm_t t1; - return (0 - (digit_t)mp_sub(a, b, c, 2*NWORDS_FIELD)); + digit_t mask = 0 - (digit_t)mp_sub(a, b, c, 2*NWORDS_FIELD); + for (int i = 0; i < NWORDS_FIELD; i++) + t1[i] = ((digit_t*)PRIME)[i] & mask; + mp_addfast((digit_t*)&c[NWORDS_FIELD], t1, (digit_t*)&c[NWORDS_FIELD]); -#elif (OS_TARGET == OS_LINUX) +#elif (OS_TARGET == OS_LINUX) - return mp_subx2_asm(a, b, c); + mp_subaddx2_asm(a, b, c); #endif } __inline static void mp_dblsubfast(const digit_t* a, const digit_t* b, digit_t* c) -{ // Multiprecision subtraction, c = c-a-b, where lng(a) = lng(b) = 2*NWORDS_FIELD. - // Inputs should be s.t. c > a and c > b +{ // Multiprecision subtraction, c = c-a-b, where lng(a) = lng(b) = 2*NWORDS_FIELD. #if (OS_TARGET == OS_WIN) || defined(GENERIC_IMPLEMENTATION) || (TARGET == TARGET_ARM) || (TARGET == TARGET_ARM64 && (NBITS_FIELD == 434 || NBITS_FIELD == 610)) mp_sub(c, a, c, 2*NWORDS_FIELD); @@ -209,23 +247,15 @@ void fp2mul_mont(const f2elm_t a, const f2elm_t b, f2elm_t c) // Output: c = c0+c1*i, where c0, c1 are in [0, 2*p-1] felm_t t1, t2; dfelm_t tt1, tt2, tt3; - digit_t mask; - unsigned int i; mp_addfast(a[0], a[1], t1); // t1 = a0+a1 mp_addfast(b[0], b[1], t2); // t2 = b0+b1 mp_mul(a[0], b[0], tt1, NWORDS_FIELD); // tt1 = a0*b0 mp_mul(a[1], b[1], tt2, NWORDS_FIELD); // tt2 = a1*b1 mp_mul(t1, t2, tt3, NWORDS_FIELD); // tt3 = (a0+a1)*(b0+b1) - mp_dblsubfast(tt1, tt2, tt3); // tt3 = (a0+a1)*(b0+b1) - a0*b0 - a1*b1 - mask = mp_subfast(tt1, tt2, tt1); // tt1 = a0*b0 - a1*b1. If tt1 < 0 then mask = 0xFF..F, else if tt1 >= 0 then mask = 0x00..0 - - for (i = 0; i < NWORDS_FIELD; i++) { - t1[i] = ((digit_t*)PRIME)[i] & mask; - } - + mp_dblsubfast(tt1, tt2, tt3); // tt3 = (a0+a1)*(b0+b1) - a0*b0 - a1*b1 + mp_subaddfast(tt1, tt2, tt1); // tt1 = a0*b0 - a1*b1 + p*2^MAXBITS_FIELD if a0*b0 - a1*b1 < 0, else tt1 = a0*b0 - a1*b1 rdc_mont(tt3, c[1]); // c[1] = (a0+a1)*(b0+b1) - a0*b0 - a1*b1 - mp_addfast((digit_t*)&tt1[NWORDS_FIELD], t1, (digit_t*)&tt1[NWORDS_FIELD]); rdc_mont(tt1, c[0]); // c[0] = a0*b0 - a1*b1 } @@ -733,4 +763,608 @@ void mp_shiftl1(digit_t* x, const unsigned int nwords) SHIFTL(x[i], x[i-1], 1, x[i], RADIX); } x[0] <<= 1; -} \ No newline at end of file +} + +#ifdef COMPRESS + +#include + +static __inline unsigned int is_felm_zero(const felm_t x) +{ // Is x = 0? return 1 (TRUE) if condition is true, 0 (FALSE) otherwise. + // SECURITY NOTE: This function does not run in constant-time. + unsigned int i; + + for (i = 0; i < NWORDS_FIELD; i++) { + if (x[i] != 0) return 0; + } + return 1; +} + + +void mul3(unsigned char *a) +{ // Computes a = 3*a + // The input is assumed to be OBOB_BITS-2 bits long and stored in SECRETKEY_B_BYTES + unsigned char temp1[NWORDS_ORDER*RADIX/8] = {0}; + + memcpy(temp1, a, SECRETKEY_B_BYTES); + mp_shiftl1((digit_t*) temp1, NWORDS_ORDER); // temp1 = 2*a + mp_add((digit_t*)a, (digit_t*)temp1, (digit_t*)a, NWORDS_ORDER); // a <- 2*a + a + + clear_words((void*)temp1, NWORDS_ORDER); +} + + +unsigned int mod3(digit_t* a) +{ // Computes the input modulo 3 + // The input is assumed to be NWORDS_ORDER long + digit_t temp; + hdigit_t *val = (hdigit_t*)a, r = 0; + + for (int i = (2*NWORDS_ORDER-1); i >= 0; i--) { + temp = ((digit_t)r << (sizeof(hdigit_t)*8)) | (digit_t)val[i]; + r = temp % 3; + } + + return r; +} + + +void fp2shl(const f2elm_t a, const int k, f2elm_t c) +{ // c = (2^k)*a + fp2copy(a, c); + for (int j = 0; j < k; j++) { + fp2add(c, c, c); + } +} + + +void fp2_conj(const f2elm_t v, f2elm_t r) +{ // r = a - b*i where v = a + b*i + fpcopy(v[0],r[0]); + fpcopy(v[1],r[1]); + + if(!is_felm_zero(r[1])) { + fpneg(r[1]); + } +} + + +void sqr_Fp2_cycl(f2elm_t a, const felm_t one) +{ // Cyclotomic squaring on elements of norm 1, using a^(p+1) = 1. + felm_t t0; + + fpadd(a[0], a[1], t0); // t0 = a0 + a1 + fpsqr_mont(t0, t0); // t0 = t0^2 + fpsub(t0, one, a[1]); // a1 = t0 - 1 + fpsqr_mont(a[0], t0); // t0 = a0^2 + fpadd(t0, t0, t0); // t0 = t0 + t0 + fpsub(t0, one, a[0]); // a0 = t0 - 1 +} + + +void cube_Fp2_cycl(f2elm_t a, const felm_t one) +{ // Cyclotomic cubing on elements of norm 1, using a^(p+1) = 1. + felm_t t0; + + fpadd(a[0], a[0], t0); // t0 = a0 + a0 + fpsqr_mont(t0, t0); // t0 = t0^2 + fpsub(t0, one, t0); // t0 = t0 - 1 + fpmul_mont(a[1], t0, a[1]); // a1 = t0*a1 + fpsub(t0, one, t0); + fpsub(t0, one, t0); // t0 = t0 - 2 + fpmul_mont(a[0], t0, a[0]); // a0 = t0*a0 +} + + +static bool is_zero(digit_t* a, unsigned int nwords) +{ // Check if multiprecision element is zero. + // SECURITY NOTE: This function does not run in constant time. + + for (unsigned int i = 0; i < nwords; i++) { + if (a[i] != 0) { + return false; + } + } + + return true; +} + + +unsigned char is_sqr_fp2(const f2elm_t a, felm_t s) +{ // Test if a is a square in GF(p^2) and return 1 if true, 0 otherwise + // If a is a quadratic residue, s will be assigned with a partially computed square root of a + int i; + felm_t a0,a1,z,temp; + + fpsqr_mont(a[0],a0); + fpsqr_mont(a[1],a1); + fpadd(a0,a1,z); + + fpcopy(z,s); + for (i = 0; i < OALICE_BITS - 2; i++) { + fpsqr_mont(s, s); + } + for (i = 0; i < OBOB_EXPON; i++) { + fpsqr_mont(s, temp); + fpmul_mont(s, temp, s); + } + fpsqr_mont(s,temp); // s = z^((p+1)/4) + fpcorrection(temp); + fpcorrection(z); + if (memcmp((unsigned char*)temp, (unsigned char*)z, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) // s^2 !=? z + return 0; + + return 1; +} + + +void sqrt_Fp2(const f2elm_t u, f2elm_t y) +{ // Computes square roots of elements in (Fp2)^2 using Hamburg's trick. + felm_t t0, t1, t2, t3; + digit_t *a = (digit_t*)u[0], *b = (digit_t*)u[1]; + unsigned int i; + + fpsqr_mont(a, t0); // t0 = a^2 + fpsqr_mont(b, t1); // t1 = b^2 + fpadd(t0, t1, t0); // t0 = t0+t1 + fpcopy(t0, t1); + for (i = 0; i < OALICE_BITS - 2; i++) { // t = t3^((p+1)/4) + fpsqr_mont(t1, t1); + } + for (i = 0; i < OBOB_EXPON; i++) { + fpsqr_mont(t1, t0); + fpmul_mont(t1, t0, t1); + } + fpadd(a, t1, t0); // t0 = a+t1 + fpdiv2(t0, t0); // t0 = t0/2 + fpcopy(t0, t2); + fpinv_chain_mont(t2); // t2 = t0^((p-3)/4) + fpmul_mont(t0, t2, t1); // t1 = t2*t0 + fpmul_mont(t2, b, t2); // t2 = t2*b + fpdiv2(t2, t2); // t2 = t2/2 + fpsqr_mont(t1, t3); // t3 = t1^2 + fpcorrection(t0); + fpcorrection(t3); + + if (memcmp(t0, t3, NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + fpcopy(t1, y[0]); + fpcopy(t2, y[1]); + } else { + fpneg(t1); + fpcopy(t2, y[0]); + fpcopy(t1, y[1]); + } +} + + +static __inline void power2_setup(digit_t* x, int mark, const unsigned int nwords) +{ // Set up the value 2^mark. + unsigned int i; + + for (i = 0; i < nwords; i++) x[i] = 0; + + i = 0; + while (mark >= 0) { + if (mark < RADIX) { + x[i] = (digit_t)1 << mark; + } + mark -= RADIX; + i += 1; + } + +} + + +static __inline unsigned int is_felm_even(const felm_t x) +{ // Is x even? return 1 (TRUE) if condition is true, 0 (FALSE) otherwise. + return (unsigned int)((x[0] & 1) ^ 1); +} + + +static __inline unsigned int is_felm_lt(const felm_t x, const felm_t y) +{ // Is x < y? return 1 (TRUE) if condition is true, 0 (FALSE) otherwise. + // SECURITY NOTE: This function does not run in constant-time. + int i; + + for (i = NWORDS_FIELD-1; i >= 0; i--) { + if (x[i] < y[i]) { + return true; + } else if (x[i] > y[i]) { + return false; + } + } + return false; +} + + +static __inline void fpinv_mont_bingcd_partial(const felm_t a, felm_t x1, unsigned int* k) +{ // Partial Montgomery inversion via the binary GCD algorithm. + felm_t u, v, x2; + unsigned int cwords; // Number of words necessary for x1, x2 + + fpcopy(a, u); + fpcopy((digit_t*)PRIME, v); + fpzero(x1); x1[0] = 1; + fpzero(x2); + *k = 0; + + while (!is_felm_zero(v)) { + cwords = ((*k + 1) / RADIX) + 1; + if ((cwords < NWORDS_FIELD)) { + if (is_felm_even(v)) { + mp_shiftr1(v, NWORDS_FIELD); + mp_shiftl1(x1, cwords); + } else if (is_felm_even(u)) { + mp_shiftr1(u, NWORDS_FIELD); + mp_shiftl1(x2, cwords); + } else if (!is_felm_lt(v, u)) { + mp_sub(v, u, v, NWORDS_FIELD); + mp_shiftr1(v, NWORDS_FIELD); + mp_add(x1, x2, x2, cwords); + mp_shiftl1(x1, cwords); + } else { + mp_sub(u, v, u, NWORDS_FIELD); + mp_shiftr1(u, NWORDS_FIELD); + mp_add(x1, x2, x1, cwords); + mp_shiftl1(x2, cwords); + } + } else { + if (is_felm_even(v)) { + mp_shiftr1(v, NWORDS_FIELD); + mp_shiftl1(x1, NWORDS_FIELD); + } else if (is_felm_even(u)) { + mp_shiftr1(u, NWORDS_FIELD); + mp_shiftl1(x2, NWORDS_FIELD); + } else if (!is_felm_lt(v, u)) { + mp_sub(v, u, v, NWORDS_FIELD); + mp_shiftr1(v, NWORDS_FIELD); + mp_add(x1, x2, x2, NWORDS_FIELD); + mp_shiftl1(x1, NWORDS_FIELD); + } else { + mp_sub(u, v, u, NWORDS_FIELD); + mp_shiftr1(u, NWORDS_FIELD); + mp_add(x1, x2, x1, NWORDS_FIELD); + mp_shiftl1(x2, NWORDS_FIELD); + } + } + *k += 1; + } + + if (is_felm_lt((digit_t*)PRIME, x1)) { + mp_sub(x1, (digit_t*)PRIME, x1, NWORDS_FIELD); + } +} + + +void fpinv_mont_bingcd(felm_t a) +{ // Field inversion via the binary GCD using Montgomery arithmetic, a = a^-1*r' mod p. + // SECURITY NOTE: This function does not run in constant-time and is therefore only suitable for + // operations not involving any secret data. + felm_t x, t; + unsigned int k; + + fpinv_mont_bingcd_partial(a, x, &k); + if (k < MAXBITS_FIELD) { + fpmul_mont(x, (digit_t*)&Montgomery_R2, x); + k += MAXBITS_FIELD; + } + fpmul_mont(x, (digit_t*)&Montgomery_R2, x); + power2_setup(t, 2*MAXBITS_FIELD - k, NWORDS_FIELD); + fpmul_mont(x, t, a); +} + + +void fp2inv_mont_bingcd(f2elm_t a) +{// GF(p^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2) + // This uses the binary GCD for inversion in fp and is NOT constant time!!! + f2elm_t t1; + + fpsqr_mont(a[0], t1[0]); // t10 = a0^2 + fpsqr_mont(a[1], t1[1]); // t11 = a1^2 + fpadd(t1[0], t1[1], t1[0]); // t10 = a0^2+a1^2 + fpinv_mont_bingcd(t1[0]); // t10 = (a0^2+a1^2)^-1 + fpneg(a[1]); // a = a0-i*a1 + fpmul_mont(a[0], t1[0], a[0]); + fpmul_mont(a[1], t1[0], a[1]); // a = (a0-i*a1)*(a0^2+a1^2)^-1 +} + + +void mont_n_way_inv(const f2elm_t* vec, const int n, f2elm_t* out) +{ // n-way simultaneous inversion using Montgomery's trick. + // SECURITY NOTE: This function does not run in constant time. + // Also, vec and out CANNOT be the same variable! + f2elm_t t1; + int i; + + fp2copy(vec[0], out[0]); // out[0] = vec[0] + for (i = 1; i < n; i++) { + fp2mul_mont(out[i-1], vec[i], out[i]); // out[i] = out[i-1]*vec[i] + } + + fp2copy(out[n-1], t1); // t1 = 1/out[n-1] + fp2inv_mont_bingcd(t1); + + for (i = n-1; i >= 1; i--) { + fp2mul_mont(out[i-1], t1, out[i]);// out[i] = t1*out[i-1] + fp2mul_mont(t1, vec[i], t1); // t1 = t1*vec[i] + } + fp2copy(t1, out[0]); // out[0] = t1 +} + + +void multiply(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords) +{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords. + // NOTE: a and c CANNOT be the same variable! + unsigned int i, j, carry = 0; + digit_t t = 0, u = 0, v = 0, UV[2]; + + for (i = 0; i < nwords; i++) { + for (j = 0; j <= i; j++) { + MUL(a[j], b[i-j], UV+1, UV[0]); + ADDC(0, UV[0], v, carry, v); + ADDC(carry, UV[1], u, carry, u); + t += carry; + } + c[i] = v; + v = u; + u = t; + t = 0; + } + for (i = nwords; i < 2*nwords-1; i++) { + for (j = i-nwords+1; j < nwords; j++) { + MUL(a[j], b[i-j], UV+1, UV[0]); + ADDC(0, UV[0], v, carry, v); + ADDC(carry, UV[1], u, carry, u); + t += carry; + } + c[i] = v; + v = u; + u = t; + t = 0; + } + c[2*nwords-1] = v; +} + + +void Montgomery_neg(digit_t* a, digit_t* order) +{ // Modular negation, a = -a mod p. + // Input/output: a in [0, 2*p-1] + unsigned int i, borrow = 0; + + for (i = 0; i < NWORDS_ORDER; i++) { + SUBC(borrow, order[i], a[i], borrow, a[i]); + } +} + + +void Montgomery_multiply_mod_order(const digit_t* ma, const digit_t* mb, digit_t* mc, const digit_t* order, const digit_t* Montgomery_rprime) +{ // Montgomery multiplication modulo the group order, mc = ma*mb*r' mod order, where ma,mb,mc in [0, order-1]. + // ma, mb and mc are assumed to be in Montgomery representation. + // The Montgomery constant r' = -r^(-1) mod 2^(log_2(r)) is the value "Montgomery_rprime", where r is the order. + // Assume log_2(r) is a multiple of RADIX bits + unsigned int i, cout = 0, bout = 0; + digit_t mask, P[2*NWORDS_ORDER] = {0}, Q[2*NWORDS_ORDER] = {0}, temp[2*NWORDS_ORDER] = {0}; + + multiply(ma, mb, P, NWORDS_ORDER); // P = ma * mb + multiply(P, Montgomery_rprime, Q, NWORDS_ORDER); // Q = P * r' mod 2^(log_2(r)) + multiply(Q, order, temp, NWORDS_ORDER); // temp = Q * r + cout = mp_add(P, temp, temp, 2*NWORDS_ORDER); // (cout, temp) = P + Q * r + + for (i = 0; i < NWORDS_ORDER; i++) { // (cout, mc) = (P + Q * r)/2^(log_2(r)) + mc[i] = temp[NWORDS_ORDER+i]; + } + + // Final, constant-time subtraction + bout = mp_sub(mc, order, mc, NWORDS_ORDER); // (cout, mc) = (cout, mc) - r + mask = (digit_t)cout - (digit_t)bout; // if (cout, mc) >= 0 then mask = 0x00..0, else if (cout, mc) < 0 then mask = 0xFF..F + + for (i = 0; i < NWORDS_ORDER; i++) { // temp = mask & r + temp[i] = (order[i] & mask); + } + + mp_add(mc, temp, mc, NWORDS_ORDER); // mc = mc + (mask & r) +} + + +void to_Montgomery_mod_order(const digit_t* a, digit_t* mc, const digit_t* order, const digit_t* Montgomery_rprime, const digit_t* Montgomery_Rprime) +{ // Conversion of elements in Z_r to Montgomery representation, where the order r is up to NBITS_ORDER bits. + Montgomery_multiply_mod_order(a, Montgomery_Rprime, mc, order, Montgomery_rprime); +} + + +void from_Montgomery_mod_order(const digit_t* ma, digit_t* c, const digit_t* order, const digit_t* Montgomery_rprime) +{ // Conversion of elements in Z_r from Montgomery to standard representation, where the order is up to NBITS_ORDER bits. + digit_t one[NWORDS_ORDER] = {0}; + one[0] = 1; + + Montgomery_multiply_mod_order(ma, one, c, order, Montgomery_rprime); +} + + +static __inline unsigned int is_zero_mod_order(const digit_t* x) +{ // Is x = 0? return 1 (TRUE) if condition is true, 0 (FALSE) otherwise + // SECURITY NOTE: This function does not run in constant time. + unsigned int i; + + for (i = 0; i < NWORDS_ORDER; i++) { + if (x[i] != 0) return false; + } + return true; +} + + +static __inline unsigned int is_even_mod_order(const digit_t* x) +{ // Is x even? return 1 (TRUE) if condition is true, 0 (FALSE) otherwise. + return (unsigned int)((x[0] & 1) ^ 1); +} + + +static __inline unsigned int is_lt_mod_order(const digit_t* x, const digit_t* y) +{ // Is x < y? return 1 (TRUE) if condition is true, 0 (FALSE) otherwise. + // SECURITY NOTE: This function does not run in constant time. + int i; + + for (i = NWORDS_ORDER-1; i >= 0; i--) { + if (x[i] < y[i]) { + return true; + } else if (x[i] > y[i]) { + return false; + } + } + return false; +} + + +static __inline void Montgomery_inversion_mod_order_bingcd_partial(const digit_t* a, digit_t* x1, unsigned int* k, const digit_t* order) +{ // Partial Montgomery inversion modulo order. + digit_t u[NWORDS_ORDER], v[NWORDS_ORDER], x2[NWORDS_ORDER] = {0}; + unsigned int cwords; // number of words necessary for x1, x2 + + copy_words(a, u, NWORDS_ORDER); + copy_words(order, v, NWORDS_ORDER); + copy_words(x2, x1, NWORDS_ORDER); + x1[0] = 1; + *k = 0; + + while (!is_zero_mod_order(v)) { + cwords = ((*k + 1) / RADIX) + 1; + if ((cwords < NWORDS_ORDER)) { + if (is_even_mod_order(v)) { + mp_shiftr1(v, NWORDS_ORDER); + mp_shiftl1(x1, cwords); + } else if (is_even_mod_order(u)) { + mp_shiftr1(u, NWORDS_ORDER); + mp_shiftl1(x2, cwords); + } else if (!is_lt_mod_order(v, u)) { + mp_sub(v, u, v, NWORDS_ORDER); + mp_shiftr1(v, NWORDS_ORDER); + mp_add(x1, x2, x2, cwords); + mp_shiftl1(x1, cwords); + } else { + mp_sub(u, v, u, NWORDS_ORDER); + mp_shiftr1(u, NWORDS_ORDER); + mp_add(x1, x2, x1, cwords); + mp_shiftl1(x2, cwords); + } + } else { + if (is_even_mod_order(v)) { + mp_shiftr1(v, NWORDS_ORDER); + mp_shiftl1(x1, NWORDS_ORDER); + } else if (is_even_mod_order(u)) { + mp_shiftr1(u, NWORDS_ORDER); + mp_shiftl1(x2, NWORDS_ORDER); + } else if (!is_lt_mod_order(v, u)) { + mp_sub(v, u, v, NWORDS_ORDER); + mp_shiftr1(v, NWORDS_ORDER); + mp_add(x1, x2, x2, NWORDS_ORDER); + mp_shiftl1(x1, NWORDS_ORDER); + } else { + mp_sub(u, v, u, NWORDS_ORDER); + mp_shiftr1(u, NWORDS_ORDER); + mp_add(x1, x2, x1, NWORDS_ORDER); + mp_shiftl1(x2, NWORDS_ORDER); + } + } + *k += 1; + } + + if (is_lt_mod_order(order, x1)) { + mp_sub(x1, order, x1, NWORDS_ORDER); + } +} + + +void Montgomery_inversion_mod_order_bingcd(const digit_t* a, digit_t* c, const digit_t* order, const digit_t* Montgomery_rprime, const digit_t* Montgomery_Rprime) +{// Montgomery inversion modulo order, a = a^(-1)*R mod order. + digit_t x[NWORDS_ORDER], t[NWORDS_ORDER]; + unsigned int k; + + Montgomery_inversion_mod_order_bingcd_partial(a, x, &k, order); + if (k < NBITS_ORDER) { + Montgomery_multiply_mod_order(x, Montgomery_Rprime, x, order, Montgomery_rprime); + k += NBITS_ORDER; + } + + Montgomery_multiply_mod_order(x, Montgomery_Rprime, x, order, Montgomery_rprime); + power2_setup(t, 2*NBITS_ORDER - k, NWORDS_ORDER); + Montgomery_multiply_mod_order(x, t, c, order, Montgomery_rprime); +} + + +void inv_mod_orderA(const digit_t* a, digit_t* c) +{ // Inversion modulo an even integer of the form 2^m. + // Algorithm 3: Explicit Quadratic Modular inverse modulo 2^m from Dumas'12: http://arxiv.org/pdf/1209.6626.pdf + unsigned int i, f, s = 0; + digit_t am1[NWORDS_ORDER] = {0}; + digit_t tmp1[NWORDS_ORDER] = {0}; + digit_t tmp2[2*NWORDS_ORDER] = {0}; + digit_t one[NWORDS_ORDER] = {0}; + digit_t order[NWORDS_ORDER] = {0}; + digit_t mask = (digit_t)((uint64_t)(-1) >> (NBITS_ORDER - OALICE_BITS)); + bool equal = true; + + order[NWORDS_ORDER-1] = (digit_t)((uint64_t)1 << (64 - (NBITS_ORDER - OALICE_BITS))); // Load most significant digit of Alice's order + one[0] = 1; + + for (i = 0; i < NWORDS_ORDER; i++) { + if (a[i] != one[0]) equal = false; + } + if (equal) { + copy_words(a, c, NWORDS_ORDER); + } else { + mp_sub(a, one, am1, NWORDS_ORDER); // am1 = a-1 + mp_sub(order, am1, c, NWORDS_ORDER); + mp_add(c, one, c, NWORDS_ORDER); // c = 2^m - a + 2 + + copy_words(am1, tmp1, NWORDS_ORDER); + while ((tmp1[0] & (digit_t)1) == 0) { + s += 1; + mp_shiftr1(tmp1, NWORDS_ORDER); + } + + f = OALICE_BITS / s; + for (i = 1; i < f; i <<= 1) { + multiply(am1, am1, tmp2, NWORDS_ORDER); // tmp2 = am1^2 + copy_words(tmp2, am1, NWORDS_ORDER); + am1[NWORDS_ORDER-1] &= mask; // am1 = tmp2 mod 2^e + mp_add(am1, one, tmp1, NWORDS_ORDER); // tmp1 = am1 + 1 + tmp1[NWORDS_ORDER-1] &= mask; // mod 2^e + multiply(c, tmp1, tmp2, NWORDS_ORDER); // c = c*tmp1 + copy_words(tmp2, c, NWORDS_ORDER); + c[NWORDS_ORDER-1] &= mask; // mod 2^e + } + } +} + + +void recover_os(const f2elm_t X1, const f2elm_t Z1, const f2elm_t X2, const f2elm_t Z2, const f2elm_t x, const f2elm_t y, const f2elm_t A, f2elm_t X3, f2elm_t Y3, f2elm_t Z3) +{ + f2elm_t t0, t1, t2, t3; + + // X3 := 2*y*Z1*Z2*X1; + // Y3 := Z2*((X1+x*Z1+2*A*Z1)*(X1*x+Z1)-2*A*Z1^2)-(X1-x*Z1)^2*X2; + // Z3 := 2*y*Z1*Z2*Z1; + + fp2add(y, y, t0); + fp2mul_mont(t0, Z1, t0); + fp2mul_mont(t0, Z2, t0); // t0 = 2*y*Z1*Z2 + fp2mul_mont(t0, Z1, Z3); // Z3 = 2*y*Z1*Z2*Z1 + fp2mul_mont(t0, X1, X3); // X3 = 2*y*Z1*Z2*X1 + fp2add(A, A, t0); + fp2mul_mont(t0, Z1, t0); // t0 = 2*A*Z1 + fp2mul_mont(x, Z1, t1); // t1 = x*Z1 + fp2add(X1, t1, t2); // t2 = X1+x*Z1 + fp2sub(X1, t1, t1); // t1 = X1-x*Z1 + fp2add(t0, t2, t3); // t3 = X1+x*Z1+2*A*Z1 + fp2mul_mont(t0, Z1, t0); // t0 = 2*A*Z1^2 + fp2sqr_mont(t1, t1); // t1 = (X1-x*Z1)^2 + fp2mul_mont(x, X1, t2); // t2 = x*X1 + fp2add(t2, Z1, t2); // t2 = X1*x+Z1 + fp2mul_mont(t2, t3, t2); // t2 = (X1+x*Z1+2*A*Z1)*(X1*x+Z1) + fp2sub(t2, t0, t0); // t0 = (X1+x*Z1+2*A*Z1)*(X1*x+Z1)-2*A*Z1^2 + fp2mul_mont(t1, X2, t1); // t1 = (X1-x*Z1)^2*X2 + fp2mul_mont(t0, Z2, t0); // t0 = Z2*[(X1+x*Z1+2*A*Z1)*(X1*x+Z1)-2*A*Z1^2] + fp2sub(t0, t1, Y3); // Y3 = Z2*[(X1+x*Z1+2*A*Z1)*(X1*x+Z1)-2*A*Z1^2] - (X1-x*Z1)^2*X2 +} + +#endif \ No newline at end of file diff --git a/src/sidh.c b/src/sidh.c index 0a05d8f..db4aee3 100644 --- a/src/sidh.c +++ b/src/sidh.c @@ -7,18 +7,6 @@ #include "random/random.h" -static void clear_words(void* mem, digit_t nwords) -{ // Clear digits from memory. "nwords" indicates the number of digits to be zeroed. - // This function uses the volatile type qualifier to inform the compiler not to optimize out the memory clearing. - unsigned int i; - volatile digit_t *v = mem; - - for (i = 0; i < nwords; i++) { - v[i] = 0; - } -} - - static void init_basis(digit_t *gen, f2elm_t XP, f2elm_t XQ, f2elm_t XR) { // Initialization of basis points @@ -31,32 +19,6 @@ static void init_basis(digit_t *gen, f2elm_t XP, f2elm_t XQ, f2elm_t XR) } -static void fp2_encode(const f2elm_t x, unsigned char *enc) -{ // Conversion of GF(p^2) element from Montgomery to standard representation, and encoding by removing leading 0 bytes - unsigned int i; - f2elm_t t; - - from_fp2mont(x, t); - for (i = 0; i < FP2_ENCODED_BYTES / 2; i++) { - enc[i] = ((unsigned char*)t)[i]; - enc[i + FP2_ENCODED_BYTES / 2] = ((unsigned char*)t)[i + MAXBITS_FIELD / 8]; - } -} - - -static void fp2_decode(const unsigned char *enc, f2elm_t x) -{ // Parse byte sequence back into GF(p^2) element, and conversion to Montgomery representation - unsigned int i; - - for (i = 0; i < 2*(MAXBITS_FIELD / 8); i++) ((unsigned char *)x)[i] = 0; - for (i = 0; i < FP2_ENCODED_BYTES / 2; i++) { - ((unsigned char*)x)[i] = enc[i]; - ((unsigned char*)x)[i + MAXBITS_FIELD / 8] = enc[i + FP2_ENCODED_BYTES / 2]; - } - to_fp2mont(x, x); -} - - void random_mod_order_A(unsigned char* random_digits) { // Generation of Alice's secret key // Outputs random value in [0, 2^eA - 1] diff --git a/tests/PQCtestKAT_kem434_compressed.c b/tests/PQCtestKAT_kem434_compressed.c new file mode 100644 index 0000000..b828e59 --- /dev/null +++ b/tests/PQCtestKAT_kem434_compressed.c @@ -0,0 +1,233 @@ +/******************************************************************************************** +* Abstract: run tests against known answer test vectors for SIKEp434_compressed +* +* Modified from a file created by Bassham, Lawrence E (Fed) on 8/29/17. +* Copyright © 2017 Bassham, Lawrence E (Fed). All rights reserved. +*********************************************************************************************/ + +#include +#include +#include +#include +#include "rng/rng.h" +#include "../src/P434/P434_compressed_api.h" + + +#define MAX_MARKER_LEN 50 +#define KAT_SUCCESS 0 +#define KAT_FILE_OPEN_ERROR -1 +#define KAT_VERIFICATION_ERROR -2 +#define KAT_DATA_ERROR -3 +#define KAT_CRYPTO_FAILURE -4 + +int FindMarker(FILE *infile, const char *marker); +int ReadHex(FILE *infile, unsigned char *A, int Length, char *str); +void fprintBstr(FILE *fp, char *S, unsigned char *A, unsigned long long L); + +int +main() +{ + char fn_rsp[32]; + FILE *fp_rsp; + unsigned char seed[48]; + unsigned char ct[CRYPTO_CIPHERTEXTBYTES], ss[CRYPTO_BYTES], ss1[CRYPTO_BYTES], ct_rsp[CRYPTO_CIPHERTEXTBYTES], ss_rsp[CRYPTO_BYTES]; + int count; + int done; + unsigned char pk[CRYPTO_PUBLICKEYBYTES], sk[CRYPTO_SECRETKEYBYTES], pk_rsp[CRYPTO_PUBLICKEYBYTES], sk_rsp[CRYPTO_SECRETKEYBYTES]; + int ret_val; + + sprintf(fn_rsp, "KAT/PQCkemKAT_%d.rsp", CRYPTO_SECRETKEYBYTES); + if ( (fp_rsp = fopen(fn_rsp, "r")) == NULL ) { + printf("Couldn't open <%s> for read\n", fn_rsp); + return KAT_FILE_OPEN_ERROR; + } + + printf("# %s\n\n", CRYPTO_ALGNAME); + done = 0; + do { + if ( FindMarker(fp_rsp, "count = ") ) { + if (fscanf(fp_rsp, "%d", &count) != 1) { + done = 1; + break; + } + } else { + done = 1; + break; + } + + if ( !ReadHex(fp_rsp, seed, 48, "seed = ") ) { + printf("ERROR: unable to read 'seed' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + randombytes_init(seed, NULL, 256); + + // Generate the public/private keypair + if ( (ret_val = crypto_kem_keypair_SIKEp434_compressed(pk, sk)) != 0) { + printf("crypto_kem_keypair returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + if ( !ReadHex(fp_rsp, pk_rsp, CRYPTO_PUBLICKEYBYTES, "pk = ") ) { + printf("ERROR: unable to read 'pk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + if ( !ReadHex(fp_rsp, sk_rsp, CRYPTO_SECRETKEYBYTES, "sk = ") ) { + printf("ERROR: unable to read 'sk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + if(memcmp(pk,pk_rsp,CRYPTO_PUBLICKEYBYTES)!=0){ + printf("ERROR: pk is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + if(memcmp(sk,sk_rsp,CRYPTO_SECRETKEYBYTES)!=0){ + printf("ERROR: sk is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + + if ( (ret_val = crypto_kem_enc_SIKEp434_compressed(ct, ss, pk)) != 0) { + printf("crypto_kem_enc returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + + if ( !ReadHex(fp_rsp, ct_rsp, CRYPTO_CIPHERTEXTBYTES, "ct = ") ) { + printf("ERROR: unable to read 'pk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + if ( !ReadHex(fp_rsp, ss_rsp, CRYPTO_BYTES, "ss = ") ) { + printf("ERROR: unable to read 'sk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + if(memcmp(ct,ct_rsp,CRYPTO_CIPHERTEXTBYTES)!=0){ + printf("ERROR: ct is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + if(memcmp(ss,ss_rsp,CRYPTO_BYTES)!=0){ + printf("ERROR: ss is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + + if ( (ret_val = crypto_kem_dec_SIKEp434_compressed(ss1, ct, sk)) != 0) { + printf("crypto_kem_dec returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + + if ( memcmp(ss, ss1, CRYPTO_BYTES) ) { + printf("crypto_kem_dec returned bad 'ss' value\n"); + return KAT_CRYPTO_FAILURE; + } + + } while ( !done ); + + fclose(fp_rsp); + printf("Known Answer Tests PASSED. \n"); + printf("\n\n"); + + return KAT_SUCCESS; +} + + +// +// ALLOW TO READ HEXADECIMAL ENTRY (KEYS, DATA, TEXT, etc.) +// + +int +FindMarker(FILE *infile, const char *marker) +{ + char line[MAX_MARKER_LEN]; + int i, len; + int curr_line; + + len = (int)strlen(marker); + if ( len > MAX_MARKER_LEN-1 ) + len = MAX_MARKER_LEN-1; + + for ( i=0; i= '0') && (ch <= '9') ) + ich = ch - '0'; + else if ( (ch >= 'A') && (ch <= 'F') ) + ich = ch - 'A' + 10; + else if ( (ch >= 'a') && (ch <= 'f') ) + ich = ch - 'a' + 10; + else // shouldn't ever get here + ich = 0; + + for ( i=0; i> 4); + A[Length-1] = (A[Length-1] << 4) | ich; + } + else + return 0; + + return 1; +} + +void +fprintBstr(FILE *fp, char *S, unsigned char *A, unsigned long long L) +{ + unsigned long long i; + + fprintf(fp, "%s", S); + + for ( i=0; i +#include +#include +#include +#include "rng/rng.h" +#include "../src/P503/P503_compressed_api.h" + + +#define MAX_MARKER_LEN 50 +#define KAT_SUCCESS 0 +#define KAT_FILE_OPEN_ERROR -1 +#define KAT_VERIFICATION_ERROR -2 +#define KAT_DATA_ERROR -3 +#define KAT_CRYPTO_FAILURE -4 + +int FindMarker(FILE *infile, const char *marker); +int ReadHex(FILE *infile, unsigned char *A, int Length, char *str); +void fprintBstr(FILE *fp, char *S, unsigned char *A, unsigned long long L); + +int +main() +{ + char fn_rsp[32]; + FILE *fp_rsp; + unsigned char seed[48]; + unsigned char ct[CRYPTO_CIPHERTEXTBYTES], ss[CRYPTO_BYTES], ss1[CRYPTO_BYTES], ct_rsp[CRYPTO_CIPHERTEXTBYTES], ss_rsp[CRYPTO_BYTES]; + int count; + int done; + unsigned char pk[CRYPTO_PUBLICKEYBYTES], sk[CRYPTO_SECRETKEYBYTES], pk_rsp[CRYPTO_PUBLICKEYBYTES], sk_rsp[CRYPTO_SECRETKEYBYTES]; + int ret_val; + + sprintf(fn_rsp, "KAT/PQCkemKAT_%d.rsp", CRYPTO_SECRETKEYBYTES); + if ( (fp_rsp = fopen(fn_rsp, "r")) == NULL ) { + printf("Couldn't open <%s> for read\n", fn_rsp); + return KAT_FILE_OPEN_ERROR; + } + + printf("# %s\n\n", CRYPTO_ALGNAME); + done = 0; + do { + if ( FindMarker(fp_rsp, "count = ") ) { + if (fscanf(fp_rsp, "%d", &count) != 1) { + done = 1; + break; + } + } else { + done = 1; + break; + } + + if ( !ReadHex(fp_rsp, seed, 48, "seed = ") ) { + printf("ERROR: unable to read 'seed' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + randombytes_init(seed, NULL, 256); + + // Generate the public/private keypair + if ( (ret_val = crypto_kem_keypair_SIKEp503_compressed(pk, sk)) != 0) { + printf("crypto_kem_keypair returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + if ( !ReadHex(fp_rsp, pk_rsp, CRYPTO_PUBLICKEYBYTES, "pk = ") ) { + printf("ERROR: unable to read 'pk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + if ( !ReadHex(fp_rsp, sk_rsp, CRYPTO_SECRETKEYBYTES, "sk = ") ) { + printf("ERROR: unable to read 'sk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + if(memcmp(pk,pk_rsp,CRYPTO_PUBLICKEYBYTES)!=0){ + printf("ERROR: pk is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + if(memcmp(sk,sk_rsp,CRYPTO_SECRETKEYBYTES)!=0){ + printf("ERROR: sk is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + + if ( (ret_val = crypto_kem_enc_SIKEp503_compressed(ct, ss, pk)) != 0) { + printf("crypto_kem_enc returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + + if ( !ReadHex(fp_rsp, ct_rsp, CRYPTO_CIPHERTEXTBYTES, "ct = ") ) { + printf("ERROR: unable to read 'pk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + if ( !ReadHex(fp_rsp, ss_rsp, CRYPTO_BYTES, "ss = ") ) { + printf("ERROR: unable to read 'sk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + if(memcmp(ct,ct_rsp,CRYPTO_CIPHERTEXTBYTES)!=0){ + printf("ERROR: ct is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + if(memcmp(ss,ss_rsp,CRYPTO_BYTES)!=0){ + printf("ERROR: ss is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + + if ( (ret_val = crypto_kem_dec_SIKEp503_compressed(ss1, ct, sk)) != 0) { + printf("crypto_kem_dec returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + + if ( memcmp(ss, ss1, CRYPTO_BYTES) ) { + printf("crypto_kem_dec returned bad 'ss' value\n"); + return KAT_CRYPTO_FAILURE; + } + + } while ( !done ); + + fclose(fp_rsp); + printf("Known Answer Tests PASSED. \n"); + printf("\n\n"); + + return KAT_SUCCESS; +} + + +// +// ALLOW TO READ HEXADECIMAL ENTRY (KEYS, DATA, TEXT, etc.) +// + +int +FindMarker(FILE *infile, const char *marker) +{ + char line[MAX_MARKER_LEN]; + int i, len; + int curr_line; + + len = (int)strlen(marker); + if ( len > MAX_MARKER_LEN-1 ) + len = MAX_MARKER_LEN-1; + + for ( i=0; i= '0') && (ch <= '9') ) + ich = ch - '0'; + else if ( (ch >= 'A') && (ch <= 'F') ) + ich = ch - 'A' + 10; + else if ( (ch >= 'a') && (ch <= 'f') ) + ich = ch - 'a' + 10; + else // shouldn't ever get here + ich = 0; + + for ( i=0; i> 4); + A[Length-1] = (A[Length-1] << 4) | ich; + } + else + return 0; + + return 1; +} + +void +fprintBstr(FILE *fp, char *S, unsigned char *A, unsigned long long L) +{ + unsigned long long i; + + fprintf(fp, "%s", S); + + for ( i=0; i +#include +#include +#include +#include "rng/rng.h" +#include "../src/P610/P610_compressed_api.h" + + +#define MAX_MARKER_LEN 50 +#define KAT_SUCCESS 0 +#define KAT_FILE_OPEN_ERROR -1 +#define KAT_VERIFICATION_ERROR -2 +#define KAT_DATA_ERROR -3 +#define KAT_CRYPTO_FAILURE -4 + +int FindMarker(FILE *infile, const char *marker); +int ReadHex(FILE *infile, unsigned char *A, int Length, char *str); +void fprintBstr(FILE *fp, char *S, unsigned char *A, unsigned long long L); + +int +main() +{ + char fn_rsp[32]; + FILE *fp_rsp; + unsigned char seed[48]; + unsigned char ct[CRYPTO_CIPHERTEXTBYTES], ss[CRYPTO_BYTES], ss1[CRYPTO_BYTES], ct_rsp[CRYPTO_CIPHERTEXTBYTES], ss_rsp[CRYPTO_BYTES]; + int count; + int done; + unsigned char pk[CRYPTO_PUBLICKEYBYTES], sk[CRYPTO_SECRETKEYBYTES], pk_rsp[CRYPTO_PUBLICKEYBYTES], sk_rsp[CRYPTO_SECRETKEYBYTES]; + int ret_val; + + sprintf(fn_rsp, "KAT/PQCkemKAT_%d.rsp", CRYPTO_SECRETKEYBYTES); + if ( (fp_rsp = fopen(fn_rsp, "r")) == NULL ) { + printf("Couldn't open <%s> for read\n", fn_rsp); + return KAT_FILE_OPEN_ERROR; + } + + printf("# %s\n\n", CRYPTO_ALGNAME); + done = 0; + do { + if ( FindMarker(fp_rsp, "count = ") ) { + if (fscanf(fp_rsp, "%d", &count) != 1) { + done = 1; + break; + } + } else { + done = 1; + break; + } + + if ( !ReadHex(fp_rsp, seed, 48, "seed = ") ) { + printf("ERROR: unable to read 'seed' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + randombytes_init(seed, NULL, 256); + + // Generate the public/private keypair + if ( (ret_val = crypto_kem_keypair_SIKEp610_compressed(pk, sk)) != 0) { + printf("crypto_kem_keypair returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + if ( !ReadHex(fp_rsp, pk_rsp, CRYPTO_PUBLICKEYBYTES, "pk = ") ) { + printf("ERROR: unable to read 'pk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + if ( !ReadHex(fp_rsp, sk_rsp, CRYPTO_SECRETKEYBYTES, "sk = ") ) { + printf("ERROR: unable to read 'sk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + if(memcmp(pk,pk_rsp,CRYPTO_PUBLICKEYBYTES)!=0){ + printf("ERROR: pk is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + if(memcmp(sk,sk_rsp,CRYPTO_SECRETKEYBYTES)!=0){ + printf("ERROR: sk is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + + if ( (ret_val = crypto_kem_enc_SIKEp610_compressed(ct, ss, pk)) != 0) { + printf("crypto_kem_enc returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + + if ( !ReadHex(fp_rsp, ct_rsp, CRYPTO_CIPHERTEXTBYTES, "ct = ") ) { + printf("ERROR: unable to read 'pk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + if ( !ReadHex(fp_rsp, ss_rsp, CRYPTO_BYTES, "ss = ") ) { + printf("ERROR: unable to read 'sk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + if(memcmp(ct,ct_rsp,CRYPTO_CIPHERTEXTBYTES)!=0){ + printf("ERROR: ct is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + if(memcmp(ss,ss_rsp,CRYPTO_BYTES)!=0){ + printf("ERROR: ss is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + + if ( (ret_val = crypto_kem_dec_SIKEp610_compressed(ss1, ct, sk)) != 0) { + printf("crypto_kem_dec returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + + if ( memcmp(ss, ss1, CRYPTO_BYTES) ) { + printf("crypto_kem_dec returned bad 'ss' value\n"); + return KAT_CRYPTO_FAILURE; + } + + } while ( !done ); + + fclose(fp_rsp); + printf("Known Answer Tests PASSED. \n"); + printf("\n\n"); + + return KAT_SUCCESS; +} + + +// +// ALLOW TO READ HEXADECIMAL ENTRY (KEYS, DATA, TEXT, etc.) +// + +int +FindMarker(FILE *infile, const char *marker) +{ + char line[MAX_MARKER_LEN]; + int i, len; + int curr_line; + + len = (int)strlen(marker); + if ( len > MAX_MARKER_LEN-1 ) + len = MAX_MARKER_LEN-1; + + for ( i=0; i= '0') && (ch <= '9') ) + ich = ch - '0'; + else if ( (ch >= 'A') && (ch <= 'F') ) + ich = ch - 'A' + 10; + else if ( (ch >= 'a') && (ch <= 'f') ) + ich = ch - 'a' + 10; + else // shouldn't ever get here + ich = 0; + + for ( i=0; i> 4); + A[Length-1] = (A[Length-1] << 4) | ich; + } + else + return 0; + + return 1; +} + +void +fprintBstr(FILE *fp, char *S, unsigned char *A, unsigned long long L) +{ + unsigned long long i; + + fprintf(fp, "%s", S); + + for ( i=0; i +#include +#include +#include +#include "rng/rng.h" +#include "../src/P751/P751_compressed_api.h" + + +#define MAX_MARKER_LEN 50 +#define KAT_SUCCESS 0 +#define KAT_FILE_OPEN_ERROR -1 +#define KAT_VERIFICATION_ERROR -2 +#define KAT_DATA_ERROR -3 +#define KAT_CRYPTO_FAILURE -4 + +int FindMarker(FILE *infile, const char *marker); +int ReadHex(FILE *infile, unsigned char *A, int Length, char *str); +void fprintBstr(FILE *fp, char *S, unsigned char *A, unsigned long long L); + +int +main() +{ + char fn_rsp[32]; + FILE *fp_rsp; + unsigned char seed[48]; + unsigned char ct[CRYPTO_CIPHERTEXTBYTES], ss[CRYPTO_BYTES], ss1[CRYPTO_BYTES], ct_rsp[CRYPTO_CIPHERTEXTBYTES], ss_rsp[CRYPTO_BYTES]; + int count; + int done; + unsigned char pk[CRYPTO_PUBLICKEYBYTES], sk[CRYPTO_SECRETKEYBYTES], pk_rsp[CRYPTO_PUBLICKEYBYTES], sk_rsp[CRYPTO_SECRETKEYBYTES]; + int ret_val; + + sprintf(fn_rsp, "KAT/PQCkemKAT_%d.rsp", CRYPTO_SECRETKEYBYTES); + if ( (fp_rsp = fopen(fn_rsp, "r")) == NULL ) { + printf("Couldn't open <%s> for read\n", fn_rsp); + return KAT_FILE_OPEN_ERROR; + } + + printf("# %s\n\n", CRYPTO_ALGNAME); + done = 0; + do { + if ( FindMarker(fp_rsp, "count = ") ) { + if (fscanf(fp_rsp, "%d", &count) != 1) { + done = 1; + break; + } + } else { + done = 1; + break; + } + + if ( !ReadHex(fp_rsp, seed, 48, "seed = ") ) { + printf("ERROR: unable to read 'seed' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + randombytes_init(seed, NULL, 256); + + // Generate the public/private keypair + if ( (ret_val = crypto_kem_keypair_SIKEp751_compressed(pk, sk)) != 0) { + printf("crypto_kem_keypair returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + if ( !ReadHex(fp_rsp, pk_rsp, CRYPTO_PUBLICKEYBYTES, "pk = ") ) { + printf("ERROR: unable to read 'pk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + if ( !ReadHex(fp_rsp, sk_rsp, CRYPTO_SECRETKEYBYTES, "sk = ") ) { + printf("ERROR: unable to read 'sk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + if(memcmp(pk,pk_rsp,CRYPTO_PUBLICKEYBYTES)!=0){ + printf("ERROR: pk is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + if(memcmp(sk,sk_rsp,CRYPTO_SECRETKEYBYTES)!=0){ + printf("ERROR: sk is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + + if ( (ret_val = crypto_kem_enc_SIKEp751_compressed(ct, ss, pk)) != 0) { + printf("crypto_kem_enc returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + + if ( !ReadHex(fp_rsp, ct_rsp, CRYPTO_CIPHERTEXTBYTES, "ct = ") ) { + printf("ERROR: unable to read 'pk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + if ( !ReadHex(fp_rsp, ss_rsp, CRYPTO_BYTES, "ss = ") ) { + printf("ERROR: unable to read 'sk' from <%s>\n", fn_rsp); + return KAT_DATA_ERROR; + } + + if(memcmp(ct,ct_rsp,CRYPTO_CIPHERTEXTBYTES)!=0){ + printf("ERROR: ct is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + if(memcmp(ss,ss_rsp,CRYPTO_BYTES)!=0){ + printf("ERROR: ss is different from <%s>\n", fn_rsp); + return KAT_VERIFICATION_ERROR; + } + + if ( (ret_val = crypto_kem_dec_SIKEp751_compressed(ss1, ct, sk)) != 0) { + printf("crypto_kem_dec returned <%d>\n", ret_val); + return KAT_CRYPTO_FAILURE; + } + + if ( memcmp(ss, ss1, CRYPTO_BYTES) ) { + printf("crypto_kem_dec returned bad 'ss' value\n"); + return KAT_CRYPTO_FAILURE; + } + + } while ( !done ); + + fclose(fp_rsp); + printf("Known Answer Tests PASSED. \n"); + printf("\n\n"); + + return KAT_SUCCESS; +} + + +// +// ALLOW TO READ HEXADECIMAL ENTRY (KEYS, DATA, TEXT, etc.) +// + +int +FindMarker(FILE *infile, const char *marker) +{ + char line[MAX_MARKER_LEN]; + int i, len; + int curr_line; + + len = (int)strlen(marker); + if ( len > MAX_MARKER_LEN-1 ) + len = MAX_MARKER_LEN-1; + + for ( i=0; i= '0') && (ch <= '9') ) + ich = ch - '0'; + else if ( (ch >= 'A') && (ch <= 'F') ) + ich = ch - 'A' + 10; + else if ( (ch >= 'a') && (ch <= 'f') ) + ich = ch - 'a' + 10; + else // shouldn't ever get here + ich = 0; + + for ( i=0; i> 4); + A[Length-1] = (A[Length-1] << 4) | ich; + } + else + return 0; + + return 1; +} + +void +fprintBstr(FILE *fp, char *S, unsigned char *A, unsigned long long L) +{ + unsigned long long i; + + fprintf(fp, "%s", S); + + for ( i=0; i +#include +#include "test_extras.h" +#include "../src/P434/P434_compressed_api.h" + + +#define SCHEME_NAME "SIDHp434_compressed" + +#define random_mod_order_A random_mod_order_A_SIDHp434 +#define random_mod_order_B random_mod_order_B_SIDHp434 +#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp434_Compressed +#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp434_Compressed +#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp434_Compressed +#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp434_Compressed + +#include "test_sidh.c" \ No newline at end of file diff --git a/tests/test_SIDHp503_compressed.c b/tests/test_SIDHp503_compressed.c new file mode 100644 index 0000000..48e2eae --- /dev/null +++ b/tests/test_SIDHp503_compressed.c @@ -0,0 +1,22 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: benchmarking/testing isogeny-based key exchange SIDHp503_compressed +*********************************************************************************************/ + +#include +#include +#include "test_extras.h" +#include "../src/P503/P503_compressed_api.h" + + +#define SCHEME_NAME "SIDHp503_compressed" + +#define random_mod_order_A random_mod_order_A_SIDHp503 +#define random_mod_order_B random_mod_order_B_SIDHp503 +#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp503_Compressed +#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp503_Compressed +#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp503_Compressed +#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp503_Compressed + +#include "test_sidh.c" \ No newline at end of file diff --git a/tests/test_SIDHp610_compressed.c b/tests/test_SIDHp610_compressed.c new file mode 100644 index 0000000..ee01803 --- /dev/null +++ b/tests/test_SIDHp610_compressed.c @@ -0,0 +1,22 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: benchmarking/testing isogeny-based key exchange SIDHp610_compressed +*********************************************************************************************/ + +#include +#include +#include "test_extras.h" +#include "../src/P610/P610_compressed_api.h" + + +#define SCHEME_NAME "SIDHp610_compressed" + +#define random_mod_order_A random_mod_order_A_SIDHp610 +#define random_mod_order_B random_mod_order_B_SIDHp610 +#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp610_Compressed +#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp610_Compressed +#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp610_Compressed +#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp610_Compressed + +#include "test_sidh.c" \ No newline at end of file diff --git a/tests/test_SIDHp751_compressed.c b/tests/test_SIDHp751_compressed.c new file mode 100644 index 0000000..d7080de --- /dev/null +++ b/tests/test_SIDHp751_compressed.c @@ -0,0 +1,22 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: benchmarking/testing isogeny-based key exchange SIDHp751_compressed +*********************************************************************************************/ + +#include +#include +#include "test_extras.h" +#include "../src/P751/P751_compressed_api.h" + + +#define SCHEME_NAME "SIDHp751_compressed" + +#define random_mod_order_A random_mod_order_A_SIDHp751 +#define random_mod_order_B random_mod_order_B_SIDHp751 +#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp751_Compressed +#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp751_Compressed +#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp751_Compressed +#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp751_Compressed + +#include "test_sidh.c" \ No newline at end of file diff --git a/tests/test_SIKEp434_compressed.c b/tests/test_SIKEp434_compressed.c new file mode 100644 index 0000000..1c84874 --- /dev/null +++ b/tests/test_SIKEp434_compressed.c @@ -0,0 +1,19 @@ +/********************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: benchmarking/testing isogeny-based key encapsulation mechanism SIKEp434_compressed +***********************************************************************************************/ + +#include +#include +#include "test_extras.h" +#include "../src/P434/P434_compressed.c" + + +#define SCHEME_NAME "SIKEp434_compressed" + +#define crypto_kem_keypair crypto_kem_keypair_SIKEp434_compressed +#define crypto_kem_enc crypto_kem_enc_SIKEp434_compressed +#define crypto_kem_dec crypto_kem_dec_SIKEp434_compressed + +#include "test_sike.c" diff --git a/tests/test_SIKEp503_compressed.c b/tests/test_SIKEp503_compressed.c new file mode 100644 index 0000000..1924f04 --- /dev/null +++ b/tests/test_SIKEp503_compressed.c @@ -0,0 +1,19 @@ +/********************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: benchmarking/testing isogeny-based key encapsulation mechanism SIKEp503_compressed +***********************************************************************************************/ + +#include +#include +#include "test_extras.h" +#include "../src/P503/P503_compressed.c" + + +#define SCHEME_NAME "SIKEp503_compressed" + +#define crypto_kem_keypair crypto_kem_keypair_SIKEp503_compressed +#define crypto_kem_enc crypto_kem_enc_SIKEp503_compressed +#define crypto_kem_dec crypto_kem_dec_SIKEp503_compressed + +#include "test_sike.c" diff --git a/tests/test_SIKEp610_compressed.c b/tests/test_SIKEp610_compressed.c new file mode 100644 index 0000000..7ca2d4e --- /dev/null +++ b/tests/test_SIKEp610_compressed.c @@ -0,0 +1,19 @@ +/********************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: benchmarking/testing isogeny-based key encapsulation mechanism SIKEp610_compressed +***********************************************************************************************/ + +#include +#include +#include "test_extras.h" +#include "../src/P610/P610_compressed.c" + + +#define SCHEME_NAME "SIKEp610_compressed" + +#define crypto_kem_keypair crypto_kem_keypair_SIKEp610_compressed +#define crypto_kem_enc crypto_kem_enc_SIKEp610_compressed +#define crypto_kem_dec crypto_kem_dec_SIKEp610_compressed + +#include "test_sike.c" diff --git a/tests/test_SIKEp751_compressed.c b/tests/test_SIKEp751_compressed.c new file mode 100644 index 0000000..a84e600 --- /dev/null +++ b/tests/test_SIKEp751_compressed.c @@ -0,0 +1,19 @@ +/********************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: benchmarking/testing isogeny-based key encapsulation mechanism SIKEp751_compressed +***********************************************************************************************/ + +#include +#include +#include "test_extras.h" +#include "../src/P751/P751_compressed.c" + + +#define SCHEME_NAME "SIKEp751_compressed" + +#define crypto_kem_keypair crypto_kem_keypair_SIKEp751_compressed +#define crypto_kem_enc crypto_kem_enc_SIKEp751_compressed +#define crypto_kem_dec crypto_kem_dec_SIKEp751_compressed + +#include "test_sike.c"