From f26c323250b6b09fd5bfffd5abbf6cf4570576de Mon Sep 17 00:00:00 2001 From: RandomLattice <128569685+RandomLattice@users.noreply.github.com> Date: Sat, 3 Feb 2024 18:52:22 -0500 Subject: [PATCH 1/2] tests: Add Wycheproof ECDH vectors Adds a test for the ECDH module using the Wycheproof vectors. We use a python script to convert the JSON-formatted vectors into C code, in the same spirit as https://github.com/bitcoin-core/secp256k1/pull/1245 Co-authored-by: Sean Andersen <6730974+andozw@users.noreply.github.com> --- Makefile.am | 14 +- src/modules/ecdh/Makefile.am.include | 1 + src/modules/ecdh/tests_impl.h | 50 + src/wycheproof/WYCHEPROOF_COPYING | 11 +- src/wycheproof/ecdh_secp256k1_test.h | 1935 ++++ src/wycheproof/ecdh_secp256k1_test.json | 8441 +++++++++++++++++ .../ecdsa_secp256k1_sha256_bitcoin_test.h | 2 +- tools/tests_wycheproof_generate_ecdh.py | 150 + ....py => tests_wycheproof_generate_ecdsa.py} | 10 +- tools/wycheproof_utils.py | 12 + 10 files changed, 10615 insertions(+), 11 deletions(-) create mode 100644 src/wycheproof/ecdh_secp256k1_test.h create mode 100644 src/wycheproof/ecdh_secp256k1_test.json create mode 100755 tools/tests_wycheproof_generate_ecdh.py rename tools/{tests_wycheproof_generate.py => tests_wycheproof_generate_ecdsa.py} (95%) create mode 100644 tools/wycheproof_utils.py diff --git a/Makefile.am b/Makefile.am index 5498617915..8123e4baa5 100644 --- a/Makefile.am +++ b/Makefile.am @@ -225,9 +225,17 @@ maintainer-clean-local: clean-precomp ### (see the comments in the previous section for detailed rationale) TESTVECTORS = src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h +if ENABLE_MODULE_ECDH +TESTVECTORS += src/wycheproof/ecdh_secp256k1_test.h +endif + src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h: mkdir -p $(@D) - python3 $(top_srcdir)/tools/tests_wycheproof_generate.py $(top_srcdir)/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json > $@ + python3 $(top_srcdir)/tools/tests_wycheproof_generate_ecdsa.py $(top_srcdir)/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json > $@ + +src/wycheproof/ecdh_secp256k1_test.h: + mkdir -p $(@D) + python3 $(top_srcdir)/tools/tests_wycheproof_generate_ecdh.py $(top_srcdir)/src/wycheproof/ecdh_secp256k1_test.json > $@ testvectors: $(TESTVECTORS) @@ -250,7 +258,9 @@ EXTRA_DIST += sage/secp256k1_params.sage EXTRA_DIST += sage/weierstrass_prover.sage EXTRA_DIST += src/wycheproof/WYCHEPROOF_COPYING EXTRA_DIST += src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json -EXTRA_DIST += tools/tests_wycheproof_generate.py +EXTRA_DIST += src/wycheproof/ecdh_secp256k1_test.json +EXTRA_DIST += tools/tests_wycheproof_generate_ecdsa.py +EXTRA_DIST += tools/tests_wycheproof_generate_ecdh.py if ENABLE_MODULE_ECDH include src/modules/ecdh/Makefile.am.include diff --git a/src/modules/ecdh/Makefile.am.include b/src/modules/ecdh/Makefile.am.include index 7f7f95f1fd..1866053529 100644 --- a/src/modules/ecdh/Makefile.am.include +++ b/src/modules/ecdh/Makefile.am.include @@ -2,3 +2,4 @@ include_HEADERS += include/secp256k1_ecdh.h noinst_HEADERS += src/modules/ecdh/main_impl.h noinst_HEADERS += src/modules/ecdh/tests_impl.h noinst_HEADERS += src/modules/ecdh/bench_impl.h +noinst_HEADERS += src/wycheproof/ecdh_secp256k1_test.h diff --git a/src/modules/ecdh/tests_impl.h b/src/modules/ecdh/tests_impl.h index 6be96eacbe..7648cac651 100644 --- a/src/modules/ecdh/tests_impl.h +++ b/src/modules/ecdh/tests_impl.h @@ -7,6 +7,14 @@ #ifndef SECP256K1_MODULE_ECDH_TESTS_H #define SECP256K1_MODULE_ECDH_TESTS_H +static int ecdh_hash_function_test_xpassthru(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { + (void)x; + (void)y; + (void)data; + memcpy(output, x, 32); + return 1; +} + static int ecdh_hash_function_test_fail(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { (void)output; (void)x; @@ -142,11 +150,53 @@ static void test_result_basepoint(void) { } } +static void test_ecdh_wycheproof(void) { +#include "../../wycheproof/ecdh_secp256k1_test.h" + int t; + for (t = 0; t < SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS; t++) { + int parsed_ok; + secp256k1_pubkey point; + const unsigned char *pk; + const unsigned char *sk; + const unsigned char *expected_shared_secret; + unsigned char output_ecdh[65] = { 0 }; + + int expected_result; + int actual; + + memset(&point, 0, sizeof(point)); + pk = &wycheproof_ecdh_public_keys[testvectors[t].pk_offset]; + parsed_ok = secp256k1_ec_pubkey_parse(CTX, &point, pk, testvectors[t].pk_len); + + expected_result = testvectors[t].expected_result; + + /* fail if public key is valid, but doesn't parse */ + CHECK(parsed_ok || expected_result == 0); + + if (!parsed_ok && expected_result == 0) { + continue; + } + + sk = &wycheproof_ecdh_private_keys[testvectors[t].sk_offset]; + CHECK(testvectors[t].sk_len == 32); + + actual = secp256k1_ecdh(CTX, output_ecdh, &point, sk, ecdh_hash_function_test_xpassthru, NULL); + expected_shared_secret = &wycheproof_ecdh_shared_secrets[testvectors[t].shared_offset]; + + CHECK(actual == expected_result); + if (expected_result == 0) { + CHECK(testvectors[t].shared_len == 0); + } + CHECK(secp256k1_memcmp_var(output_ecdh, expected_shared_secret, testvectors[t].shared_len) == 0); + } +} + static void run_ecdh_tests(void) { test_ecdh_api(); test_ecdh_generator_basepoint(); test_bad_scalar(); test_result_basepoint(); + test_ecdh_wycheproof(); } #endif /* SECP256K1_MODULE_ECDH_TESTS_H */ diff --git a/src/wycheproof/WYCHEPROOF_COPYING b/src/wycheproof/WYCHEPROOF_COPYING index cddf9d9182..efe3e8bf4e 100644 --- a/src/wycheproof/WYCHEPROOF_COPYING +++ b/src/wycheproof/WYCHEPROOF_COPYING @@ -3,9 +3,18 @@ `b063b4aedae951c69df014cd25fa6d69ae9e8cb9`, see https://github.com/google/wycheproof/blob/b063b4aedae951c69df014cd25fa6d69ae9e8cb9/testvectors_v1/ecdsa_secp256k1_sha256_bitcoin_test.json +* The file `ecdh_secp256k1_test.json` in this directory + comes from Google's project Wycheproof with git commit + `d9f6ec7d8bd8c96da05368999094e4a75ba5cb3d`, see + https://github.com/google/wycheproof/blob/d9f6ec7d8bd8c96da05368999094e4a75ba5cb3d/testvectors_v1/ecdh_secp256k1_test.json + * The file `ecdsa_secp256k1_sha256_bitcoin_test.h` is generated from `ecdsa_secp256k1_sha256_bitcoin_test.json` using the script - `tests_wycheproof_generate.py`. + `tests_wycheproof_generate_ecdsa.py`. + +* The file `ecdh_secp256k1_test.h` is generated from + `ecdh_secp256k1_test.json` using the script + `tests_wycheproof_generate_ecdh.py`. ------------------------------------------------------------------------------- diff --git a/src/wycheproof/ecdh_secp256k1_test.h b/src/wycheproof/ecdh_secp256k1_test.h new file mode 100644 index 0000000000..dd13829680 --- /dev/null +++ b/src/wycheproof/ecdh_secp256k1_test.h @@ -0,0 +1,1935 @@ +/* Note: this file was autogenerated using tests_wycheproof_ecdh.py. Do not edit. */ +#define SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS (479) + +typedef struct { + size_t pk_offset; + size_t pk_len; + size_t sk_offset; + size_t sk_len; + size_t shared_offset; + size_t shared_len; + int expected_result; +} wycheproof_ecdh_testvector; + +static const unsigned char wycheproof_ecdh_private_keys[] = { 0xf4,0xb7,0xff,0x7c,0xcc,0xc9,0x88,0x13,0xa6,0x9f,0xae,0x3d,0xf2,0x22,0xbf,0xe3,0xf4,0xe2,0x8f,0x76,0x4b,0xf9,0x1b,0x4a,0x10,0xd8,0x09,0x6c,0xe4,0x46,0xb2,0x54, + 0xa2,0xb6,0x44,0x2a,0x37,0xf8,0xa3,0x76,0x4a,0xef,0xf4,0x01,0x1a,0x4c,0x42,0x2b,0x38,0x9a,0x1e,0x50,0x96,0x69,0xc4,0x3f,0x27,0x9c,0x8b,0x7e,0x32,0xd8,0x0c,0x3a, + 0x2b,0xc1,0x5c,0xf3,0x98,0x1e,0xab,0x61,0xe5,0x94,0xeb,0xf5,0x91,0x29,0x0a,0x04,0x5c,0xa9,0x32,0x6a,0x8d,0x3d,0xd4,0x9f,0x3d,0xe1,0x19,0x0d,0x39,0x27,0x0b,0xb8, + 0x93,0x8f,0x3d,0xbe,0x37,0x13,0x5c,0xd8,0xc8,0xc4,0x8a,0x67,0x6b,0x28,0xb2,0x33,0x4b,0x72,0xa3,0xf0,0x98,0x14,0xc8,0xef,0xb6,0xa4,0x51,0xbe,0x00,0xc9,0x3d,0x23, + 0xc1,0x78,0x1d,0x86,0xca,0xc2,0xc0,0x52,0xb8,0x65,0xf2,0x28,0xe6,0x4b,0xd1,0xce,0x43,0x3c,0x78,0xca,0x7d,0xfc,0xa9,0xe8,0xb8,0x10,0x47,0x3e,0x2c,0xe1,0x7d,0xa5, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x03, + 0x00,0x00,0x00,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff, + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3a,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xc2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xca,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8b,0xd0,0x36,0x41,0x41, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x40,0xc3, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x03, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x23, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x33, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x3b, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x3e, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x3f, + 0xcf,0xe7,0x5e,0xe7,0x64,0x19,0x7a,0xa7,0x73,0x2a,0x54,0x78,0x55,0x6b,0x47,0x88,0x98,0x42,0x3d,0x2b,0xc0,0xe4,0x84,0xa6,0xeb,0xb3,0x67,0x4a,0x60,0x36,0xa6,0x5d, + 0xd0,0x91,0x82,0xa4,0xd0,0xc9,0x4b,0xa8,0x5f,0x82,0xef,0xf9,0xfc,0x1b,0xdd,0xb0,0xb0,0x7d,0x3f,0x2a,0xf8,0x63,0x2f,0xc1,0xc7,0x3a,0x36,0x04,0xe8,0xf0,0xb3,0x35}; + +static const unsigned char wycheproof_ecdh_public_keys[] = { 0x04,0xd8,0x09,0x6a,0xf8,0xa1,0x1e,0x0b,0x80,0x03,0x7e,0x1e,0xe6,0x82,0x46,0xb5,0xdc,0xbb,0x0a,0xeb,0x1c,0xf1,0x24,0x4f,0xd7,0x67,0xdb,0x80,0xf3,0xfa,0x27,0xda,0x2b,0x39,0x68,0x12,0xea,0x16,0x86,0xe7,0x47,0x2e,0x96,0x92,0xea,0xf3,0xe9,0x58,0xe5,0x0e,0x95,0x00,0xd3,0xb4,0xc7,0x72,0x43,0xdb,0x1f,0x2a,0xcd,0x67,0xba,0x9c,0xc4, + 0x02,0xd8,0x09,0x6a,0xf8,0xa1,0x1e,0x0b,0x80,0x03,0x7e,0x1e,0xe6,0x82,0x46,0xb5,0xdc,0xbb,0x0a,0xeb,0x1c,0xf1,0x24,0x4f,0xd7,0x67,0xdb,0x80,0xf3,0xfa,0x27,0xda,0x2b, + 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0x04,0x32,0xbd,0xd9,0x78,0xeb,0x62,0xb1,0xf3,0x69,0xa5,0x6d,0x09,0x49,0xab,0x85,0x51,0xa7,0xad,0x52,0x7d,0x96,0x02,0xe8,0x91,0xce,0x45,0x75,0x86,0xc2,0xa8,0x56,0x9e,0x98,0x1e,0x67,0xfa,0xe0,0x53,0xb0,0x3f,0xc3,0x3e,0x1a,0x29,0x1f,0x0a,0x3b,0xeb,0x58,0xfc,0xeb,0x2e,0x85,0xbb,0x12,0x05,0xda,0xce,0xe1,0x23,0x2d,0xfd,0x31,0x6b, + 0x04,0x49,0xc2,0x48,0xed,0xc6,0x59,0xe1,0x84,0x82,0xb7,0x10,0x57,0x48,0xa4,0xb9,0x5d,0x3a,0x46,0x95,0x2a,0x5b,0xa7,0x2d,0xa0,0xd7,0x02,0xdc,0x97,0xa6,0x4e,0x99,0x79,0x9d,0x8c,0xff,0x7a,0x5c,0x4b,0x92,0x5e,0x43,0x60,0xec,0xe2,0x5c,0xcf,0x30,0x7d,0x7a,0x9a,0x70,0x63,0x28,0x6b,0xbd,0x16,0xef,0x64,0xc6,0x5f,0x54,0x67,0x57,0xe4, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0x07,0x4f,0x56,0xdc,0x2e,0xa6,0x48,0xef,0x89,0xc3,0xb7,0x2e,0x23,0xbb,0xd2,0xda,0x36,0xf6,0x02,0x43,0xe4,0xd2,0x06,0x7b,0x70,0x60,0x4a,0xf1,0xc2,0x16,0x5c,0xec,0x2f,0x86,0x60,0x3d,0x60,0xc8,0xa6,0x11,0xd5,0xb8,0x4b,0xa3,0xd9,0x1d,0xfe,0x1a,0x48,0x08,0x25,0xbc,0xc4,0xaf,0x3b,0xcf, + 0x04,0xcb,0xf6,0x60,0x65,0x95,0xa3,0xee,0x50,0xf9,0xfc,0xea,0xa2,0x79,0x8c,0x27,0x40,0xc8,0x25,0x40,0x51,0x6b,0x4e,0x5a,0x7d,0x36,0x1f,0xf2,0x4e,0x9d,0xd1,0x53,0x64,0xe5,0x40,0x8b,0x2e,0x67,0x9f,0x9d,0x53,0x10,0xd1,0xf6,0x89,0x3b,0x36,0xce,0x16,0xb4,0xa5,0x07,0x50,0x91,0x75,0xfc,0xb5,0x2a,0xea,0x53,0xb7,0x81,0x55,0x6b,0x39, + 0x02,0x97,0x7c,0xb7,0xfb,0x9a,0x0e,0xc5,0xb2,0x08,0xe8,0x11,0xd6,0xa0,0x79,0x5e,0xb7,0x8d,0x76,0x42,0xe3,0xca,0xc4,0x2a,0x80,0x1b,0xcc,0x8f,0xc0,0xf0,0x64,0x72,0xd4}; + +static const unsigned char wycheproof_ecdh_shared_secrets[] = { 0x54,0x4d,0xfa,0xe2,0x2a,0xf6,0xaf,0x93,0x90,0x42,0xb1,0xd8,0x5b,0x71,0xa1,0xe4,0x9e,0x9a,0x56,0x14,0x12,0x3c,0x4d,0x6a,0xd0,0xc8,0xaf,0x65,0xba,0xf8,0x7d,0x65, + 0x54,0x4d,0xfa,0xe2,0x2a,0xf6,0xaf,0x93,0x90,0x42,0xb1,0xd8,0x5b,0x71,0xa1,0xe4,0x9e,0x9a,0x56,0x14,0x12,0x3c,0x4d,0x6a,0xd0,0xc8,0xaf,0x65,0xba,0xf8,0x7d,0x65, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x02, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x03, + 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2c, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00,0x00,0x07, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x0b,0x7b,0xeb,0xa3,0x4f,0xeb,0x64,0x7d,0xa2,0x00,0xbe,0xd0,0x5f,0xad,0x57,0xc0,0x34,0x8d,0x24,0x9e,0x2a,0x90,0xc8,0x8f,0x31,0xf9,0x94,0x8b,0xb6,0x5d,0x52,0x07, + 0x21,0x0c,0x79,0x05,0x73,0x63,0x23,0x59,0xb1,0xed,0xb4,0x30,0x2c,0x11,0x7d,0x8a,0x13,0x26,0x54,0x69,0x2c,0x3f,0xee,0xb7,0xde,0x3a,0x86,0xac,0x3f,0x3b,0x53,0xf7, + 0x42,0x18,0xf2,0x0a,0xe6,0xc6,0x46,0xb3,0x63,0xdb,0x68,0x60,0x58,0x22,0xfb,0x14,0x26,0x4c,0xa8,0xd2,0x58,0x7f,0xdd,0x6f,0xbc,0x75,0x0d,0x58,0x7e,0x76,0xa7,0xee, + 0x39,0xf8,0x83,0xf1,0x05,0xac,0x7f,0x09,0xf4,0xe7,0xe4,0xdc,0xc8,0x4b,0xc7,0xff,0x4b,0x3b,0x74,0xf3,0x01,0xef,0xaa,0xaf,0x8b,0x63,0x8f,0x47,0x72,0x0f,0xda,0xec, + 0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x50, + 0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa, + 0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33, + 0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcc,0xcb, + 0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0f,0x0c, + 0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0,0xf0, + 0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff, + 0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00,0xff,0x00, + 0x7f,0xff,0x00,0x01,0xff,0xfc,0x00,0x07,0xff,0xf0,0x00,0x1f,0xff,0xc0,0x00,0x7f,0xff,0x00,0x01,0xff,0xfc,0x00,0x07,0xff,0xf0,0x00,0x1f,0xff,0xc0,0x00,0x7f,0xff, + 0x80,0x00,0xff,0xfe,0x00,0x03,0xff,0xf8,0x00,0x0f,0xff,0xe0,0x00,0x3f,0xff,0x80,0x00,0xff,0xfe,0x00,0x03,0xff,0xf8,0x00,0x0f,0xff,0xe0,0x00,0x3f,0xff,0x7f,0xff, + 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0x5b,0x34,0xa2,0x9b,0x1c,0x4d,0xdc,0xb2,0x10,0x11,0x62,0xd3,0x4b,0xed,0x9f,0x07,0x02,0x36,0x1f,0xe5,0xaf,0x50,0x5d,0xf3,0x15,0xef,0xf7,0xbe,0xfd,0x0e,0x47,0x19, + 0xce,0xce,0x52,0x1b,0x8b,0x5a,0x32,0xbb,0xee,0x38,0x93,0x6b,0xa7,0xd6,0x45,0x82,0x4f,0x23,0x8e,0x56,0x17,0x01,0xa3,0x86,0xfb,0x88,0x8e,0x01,0x0d,0xb5,0x4b,0x2f, + 0x82,0x95,0x21,0xb7,0x9d,0x71,0xf5,0x01,0x1e,0x07,0x97,0x56,0xb8,0x51,0xa0,0xd5,0xc8,0x35,0x57,0x86,0x61,0x89,0xa6,0x25,0x8c,0x1e,0x78,0xa1,0x70,0x0c,0x69,0x04, + 0x8c,0x59,0x34,0x79,0x35,0x05,0xa6,0xa1,0xf8,0x4d,0x41,0x28,0x33,0x41,0x68,0x0c,0x49,0x23,0xf1,0xf4,0xd5,0x62,0x98,0x9a,0x11,0xcc,0x62,0x6f,0xea,0x5e,0xda,0x5a, + 0x35,0x6c,0xae,0xe7,0xe7,0xee,0xe0,0x31,0xa1,0x5e,0x54,0xc3,0xa5,0xc4,0xe7,0x2f,0x9c,0x74,0xbb,0x28,0x7c,0xe6,0x01,0x61,0x9e,0xf8,0x5e,0xb9,0x6c,0x28,0x94,0x52, + 0x09,0xc7,0x33,0x7d,0xf6,0xc2,0xb3,0x5e,0xdf,0x3a,0x21,0x38,0x25,0x11,0xcc,0x5a,0xdd,0x1a,0x71,0xa8,0x4c,0xbf,0x8d,0x33,0x96,0xa5,0xbe,0x54,0x8d,0x92,0xfa,0x67, + 0xd1,0x6c,0xae,0xdd,0x25,0x79,0x36,0x66,0xf9,0xe2,0x6f,0x53,0x31,0x38,0x21,0x06,0xf5,0x40,0x95,0xb3,0xd2,0x0d,0x40,0xc7,0x45,0xb6,0x8c,0xa7,0x6c,0x0e,0x69,0x83, + 0xb8,0xae,0x1e,0x21,0xd8,0xb3,0x4c,0xe4,0xca,0xff,0xed,0x71,0x67,0xa2,0x68,0x68,0xec,0x80,0xa7,0xd4,0xa6,0xa9,0x8b,0x63,0x9d,0x4d,0x05,0xcd,0x22,0x65,0x04,0xde, + 0x02,0x77,0x63,0x15,0xfe,0x14,0x7a,0x36,0xa4,0xb0,0x98,0x74,0x92,0xb6,0x50,0x3a,0xcd,0xea,0x60,0xf9,0x26,0x45,0x0e,0x5e,0xdd,0xb9,0xf8,0x8f,0xc8,0x21,0x78,0xd3, + 0x39,0x88,0xc9,0xc7,0x05,0x0a,0x28,0x79,0x49,0x34,0xe5,0xbd,0x67,0x62,0x9b,0x55,0x6d,0x97,0xa4,0x85,0x8d,0x22,0x81,0x28,0x35,0xf4,0xa3,0x7d,0xca,0x35,0x19,0x43, + 0x34,0x00,0x56,0x94,0xe3,0xca,0xc0,0x93,0x32,0xaa,0x42,0x80,0x7e,0x3a,0xfd,0xc3,0xb3,0xb3,0xbc,0x7c,0x7b,0xe8,0x87,0xd1,0xf9,0x8d,0x76,0x77,0x8c,0x55,0xcf,0xd7, + 0x4b,0x52,0x25,0x7d,0x8b,0x3b,0xa3,0x87,0x79,0x7f,0xdf,0x7a,0x75,0x2f,0x19,0x5d,0xdc,0x4f,0x7d,0x76,0x26,0x3d,0xe6,0x1d,0x0d,0x52,0xa5,0xec,0x14,0xa3,0x6c,0xbf}; + +static const wycheproof_ecdh_testvector testvectors[SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS] = { + /* tcId: 1. normal case */ + {0, 65, 0, 32, 0, 32, 1 }, + /* tcId: 2. compressed public key */ + {65, 33, 0, 32, 32, 32, 1 }, + /* tcId: 3. shared secret has x-coordinate that satisfies x**2 + a = 1 */ + {98, 65, 32, 32, 64, 32, 1 }, + /* tcId: 4. shared secret has x-coordinate that satisfies x**2 + a = 4 */ + {163, 65, 32, 32, 96, 32, 1 }, + /* tcId: 5. shared secret has x-coordinate that satisfies x**2 + a = 9 */ + {228, 65, 32, 32, 128, 32, 1 }, + /* tcId: 6. shared secret has x-coordinate p-3 */ + {293, 65, 32, 32, 160, 32, 1 }, + /* tcId: 7. shared secret has x-coordinate 2**16 + 0 */ + {358, 65, 32, 32, 192, 32, 1 }, + /* tcId: 8. shared secret has x-coordinate 2**32 + 7 */ + {423, 65, 32, 32, 224, 32, 1 }, + /* tcId: 9. shared secret has x-coordinate 2**64 + 1 */ + {488, 65, 32, 32, 256, 32, 1 }, + /* tcId: 10. shared secret has x-coordinate 2**96 + 1 */ + {553, 65, 32, 32, 288, 32, 1 }, + /* tcId: 11. shared secret has x-coordinate that satisfies x**2 + a = -6 */ + {618, 65, 32, 32, 320, 32, 1 }, + /* tcId: 12. shared secret has x-coordinate that satisfies x**2 + a = 2 */ + {683, 65, 32, 32, 352, 32, 1 }, + /* tcId: 13. shared secret has x-coordinate that satisfies x**2 + a = 8 */ + {748, 65, 32, 32, 384, 32, 1 }, + /* tcId: 14. shared secret has x-coordinate that satisfies x**2 = 2**96 + 2 */ + {813, 65, 32, 32, 416, 32, 1 }, + /* tcId: 15. shared secret has x-coordinate with repeating bit-pattern of size 2 */ + {878, 65, 32, 32, 448, 32, 1 }, + /* tcId: 16. shared secret has x-coordinate with repeating bit-pattern of size 2 */ + {943, 65, 32, 32, 480, 32, 1 }, + /* tcId: 17. shared secret has x-coordinate with repeating bit-pattern of size 4 */ + {1008, 65, 32, 32, 512, 32, 1 }, + /* tcId: 18. shared secret has x-coordinate with repeating bit-pattern of size 4 */ + {1073, 65, 32, 32, 544, 32, 1 }, + /* tcId: 19. shared secret has x-coordinate with repeating bit-pattern of size 8 */ + {1138, 65, 32, 32, 576, 32, 1 }, + /* tcId: 20. shared secret has x-coordinate with repeating bit-pattern of size 8 */ + {1203, 65, 32, 32, 608, 32, 1 }, + /* tcId: 21. shared secret has x-coordinate with repeating bit-pattern of size 16 */ + {1268, 65, 32, 32, 640, 32, 1 }, + /* tcId: 22. shared secret has x-coordinate with repeating bit-pattern of size 16 */ + {1333, 65, 32, 32, 672, 32, 1 }, + /* tcId: 23. shared secret has x-coordinate with repeating bit-pattern of size 30 */ + {1398, 65, 32, 32, 704, 32, 1 }, + /* tcId: 24. shared secret has x-coordinate with repeating bit-pattern of size 30 */ + {1463, 65, 32, 32, 736, 32, 1 }, + /* tcId: 25. shared secret has x-coordinate with repeating bit-pattern of size 32 */ + {1528, 65, 32, 32, 768, 32, 1 }, + /* tcId: 26. shared secret has x-coordinate with repeating bit-pattern of size 32 */ + {1593, 65, 32, 32, 800, 32, 1 }, + /* tcId: 27. shared secret has x-coordinate with repeating bit-pattern of size 51 */ + {1658, 65, 32, 32, 832, 32, 1 }, + /* tcId: 28. shared secret has x-coordinate with repeating bit-pattern of size 51 */ + {1723, 65, 32, 32, 864, 32, 1 }, + /* tcId: 29. shared secret has x-coordinate with repeating bit-pattern of size 52 */ + {1788, 65, 32, 32, 896, 32, 1 }, + /* tcId: 30. shared secret has x-coordinate with repeating bit-pattern of size 52 */ + {1853, 65, 32, 32, 928, 32, 1 }, + /* tcId: 31. shared secret has x-coordinate with repeating bit-pattern of size 60 */ + {1918, 65, 32, 32, 960, 32, 1 }, + /* tcId: 32. shared secret has x-coordinate with repeating bit-pattern of size 60 */ + {1983, 65, 32, 32, 992, 32, 1 }, + /* tcId: 33. shared secret has x-coordinate with repeating bit-pattern of size 62 */ + {2048, 65, 32, 32, 1024, 32, 1 }, + /* tcId: 34. shared secret has x-coordinate with repeating bit-pattern of size 62 */ + {2113, 65, 32, 32, 1056, 32, 1 }, + /* tcId: 35. shared secret has x-coordinate with repeating bit-pattern of size 64 */ + {2178, 65, 32, 32, 1088, 32, 1 }, + /* tcId: 36. shared secret has x-coordinate with repeating bit-pattern of size 64 */ + {2243, 65, 32, 32, 1120, 32, 1 }, + /* tcId: 37. shared secret has x-coordinate with repeating bit-pattern of size 112 */ + {2308, 65, 32, 32, 1152, 32, 1 }, + /* tcId: 38. shared secret has x-coordinate with repeating bit-pattern of size 112 */ + {2373, 65, 32, 32, 1184, 32, 1 }, + /* tcId: 39. shared secret has x-coordinate with repeating bit-pattern of size 128 */ + {2438, 65, 32, 32, 1216, 32, 1 }, + /* tcId: 40. shared secret has x-coordinate with repeating bit-pattern of size 128 */ + {2503, 65, 32, 32, 1248, 32, 1 }, + /* tcId: 41. shared secret has an x-coordinate of approx p//3 */ + {2568, 65, 32, 32, 1280, 32, 1 }, + /* tcId: 42. shared secret has an x-coordinate of approx p//5 */ + {2633, 65, 32, 32, 1312, 32, 1 }, + /* tcId: 43. shared secret has an x-coordinate of approx p//7 */ + {2698, 65, 32, 32, 1344, 32, 1 }, + /* tcId: 44. shared secret has an x-coordinate of approx p//9 */ + {2763, 65, 32, 32, 1376, 32, 1 }, + /* tcId: 45. y-coordinate of the public key has many trailing 1's */ + {2828, 65, 32, 32, 1408, 32, 1 }, + /* tcId: 46. y-coordinate of the public key has many trailing 1's */ + {2893, 65, 64, 32, 1440, 32, 1 }, + /* tcId: 47. y-coordinate of the public key is small */ + {2958, 65, 32, 32, 1472, 32, 1 }, + /* tcId: 48. y-coordinate of the public key is small */ + {3023, 65, 32, 32, 1504, 32, 1 }, + /* tcId: 49. y-coordinate of the public key is small */ + {3088, 65, 64, 32, 1536, 32, 1 }, + /* tcId: 50. y-coordinate of the public key is small */ + {3153, 65, 64, 32, 1568, 32, 1 }, + /* tcId: 51. y-coordinate of the public key is large */ + {3218, 65, 32, 32, 1600, 32, 1 }, + /* tcId: 52. y-coordinate of the public key is large */ + {3283, 65, 32, 32, 1632, 32, 1 }, + /* tcId: 53. y-coordinate of the public key is large */ + {3348, 65, 64, 32, 1664, 32, 1 }, + /* tcId: 54. y-coordinate of the public key is large */ + {3413, 65, 64, 32, 1696, 32, 1 }, + /* tcId: 55. y-coordinate of the public key has many trailing 0's */ + {3478, 65, 32, 32, 1728, 32, 1 }, + /* tcId: 56. y-coordinate of the public key has many trailing 0's */ + {3543, 65, 64, 32, 1760, 32, 1 }, + /* tcId: 57. ephemeral key has x-coordinate that satisfies x**2 + a = 1 */ + {3608, 65, 64, 32, 1792, 32, 1 }, + /* tcId: 58. ephemeral key has x-coordinate that satisfies x**2 + a = 4 */ + {3673, 65, 64, 32, 1824, 32, 1 }, + /* tcId: 59. ephemeral key has x-coordinate that satisfies x**2 + a = 9 */ + {3738, 65, 64, 32, 1856, 32, 1 }, + /* tcId: 60. ephemeral key has x-coordinate p-3 */ + {3803, 65, 64, 32, 1888, 32, 1 }, + /* tcId: 61. ephemeral key has x-coordinate 2**16 + 0 */ + {3868, 65, 64, 32, 1920, 32, 1 }, + /* tcId: 62. ephemeral key has x-coordinate 2**32 + 7 */ + {3933, 65, 64, 32, 1952, 32, 1 }, + /* tcId: 63. ephemeral key has x-coordinate 2**64 + 1 */ + {3998, 65, 64, 32, 1984, 32, 1 }, + /* tcId: 64. ephemeral key has x-coordinate 2**96 + 1 */ + {4063, 65, 64, 32, 2016, 32, 1 }, + /* tcId: 65. ephemeral key has x-coordinate that satisfies x**2 + a = -6 */ + {4128, 65, 64, 32, 2048, 32, 1 }, + /* tcId: 66. ephemeral key has x-coordinate that satisfies x**2 + a = 2 */ + {4193, 65, 64, 32, 2080, 32, 1 }, + /* tcId: 67. ephemeral key has x-coordinate that satisfies x**2 + a = 8 */ + {4258, 65, 64, 32, 2112, 32, 1 }, + /* tcId: 68. ephemeral key has x-coordinate that satisfies x**2 = 2**96 + 2 */ + {4323, 65, 64, 32, 2144, 32, 1 }, + /* tcId: 69. ephemeral key has x-coordinate with repeating bit-pattern of size 2 */ + {4388, 65, 64, 32, 2176, 32, 1 }, + /* tcId: 70. ephemeral key has x-coordinate with repeating bit-pattern of size 2 */ + {4453, 65, 64, 32, 2208, 32, 1 }, + /* tcId: 71. ephemeral key has x-coordinate with repeating bit-pattern of size 4 */ + {4518, 65, 64, 32, 2240, 32, 1 }, + /* tcId: 72. ephemeral key has x-coordinate with repeating bit-pattern of size 4 */ + {4583, 65, 64, 32, 2272, 32, 1 }, + /* tcId: 73. ephemeral key has x-coordinate with repeating bit-pattern of size 8 */ + {4648, 65, 64, 32, 2304, 32, 1 }, + /* tcId: 74. ephemeral key has x-coordinate with repeating bit-pattern of size 8 */ + {4713, 65, 64, 32, 2336, 32, 1 }, + /* tcId: 75. ephemeral key has x-coordinate with repeating bit-pattern of size 16 */ + {4778, 65, 64, 32, 2368, 32, 1 }, + /* tcId: 76. ephemeral key has x-coordinate with repeating bit-pattern of size 16 */ + {4843, 65, 64, 32, 2400, 32, 1 }, + /* tcId: 77. ephemeral key has x-coordinate with repeating bit-pattern of size 30 */ + {4908, 65, 64, 32, 2432, 32, 1 }, + /* tcId: 78. ephemeral key has x-coordinate with repeating bit-pattern of size 30 */ + {4973, 65, 64, 32, 2464, 32, 1 }, + /* tcId: 79. ephemeral key has x-coordinate with repeating bit-pattern of size 32 */ + {5038, 65, 64, 32, 2496, 32, 1 }, + /* tcId: 80. ephemeral key has x-coordinate with repeating bit-pattern of size 32 */ + {5103, 65, 64, 32, 2528, 32, 1 }, + /* tcId: 81. ephemeral key has x-coordinate with repeating bit-pattern of size 51 */ + {5168, 65, 64, 32, 2560, 32, 1 }, + /* tcId: 82. ephemeral key has x-coordinate with repeating bit-pattern of size 51 */ + {5233, 65, 64, 32, 2592, 32, 1 }, + /* tcId: 83. ephemeral key has x-coordinate with repeating bit-pattern of size 52 */ + {5298, 65, 64, 32, 2624, 32, 1 }, + /* tcId: 84. ephemeral key has x-coordinate with repeating bit-pattern of size 52 */ + {5363, 65, 64, 32, 2656, 32, 1 }, + /* tcId: 85. ephemeral key has x-coordinate with repeating bit-pattern of size 60 */ + {5428, 65, 64, 32, 2688, 32, 1 }, + /* tcId: 86. ephemeral key has x-coordinate with repeating bit-pattern of size 60 */ + {5493, 65, 64, 32, 2720, 32, 1 }, + /* tcId: 87. ephemeral key has x-coordinate with repeating bit-pattern of size 62 */ + {5558, 65, 64, 32, 2752, 32, 1 }, + /* tcId: 88. ephemeral key has x-coordinate with repeating bit-pattern of size 62 */ + {5623, 65, 64, 32, 2784, 32, 1 }, + /* tcId: 89. ephemeral key has x-coordinate with repeating bit-pattern of size 64 */ + {5688, 65, 64, 32, 2816, 32, 1 }, + /* tcId: 90. ephemeral key has x-coordinate with repeating bit-pattern of size 64 */ + {5753, 65, 64, 32, 2848, 32, 1 }, + /* tcId: 91. ephemeral key has x-coordinate with repeating bit-pattern of size 112 */ + {5818, 65, 64, 32, 2880, 32, 1 }, + /* tcId: 92. ephemeral key has x-coordinate with repeating bit-pattern of size 112 */ + {5883, 65, 64, 32, 2912, 32, 1 }, + /* tcId: 93. ephemeral key has x-coordinate with repeating bit-pattern of size 128 */ + {5948, 65, 64, 32, 2944, 32, 1 }, + /* tcId: 94. ephemeral key has x-coordinate with repeating bit-pattern of size 128 */ + {6013, 65, 64, 32, 2976, 32, 1 }, + /* tcId: 95. ephemeral key has an x-coordinate of approx p//3 */ + {6078, 65, 64, 32, 3008, 32, 1 }, + /* tcId: 96. ephemeral key has an x-coordinate of approx p//5 */ + {6143, 65, 64, 32, 3040, 32, 1 }, + /* tcId: 97. ephemeral key has an x-coordinate of approx p//7 */ + {6208, 65, 64, 32, 3072, 32, 1 }, + /* tcId: 98. ephemeral key has an x-coordinate of approx p//9 */ + {6273, 65, 64, 32, 3104, 32, 1 }, + /* tcId: 99. edge case for Jacobian and projective coordinates */ + {6338, 65, 96, 32, 3136, 32, 1 }, + /* tcId: 100. edge case for Jacobian and projective coordinates */ + {6403, 65, 96, 32, 3168, 32, 1 }, + /* tcId: 101. edge case for Jacobian and projective coordinates */ + {6468, 65, 96, 32, 3200, 32, 1 }, + /* tcId: 102. edge case for Jacobian and projective coordinates */ + {6533, 65, 128, 32, 3232, 32, 1 }, + /* tcId: 103. edge case for Jacobian and projective coordinates */ + {6598, 65, 128, 32, 3264, 32, 1 }, + /* tcId: 104. edge case for Jacobian and projective coordinates */ + {6663, 65, 128, 32, 3296, 32, 1 }, + /* tcId: 105. edge case for Jacobian and projective coordinates in left to right addition chain */ + {6728, 65, 96, 32, 3328, 32, 1 }, + /* tcId: 106. edge case for Jacobian and projective coordinates in left to right addition chain */ + {6793, 65, 96, 32, 3360, 32, 1 }, + /* tcId: 107. edge case for Jacobian and projective coordinates in left to right addition chain */ + {6858, 65, 96, 32, 3392, 32, 1 }, + /* tcId: 108. edge case for Jacobian and projective coordinates in left to right addition chain */ + {6923, 65, 96, 32, 3424, 32, 1 }, + /* tcId: 109. edge case for Jacobian and projective coordinates in left to right addition chain */ + {6988, 65, 96, 32, 3456, 32, 1 }, + /* tcId: 110. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7053, 65, 96, 32, 3488, 32, 1 }, + /* tcId: 111. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7118, 65, 96, 32, 3520, 32, 1 }, + /* tcId: 112. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7183, 65, 96, 32, 3552, 32, 1 }, + /* tcId: 113. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7248, 65, 96, 32, 3584, 32, 1 }, + /* tcId: 114. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7313, 65, 96, 32, 3616, 32, 1 }, + /* tcId: 115. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7378, 65, 96, 32, 3648, 32, 1 }, + /* tcId: 116. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7443, 65, 96, 32, 3680, 32, 1 }, + /* tcId: 117. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7508, 65, 96, 32, 3712, 32, 1 }, + /* tcId: 118. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7573, 65, 96, 32, 3744, 32, 1 }, + /* tcId: 119. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7638, 65, 96, 32, 3776, 32, 1 }, + /* tcId: 120. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7703, 65, 96, 32, 3808, 32, 1 }, + /* tcId: 121. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7768, 65, 128, 32, 3840, 32, 1 }, + /* tcId: 122. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7833, 65, 128, 32, 3872, 32, 1 }, + /* tcId: 123. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7898, 65, 128, 32, 3904, 32, 1 }, + /* tcId: 124. edge case for Jacobian and projective coordinates in left to right addition chain */ + {7963, 65, 128, 32, 3936, 32, 1 }, + /* tcId: 125. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8028, 65, 128, 32, 3968, 32, 1 }, + /* tcId: 126. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8093, 65, 128, 32, 4000, 32, 1 }, + /* tcId: 127. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8158, 65, 128, 32, 4032, 32, 1 }, + /* tcId: 128. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8223, 65, 128, 32, 4064, 32, 1 }, + /* tcId: 129. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8288, 65, 128, 32, 4096, 32, 1 }, + /* tcId: 130. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8353, 65, 128, 32, 4128, 32, 1 }, + /* tcId: 131. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8418, 65, 128, 32, 4160, 32, 1 }, + /* tcId: 132. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8483, 65, 128, 32, 4192, 32, 1 }, + /* tcId: 133. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8548, 65, 128, 32, 4224, 32, 1 }, + /* tcId: 134. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8613, 65, 128, 32, 4256, 32, 1 }, + /* tcId: 135. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8678, 65, 128, 32, 4288, 32, 1 }, + /* tcId: 136. edge case for Jacobian and projective coordinates in left to right addition chain */ + {8743, 65, 128, 32, 4320, 32, 1 }, + /* tcId: 137. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {8808, 65, 128, 32, 4352, 32, 1 }, + /* tcId: 138. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {8873, 65, 128, 32, 4384, 32, 1 }, + /* tcId: 139. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {8938, 65, 128, 32, 4416, 32, 1 }, + /* tcId: 140. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9003, 65, 128, 32, 4448, 32, 1 }, + /* tcId: 141. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9068, 65, 128, 32, 4480, 32, 1 }, + /* tcId: 142. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9133, 65, 128, 32, 4512, 32, 1 }, + /* tcId: 143. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9198, 65, 128, 32, 4544, 32, 1 }, + /* tcId: 144. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9263, 65, 128, 32, 4576, 32, 1 }, + /* tcId: 145. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9328, 65, 128, 32, 4608, 32, 1 }, + /* tcId: 146. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9393, 65, 128, 32, 4640, 32, 1 }, + /* tcId: 147. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9458, 65, 128, 32, 4672, 32, 1 }, + /* tcId: 148. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ + {9523, 65, 128, 32, 4704, 32, 1 }, + /* tcId: 149. edge case for Jacobian and projective coordinates in right to left addition chain */ + {9588, 65, 128, 32, 4736, 32, 1 }, + /* tcId: 150. edge case for Jacobian and projective coordinates in right to left addition chain */ + {9653, 65, 128, 32, 4768, 32, 1 }, + /* tcId: 151. edge case for Jacobian and projective coordinates in right to left addition chain */ + {9718, 65, 128, 32, 4800, 32, 1 }, + /* tcId: 152. edge case for Jacobian and projective coordinates in right to left addition chain */ + {9783, 65, 128, 32, 4832, 32, 1 }, + /* tcId: 153. edge case for Jacobian and projective coordinates in right to left addition chain */ + {9848, 65, 128, 32, 4864, 32, 1 }, + /* tcId: 154. edge case for Jacobian and projective coordinates in right to left addition chain */ + {9913, 65, 128, 32, 4896, 32, 1 }, + /* tcId: 155. edge case for Jacobian and projective coordinates in right to left addition chain */ + {9978, 65, 128, 32, 4928, 32, 1 }, + /* tcId: 156. edge case for Jacobian and projective coordinates in right to left addition chain */ + {10043, 65, 128, 32, 4960, 32, 1 }, + /* tcId: 157. edge case for Jacobian and projective coordinates in right to left addition chain */ + {10108, 65, 128, 32, 4992, 32, 1 }, + /* tcId: 158. edge case for Jacobian and projective coordinates in right to left addition chain */ + {10173, 65, 128, 32, 5024, 32, 1 }, + /* tcId: 159. edge case for computation of x with projective coordinates */ + {10238, 65, 128, 32, 5056, 32, 1 }, + /* tcId: 160. edge case for computation of x with projective coordinates */ + {10303, 65, 128, 32, 5088, 32, 1 }, + /* tcId: 161. edge case for computation of x with projective coordinates */ + {10368, 65, 128, 32, 5120, 32, 1 }, + /* tcId: 162. edge case for computation of x with projective coordinates */ + {10433, 65, 128, 32, 5152, 32, 1 }, + /* tcId: 163. edge case for computation of x with projective coordinates */ + {10498, 65, 128, 32, 5184, 32, 1 }, + /* tcId: 164. edge case for computation of x with projective coordinates */ + {10563, 65, 128, 32, 5216, 32, 1 }, + /* tcId: 165. edge case for computation of x with projective coordinates */ + {10628, 65, 128, 32, 5248, 32, 1 }, + /* tcId: 166. edge case for computation of x with projective coordinates */ + {10693, 65, 128, 32, 5280, 32, 1 }, + /* tcId: 167. edge case for computation of x with projective coordinates */ + {10758, 65, 128, 32, 5312, 32, 1 }, + /* tcId: 168. edge case for computation of x with projective coordinates in left to right addition chain */ + {10823, 65, 128, 32, 5344, 32, 1 }, + /* tcId: 169. edge case for computation of x with projective coordinates in left to right addition chain */ + {10888, 65, 128, 32, 5376, 32, 1 }, + /* tcId: 170. edge case for computation of x with projective coordinates in left to right addition chain */ + {10953, 65, 128, 32, 5408, 32, 1 }, + /* tcId: 171. edge case for computation of x with projective coordinates in left to right addition chain */ + {11018, 65, 128, 32, 5440, 32, 1 }, + /* tcId: 172. edge case for computation of x with projective coordinates in left to right addition chain */ + {11083, 65, 128, 32, 5472, 32, 1 }, + /* tcId: 173. edge case for computation of x with projective coordinates in left to right addition chain */ + {11148, 65, 128, 32, 5504, 32, 1 }, + /* tcId: 174. edge case for computation of x with projective coordinates in left to right addition chain */ + {11213, 65, 128, 32, 5536, 32, 1 }, + /* tcId: 175. edge case for computation of x with projective coordinates in left to right addition chain */ + {11278, 65, 128, 32, 5568, 32, 1 }, + /* tcId: 176. edge case for computation of x with projective coordinates in left to right addition chain */ + {11343, 65, 128, 32, 5600, 32, 1 }, + /* tcId: 177. edge case for computation of x with projective coordinates in left to right addition chain */ + {11408, 65, 128, 32, 5632, 32, 1 }, + /* tcId: 178. edge case for computation of x with projective coordinates in left to right addition chain */ + {11473, 65, 128, 32, 5664, 32, 1 }, + /* tcId: 179. edge case for computation of x with projective coordinates in left to right addition chain */ + {11538, 65, 128, 32, 5696, 32, 1 }, + /* tcId: 180. edge case for computation of x with projective coordinates in left to right addition chain */ + {11603, 65, 128, 32, 5728, 32, 1 }, + /* tcId: 181. edge case for computation of x with projective coordinates in left to right addition chain */ + {11668, 65, 128, 32, 5760, 32, 1 }, + /* tcId: 182. edge case for computation of x with projective coordinates in left to right addition chain */ + {11733, 65, 128, 32, 5792, 32, 1 }, + /* tcId: 183. edge case for computation of x with projective coordinates in left to right addition chain */ + {11798, 65, 128, 32, 5824, 32, 1 }, + /* tcId: 184. edge case for computation of x with projective coordinates in left to right addition chain */ + {11863, 65, 128, 32, 5856, 32, 1 }, + /* tcId: 185. edge case for computation of x with projective coordinates in left to right addition chain */ + {11928, 65, 128, 32, 5888, 32, 1 }, + /* tcId: 186. edge case for computation of x with projective coordinates in left to right addition chain */ + {11993, 65, 128, 32, 5920, 32, 1 }, + /* tcId: 187. edge case for computation of x with projective coordinates in left to right addition chain */ + {12058, 65, 128, 32, 5952, 32, 1 }, + /* tcId: 188. edge case for computation of x with projective coordinates in left to right addition chain */ + {12123, 65, 128, 32, 5984, 32, 1 }, + /* tcId: 189. edge case for computation of x with projective coordinates in left to right addition chain */ + {12188, 65, 128, 32, 6016, 32, 1 }, + /* tcId: 190. edge case for computation of x with projective coordinates in left to right addition chain */ + {12253, 65, 128, 32, 6048, 32, 1 }, + /* tcId: 191. edge case for computation of x with projective coordinates in left to right addition chain */ + {12318, 65, 128, 32, 6080, 32, 1 }, + /* tcId: 192. edge case for computation of x with projective coordinates in left to right addition chain */ + {12383, 65, 128, 32, 6112, 32, 1 }, + /* tcId: 193. edge case for computation of x with projective coordinates in left to right addition chain */ + {12448, 65, 128, 32, 6144, 32, 1 }, + /* tcId: 194. edge case for computation of x with projective coordinates in left to right addition chain */ + {12513, 65, 128, 32, 6176, 32, 1 }, + /* tcId: 195. edge case for computation of x with projective coordinates in left to right addition chain */ + {12578, 65, 128, 32, 6208, 32, 1 }, + /* tcId: 196. edge case for computation of x with projective coordinates in left to right addition chain */ + {12643, 65, 128, 32, 6240, 32, 1 }, + /* tcId: 197. edge case for computation of x with projective coordinates in left to right addition chain */ + {12708, 65, 128, 32, 6272, 32, 1 }, + /* tcId: 198. edge case for computation of x with projective coordinates in left to right addition chain */ + {12773, 65, 128, 32, 6304, 32, 1 }, + /* tcId: 199. edge case for computation of x with projective coordinates in left to right addition chain */ + {12838, 65, 128, 32, 6336, 32, 1 }, + /* tcId: 200. edge case for computation of x with projective coordinates in left to right addition chain */ + {12903, 65, 128, 32, 6368, 32, 1 }, + /* tcId: 201. edge case for computation of x with projective coordinates in left to right addition chain */ + {12968, 65, 128, 32, 6400, 32, 1 }, + /* tcId: 202. edge case for computation of x with projective coordinates in left to right addition chain */ + {13033, 65, 128, 32, 6432, 32, 1 }, + /* tcId: 203. edge case for computation of x with projective coordinates in left to right addition chain */ + {13098, 65, 128, 32, 6464, 32, 1 }, + /* tcId: 204. edge case for computation of x with projective coordinates in left to right addition chain */ + {13163, 65, 128, 32, 6496, 32, 1 }, + /* tcId: 205. edge case for computation of x with projective coordinates in left to right addition chain */ + {13228, 65, 128, 32, 6528, 32, 1 }, + /* tcId: 206. edge case for computation of x with projective coordinates in left to right addition chain */ + {13293, 65, 128, 32, 6560, 32, 1 }, + /* tcId: 207. edge case for computation of x with projective coordinates in left to right addition chain */ + {13358, 65, 128, 32, 6592, 32, 1 }, + /* tcId: 208. edge case for computation of x with projective coordinates in left to right addition chain */ + {13423, 65, 128, 32, 6624, 32, 1 }, + /* tcId: 209. edge case for computation of x with projective coordinates in left to right addition chain */ + {13488, 65, 128, 32, 6656, 32, 1 }, + /* tcId: 210. edge case for computation of x with projective coordinates in left to right addition chain */ + {13553, 65, 128, 32, 6688, 32, 1 }, + /* tcId: 211. edge case for computation of x with projective coordinates in left to right addition chain */ + {13618, 65, 128, 32, 6720, 32, 1 }, + /* tcId: 212. edge case for computation of x with projective coordinates in left to right addition chain */ + {13683, 65, 128, 32, 6752, 32, 1 }, + /* tcId: 213. edge case for computation of x with projective coordinates in left to right addition chain */ + {13748, 65, 128, 32, 6784, 32, 1 }, + /* tcId: 214. edge case for computation of x with projective coordinates in left to right addition chain */ + {13813, 65, 128, 32, 6816, 32, 1 }, + /* tcId: 215. edge case for computation of x with projective coordinates in left to right addition chain */ + {13878, 65, 128, 32, 6848, 32, 1 }, + /* tcId: 216. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {13943, 65, 128, 32, 6880, 32, 1 }, + /* tcId: 217. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14008, 65, 128, 32, 6912, 32, 1 }, + /* tcId: 218. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14073, 65, 128, 32, 6944, 32, 1 }, + /* tcId: 219. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14138, 65, 128, 32, 6976, 32, 1 }, + /* tcId: 220. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14203, 65, 128, 32, 7008, 32, 1 }, + /* tcId: 221. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14268, 65, 128, 32, 7040, 32, 1 }, + /* tcId: 222. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14333, 65, 128, 32, 7072, 32, 1 }, + /* tcId: 223. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14398, 65, 128, 32, 7104, 32, 1 }, + /* tcId: 224. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14463, 65, 128, 32, 7136, 32, 1 }, + /* tcId: 225. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14528, 65, 128, 32, 7168, 32, 1 }, + /* tcId: 226. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14593, 65, 128, 32, 7200, 32, 1 }, + /* tcId: 227. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14658, 65, 128, 32, 7232, 32, 1 }, + /* tcId: 228. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14723, 65, 128, 32, 7264, 32, 1 }, + /* tcId: 229. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14788, 65, 128, 32, 7296, 32, 1 }, + /* tcId: 230. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14853, 65, 128, 32, 7328, 32, 1 }, + /* tcId: 231. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14918, 65, 128, 32, 7360, 32, 1 }, + /* tcId: 232. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {14983, 65, 128, 32, 7392, 32, 1 }, + /* tcId: 233. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ + {15048, 65, 128, 32, 7424, 32, 1 }, + /* tcId: 234. edge case for computation of x with projective coordinates in right to left addition chain */ + {15113, 65, 128, 32, 7456, 32, 1 }, + /* tcId: 235. edge case for computation of x with projective coordinates in right to left addition chain */ + {15178, 65, 128, 32, 7488, 32, 1 }, + /* tcId: 236. edge case for computation of x with projective coordinates in right to left addition chain */ + {15243, 65, 128, 32, 7520, 32, 1 }, + /* tcId: 237. edge case for computation of x with projective coordinates in right to left addition chain */ + {15308, 65, 128, 32, 7552, 32, 1 }, + /* tcId: 238. edge case for computation of x with projective coordinates in right to left addition chain */ + {15373, 65, 128, 32, 7584, 32, 1 }, + /* tcId: 239. edge case for computation of x with projective coordinates in right to left addition chain */ + {15438, 65, 128, 32, 7616, 32, 1 }, + /* tcId: 240. edge case for computation of x with projective coordinates in right to left addition chain */ + {15503, 65, 128, 32, 7648, 32, 1 }, + /* tcId: 241. edge case for computation of x with projective coordinates in right to left addition chain */ + {15568, 65, 128, 32, 7680, 32, 1 }, + /* tcId: 242. edge case for computation of x with projective coordinates in right to left addition chain */ + {15633, 65, 128, 32, 7712, 32, 1 }, + /* tcId: 243. edge case for computation of x with projective coordinates in right to left addition chain */ + {15698, 65, 128, 32, 7744, 32, 1 }, + /* tcId: 244. edge case for computation of x with projective coordinates in right to left addition chain */ + {15763, 65, 128, 32, 7776, 32, 1 }, + /* tcId: 245. edge case for computation of x with projective coordinates in right to left addition chain */ + {15828, 65, 128, 32, 7808, 32, 1 }, + /* tcId: 246. edge case for computation of x with projective coordinates in right to left addition chain */ + {15893, 65, 128, 32, 7840, 32, 1 }, + /* tcId: 247. edge case for computation of x with projective coordinates in right to left addition chain */ + {15958, 65, 128, 32, 7872, 32, 1 }, + /* tcId: 248. edge case for computation of x with projective coordinates in right to left addition chain */ + {16023, 65, 128, 32, 7904, 32, 1 }, + /* tcId: 249. edge case for computation of y with projective coordinates */ + {16088, 65, 128, 32, 7936, 32, 1 }, + /* tcId: 250. edge case for computation of y with projective coordinates */ + {16153, 65, 128, 32, 7968, 32, 1 }, + /* tcId: 251. edge case for computation of y with projective coordinates */ + {16218, 65, 128, 32, 8000, 32, 1 }, + /* tcId: 252. edge case for computation of y with projective coordinates in left to right addition chain */ + {16283, 65, 128, 32, 8032, 32, 1 }, + /* tcId: 253. edge case for computation of y with projective coordinates in left to right addition chain */ + {16348, 65, 128, 32, 8064, 32, 1 }, + /* tcId: 254. edge case for computation of y with projective coordinates in left to right addition chain */ + {16413, 65, 128, 32, 8096, 32, 1 }, + /* tcId: 255. edge case for computation of y with projective coordinates in left to right addition chain */ + {16478, 65, 128, 32, 8128, 32, 1 }, + /* tcId: 256. edge case for computation of y with projective coordinates in left to right addition chain */ + {16543, 65, 128, 32, 8160, 32, 1 }, + /* tcId: 257. edge case for computation of y with projective coordinates in left to right addition chain */ + {16608, 65, 128, 32, 8192, 32, 1 }, + /* tcId: 258. edge case for computation of y with projective coordinates in left to right addition chain */ + {16673, 65, 128, 32, 8224, 32, 1 }, + /* tcId: 259. edge case for computation of y with projective coordinates in left to right addition chain */ + {16738, 65, 128, 32, 8256, 32, 1 }, + /* tcId: 260. edge case for computation of y with projective coordinates in left to right addition chain */ + {16803, 65, 128, 32, 8288, 32, 1 }, + /* tcId: 261. edge case for computation of y with projective coordinates in left to right addition chain */ + {16868, 65, 128, 32, 8320, 32, 1 }, + /* tcId: 262. edge case for computation of y with projective coordinates in left to right addition chain */ + {16933, 65, 128, 32, 8352, 32, 1 }, + /* tcId: 263. edge case for computation of y with projective coordinates in left to right addition chain */ + {16998, 65, 128, 32, 8384, 32, 1 }, + /* tcId: 264. edge case for computation of y with projective coordinates in left to right addition chain */ + {17063, 65, 128, 32, 8416, 32, 1 }, + /* tcId: 265. edge case for computation of y with projective coordinates in left to right addition chain */ + {17128, 65, 128, 32, 8448, 32, 1 }, + /* tcId: 266. edge case for computation of y with projective coordinates in left to right addition chain */ + {17193, 65, 128, 32, 8480, 32, 1 }, + /* tcId: 267. edge case for computation of y with projective coordinates in left to right addition chain */ + {17258, 65, 128, 32, 8512, 32, 1 }, + /* tcId: 268. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ + {17323, 65, 128, 32, 8544, 32, 1 }, + /* tcId: 269. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ + {17388, 65, 128, 32, 8576, 32, 1 }, + /* tcId: 270. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ + {17453, 65, 128, 32, 8608, 32, 1 }, + /* tcId: 271. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ + {17518, 65, 128, 32, 8640, 32, 1 }, + /* tcId: 272. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ + {17583, 65, 128, 32, 8672, 32, 1 }, + /* tcId: 273. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ + {17648, 65, 128, 32, 8704, 32, 1 }, + /* tcId: 274. edge case for computation of y with projective coordinates in right to left addition chain */ + {17713, 65, 128, 32, 8736, 32, 1 }, + /* tcId: 275. edge case for computation of y with projective coordinates in right to left addition chain */ + {17778, 65, 128, 32, 8768, 32, 1 }, + /* tcId: 276. edge case for computation of y with projective coordinates in right to left addition chain */ + {17843, 65, 128, 32, 8800, 32, 1 }, + /* tcId: 277. edge case for computation of y with projective coordinates in right to left addition chain */ + {17908, 65, 128, 32, 8832, 32, 1 }, + /* tcId: 278. edge case for computation of y with projective coordinates in right to left addition chain */ + {17973, 65, 128, 32, 8864, 32, 1 }, + /* tcId: 279. point with coordinate x = 1 */ + {3608, 65, 128, 32, 8896, 32, 1 }, + /* tcId: 280. point with coordinate x = 1 */ + {18038, 65, 128, 32, 8928, 32, 1 }, + /* tcId: 281. point with coordinate x = 1 */ + {18103, 65, 128, 32, 8960, 32, 1 }, + /* tcId: 282. point with coordinate x = 1 in left to right addition chain */ + {18168, 65, 128, 32, 8992, 32, 1 }, + /* tcId: 283. point with coordinate x = 1 in left to right addition chain */ + {18233, 65, 128, 32, 9024, 32, 1 }, + /* tcId: 284. point with coordinate x = 1 in left to right addition chain */ + {18298, 65, 128, 32, 9056, 32, 1 }, + /* tcId: 285. point with coordinate x = 1 in left to right addition chain */ + {18363, 65, 128, 32, 9088, 32, 1 }, + /* tcId: 286. point with coordinate x = 1 in left to right addition chain */ + {18428, 65, 128, 32, 9120, 32, 1 }, + /* tcId: 287. point with coordinate x = 1 in left to right addition chain */ + {18493, 65, 128, 32, 9152, 32, 1 }, + /* tcId: 288. point with coordinate x = 1 in left to right addition chain */ + {18558, 65, 128, 32, 9184, 32, 1 }, + /* tcId: 289. point with coordinate x = 1 in left to right addition chain */ + {18623, 65, 128, 32, 9216, 32, 1 }, + /* tcId: 290. point with coordinate x = 1 in left to right addition chain */ + {18688, 65, 128, 32, 9248, 32, 1 }, + /* tcId: 291. point with coordinate x = 1 in left to right addition chain */ + {18753, 65, 128, 32, 9280, 32, 1 }, + /* tcId: 292. point with coordinate x = 1 in left to right addition chain */ + {18818, 65, 128, 32, 9312, 32, 1 }, + /* tcId: 293. point with coordinate x = 1 in left to right addition chain */ + {18883, 65, 128, 32, 9344, 32, 1 }, + /* tcId: 294. point with coordinate x = 1 in left to right addition chain */ + {18948, 65, 128, 32, 9376, 32, 1 }, + /* tcId: 295. point with coordinate x = 1 in left to right addition chain */ + {19013, 65, 128, 32, 9408, 32, 1 }, + /* tcId: 296. point with coordinate x = 1 in left to right addition chain */ + {19078, 65, 128, 32, 9440, 32, 1 }, + /* tcId: 297. point with coordinate x = 1 in left to right addition chain */ + {19143, 65, 128, 32, 9472, 32, 1 }, + /* tcId: 298. point with coordinate x = 1 in precomputation or right to left addition chain */ + {19208, 65, 128, 32, 9504, 32, 1 }, + /* tcId: 299. point with coordinate x = 1 in precomputation or right to left addition chain */ + {19273, 65, 128, 32, 9536, 32, 1 }, + /* tcId: 300. point with coordinate x = 1 in precomputation or right to left addition chain */ + {19338, 65, 128, 32, 9568, 32, 1 }, + /* tcId: 301. point with coordinate x = 1 in precomputation or right to left addition chain */ + {19403, 65, 128, 32, 9600, 32, 1 }, + /* tcId: 302. point with coordinate x = 1 in precomputation or right to left addition chain */ + {19468, 65, 128, 32, 9632, 32, 1 }, + /* tcId: 303. point with coordinate x = 1 in precomputation or right to left addition chain */ + {19533, 65, 128, 32, 9664, 32, 1 }, + /* tcId: 304. point with coordinate x = 1 in right to left addition chain */ + {19598, 65, 128, 32, 9696, 32, 1 }, + /* tcId: 305. point with coordinate x = 1 in right to left addition chain */ + {19663, 65, 128, 32, 9728, 32, 1 }, + /* tcId: 306. point with coordinate x = 1 in right to left addition chain */ + {19728, 65, 128, 32, 9760, 32, 1 }, + /* tcId: 307. point with coordinate x = 1 in right to left addition chain */ + {19793, 65, 128, 32, 9792, 32, 1 }, + /* tcId: 308. point with coordinate x = 1 in right to left addition chain */ + {19858, 65, 128, 32, 9824, 32, 1 }, + /* tcId: 309. point with coordinate x = 2 */ + {3673, 65, 128, 32, 9856, 32, 1 }, + /* tcId: 310. point with coordinate x = 2 */ + {19923, 65, 128, 32, 9888, 32, 1 }, + /* tcId: 311. point with coordinate x = 2 */ + {19988, 65, 128, 32, 9920, 32, 1 }, + /* tcId: 312. point with coordinate x = 2 in left to right addition chain */ + {20053, 65, 128, 32, 9952, 32, 1 }, + /* tcId: 313. point with coordinate x = 2 in left to right addition chain */ + {20118, 65, 128, 32, 9984, 32, 1 }, + /* tcId: 314. point with coordinate x = 2 in left to right addition chain */ + {20183, 65, 128, 32, 10016, 32, 1 }, + /* tcId: 315. point with coordinate x = 2 in left to right addition chain */ + {20248, 65, 128, 32, 10048, 32, 1 }, + /* tcId: 316. point with coordinate x = 2 in left to right addition chain */ + {20313, 65, 128, 32, 10080, 32, 1 }, + /* tcId: 317. point with coordinate x = 2 in left to right addition chain */ + {20378, 65, 128, 32, 10112, 32, 1 }, + /* tcId: 318. point with coordinate x = 2 in left to right addition chain */ + {20443, 65, 128, 32, 10144, 32, 1 }, + /* tcId: 319. point with coordinate x = 2 in left to right addition chain */ + {20508, 65, 128, 32, 10176, 32, 1 }, + /* tcId: 320. point with coordinate x = 2 in left to right addition chain */ + {20573, 65, 128, 32, 10208, 32, 1 }, + /* tcId: 321. point with coordinate x = 2 in left to right addition chain */ + {20638, 65, 128, 32, 10240, 32, 1 }, + /* tcId: 322. point with coordinate x = 2 in left to right addition chain */ + {20703, 65, 128, 32, 10272, 32, 1 }, + /* tcId: 323. point with coordinate x = 2 in left to right addition chain */ + {20768, 65, 128, 32, 10304, 32, 1 }, + /* tcId: 324. point with coordinate x = 2 in left to right addition chain */ + {20833, 65, 128, 32, 10336, 32, 1 }, + /* tcId: 325. point with coordinate x = 2 in left to right addition chain */ + {20898, 65, 128, 32, 10368, 32, 1 }, + /* tcId: 326. point with coordinate x = 2 in left to right addition chain */ + {20963, 65, 128, 32, 10400, 32, 1 }, + /* tcId: 327. point with coordinate x = 2 in left to right addition chain */ + {21028, 65, 128, 32, 10432, 32, 1 }, + /* tcId: 328. point with coordinate x = 2 in precomputation or right to left addition chain */ + {21093, 65, 128, 32, 10464, 32, 1 }, + /* tcId: 329. point with coordinate x = 2 in precomputation or right to left addition chain */ + {21158, 65, 128, 32, 10496, 32, 1 }, + /* tcId: 330. point with coordinate x = 2 in precomputation or right to left addition chain */ + {21223, 65, 128, 32, 10528, 32, 1 }, + /* tcId: 331. point with coordinate x = 2 in precomputation or right to left addition chain */ + {21288, 65, 128, 32, 10560, 32, 1 }, + /* tcId: 332. point with coordinate x = 2 in precomputation or right to left addition chain */ + {21353, 65, 128, 32, 10592, 32, 1 }, + /* tcId: 333. point with coordinate x = 2 in precomputation or right to left addition chain */ + {21418, 65, 128, 32, 10624, 32, 1 }, + /* tcId: 334. point with coordinate x = 2 in right to left addition chain */ + {21483, 65, 128, 32, 10656, 32, 1 }, + /* tcId: 335. point with coordinate x = 2 in right to left addition chain */ + {21548, 65, 128, 32, 10688, 32, 1 }, + /* tcId: 336. point with coordinate x = 2 in right to left addition chain */ + {21613, 65, 128, 32, 10720, 32, 1 }, + /* tcId: 337. point with coordinate x = 2 in right to left addition chain */ + {21678, 65, 128, 32, 10752, 32, 1 }, + /* tcId: 338. point with coordinate x = 2 in right to left addition chain */ + {21743, 65, 128, 32, 10784, 32, 1 }, + /* tcId: 339. point with coordinate x = 3 */ + {3738, 65, 128, 32, 10816, 32, 1 }, + /* tcId: 340. point with coordinate x = 3 */ + {21808, 65, 128, 32, 10848, 32, 1 }, + /* tcId: 341. point with coordinate x = 3 */ + {21873, 65, 128, 32, 10880, 32, 1 }, + /* tcId: 342. point with coordinate x = 3 in left to right addition chain */ + {21938, 65, 128, 32, 10912, 32, 1 }, + /* tcId: 343. point with coordinate x = 3 in left to right addition chain */ + {22003, 65, 128, 32, 10944, 32, 1 }, + /* tcId: 344. point with coordinate x = 3 in left to right addition chain */ + {22068, 65, 128, 32, 10976, 32, 1 }, + /* tcId: 345. point with coordinate x = 3 in left to right addition chain */ + {22133, 65, 128, 32, 11008, 32, 1 }, + /* tcId: 346. point with coordinate x = 3 in left to right addition chain */ + {22198, 65, 128, 32, 11040, 32, 1 }, + /* tcId: 347. point with coordinate x = 3 in left to right addition chain */ + {22263, 65, 128, 32, 11072, 32, 1 }, + /* tcId: 348. point with coordinate x = 3 in left to right addition chain */ + {22328, 65, 128, 32, 11104, 32, 1 }, + /* tcId: 349. point with coordinate x = 3 in left to right addition chain */ + {22393, 65, 128, 32, 11136, 32, 1 }, + /* tcId: 350. point with coordinate x = 3 in left to right addition chain */ + {22458, 65, 128, 32, 11168, 32, 1 }, + /* tcId: 351. point with coordinate x = 3 in left to right addition chain */ + {22523, 65, 128, 32, 11200, 32, 1 }, + /* tcId: 352. point with coordinate x = 3 in left to right addition chain */ + {22588, 65, 128, 32, 11232, 32, 1 }, + /* tcId: 353. point with coordinate x = 3 in left to right addition chain */ + {22653, 65, 128, 32, 11264, 32, 1 }, + /* tcId: 354. point with coordinate x = 3 in left to right addition chain */ + {22718, 65, 128, 32, 11296, 32, 1 }, + /* tcId: 355. point with coordinate x = 3 in left to right addition chain */ + {22783, 65, 128, 32, 11328, 32, 1 }, + /* tcId: 356. point with coordinate x = 3 in left to right addition chain */ + {22848, 65, 128, 32, 11360, 32, 1 }, + /* tcId: 357. point with coordinate x = 3 in left to right addition chain */ + {22913, 65, 128, 32, 11392, 32, 1 }, + /* tcId: 358. point with coordinate x = 3 in precomputation or right to left addition chain */ + {22978, 65, 128, 32, 11424, 32, 1 }, + /* tcId: 359. point with coordinate x = 3 in precomputation or right to left addition chain */ + {23043, 65, 128, 32, 11456, 32, 1 }, + /* tcId: 360. point with coordinate x = 3 in precomputation or right to left addition chain */ + {23108, 65, 128, 32, 11488, 32, 1 }, + /* tcId: 361. point with coordinate x = 3 in precomputation or right to left addition chain */ + {23173, 65, 128, 32, 11520, 32, 1 }, + /* tcId: 362. point with coordinate x = 3 in precomputation or right to left addition chain */ + {23238, 65, 128, 32, 11552, 32, 1 }, + /* tcId: 363. point with coordinate x = 3 in precomputation or right to left addition chain */ + {23303, 65, 128, 32, 11584, 32, 1 }, + /* tcId: 364. point with coordinate x = 3 in right to left addition chain */ + {23368, 65, 128, 32, 11616, 32, 1 }, + /* tcId: 365. point with coordinate x = 3 in right to left addition chain */ + {23433, 65, 128, 32, 11648, 32, 1 }, + /* tcId: 366. point with coordinate x = 3 in right to left addition chain */ + {23498, 65, 128, 32, 11680, 32, 1 }, + /* tcId: 367. point with coordinate x = 3 in right to left addition chain */ + {23563, 65, 128, 32, 11712, 32, 1 }, + /* tcId: 368. point with coordinate x = 3 in right to left addition chain */ + {23628, 65, 128, 32, 11744, 32, 1 }, + /* tcId: 369. point with coordinate y = 1 */ + {23693, 65, 128, 32, 11776, 32, 1 }, + /* tcId: 370. point with coordinate y = 1 */ + {23758, 65, 128, 32, 11808, 32, 1 }, + /* tcId: 371. point with coordinate y = 1 */ + {23823, 65, 128, 32, 11840, 32, 1 }, + /* tcId: 372. point with coordinate y = 1 */ + {23888, 65, 128, 32, 11872, 32, 1 }, + /* tcId: 373. point with coordinate y = 1 */ + {23953, 65, 128, 32, 11904, 32, 1 }, + /* tcId: 374. point with coordinate y = 1 */ + {24018, 65, 128, 32, 11936, 32, 1 }, + /* tcId: 375. point with coordinate y = 1 */ + {24083, 65, 128, 32, 11968, 32, 1 }, + /* tcId: 376. point with coordinate y = 1 */ + {24148, 65, 128, 32, 12000, 32, 1 }, + /* tcId: 377. point with coordinate y = 1 */ + {24213, 65, 128, 32, 12032, 32, 1 }, + /* tcId: 378. point with coordinate y = 1 in left to right addition chain */ + {24278, 65, 128, 32, 12064, 32, 1 }, + /* tcId: 379. point with coordinate y = 1 in left to right addition chain */ + {24343, 65, 128, 32, 12096, 32, 1 }, + /* tcId: 380. point with coordinate y = 1 in left to right addition chain */ + {24408, 65, 128, 32, 12128, 32, 1 }, + /* tcId: 381. point with coordinate y = 1 in left to right addition chain */ + {24473, 65, 128, 32, 12160, 32, 1 }, + /* tcId: 382. point with coordinate y = 1 in left to right addition chain */ + {24538, 65, 128, 32, 12192, 32, 1 }, + /* tcId: 383. point with coordinate y = 1 in left to right addition chain */ + {24603, 65, 128, 32, 12224, 32, 1 }, + /* tcId: 384. point with coordinate y = 1 in left to right addition chain */ + {24668, 65, 128, 32, 12256, 32, 1 }, + /* tcId: 385. point with coordinate y = 1 in left to right addition chain */ + {24733, 65, 128, 32, 12288, 32, 1 }, + /* tcId: 386. point with coordinate y = 1 in left to right addition chain */ + {24798, 65, 128, 32, 12320, 32, 1 }, + /* tcId: 387. point with coordinate y = 1 in left to right addition chain */ + {24863, 65, 128, 32, 12352, 32, 1 }, + /* tcId: 388. point with coordinate y = 1 in left to right addition chain */ + {24928, 65, 128, 32, 12384, 32, 1 }, + /* tcId: 389. point with coordinate y = 1 in left to right addition chain */ + {24993, 65, 128, 32, 12416, 32, 1 }, + /* tcId: 390. point with coordinate y = 1 in left to right addition chain */ + {25058, 65, 128, 32, 12448, 32, 1 }, + /* tcId: 391. point with coordinate y = 1 in left to right addition chain */ + {25123, 65, 128, 32, 12480, 32, 1 }, + /* tcId: 392. point with coordinate y = 1 in left to right addition chain */ + {25188, 65, 128, 32, 12512, 32, 1 }, + /* tcId: 393. point with coordinate y = 1 in left to right addition chain */ + {25253, 65, 128, 32, 12544, 32, 1 }, + /* tcId: 394. point with coordinate y = 1 in left to right addition chain */ + {25318, 65, 128, 32, 12576, 32, 1 }, + /* tcId: 395. point with coordinate y = 1 in left to right addition chain */ + {25383, 65, 128, 32, 12608, 32, 1 }, + /* tcId: 396. point with coordinate y = 1 in left to right addition chain */ + {25448, 65, 128, 32, 12640, 32, 1 }, + /* tcId: 397. point with coordinate y = 1 in left to right addition chain */ + {25513, 65, 128, 32, 12672, 32, 1 }, + /* tcId: 398. point with coordinate y = 1 in left to right addition chain */ + {25578, 65, 128, 32, 12704, 32, 1 }, + /* tcId: 399. point with coordinate y = 1 in left to right addition chain */ + {25643, 65, 128, 32, 12736, 32, 1 }, + /* tcId: 400. point with coordinate y = 1 in left to right addition chain */ + {25708, 65, 128, 32, 12768, 32, 1 }, + /* tcId: 401. point with coordinate y = 1 in left to right addition chain */ + {25773, 65, 128, 32, 12800, 32, 1 }, + /* tcId: 402. point with coordinate y = 1 in left to right addition chain */ + {25838, 65, 128, 32, 12832, 32, 1 }, + /* tcId: 403. point with coordinate y = 1 in left to right addition chain */ + {25903, 65, 128, 32, 12864, 32, 1 }, + /* tcId: 404. point with coordinate y = 1 in left to right addition chain */ + {25968, 65, 128, 32, 12896, 32, 1 }, + /* tcId: 405. point with coordinate y = 1 in left to right addition chain */ + {26033, 65, 128, 32, 12928, 32, 1 }, + /* tcId: 406. point with coordinate y = 1 in left to right addition chain */ + {26098, 65, 128, 32, 12960, 32, 1 }, + /* tcId: 407. point with coordinate y = 1 in left to right addition chain */ + {26163, 65, 128, 32, 12992, 32, 1 }, + /* tcId: 408. point with coordinate y = 1 in left to right addition chain */ + {26228, 65, 128, 32, 13024, 32, 1 }, + /* tcId: 409. point with coordinate y = 1 in left to right addition chain */ + {26293, 65, 128, 32, 13056, 32, 1 }, + /* tcId: 410. point with coordinate y = 1 in left to right addition chain */ + {26358, 65, 128, 32, 13088, 32, 1 }, + /* tcId: 411. point with coordinate y = 1 in left to right addition chain */ + {26423, 65, 128, 32, 13120, 32, 1 }, + /* tcId: 412. point with coordinate y = 1 in left to right addition chain */ + {26488, 65, 128, 32, 13152, 32, 1 }, + /* tcId: 413. point with coordinate y = 1 in left to right addition chain */ + {26553, 65, 128, 32, 13184, 32, 1 }, + /* tcId: 414. point with coordinate y = 1 in left to right addition chain */ + {26618, 65, 128, 32, 13216, 32, 1 }, + /* tcId: 415. point with coordinate y = 1 in left to right addition chain */ + {26683, 65, 128, 32, 13248, 32, 1 }, + /* tcId: 416. point with coordinate y = 1 in left to right addition chain */ + {26748, 65, 128, 32, 13280, 32, 1 }, + /* tcId: 417. point with coordinate y = 1 in left to right addition chain */ + {26813, 65, 128, 32, 13312, 32, 1 }, + /* tcId: 418. point with coordinate y = 1 in left to right addition chain */ + {26878, 65, 128, 32, 13344, 32, 1 }, + /* tcId: 419. point with coordinate y = 1 in left to right addition chain */ + {26943, 65, 128, 32, 13376, 32, 1 }, + /* tcId: 420. point with coordinate y = 1 in left to right addition chain */ + {27008, 65, 128, 32, 13408, 32, 1 }, + /* tcId: 421. point with coordinate y = 1 in left to right addition chain */ + {27073, 65, 128, 32, 13440, 32, 1 }, + /* tcId: 422. point with coordinate y = 1 in left to right addition chain */ + {27138, 65, 128, 32, 13472, 32, 1 }, + /* tcId: 423. point with coordinate y = 1 in left to right addition chain */ + {27203, 65, 128, 32, 13504, 32, 1 }, + /* tcId: 424. point with coordinate y = 1 in left to right addition chain */ + {27268, 65, 128, 32, 13536, 32, 1 }, + /* tcId: 425. point with coordinate y = 1 in left to right addition chain */ + {27333, 65, 128, 32, 13568, 32, 1 }, + /* tcId: 426. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27398, 65, 128, 32, 13600, 32, 1 }, + /* tcId: 427. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27463, 65, 128, 32, 13632, 32, 1 }, + /* tcId: 428. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27528, 65, 128, 32, 13664, 32, 1 }, + /* tcId: 429. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27593, 65, 128, 32, 13696, 32, 1 }, + /* tcId: 430. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27658, 65, 128, 32, 13728, 32, 1 }, + /* tcId: 431. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27723, 65, 128, 32, 13760, 32, 1 }, + /* tcId: 432. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27788, 65, 128, 32, 13792, 32, 1 }, + /* tcId: 433. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27853, 65, 128, 32, 13824, 32, 1 }, + /* tcId: 434. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27918, 65, 128, 32, 13856, 32, 1 }, + /* tcId: 435. point with coordinate y = 1 in precomputation or right to left addition chain */ + {27983, 65, 128, 32, 13888, 32, 1 }, + /* tcId: 436. point with coordinate y = 1 in precomputation or right to left addition chain */ + {28048, 65, 128, 32, 13920, 32, 1 }, + /* tcId: 437. point with coordinate y = 1 in precomputation or right to left addition chain */ + {28113, 65, 128, 32, 13952, 32, 1 }, + /* tcId: 438. point with coordinate y = 1 in precomputation or right to left addition chain */ + {28178, 65, 128, 32, 13984, 32, 1 }, + /* tcId: 439. point with coordinate y = 1 in precomputation or right to left addition chain */ + {28243, 65, 128, 32, 14016, 32, 1 }, + /* tcId: 440. point with coordinate y = 1 in precomputation or right to left addition chain */ + {28308, 65, 128, 32, 14048, 32, 1 }, + /* tcId: 441. point with coordinate y = 1 in precomputation or right to left addition chain */ + {28373, 65, 128, 32, 14080, 32, 1 }, + /* tcId: 442. point with coordinate y = 1 in precomputation or right to left addition chain */ + {28438, 65, 128, 32, 14112, 32, 1 }, + /* tcId: 443. point with coordinate y = 1 in precomputation or right to left addition chain */ + {28503, 65, 128, 32, 14144, 32, 1 }, + /* tcId: 444. point with coordinate y = 1 in right to left addition chain */ + {28568, 65, 128, 32, 14176, 32, 1 }, + /* tcId: 445. point with coordinate y = 1 in right to left addition chain */ + {28633, 65, 128, 32, 14208, 32, 1 }, + /* tcId: 446. point with coordinate y = 1 in right to left addition chain */ + {28698, 65, 128, 32, 14240, 32, 1 }, + /* tcId: 447. point with coordinate y = 1 in right to left addition chain */ + {28763, 65, 128, 32, 14272, 32, 1 }, + /* tcId: 448. point with coordinate y = 1 in right to left addition chain */ + {28828, 65, 128, 32, 14304, 32, 1 }, + /* tcId: 449. point with coordinate y = 1 in right to left addition chain */ + {28893, 65, 128, 32, 14336, 32, 1 }, + /* tcId: 450. point with coordinate y = 1 in right to left addition chain */ + {28958, 65, 128, 32, 14368, 32, 1 }, + /* tcId: 451. point with coordinate y = 1 in right to left addition chain */ + {29023, 65, 128, 32, 14400, 32, 1 }, + /* tcId: 452. point with coordinate y = 1 in right to left addition chain */ + {29088, 65, 128, 32, 14432, 32, 1 }, + /* tcId: 453. point with coordinate y = 1 in right to left addition chain */ + {29153, 65, 128, 32, 14464, 32, 1 }, + /* tcId: 454. point with coordinate y = 1 in right to left addition chain */ + {29218, 65, 128, 32, 14496, 32, 1 }, + /* tcId: 455. point with coordinate y = 1 in right to left addition chain */ + {29283, 65, 128, 32, 14528, 32, 1 }, + /* tcId: 456. point with coordinate y = 1 in right to left addition chain */ + {29348, 65, 128, 32, 14560, 32, 1 }, + /* tcId: 457. point with coordinate y = 1 in right to left addition chain */ + {29413, 65, 128, 32, 14592, 32, 1 }, + /* tcId: 458. point with coordinate y = 1 in right to left addition chain */ + {29478, 65, 128, 32, 14624, 32, 1 }, + /* tcId: 459. edge case private key */ + {29543, 65, 160, 32, 14656, 32, 1 }, + /* tcId: 460. edge case private key */ + {29543, 65, 192, 32, 14688, 32, 1 }, + /* tcId: 461. edge case private key */ + {29543, 65, 224, 32, 14720, 32, 1 }, + /* tcId: 462. edge case private key */ + {29543, 65, 256, 32, 14752, 32, 1 }, + /* tcId: 463. edge case private key */ + {29543, 65, 288, 32, 14784, 32, 1 }, + /* tcId: 464. edge case private key */ + {29543, 65, 320, 32, 14816, 32, 1 }, + /* tcId: 465. edge case private key */ + {29543, 65, 352, 32, 14848, 32, 1 }, + /* tcId: 466. edge case private key */ + {29543, 65, 384, 32, 14880, 32, 1 }, + /* tcId: 467. edge case private key */ + {29543, 65, 416, 32, 14912, 32, 1 }, + /* tcId: 468. edge case private key */ + {29543, 65, 448, 32, 14944, 32, 1 }, + /* tcId: 469. edge case private key */ + {29543, 65, 480, 32, 14976, 32, 1 }, + /* tcId: 470. edge case private key */ + {29543, 65, 512, 32, 15008, 32, 1 }, + /* tcId: 471. edge case private key */ + {29543, 65, 544, 32, 15040, 32, 1 }, + /* tcId: 472. edge case private key */ + {29543, 65, 576, 32, 15072, 32, 1 }, + /* tcId: 473. edge case private key */ + {29543, 65, 608, 32, 15104, 32, 1 }, + /* tcId: 474. edge case private key */ + {29543, 65, 640, 32, 15136, 32, 1 }, + /* tcId: 494. public point not on curve */ + {29608, 65, 672, 32, 15168, 0, 0 }, + /* tcId: 495. public point = (0,0) */ + {29673, 65, 672, 32, 15168, 0, 0 }, + /* tcId: 508. using secp224r1 */ + {29738, 57, 672, 32, 15168, 0, 0 }, + /* tcId: 509. using secp256r1 */ + {29795, 65, 672, 32, 15168, 0, 0 }, + /* tcId: 528. invalid public key */ + {29860, 33, 704, 32, 15168, 0, 0 }, + +}; diff --git a/src/wycheproof/ecdh_secp256k1_test.json b/src/wycheproof/ecdh_secp256k1_test.json new file mode 100644 index 0000000000..16db618912 --- /dev/null +++ b/src/wycheproof/ecdh_secp256k1_test.json @@ -0,0 +1,8441 @@ +{ + "algorithm" : "ECDH", + "schema" : "ecdh_test_schema.json", + "generatorVersion" : "0.9rc5", + "numberOfTests" : 752, + "header" : [ + "Test vectors of type EcdhTest are intended for", + "testing an ECDH implementations using X509 encoded", + "public keys and integers for private keys.", + "Test vectors of this format are useful for testing", + "Java providers." + ], + "notes" : { + "AdditionChain" : { + "bugType" : "KNOWN_BUG", + "description" : "The private key has an unusual bit pattern, such as high or low Hamming weight. The goal is to test edge cases for addition chain implementations." + }, + "CompressedPoint" : { + "bugType" : "UNKNOWN", + "description" : "The point in the public key is compressed. Not every library supports points in compressed format." + }, + "CompressedPublic" : { + "bugType" : "FUNCTIONALITY", + "description" : "The public key in the test vector is compressed. Some implementations do not support compressed points." + }, + "EdgeCaseDoubling" : { + "bugType" : "EDGE_CASE", + "description" : "The test vector contains an EC point that hits an edge case (e.g. a coordinate 0) when doubled. The goal of the test vector is to check for arithmetic errors in these test cases.", + "effect" : "The effect of such arithmetic errors is unclear and requires further analysis." + }, + "EdgeCaseEphemeralKey" : { + "bugType" : "EDGE_CASE", + "description" : "The test vector contains an ephemeral public key that is an edge case." + }, + "EdgeCaseSharedSecret" : { + "bugType" : "EDGE_CASE", + "description" : "The test vector contains a public key and private key such that the shared ECDH secret is a special case. The goal of this test vector is to detect arithmetic errors.", + "effect" : "The seriousness of an arithmetic error is unclear. It requires further analysis to determine if the bug is exploitable." + }, + "InvalidAsn" : { + "bugType" : "UNKNOWN", + "description" : "The public key in this test uses an invalid ASN encoding. Some cases where the ASN parser is not strictly checking the ASN format are benign as long as the ECDH computation still returns the correct shared value." + }, + "InvalidCompressedPublic" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The test vector contains a compressed public key that does not exist. I.e., it contains an x-coordinate that does not correspond to any points on the curve. Such keys should be rejected " + }, + "InvalidCurveAttack" : { + "bugType" : "CONFIDENTIALITY", + "description" : "The point of the public key is not on the curve. ", + "effect" : "If an implementation does not check whether a point is on the curve then it is likely that the implementation is susceptible to an invalid curve attack. Many implementations compute the shared ECDH secret over a curve defined by the point on the public key. This curve can be weak and hence leak information about the private key." + }, + "InvalidEncoding" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The test vector contains a public key with an invalid encoding." + }, + "InvalidPublic" : { + "bugType" : "CAN_OF_WORMS", + "description" : "The public key has been modified and is invalid. An implementation should always check whether the public key is valid and on the same curve as the private key. The test vector includes the shared secret computed with the original public key if the public point is on the curve of the private key.", + "effect" : "Generating a shared secret other than the one with the original key likely indicates that the bug is exploitable." + }, + "LargeCofactor" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The cofactor is larger than the limits specified in FIPS-PUB 186-4 table 1, p.36." + }, + "Modified curve parameter" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The parameters a and b of the curve have been modified. The parameters haven been chosen so that public key or generator still are also valid points on the new curve." + }, + "ModifiedCofactor" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The cofactor has been modified. ", + "effect" : "The seriousness of accepting a key with modified cofactor depends on whether the primitive using the key actually uses the cofactor." + }, + "ModifiedGenerator" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The generator of the EC group has been modified.", + "effect" : "The seriousness of the modification depends on whether the cryptographic primitive uses the generator. In the worst case such a modification allows an invalid curve attack." + }, + "ModifiedGroup" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The EC curve of the public key has been modified. EC curve primitives should always check that the keys are on the expected curve." + }, + "ModifiedPrime" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The modulus of the public key has been modified. The public point of the public key has been chosen so that it is both a point on both the curve of the modified public key and the private key." + }, + "ModifiedPublicPoint" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The public point of the key has been modified and is not on the curve.", + "effect" : "Not checking that a public point is on the curve may allow an invalid curve attack." + }, + "NegativeCofactor" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The cofactor of the curve is negative." + }, + "Normal" : { + "bugType" : "BASIC", + "description" : "The test vector contains a pseudorandomly generated, valid test case. Implementations are expected to pass this test." + }, + "UnnamedCurve" : { + "bugType" : "UNKNOWN", + "description" : "The public key does not use a named curve. RFC 3279 allows to encode such curves by explicitly encoding, the parameters of the curve equation, modulus, generator, order and cofactor. However, many crypto libraries only support named curves. Modifying some of the EC parameters and encoding the corresponding public key as an unnamed curve is a potential attack vector." + }, + "UnusedParam" : { + "bugType" : "MALLEABILITY", + "description" : "A parameter that is typically not used for ECDH has been modified. Sometimes libraries ignore small differences between public and private key. For example, a library might ignore an incorrect cofactor in the public key. We consider ignoring such changes as acceptable as long as these differences do not change the outcome of the ECDH computation, i.e. as long as the computation is done on the curve from the private key." + }, + "WeakPublicKey" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The vector contains a weak public key. The curve is not a named curve, the public key point has order 3 and has been chosen to be on the same curve as the private key. This test vector is used to check ECC implementations for missing steps in the verification of the public key." + }, + "WrongCurve" : { + "bugType" : "CONFIDENTIALITY", + "description" : "The public key and private key use distinct curves. Implementations are expected to reject such parameters.", + "effect" : "Computing an ECDH key exchange with public and private keys can in the worst case lead to an invalid curve attack. Hence, it is important that ECDH implementations check the input parameters. The severity of such bugs is typically smaller if an implementation ensures that the point is on the curve and that the ECDH computation is performed on the curve of the private key. Some of the test vectors with modified public key contain shared ECDH secrets, that were computed over the curve of the private key." + }, + "WrongOrder" : { + "bugType" : "MODIFIED_PARAMETER", + "description" : "The order of the public key has been modified.", + "effect" : "If this order is used in a cryptographic primitive instead of the correct order then an invalid curve attack is possible and the private keys may leak. E.g. ECDHC in BC 1.52 suffered from this." + } + }, + "testGroups" : [ + { + "type" : "EcdhTest", + "curve" : "secp256k1", + "encoding" : "asn", + "tests" : [ + { + "tcId" : 1, + "comment" : "normal case", + "flags" : [ + "Normal" + ], + "public" : "3056301006072a8648ce3d020106052b8104000a03420004d8096af8a11e0b80037e1ee68246b5dcbb0aeb1cf1244fd767db80f3fa27da2b396812ea1686e7472e9692eaf3e958e50e9500d3b4c77243db1f2acd67ba9cc4", + "private" : "00f4b7ff7cccc98813a69fae3df222bfe3f4e28f764bf91b4a10d8096ce446b254", + "shared" : "544dfae22af6af939042b1d85b71a1e49e9a5614123c4d6ad0c8af65baf87d65", + "result" : "valid" + }, + { + "tcId" : 2, + "comment" : "compressed public key", + "flags" : [ + "CompressedPublic", + "CompressedPoint" + ], + "public" : "3036301006072a8648ce3d020106052b8104000a03220002d8096af8a11e0b80037e1ee68246b5dcbb0aeb1cf1244fd767db80f3fa27da2b", + "private" : "00f4b7ff7cccc98813a69fae3df222bfe3f4e28f764bf91b4a10d8096ce446b254", + "shared" : 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"3055301006072a8648ce3d020106052b8104000a03410004e03faca42a8b811759211d49b69dd0e0a686b28ff7b5817789a2f80050791335bf34cf495029075de25603fd56dd3cef36ee8503b9f3b0c1340c8e4012da32", + "private" : "0495800a83e6c1d61886d332e2613aa3f70df22865b0387ca6ca195cfcd2b2b1", + "shared" : "ebdca74dbf2c8ef63af8d86e0e0ee4511399bc08a395c4ea050bab43a29d2646", + "result" : "acceptable" + }, + { + "tcId" : 747, + "comment" : "truncated bit string", + "flags" : [ + "InvalidAsn" + ], + "public" : "3055301006072a8648ce3d020106052b8104000a034104e03faca42a8b811759211d49b69dd0e0a686b28ff7b5817789a2f80050791335bf34cf495029075de25603fd56dd3cef36ee8503b9f3b0c1340c8e4012da3267", + "private" : "0495800a83e6c1d61886d332e2613aa3f70df22865b0387ca6ca195cfcd2b2b1", + "shared" : "ebdca74dbf2c8ef63af8d86e0e0ee4511399bc08a395c4ea050bab43a29d2646", + "result" : "acceptable" + }, + { + "tcId" : 748, + "comment" : "bit string of size 4163 to check for overflows", + "flags" : [ + "InvalidAsn" + ], + "public" : "30821059301006072a8648ce3d020106052b8104000a038210430004e03faca42a8b811759211d49b69dd0e0a686b28ff7b5817789a2f80050791335bf34cf495029075de25603fd56dd3cef36ee8503b9f3b0c1340c8e4012da3267000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000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+ "private" : "0495800a83e6c1d61886d332e2613aa3f70df22865b0387ca6ca195cfcd2b2b1", + "shared" : "ebdca74dbf2c8ef63af8d86e0e0ee4511399bc08a395c4ea050bab43a29d2646", + "result" : "acceptable" + }, + { + "tcId" : 749, + "comment" : "declaring bits as unused in bit string", + "flags" : [ + "InvalidAsn" + ], + "public" : "3056301006072a8648ce3d020106052b8104000a03420104e03faca42a8b811759211d49b69dd0e0a686b28ff7b5817789a2f80050791335bf34cf495029075de25603fd56dd3cef36ee8503b9f3b0c1340c8e4012da3267", + "private" : "0495800a83e6c1d61886d332e2613aa3f70df22865b0387ca6ca195cfcd2b2b1", + "shared" : "ebdca74dbf2c8ef63af8d86e0e0ee4511399bc08a395c4ea050bab43a29d2646", + "result" : "acceptable" + }, + { + "tcId" : 750, + "comment" : "unused bits in bit string", + "flags" : [ + "InvalidAsn" + ], + "public" : "305a301006072a8648ce3d020106052b8104000a03462004e03faca42a8b811759211d49b69dd0e0a686b28ff7b5817789a2f80050791335bf34cf495029075de25603fd56dd3cef36ee8503b9f3b0c1340c8e4012da326701020304", + "private" : "0495800a83e6c1d61886d332e2613aa3f70df22865b0387ca6ca195cfcd2b2b1", + "shared" : "ebdca74dbf2c8ef63af8d86e0e0ee4511399bc08a395c4ea050bab43a29d2646", + "result" : "acceptable" + }, + { + "tcId" : 751, + "comment" : "unused bits in empty bit-string", + "flags" : [ + "InvalidAsn" + ], + "public" : "3015301006072a8648ce3d020106052b8104000a030103", + "private" : "0495800a83e6c1d61886d332e2613aa3f70df22865b0387ca6ca195cfcd2b2b1", + "shared" : "ebdca74dbf2c8ef63af8d86e0e0ee4511399bc08a395c4ea050bab43a29d2646", + "result" : "acceptable" + }, + { + "tcId" : 752, + "comment" : "128 unused bits", + "flags" : [ + "InvalidAsn" + ], + "public" : "3056301006072a8648ce3d020106052b8104000a03428004e03faca42a8b811759211d49b69dd0e0a686b28ff7b5817789a2f80050791335bf34cf495029075de25603fd56dd3cef36ee8503b9f3b0c1340c8e4012da3267", + "private" : "0495800a83e6c1d61886d332e2613aa3f70df22865b0387ca6ca195cfcd2b2b1", + "shared" : "ebdca74dbf2c8ef63af8d86e0e0ee4511399bc08a395c4ea050bab43a29d2646", + "result" : "acceptable" + } + ] + } + ] +} diff --git a/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h b/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h index 736737fd61..556c235689 100644 --- a/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h +++ b/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h @@ -1,4 +1,4 @@ -/* Note: this file was autogenerated using tests_wycheproof_generate.py. Do not edit. */ +/* Note: this file was autogenerated using tests_wycheproof_generate_ecdsa.py. Do not edit. */ #define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS (463) typedef struct { diff --git a/tools/tests_wycheproof_generate_ecdh.py b/tools/tests_wycheproof_generate_ecdh.py new file mode 100755 index 0000000000..26dd8a1eac --- /dev/null +++ b/tools/tests_wycheproof_generate_ecdh.py @@ -0,0 +1,150 @@ +#!/usr/bin/env python3 +# Copyright (c) 2024 Random "Randy" Lattice and Sean Andersen +# Distributed under the MIT software license, see the accompanying +# file COPYING or https://www.opensource.org/licenses/mit-license.php. +''' +Generate a C file with ECDH testvectors from the Wycheproof project. +''' + +import json +import sys + +from binascii import hexlify, unhexlify +from wycheproof_utils import to_c_array + +def should_skip(test_vector_flags): + # skip these vectors because they are for ASN.1 encoding issues and other curves + flags_to_skip = {"InvalidAsn", "InvalidCurveAttack", "InvalidEncoding", "WrongCurve", "UnnamedCurve"} + return any(flag in test_vector_flags for flag in flags_to_skip) + +# Rudimentary ASN.1 DER public key parser. +# This should not be used for anything other than parsing Wycheproof test vectors. +def parse_der_pk(s): + tag = s[0] + L = int(s[1]) + value = s[2:(L+2)] + rest = s[(L+2):] + + if len(rest) > 0 or tag == 0x06: # OBJECT IDENTIFIER + return parse_der_pk(rest) + if tag == 0x03: # BIT STRING + return value + if tag == 0x30: # SEQUENCE + return parse_der_pk(value) + raise ValueError("unknown tag") + +def parse_public_key(pk): + der_pub_key = parse_der_pk(unhexlify(pk)) # Convert back to str and strip off the `0x` + return hexlify(der_pub_key).decode('utf-8')[2:] + +def normalize_private_key(sk): + # Ensure the private key is at most 64 characters long, retaining the last 64 if longer. + normalized = sk[-64:].zfill(64) + assert len(normalized) == 64, "private key must be exactly 64 characters long." + return normalized + +def normalize_expected_result(er): + result_mapping = {"invalid": 0, "valid": 1, "acceptable": 1} + return result_mapping[er] + +filename_input = sys.argv[1] + +with open(filename_input) as f: + doc = json.load(f) + +num_groups = len(doc['testGroups']) + +num_vectors = 0 +offset_sk_running, offset_pk_running, offset_shared = 0, 0, 0 +out = "" +private_keys = "" +shared_secrets = "" +public_keys = "" +cache_sks = {} +cache_public_keys = {} + +for i in range(num_groups): + group = doc['testGroups'][i] + num_tests = len(group['tests']) + assert group["type"] == "EcdhTest" + assert group["curve"] == "secp256k1" + for j in range(num_tests): + test_vector = group['tests'][j] + + if should_skip(test_vector['flags']): + continue + + public_key = parse_public_key(test_vector['public']) + private_key = normalize_private_key(test_vector['private']) + expected_result = normalize_expected_result(test_vector['result']) + + # // 2 to convert hex to byte length + shared_size = len(test_vector['shared']) // 2 + sk_size = len(private_key) // 2 + pk_size = len(public_key) // 2 + + shared_secrets += ",\n " if num_vectors and shared_size else "" + + new_sk = False + sk = to_c_array(private_key) + sk_offset = offset_sk_running + + # check for repeated sk + if sk not in cache_sks: + if num_vectors != 0 and sk_size != 0: + private_keys += ",\n " + cache_sks[sk] = offset_sk_running + private_keys += sk + new_sk = True + else: + sk_offset = cache_sks[sk] + + new_pk = False + pk = to_c_array(public_key) if public_key != '0x' else '' + + pk_offset = offset_pk_running + # check for repeated pk + if pk not in cache_public_keys: + if num_vectors != 0 and len(pk) != 0: + public_keys += ",\n " + cache_public_keys[pk] = offset_pk_running + public_keys += pk + new_pk = True + else: + pk_offset = cache_public_keys[pk] + + shared_secrets += to_c_array(test_vector['shared']) + + out += " /" + "* tcId: " + str(test_vector['tcId']) + ". " + test_vector['comment'] + " *" + "/\n" + out += f" {{{pk_offset}, {pk_size}, {sk_offset}, {sk_size}, {offset_shared}, {shared_size}, {expected_result} }},\n" + if new_sk: + offset_sk_running += sk_size + if new_pk: + offset_pk_running += pk_size + offset_shared += shared_size + num_vectors += 1 + +struct_definition = """ +typedef struct { + size_t pk_offset; + size_t pk_len; + size_t sk_offset; + size_t sk_len; + size_t shared_offset; + size_t shared_len; + int expected_result; +} wycheproof_ecdh_testvector; +""" + +print("/* Note: this file was autogenerated using tests_wycheproof_ecdh.py. Do not edit. */") +print(f"#define SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS ({num_vectors})") + +print(struct_definition) + +print("static const unsigned char wycheproof_ecdh_private_keys[] = { " + private_keys + "};\n") +print("static const unsigned char wycheproof_ecdh_public_keys[] = { " + public_keys + "};\n") +print("static const unsigned char wycheproof_ecdh_shared_secrets[] = { " + shared_secrets + "};\n") + +print("static const wycheproof_ecdh_testvector testvectors[SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS] = {") +print(out) +print("};") diff --git a/tools/tests_wycheproof_generate.py b/tools/tests_wycheproof_generate_ecdsa.py similarity index 95% rename from tools/tests_wycheproof_generate.py rename to tools/tests_wycheproof_generate_ecdsa.py index b26dfa89d6..91ff9e318a 100755 --- a/tools/tests_wycheproof_generate.py +++ b/tools/tests_wycheproof_generate_ecdsa.py @@ -9,6 +9,8 @@ import json import sys +from wycheproof_utils import to_c_array + filename_input = sys.argv[1] with open(filename_input) as f: @@ -16,12 +18,6 @@ num_groups = len(doc['testGroups']) -def to_c_array(x): - if x == "": - return "" - s = ',0x'.join(a+b for a,b in zip(x[::2], x[1::2])) - return "0x" + s - num_vectors = 0 offset_msg_running, offset_pk_running, offset_sig = 0, 0, 0 @@ -101,7 +97,7 @@ def to_c_array(x): """ -print("/* Note: this file was autogenerated using tests_wycheproof_generate.py. Do not edit. */") +print("/* Note: this file was autogenerated using tests_wycheproof_generate_ecdsa.py. Do not edit. */") print(f"#define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS ({num_vectors})") print(struct_definition) diff --git a/tools/wycheproof_utils.py b/tools/wycheproof_utils.py new file mode 100644 index 0000000000..4a171d3fb7 --- /dev/null +++ b/tools/wycheproof_utils.py @@ -0,0 +1,12 @@ +# Copyright (c) 2024 Random "Randy" Lattice and Sean Andersen +# Distributed under the MIT software license, see the accompanying +# file COPYING or https://www.opensource.org/licenses/mit-license.php. +''' +Utility functions for generating C files for testvectors from the Wycheproof project. +''' + +def to_c_array(x): + if x == "": + return "" + s = ',0x'.join(a+b for a,b in zip(x[::2], x[1::2])) + return "0x" + s From 3cba981aef2b5c64581f750d929775e30ab34616 Mon Sep 17 00:00:00 2001 From: RandomLattice <128569685+RandomLattice@users.noreply.github.com> Date: Thu, 17 Oct 2024 16:52:56 +0700 Subject: [PATCH 2/2] PR feedback: add more wycheproof ECDH test cases Co-authored-by: Sean Andersen <6730974+andozw@users.noreply.github.com> --- src/modules/ecdh/tests_impl.h | 4 +- src/wycheproof/ecdh_secp256k1_test.h | 1037 ++++++++++++----------- tools/tests_wycheproof_generate_ecdh.py | 33 +- 3 files changed, 583 insertions(+), 491 deletions(-) diff --git a/src/modules/ecdh/tests_impl.h b/src/modules/ecdh/tests_impl.h index 7648cac651..bf2a3d3bb2 100644 --- a/src/modules/ecdh/tests_impl.h +++ b/src/modules/ecdh/tests_impl.h @@ -8,7 +8,6 @@ #define SECP256K1_MODULE_ECDH_TESTS_H static int ecdh_hash_function_test_xpassthru(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { - (void)x; (void)y; (void)data; memcpy(output, x, 32); @@ -170,8 +169,7 @@ static void test_ecdh_wycheproof(void) { expected_result = testvectors[t].expected_result; - /* fail if public key is valid, but doesn't parse */ - CHECK(parsed_ok || expected_result == 0); + CHECK(parsed_ok == expected_result); if (!parsed_ok && expected_result == 0) { continue; diff --git a/src/wycheproof/ecdh_secp256k1_test.h b/src/wycheproof/ecdh_secp256k1_test.h index dd13829680..02a087e53c 100644 --- a/src/wycheproof/ecdh_secp256k1_test.h +++ b/src/wycheproof/ecdh_secp256k1_test.h @@ -1,5 +1,5 @@ /* Note: this file was autogenerated using tests_wycheproof_ecdh.py. Do not edit. */ -#define SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS (479) +#define SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS (503) typedef struct { size_t pk_offset; @@ -9,6 +9,7 @@ typedef struct { size_t shared_offset; size_t shared_len; int expected_result; + int wycheproof_tcid; } wycheproof_ecdh_testvector; static const unsigned char wycheproof_ecdh_private_keys[] = { 0xf4,0xb7,0xff,0x7c,0xcc,0xc9,0x88,0x13,0xa6,0x9f,0xae,0x3d,0xf2,0x22,0xbf,0xe3,0xf4,0xe2,0x8f,0x76,0x4b,0xf9,0x1b,0x4a,0x10,0xd8,0x09,0x6c,0xe4,0x46,0xb2,0x54, @@ -32,6 +33,7 @@ static const unsigned char wycheproof_ecdh_private_keys[] = { 0xf4,0xb7,0xff, 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x3b, 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x3e, 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x3f, + 0xc6,0xca,0xfb,0x74,0xe2,0xa5,0x0c,0x83,0xb3,0xd2,0x32,0xc4,0x58,0x52,0x37,0xf4,0x4d,0x4c,0x54,0x33,0xc4,0xb3,0xf5,0x0c,0xe9,0x78,0xe6,0xae,0xda,0x3a,0x4f,0x5d, 0xcf,0xe7,0x5e,0xe7,0x64,0x19,0x7a,0xa7,0x73,0x2a,0x54,0x78,0x55,0x6b,0x47,0x88,0x98,0x42,0x3d,0x2b,0xc0,0xe4,0x84,0xa6,0xeb,0xb3,0x67,0x4a,0x60,0x36,0xa6,0x5d, 0xd0,0x91,0x82,0xa4,0xd0,0xc9,0x4b,0xa8,0x5f,0x82,0xef,0xf9,0xfc,0x1b,0xdd,0xb0,0xb0,0x7d,0x3f,0x2a,0xf8,0x63,0x2f,0xc1,0xc7,0x3a,0x36,0x04,0xe8,0xf0,0xb3,0x35}; @@ -491,10 +493,27 @@ static const unsigned char wycheproof_ecdh_public_keys[] = { 0x04,0xd8,0x09,0x6a 0x04,0x35,0x67,0x0f,0x86,0xc5,0xf7,0x2b,0x93,0xab,0xe4,0x13,0x1d,0x2b,0xea,0x1f,0xce,0x87,0x6a,0xd4,0xe2,0x5b,0x40,0xd4,0x2d,0x44,0x7d,0x68,0xcf,0xf9,0x0c,0xa0,0xbe,0x0b,0x6d,0x3b,0x9e,0x57,0x0b,0xa0,0x04,0x87,0x7c,0x9a,0x69,0xe4,0x81,0xfe,0x21,0x5d,0xe0,0x3a,0x70,0x12,0x63,0x05,0xa4,0x52,0x82,0x6e,0x66,0xd9,0xb5,0x58,0x3e, 0x04,0xdf,0xca,0x67,0x8a,0x1b,0x8e,0x6f,0x67,0x99,0x6a,0x09,0x7f,0xc9,0xce,0x37,0x41,0x2d,0xe9,0xfb,0xd9,0xcf,0xa1,0xa2,0x1b,0x75,0x0c,0xef,0x48,0xe5,0xe5,0x95,0xa1,0x30,0x7d,0x8f,0x1d,0x02,0xc6,0xf0,0x71,0x46,0x65,0x5e,0x63,0x83,0xb0,0xef,0x30,0x35,0xbe,0xe7,0x06,0x7c,0x33,0x6f,0xdb,0x91,0x36,0x5e,0x19,0x7a,0x97,0xb6,0x16, 0x04,0x32,0xbd,0xd9,0x78,0xeb,0x62,0xb1,0xf3,0x69,0xa5,0x6d,0x09,0x49,0xab,0x85,0x51,0xa7,0xad,0x52,0x7d,0x96,0x02,0xe8,0x91,0xce,0x45,0x75,0x86,0xc2,0xa8,0x56,0x9e,0x98,0x1e,0x67,0xfa,0xe0,0x53,0xb0,0x3f,0xc3,0x3e,0x1a,0x29,0x1f,0x0a,0x3b,0xeb,0x58,0xfc,0xeb,0x2e,0x85,0xbb,0x12,0x05,0xda,0xce,0xe1,0x23,0x2d,0xfd,0x31,0x6b, - 0x04,0x49,0xc2,0x48,0xed,0xc6,0x59,0xe1,0x84,0x82,0xb7,0x10,0x57,0x48,0xa4,0xb9,0x5d,0x3a,0x46,0x95,0x2a,0x5b,0xa7,0x2d,0xa0,0xd7,0x02,0xdc,0x97,0xa6,0x4e,0x99,0x79,0x9d,0x8c,0xff,0x7a,0x5c,0x4b,0x92,0x5e,0x43,0x60,0xec,0xe2,0x5c,0xcf,0x30,0x7d,0x7a,0x9a,0x70,0x63,0x28,0x6b,0xbd,0x16,0xef,0x64,0xc6,0x5f,0x54,0x67,0x57,0xe4, 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2e, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2e, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x04,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2e,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2e,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x04,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2e,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2e, + 0x04,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2e,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x04,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x04,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2e, + 0x04,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x04,0x49,0xc2,0x48,0xed,0xc6,0x59,0xe1,0x84,0x82,0xb7,0x10,0x57,0x48,0xa4,0xb9,0x5d,0x3a,0x46,0x95,0x2a,0x5b,0xa7,0x2d,0xa0,0xd7,0x02,0xdc,0x97,0xa6,0x4e,0x99,0x79,0x9d,0x8c,0xff,0x7a,0x5c,0x4b,0x92,0x5e,0x43,0x60,0xec,0xe2,0x5c,0xcf,0x30,0x7d,0x7a,0x9a,0x70,0x63,0x28,0x6b,0xbd,0x16,0xef,0x64,0xc6,0x5f,0x54,0x67,0x57,0xe4, + 0x04,0x49,0xc2,0x48,0xed,0xc6,0x59,0xe1,0x84,0x82,0xb7,0x10,0x57,0x48,0xa4,0xb9,0x5d,0x3a,0x46,0x95,0x2a,0x5b,0xa7,0x2d,0xa0,0xd7,0x02,0xdc,0x97,0xa6,0x4e,0x99,0x79,0x9d,0x8c,0xff,0x7a,0x5c,0x4b,0x92,0x5e,0x43,0x60,0xec,0xe2,0x5c,0xcf,0x30,0x7d,0x7a,0x9a,0x70,0x63,0x28,0x6b,0xbd,0x16,0xef,0x64,0xc6,0x5f,0x54,0x67,0x57,0xe2, 0x04,0x07,0x4f,0x56,0xdc,0x2e,0xa6,0x48,0xef,0x89,0xc3,0xb7,0x2e,0x23,0xbb,0xd2,0xda,0x36,0xf6,0x02,0x43,0xe4,0xd2,0x06,0x7b,0x70,0x60,0x4a,0xf1,0xc2,0x16,0x5c,0xec,0x2f,0x86,0x60,0x3d,0x60,0xc8,0xa6,0x11,0xd5,0xb8,0x4b,0xa3,0xd9,0x1d,0xfe,0x1a,0x48,0x08,0x25,0xbc,0xc4,0xaf,0x3b,0xcf, 0x04,0xcb,0xf6,0x60,0x65,0x95,0xa3,0xee,0x50,0xf9,0xfc,0xea,0xa2,0x79,0x8c,0x27,0x40,0xc8,0x25,0x40,0x51,0x6b,0x4e,0x5a,0x7d,0x36,0x1f,0xf2,0x4e,0x9d,0xd1,0x53,0x64,0xe5,0x40,0x8b,0x2e,0x67,0x9f,0x9d,0x53,0x10,0xd1,0xf6,0x89,0x3b,0x36,0xce,0x16,0xb4,0xa5,0x07,0x50,0x91,0x75,0xfc,0xb5,0x2a,0xea,0x53,0xb7,0x81,0x55,0x6b,0x39, + 0x04,0xfb,0x60,0x75,0xd2,0x6c,0x35,0x01,0xc0,0x14,0xe4,0x8c,0x79,0xb3,0x46,0x3c,0xd7,0x68,0x37,0x8c,0x39,0x0d,0x7e,0x6e,0xeb,0x37,0x97,0x17,0xd4,0x90,0xc4,0xe6,0x34,0x78,0x04,0x35,0x77,0x19,0x79,0x87,0x88,0x16,0x70,0xbc,0x13,0xfd,0x0b,0x5f,0x0b,0xa1,0x0f,0x06,0xbc,0xef,0x27,0x11,0xc2,0x8f,0x5e,0xfd,0x7e,0x31,0xd5,0x15,0x7c, 0x02,0x97,0x7c,0xb7,0xfb,0x9a,0x0e,0xc5,0xb2,0x08,0xe8,0x11,0xd6,0xa0,0x79,0x5e,0xb7,0x8d,0x76,0x42,0xe3,0xca,0xc4,0x2a,0x80,0x1b,0xcc,0x8f,0xc0,0xf0,0x64,0x72,0xd4}; static const unsigned char wycheproof_ecdh_shared_secrets[] = { 0x54,0x4d,0xfa,0xe2,0x2a,0xf6,0xaf,0x93,0x90,0x42,0xb1,0xd8,0x5b,0x71,0xa1,0xe4,0x9e,0x9a,0x56,0x14,0x12,0x3c,0x4d,0x6a,0xd0,0xc8,0xaf,0x65,0xba,0xf8,0x7d,0x65, @@ -970,966 +989,1020 @@ static const unsigned char wycheproof_ecdh_shared_secrets[] = { 0x54,0x4d,0xfa, 0x02,0x77,0x63,0x15,0xfe,0x14,0x7a,0x36,0xa4,0xb0,0x98,0x74,0x92,0xb6,0x50,0x3a,0xcd,0xea,0x60,0xf9,0x26,0x45,0x0e,0x5e,0xdd,0xb9,0xf8,0x8f,0xc8,0x21,0x78,0xd3, 0x39,0x88,0xc9,0xc7,0x05,0x0a,0x28,0x79,0x49,0x34,0xe5,0xbd,0x67,0x62,0x9b,0x55,0x6d,0x97,0xa4,0x85,0x8d,0x22,0x81,0x28,0x35,0xf4,0xa3,0x7d,0xca,0x35,0x19,0x43, 0x34,0x00,0x56,0x94,0xe3,0xca,0xc0,0x93,0x32,0xaa,0x42,0x80,0x7e,0x3a,0xfd,0xc3,0xb3,0xb3,0xbc,0x7c,0x7b,0xe8,0x87,0xd1,0xf9,0x8d,0x76,0x77,0x8c,0x55,0xcf,0xd7, - 0x4b,0x52,0x25,0x7d,0x8b,0x3b,0xa3,0x87,0x79,0x7f,0xdf,0x7a,0x75,0x2f,0x19,0x5d,0xdc,0x4f,0x7d,0x76,0x26,0x3d,0xe6,0x1d,0x0d,0x52,0xa5,0xec,0x14,0xa3,0x6c,0xbf}; + 0x4b,0x52,0x25,0x7d,0x8b,0x3b,0xa3,0x87,0x79,0x7f,0xdf,0x7a,0x75,0x2f,0x19,0x5d,0xdc,0x4f,0x7d,0x76,0x26,0x3d,0xe6,0x1d,0x0d,0x52,0xa5,0xec,0x14,0xa3,0x6c,0xbf, + 0x38,0x0c,0x53,0xe0,0xa5,0x09,0xeb,0xb3,0xb6,0x33,0x46,0x59,0x81,0x05,0x21,0x9b,0x43,0xd5,0x1a,0xe1,0x96,0xb4,0x55,0x7d,0x59,0xbb,0xd6,0x78,0x24,0x03,0x2d,0xff, + 0x38,0x0c,0x53,0xe0,0xa5,0x09,0xeb,0xb3,0xb6,0x33,0x46,0x59,0x81,0x05,0x21,0x9b,0x43,0xd5,0x1a,0xe1,0x96,0xb4,0x55,0x7d,0x59,0xbb,0xd6,0x78,0x24,0x03,0x2d,0xff, + 0x38,0x0c,0x53,0xe0,0xa5,0x09,0xeb,0xb3,0xb6,0x33,0x46,0x59,0x81,0x05,0x21,0x9b,0x43,0xd5,0x1a,0xe1,0x96,0xb4,0x55,0x7d,0x59,0xbb,0xd6,0x78,0x24,0x03,0x2d,0xff, + 0x38,0x0c,0x53,0xe0,0xa5,0x09,0xeb,0xb3,0xb6,0x33,0x46,0x59,0x81,0x05,0x21,0x9b,0x43,0xd5,0x1a,0xe1,0x96,0xb4,0x55,0x7d,0x59,0xbb,0xd6,0x78,0x24,0x03,0x2d,0xff, + 0x38,0x0c,0x53,0xe0,0xa5,0x09,0xeb,0xb3,0xb6,0x33,0x46,0x59,0x81,0x05,0x21,0x9b,0x43,0xd5,0x1a,0xe1,0x96,0xb4,0x55,0x7d,0x59,0xbb,0xd6,0x78,0x24,0x03,0x2d,0xff, + 0x38,0x0c,0x53,0xe0,0xa5,0x09,0xeb,0xb3,0xb6,0x33,0x46,0x59,0x81,0x05,0x21,0x9b,0x43,0xd5,0x1a,0xe1,0x96,0xb4,0x55,0x7d,0x59,0xbb,0xd6,0x78,0x24,0x03,0x2d,0xff}; static const wycheproof_ecdh_testvector testvectors[SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS] = { /* tcId: 1. normal case */ - {0, 65, 0, 32, 0, 32, 1 }, + {0, 65, 0, 32, 0, 32, 1, 1 }, /* tcId: 2. compressed public key */ - {65, 33, 0, 32, 32, 32, 1 }, + {65, 33, 0, 32, 32, 32, 1, 2 }, /* tcId: 3. shared secret has x-coordinate that satisfies x**2 + a = 1 */ - {98, 65, 32, 32, 64, 32, 1 }, + {98, 65, 32, 32, 64, 32, 1, 3 }, /* tcId: 4. shared secret has x-coordinate that satisfies x**2 + a = 4 */ - {163, 65, 32, 32, 96, 32, 1 }, + {163, 65, 32, 32, 96, 32, 1, 4 }, /* tcId: 5. shared secret has x-coordinate that satisfies x**2 + a = 9 */ - {228, 65, 32, 32, 128, 32, 1 }, + {228, 65, 32, 32, 128, 32, 1, 5 }, /* tcId: 6. shared secret has x-coordinate p-3 */ - {293, 65, 32, 32, 160, 32, 1 }, + {293, 65, 32, 32, 160, 32, 1, 6 }, /* tcId: 7. shared secret has x-coordinate 2**16 + 0 */ - {358, 65, 32, 32, 192, 32, 1 }, + {358, 65, 32, 32, 192, 32, 1, 7 }, /* tcId: 8. shared secret has x-coordinate 2**32 + 7 */ - {423, 65, 32, 32, 224, 32, 1 }, + {423, 65, 32, 32, 224, 32, 1, 8 }, /* tcId: 9. shared secret has x-coordinate 2**64 + 1 */ - {488, 65, 32, 32, 256, 32, 1 }, + {488, 65, 32, 32, 256, 32, 1, 9 }, /* tcId: 10. shared secret has x-coordinate 2**96 + 1 */ - {553, 65, 32, 32, 288, 32, 1 }, + {553, 65, 32, 32, 288, 32, 1, 10 }, /* tcId: 11. shared secret has x-coordinate that satisfies x**2 + a = -6 */ - {618, 65, 32, 32, 320, 32, 1 }, + {618, 65, 32, 32, 320, 32, 1, 11 }, /* tcId: 12. shared secret has x-coordinate that satisfies x**2 + a = 2 */ - {683, 65, 32, 32, 352, 32, 1 }, + {683, 65, 32, 32, 352, 32, 1, 12 }, /* tcId: 13. shared secret has x-coordinate that satisfies x**2 + a = 8 */ - {748, 65, 32, 32, 384, 32, 1 }, + {748, 65, 32, 32, 384, 32, 1, 13 }, /* tcId: 14. shared secret has x-coordinate that satisfies x**2 = 2**96 + 2 */ - {813, 65, 32, 32, 416, 32, 1 }, + {813, 65, 32, 32, 416, 32, 1, 14 }, /* tcId: 15. shared secret has x-coordinate with repeating bit-pattern of size 2 */ - {878, 65, 32, 32, 448, 32, 1 }, + {878, 65, 32, 32, 448, 32, 1, 15 }, /* tcId: 16. shared secret has x-coordinate with repeating bit-pattern of size 2 */ - {943, 65, 32, 32, 480, 32, 1 }, + {943, 65, 32, 32, 480, 32, 1, 16 }, /* tcId: 17. shared secret has x-coordinate with repeating bit-pattern of size 4 */ - {1008, 65, 32, 32, 512, 32, 1 }, + {1008, 65, 32, 32, 512, 32, 1, 17 }, /* tcId: 18. shared secret has x-coordinate with repeating bit-pattern of size 4 */ - {1073, 65, 32, 32, 544, 32, 1 }, + {1073, 65, 32, 32, 544, 32, 1, 18 }, /* tcId: 19. shared secret has x-coordinate with repeating bit-pattern of size 8 */ - {1138, 65, 32, 32, 576, 32, 1 }, + {1138, 65, 32, 32, 576, 32, 1, 19 }, /* tcId: 20. shared secret has x-coordinate with repeating bit-pattern of size 8 */ - {1203, 65, 32, 32, 608, 32, 1 }, + {1203, 65, 32, 32, 608, 32, 1, 20 }, /* tcId: 21. shared secret has x-coordinate with repeating bit-pattern of size 16 */ - {1268, 65, 32, 32, 640, 32, 1 }, + {1268, 65, 32, 32, 640, 32, 1, 21 }, /* tcId: 22. shared secret has x-coordinate with repeating bit-pattern of size 16 */ - {1333, 65, 32, 32, 672, 32, 1 }, + {1333, 65, 32, 32, 672, 32, 1, 22 }, /* tcId: 23. shared secret has x-coordinate with repeating bit-pattern of size 30 */ - {1398, 65, 32, 32, 704, 32, 1 }, + {1398, 65, 32, 32, 704, 32, 1, 23 }, /* tcId: 24. shared secret has x-coordinate with repeating bit-pattern of size 30 */ - {1463, 65, 32, 32, 736, 32, 1 }, + {1463, 65, 32, 32, 736, 32, 1, 24 }, /* tcId: 25. shared secret has x-coordinate with repeating bit-pattern of size 32 */ - {1528, 65, 32, 32, 768, 32, 1 }, + {1528, 65, 32, 32, 768, 32, 1, 25 }, /* tcId: 26. shared secret has x-coordinate with repeating bit-pattern of size 32 */ - {1593, 65, 32, 32, 800, 32, 1 }, + {1593, 65, 32, 32, 800, 32, 1, 26 }, /* tcId: 27. shared secret has x-coordinate with repeating bit-pattern of size 51 */ - {1658, 65, 32, 32, 832, 32, 1 }, + {1658, 65, 32, 32, 832, 32, 1, 27 }, /* tcId: 28. shared secret has x-coordinate with repeating bit-pattern of size 51 */ - {1723, 65, 32, 32, 864, 32, 1 }, + {1723, 65, 32, 32, 864, 32, 1, 28 }, /* tcId: 29. shared secret has x-coordinate with repeating bit-pattern of size 52 */ - {1788, 65, 32, 32, 896, 32, 1 }, + {1788, 65, 32, 32, 896, 32, 1, 29 }, /* tcId: 30. shared secret has x-coordinate with repeating bit-pattern of size 52 */ - {1853, 65, 32, 32, 928, 32, 1 }, + {1853, 65, 32, 32, 928, 32, 1, 30 }, /* tcId: 31. shared secret has x-coordinate with repeating bit-pattern of size 60 */ - {1918, 65, 32, 32, 960, 32, 1 }, + {1918, 65, 32, 32, 960, 32, 1, 31 }, /* tcId: 32. shared secret has x-coordinate with repeating bit-pattern of size 60 */ - {1983, 65, 32, 32, 992, 32, 1 }, + {1983, 65, 32, 32, 992, 32, 1, 32 }, /* tcId: 33. shared secret has x-coordinate with repeating bit-pattern of size 62 */ - {2048, 65, 32, 32, 1024, 32, 1 }, + {2048, 65, 32, 32, 1024, 32, 1, 33 }, /* tcId: 34. shared secret has x-coordinate with repeating bit-pattern of size 62 */ - {2113, 65, 32, 32, 1056, 32, 1 }, + {2113, 65, 32, 32, 1056, 32, 1, 34 }, /* tcId: 35. shared secret has x-coordinate with repeating bit-pattern of size 64 */ - {2178, 65, 32, 32, 1088, 32, 1 }, + {2178, 65, 32, 32, 1088, 32, 1, 35 }, /* tcId: 36. shared secret has x-coordinate with repeating bit-pattern of size 64 */ - {2243, 65, 32, 32, 1120, 32, 1 }, + {2243, 65, 32, 32, 1120, 32, 1, 36 }, /* tcId: 37. shared secret has x-coordinate with repeating bit-pattern of size 112 */ - {2308, 65, 32, 32, 1152, 32, 1 }, + {2308, 65, 32, 32, 1152, 32, 1, 37 }, /* tcId: 38. shared secret has x-coordinate with repeating bit-pattern of size 112 */ - {2373, 65, 32, 32, 1184, 32, 1 }, + {2373, 65, 32, 32, 1184, 32, 1, 38 }, /* tcId: 39. shared secret has x-coordinate with repeating bit-pattern of size 128 */ - {2438, 65, 32, 32, 1216, 32, 1 }, + {2438, 65, 32, 32, 1216, 32, 1, 39 }, /* tcId: 40. shared secret has x-coordinate with repeating bit-pattern of size 128 */ - {2503, 65, 32, 32, 1248, 32, 1 }, + {2503, 65, 32, 32, 1248, 32, 1, 40 }, /* tcId: 41. shared secret has an x-coordinate of approx p//3 */ - {2568, 65, 32, 32, 1280, 32, 1 }, + {2568, 65, 32, 32, 1280, 32, 1, 41 }, /* tcId: 42. shared secret has an x-coordinate of approx p//5 */ - {2633, 65, 32, 32, 1312, 32, 1 }, + {2633, 65, 32, 32, 1312, 32, 1, 42 }, /* tcId: 43. shared secret has an x-coordinate of approx p//7 */ - {2698, 65, 32, 32, 1344, 32, 1 }, + {2698, 65, 32, 32, 1344, 32, 1, 43 }, /* tcId: 44. shared secret has an x-coordinate of approx p//9 */ - {2763, 65, 32, 32, 1376, 32, 1 }, + {2763, 65, 32, 32, 1376, 32, 1, 44 }, /* tcId: 45. y-coordinate of the public key has many trailing 1's */ - {2828, 65, 32, 32, 1408, 32, 1 }, + {2828, 65, 32, 32, 1408, 32, 1, 45 }, /* tcId: 46. y-coordinate of the public key has many trailing 1's */ - {2893, 65, 64, 32, 1440, 32, 1 }, + {2893, 65, 64, 32, 1440, 32, 1, 46 }, /* tcId: 47. y-coordinate of the public key is small */ - {2958, 65, 32, 32, 1472, 32, 1 }, + {2958, 65, 32, 32, 1472, 32, 1, 47 }, /* tcId: 48. y-coordinate of the public key is small */ - {3023, 65, 32, 32, 1504, 32, 1 }, + {3023, 65, 32, 32, 1504, 32, 1, 48 }, /* tcId: 49. y-coordinate of the public key is small */ - {3088, 65, 64, 32, 1536, 32, 1 }, + {3088, 65, 64, 32, 1536, 32, 1, 49 }, /* tcId: 50. y-coordinate of the public key is small */ - {3153, 65, 64, 32, 1568, 32, 1 }, + {3153, 65, 64, 32, 1568, 32, 1, 50 }, /* tcId: 51. y-coordinate of the public key is large */ - {3218, 65, 32, 32, 1600, 32, 1 }, + {3218, 65, 32, 32, 1600, 32, 1, 51 }, /* tcId: 52. y-coordinate of the public key is large */ - {3283, 65, 32, 32, 1632, 32, 1 }, + {3283, 65, 32, 32, 1632, 32, 1, 52 }, /* tcId: 53. y-coordinate of the public key is large */ - {3348, 65, 64, 32, 1664, 32, 1 }, + {3348, 65, 64, 32, 1664, 32, 1, 53 }, /* tcId: 54. y-coordinate of the public key is large */ - {3413, 65, 64, 32, 1696, 32, 1 }, + {3413, 65, 64, 32, 1696, 32, 1, 54 }, /* tcId: 55. y-coordinate of the public key has many trailing 0's */ - {3478, 65, 32, 32, 1728, 32, 1 }, + {3478, 65, 32, 32, 1728, 32, 1, 55 }, /* tcId: 56. y-coordinate of the public key has many trailing 0's */ - {3543, 65, 64, 32, 1760, 32, 1 }, + {3543, 65, 64, 32, 1760, 32, 1, 56 }, /* tcId: 57. ephemeral key has x-coordinate that satisfies x**2 + a = 1 */ - {3608, 65, 64, 32, 1792, 32, 1 }, + {3608, 65, 64, 32, 1792, 32, 1, 57 }, /* tcId: 58. ephemeral key has x-coordinate that satisfies x**2 + a = 4 */ - {3673, 65, 64, 32, 1824, 32, 1 }, + {3673, 65, 64, 32, 1824, 32, 1, 58 }, /* tcId: 59. ephemeral key has x-coordinate that satisfies x**2 + a = 9 */ - {3738, 65, 64, 32, 1856, 32, 1 }, + {3738, 65, 64, 32, 1856, 32, 1, 59 }, /* tcId: 60. ephemeral key has x-coordinate p-3 */ - {3803, 65, 64, 32, 1888, 32, 1 }, + {3803, 65, 64, 32, 1888, 32, 1, 60 }, /* tcId: 61. ephemeral key has x-coordinate 2**16 + 0 */ - {3868, 65, 64, 32, 1920, 32, 1 }, + {3868, 65, 64, 32, 1920, 32, 1, 61 }, /* tcId: 62. ephemeral key has x-coordinate 2**32 + 7 */ - {3933, 65, 64, 32, 1952, 32, 1 }, + {3933, 65, 64, 32, 1952, 32, 1, 62 }, /* tcId: 63. ephemeral key has x-coordinate 2**64 + 1 */ - {3998, 65, 64, 32, 1984, 32, 1 }, + {3998, 65, 64, 32, 1984, 32, 1, 63 }, /* tcId: 64. ephemeral key has x-coordinate 2**96 + 1 */ - {4063, 65, 64, 32, 2016, 32, 1 }, + {4063, 65, 64, 32, 2016, 32, 1, 64 }, /* tcId: 65. ephemeral key has x-coordinate that satisfies x**2 + a = -6 */ - {4128, 65, 64, 32, 2048, 32, 1 }, + {4128, 65, 64, 32, 2048, 32, 1, 65 }, /* tcId: 66. ephemeral key has x-coordinate that satisfies x**2 + a = 2 */ - {4193, 65, 64, 32, 2080, 32, 1 }, + {4193, 65, 64, 32, 2080, 32, 1, 66 }, /* tcId: 67. ephemeral key has x-coordinate that satisfies x**2 + a = 8 */ - {4258, 65, 64, 32, 2112, 32, 1 }, + {4258, 65, 64, 32, 2112, 32, 1, 67 }, /* tcId: 68. ephemeral key has x-coordinate that satisfies x**2 = 2**96 + 2 */ - {4323, 65, 64, 32, 2144, 32, 1 }, + {4323, 65, 64, 32, 2144, 32, 1, 68 }, /* tcId: 69. ephemeral key has x-coordinate with repeating bit-pattern of size 2 */ - {4388, 65, 64, 32, 2176, 32, 1 }, + {4388, 65, 64, 32, 2176, 32, 1, 69 }, /* tcId: 70. ephemeral key has x-coordinate with repeating bit-pattern of size 2 */ - {4453, 65, 64, 32, 2208, 32, 1 }, + {4453, 65, 64, 32, 2208, 32, 1, 70 }, /* tcId: 71. ephemeral key has x-coordinate with repeating bit-pattern of size 4 */ - {4518, 65, 64, 32, 2240, 32, 1 }, + {4518, 65, 64, 32, 2240, 32, 1, 71 }, /* tcId: 72. ephemeral key has x-coordinate with repeating bit-pattern of size 4 */ - {4583, 65, 64, 32, 2272, 32, 1 }, + {4583, 65, 64, 32, 2272, 32, 1, 72 }, /* tcId: 73. ephemeral key has x-coordinate with repeating bit-pattern of size 8 */ - {4648, 65, 64, 32, 2304, 32, 1 }, + {4648, 65, 64, 32, 2304, 32, 1, 73 }, /* tcId: 74. ephemeral key has x-coordinate with repeating bit-pattern of size 8 */ - {4713, 65, 64, 32, 2336, 32, 1 }, + {4713, 65, 64, 32, 2336, 32, 1, 74 }, /* tcId: 75. ephemeral key has x-coordinate with repeating bit-pattern of size 16 */ - {4778, 65, 64, 32, 2368, 32, 1 }, + {4778, 65, 64, 32, 2368, 32, 1, 75 }, /* tcId: 76. ephemeral key has x-coordinate with repeating bit-pattern of size 16 */ - {4843, 65, 64, 32, 2400, 32, 1 }, + {4843, 65, 64, 32, 2400, 32, 1, 76 }, /* tcId: 77. ephemeral key has x-coordinate with repeating bit-pattern of size 30 */ - {4908, 65, 64, 32, 2432, 32, 1 }, + {4908, 65, 64, 32, 2432, 32, 1, 77 }, /* tcId: 78. ephemeral key has x-coordinate with repeating bit-pattern of size 30 */ - {4973, 65, 64, 32, 2464, 32, 1 }, + {4973, 65, 64, 32, 2464, 32, 1, 78 }, /* tcId: 79. ephemeral key has x-coordinate with repeating bit-pattern of size 32 */ - {5038, 65, 64, 32, 2496, 32, 1 }, + {5038, 65, 64, 32, 2496, 32, 1, 79 }, /* tcId: 80. ephemeral key has x-coordinate with repeating bit-pattern of size 32 */ - {5103, 65, 64, 32, 2528, 32, 1 }, + {5103, 65, 64, 32, 2528, 32, 1, 80 }, /* tcId: 81. ephemeral key has x-coordinate with repeating bit-pattern of size 51 */ - {5168, 65, 64, 32, 2560, 32, 1 }, + {5168, 65, 64, 32, 2560, 32, 1, 81 }, /* tcId: 82. ephemeral key has x-coordinate with repeating bit-pattern of size 51 */ - {5233, 65, 64, 32, 2592, 32, 1 }, + {5233, 65, 64, 32, 2592, 32, 1, 82 }, /* tcId: 83. ephemeral key has x-coordinate with repeating bit-pattern of size 52 */ - {5298, 65, 64, 32, 2624, 32, 1 }, + {5298, 65, 64, 32, 2624, 32, 1, 83 }, /* tcId: 84. ephemeral key has x-coordinate with repeating bit-pattern of size 52 */ - {5363, 65, 64, 32, 2656, 32, 1 }, + {5363, 65, 64, 32, 2656, 32, 1, 84 }, /* tcId: 85. ephemeral key has x-coordinate with repeating bit-pattern of size 60 */ - {5428, 65, 64, 32, 2688, 32, 1 }, + {5428, 65, 64, 32, 2688, 32, 1, 85 }, /* tcId: 86. ephemeral key has x-coordinate with repeating bit-pattern of size 60 */ - {5493, 65, 64, 32, 2720, 32, 1 }, + {5493, 65, 64, 32, 2720, 32, 1, 86 }, /* tcId: 87. ephemeral key has x-coordinate with repeating bit-pattern of size 62 */ - {5558, 65, 64, 32, 2752, 32, 1 }, + {5558, 65, 64, 32, 2752, 32, 1, 87 }, /* tcId: 88. ephemeral key has x-coordinate with repeating bit-pattern of size 62 */ - {5623, 65, 64, 32, 2784, 32, 1 }, + {5623, 65, 64, 32, 2784, 32, 1, 88 }, /* tcId: 89. ephemeral key has x-coordinate with repeating bit-pattern of size 64 */ - {5688, 65, 64, 32, 2816, 32, 1 }, + {5688, 65, 64, 32, 2816, 32, 1, 89 }, /* tcId: 90. ephemeral key has x-coordinate with repeating bit-pattern of size 64 */ - {5753, 65, 64, 32, 2848, 32, 1 }, + {5753, 65, 64, 32, 2848, 32, 1, 90 }, /* tcId: 91. ephemeral key has x-coordinate with repeating bit-pattern of size 112 */ - {5818, 65, 64, 32, 2880, 32, 1 }, + {5818, 65, 64, 32, 2880, 32, 1, 91 }, /* tcId: 92. ephemeral key has x-coordinate with repeating bit-pattern of size 112 */ - {5883, 65, 64, 32, 2912, 32, 1 }, + {5883, 65, 64, 32, 2912, 32, 1, 92 }, /* tcId: 93. ephemeral key has x-coordinate with repeating bit-pattern of size 128 */ - {5948, 65, 64, 32, 2944, 32, 1 }, + {5948, 65, 64, 32, 2944, 32, 1, 93 }, /* tcId: 94. ephemeral key has x-coordinate with repeating bit-pattern of size 128 */ - {6013, 65, 64, 32, 2976, 32, 1 }, + {6013, 65, 64, 32, 2976, 32, 1, 94 }, /* tcId: 95. ephemeral key has an x-coordinate of approx p//3 */ - {6078, 65, 64, 32, 3008, 32, 1 }, + {6078, 65, 64, 32, 3008, 32, 1, 95 }, /* tcId: 96. ephemeral key has an x-coordinate of approx p//5 */ - {6143, 65, 64, 32, 3040, 32, 1 }, + {6143, 65, 64, 32, 3040, 32, 1, 96 }, /* tcId: 97. ephemeral key has an x-coordinate of approx p//7 */ - {6208, 65, 64, 32, 3072, 32, 1 }, + {6208, 65, 64, 32, 3072, 32, 1, 97 }, /* tcId: 98. ephemeral key has an x-coordinate of approx p//9 */ - {6273, 65, 64, 32, 3104, 32, 1 }, + {6273, 65, 64, 32, 3104, 32, 1, 98 }, /* tcId: 99. edge case for Jacobian and projective coordinates */ - {6338, 65, 96, 32, 3136, 32, 1 }, + {6338, 65, 96, 32, 3136, 32, 1, 99 }, /* tcId: 100. edge case for Jacobian and projective coordinates */ - {6403, 65, 96, 32, 3168, 32, 1 }, + {6403, 65, 96, 32, 3168, 32, 1, 100 }, /* tcId: 101. edge case for Jacobian and projective coordinates */ - {6468, 65, 96, 32, 3200, 32, 1 }, + {6468, 65, 96, 32, 3200, 32, 1, 101 }, /* tcId: 102. edge case for Jacobian and projective coordinates */ - {6533, 65, 128, 32, 3232, 32, 1 }, + {6533, 65, 128, 32, 3232, 32, 1, 102 }, /* tcId: 103. edge case for Jacobian and projective coordinates */ - {6598, 65, 128, 32, 3264, 32, 1 }, + {6598, 65, 128, 32, 3264, 32, 1, 103 }, /* tcId: 104. edge case for Jacobian and projective coordinates */ - {6663, 65, 128, 32, 3296, 32, 1 }, + {6663, 65, 128, 32, 3296, 32, 1, 104 }, /* tcId: 105. edge case for Jacobian and projective coordinates in left to right addition chain */ - {6728, 65, 96, 32, 3328, 32, 1 }, + {6728, 65, 96, 32, 3328, 32, 1, 105 }, /* tcId: 106. edge case for Jacobian and projective coordinates in left to right addition chain */ - {6793, 65, 96, 32, 3360, 32, 1 }, + {6793, 65, 96, 32, 3360, 32, 1, 106 }, /* tcId: 107. edge case for Jacobian and projective coordinates in left to right addition chain */ - {6858, 65, 96, 32, 3392, 32, 1 }, + {6858, 65, 96, 32, 3392, 32, 1, 107 }, /* tcId: 108. edge case for Jacobian and projective coordinates in left to right addition chain */ - {6923, 65, 96, 32, 3424, 32, 1 }, + {6923, 65, 96, 32, 3424, 32, 1, 108 }, /* tcId: 109. edge case for Jacobian and projective coordinates in left to right addition chain */ - {6988, 65, 96, 32, 3456, 32, 1 }, + {6988, 65, 96, 32, 3456, 32, 1, 109 }, /* tcId: 110. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7053, 65, 96, 32, 3488, 32, 1 }, + {7053, 65, 96, 32, 3488, 32, 1, 110 }, /* tcId: 111. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7118, 65, 96, 32, 3520, 32, 1 }, + {7118, 65, 96, 32, 3520, 32, 1, 111 }, /* tcId: 112. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7183, 65, 96, 32, 3552, 32, 1 }, + {7183, 65, 96, 32, 3552, 32, 1, 112 }, /* tcId: 113. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7248, 65, 96, 32, 3584, 32, 1 }, + {7248, 65, 96, 32, 3584, 32, 1, 113 }, /* tcId: 114. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7313, 65, 96, 32, 3616, 32, 1 }, + {7313, 65, 96, 32, 3616, 32, 1, 114 }, /* tcId: 115. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7378, 65, 96, 32, 3648, 32, 1 }, + {7378, 65, 96, 32, 3648, 32, 1, 115 }, /* tcId: 116. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7443, 65, 96, 32, 3680, 32, 1 }, + {7443, 65, 96, 32, 3680, 32, 1, 116 }, /* tcId: 117. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7508, 65, 96, 32, 3712, 32, 1 }, + {7508, 65, 96, 32, 3712, 32, 1, 117 }, /* tcId: 118. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7573, 65, 96, 32, 3744, 32, 1 }, + {7573, 65, 96, 32, 3744, 32, 1, 118 }, /* tcId: 119. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7638, 65, 96, 32, 3776, 32, 1 }, + {7638, 65, 96, 32, 3776, 32, 1, 119 }, /* tcId: 120. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7703, 65, 96, 32, 3808, 32, 1 }, + {7703, 65, 96, 32, 3808, 32, 1, 120 }, /* tcId: 121. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7768, 65, 128, 32, 3840, 32, 1 }, + {7768, 65, 128, 32, 3840, 32, 1, 121 }, /* tcId: 122. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7833, 65, 128, 32, 3872, 32, 1 }, + {7833, 65, 128, 32, 3872, 32, 1, 122 }, /* tcId: 123. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7898, 65, 128, 32, 3904, 32, 1 }, + {7898, 65, 128, 32, 3904, 32, 1, 123 }, /* tcId: 124. edge case for Jacobian and projective coordinates in left to right addition chain */ - {7963, 65, 128, 32, 3936, 32, 1 }, + {7963, 65, 128, 32, 3936, 32, 1, 124 }, /* tcId: 125. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8028, 65, 128, 32, 3968, 32, 1 }, + {8028, 65, 128, 32, 3968, 32, 1, 125 }, /* tcId: 126. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8093, 65, 128, 32, 4000, 32, 1 }, + {8093, 65, 128, 32, 4000, 32, 1, 126 }, /* tcId: 127. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8158, 65, 128, 32, 4032, 32, 1 }, + {8158, 65, 128, 32, 4032, 32, 1, 127 }, /* tcId: 128. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8223, 65, 128, 32, 4064, 32, 1 }, + {8223, 65, 128, 32, 4064, 32, 1, 128 }, /* tcId: 129. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8288, 65, 128, 32, 4096, 32, 1 }, + {8288, 65, 128, 32, 4096, 32, 1, 129 }, /* tcId: 130. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8353, 65, 128, 32, 4128, 32, 1 }, + {8353, 65, 128, 32, 4128, 32, 1, 130 }, /* tcId: 131. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8418, 65, 128, 32, 4160, 32, 1 }, + {8418, 65, 128, 32, 4160, 32, 1, 131 }, /* tcId: 132. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8483, 65, 128, 32, 4192, 32, 1 }, + {8483, 65, 128, 32, 4192, 32, 1, 132 }, /* tcId: 133. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8548, 65, 128, 32, 4224, 32, 1 }, + {8548, 65, 128, 32, 4224, 32, 1, 133 }, /* tcId: 134. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8613, 65, 128, 32, 4256, 32, 1 }, + {8613, 65, 128, 32, 4256, 32, 1, 134 }, /* tcId: 135. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8678, 65, 128, 32, 4288, 32, 1 }, + {8678, 65, 128, 32, 4288, 32, 1, 135 }, /* tcId: 136. edge case for Jacobian and projective coordinates in left to right addition chain */ - {8743, 65, 128, 32, 4320, 32, 1 }, + {8743, 65, 128, 32, 4320, 32, 1, 136 }, /* tcId: 137. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {8808, 65, 128, 32, 4352, 32, 1 }, + {8808, 65, 128, 32, 4352, 32, 1, 137 }, /* tcId: 138. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {8873, 65, 128, 32, 4384, 32, 1 }, + {8873, 65, 128, 32, 4384, 32, 1, 138 }, /* tcId: 139. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {8938, 65, 128, 32, 4416, 32, 1 }, + {8938, 65, 128, 32, 4416, 32, 1, 139 }, /* tcId: 140. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9003, 65, 128, 32, 4448, 32, 1 }, + {9003, 65, 128, 32, 4448, 32, 1, 140 }, /* tcId: 141. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9068, 65, 128, 32, 4480, 32, 1 }, + {9068, 65, 128, 32, 4480, 32, 1, 141 }, /* tcId: 142. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9133, 65, 128, 32, 4512, 32, 1 }, + {9133, 65, 128, 32, 4512, 32, 1, 142 }, /* tcId: 143. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9198, 65, 128, 32, 4544, 32, 1 }, + {9198, 65, 128, 32, 4544, 32, 1, 143 }, /* tcId: 144. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9263, 65, 128, 32, 4576, 32, 1 }, + {9263, 65, 128, 32, 4576, 32, 1, 144 }, /* tcId: 145. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9328, 65, 128, 32, 4608, 32, 1 }, + {9328, 65, 128, 32, 4608, 32, 1, 145 }, /* tcId: 146. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9393, 65, 128, 32, 4640, 32, 1 }, + {9393, 65, 128, 32, 4640, 32, 1, 146 }, /* tcId: 147. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9458, 65, 128, 32, 4672, 32, 1 }, + {9458, 65, 128, 32, 4672, 32, 1, 147 }, /* tcId: 148. edge case for Jacobian and projective coordinates in precomputation or right to left addition chain */ - {9523, 65, 128, 32, 4704, 32, 1 }, + {9523, 65, 128, 32, 4704, 32, 1, 148 }, /* tcId: 149. edge case for Jacobian and projective coordinates in right to left addition chain */ - {9588, 65, 128, 32, 4736, 32, 1 }, + {9588, 65, 128, 32, 4736, 32, 1, 149 }, /* tcId: 150. edge case for Jacobian and projective coordinates in right to left addition chain */ - {9653, 65, 128, 32, 4768, 32, 1 }, + {9653, 65, 128, 32, 4768, 32, 1, 150 }, /* tcId: 151. edge case for Jacobian and projective coordinates in right to left addition chain */ - {9718, 65, 128, 32, 4800, 32, 1 }, + {9718, 65, 128, 32, 4800, 32, 1, 151 }, /* tcId: 152. edge case for Jacobian and projective coordinates in right to left addition chain */ - {9783, 65, 128, 32, 4832, 32, 1 }, + {9783, 65, 128, 32, 4832, 32, 1, 152 }, /* tcId: 153. edge case for Jacobian and projective coordinates in right to left addition chain */ - {9848, 65, 128, 32, 4864, 32, 1 }, + {9848, 65, 128, 32, 4864, 32, 1, 153 }, /* tcId: 154. edge case for Jacobian and projective coordinates in right to left addition chain */ - {9913, 65, 128, 32, 4896, 32, 1 }, + {9913, 65, 128, 32, 4896, 32, 1, 154 }, /* tcId: 155. edge case for Jacobian and projective coordinates in right to left addition chain */ - {9978, 65, 128, 32, 4928, 32, 1 }, + {9978, 65, 128, 32, 4928, 32, 1, 155 }, /* tcId: 156. edge case for Jacobian and projective coordinates in right to left addition chain */ - {10043, 65, 128, 32, 4960, 32, 1 }, + {10043, 65, 128, 32, 4960, 32, 1, 156 }, /* tcId: 157. edge case for Jacobian and projective coordinates in right to left addition chain */ - {10108, 65, 128, 32, 4992, 32, 1 }, + {10108, 65, 128, 32, 4992, 32, 1, 157 }, /* tcId: 158. edge case for Jacobian and projective coordinates in right to left addition chain */ - {10173, 65, 128, 32, 5024, 32, 1 }, + {10173, 65, 128, 32, 5024, 32, 1, 158 }, /* tcId: 159. edge case for computation of x with projective coordinates */ - {10238, 65, 128, 32, 5056, 32, 1 }, + {10238, 65, 128, 32, 5056, 32, 1, 159 }, /* tcId: 160. edge case for computation of x with projective coordinates */ - {10303, 65, 128, 32, 5088, 32, 1 }, + {10303, 65, 128, 32, 5088, 32, 1, 160 }, /* tcId: 161. edge case for computation of x with projective coordinates */ - {10368, 65, 128, 32, 5120, 32, 1 }, + {10368, 65, 128, 32, 5120, 32, 1, 161 }, /* tcId: 162. edge case for computation of x with projective coordinates */ - {10433, 65, 128, 32, 5152, 32, 1 }, + {10433, 65, 128, 32, 5152, 32, 1, 162 }, /* tcId: 163. edge case for computation of x with projective coordinates */ - {10498, 65, 128, 32, 5184, 32, 1 }, + {10498, 65, 128, 32, 5184, 32, 1, 163 }, /* tcId: 164. edge case for computation of x with projective coordinates */ - {10563, 65, 128, 32, 5216, 32, 1 }, + {10563, 65, 128, 32, 5216, 32, 1, 164 }, /* tcId: 165. edge case for computation of x with projective coordinates */ - {10628, 65, 128, 32, 5248, 32, 1 }, + {10628, 65, 128, 32, 5248, 32, 1, 165 }, /* tcId: 166. edge case for computation of x with projective coordinates */ - {10693, 65, 128, 32, 5280, 32, 1 }, + {10693, 65, 128, 32, 5280, 32, 1, 166 }, /* tcId: 167. edge case for computation of x with projective coordinates */ - {10758, 65, 128, 32, 5312, 32, 1 }, + {10758, 65, 128, 32, 5312, 32, 1, 167 }, /* tcId: 168. edge case for computation of x with projective coordinates in left to right addition chain */ - {10823, 65, 128, 32, 5344, 32, 1 }, + {10823, 65, 128, 32, 5344, 32, 1, 168 }, /* tcId: 169. edge case for computation of x with projective coordinates in left to right addition chain */ - {10888, 65, 128, 32, 5376, 32, 1 }, + {10888, 65, 128, 32, 5376, 32, 1, 169 }, /* tcId: 170. edge case for computation of x with projective coordinates in left to right addition chain */ - {10953, 65, 128, 32, 5408, 32, 1 }, + {10953, 65, 128, 32, 5408, 32, 1, 170 }, /* tcId: 171. edge case for computation of x with projective coordinates in left to right addition chain */ - {11018, 65, 128, 32, 5440, 32, 1 }, + {11018, 65, 128, 32, 5440, 32, 1, 171 }, /* tcId: 172. edge case for computation of x with projective coordinates in left to right addition chain */ - {11083, 65, 128, 32, 5472, 32, 1 }, + {11083, 65, 128, 32, 5472, 32, 1, 172 }, /* tcId: 173. edge case for computation of x with projective coordinates in left to right addition chain */ - {11148, 65, 128, 32, 5504, 32, 1 }, + {11148, 65, 128, 32, 5504, 32, 1, 173 }, /* tcId: 174. edge case for computation of x with projective coordinates in left to right addition chain */ - {11213, 65, 128, 32, 5536, 32, 1 }, + {11213, 65, 128, 32, 5536, 32, 1, 174 }, /* tcId: 175. edge case for computation of x with projective coordinates in left to right addition chain */ - {11278, 65, 128, 32, 5568, 32, 1 }, + {11278, 65, 128, 32, 5568, 32, 1, 175 }, /* tcId: 176. edge case for computation of x with projective coordinates in left to right addition chain */ - {11343, 65, 128, 32, 5600, 32, 1 }, + {11343, 65, 128, 32, 5600, 32, 1, 176 }, /* tcId: 177. edge case for computation of x with projective coordinates in left to right addition chain */ - {11408, 65, 128, 32, 5632, 32, 1 }, + {11408, 65, 128, 32, 5632, 32, 1, 177 }, /* tcId: 178. edge case for computation of x with projective coordinates in left to right addition chain */ - {11473, 65, 128, 32, 5664, 32, 1 }, + {11473, 65, 128, 32, 5664, 32, 1, 178 }, /* tcId: 179. edge case for computation of x with projective coordinates in left to right addition chain */ - {11538, 65, 128, 32, 5696, 32, 1 }, + {11538, 65, 128, 32, 5696, 32, 1, 179 }, /* tcId: 180. edge case for computation of x with projective coordinates in left to right addition chain */ - {11603, 65, 128, 32, 5728, 32, 1 }, + {11603, 65, 128, 32, 5728, 32, 1, 180 }, /* tcId: 181. edge case for computation of x with projective coordinates in left to right addition chain */ - {11668, 65, 128, 32, 5760, 32, 1 }, + {11668, 65, 128, 32, 5760, 32, 1, 181 }, /* tcId: 182. edge case for computation of x with projective coordinates in left to right addition chain */ - {11733, 65, 128, 32, 5792, 32, 1 }, + {11733, 65, 128, 32, 5792, 32, 1, 182 }, /* tcId: 183. edge case for computation of x with projective coordinates in left to right addition chain */ - {11798, 65, 128, 32, 5824, 32, 1 }, + {11798, 65, 128, 32, 5824, 32, 1, 183 }, /* tcId: 184. edge case for computation of x with projective coordinates in left to right addition chain */ - {11863, 65, 128, 32, 5856, 32, 1 }, + {11863, 65, 128, 32, 5856, 32, 1, 184 }, /* tcId: 185. edge case for computation of x with projective coordinates in left to right addition chain */ - {11928, 65, 128, 32, 5888, 32, 1 }, + {11928, 65, 128, 32, 5888, 32, 1, 185 }, /* tcId: 186. edge case for computation of x with projective coordinates in left to right addition chain */ - {11993, 65, 128, 32, 5920, 32, 1 }, + {11993, 65, 128, 32, 5920, 32, 1, 186 }, /* tcId: 187. edge case for computation of x with projective coordinates in left to right addition chain */ - {12058, 65, 128, 32, 5952, 32, 1 }, + {12058, 65, 128, 32, 5952, 32, 1, 187 }, /* tcId: 188. edge case for computation of x with projective coordinates in left to right addition chain */ - {12123, 65, 128, 32, 5984, 32, 1 }, + {12123, 65, 128, 32, 5984, 32, 1, 188 }, /* tcId: 189. edge case for computation of x with projective coordinates in left to right addition chain */ - {12188, 65, 128, 32, 6016, 32, 1 }, + {12188, 65, 128, 32, 6016, 32, 1, 189 }, /* tcId: 190. edge case for computation of x with projective coordinates in left to right addition chain */ - {12253, 65, 128, 32, 6048, 32, 1 }, + {12253, 65, 128, 32, 6048, 32, 1, 190 }, /* tcId: 191. edge case for computation of x with projective coordinates in left to right addition chain */ - {12318, 65, 128, 32, 6080, 32, 1 }, + {12318, 65, 128, 32, 6080, 32, 1, 191 }, /* tcId: 192. edge case for computation of x with projective coordinates in left to right addition chain */ - {12383, 65, 128, 32, 6112, 32, 1 }, + {12383, 65, 128, 32, 6112, 32, 1, 192 }, /* tcId: 193. edge case for computation of x with projective coordinates in left to right addition chain */ - {12448, 65, 128, 32, 6144, 32, 1 }, + {12448, 65, 128, 32, 6144, 32, 1, 193 }, /* tcId: 194. edge case for computation of x with projective coordinates in left to right addition chain */ - {12513, 65, 128, 32, 6176, 32, 1 }, + {12513, 65, 128, 32, 6176, 32, 1, 194 }, /* tcId: 195. edge case for computation of x with projective coordinates in left to right addition chain */ - {12578, 65, 128, 32, 6208, 32, 1 }, + {12578, 65, 128, 32, 6208, 32, 1, 195 }, /* tcId: 196. edge case for computation of x with projective coordinates in left to right addition chain */ - {12643, 65, 128, 32, 6240, 32, 1 }, + {12643, 65, 128, 32, 6240, 32, 1, 196 }, /* tcId: 197. edge case for computation of x with projective coordinates in left to right addition chain */ - {12708, 65, 128, 32, 6272, 32, 1 }, + {12708, 65, 128, 32, 6272, 32, 1, 197 }, /* tcId: 198. edge case for computation of x with projective coordinates in left to right addition chain */ - {12773, 65, 128, 32, 6304, 32, 1 }, + {12773, 65, 128, 32, 6304, 32, 1, 198 }, /* tcId: 199. edge case for computation of x with projective coordinates in left to right addition chain */ - {12838, 65, 128, 32, 6336, 32, 1 }, + {12838, 65, 128, 32, 6336, 32, 1, 199 }, /* tcId: 200. edge case for computation of x with projective coordinates in left to right addition chain */ - {12903, 65, 128, 32, 6368, 32, 1 }, + {12903, 65, 128, 32, 6368, 32, 1, 200 }, /* tcId: 201. edge case for computation of x with projective coordinates in left to right addition chain */ - {12968, 65, 128, 32, 6400, 32, 1 }, + {12968, 65, 128, 32, 6400, 32, 1, 201 }, /* tcId: 202. edge case for computation of x with projective coordinates in left to right addition chain */ - {13033, 65, 128, 32, 6432, 32, 1 }, + {13033, 65, 128, 32, 6432, 32, 1, 202 }, /* tcId: 203. edge case for computation of x with projective coordinates in left to right addition chain */ - {13098, 65, 128, 32, 6464, 32, 1 }, + {13098, 65, 128, 32, 6464, 32, 1, 203 }, /* tcId: 204. edge case for computation of x with projective coordinates in left to right addition chain */ - {13163, 65, 128, 32, 6496, 32, 1 }, + {13163, 65, 128, 32, 6496, 32, 1, 204 }, /* tcId: 205. edge case for computation of x with projective coordinates in left to right addition chain */ - {13228, 65, 128, 32, 6528, 32, 1 }, + {13228, 65, 128, 32, 6528, 32, 1, 205 }, /* tcId: 206. edge case for computation of x with projective coordinates in left to right addition chain */ - {13293, 65, 128, 32, 6560, 32, 1 }, + {13293, 65, 128, 32, 6560, 32, 1, 206 }, /* tcId: 207. edge case for computation of x with projective coordinates in left to right addition chain */ - {13358, 65, 128, 32, 6592, 32, 1 }, + {13358, 65, 128, 32, 6592, 32, 1, 207 }, /* tcId: 208. edge case for computation of x with projective coordinates in left to right addition chain */ - {13423, 65, 128, 32, 6624, 32, 1 }, + {13423, 65, 128, 32, 6624, 32, 1, 208 }, /* tcId: 209. edge case for computation of x with projective coordinates in left to right addition chain */ - {13488, 65, 128, 32, 6656, 32, 1 }, + {13488, 65, 128, 32, 6656, 32, 1, 209 }, /* tcId: 210. edge case for computation of x with projective coordinates in left to right addition chain */ - {13553, 65, 128, 32, 6688, 32, 1 }, + {13553, 65, 128, 32, 6688, 32, 1, 210 }, /* tcId: 211. edge case for computation of x with projective coordinates in left to right addition chain */ - {13618, 65, 128, 32, 6720, 32, 1 }, + {13618, 65, 128, 32, 6720, 32, 1, 211 }, /* tcId: 212. edge case for computation of x with projective coordinates in left to right addition chain */ - {13683, 65, 128, 32, 6752, 32, 1 }, + {13683, 65, 128, 32, 6752, 32, 1, 212 }, /* tcId: 213. edge case for computation of x with projective coordinates in left to right addition chain */ - {13748, 65, 128, 32, 6784, 32, 1 }, + {13748, 65, 128, 32, 6784, 32, 1, 213 }, /* tcId: 214. edge case for computation of x with projective coordinates in left to right addition chain */ - {13813, 65, 128, 32, 6816, 32, 1 }, + {13813, 65, 128, 32, 6816, 32, 1, 214 }, /* tcId: 215. edge case for computation of x with projective coordinates in left to right addition chain */ - {13878, 65, 128, 32, 6848, 32, 1 }, + {13878, 65, 128, 32, 6848, 32, 1, 215 }, /* tcId: 216. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {13943, 65, 128, 32, 6880, 32, 1 }, + {13943, 65, 128, 32, 6880, 32, 1, 216 }, /* tcId: 217. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14008, 65, 128, 32, 6912, 32, 1 }, + {14008, 65, 128, 32, 6912, 32, 1, 217 }, /* tcId: 218. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14073, 65, 128, 32, 6944, 32, 1 }, + {14073, 65, 128, 32, 6944, 32, 1, 218 }, /* tcId: 219. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14138, 65, 128, 32, 6976, 32, 1 }, + {14138, 65, 128, 32, 6976, 32, 1, 219 }, /* tcId: 220. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14203, 65, 128, 32, 7008, 32, 1 }, + {14203, 65, 128, 32, 7008, 32, 1, 220 }, /* tcId: 221. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14268, 65, 128, 32, 7040, 32, 1 }, + {14268, 65, 128, 32, 7040, 32, 1, 221 }, /* tcId: 222. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14333, 65, 128, 32, 7072, 32, 1 }, + {14333, 65, 128, 32, 7072, 32, 1, 222 }, /* tcId: 223. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14398, 65, 128, 32, 7104, 32, 1 }, + {14398, 65, 128, 32, 7104, 32, 1, 223 }, /* tcId: 224. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14463, 65, 128, 32, 7136, 32, 1 }, + {14463, 65, 128, 32, 7136, 32, 1, 224 }, /* tcId: 225. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14528, 65, 128, 32, 7168, 32, 1 }, + {14528, 65, 128, 32, 7168, 32, 1, 225 }, /* tcId: 226. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14593, 65, 128, 32, 7200, 32, 1 }, + {14593, 65, 128, 32, 7200, 32, 1, 226 }, /* tcId: 227. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14658, 65, 128, 32, 7232, 32, 1 }, + {14658, 65, 128, 32, 7232, 32, 1, 227 }, /* tcId: 228. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14723, 65, 128, 32, 7264, 32, 1 }, + {14723, 65, 128, 32, 7264, 32, 1, 228 }, /* tcId: 229. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14788, 65, 128, 32, 7296, 32, 1 }, + {14788, 65, 128, 32, 7296, 32, 1, 229 }, /* tcId: 230. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14853, 65, 128, 32, 7328, 32, 1 }, + {14853, 65, 128, 32, 7328, 32, 1, 230 }, /* tcId: 231. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14918, 65, 128, 32, 7360, 32, 1 }, + {14918, 65, 128, 32, 7360, 32, 1, 231 }, /* tcId: 232. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {14983, 65, 128, 32, 7392, 32, 1 }, + {14983, 65, 128, 32, 7392, 32, 1, 232 }, /* tcId: 233. edge case for computation of x with projective coordinates in precomputation or right to left addition chain */ - {15048, 65, 128, 32, 7424, 32, 1 }, + {15048, 65, 128, 32, 7424, 32, 1, 233 }, /* tcId: 234. edge case for computation of x with projective coordinates in right to left addition chain */ - {15113, 65, 128, 32, 7456, 32, 1 }, + {15113, 65, 128, 32, 7456, 32, 1, 234 }, /* tcId: 235. edge case for computation of x with projective coordinates in right to left addition chain */ - {15178, 65, 128, 32, 7488, 32, 1 }, + {15178, 65, 128, 32, 7488, 32, 1, 235 }, /* tcId: 236. edge case for computation of x with projective coordinates in right to left addition chain */ - {15243, 65, 128, 32, 7520, 32, 1 }, + {15243, 65, 128, 32, 7520, 32, 1, 236 }, /* tcId: 237. edge case for computation of x with projective coordinates in right to left addition chain */ - {15308, 65, 128, 32, 7552, 32, 1 }, + {15308, 65, 128, 32, 7552, 32, 1, 237 }, /* tcId: 238. edge case for computation of x with projective coordinates in right to left addition chain */ - {15373, 65, 128, 32, 7584, 32, 1 }, + {15373, 65, 128, 32, 7584, 32, 1, 238 }, /* tcId: 239. edge case for computation of x with projective coordinates in right to left addition chain */ - {15438, 65, 128, 32, 7616, 32, 1 }, + {15438, 65, 128, 32, 7616, 32, 1, 239 }, /* tcId: 240. edge case for computation of x with projective coordinates in right to left addition chain */ - {15503, 65, 128, 32, 7648, 32, 1 }, + {15503, 65, 128, 32, 7648, 32, 1, 240 }, /* tcId: 241. edge case for computation of x with projective coordinates in right to left addition chain */ - {15568, 65, 128, 32, 7680, 32, 1 }, + {15568, 65, 128, 32, 7680, 32, 1, 241 }, /* tcId: 242. edge case for computation of x with projective coordinates in right to left addition chain */ - {15633, 65, 128, 32, 7712, 32, 1 }, + {15633, 65, 128, 32, 7712, 32, 1, 242 }, /* tcId: 243. edge case for computation of x with projective coordinates in right to left addition chain */ - {15698, 65, 128, 32, 7744, 32, 1 }, + {15698, 65, 128, 32, 7744, 32, 1, 243 }, /* tcId: 244. edge case for computation of x with projective coordinates in right to left addition chain */ - {15763, 65, 128, 32, 7776, 32, 1 }, + {15763, 65, 128, 32, 7776, 32, 1, 244 }, /* tcId: 245. edge case for computation of x with projective coordinates in right to left addition chain */ - {15828, 65, 128, 32, 7808, 32, 1 }, + {15828, 65, 128, 32, 7808, 32, 1, 245 }, /* tcId: 246. edge case for computation of x with projective coordinates in right to left addition chain */ - {15893, 65, 128, 32, 7840, 32, 1 }, + {15893, 65, 128, 32, 7840, 32, 1, 246 }, /* tcId: 247. edge case for computation of x with projective coordinates in right to left addition chain */ - {15958, 65, 128, 32, 7872, 32, 1 }, + {15958, 65, 128, 32, 7872, 32, 1, 247 }, /* tcId: 248. edge case for computation of x with projective coordinates in right to left addition chain */ - {16023, 65, 128, 32, 7904, 32, 1 }, + {16023, 65, 128, 32, 7904, 32, 1, 248 }, /* tcId: 249. edge case for computation of y with projective coordinates */ - {16088, 65, 128, 32, 7936, 32, 1 }, + {16088, 65, 128, 32, 7936, 32, 1, 249 }, /* tcId: 250. edge case for computation of y with projective coordinates */ - {16153, 65, 128, 32, 7968, 32, 1 }, + {16153, 65, 128, 32, 7968, 32, 1, 250 }, /* tcId: 251. edge case for computation of y with projective coordinates */ - {16218, 65, 128, 32, 8000, 32, 1 }, + {16218, 65, 128, 32, 8000, 32, 1, 251 }, /* tcId: 252. edge case for computation of y with projective coordinates in left to right addition chain */ - {16283, 65, 128, 32, 8032, 32, 1 }, + {16283, 65, 128, 32, 8032, 32, 1, 252 }, /* tcId: 253. edge case for computation of y with projective coordinates in left to right addition chain */ - {16348, 65, 128, 32, 8064, 32, 1 }, + {16348, 65, 128, 32, 8064, 32, 1, 253 }, /* tcId: 254. edge case for computation of y with projective coordinates in left to right addition chain */ - {16413, 65, 128, 32, 8096, 32, 1 }, + {16413, 65, 128, 32, 8096, 32, 1, 254 }, /* tcId: 255. edge case for computation of y with projective coordinates in left to right addition chain */ - {16478, 65, 128, 32, 8128, 32, 1 }, + {16478, 65, 128, 32, 8128, 32, 1, 255 }, /* tcId: 256. edge case for computation of y with projective coordinates in left to right addition chain */ - {16543, 65, 128, 32, 8160, 32, 1 }, + {16543, 65, 128, 32, 8160, 32, 1, 256 }, /* tcId: 257. edge case for computation of y with projective coordinates in left to right addition chain */ - {16608, 65, 128, 32, 8192, 32, 1 }, + {16608, 65, 128, 32, 8192, 32, 1, 257 }, /* tcId: 258. edge case for computation of y with projective coordinates in left to right addition chain */ - {16673, 65, 128, 32, 8224, 32, 1 }, + {16673, 65, 128, 32, 8224, 32, 1, 258 }, /* tcId: 259. edge case for computation of y with projective coordinates in left to right addition chain */ - {16738, 65, 128, 32, 8256, 32, 1 }, + {16738, 65, 128, 32, 8256, 32, 1, 259 }, /* tcId: 260. edge case for computation of y with projective coordinates in left to right addition chain */ - {16803, 65, 128, 32, 8288, 32, 1 }, + {16803, 65, 128, 32, 8288, 32, 1, 260 }, /* tcId: 261. edge case for computation of y with projective coordinates in left to right addition chain */ - {16868, 65, 128, 32, 8320, 32, 1 }, + {16868, 65, 128, 32, 8320, 32, 1, 261 }, /* tcId: 262. edge case for computation of y with projective coordinates in left to right addition chain */ - {16933, 65, 128, 32, 8352, 32, 1 }, + {16933, 65, 128, 32, 8352, 32, 1, 262 }, /* tcId: 263. edge case for computation of y with projective coordinates in left to right addition chain */ - {16998, 65, 128, 32, 8384, 32, 1 }, + {16998, 65, 128, 32, 8384, 32, 1, 263 }, /* tcId: 264. edge case for computation of y with projective coordinates in left to right addition chain */ - {17063, 65, 128, 32, 8416, 32, 1 }, + {17063, 65, 128, 32, 8416, 32, 1, 264 }, /* tcId: 265. edge case for computation of y with projective coordinates in left to right addition chain */ - {17128, 65, 128, 32, 8448, 32, 1 }, + {17128, 65, 128, 32, 8448, 32, 1, 265 }, /* tcId: 266. edge case for computation of y with projective coordinates in left to right addition chain */ - {17193, 65, 128, 32, 8480, 32, 1 }, + {17193, 65, 128, 32, 8480, 32, 1, 266 }, /* tcId: 267. edge case for computation of y with projective coordinates in left to right addition chain */ - {17258, 65, 128, 32, 8512, 32, 1 }, + {17258, 65, 128, 32, 8512, 32, 1, 267 }, /* tcId: 268. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ - {17323, 65, 128, 32, 8544, 32, 1 }, + {17323, 65, 128, 32, 8544, 32, 1, 268 }, /* tcId: 269. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ - {17388, 65, 128, 32, 8576, 32, 1 }, + {17388, 65, 128, 32, 8576, 32, 1, 269 }, /* tcId: 270. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ - {17453, 65, 128, 32, 8608, 32, 1 }, + {17453, 65, 128, 32, 8608, 32, 1, 270 }, /* tcId: 271. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ - {17518, 65, 128, 32, 8640, 32, 1 }, + {17518, 65, 128, 32, 8640, 32, 1, 271 }, /* tcId: 272. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ - {17583, 65, 128, 32, 8672, 32, 1 }, + {17583, 65, 128, 32, 8672, 32, 1, 272 }, /* tcId: 273. edge case for computation of y with projective coordinates in precomputation or right to left addition chain */ - {17648, 65, 128, 32, 8704, 32, 1 }, + {17648, 65, 128, 32, 8704, 32, 1, 273 }, /* tcId: 274. edge case for computation of y with projective coordinates in right to left addition chain */ - {17713, 65, 128, 32, 8736, 32, 1 }, + {17713, 65, 128, 32, 8736, 32, 1, 274 }, /* tcId: 275. edge case for computation of y with projective coordinates in right to left addition chain */ - {17778, 65, 128, 32, 8768, 32, 1 }, + {17778, 65, 128, 32, 8768, 32, 1, 275 }, /* tcId: 276. edge case for computation of y with projective coordinates in right to left addition chain */ - {17843, 65, 128, 32, 8800, 32, 1 }, + {17843, 65, 128, 32, 8800, 32, 1, 276 }, /* tcId: 277. edge case for computation of y with projective coordinates in right to left addition chain */ - {17908, 65, 128, 32, 8832, 32, 1 }, + {17908, 65, 128, 32, 8832, 32, 1, 277 }, /* tcId: 278. edge case for computation of y with projective coordinates in right to left addition chain */ - {17973, 65, 128, 32, 8864, 32, 1 }, + {17973, 65, 128, 32, 8864, 32, 1, 278 }, /* tcId: 279. point with coordinate x = 1 */ - {3608, 65, 128, 32, 8896, 32, 1 }, + {3608, 65, 128, 32, 8896, 32, 1, 279 }, /* tcId: 280. point with coordinate x = 1 */ - {18038, 65, 128, 32, 8928, 32, 1 }, + {18038, 65, 128, 32, 8928, 32, 1, 280 }, /* tcId: 281. point with coordinate x = 1 */ - {18103, 65, 128, 32, 8960, 32, 1 }, + {18103, 65, 128, 32, 8960, 32, 1, 281 }, /* tcId: 282. point with coordinate x = 1 in left to right addition chain */ - {18168, 65, 128, 32, 8992, 32, 1 }, + {18168, 65, 128, 32, 8992, 32, 1, 282 }, /* tcId: 283. point with coordinate x = 1 in left to right addition chain */ - {18233, 65, 128, 32, 9024, 32, 1 }, + {18233, 65, 128, 32, 9024, 32, 1, 283 }, /* tcId: 284. point with coordinate x = 1 in left to right addition chain */ - {18298, 65, 128, 32, 9056, 32, 1 }, + {18298, 65, 128, 32, 9056, 32, 1, 284 }, /* tcId: 285. point with coordinate x = 1 in left to right addition chain */ - {18363, 65, 128, 32, 9088, 32, 1 }, + {18363, 65, 128, 32, 9088, 32, 1, 285 }, /* tcId: 286. point with coordinate x = 1 in left to right addition chain */ - {18428, 65, 128, 32, 9120, 32, 1 }, + {18428, 65, 128, 32, 9120, 32, 1, 286 }, /* tcId: 287. point with coordinate x = 1 in left to right addition chain */ - {18493, 65, 128, 32, 9152, 32, 1 }, + {18493, 65, 128, 32, 9152, 32, 1, 287 }, /* tcId: 288. point with coordinate x = 1 in left to right addition chain */ - {18558, 65, 128, 32, 9184, 32, 1 }, + {18558, 65, 128, 32, 9184, 32, 1, 288 }, /* tcId: 289. point with coordinate x = 1 in left to right addition chain */ - {18623, 65, 128, 32, 9216, 32, 1 }, + {18623, 65, 128, 32, 9216, 32, 1, 289 }, /* tcId: 290. point with coordinate x = 1 in left to right addition chain */ - {18688, 65, 128, 32, 9248, 32, 1 }, + {18688, 65, 128, 32, 9248, 32, 1, 290 }, /* tcId: 291. point with coordinate x = 1 in left to right addition chain */ - {18753, 65, 128, 32, 9280, 32, 1 }, + {18753, 65, 128, 32, 9280, 32, 1, 291 }, /* tcId: 292. point with coordinate x = 1 in left to right addition chain */ - {18818, 65, 128, 32, 9312, 32, 1 }, + {18818, 65, 128, 32, 9312, 32, 1, 292 }, /* tcId: 293. point with coordinate x = 1 in left to right addition chain */ - {18883, 65, 128, 32, 9344, 32, 1 }, + {18883, 65, 128, 32, 9344, 32, 1, 293 }, /* tcId: 294. point with coordinate x = 1 in left to right addition chain */ - {18948, 65, 128, 32, 9376, 32, 1 }, + {18948, 65, 128, 32, 9376, 32, 1, 294 }, /* tcId: 295. point with coordinate x = 1 in left to right addition chain */ - {19013, 65, 128, 32, 9408, 32, 1 }, + {19013, 65, 128, 32, 9408, 32, 1, 295 }, /* tcId: 296. point with coordinate x = 1 in left to right addition chain */ - {19078, 65, 128, 32, 9440, 32, 1 }, + {19078, 65, 128, 32, 9440, 32, 1, 296 }, /* tcId: 297. point with coordinate x = 1 in left to right addition chain */ - {19143, 65, 128, 32, 9472, 32, 1 }, + {19143, 65, 128, 32, 9472, 32, 1, 297 }, /* tcId: 298. point with coordinate x = 1 in precomputation or right to left addition chain */ - {19208, 65, 128, 32, 9504, 32, 1 }, + {19208, 65, 128, 32, 9504, 32, 1, 298 }, /* tcId: 299. point with coordinate x = 1 in precomputation or right to left addition chain */ - {19273, 65, 128, 32, 9536, 32, 1 }, + {19273, 65, 128, 32, 9536, 32, 1, 299 }, /* tcId: 300. point with coordinate x = 1 in precomputation or right to left addition chain */ - {19338, 65, 128, 32, 9568, 32, 1 }, + {19338, 65, 128, 32, 9568, 32, 1, 300 }, /* tcId: 301. point with coordinate x = 1 in precomputation or right to left addition chain */ - {19403, 65, 128, 32, 9600, 32, 1 }, + {19403, 65, 128, 32, 9600, 32, 1, 301 }, /* tcId: 302. point with coordinate x = 1 in precomputation or right to left addition chain */ - {19468, 65, 128, 32, 9632, 32, 1 }, + {19468, 65, 128, 32, 9632, 32, 1, 302 }, /* tcId: 303. point with coordinate x = 1 in precomputation or right to left addition chain */ - {19533, 65, 128, 32, 9664, 32, 1 }, + {19533, 65, 128, 32, 9664, 32, 1, 303 }, /* tcId: 304. point with coordinate x = 1 in right to left addition chain */ - {19598, 65, 128, 32, 9696, 32, 1 }, + {19598, 65, 128, 32, 9696, 32, 1, 304 }, /* tcId: 305. point with coordinate x = 1 in right to left addition chain */ - {19663, 65, 128, 32, 9728, 32, 1 }, + {19663, 65, 128, 32, 9728, 32, 1, 305 }, /* tcId: 306. point with coordinate x = 1 in right to left addition chain */ - {19728, 65, 128, 32, 9760, 32, 1 }, + {19728, 65, 128, 32, 9760, 32, 1, 306 }, /* tcId: 307. point with coordinate x = 1 in right to left addition chain */ - {19793, 65, 128, 32, 9792, 32, 1 }, + {19793, 65, 128, 32, 9792, 32, 1, 307 }, /* tcId: 308. point with coordinate x = 1 in right to left addition chain */ - {19858, 65, 128, 32, 9824, 32, 1 }, + {19858, 65, 128, 32, 9824, 32, 1, 308 }, /* tcId: 309. point with coordinate x = 2 */ - {3673, 65, 128, 32, 9856, 32, 1 }, + {3673, 65, 128, 32, 9856, 32, 1, 309 }, /* tcId: 310. point with coordinate x = 2 */ - {19923, 65, 128, 32, 9888, 32, 1 }, + {19923, 65, 128, 32, 9888, 32, 1, 310 }, /* tcId: 311. point with coordinate x = 2 */ - {19988, 65, 128, 32, 9920, 32, 1 }, + {19988, 65, 128, 32, 9920, 32, 1, 311 }, /* tcId: 312. point with coordinate x = 2 in left to right addition chain */ - {20053, 65, 128, 32, 9952, 32, 1 }, + {20053, 65, 128, 32, 9952, 32, 1, 312 }, /* tcId: 313. point with coordinate x = 2 in left to right addition chain */ - {20118, 65, 128, 32, 9984, 32, 1 }, + {20118, 65, 128, 32, 9984, 32, 1, 313 }, /* tcId: 314. point with coordinate x = 2 in left to right addition chain */ - {20183, 65, 128, 32, 10016, 32, 1 }, + {20183, 65, 128, 32, 10016, 32, 1, 314 }, /* tcId: 315. point with coordinate x = 2 in left to right addition chain */ - {20248, 65, 128, 32, 10048, 32, 1 }, + {20248, 65, 128, 32, 10048, 32, 1, 315 }, /* tcId: 316. point with coordinate x = 2 in left to right addition chain */ - {20313, 65, 128, 32, 10080, 32, 1 }, + {20313, 65, 128, 32, 10080, 32, 1, 316 }, /* tcId: 317. point with coordinate x = 2 in left to right addition chain */ - {20378, 65, 128, 32, 10112, 32, 1 }, + {20378, 65, 128, 32, 10112, 32, 1, 317 }, /* tcId: 318. point with coordinate x = 2 in left to right addition chain */ - {20443, 65, 128, 32, 10144, 32, 1 }, + {20443, 65, 128, 32, 10144, 32, 1, 318 }, /* tcId: 319. point with coordinate x = 2 in left to right addition chain */ - {20508, 65, 128, 32, 10176, 32, 1 }, + {20508, 65, 128, 32, 10176, 32, 1, 319 }, /* tcId: 320. point with coordinate x = 2 in left to right addition chain */ - {20573, 65, 128, 32, 10208, 32, 1 }, + {20573, 65, 128, 32, 10208, 32, 1, 320 }, /* tcId: 321. point with coordinate x = 2 in left to right addition chain */ - {20638, 65, 128, 32, 10240, 32, 1 }, + {20638, 65, 128, 32, 10240, 32, 1, 321 }, /* tcId: 322. point with coordinate x = 2 in left to right addition chain */ - {20703, 65, 128, 32, 10272, 32, 1 }, + {20703, 65, 128, 32, 10272, 32, 1, 322 }, /* tcId: 323. point with coordinate x = 2 in left to right addition chain */ - {20768, 65, 128, 32, 10304, 32, 1 }, + {20768, 65, 128, 32, 10304, 32, 1, 323 }, /* tcId: 324. point with coordinate x = 2 in left to right addition chain */ - {20833, 65, 128, 32, 10336, 32, 1 }, + {20833, 65, 128, 32, 10336, 32, 1, 324 }, /* tcId: 325. point with coordinate x = 2 in left to right addition chain */ - {20898, 65, 128, 32, 10368, 32, 1 }, + {20898, 65, 128, 32, 10368, 32, 1, 325 }, /* tcId: 326. point with coordinate x = 2 in left to right addition chain */ - {20963, 65, 128, 32, 10400, 32, 1 }, + {20963, 65, 128, 32, 10400, 32, 1, 326 }, /* tcId: 327. point with coordinate x = 2 in left to right addition chain */ - {21028, 65, 128, 32, 10432, 32, 1 }, + {21028, 65, 128, 32, 10432, 32, 1, 327 }, /* tcId: 328. point with coordinate x = 2 in precomputation or right to left addition chain */ - {21093, 65, 128, 32, 10464, 32, 1 }, + {21093, 65, 128, 32, 10464, 32, 1, 328 }, /* tcId: 329. point with coordinate x = 2 in precomputation or right to left addition chain */ - {21158, 65, 128, 32, 10496, 32, 1 }, + {21158, 65, 128, 32, 10496, 32, 1, 329 }, /* tcId: 330. point with coordinate x = 2 in precomputation or right to left addition chain */ - {21223, 65, 128, 32, 10528, 32, 1 }, + {21223, 65, 128, 32, 10528, 32, 1, 330 }, /* tcId: 331. point with coordinate x = 2 in precomputation or right to left addition chain */ - {21288, 65, 128, 32, 10560, 32, 1 }, + {21288, 65, 128, 32, 10560, 32, 1, 331 }, /* tcId: 332. point with coordinate x = 2 in precomputation or right to left addition chain */ - {21353, 65, 128, 32, 10592, 32, 1 }, + {21353, 65, 128, 32, 10592, 32, 1, 332 }, /* tcId: 333. point with coordinate x = 2 in precomputation or right to left addition chain */ - {21418, 65, 128, 32, 10624, 32, 1 }, + {21418, 65, 128, 32, 10624, 32, 1, 333 }, /* tcId: 334. point with coordinate x = 2 in right to left addition chain */ - {21483, 65, 128, 32, 10656, 32, 1 }, + {21483, 65, 128, 32, 10656, 32, 1, 334 }, /* tcId: 335. point with coordinate x = 2 in right to left addition chain */ - {21548, 65, 128, 32, 10688, 32, 1 }, + {21548, 65, 128, 32, 10688, 32, 1, 335 }, /* tcId: 336. point with coordinate x = 2 in right to left addition chain */ - {21613, 65, 128, 32, 10720, 32, 1 }, + {21613, 65, 128, 32, 10720, 32, 1, 336 }, /* tcId: 337. point with coordinate x = 2 in right to left addition chain */ - {21678, 65, 128, 32, 10752, 32, 1 }, + {21678, 65, 128, 32, 10752, 32, 1, 337 }, /* tcId: 338. point with coordinate x = 2 in right to left addition chain */ - {21743, 65, 128, 32, 10784, 32, 1 }, + {21743, 65, 128, 32, 10784, 32, 1, 338 }, /* tcId: 339. point with coordinate x = 3 */ - {3738, 65, 128, 32, 10816, 32, 1 }, + {3738, 65, 128, 32, 10816, 32, 1, 339 }, /* tcId: 340. point with coordinate x = 3 */ - {21808, 65, 128, 32, 10848, 32, 1 }, + {21808, 65, 128, 32, 10848, 32, 1, 340 }, /* tcId: 341. point with coordinate x = 3 */ - {21873, 65, 128, 32, 10880, 32, 1 }, + {21873, 65, 128, 32, 10880, 32, 1, 341 }, /* tcId: 342. point with coordinate x = 3 in left to right addition chain */ - {21938, 65, 128, 32, 10912, 32, 1 }, + {21938, 65, 128, 32, 10912, 32, 1, 342 }, /* tcId: 343. point with coordinate x = 3 in left to right addition chain */ - {22003, 65, 128, 32, 10944, 32, 1 }, + {22003, 65, 128, 32, 10944, 32, 1, 343 }, /* tcId: 344. point with coordinate x = 3 in left to right addition chain */ - {22068, 65, 128, 32, 10976, 32, 1 }, + {22068, 65, 128, 32, 10976, 32, 1, 344 }, /* tcId: 345. point with coordinate x = 3 in left to right addition chain */ - {22133, 65, 128, 32, 11008, 32, 1 }, + {22133, 65, 128, 32, 11008, 32, 1, 345 }, /* tcId: 346. point with coordinate x = 3 in left to right addition chain */ - {22198, 65, 128, 32, 11040, 32, 1 }, + {22198, 65, 128, 32, 11040, 32, 1, 346 }, /* tcId: 347. point with coordinate x = 3 in left to right addition chain */ - {22263, 65, 128, 32, 11072, 32, 1 }, + {22263, 65, 128, 32, 11072, 32, 1, 347 }, /* tcId: 348. point with coordinate x = 3 in left to right addition chain */ - {22328, 65, 128, 32, 11104, 32, 1 }, + {22328, 65, 128, 32, 11104, 32, 1, 348 }, /* tcId: 349. point with coordinate x = 3 in left to right addition chain */ - {22393, 65, 128, 32, 11136, 32, 1 }, + {22393, 65, 128, 32, 11136, 32, 1, 349 }, /* tcId: 350. point with coordinate x = 3 in left to right addition chain */ - {22458, 65, 128, 32, 11168, 32, 1 }, + {22458, 65, 128, 32, 11168, 32, 1, 350 }, /* tcId: 351. point with coordinate x = 3 in left to right addition chain */ - {22523, 65, 128, 32, 11200, 32, 1 }, + {22523, 65, 128, 32, 11200, 32, 1, 351 }, /* tcId: 352. point with coordinate x = 3 in left to right addition chain */ - {22588, 65, 128, 32, 11232, 32, 1 }, + {22588, 65, 128, 32, 11232, 32, 1, 352 }, /* tcId: 353. point with coordinate x = 3 in left to right addition chain */ - {22653, 65, 128, 32, 11264, 32, 1 }, + {22653, 65, 128, 32, 11264, 32, 1, 353 }, /* tcId: 354. point with coordinate x = 3 in left to right addition chain */ - {22718, 65, 128, 32, 11296, 32, 1 }, + {22718, 65, 128, 32, 11296, 32, 1, 354 }, /* tcId: 355. point with coordinate x = 3 in left to right addition chain */ - {22783, 65, 128, 32, 11328, 32, 1 }, + {22783, 65, 128, 32, 11328, 32, 1, 355 }, /* tcId: 356. point with coordinate x = 3 in left to right addition chain */ - {22848, 65, 128, 32, 11360, 32, 1 }, + {22848, 65, 128, 32, 11360, 32, 1, 356 }, /* tcId: 357. point with coordinate x = 3 in left to right addition chain */ - {22913, 65, 128, 32, 11392, 32, 1 }, + {22913, 65, 128, 32, 11392, 32, 1, 357 }, /* tcId: 358. point with coordinate x = 3 in precomputation or right to left addition chain */ - {22978, 65, 128, 32, 11424, 32, 1 }, + {22978, 65, 128, 32, 11424, 32, 1, 358 }, /* tcId: 359. point with coordinate x = 3 in precomputation or right to left addition chain */ - {23043, 65, 128, 32, 11456, 32, 1 }, + {23043, 65, 128, 32, 11456, 32, 1, 359 }, /* tcId: 360. point with coordinate x = 3 in precomputation or right to left addition chain */ - {23108, 65, 128, 32, 11488, 32, 1 }, + {23108, 65, 128, 32, 11488, 32, 1, 360 }, /* tcId: 361. point with coordinate x = 3 in precomputation or right to left addition chain */ - {23173, 65, 128, 32, 11520, 32, 1 }, + {23173, 65, 128, 32, 11520, 32, 1, 361 }, /* tcId: 362. point with coordinate x = 3 in precomputation or right to left addition chain */ - {23238, 65, 128, 32, 11552, 32, 1 }, + {23238, 65, 128, 32, 11552, 32, 1, 362 }, /* tcId: 363. point with coordinate x = 3 in precomputation or right to left addition chain */ - {23303, 65, 128, 32, 11584, 32, 1 }, + {23303, 65, 128, 32, 11584, 32, 1, 363 }, /* tcId: 364. point with coordinate x = 3 in right to left addition chain */ - {23368, 65, 128, 32, 11616, 32, 1 }, + {23368, 65, 128, 32, 11616, 32, 1, 364 }, /* tcId: 365. point with coordinate x = 3 in right to left addition chain */ - {23433, 65, 128, 32, 11648, 32, 1 }, + {23433, 65, 128, 32, 11648, 32, 1, 365 }, /* tcId: 366. point with coordinate x = 3 in right to left addition chain */ - {23498, 65, 128, 32, 11680, 32, 1 }, + {23498, 65, 128, 32, 11680, 32, 1, 366 }, /* tcId: 367. point with coordinate x = 3 in right to left addition chain */ - {23563, 65, 128, 32, 11712, 32, 1 }, + {23563, 65, 128, 32, 11712, 32, 1, 367 }, /* tcId: 368. point with coordinate x = 3 in right to left addition chain */ - {23628, 65, 128, 32, 11744, 32, 1 }, + {23628, 65, 128, 32, 11744, 32, 1, 368 }, /* tcId: 369. point with coordinate y = 1 */ - {23693, 65, 128, 32, 11776, 32, 1 }, + {23693, 65, 128, 32, 11776, 32, 1, 369 }, /* tcId: 370. point with coordinate y = 1 */ - {23758, 65, 128, 32, 11808, 32, 1 }, + {23758, 65, 128, 32, 11808, 32, 1, 370 }, /* tcId: 371. point with coordinate y = 1 */ - {23823, 65, 128, 32, 11840, 32, 1 }, + {23823, 65, 128, 32, 11840, 32, 1, 371 }, /* tcId: 372. point with coordinate y = 1 */ - {23888, 65, 128, 32, 11872, 32, 1 }, + {23888, 65, 128, 32, 11872, 32, 1, 372 }, /* tcId: 373. point with coordinate y = 1 */ - {23953, 65, 128, 32, 11904, 32, 1 }, + {23953, 65, 128, 32, 11904, 32, 1, 373 }, /* tcId: 374. point with coordinate y = 1 */ - {24018, 65, 128, 32, 11936, 32, 1 }, + {24018, 65, 128, 32, 11936, 32, 1, 374 }, /* tcId: 375. point with coordinate y = 1 */ - {24083, 65, 128, 32, 11968, 32, 1 }, + {24083, 65, 128, 32, 11968, 32, 1, 375 }, /* tcId: 376. point with coordinate y = 1 */ - {24148, 65, 128, 32, 12000, 32, 1 }, + {24148, 65, 128, 32, 12000, 32, 1, 376 }, /* tcId: 377. point with coordinate y = 1 */ - {24213, 65, 128, 32, 12032, 32, 1 }, + {24213, 65, 128, 32, 12032, 32, 1, 377 }, /* tcId: 378. point with coordinate y = 1 in left to right addition chain */ - {24278, 65, 128, 32, 12064, 32, 1 }, + {24278, 65, 128, 32, 12064, 32, 1, 378 }, /* tcId: 379. point with coordinate y = 1 in left to right addition chain */ - {24343, 65, 128, 32, 12096, 32, 1 }, + {24343, 65, 128, 32, 12096, 32, 1, 379 }, /* tcId: 380. point with coordinate y = 1 in left to right addition chain */ - {24408, 65, 128, 32, 12128, 32, 1 }, + {24408, 65, 128, 32, 12128, 32, 1, 380 }, /* tcId: 381. point with coordinate y = 1 in left to right addition chain */ - {24473, 65, 128, 32, 12160, 32, 1 }, + {24473, 65, 128, 32, 12160, 32, 1, 381 }, /* tcId: 382. point with coordinate y = 1 in left to right addition chain */ - {24538, 65, 128, 32, 12192, 32, 1 }, + {24538, 65, 128, 32, 12192, 32, 1, 382 }, /* tcId: 383. point with coordinate y = 1 in left to right addition chain */ - {24603, 65, 128, 32, 12224, 32, 1 }, + {24603, 65, 128, 32, 12224, 32, 1, 383 }, /* tcId: 384. point with coordinate y = 1 in left to right addition chain */ - {24668, 65, 128, 32, 12256, 32, 1 }, + {24668, 65, 128, 32, 12256, 32, 1, 384 }, /* tcId: 385. point with coordinate y = 1 in left to right addition chain */ - {24733, 65, 128, 32, 12288, 32, 1 }, + {24733, 65, 128, 32, 12288, 32, 1, 385 }, /* tcId: 386. point with coordinate y = 1 in left to right addition chain */ - {24798, 65, 128, 32, 12320, 32, 1 }, + {24798, 65, 128, 32, 12320, 32, 1, 386 }, /* tcId: 387. point with coordinate y = 1 in left to right addition chain */ - {24863, 65, 128, 32, 12352, 32, 1 }, + {24863, 65, 128, 32, 12352, 32, 1, 387 }, /* tcId: 388. point with coordinate y = 1 in left to right addition chain */ - {24928, 65, 128, 32, 12384, 32, 1 }, + {24928, 65, 128, 32, 12384, 32, 1, 388 }, /* tcId: 389. point with coordinate y = 1 in left to right addition chain */ - {24993, 65, 128, 32, 12416, 32, 1 }, + {24993, 65, 128, 32, 12416, 32, 1, 389 }, /* tcId: 390. point with coordinate y = 1 in left to right addition chain */ - {25058, 65, 128, 32, 12448, 32, 1 }, + {25058, 65, 128, 32, 12448, 32, 1, 390 }, /* tcId: 391. point with coordinate y = 1 in left to right addition chain */ - {25123, 65, 128, 32, 12480, 32, 1 }, + {25123, 65, 128, 32, 12480, 32, 1, 391 }, /* tcId: 392. point with coordinate y = 1 in left to right addition chain */ - {25188, 65, 128, 32, 12512, 32, 1 }, + {25188, 65, 128, 32, 12512, 32, 1, 392 }, /* tcId: 393. point with coordinate y = 1 in left to right addition chain */ - {25253, 65, 128, 32, 12544, 32, 1 }, + {25253, 65, 128, 32, 12544, 32, 1, 393 }, /* tcId: 394. point with coordinate y = 1 in left to right addition chain */ - {25318, 65, 128, 32, 12576, 32, 1 }, + {25318, 65, 128, 32, 12576, 32, 1, 394 }, /* tcId: 395. point with coordinate y = 1 in left to right addition chain */ - {25383, 65, 128, 32, 12608, 32, 1 }, + {25383, 65, 128, 32, 12608, 32, 1, 395 }, /* tcId: 396. point with coordinate y = 1 in left to right addition chain */ - {25448, 65, 128, 32, 12640, 32, 1 }, + {25448, 65, 128, 32, 12640, 32, 1, 396 }, /* tcId: 397. point with coordinate y = 1 in left to right addition chain */ - {25513, 65, 128, 32, 12672, 32, 1 }, + {25513, 65, 128, 32, 12672, 32, 1, 397 }, /* tcId: 398. point with coordinate y = 1 in left to right addition chain */ - {25578, 65, 128, 32, 12704, 32, 1 }, + {25578, 65, 128, 32, 12704, 32, 1, 398 }, /* tcId: 399. point with coordinate y = 1 in left to right addition chain */ - {25643, 65, 128, 32, 12736, 32, 1 }, + {25643, 65, 128, 32, 12736, 32, 1, 399 }, /* tcId: 400. point with coordinate y = 1 in left to right addition chain */ - {25708, 65, 128, 32, 12768, 32, 1 }, + {25708, 65, 128, 32, 12768, 32, 1, 400 }, /* tcId: 401. point with coordinate y = 1 in left to right addition chain */ - {25773, 65, 128, 32, 12800, 32, 1 }, + {25773, 65, 128, 32, 12800, 32, 1, 401 }, /* tcId: 402. point with coordinate y = 1 in left to right addition chain */ - {25838, 65, 128, 32, 12832, 32, 1 }, + {25838, 65, 128, 32, 12832, 32, 1, 402 }, /* tcId: 403. point with coordinate y = 1 in left to right addition chain */ - {25903, 65, 128, 32, 12864, 32, 1 }, + {25903, 65, 128, 32, 12864, 32, 1, 403 }, /* tcId: 404. point with coordinate y = 1 in left to right addition chain */ - {25968, 65, 128, 32, 12896, 32, 1 }, + {25968, 65, 128, 32, 12896, 32, 1, 404 }, /* tcId: 405. point with coordinate y = 1 in left to right addition chain */ - {26033, 65, 128, 32, 12928, 32, 1 }, + {26033, 65, 128, 32, 12928, 32, 1, 405 }, /* tcId: 406. point with coordinate y = 1 in left to right addition chain */ - {26098, 65, 128, 32, 12960, 32, 1 }, + {26098, 65, 128, 32, 12960, 32, 1, 406 }, /* tcId: 407. point with coordinate y = 1 in left to right addition chain */ - {26163, 65, 128, 32, 12992, 32, 1 }, + {26163, 65, 128, 32, 12992, 32, 1, 407 }, /* tcId: 408. point with coordinate y = 1 in left to right addition chain */ - {26228, 65, 128, 32, 13024, 32, 1 }, + {26228, 65, 128, 32, 13024, 32, 1, 408 }, /* tcId: 409. point with coordinate y = 1 in left to right addition chain */ - {26293, 65, 128, 32, 13056, 32, 1 }, + {26293, 65, 128, 32, 13056, 32, 1, 409 }, /* tcId: 410. point with coordinate y = 1 in left to right addition chain */ - {26358, 65, 128, 32, 13088, 32, 1 }, + {26358, 65, 128, 32, 13088, 32, 1, 410 }, /* tcId: 411. point with coordinate y = 1 in left to right addition chain */ - {26423, 65, 128, 32, 13120, 32, 1 }, + {26423, 65, 128, 32, 13120, 32, 1, 411 }, /* tcId: 412. point with coordinate y = 1 in left to right addition chain */ - {26488, 65, 128, 32, 13152, 32, 1 }, + {26488, 65, 128, 32, 13152, 32, 1, 412 }, /* tcId: 413. point with coordinate y = 1 in left to right addition chain */ - {26553, 65, 128, 32, 13184, 32, 1 }, + {26553, 65, 128, 32, 13184, 32, 1, 413 }, /* tcId: 414. point with coordinate y = 1 in left to right addition chain */ - {26618, 65, 128, 32, 13216, 32, 1 }, + {26618, 65, 128, 32, 13216, 32, 1, 414 }, /* tcId: 415. point with coordinate y = 1 in left to right addition chain */ - {26683, 65, 128, 32, 13248, 32, 1 }, + {26683, 65, 128, 32, 13248, 32, 1, 415 }, /* tcId: 416. point with coordinate y = 1 in left to right addition chain */ - {26748, 65, 128, 32, 13280, 32, 1 }, + {26748, 65, 128, 32, 13280, 32, 1, 416 }, /* tcId: 417. point with coordinate y = 1 in left to right addition chain */ - {26813, 65, 128, 32, 13312, 32, 1 }, + {26813, 65, 128, 32, 13312, 32, 1, 417 }, /* tcId: 418. point with coordinate y = 1 in left to right addition chain */ - {26878, 65, 128, 32, 13344, 32, 1 }, + {26878, 65, 128, 32, 13344, 32, 1, 418 }, /* tcId: 419. point with coordinate y = 1 in left to right addition chain */ - {26943, 65, 128, 32, 13376, 32, 1 }, + {26943, 65, 128, 32, 13376, 32, 1, 419 }, /* tcId: 420. point with coordinate y = 1 in left to right addition chain */ - {27008, 65, 128, 32, 13408, 32, 1 }, + {27008, 65, 128, 32, 13408, 32, 1, 420 }, /* tcId: 421. point with coordinate y = 1 in left to right addition chain */ - {27073, 65, 128, 32, 13440, 32, 1 }, + {27073, 65, 128, 32, 13440, 32, 1, 421 }, /* tcId: 422. point with coordinate y = 1 in left to right addition chain */ - {27138, 65, 128, 32, 13472, 32, 1 }, + {27138, 65, 128, 32, 13472, 32, 1, 422 }, /* tcId: 423. point with coordinate y = 1 in left to right addition chain */ - {27203, 65, 128, 32, 13504, 32, 1 }, + {27203, 65, 128, 32, 13504, 32, 1, 423 }, /* tcId: 424. point with coordinate y = 1 in left to right addition chain */ - {27268, 65, 128, 32, 13536, 32, 1 }, + {27268, 65, 128, 32, 13536, 32, 1, 424 }, /* tcId: 425. point with coordinate y = 1 in left to right addition chain */ - {27333, 65, 128, 32, 13568, 32, 1 }, + {27333, 65, 128, 32, 13568, 32, 1, 425 }, /* tcId: 426. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27398, 65, 128, 32, 13600, 32, 1 }, + {27398, 65, 128, 32, 13600, 32, 1, 426 }, /* tcId: 427. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27463, 65, 128, 32, 13632, 32, 1 }, + {27463, 65, 128, 32, 13632, 32, 1, 427 }, /* tcId: 428. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27528, 65, 128, 32, 13664, 32, 1 }, + {27528, 65, 128, 32, 13664, 32, 1, 428 }, /* tcId: 429. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27593, 65, 128, 32, 13696, 32, 1 }, + {27593, 65, 128, 32, 13696, 32, 1, 429 }, /* tcId: 430. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27658, 65, 128, 32, 13728, 32, 1 }, + {27658, 65, 128, 32, 13728, 32, 1, 430 }, /* tcId: 431. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27723, 65, 128, 32, 13760, 32, 1 }, + {27723, 65, 128, 32, 13760, 32, 1, 431 }, /* tcId: 432. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27788, 65, 128, 32, 13792, 32, 1 }, + {27788, 65, 128, 32, 13792, 32, 1, 432 }, /* tcId: 433. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27853, 65, 128, 32, 13824, 32, 1 }, + {27853, 65, 128, 32, 13824, 32, 1, 433 }, /* tcId: 434. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27918, 65, 128, 32, 13856, 32, 1 }, + {27918, 65, 128, 32, 13856, 32, 1, 434 }, /* tcId: 435. point with coordinate y = 1 in precomputation or right to left addition chain */ - {27983, 65, 128, 32, 13888, 32, 1 }, + {27983, 65, 128, 32, 13888, 32, 1, 435 }, /* tcId: 436. point with coordinate y = 1 in precomputation or right to left addition chain */ - {28048, 65, 128, 32, 13920, 32, 1 }, + {28048, 65, 128, 32, 13920, 32, 1, 436 }, /* tcId: 437. point with coordinate y = 1 in precomputation or right to left addition chain */ - {28113, 65, 128, 32, 13952, 32, 1 }, + {28113, 65, 128, 32, 13952, 32, 1, 437 }, /* tcId: 438. point with coordinate y = 1 in precomputation or right to left addition chain */ - {28178, 65, 128, 32, 13984, 32, 1 }, + {28178, 65, 128, 32, 13984, 32, 1, 438 }, /* tcId: 439. point with coordinate y = 1 in precomputation or right to left addition chain */ - {28243, 65, 128, 32, 14016, 32, 1 }, + {28243, 65, 128, 32, 14016, 32, 1, 439 }, /* tcId: 440. point with coordinate y = 1 in precomputation or right to left addition chain */ - {28308, 65, 128, 32, 14048, 32, 1 }, + {28308, 65, 128, 32, 14048, 32, 1, 440 }, /* tcId: 441. point with coordinate y = 1 in precomputation or right to left addition chain */ - {28373, 65, 128, 32, 14080, 32, 1 }, + {28373, 65, 128, 32, 14080, 32, 1, 441 }, /* tcId: 442. point with coordinate y = 1 in precomputation or right to left addition chain */ - {28438, 65, 128, 32, 14112, 32, 1 }, + {28438, 65, 128, 32, 14112, 32, 1, 442 }, /* tcId: 443. point with coordinate y = 1 in precomputation or right to left addition chain */ - {28503, 65, 128, 32, 14144, 32, 1 }, + {28503, 65, 128, 32, 14144, 32, 1, 443 }, /* tcId: 444. point with coordinate y = 1 in right to left addition chain */ - {28568, 65, 128, 32, 14176, 32, 1 }, + {28568, 65, 128, 32, 14176, 32, 1, 444 }, /* tcId: 445. point with coordinate y = 1 in right to left addition chain */ - {28633, 65, 128, 32, 14208, 32, 1 }, + {28633, 65, 128, 32, 14208, 32, 1, 445 }, /* tcId: 446. point with coordinate y = 1 in right to left addition chain */ - {28698, 65, 128, 32, 14240, 32, 1 }, + {28698, 65, 128, 32, 14240, 32, 1, 446 }, /* tcId: 447. point with coordinate y = 1 in right to left addition chain */ - {28763, 65, 128, 32, 14272, 32, 1 }, + {28763, 65, 128, 32, 14272, 32, 1, 447 }, /* tcId: 448. point with coordinate y = 1 in right to left addition chain */ - {28828, 65, 128, 32, 14304, 32, 1 }, + {28828, 65, 128, 32, 14304, 32, 1, 448 }, /* tcId: 449. point with coordinate y = 1 in right to left addition chain */ - {28893, 65, 128, 32, 14336, 32, 1 }, + {28893, 65, 128, 32, 14336, 32, 1, 449 }, /* tcId: 450. point with coordinate y = 1 in right to left addition chain */ - {28958, 65, 128, 32, 14368, 32, 1 }, + {28958, 65, 128, 32, 14368, 32, 1, 450 }, /* tcId: 451. point with coordinate y = 1 in right to left addition chain */ - {29023, 65, 128, 32, 14400, 32, 1 }, + {29023, 65, 128, 32, 14400, 32, 1, 451 }, /* tcId: 452. point with coordinate y = 1 in right to left addition chain */ - {29088, 65, 128, 32, 14432, 32, 1 }, + {29088, 65, 128, 32, 14432, 32, 1, 452 }, /* tcId: 453. point with coordinate y = 1 in right to left addition chain */ - {29153, 65, 128, 32, 14464, 32, 1 }, + {29153, 65, 128, 32, 14464, 32, 1, 453 }, /* tcId: 454. point with coordinate y = 1 in right to left addition chain */ - {29218, 65, 128, 32, 14496, 32, 1 }, + {29218, 65, 128, 32, 14496, 32, 1, 454 }, /* tcId: 455. point with coordinate y = 1 in right to left addition chain */ - {29283, 65, 128, 32, 14528, 32, 1 }, + {29283, 65, 128, 32, 14528, 32, 1, 455 }, /* tcId: 456. point with coordinate y = 1 in right to left addition chain */ - {29348, 65, 128, 32, 14560, 32, 1 }, + {29348, 65, 128, 32, 14560, 32, 1, 456 }, /* tcId: 457. point with coordinate y = 1 in right to left addition chain */ - {29413, 65, 128, 32, 14592, 32, 1 }, + {29413, 65, 128, 32, 14592, 32, 1, 457 }, /* tcId: 458. point with coordinate y = 1 in right to left addition chain */ - {29478, 65, 128, 32, 14624, 32, 1 }, + {29478, 65, 128, 32, 14624, 32, 1, 458 }, /* tcId: 459. edge case private key */ - {29543, 65, 160, 32, 14656, 32, 1 }, + {29543, 65, 160, 32, 14656, 32, 1, 459 }, /* tcId: 460. edge case private key */ - {29543, 65, 192, 32, 14688, 32, 1 }, + {29543, 65, 192, 32, 14688, 32, 1, 460 }, /* tcId: 461. edge case private key */ - {29543, 65, 224, 32, 14720, 32, 1 }, + {29543, 65, 224, 32, 14720, 32, 1, 461 }, /* tcId: 462. edge case private key */ - {29543, 65, 256, 32, 14752, 32, 1 }, + {29543, 65, 256, 32, 14752, 32, 1, 462 }, /* tcId: 463. edge case private key */ - {29543, 65, 288, 32, 14784, 32, 1 }, + {29543, 65, 288, 32, 14784, 32, 1, 463 }, /* tcId: 464. edge case private key */ - {29543, 65, 320, 32, 14816, 32, 1 }, + {29543, 65, 320, 32, 14816, 32, 1, 464 }, /* tcId: 465. edge case private key */ - {29543, 65, 352, 32, 14848, 32, 1 }, + {29543, 65, 352, 32, 14848, 32, 1, 465 }, /* tcId: 466. edge case private key */ - {29543, 65, 384, 32, 14880, 32, 1 }, + {29543, 65, 384, 32, 14880, 32, 1, 466 }, /* tcId: 467. edge case private key */ - {29543, 65, 416, 32, 14912, 32, 1 }, + {29543, 65, 416, 32, 14912, 32, 1, 467 }, /* tcId: 468. edge case private key */ - {29543, 65, 448, 32, 14944, 32, 1 }, + {29543, 65, 448, 32, 14944, 32, 1, 468 }, /* tcId: 469. edge case private key */ - {29543, 65, 480, 32, 14976, 32, 1 }, + {29543, 65, 480, 32, 14976, 32, 1, 469 }, /* tcId: 470. edge case private key */ - {29543, 65, 512, 32, 15008, 32, 1 }, + {29543, 65, 512, 32, 15008, 32, 1, 470 }, /* tcId: 471. edge case private key */ - {29543, 65, 544, 32, 15040, 32, 1 }, + {29543, 65, 544, 32, 15040, 32, 1, 471 }, /* tcId: 472. edge case private key */ - {29543, 65, 576, 32, 15072, 32, 1 }, + {29543, 65, 576, 32, 15072, 32, 1, 472 }, /* tcId: 473. edge case private key */ - {29543, 65, 608, 32, 15104, 32, 1 }, + {29543, 65, 608, 32, 15104, 32, 1, 473 }, /* tcId: 474. edge case private key */ - {29543, 65, 640, 32, 15136, 32, 1 }, + {29543, 65, 640, 32, 15136, 32, 1, 474 }, + /* tcId: 475. point is not on curve */ + {29608, 65, 672, 32, 15168, 0, 0, 475 }, + /* tcId: 476. point is not on curve */ + {29673, 65, 672, 32, 15168, 0, 0, 476 }, + /* tcId: 477. point is not on curve */ + {29738, 65, 672, 32, 15168, 0, 0, 477 }, + /* tcId: 478. point is not on curve */ + {29803, 65, 672, 32, 15168, 0, 0, 478 }, + /* tcId: 479. point is not on curve */ + {29868, 65, 672, 32, 15168, 0, 0, 479 }, + /* tcId: 480. point is not on curve */ + {29933, 65, 672, 32, 15168, 0, 0, 480 }, + /* tcId: 481. point is not on curve */ + {29998, 65, 672, 32, 15168, 0, 0, 481 }, + /* tcId: 482. point is not on curve */ + {30063, 65, 672, 32, 15168, 0, 0, 482 }, + /* tcId: 483. point is not on curve */ + {30128, 65, 672, 32, 15168, 0, 0, 483 }, + /* tcId: 484. point is not on curve */ + {30193, 65, 672, 32, 15168, 0, 0, 484 }, + /* tcId: 485. point is not on curve */ + {30258, 65, 672, 32, 15168, 0, 0, 485 }, + /* tcId: 486. point is not on curve */ + {30323, 65, 672, 32, 15168, 0, 0, 486 }, + /* tcId: 487. point is not on curve */ + {30388, 65, 672, 32, 15168, 0, 0, 487 }, + /* tcId: 488. point is not on curve */ + {30453, 65, 672, 32, 15168, 0, 0, 488 }, + /* tcId: 489. point is not on curve */ + {30518, 65, 672, 32, 15168, 0, 0, 489 }, + /* tcId: 490. point is not on curve */ + {30583, 65, 672, 32, 15168, 0, 0, 490 }, + /* tcId: 491. */ + {30648, 0, 672, 32, 15168, 0, 0, 491 }, /* tcId: 494. public point not on curve */ - {29608, 65, 672, 32, 15168, 0, 0 }, + {30648, 65, 704, 32, 15168, 0, 0, 494 }, /* tcId: 495. public point = (0,0) */ - {29673, 65, 672, 32, 15168, 0, 0 }, + {29608, 65, 704, 32, 15168, 0, 0, 495 }, + /* tcId: 498. order = 1 */ + {30713, 65, 704, 32, 15168, 32, 1, 498 }, + /* tcId: 499. order = 26959946667150639794667015087019630673536463705607434823784316690060 */ + {30713, 65, 704, 32, 15200, 32, 1, 499 }, + /* tcId: 500. generator = (0,0) */ + {30713, 65, 704, 32, 15232, 32, 1, 500 }, + /* tcId: 501. generator not on curve */ + {30713, 65, 704, 32, 15264, 32, 1, 501 }, + /* tcId: 506. cofactor = None */ + {30713, 65, 704, 32, 15296, 32, 1, 506 }, /* tcId: 508. using secp224r1 */ - {29738, 57, 672, 32, 15168, 0, 0 }, + {30778, 57, 704, 32, 15328, 0, 0, 508 }, /* tcId: 509. using secp256r1 */ - {29795, 65, 672, 32, 15168, 0, 0 }, + {30835, 65, 704, 32, 15328, 0, 0, 509 }, + /* tcId: 510. a = 0 */ + {30713, 65, 704, 32, 15328, 32, 1, 510 }, + /* tcId: 511. public key of order 3 */ + {30900, 65, 704, 32, 15360, 0, 0, 511 }, /* tcId: 528. invalid public key */ - {29860, 33, 704, 32, 15168, 0, 0 }, + {30965, 33, 736, 32, 15360, 0, 0, 528 }, }; diff --git a/tools/tests_wycheproof_generate_ecdh.py b/tools/tests_wycheproof_generate_ecdh.py index 26dd8a1eac..706233cbe6 100755 --- a/tools/tests_wycheproof_generate_ecdh.py +++ b/tools/tests_wycheproof_generate_ecdh.py @@ -12,18 +12,37 @@ from binascii import hexlify, unhexlify from wycheproof_utils import to_c_array -def should_skip(test_vector_flags): +def should_skip_flags(test_vector_flags): # skip these vectors because they are for ASN.1 encoding issues and other curves - flags_to_skip = {"InvalidAsn", "InvalidCurveAttack", "InvalidEncoding", "WrongCurve", "UnnamedCurve"} + flags_to_skip = {"InvalidAsn", "WrongCurve"} return any(flag in test_vector_flags for flag in flags_to_skip) +def should_skip_tcid(test_vector_tcid): + ''' + We skip some test case IDs that have a public key whose custom ASN.1 representation explicitly + encodes some curve parameters that are invalid. libsecp256k1 never parses this part so we do + not care testing those. See https://github.com/bitcoin-core/secp256k1/pull/1492#discussion_r1572491546 + ''' + tcids_to_skip = [496, 497, 502, 503, 504, 505, 507] + return test_vector_tcid in tcids_to_skip + # Rudimentary ASN.1 DER public key parser. # This should not be used for anything other than parsing Wycheproof test vectors. def parse_der_pk(s): tag = s[0] L = int(s[1]) - value = s[2:(L+2)] - rest = s[(L+2):] + offset = 0 + if L & 0x80: + if L == 0x81: + L = int(s[2]) + offset = 1 + elif L == 0x82: + L = 256*int(s[2]) + int(s[3]) + offset = 2 + else: + raise ValueError("invalid L") + value = s[(offset+2):(L+2+offset)] + rest = s[(L+2+offset):] if len(rest) > 0 or tag == 0x06: # OBJECT IDENTIFIER return parse_der_pk(rest) @@ -71,7 +90,7 @@ def normalize_expected_result(er): for j in range(num_tests): test_vector = group['tests'][j] - if should_skip(test_vector['flags']): + if should_skip_flags(test_vector['flags']) or should_skip_tcid(test_vector['tcId']): continue public_key = parse_public_key(test_vector['public']) @@ -114,9 +133,10 @@ def normalize_expected_result(er): pk_offset = cache_public_keys[pk] shared_secrets += to_c_array(test_vector['shared']) + wycheproof_tcid = test_vector['tcId'] out += " /" + "* tcId: " + str(test_vector['tcId']) + ". " + test_vector['comment'] + " *" + "/\n" - out += f" {{{pk_offset}, {pk_size}, {sk_offset}, {sk_size}, {offset_shared}, {shared_size}, {expected_result} }},\n" + out += f" {{{pk_offset}, {pk_size}, {sk_offset}, {sk_size}, {offset_shared}, {shared_size}, {expected_result}, {wycheproof_tcid} }},\n" if new_sk: offset_sk_running += sk_size if new_pk: @@ -133,6 +153,7 @@ def normalize_expected_result(er): size_t shared_offset; size_t shared_len; int expected_result; + int wycheproof_tcid; } wycheproof_ecdh_testvector; """