diff --git a/src/P434/P434_compressed.c b/src/P434/P434_compressed.c index 3b0ffd9..ad69e4c 100644 --- a/src/P434/P434_compressed.c +++ b/src/P434/P434_compressed.c @@ -171,7 +171,7 @@ const unsigned int strat_Bob[MAX_Bob-1] = { // Fixed traversal strategies for Pohlig-Hellman discrete logs const unsigned int ph2_path[PLEN_2] = { #ifdef COMPRESSED_TABLES - #ifdef ELL2_FULL_SIGNED + #ifdef ELL2_TORUS #if (W_2 == 4) 0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 13, 13, 13, 14, 14, 15, 16, 17, 18, 19, 19, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 28, 28, 28, 28, 29, 30, 31, 32, 33, 34, 34, 35 #endif diff --git a/src/P434/P434_compressed_dlog_tables.c b/src/P434/P434_compressed_dlog_tables.c index 66bf5b2..2356ebf 100644 --- a/src/P434/P434_compressed_dlog_tables.c +++ b/src/P434/P434_compressed_dlog_tables.c @@ -6,16 +6,32 @@ // This is for \ell=2 case. Two different cases must be handled: w divides e, and not. #if defined(COMPRESSED_TABLES) - #ifdef ELL2_FULL_SIGNED + #ifdef ELL2_TORUS #if (W_2 == 4) - const uint64_t ph2_T[DLEN_2*(ELL2_W >> 1)*2*NWORDS64_FIELD] = { - 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6F,0xB133F39BA3754769,0xD22BD3FAB2A9C724,0x1AD1D5BB8315B8B2,0xCB0223B1B47CEF78,0x9FB7A0CDE92AF603,0x4B18BF9CA0AD85F1,0x2194A47A2282D,0x2171B8EBD566C70,0x5E65AFB3798E0EB2,0x10425651F695F8F4,0x5D27852843C18C0,0x2005AEDEC2AA6DA6,0xD9E345EE5A5506DF,0x10A660867C68F,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x742C,0x0,0x0,0xB90FF404FC000000,0xD801A4FB559FACD4,0xE93254545F77410C,0xECEEA7BD2EDA,0x4ECC0C645C8AB896,0x2DD42C054D5638DB,0xE52E2A447CEA474D,0x32BF52C92E831087,0xDC0EBBAA482DB8A0,0x21E3A039E1179A64,0x1AD4DF754B17,0x2171B8EBD566C70,0x5E65AFB3798E0EB2,0x10425651F695F8F4,0x5D27852843C18C0,0x2005AEDEC2AA6DA6,0xD9E345EE5A5506DF,0x10A660867C68F,0x6263A3DDA1BCBD39,0x3884DDEB7C542501,0x4B09E30172434E3E,0xE6618A7CA54A4B2D,0x38AA3C484A7A59C6,0x4FB5B5B7DD88D00A,0x1922704B96FD5,0x9D9C5C225E4342C6,0xC77B221483ABDAFE,0xB4F61CFE8DBCB1C1,0x175FEBFE3DB5B4D2,0x431C202FE6DE54DD,0x1D46AA1EA43C504C,0xA1F8225E036F,0xFDE8E47142A9938F,0xA19A504C8671F14D,0xEFBDA9AE096A070B,0xF7EEFE285EC3E73F,0x5BC0AD996EAE40FD,0x931919E827701977,0x129B91EAFACB4,0xB133F39BA3754769,0xD22BD3FAB2A9C724,0x1AD1D5BB8315B8B2,0xCB0223B1B47CEF78,0x9FB7A0CDE92AF603,0x4B18BF9CA0AD85F1,0x2194A47A2282D,0xFFFFFFFFFFFF8BD3,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0x44B18275E6FFFFFF,0xA3C4B77CDBB901CF,0x83CA0B82224DDF49,0x147307F5A4469,0x0,0x0,0x0,0x0,0x0,0x0,0x0 - }; - const uint64_t *ph2_T1 = {0}; - const uint64_t *ph2_T2 = {0}; - #endif - #endif // Closing ELL2_FULL_SIGNED and ELL2_HYBRID cases for l=2 -#endif //COMPRESSED_TABLES closing for the case of \ell=2 + + // Texp table for ell=2, W2=4, W2_1=3 + const uint64_t ph2_Texp[((1<<(W_2_1-2))-1)*NWORDS64_FIELD] = { + 0xC4C747BB43797A73,0x7109BBD6F8A84A02,0x9613C602E4869C7C,0xCF019E7E6794965A,0xF58E1C18639C04E9,0x326F0B99394C7FBD,0xF02EE25B6C66 + }; + + // Log table for ell=2, W2_1=3 + const int ph2_Log[(1<<(W_2_1))-1] = { + 4, -2, 2, 3, -1, 1, -3, + }; + + // G table for ell=2, W2=W2_1+W2_2=4 + const uint64_t ph2_G[(1<<(W_2-2))*NWORDS64_FIELD] = { + 0xFFFFFFFFFFFF8BD3,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0x44B18275E6FFFFFF,0xA3C4B77CDBB901CF,0x83CA0B82224DDF49,0x147307F5A4469,0xC4C747BB43790647,0x7109BBD6F8A84A02,0x9613C602E4869C7C,0x15F1AA796B94965A,0x1D8C771D0DFC5815,0x493CB744D9D53EB1,0x3403A9E3D8B,0x5E31296681E19E92,0xFE6B47AA0389E55,0x3FEB6DE7F12F392E,0x6D8CD5E1A32285EA,0x1164ED2C4A5B9CAD,0x4639CBB2691F8613,0x583D0FD0B9DE,0x9972685E88C3C753,0x76828CB7798F26E2,0x7F0B38D03478E300,0x24DC43AFCED1715,0x31D422CA93C55EFD,0xC6C9936EF3ED3D5A,0x40AAF45C27F9 + }; + + // TORUS + SIGNED W2=4 + const uint64_t ph2_CT[DLEN_2*(ELL2_W >> 1)*NWORDS64_FIELD] = { + 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+ }; + + #endif + #endif +#endif // This is for \ell=3 case. Note: Two different cases must be handled: w divides e, and not. #if defined(COMPRESSED_TABLES) @@ -29,5 +45,5 @@ 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}; #endif - #endif // Closing ELL3_FULL_SIGNED and l=3 -#endif // Closing COMPRESSED TABLES, for l=3 \ No newline at end of file + #endif +#endif \ No newline at end of file diff --git a/src/P434/P434_internal.h b/src/P434/P434_internal.h index dc8923d..52c5705 100644 --- a/src/P434/P434_internal.h +++ b/src/P434/P434_internal.h @@ -76,14 +76,17 @@ #define DLEN_3 ((OBOB_EXPON+W_3-1)/W_3) // ceil(eB/W_3) // Use compressed tables: FULL_SIGNED #define COMPRESSED_TABLES - #define ELL2_FULL_SIGNED // Uses signed digits to reduce table size by half + #define ELL2_TORUS #define ELL3_FULL_SIGNED // Uses signed digits to reduce table size by half // Length of the optimal strategy path for Pohlig-Hellman - #ifdef COMPRESSED_TABLES - #ifdef ELL2_FULL_SIGNED - #if W_2 == 4 - #define PLEN_2 55 - #endif + #ifdef COMPRESSED_TABLES + #if W_2 == 4 + #define PLEN_2 55 + #endif + #ifdef ELL2_TORUS + #define W_2_1 3 + #endif + #ifdef ELL3_FULL_SIGNED #if W_3 == 3 #define PLEN_3 47 #endif diff --git a/src/P503/P503_compressed.c b/src/P503/P503_compressed.c index 0973d20..47e0f71 100644 --- a/src/P503/P503_compressed.c +++ b/src/P503/P503_compressed.c @@ -174,7 +174,7 @@ const unsigned int strat_Bob[MAX_Bob - 1] = { // Fixed traversal strategies for Pohlig-Hellman discrete logs const unsigned int ph2_path[PLEN_2] = { #ifdef COMPRESSED_TABLES - #ifdef ELL2_FULL_SIGNED + #ifdef ELL2_TORUS #if W_2 == 5 0, 0, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 14, 15, 16, 17, 18, 18, 18, 19, 20, 20, 21, 22, 23, 24, 25, 25, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 35, 35 #endif diff --git a/src/P503/P503_compressed_dlog_tables.c b/src/P503/P503_compressed_dlog_tables.c index 1635f17..4ebb910 100644 --- a/src/P503/P503_compressed_dlog_tables.c +++ b/src/P503/P503_compressed_dlog_tables.c @@ -5,16 +5,35 @@ *********************************************************************************************/ #if defined(COMPRESSED_TABLES) - #ifdef ELL2_FULL_SIGNED + #ifdef ELL2_TORUS #if W_2 == 5 - const uint64_t ph2_T[DLEN_2*(ELL2_W >> 1)*2*NWORDS64_FIELD] = { - 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857105637C70,0xE71E430DCA52DA35,0x4A0CF742B7A2B7A9,0x35D567F9B73734,0xE263D6EEA7C1B1D,0x551EAE12F0F2E18B,0xB0AA582A236EA512,0xA51292B0FC177133,0xF6B9D6691CAE6B30,0x347DB3BAB12BA379,0x1638CF7B22D4ED26,0xA918D47C9E6EA,0x61CC4A98F36F8215,0xC07BA4B8E63EB3D1,0xA137FA8ECCE82F30,0xE78CC9A4A03882D7,0xB4E8CAAD3634B70,0xDDC44DA9679D3B53,0xAF161AEB7C6D2565,0x280C10C6BABE21,0x123D14887026B926,0x87B89B004B0A9F1F,0x93D6B359A2F4126B,0x24816BBAE36DD1BD,0x7FE14990096D19B2,0x20B2CBCD9DC9135E,0x73DC4D732E422CD7,0x1400D10E9B874,0xBB8DEE3E69808717,0xE3171073A8989DB3,0x73A762FCC404CBE7,0xE4DAD49D30F79B16,0xB8E167E22887F110,0x36B9C4A7365AC473,0x16FA457EC2CBF010,0x3725B3919486BE,0x1466ABECBC90153E,0x13FA4A4B6EA544E3,0xBEFA3823091CB000,0xF18E70EAB661ABC6,0x2D17AEAE098EF1C9,0x655B3A21E4448B49,0x4841893D3729816A,0x3C83FDC04A8688,0x2F9FAF668BA2C327,0x373C6E7E108D890D,0x3308B78EDF9A8CDA,0x3D258F08813B90DF,0xCF2E3B17FB0AC108,0x34B8C97B5E23BCBC,0x748967ADB32849C5,0x1745ED1C680E50,0xBDEED4832E1C525D,0x2E75D4C62228BB24,0xDE8B525B98E1C5AD,0x329E283DE990E07,0x523DAEFC12681C5B,0xFB41377E83547ED5,0x1A7788F89F9A83DE,0x56955F92F900C,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0xFFFFFFFFFFFFFC06,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xF7FFFFFFFFFFFFFF,0xAF3D416B7B3314EB,0xCA33593B14FFCA31,0xD5784EF6BFC5638D,0x196B467B71C4CA,0xD0605099745D3CD8,0xC8C39181EF7276F2,0xCCF7487120657325,0x6EDA70F77EC46F20,0x43DA20C227072698,0xE6E32D4D1D5AC0F2,0xEBBC5F10274F5B0A,0x29210825190FCD,0xBDEED4832E1C525D,0x2E75D4C62228BB24,0xDE8B525B98E1C5AD,0x329E283DE990E07,0x523DAEFC12681C5B,0xFB41377E83547ED5,0x1A7788F89F9A83DE,0x56955F92F900C,0x447211C1967F78E8,0x1CE8EF8C5767624C,0x8C589D033BFB3418,0xC7252B62CF0864E9,0x5A26F3F7F989F68F,0xE4E232214523B93B,0x494B813F17ABB4BF,0x94141AFEC9760,0x1466ABECBC90153E,0x13FA4A4B6EA544E3,0xBEFA3823091CB000,0xF18E70EAB661ABC6,0x2D17AEAE098EF1C9,0x655B3A21E4448B49,0x4841893D3729816A,0x3C83FDC04A8688,0x9E33B5670C907DEA,0x3F845B4719C14C2E,0x5EC805713317D0CF,0xC473365B5FC77D28,0x7B9CF2F4EAE9C2F,0x3DD7A91F13E1425C,0xB12FABD25E0A7F6A,0x185AE47AC65FFC,0x123D14887026B926,0x87B89B004B0A9F1F,0x93D6B359A2F4126B,0x24816BBAE36DD1BD,0x7FE14990096D19B2,0x20B2CBCD9DC9135E,0x73DC4D732E422CD7,0x1400D10E9B874,0xE263D6EEA7C1B1D,0x551EAE12F0F2E18B,0xB0AA582A236EA512,0xA51292B0FC177133,0xF6B9D6691CAE6B30,0x347DB3BAB12BA379,0x1638CF7B22D4ED26,0xA918D47C9E6EA,0xE263D6EEA7C1B1D,0x551EAE12F0F2E18B,0xB0AA582A236EA512,0xA51292B0FC177133,0xF6B9D6691CAE6B30,0x347DB3BAB12BA379,0x1638CF7B22D4ED26,0xA918D47C9E6EA,0x123D14887026B926,0x87B89B004B0A9F1F,0x93D6B359A2F4126B,0x24816BBAE36DD1BD,0x7FE14990096D19B2,0x20B2CBCD9DC9135E,0x73DC4D732E422CD7,0x1400D10E9B874,0x9E33B5670C907DEA,0x3F845B4719C14C2E,0x5EC805713317D0CF,0xC473365B5FC77D28,0x7B9CF2F4EAE9C2F,0x3DD7A91F13E1425C,0xB12FABD25E0A7F6A,0x185AE47AC65FFC,0x1466ABECBC90153E,0x13FA4A4B6EA544E3,0xBEFA3823091CB000,0xF18E70EAB661ABC6,0x2D17AEAE098EF1C9,0x655B3A21E4448B49,0x4841893D3729816A,0x3C83FDC04A8688,0x447211C1967F78E8,0x1CE8EF8C5767624C,0x8C589D033BFB3418,0xC7252B62CF0864E9,0x5A26F3F7F989F68F,0xE4E232214523B93B,0x494B813F17ABB4BF,0x94141AFEC9760,0xBDEED4832E1C525D,0x2E75D4C62228BB24,0xDE8B525B98E1C5AD,0x329E283DE990E07,0x523DAEFC12681C5B,0xFB41377E83547ED5,0x1A7788F89F9A83DE,0x56955F92F900C,0xD0605099745D3CD8,0xC8C39181EF7276F2,0xCCF7487120657325,0x6EDA70F77EC46F20,0x43DA20C227072698,0xE6E32D4D1D5AC0F2,0xEBBC5F10274F5B0A,0x29210825190FCD,0xFFFFFFFFFFFFFC06,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xF7FFFFFFFFFFFFFF,0xAF3D416B7B3314EB,0xCA33593B14FFCA31,0xD5784EF6BFC5638D,0x196B467B71C4CA,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0 + + // Texp table for ell=2, W2=5, W2_1=4 + const uint64_t ph2_Texp[((1<<(W_2_1-2))-1)*NWORDS64_FIELD] = { + 0x1C4C7ADDD4F8363A,0xAA3D5C25E1E5C316,0x6154B05446DD4A24,0x4A252561F82EE267,0xED73ACD2395CD661,0x68FB6775625746F3,0x2C719EF645A9DA4C,0x15231A8F93CDD4,0x9FE934564C2138AD,0xEE22B57E2E7BC52D,0x6543363F9A42F7CF,0xA8D28B0FCEB28DBA,0x92D91991FDF80ED3,0xE5561938C2C3266C,0x9DA6493E6483F484,0x261E82DF3AC031,0x4E4E84A359E0E3B1,0x9E398C5073E6B1A1,0x695A55B375D037CF,0x9298C764F52BDE9F,0x2A9BCE426003E62E,0xBE590BD31FAAF004,0xFDB73F40F1BC821B,0x35AA60E4151E89 }; - const uint64_t *ph2_T1 = {0}; - const uint64_t *ph2_T2 = {0}; - #endif + + + // Log table for ell=2, W2_1=4 + const int ph2_Log[(1<<(W_2_1))-1] = { + 8, 4, -4, -6, 2, -2, 6, -3, 5, 1, -7, 7, -1, -5, 3, + }; + + + // G table for ell=2, W2=W2_1+W2_2=5 + const uint64_t ph2_G[(1<<(W_2-2))*NWORDS64_FIELD] = { + 0x3F9,0x0,0x0,0xB400000000000000,0x63CB1A6EA6DED2B4,0x51689D8D667EB37D,0x8ACD77C71AB24142,0x26FBAEC60F5953,0xE3B385222B07CDBF,0x55C2A3DA1E1A3CE9,0x9EAB4FABB922B5DB,0x69DADA9E07D11D98,0x76576D9C6D81FC53,0xE86D361804276C89,0x5E5BD8D0D50866F5,0x11D894367B8B7F,0x320209C584E8B171,0xF3FC302A9200EE8B,0x805A55F2EF2EDAA,0x5073A202FCFCFC38,0x8DEAE004AB73FAE1,0x8B2A4B22A853DEDE,0xFBCD5153EC4D4441,0x71BFFD90F8BEA,0x7C63468788D70186,0xBC1AA6A7B369FDE8,0xFC117A14AC9A5254,0x55529A52297C54AC,0xBE65ADAEE2439A42,0xD50DEBCA0612D404,0x1998CD7EFBD82709,0x160046766866F6,0xB4822BAD468724E4,0x770F770BA532B3C0,0xCBC2FE30104CB58F,0x9E81B6DFBBD7641A,0x8B9E2297EE93C018,0x5CA07C0B761C2CE7,0xC61EE2F0D5471C5B,0x38064049A175AF,0xA25AB6EE24D5357B,0x7C8D1073A759A8C5,0x7C4641F432125C35,0x1ABF9ADF5A48AA55,0x324BD381CE4B0D45,0xE2AA5207A7D72073,0xE8CD4FBE6D9C92DB,0x35CEDE18013B86,0xF69EBA7C02E6BE6E,0xF90540A14F3EAFB0,0x39FC1C53F17B30ED,0x408393E62BAF4AF,0xF20750584CF1E945,0x77ED03E465AE9FB3,0xED82BC4088C469CF,0x1C28E98A3772CC,0x87AA233DA352CAED,0x3A55C4864FBDC9F5,0xD9B00CCB4E4A5387,0x2F0B743A13731EFA,0xBB3F91F202E414A8,0xBCC390C9D988C102,0x2E1C99E9B1F351E9,0x1759D6661476B3 + }; + + + // Torus tables for W_2 = 5 + const uint64_t ph2_CT[DLEN_2*(ELL2_W >> 1)*NWORDS64_FIELD] = { + 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5E6E6BA4BDC7,0x507436F7929C1FFD,0x6317BF815C3F656E,0x651C24591FA94821,0xDB445A6C1F27861F,0xC87893BDEE02D,0x2B65D4F0CBFB5EAF,0xD2477CE367A6D72B,0x5D76AA0E6E3B5C86,0x35B248558D060F2F,0x76B3562BFD12E042,0x79C5D1CC53BC887E,0xE8E07A4E0F9339C0,0x3144A1BF00EC1B,0x4D604336A63DBE0A,0x9E69AFD8A30B44A,0x5DA137373FC78A24,0xFB10C32154311A03,0x758E2FEFA7E6FF22,0x90B5F6255C623CC7,0x3B4685648365A67F,0x141F1A5C0ED838,0xCFBDEC07A69C889F,0xEC398AA4419496FD,0xD2BF5A093D59E94E,0x8540005443DFD62A,0x2267C59D674010C9,0xA6F33EAD33ECC0D8,0x348F23D0936B3DA3,0x4BD79F814FABF,0x6345CCE818CD838A,0xA77139FBFDFAE957,0xD25FE3147FF7D96E,0x4EFA0CF7A6112475,0x15C45F5085E4A353,0xE73732C9CC5FF269,0xE996BEFF106B871,0x3B652F519A5BD4,0x1A95BF497F76A1FD,0x1F70A1551AF38EB8,0xF50065E7EA6CA3E8,0x25F134A35B99076E,0xBBD8FB6376E525E2,0xF0FFBCE10A893019,0xAF2C72ECDA2BED13,0x278CE158ECC0B1,0x4E56A23754122DC9,0x8D22FDA95CDAA59B,0x544A5868410737DC,0x23AD95582745F993,0x9D929FF4AF71F8FF,0xDD4E9E6822DC352E,0xB634B894F0823CF9,0x3FCA0B549F2A3C,0xFC2D3CC320508EEF,0xFE78A4ABC75D87E1,0x5DC21906431F9E82,0x230B3AB7B5D30D43,0x867399292F711EB6,0x66F179E6373ADF21,0x987DBB4389FEC706,0x3B8C7DCF73437D,0x384606D543BD113B,0x9095A60044A82B51,0x755D241713D2220A,0x83E6E96E37A241C6,0x154719F4C69FDED8,0xF390370BACA42975,0xC5542D3B476BE32D,0x3A0C9D9339AD97,0xF2197F41F902917,0xE09C353ADD496807,0x93DB389D49AA332E,0xEA608361B6EEB516,0x2098AE256672F468,0xC6BFBA80D643DC9F,0xDCD4780A91675AEF,0x14AC6F5090D8CD,0x67CE4391984F33A9,0x1EEB3E0DDD3759A4,0x7A388F4EB23D2323,0x4027D80BB6DF5B27,0x759314F330AC7E28,0xD0CB94B5A0A5415C,0x65D7234F80A5F6A6,0x25CDC8BCBBC013,0x4EE8B7AD41B63A0C,0xF46B8E6BCB6AF717,0x861FFD8598B81072,0x8790A2E2C023EEA9,0xA38025375500E974,0xC928B19363D4384,0x4CEEE9AB84E9A4A1,0x67C7AFEF69954,0x1C9842CC007BD664,0xEDA4010DDB8B676D,0x1C5171107CC0034E,0x77DE5921311D28D3,0xB49D47A40A0A85A,0xB0147990253145C5,0xD44E2BC263BA38D1,0xEDD0F37A23DA8,0x753A7DE3AA1A2B7F,0x281F4A5EFDD3AD30,0xF0B660AB3DADB39D,0x6060294596B6BE3,0x48A3270D8B6CBAD0,0xD608085EF72BA9D5,0x8CD93CD661F1F1E0,0x29A05739DECE57 + }; + + #endif #endif -#endif // Closing COMPRESSED_TABLES +#endif // This is for \ell=3 case. Note: Two different cases must be handled: w divides e, and not #if defined(COMPRESSED_TABLES) @@ -26,5 +45,5 @@ const uint64_t *ph3_T1 = {0}; const uint64_t *ph3_T2 = {0}; #endif - #endif // Closing ELL3_FULL_SIGNED -#endif // Closing COMPRESSED_TABLES for ell=3 \ No newline at end of file + #endif +#endif \ No newline at end of file diff --git a/src/P503/P503_internal.h b/src/P503/P503_internal.h index fa84f00..53afc48 100644 --- a/src/P503/P503_internal.h +++ b/src/P503/P503_internal.h @@ -76,15 +76,16 @@ #define DLEN_3 ((OBOB_EXPON + W_3 - 1) / W_3) // ceil(eB/W_3) // Use compressed tables: FULL_SIGNED #define COMPRESSED_TABLES - #define ELL2_FULL_SIGNED // Uses signed digits to reduce table size by half + #define ELL2_TORUS #define ELL3_FULL_SIGNED // Uses signed digits to reduce table size by half // Length of the optimal strategy path for Pohlig-Hellman #ifdef COMPRESSED_TABLES - #ifdef ELL2_FULL_SIGNED - #if W_2 == 5 - #define PLEN_2 51 - #endif + #if W_2 == 5 + #define PLEN_2 51 #endif + #ifdef ELL2_TORUS + #define W_2_1 4 + #endif #ifdef ELL3_FULL_SIGNED #if W_3 == 3 #define PLEN_3 54 diff --git a/src/P610/P610_compressed.c b/src/P610/P610_compressed.c index 4a73152..e95d05e 100644 --- a/src/P610/P610_compressed.c +++ b/src/P610/P610_compressed.c @@ -164,7 +164,7 @@ const unsigned int strat_Bob[MAX_Bob-1] = { 86, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, // Fixed traversal strategies for Pohlig-Hellman discrete logs const unsigned int ph2_path[PLEN_2] = { #ifdef COMPRESSED_TABLES - #ifdef ELL2_FULL_SIGNED + #ifdef ELL2_TORUS #if (W_2 == 5) 0, 0, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 14, 15, 16, 17, 18, 18, 18, 19, 20, 20, 21, 22, 23, 24, 25, 25, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 35, 35, 35, 35, 35, 36, 37, 38, 39, 40, 41, 41, 42 #endif diff --git a/src/P610/P610_compressed_dlog_tables.c b/src/P610/P610_compressed_dlog_tables.c index d569b98..ed63f3a 100644 --- a/src/P610/P610_compressed_dlog_tables.c +++ b/src/P610/P610_compressed_dlog_tables.c @@ -6,16 +6,35 @@ // This is for \ell=2 case. Two different cases must be handled: w divides e, and not. #if defined(COMPRESSED_TABLES) - #ifdef ELL2_FULL_SIGNED + #ifdef ELL2_TORUS #if (W_2 == 5) - const uint64_t ph2_T[DLEN_2*(ELL2_W >> 1)*2*NWORDS64_FIELD] = { - 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0xAB4EDA2E9E71CD61,0xAFC6D01EE592C9D1,0x1BA188040,0x6BD954CA55EEABE4,0x86271714EB2B5502,0x66E0BE067A1F6866,0xEFF51D69878AA021,0xAAB2AA55B7712426,0xEB7F46FB7530FB2E,0xA9F9C43216E77869,0xCEFACFBB6EAF1CF,0x11B07D2D08796D90,0x8556071F,0x203FD5606B2CFEFE,0xF939E8B78A9CC23F,0x10CB04495DC18B50,0x7246DD7563D4469E,0x59E864683C1FEA56,0x89DC24C39A5802C6,0xDAE1BE135815439,0x4159163E3C1E30CA,0x13130C6B64E83C8F,0x1CAF4737B,0xBE637E8791DF8BE2,0xDDAD13B5407410D4,0x460F51C020DD96D6,0xF0CD28EB1E23973C,0x40B5DDEDA66F7559,0x118857E99A78BE63,0xE350EB857FCB18A,0xF16C8B58ECDEF4A9,0xED99D9277BEF6393,0x1A4C91547,0xBE637E8791DF8BE2,0xDDAD13B5407410D4,0x460F51C020DD96D6,0xF0CD28EB1E23973C,0x40B5DDEDA66F7559,0x118857E99A78BE63,0xE350EB857FCB18A,0xF16C8B58ECDEF4A9,0xED99D9277BEF6393,0x1A4C91547,0x203FD5606B2CFEFE,0xF939E8B78A9CC23F,0x10CB04495DC18B50,0x7246DD7563D4469E,0x59E864683C1FEA56,0x89DC24C39A5802C6,0xDAE1BE135815439,0x4159163E3C1E30CA,0x13130C6B64E83C8F,0x1CAF4737B,0x6BD954CA55EEABE4,0x86271714EB2B5502,0x66E0BE067A1F6866,0xEFF51D69878AA021,0xAAB2AA55B7712426,0xEB7F46FB7530FB2E,0xA9F9C43216E77869,0xCEFACFBB6EAF1CF,0x11B07D2D08796D90,0x8556071F,0xA0F896E0A8F5F891,0xD0D6227C27250BE5,0xEEFEF5AC5190D9EE,0x5F1D1955E37E17A4,0xC68B9B133134C106,0x583846BFEF02F022,0xF9A36AFBBDCD3ED8,0xAB4EDA2E9E71CD61,0xAFC6D01EE592C9D1,0x1BA188040,0xF2F8F5B499E64AC6,0x832A15C6069B2B91,0xF797DFB661EE87D1,0xA11AF1AEF484AD,0xEDA42010A021C449,0xF93DB64723686963,0x6751CB2FA70875BC,0x43132B1C80B67AC3,0x9B4B243FA666F7D0,0x323E62B9,0xE9862C5119DFF1E7,0xAF97AD5F0E7A1907,0xD7DD50183125095E,0x3F44DA450F117011,0xF94CD0EB56CFD9AF,0xABCD01589BFABD2D,0x27731BE9F852637F,0x5956994FFFBDAE2D,0xA414C03BDEC2AAC6,0x11B0B8360,0xEF6504D05C86EFAC,0x4FA4A676813301F8,0xEC46ED611A74D0C0,0x951640C7ED0094FF,0xD9BCC8D9FBEF1EFD,0x9320A2FFFC9C04C3,0x24D40B5D598D1939,0x31DAB1686547F538,0xEDCBD62CD326D25A,0xDD64BA85,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x670CC8E6,0x0,0x0,0x0,0x9A34000000000000,0x4D99C2BD28717A3F,0xA4A1839A323D41C,0xD2B62215D06AD1E2,0x1369026E862CAF3D,0x10894E964,0x1679D3AEE6200E18,0x506852A0F185E6F8,0x2822AFE7CEDAF6A1,0xC0BB25BAF0EE8FEE,0x74B52F14A9302650,0x5AB4C900E5FF300,0x7374A35B0C3D962C,0x58FF19AA110676FD,0xDD7B508673252DC6,0x160EB2407,0xEF6504D05C86EFAC,0x4FA4A676813301F8,0xEC46ED611A74D0C0,0x951640C7ED0094FF,0xD9BCC8D9FBEF1EFD,0x9320A2FFFC9C04C3,0x24D40B5D598D1939,0x31DAB1686547F538,0xEDCBD62CD326D25A,0xDD64BA85,0x5F07691F570A076E,0x2F29DD83D8DAF41A,0x11010A53AE6F2611,0xA0E2E6AA1C81E85B,0xA77664ECCECB3EF9,0x59400728BB57C00B,0xA144544946C2BAD3,0x706D8CB725257C8,0xD1C940A36C550EBB,0xC1DE2727,0xF2F8F5B499E64AC6,0x832A15C6069B2B91,0xF797DFB661EE87D1,0xA11AF1AEF484AD,0xEDA42010A021C449,0xF93DB64723686963,0x6751CB2FA70875BC,0x43132B1C80B67AC3,0x9B4B243FA666F7D0,0x323E62B9,0xDFC02A9F94D30101,0x6C6174875633DC0,0xEF34FBB6A23E74AF,0x8DB9228A9C2BB961,0x14199B97C3E015A9,0x279C29251002AD68,0x8D39A363CF0EA572,0x70FC9CBBD4A5F460,0x6E7D0456ECFF9BFD,0xB10233ED,0x6BD954CA55EEABE4,0x86271714EB2B5502,0x66E0BE067A1F6866,0xEFF51D69878AA021,0xAAB2AA55B7712426,0xEB7F46FB7530FB2E,0xA9F9C43216E77869,0xCEFACFBB6EAF1CF,0x11B07D2D08796D90,0x8556071F,0x419C81786E20741D,0x2252EC4ABF8BEF2B,0xB9F0AE3FDF226929,0xF32D714E1DC68C3,0x2D4C221259908AA6,0x9FEFF5FF0FE1F1CB,0x8CB2B08CAC934821,0xC0E927A123E53081,0x93F6379AD5F874F8,0xD72D9220,0xBE637E8791DF8BE2,0xDDAD13B5407410D4,0x460F51C020DD96D6,0xF0CD28EB1E23973C,0x40B5DDEDA66F7559,0x118857E99A78BE63,0xE350EB857FCB18A,0xF16C8B58ECDEF4A9,0xED99D9277BEF6393,0x1A4C91547,0x9426AB35AA11541B,0x79D8E8EB14D4AAFD,0x991F41F985E09799,0x100AE29678755FDE,0xC34F55AA488EDBD9,0xC5F906ED3529B4FF,0xF0EDFB12EDA88141,0xA56605FE59D9335A,0x6FDF9395496E6AFC,0x1F6A0A049,0x203FD5606B2CFEFE,0xF939E8B78A9CC23F,0x10CB04495DC18B50,0x7246DD7563D4469E,0x59E864683C1FEA56,0x89DC24C39A5802C6,0xDAE1BE135815439,0x4159163E3C1E30CA,0x13130C6B64E83C8F,0x1CAF4737B,0xD070A4B6619B539,0x7CD5EA39F964D46E,0x86820499E11782E,0xFF5EE50E510B7B52,0x805DDFEF5FDE3BB6,0xB83A97A186F246CA,0x3395F4155D8783EE,0x6F4287DD900DAA67,0xE644EC82AB80E0BC,0x249B844AE,0xA0F896E0A8F5F891,0xD0D6227C27250BE5,0xEEFEF5AC5190D9EE,0x5F1D1955E37E17A4,0xC68B9B133134C106,0x583846BFEF02F022,0xF9A36AFBBDCD3ED8,0xAB4EDA2E9E71CD61,0xAFC6D01EE592C9D1,0x1BA188040,0x109AFB2FA3791053,0xB05B59897ECCFE07,0x13B9129EE58B2F3F,0x6AE9BF3812FF6B00,0x944537260410E102,0x1E57AAE8ADBEAB6A,0x7613B3E7AB02E072,0x807B0191AB7C2FF2,0x93C43A957EC10632,0x19E91ECE2,0xE9862C5119DFF1E7,0xAF97AD5F0E7A1907,0xD7DD50183125095E,0x3F44DA450F117011,0xF94CD0EB56CFD9AF,0xABCD01589BFABD2D,0x27731BE9F852637F,0x5956994FFFBDAE2D,0xA414C03BDEC2AAC6,0x11B0B8360,0xFFFFFFFF98F33719,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xD3CDFFFFFFFFFFFF,0x63DE8B2B81E935EE,0x909DA70B616C258F,0xDF9F90E440595348,0x6E270E53CBBB294E,0x17361BE04,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0 - }; - const uint64_t *ph2_T1 = {0}; - const uint64_t *ph2_T2 = {0}; - #endif - #endif // Closing ELL2_FULL_SIGNED and ELL2_HYBRID cases for l=2 -#endif //COMPRESSED_TABLES closing for the case of \ell=2 + + // Texp table for ell=2, W2=5, W2_1=4 + const uint64_t ph2_Texp[((1<<(W_2_1-2))-1)*NWORDS64_FIELD] = { + 0x7CC6FD0F23BF17C5,0xBB5A276A80E821A9,0x8C1EA38041BB2DAD,0xE19A51D63C472E78,0x1369BBDB4CDEEAB3,0x719861EA8A96CC98,0x81825E2BAB696968,0x308363B7C8F9C427,0x59A3A18CA5F6EE9B,0xCD9B8327,0xD81CE6D57A477950,0x57FF8F7BA47F9110,0x32D2553A99013C7F,0x40839770DB1AC75A,0x73A489B85D52F561,0xC004A1C32FDEAD4F,0x73E512333F748A2C,0x87E75B5DE337BA0A,0x6CFC38C78BDC2DD5,0x11F3F88DC,0x5BFF42581E1F5B97,0x9B58196C4113C0A7,0xEECE2BEBDF44A43A,0xBCF7FCC8691325ED,0x43CCF6052225F97A,0xC7CD308ECDA5D4F,0x89BB805328F9988B,0x1E21AB2A2AB28012,0xA76746FC2C6FCB76,0x93BD93A5 + }; + + + // Log table for ell=2, W2_1=4 + const int ph2_Log[(1<<(W_2_1))-1] = { + 8, -4, 4, -2, 6, -6, 2, 7, -1, 3, -5, 5, -3, 1, -7, + }; + + + // G table for ell=2, W2=W2_1+W2_2=5 + const uint64_t ph2_G[(1<<(W_2-2))*NWORDS64_FIELD] = { + 0xFFFFFFFF98F33719,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xD3CDFFFFFFFFFFFF,0x63DE8B2B81E935EE,0x909DA70B616C258F,0xDF9F90E440595348,0x6E270E53CBBB294E,0x17361BE04,0x833902F075341F54,0x44A5D8957F17DE56,0x73E15C7FBE44D252,0x1E65AE29C3B8D187,0xC0644424B321154C,0xF2462940F7526956,0xF1B48DFB602BC26,0xAF1C2D2C775F8F21,0x14836CC725C43AB3,0xA5C63ADD,0x5B55E9C5EF7B98A4,0x9CA5681123976F67,0xA6B3B1BA57460ED1,0x5EE9459A9ED398E1,0x3408CDDD10740AAD,0xB24ACB04273116A6,0x83005B12F5774653,0x3703888A5A97492B,0x817FA58EB1A06889,0x1C505C3B9,0xD8C63F66DAD1AA76,0x56B240D6C1FBE250,0x7AECCF6C20FFD1E8,0x9E924E9EA55A5466,0xBD02B1E06F04E42E,0x307B72364EFFAFA7,0xF3C645313F2DD7,0x7BEEECCC23417258,0xEDA1E61A4C3A0AD3,0x58C42D68,0x914D332D80767FB7,0x9F6AC0CD18AD0AE2,0x2F13B22810507324,0xF1BB19C2CFF1C13F,0xCEC57CD683D3FC58,0x5E21948ED601A763,0x4BD98A2CC696A09D,0x9B108593DCC62CAD,0x98E797D368C1A3AF,0xA77448F1,0x369169F04B220444,0xC666B3A5B643A0EA,0xC467402D8B5FC13A,0x2D9BC99B742C7357,0x978566A023208EF,0x89D1247010987E09,0xEDB26F18005023E,0x7205350CE0351361,0x14740B259C11D0D1,0x26E84B9CF,0xCC519C0FDDE8503A,0x980A336CBBDD85AF,0xB468855E43DD793C,0x85BD25E68A7AD0C3,0x50B08441D22151D0,0x775C79D845E5A346,0xC235638F6402F35B,0xF510FC7D29CC058F,0x3AA9204FFE0EB6D5,0x34CEF550,0x6245747874889EB,0x3B63C30DE1975087,0xC133701C03FE8F60,0x77489EDC227CB16D,0x7AF01E267BDD7380,0x7155B19CF8DF7281,0x5E3D05810C0938B2,0xD77747702BB71CF3,0xFCFD3F1ACC61654D,0x290FA7D1 + }; + + + // Torus tables for W_2 = 5 + const uint64_t ph2_CT[DLEN_2*(ELL2_W >> 1)*NWORDS64_FIELD] = { + 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+ }; + + #endif + #endif +#endif // This is for \ell=3 case. Note: Two different cases must be handled: w divides e, and not. #if defined(COMPRESSED_TABLES) @@ -27,6 +46,6 @@ const uint64_t *ph3_T1 = {0}; const uint64_t *ph3_T2 = {0}; #endif - #endif // Closing ELL3_FULL_SIGNED and l=3 -#endif // Closing COMPRESSED TABLES, for l=3 + #endif +#endif diff --git a/src/P610/P610_internal.h b/src/P610/P610_internal.h index 2008669..b933c42 100644 --- a/src/P610/P610_internal.h +++ b/src/P610/P610_internal.h @@ -76,15 +76,17 @@ #define DLEN_3 ((OBOB_EXPON+W_3-1)/W_3) // ceil(eB/W_3) // Use compressed tables: FULL_SIGNED #define COMPRESSED_TABLES - #define ELL2_FULL_SIGNED // Uses signed digits to reduce table size by half + #define ELL2_TORUS #define ELL3_FULL_SIGNED // Uses signed digits to reduce table size by half // Length of the optimal strategy path for Pohlig-Hellman #ifdef COMPRESSED_TABLES - #ifdef ELL2_FULL_SIGNED - #if W_2 == 5 - #define PLEN_2 62 - #endif + #if W_2 == 5 + #define PLEN_2 62 + #endif + #ifdef ELL2_TORUS + #define W_2_1 4 #endif + #ifdef ELL3_FULL_SIGNED #if W_3 == 3 #define PLEN_3 65 diff --git a/src/P751/P751_compressed.c b/src/P751/P751_compressed.c index 5c93ac5..5e49482 100644 --- a/src/P751/P751_compressed.c +++ b/src/P751/P751_compressed.c @@ -177,7 +177,7 @@ const unsigned int strat_Bob[MAX_Bob-1] = { // Fixed traversal strategies for Pohlig-Hellman discrete logs const unsigned int ph2_path[PLEN_2] = { #ifdef COMPRESSED_TABLES - #ifdef ELL2_FULL_SIGNED + #ifdef ELL2_TORUS #if W_2 == 4 0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 13, 13, 13, 14, 14, 15, 16, 17, 18, 19, 19, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 28, 28, 28, 28, 29, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 39, 40, 40, 40, 40, 41, 42, 42, 42, 42, 42, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 52, 53, 54, 55, 56, 57, 58, 59, 59, 59, 59, 59, 59, 59 #endif diff --git a/src/P751/P751_compressed_dlog_tables.c b/src/P751/P751_compressed_dlog_tables.c index 4e71900..d660d07 100644 --- a/src/P751/P751_compressed_dlog_tables.c +++ b/src/P751/P751_compressed_dlog_tables.c @@ -6,16 +6,34 @@ // This is for \ell=2 case. Note: Two different cases must be handled: w divides e, and not #if defined(COMPRESSED_TABLES) - #ifdef ELL2_FULL_SIGNED + #ifdef ELL2_TORUS #if (W_2 == 4) - const uint64_t ph2_T[DLEN_2*(ELL2_W >> 1)*2*NWORDS64_FIELD] = { - 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B,0xE24DA352CEED8B82,0xBC15BA90BCC55682,0x382F1913547AAC13,0x9B6A71F2FF923FB8,0x1E6B152C3F7F55FC,0x8AD2E9910F9A6AF,0x50A702A11CAF,0x4DCA3B50388E0559,0xFAE384D32990D875,0x40E3A57393025DC9,0xD45F07643DE98C8A,0x8FFF53F8943844B6,0xD52AD9579C28B585,0x659B203F4B477768,0xB330E8F6D1009643,0xDA73A996FE44DA14,0x4D9117A401E123B1,0xDC7899528B71B286,0x1A882CA55E85,0xCABF5D6A44FB3E37,0x4A463EE81BE2326A,0x292B1371F2D49BC1,0xB467A4E46981CC0,0x81E9E78ACD0246D5,0x9B1A02772D0BC5E4,0x99272F66C368B766,0x123A861FAC0784AA,0x2F590470894DA4CA,0x81C5DF3CDA17A448,0x52FB592E19D1B364,0x61AB25B7DB60,0x3540A295BB04C1C8,0xB5B9C117E41DCD95,0xD6D4EC8E0D2B643E,0xF4B985B1B967E33F,0x7E16187532FDB92A,0x5395FD88D2F43A1B,0x4AC5671E868FC142,0xC85B14FA67F047CC,0xD8F593F74D9E43AC,0x39CD5C7829AB2FF,0xBB1737717DE92902,0xE3AAF8A1BBB,0xB235C4AFC771FAA6,0x51C7B2CD66F278A,0xBF1C5A8C6CFDA236,0x2BA0F89BC2167375,0x7000AC076BC7BB49,0x198526A863D74A7A,0x7E517645FEB10140,0x2764B22342F73633,0x2DDAEED0D8A70E62,0x37D19D605AD13396,0x3199F74D0C4929E0,0x555DA89C9896,0x395A11C8CE4ACDA6,0x7F7CC0E508F76CCB,0xE23AF39F94293F75,0xF1BA73C95B293AA,0xF0AC1C38F69BB8C4,0xC625CAD3112747D,0x27D6DBF48D332226,0xA2668206BF7D2063,0x6CE42674D759A8BE,0x66F79FD81D33014B,0x565620686C135B7,0x1F3ED2A0DA6D,0xFFFFFFFFFFFDB652,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0x6B9FFFFFFFFFFFFF,0x8EC4E4A1129C0C42,0x711E035AD4A8A7A6,0x3FB0E0B52A8F9A48,0x38BE00CA8AAAEDF1,0xFD1AFE3322A8147D,0x428AB0851139,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0 + + // Texp table for ell=2, W2=4, W2_1=3 + const uint64_t ph2_Texp[((1<<(W_2_1-2))-1)*NWORDS64_FIELD] = { + 0x6A81452B76098390,0x6B73822FC83B9B2A,0xADA9D91C1A56C87D,0xE9730B6372CFC67F,0xFC2C30EA65FB7255,0xA72BFB11A5E87436,0x958ACE3D0D1F8284,0x90B629F4CFE08F98,0xB1EB27EE9B3C8759,0x739AB8F053565FF,0x762E6EE2FBD25204,0x1C755F143777 }; - const uint64_t *ph2_T1 = {0}; - const uint64_t *ph2_T2 = {0}; + + + // Log table for ell=2, W2_1=3 + const int ph2_Log[(1<<(W_2_1))-1] = { + 4, -2, 2, -1, 3, -3, 1, + }; + + + // G table for ell=2, W2=W2_1+W2_2=4 + const uint64_t ph2_G[(1<<(W_2-2))*NWORDS64_FIELD] = { + 0xFFFFFFFFFFFDB652,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0x6B9FFFFFFFFFFFFF,0x8EC4E4A1129C0C42,0x711E035AD4A8A7A6,0x3FB0E0B52A8F9A48,0x38BE00CA8AAAEDF1,0xFD1AFE3322A8147D,0x428AB0851139,0x957EBAD489F432C2,0x948C7DD037C464D5,0x525626E3E5A93782,0x168CF49C8D303980,0x3D3CF159A048DAA,0xC47404EE5A178BC9,0xF93A1664057C89BD,0xE067D96604C8180D,0x8DC5B8C68F5312EE,0x3184553B857587F1,0x86EC8F5026D5C279,0x26155170D9C2,0x873620A27C428CC3,0x9FCBF25FD2B3DA54,0xC18F4BD9751FD03,0x4F97975AE5F7F916,0x27CEEB2845C92B4,0xF00998E4BFA137C2,0xC242B4819E7FCF48,0xFCE9E84F7C47737,0x764B116BB01F5BF,0x4DD59B47A3FF953F,0xD143293D9A2ACE64,0x226D28265EF8,0x41A0F21CA180CA7C,0x74A5FA538708C3D6,0xF05875741CA48BD4,0x5EEC4B142261D4C0,0xBD85C16B2AC25A70,0x813B01BCCFBBF227,0xA8C72A48A392E441,0xE03F5F6F81824B7E,0x167D025F77F5BEF5,0x72C4BCC1C6840F24,0xC522FE7E15196CE3,0x686D5B90407F + }; + + // Torus tables for W_2 = 4 + const uint64_t ph2_CT[DLEN_2*(ELL2_W >> 1)*NWORDS64_FIELD] = { + 0x8C13FD3A88DD1EB5,0x826703E958F24192,0xDA2D4E4F70B25690,0x7FDCAF828334BF4D,0xEEC9A6FAAFB30BD4,0x8C3C0978ACC9D76C,0x9993A706A84A8E08,0x2B93F97181FEF9F4,0x79D4300DD320DD39,0x5003EA0F91E4E091,0x6BE743090F07340,0x6141886AA145,0xF9BDAE6237253449,0xFC685B95207FF63A,0x3C5C0CBEC2AF253D,0xECCAF6696C92D409,0xD085ADF6900FA232,0xCAF48DC48310A9A3,0x9EB61DD752C35879,0xD4B9848571242C98,0x440F68AF1D8EBBFC,0x2DD9D4003E2B8124,0x4239D4E592733586,0x48BBB58C80D0,0x7BFF42D8BE1D15FE,0x42FF2078438D29B2,0xDF176D64B40FAA36,0x2D09272D956FFF86,0x4917550DEACD45DF,0xD7DF615598D60590,0xCDB010BD1CEF82EF,0x5A484B4B2B97C6B5,0x72484F1E600891,0xFE7E8DF16417FA7D,0x235D29F4BD53E3D0,0x277DC91AD2FE,0x7A6C94F1C70C63D2,0x6062C79A031AEF71,0xAE09A41FAEDE7C5F,0xB7A9E835BD1FC032,0x769057F281DEB575,0x2341724FCD3C783A,0xFA29725084044445,0x2F1C8C26C9678FC,0xDB4E3A5CE1232D5A,0xCA6BA05078FE3202,0xFF9D6E11343245F9,0x4042699FDAB4,0x3318C82849D29932,0xC48B3E7063C086D9,0x293B7D2BC95FD69C,0x3C5ED4EFE76A3880,0x2C4F4D1DDE774ED,0x604872AEBEAD830A,0xDAF4A4117B6AAD86,0x1927D42FF252CB29,0xC51A7A4B64E337BA,0x97924C6D7D17970C,0xFBCE7976052A7202,0x1690D6AE75C0,0xF55B7CACD84D8909,0x44FC4DE74D6CDFD7,0xF6148606835EEC91,0x54092A48EB80507D,0x1B38C0E9887342EE,0x9467B970EDB1C119,0x793EA3A3699C0213,0xAEB8DC517C3830F1,0xB82AC24D3F422C38,0xE056D4D14BEB3DFA,0xD028127C6A936C2,0x1B62DB7D1DB1,0xF69335E2EA20AC48,0xC2E0FF09057F27D7,0x25B5E94A0BCFFF04,0x70E4B0B98C74F5C7,0xF7D55801BAC15AF8,0xE41A50FF7E822DCA,0x9633D039609C2166,0x910776B458F98174,0x7A952A9EC18D413E,0x440C3920407EAE62,0xB55BE8CF3AC15DA3,0x5217FEE2432A,0xC77B8E20C74BF05F,0xB2BEAFBB54E69655,0x681E4F47B8E76591,0xCDA5870C9270DF67,0xEA2DDF408B4235B9,0x489E1CFEDDFC16FC,0x9151DFFC9CD5A91D,0x58F8E9A66A03D9FD,0xF663E5D661D10C26,0x536B8FF51A16FA0C,0xEC0ACA7173729751,0x586350F79627,0x86D2D70685AE646F,0x56B1FF6CD74206B0,0xA45FD89F18CC9571,0xF98D10A416B57622,0x9A08776A5B524D47,0x318DCED278ABCA19,0xADF04E04F86AB8E2,0xD96E994290C0E8D2,0xC7109FDCDCB9C718,0xAD52343E86E1D28D,0x2D42306587F7C26E,0x1B07D61A42AE,0xAF0FCB2E311A70E8,0x4457709853B47435,0x37753C74A5857FB9,0x3D9688594BC7A42E,0x8CA8DEF33E52A39F,0x87687FBDA656D29,0x18017B7EA24A2C53,0x18A03D90992552E,0x7969734F26FDE4A3,0x680BAA2A0EB6B071,0xF62D12D4349CF171,0x1796C3836D4B,0x78A44BFC08739709,0x2AF84F17DBA931AF,0xA1CFA713604334E3,0x4BB9B48F968B6E8B,0x49EE11C82F50EB1D,0x68DAD423617DE835,0x92BC40A069355034,0x244E172669B9EE36,0x8321C15F2A021104,0x837F83CC0FD76013,0xF62D00C8A8C42262,0x3EDD7E535984,0xB191B7712CB5D171,0x3C1F758F82FF64F6,0xBD8B54F2CFB0E62D,0x47E9F14421850AFF,0xB869383990C57E47,0x85EAE37AEA5A2262,0x749524134B8E1E72,0x487AD666756F5B6D,0xC9F11728A934E989,0xABF5542F6D0D435E,0x222C39441A301CEF,0x3F76DF67FF7B,0xE4722D28BB1A3C4B,0xF2961EA5B1E8E80D,0xF6D1137C61F3EA3C,0x8C8D1046E936CD43,0x81605DC229DFEA60,0x296F65CCC4350AEC,0x43E22616AF23CE42,0x6F7016A903C95B19,0x5AFC743A7E758DF3,0x6C4BBB214D2BB854,0xC2A799941D8E2E6F,0x598419831415,0xDE755DD8DF9F6322,0x8BBD139E6E407B4A,0x9892783742A301BD,0x3FCF8E980A70689C,0xACADDC8889131B2C,0xAA5F810C957E9DC5,0x230C68C22CE7B8C4,0xCD410BF5AE647F39,0x4A32D20D59E85743,0x9E8B96E4775B1045,0x6E11B07DE3528138,0x236ACFDB2841,0x52395441B841B9E,0xBCEEECD3C856FF71,0xB31CFB0B3AA82A72,0x2B438E304F2AC81D,0x756AC60EEA5DC1BD,0xF89AB62F0DF8F90E,0x5FD74A59724B0AC8,0x3DC671B04760A41A,0xDE5B06E47CB041B6,0x65F57303866C8114,0x519ABEE95AC0D32B,0x3E3F42F63B9A,0x1AE362DAA6D63D4C,0xE0D21147B09CEC6E,0x3682AFA4234AEE70,0x597C61E6209BFA0B,0xC00506AE81DD1A3F,0x68FBDD56A4B58B5C,0x5521481316B27EDE,0xBE1D286E3E90A8C4,0x84B72C86B576B8A7,0xB160A55969DE3F55,0xE0CAB47FB1C7E53B,0x6D6D5CBC8050,0xF9DA9E89C82967BC,0x3045006B355CE428,0x7A89AE56CC02F9B8,0x36B9F53099DF41C1,0x9ED3E55C3AB8288C,0x72B1565C8A0BADE5,0xF029C4ADADB5AEF0,0xFA5754BDA48BCC49,0xD9A0C933BCCF1BCA,0xB2FB59E7A616AF52,0xB15F7383D6778EB4,0x31B1B687B018,0x6788C415598C10EC,0x3F2FA7E32E37498D,0xC26DBE8B576AC232,0xA30059C62FD85940,0xDFA44C9790D9F71D,0xAAEB7E458E257AA5,0x33AA285F4F2B5F16,0x5ED2A827FED3DFE0,0x50C6C68FD7349040,0x5240D10D107C32AD,0x7CF7BC854C84063,0x3856F44D6C29,0x273B1B7105F3D4AD,0x6E421F5517ECFBF5,0xF0F5182F435A8366,0xC9F4C6B579D25954,0xBEFF3E0FF11F55BD,0x2395CB717EE2F00A,0xCED5B94807A9A92C,0x11D7348AB5D79B70,0x73C48EB3EE4E0129,0x43AEAECCE099401C,0x3FA03BF8D788008D,0x6327D1D27B3B,0x6AA5469C78A82DE9,0x7917D227C824EA3F,0x1B63BDAFFA1415E0,0x81606A42D703BCC3,0x947192340B73E689,0x1B06C35ADB2692E8,0x5FA6EDB4BD0D20B6,0xC58572BB508A06C3,0x5729A72E833D3BAC,0xD3BADFE35FEB5AD1,0x2151501150EFEB6A,0x2FE8002BCF50,0x8B63B65CAA8DE9BC,0x6551C0F0267EBE11,0x3977E8EC7C8408F3,0x913594F88F0C8F9D,0xF36F8B6D4A4A8126,0xD11D15284C54699E,0xEF389463BAC39486,0x5C2106F42FDC2F4F,0xE4CF0DE9978D8E99,0x8C8B6D2F7F767466,0x204D7A9C886D1BE1,0x2CEBD919258A,0xD9EA8C384BBA8FDF,0xA621660BC917980D,0xD24C99FFF689B7F8,0xBFB9A5BA01B391CD,0x254BA3B317001E4F,0x39B119C7A0520F35,0xC90A55D98EAE20E2,0xA1CC2E81996264C5,0xDB61CD5B9A20F996,0x755CE112C6A0BF1,0xE271C1B6C7FC4AEA,0x1991B590023C,0xF23804BB419850A5,0xD0A7890864565FF3,0x33A891182246B6E9,0xD3AF8861B517D889,0xFF64F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+ }; + #endif - #endif // Closing ELL2_FULL_SIGNED and ELL2_HYBRID for ell=2 -#endif // Closing COMPRESSED_TABLES + #endif +#endif // This is for \ell=3 case. Note: Two different cases must be handled: w divides e, and not #if defined(COMPRESSED_TABLES) @@ -29,5 +47,5 @@ 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}; #endif - #endif // Closing ELL3_FULL_SIGNED -#endif // Closing COMPRESSED_TABLES for ell=3 \ No newline at end of file + #endif +#endif \ No newline at end of file diff --git a/src/P751/P751_internal.h b/src/P751/P751_internal.h index b6036e8..d636e7c 100644 --- a/src/P751/P751_internal.h +++ b/src/P751/P751_internal.h @@ -63,7 +63,7 @@ #define TABLE_V3_LEN 20 // Parameters for discrete log computations // Binary Pohlig-Hellman reduced to smaller logs of order ell^W - #define W_2 4 + #define W_2 4 #define W_3 3 // ell^w #define ELL2_W (1 << W_2) @@ -76,15 +76,17 @@ #define DLEN_3 ((OBOB_EXPON + W_3 - 1) / W_3) // ceil(eB/W_3) // Use compressed tables: FULL_SIGNED #define COMPRESSED_TABLES - #define ELL2_FULL_SIGNED // Uses signed digits to reduce table size by half + #define ELL2_TORUS #define ELL3_FULL_SIGNED // Uses signed digits to reduce table size by half // Length of the optimal strategy path for Pohlig-Hellman #ifdef COMPRESSED_TABLES - #ifdef ELL2_FULL_SIGNED - #if W_2 == 4 - #define PLEN_2 94 - #endif + #if W_2 == 4 + #define PLEN_2 94 + #endif + #ifdef ELL2_TORUS + #define W_2_1 3 #endif + #ifdef ELL3_FULL_SIGNED #if W_3 == 3 #define PLEN_3 81 diff --git a/src/compression/dlog.c b/src/compression/dlog.c index 4621330..36786db 100644 --- a/src/compression/dlog.c +++ b/src/compression/dlog.c @@ -8,7 +8,7 @@ void from_base(int *D, digit_t *r, int Dlen, int base) { // Convert a number in base "base" with signed digits: (D[k-1]D[k-2]...D[1]D[0])_base < 2^(NWORDS_ORDER*RADIX) into decimal - // Output: r = D[k-1]*base^(k-1) + ... + D[1]*base + D[0] + // Output: r = (D[k-1]*base^(k-1) + ... + D[1]*base + D[0])_10 digit_t ell[NWORDS_ORDER] = {0}, digit[NWORDS_ORDER] = {0}, temp[NWORDS_ORDER] = {0}; int ellw; @@ -88,7 +88,174 @@ void from_base(int *D, digit_t *r, int Dlen, int base) #ifdef COMPRESSED_TABLES -#if defined(ELL2_FULL_SIGNED) || defined(ELL3_FULL_SIGNED) + +#ifdef ELL2_TORUS + +int ord2w_dlog(const felm_t *r, const int *logT, const felm_t *Texp) +{ // Given a generator rho_2 of order 2^w1, input elements r=[x:y] and w1, compute d <- log_{rho_2}r, + // where r = [x,y] \equiv [a_k:1] for some k in {1,2,..2^w1-1} or r \equiv [1:0] + // Output: corresponding digit d in [-2^{w1-1},2^{w1-1}] + felm_t x, y; + felm_t sum = {0}, prods[1<<(W_2_1-1)] = {0}; + f2elm_t tmp; + + fpcopy(r[0], x); + fpcopy(r[1], y); + + fpcorrection(x); + fpcorrection(y); + + if (is_felm_zero(y)) return 0; + if (is_felm_zero(x)) return logT[0]; + if (memcmp(x, y, NBITS_TO_NBYTES(NBITS_FIELD)) == 0) return logT[1]; + fpcopy(y, sum); + fpneg(sum); + fpcorrection(sum); + if (memcmp(x, sum, NBITS_TO_NBYTES(NBITS_FIELD)) == 0) return logT[2]; + for (int j = 2; j < W_2; ++j) + { + for (int i = 0; i < (1<<(j-1)); ++i) + { + if ((i % 2) == 0) fpmul_mont(y, Texp[(1<<(j-2)) + (i/2) - 1], prods[(1<<(j-2)) + (i/2) - 1]); + fpcopy(y, sum); + for (int k = 0; k <= j-2; ++k) { + if (((i>>(j-k-2)) % 2) == 0) + fpadd(sum, prods[(1<> (j-k-1)) - 1], sum); + else + fpsub(sum, prods[(1<> (j-k-1)) - 1], sum); + } + fpcorrection(sum); + if (memcmp(x, sum, NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + return logT[(1<= 0; j--) fp2copy(H[j], H[j+1]); + sqr_Fp2_cycl_proj(H[0]); + k++; + } else { + break; + } + } + + fpcorrection(H[0][1]); + if (is_felm_zero(H[0][1]) && k <= W_2_1) return ord2w_dlog(H[k], logT, Texp) << w2; + + if (!is_felm_zero(H[0][1])) { + d = mod(ord2w_dlog(H[0], logT, Texp), (1 << W_2_1)); + index = 0; + } else { + d = mod(ord2w_dlog(&H[W_2_1][0], logT, Texp), (1 << W_2_1)); + index = W_2_1; + } + + t = highest_t(d); + ord = W_2_1 - t; + tmp = ((d >> (W_2_1-ord))-1) >> 1; + i_j = reverse_bits(tmp,ord-1); + if (is_felm_zero(H[0][0])) { // check if compressed Fp2 element H[0] is -1 + fpneg(one); + fpcorrection(one); + if ( ((memcmp(G[0],&Montgomery_one,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) && (memcmp(H[1][0],H[1][1],NBITS_TO_NBYTES(NBITS_FIELD)) != 0)) || + ((memcmp(G[0],one,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) && (memcmp(H[1][0],H[1][1],NBITS_TO_NBYTES(NBITS_FIELD)) == 0))) { // check if G[0] != H[1] + for (int i = 0; i <= k; ++i) inv_Fp2_cycl_proj(H[i]); + inv = 1; + } + } else { + if (i_j >= (1 << (ord-2))) { + i_j = (1 << (ord-1)) - i_j - 1; + d = (1 << (W_2_1)) - d; + for (int i = 0; i <= k; ++i) inv_Fp2_cycl_proj(H[i]); + inv = 1; + } + } + d <<= w2; + for (int j = index+1; j <= k; ++j) { + i_j <<= 1; + d >>= 1; + + if ((j-index+ord-3) < 0) { + fpmul_mont(G[0], H[j][1], one); + } else { + fpmul_mont(G[(1 << (j-index+ord-2)) - (1 << (j-index+ord-3)) + (i_j >> 1)], H[j][1], one); + } + fpcorrection(one); + if (memcmp(H[j][0], one, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + d += 1 << (w-1); + i_j++; + flag = 1; + } + } + + if (d > (1 << (w-1))) d = (1 << w) - d; + if (inv ^ flag) d = -d; + + return d; +} + + +void Traverse_w_div_e_torus(const felm_t *r, int j, int k, int z, const unsigned int *P, const felm_t *CT, int *D, int Dlen, int ellw, int w) +{// Traverse a Pohlig-Hellman optimal strategy to solve a discrete log in a group of order 2^e + // The leaves of the tree will be used to recover the signed digits which are numbers from +/-{0,1... Ceil((2^w-1)/2)} + // Assume the integer w divides the exponent e + felm_t rp[2] = {0}, alpha = {0}; + + if (z > 1) { + int t = P[z]; + fp2copy(r, rp); + for (int i = 0; i < (z-t)*w; i++) sqr_Fp2_cycl_proj(rp); + + Traverse_w_div_e_torus(rp, j + (z - t), k, t, P, CT, D, Dlen, ellw, w); + + fp2copy(r, rp); + for (int h = k; h < k + t; h++) { + if (D[h] != 0) { + if(D[h] < 0) { + fpcopy(CT[(j + h)*(ellw/2) - (D[h]+1)], alpha); + fpneg(alpha); + mulmixed_montproj(rp, alpha, rp); + } else { + mulmixed_montproj(rp, CT[(j + h)*(ellw/2) + (D[h]-1)], rp); + } + } + } + Traverse_w_div_e_torus(rp, j, k + t, z - t, P, CT, D, Dlen, ellw, w); + } else { + fpcorrection((digit_t*)&r[0]); + fpcorrection((digit_t*)&r[1]); + + D[k] = ord2w_dloghyb(r, (const int *)&ph2_Log, (const felm_t *)&ph2_Texp, (const felm_t *)&ph2_G); + } +} + +#endif // Closing ELL2_TORUS + +#if defined(ELL3_FULL_SIGNED) void Traverse_w_div_e_fullsigned(const f2elm_t r, int j, int k, int z, const unsigned int *P, const felm_t *CT, int *D, int Dlen, int ellw, int w) @@ -129,11 +296,11 @@ void Traverse_w_div_e_fullsigned(const f2elm_t r, int j, int k, int z, const uns fp2copy(r, rp); fp2correction(rp); - if (is_felm_zero(rp[1]) && memcmp((unsigned char *)&rp[0],&Montgomery_one,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + if (is_felm_zero(rp[1]) && memcmp(rp[0],&Montgomery_one,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { D[k] = 0; } else { for (int t = 1; t <= ellw/2; t++) { - if (memcmp(rp, (unsigned char*)&CT[2*((Dlen - 1)*(ellw/2) + (t-1))], 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + if (memcmp(rp, CT[2*((Dlen - 1)*(ellw/2) + (t-1))], 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { D[k] = -t; break; } else { @@ -144,8 +311,8 @@ void Traverse_w_div_e_fullsigned(const f2elm_t r, int j, int k, int z, const uns D[k] = t; break; } - } - } + } + } } } } @@ -200,12 +367,12 @@ void Traverse_w_notdiv_e_fullsigned(const f2elm_t r, int j, int k, int z, const fp2copy(r, rp); fp2correction(rp); - if (is_felm_zero(rp[1]) && memcmp((unsigned char *)&rp[0],&Montgomery_one,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + if (is_felm_zero(rp[1]) && memcmp(rp[0],&Montgomery_one,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { D[k] = 0; } else { if (!(j == 0 && k == Dlen - 1)) { for (int t = 1; t <= (ellw/2); t++) { - if (memcmp((unsigned char*)&CT2[2*(ellw/2)*(Dlen-1) + 2*(t-1)], rp, 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + if (memcmp(CT2[2*(ellw/2)*(Dlen-1) + 2*(t-1)], rp, 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { D[k] = -t; break; } else { @@ -220,7 +387,7 @@ void Traverse_w_notdiv_e_fullsigned(const f2elm_t r, int j, int k, int z, const } } else { for (int t = 1; t <= ell_emodw/2; t++) { - if (memcmp((unsigned char*)&CT1[2*(ellw/2)*(Dlen - 1) + 2*(t-1)], rp, 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { + if (memcmp(CT1[2*(ellw/2)*(Dlen - 1) + 2*(t-1)], rp, 2*NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { D[k] = -t; break; } else { @@ -238,7 +405,7 @@ void Traverse_w_notdiv_e_fullsigned(const f2elm_t r, int j, int k, int z, const } } } -#endif //Closing ELL2_FULL_SIGNED or ELL3_FULL_SIGNED +#endif //Closing ELL3_FULL_SIGNED #endif // Closing COMPRESSED_TABLES @@ -247,70 +414,19 @@ void solve_dlog(const f2elm_t r, int *D, digit_t* d, int ell) { // Computes the discrete log of input r = g^d where g = e(P,Q)^ell^e, and P,Q are torsion generators in the initial curve // Return the integer d if (ell == 2) { - #if (OALICE_BITS % W_2 == 0) - #if defined(COMPRESSED_TABLES) - #if defined(ELL2_FULL_SIGNED) - Traverse_w_div_e_fullsigned(r, 0, 0, PLEN_2 - 1, ph2_path, (const felm_t *)&ph2_T, D, DLEN_2, ELL2_W, W_2); - #endif - #endif - #else - #if defined(COMPRESSED_TABLES) - #if defined(ELL2_FULL_SIGNED) - Traverse_w_notdiv_e_fullsigned(r, 0, 0, PLEN_2 - 1, ph2_path, (const felm_t *)&ph2_T1, (const felm_t *)&ph2_T2, D, DLEN_2, ell, ELL2_W, ELL2_EMODW, W_2, OALICE_BITS); - #endif - #endif - #endif + felm_t rproj[2]; + toproj(r, rproj); + Traverse_w_div_e_torus(rproj, 0, 0, PLEN_2 - 1, ph2_path, (const felm_t *)&ph2_CT, D, DLEN_2, ELL2_W, W_2); + from_base(D, d, DLEN_2, ELL2_W); } else if (ell == 3) { #if (OBOB_EXPON % W_3 == 0) - #if defined(COMPRESSED_TABLES) - #if defined(ELL3_FULL_SIGNED) - Traverse_w_div_e_fullsigned(r, 0, 0, PLEN_3 - 1, ph3_path, (const felm_t *)&ph3_T, D, DLEN_3, ELL3_W, W_3); - #endif - #endif + Traverse_w_div_e_fullsigned(r, 0, 0, PLEN_3 - 1, ph3_path, (const felm_t *)&ph3_T, D, DLEN_3, ELL3_W, W_3); #else - #if defined(COMPRESSED_TABLES) - #if defined(ELL3_FULL_SIGNED) - Traverse_w_notdiv_e_fullsigned(r, 0, 0, PLEN_3 - 1, ph3_path, (const felm_t *)&ph3_T1, (const felm_t *)&ph3_T2, D, DLEN_3, ell, ELL3_W, ELL3_EMODW, W_3, OBOB_EXPON); - #endif - #endif + Traverse_w_notdiv_e_fullsigned(r, 0, 0, PLEN_3 - 1, ph3_path, (const felm_t *)&ph3_T1, (const felm_t *)&ph3_T2, D, DLEN_3, ell, ELL3_W, ELL3_EMODW, W_3, OBOB_EXPON); #endif from_base(D, d, DLEN_3, ELL3_W); } } -void ph2(const point_full_proj_t phiP, const point_full_proj_t phiQ, const point_t PS, const point_t QS, const f2elm_t A, digit_t* c0, digit_t* d0, digit_t* c1, digit_t* d1) -{ // Computes the 4 coefficients of the change of basis matrix between the bases {phiP,phiQ} and {PS, QS} - // Assume both bases generate the full 2^eA torsion - f2elm_t n[4] = {0}; - int D[DLEN_2]; - - // Compute the four pairings - Tate_4_pairings_2_torsion(phiP, phiQ, PS, QS, A, n); - - solve_dlog(n[0], D, d0, 2); - solve_dlog(n[2], D, c0, 2); - mp_sub((digit_t*)Alice_order, c0, c0, NWORDS_ORDER); - solve_dlog(n[1], D, d1, 2); - solve_dlog(n[3], D, c1, 2); - mp_sub((digit_t*)Alice_order, c1, c1, NWORDS_ORDER); -} - - -void ph3(point_full_proj_t phiP, point_full_proj_t phiQ, point_full_proj_t PS, point_full_proj_t QS, f2elm_t A, digit_t* c0, digit_t* d0, digit_t* c1, digit_t* d1) -{ // Computes the 4 coefficients of the change of basis matrix between the bases {phiP,phiQ} and {PS, QS} - // Assume both bases generate the full 3^eA torsion - f2elm_t n[4] = {0}; - int D[DLEN_3]; - - // Compute the four pairings - Tate_4_pairings_3_torsion(phiP, phiQ, PS, QS, A, n); - - solve_dlog(n[0], D, d0, 3); - solve_dlog(n[2], D, c0, 3); - mp_sub((digit_t*)Bob_order, c0, c0, NWORDS_ORDER); - solve_dlog(n[1], D, d1, 3); - solve_dlog(n[3], D, c1, 3); - mp_sub((digit_t*)Bob_order, c1, c1, NWORDS_ORDER); -} \ No newline at end of file diff --git a/src/compression/pairing.c b/src/compression/pairing.c index 7307062..23e1374 100644 --- a/src/compression/pairing.c +++ b/src/compression/pairing.c @@ -7,51 +7,6 @@ #define t_points 2 -void get_A_compression(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xR, f2elm_t A) -{ // Given the x-coordinates of P, Q, and R, returns the value A corresponding to the Montgomery curve E_A: y^2=x^3+A*x^2+x such that R=Q-P on E_A. - // Input: the x-coordinates xP, xQ, and xR of the points P, Q and R. - // Output: the coefficient A corresponding to the curve E_A: y^2=x^3+A*x^2+x. - f2elm_t t0, t1, one = {0}; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - fp2add(xP, xQ, t1); // t1 = xP+xQ - fp2mul_mont(xP, xQ, t0); // t0 = xP*xQ - fp2mul_mont(xR, t1, A); // A = xR*t1 - fp2add(t0, A, A); // A = A+t0 - fp2mul_mont(t0, xR, t0); // t0 = t0*xR - fp2sub(A, one, A); // A = A-1 - fp2add(t0, t0, t0); // t0 = t0+t0 - fp2add(t1, xR, t1); // t1 = t1+xR - fp2add(t0, t0, t0); // t0 = t0+t0 - fp2sqr_mont(A, A); // A = A^2 - fp2inv_mont_bingcd(t0); // t0 = 1/t0 - fp2mul_mont(A, t0, A); // A = A*t0 - fp2sub(A, t1, A); // Afinal = A-t1 -} - - -void recover_y(const publickey_t PK, point_full_proj_t phiP, point_full_proj_t phiQ, point_full_proj_t phiX, f2elm_t A) -{ // Recover the y-coordinates of the public key - // The three resulting points are (simultaneously) correct up to sign - f2elm_t tmp, phiXY, one = {0}; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - get_A_compression(PK[0], PK[1], PK[2], A); // NOTE: don't have to compress this, can output in keygen - - fp2add(PK[2], A, tmp); - fp2mul_mont(PK[2], tmp, tmp); - fp2add(tmp, one, tmp); - fp2mul_mont(PK[2], tmp, tmp); // tmp = PK[2]^3+A*PK[2]^2+PK[2]; - sqrt_Fp2(tmp, phiXY); - fp2copy(PK[2], phiX->X); - fp2copy(phiXY, phiX->Y); - fp2copy(one, phiX->Z); // phiX = [PK[2],phiXY,1]; - - recover_os(PK[1], one, PK[0], one, PK[2], phiXY, A, phiQ->X, phiQ->Y, phiQ->Z); - fp2neg(phiXY); - recover_os(PK[0], one, PK[1], one, PK[2], phiXY, A, phiP->X, phiP->Y, phiP->Z); -} - static void final_exponentiation_2_torsion(f2elm_t f, const f2elm_t finv, f2elm_t fout) { // The final exponentiation for pairings in the 2^eA-torsion group. Raising the value f to the power (p^2-1)/2^eA. @@ -72,171 +27,6 @@ static void final_exponentiation_2_torsion(f2elm_t f, const f2elm_t finv, f2elm_ } -void Tate_pairings_2_torsion(const point_full_proj_t P, point_full_proj_t *Qj, f2elm_t a, f2elm_t* n) -{ // Compute the reduced Tate pairings e_{2^m}(P, Q_j) for the curve y^2 = x^3 + a*x + b: - f2elm_t h[t_points], one = {0}; - f2elm_t X, Y, Z, X2, Y2, Y4, M, S, T, temp; - f2elm_t Xp, Yp, Zp, Tp; - f2elm_t L, W, g; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - fp2copy(P->X, X); - fp2copy(P->Y, Y); - fp2copy(P->Z, Z); - fp2sqr_mont(Z, T); - - for (int j = 0; j < t_points; j++) { - fp2copy(one, n[j]); - fp2mul_mont(T, Qj[j]->X, temp); - fp2sub(temp, X, h[j]); - } - - for (int k = 0; k < OALICE_BITS; k++) { - // Point doubling and line function construction: - fp2sqr_mont(X, X2); - fp2sqr_mont(Y, Y2); - fp2sqr_mont(Y2, Y4); - fp2sqr_mont(T, temp); - fp2mul_mont(a, temp, temp); - fp2add(X2, X2, M); - fp2add(M, X2, M); - fp2add(M, temp, M); // M = 3*X_2 + a*T^2 - fp2add(X, Y2, S); - fp2sqr_mont(S, S); - fp2sub(S, X2, S); - fp2sub(S, Y4, S); - fp2add(S, S, S); // S = 2*((X + Y2)^2 - X2 - Y4) - fp2sqr_mont(M, temp); - fp2add(S, S, Xp); - fp2sub(temp, Xp, Xp); // Xp = M^2 - 2*S - fp2sub(S, Xp, temp); - fp2mul_mont(M, temp, temp); - fp2shl(Y4, 3, Yp); - fp2sub(temp, Yp, Yp); // Yp = M*(S - Xp) - 8*Y4 - fp2add(Y, Z, temp); - fp2sqr_mont(temp, temp); - fp2sub(temp, Y2, temp); - fp2sub(temp, T, Zp); // Zp = (Y + Z)^2 - Y2 - T - fp2sqr_mont(Zp, Tp); // Tp = Zp^2 - fp2mul_mont(Zp, T, L); // L = Zp*T - fp2add(Y2, Y2, W); // W = 2*Y2 - - fp2correction(Zp); - if (is_felm_zero(Zp[0]) && is_felm_zero(Zp[1])) { // Doubling exception for points in 2*E - fp2copy(one, Xp); - fp2copy(one, Yp); - } - - // Line function evaluation and accumulation: - for (int j = 0; j < t_points; j++) { - if (!is_felm_zero(Zp[0]) || !is_felm_zero(Zp[1])) { - fp2mul_mont(M, h[j], temp); - fp2add(temp, W, temp); - fp2mul_mont(L, Qj[j]->Y, g); - fp2sub(temp, g, g); // g = M*hj + W - L*Y_{Qj} - fp2mul_mont(Tp, Qj[j]->X, temp); - fp2sub(temp, Xp, h[j]); // hj = Tp*X_{Qj} - Xp - fp2_conj(h[j], temp); - fp2mul_mont(temp, g, g); // g = g*hj^* - } else { - fp2copy(h[j], g); - } - fp2sqr_mont(n[j], n[j]); - fp2mul_mont(n[j], g, n[j]); - } - fp2copy(Xp, X); - fp2copy(Yp, Y); - fp2copy(Zp, Z); - fp2copy(Tp, T); - } - - // Final exponentiation: - mont_n_way_inv(n, t_points, h); - for (int j = 0; j < t_points; j++) { - fp2correction(Qj[j]->Z); - if (is_felm_zero(Qj[j]->Z[0]) && is_felm_zero(Qj[j]->Z[1])) - fp2copy(one, n[j]); - else { - final_exponentiation_2_torsion(n[j], h[j], n[j]); - } - } -} - - -void Monty2Weier(const f2elm_t A, f2elm_t a, f2elm_t b) -{ // Convert a Montgomery curve EM: y^2 = x^3 + A*x^2 + x into its short Weierstrass form EW: v^2 = u^3 + a*u + b. - f2elm_t one = {0}, temp, A2, AA; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - // a = 1 - A^2/3 - fp2sqr_mont(A, A2); - fpmul_mont(A2[0], (digit_t*)threeinv, temp[0]); - fpmul_mont(A2[1], (digit_t*)threeinv, temp[1]); - fp2sub(one, temp, a); - - // b = (2*A^3 - 9*A)/27 - fp2add(A, A, AA); // AA = 2*A - fp2mul_mont(AA, A2, temp); // temp = 2A^3 - fp2add(AA, AA, A2); // A2 = 4*A - fp2add(A2, A2, A2); // A2 = 8*A - fp2add(A2, A, A2); // A2 = 9*A - fp2sub(temp, A2, b); // b = 2A^3 - 9*A - fpmul_mont((digit_t*)threeinv, (digit_t*)threeinv, temp[0]); - fpmul_mont(temp[0], (digit_t*)threeinv, temp[0]); - fpmul_mont(temp[0], b[0], b[0]); - fpmul_mont(temp[0], b[1], b[1]); -} - - -void PointMonty2Weier(const point_full_proj_t PM, point_full_proj_t PW, const f2elm_t A) -{ // Convert a point PM on a Montgomery curve y^2 = x^3 + A*x^2 + x into the corresponding point on its short Weierstrass form EW. - f2elm_t zero = {0}, one = {0}, temp; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - - if (is_felm_zero(PM->Z[0]) && is_felm_zero(PM->Z[1])) { - fp2copy(zero,PW->X); - fp2copy(one, PW->Y); - fp2copy(zero,PW->Z); - return; - } - fpmul_mont((digit_t*)threeinv, A[0], temp[0]); - fpmul_mont((digit_t*)threeinv, A[1], temp[1]); - - // PW = EW(PM->X + A/3, PM->Y, 1) - fp2add(temp, PM->X, PW->X); - fp2copy(PM->Y, PW->Y); - fp2copy(one, PW->Z); -} - - -void Tate_4_pairings_2_torsion(const point_full_proj_t P, const point_full_proj_t Q, const point_t S1, const point_t S2, const f2elm_t A, f2elm_t* n) -{ // The doubling only 2-torsion Tate pairing of order 2^eA, consisting of the doubling only Miller loop and the final exponentiation.] - // Computes 4 pairings at once: e(P, S1), e(P, S2), e(Q, S1), e(Q, S2). - point_full_proj_t Qj[2], PW, QW, QjW[2]; - f2elm_t a, b, one = {0}; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - Monty2Weier(A, a, b); - - // Assume S1 and S2 are normalized - fp2copy(S1->x, Qj[0]->X); - fp2copy(S1->y, Qj[0]->Y); - fp2copy(one, Qj[0]->Z); - fp2copy(S2->x, Qj[1]->X); - fp2copy(S2->y, Qj[1]->Y); - fp2copy(one, Qj[1]->Z); - - PointMonty2Weier(P, PW, A); - PointMonty2Weier(Q, QW, A); - PointMonty2Weier(Qj[0], QjW[0], A); - PointMonty2Weier(Qj[1], QjW[1], A); - - Tate_pairings_2_torsion(PW, QjW, a, n); - Tate_pairings_2_torsion(QW, QjW, a, n + 2); -} - - static void final_exponentiation_3_torsion(f2elm_t f, const f2elm_t finv, f2elm_t fout) { // The final exponentiation for pairings in the 3-torsion group. Raising the value f to the power (p^2-1)/3^eB. felm_t one = {0}; @@ -256,152 +46,6 @@ static void final_exponentiation_3_torsion(f2elm_t f, const f2elm_t finv, f2elm_ } -void Tate_pairings_3_torsion(const point_full_proj_t P, point_full_proj_t *Qj, f2elm_t a, f2elm_t* n) -{ // The tripling only 3-torsion Tate pairing of order 3^eB, consisting of the tripling only Miller loop and the final exponentiation. - // Computes 4 pairings at once: e(P, R1), e(P, R2), e(Q, R1), e(Q, R2). - f2elm_t h[t_points], one = {0}; - f2elm_t X, Y, Z, X2, Y2, Y4, M, S, T; - f2elm_t Xp, Yp, Zp, Tp, D, U, Up, Fp; - f2elm_t L, W, Wp, g, T2, M2, F, F2, d; - f2elm_t temp, temp1; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - fp2copy(P->X, X); - fp2copy(P->Y, Y); - fp2copy(P->Z, Z); - fp2sqr_mont(Z, T); - - for (int j = 0; j < t_points; j++) { - fp2copy(one, n[j]); - fp2mul_mont(T, Qj[j]->X, temp); - fp2sub(temp, X, h[j]); - } - - for (int k = 0; k < OBOB_EXPON; k++) { - // Point tripling and parabola function construction: - fp2sqr_mont(X, X2); - fp2sqr_mont(Y, Y2); - fp2sqr_mont(Y2, Y4); - fp2sqr_mont(T, T2); - fp2add(X2, X2, temp); - fp2add(temp, X2, temp); - fp2mul_mont(a, T2, M); - fp2add(temp, M, M); // M = 3*X2 + a*T2 - fp2sqr_mont(M, M2); - fp2add(X, Y2, temp); - fp2sqr_mont(temp, temp); - fp2sub(temp, X2, temp); - fp2sub(temp, Y4, D); // D = (X + Y2)^2 - X2 - Y4 - fp2add(D, D, temp); - fp2add(temp, D, temp); - fp2add(temp, temp, temp); - fp2sub(temp, M2, F); // F = 6*D - M2 - fp2sqr_mont(F, F2); - fp2add(Y2, Y2, W); - fp2add(W, W, Wp); - fp2shl(Y4, 4, S); - fp2add(M, F, temp); - fp2sqr_mont(temp, temp); - fp2sub(temp, M2, temp); - fp2sub(temp, F2, temp); - fp2sub(temp, S, U); // U = (M + F)^2 - M2 - F2 - S - fp2sub(S, U, Up); - fp2mul_mont(X, F2, temp); - fp2mul_mont(Wp, U, Xp); - fp2sub(temp, Xp, Xp); - fp2shl(Xp, 2, Xp); // Xp = 4*(X*F2 - Wp*U) - fp2mul_mont(U, Up, temp); - fp2mul_mont(F, F2, Yp); - fp2sub(temp, Yp, Yp); - fp2mul_mont(Y, Yp, Yp); - fp2shl(Yp, 3, Yp); // Yp = 8*Y*(U*Up - F*F2) - fp2add(Z, F, temp); - fp2sqr_mont(temp, temp); - fp2sub(temp, T, temp); - fp2sub(temp, F2, Zp); // Zp = (Z + F)^2 - T - F2 - fp2sqr_mont(Zp, Tp); - fp2add(Y, Z, temp); - fp2sqr_mont(temp, temp); - fp2sub(temp, Y2, temp); - fp2sub(temp, T, temp); - fp2mul_mont(temp, T, L); - fp2add(F, F, Fp); - - fp2correction(Zp); - if (is_felm_zero(Zp[0]) && is_felm_zero(Zp[1])) { - fp2copy(one, Xp); - fp2copy(one, Yp); - } - - // Parabola function evaluation and accumulation - for (int j = 0; j < t_points; j++) { - fp2mul_mont(L, Qj[j]->Y, temp); - fp2sub(W, temp, d); - if (!is_felm_zero(Zp[0]) || !is_felm_zero(Zp[1])) { - fp2mul_mont(M, h[j], temp); - fp2add(d, temp, g); // g = (M*h + d) - fp2mul_mont(Up, h[j], temp); - fp2mul_mont(Fp, d, temp1); - fp2add(temp, temp1, temp1); - fp2mul_mont(temp1, g, g); // g = (M*h + d)*(Up*h + Fp*d) - fp2mul_mont(Wp, h[j], temp); - fp2add(F, temp, temp); - fp2_conj(temp, temp); - fp2mul_mont(temp, g, g); // g = (M*h + d)*(Up*h + Fp*d)*(Wp*h + F)^* - fp2mul_mont(Tp, Qj[j]->X, temp); - fp2sub(temp, Xp, h[j]); // h = Tp*X_{Qj} - Xp - fp2_conj(h[j], temp); - fp2mul_mont(temp, g, g); - } else { - fp2mul_mont(M, h[j], temp); - fp2add(temp, d, g); - } - fp2sqr_mont(n[j], temp); - fp2mul_mont(temp, n[j], n[j]); - fp2mul_mont(g, n[j], n[j]); - } - fp2copy(Xp, X); - fp2copy(Yp, Y); - fp2copy(Zp, Z); - fp2copy(Tp, T); - } - - // Final exponentiation: - mont_n_way_inv(n, t_points, h); - for (int j = 0; j < t_points; j++) { - fp2correction(Qj[j]->Z); - if (is_felm_zero(Qj[j]->Z[0]) && is_felm_zero(Qj[j]->Z[1])) - fp2copy(one, n[j]); - else { - final_exponentiation_3_torsion(n[j], h[j], n[j]); - } - } -} - - -void Tate_4_pairings_3_torsion(const point_full_proj_t P, const point_full_proj_t Q, const point_full_proj_t R1, const point_full_proj_t R2, const f2elm_t A, f2elm_t* n) -{ // The tripling only 3-torsion Tate pairing of order 3^eB, consisting of the tripling only Miller loop and the final exponentiation. - // Computes 4 pairings at once: e(P, S1), e(P, S2), e(Q, S1), e(Q,S2). - point_full_proj_t Qj[2] = {0}, PW, QW, QjW[2] = {0}; - f2elm_t a, b; - - Monty2Weier(A, a, b); - fp2copy(R1->X, Qj[0]->X); - fp2copy(R1->Y, Qj[0]->Y); - fp2copy(R1->Z, Qj[0]->Z); - fp2copy(R2->X, Qj[1]->X); - fp2copy(R2->Y, Qj[1]->Y); - fp2copy(R2->Z, Qj[1]->Z); - - PointMonty2Weier(P, PW, A); - PointMonty2Weier(Q, QW, A); - PointMonty2Weier(Qj[0], QjW[0], A); - PointMonty2Weier(Qj[1], QjW[1], A); - Tate_pairings_3_torsion(PW, QjW, a, n); - Tate_pairings_3_torsion(QW, QjW, a, n + 2); -} - - void Tate3_pairings(point_full_proj_t *Qj, f2elm_t* f) { felm_t *x, *y, *l1, *l2, *n1, *n2, *x2, *x23, *x2p3; diff --git a/src/compression/sidh_compressed.c b/src/compression/sidh_compressed.c index 12c62c1..e3357d6 100644 --- a/src/compression/sidh_compressed.c +++ b/src/compression/sidh_compressed.c @@ -7,8 +7,7 @@ #include "../random/random.h" #include -#define COMPRESSION 0 -#define DECOMPRESSION 1 + static void init_basis(digit_t *gen, f2elm_t XP, f2elm_t XQ, f2elm_t XR) @@ -51,472 +50,6 @@ void random_mod_order_B(unsigned char* random_digits) } -static void Ladder3pt_dual(const point_proj_t *Rs, const digit_t* m, const unsigned int AliceOrBob, point_proj_t R, const f2elm_t A24) -{ // Project 3-point ladder - point_proj_t R0 = {0}, R2 = {0}; - digit_t mask; - int i, nbits, bit, swap, prevbit = 0; - - if (AliceOrBob == ALICE) { - nbits = OALICE_BITS; - } else { - nbits = OBOB_BITS; - } - - fp2copy(Rs[1]->X, R0->X); - fp2copy(Rs[1]->Z, R0->Z); - fp2copy(Rs[2]->X, R2->X); - fp2copy(Rs[2]->Z, R2->Z); - fp2copy(Rs[0]->X, R->X); - fp2copy(Rs[0]->Z, R->Z); - - // Main loop - for (i = 0; i < nbits; i++) { - bit = (m[i >> LOG2RADIX] >> (i & (RADIX-1))) & 1; - swap = bit ^ prevbit; - prevbit = bit; - mask = 0 - (digit_t)swap; - - swap_points(R, R2, mask); - xDBLADD(R0, R2, R->X, A24); - fp2mul_mont(R2->X, R->Z, R2->X); - } - swap = 0 ^ prevbit; - mask = 0 - (digit_t)swap; - swap_points(R, R2, mask); -} - - -static void Elligator2(const f2elm_t a24, const unsigned int r, f2elm_t x, unsigned char *bit, const unsigned char COMPorDEC) -{ // Generate an x-coordinate of a point on curve with (affine) coefficient a24 - // Use the counter r - int i; - felm_t one_fp, a2, b2, N, temp0, temp1; - f2elm_t A, y2, *t_ptr; - - fpcopy((digit_t*)&Montgomery_one, one_fp); - fp2add(a24, a24, A); - fpsub(A[0], one_fp, A[0]); - fp2add(A, A, A); // A = 4*a24-2 - - // Elligator computation - t_ptr = (f2elm_t *)&v_3_torsion[r]; - fp2mul_mont(A, (felm_t*)t_ptr, x); // x = A*v; v := 1/(1 + U*r^2) table lookup - fp2neg(x); // x = -A*v; - - if (COMPorDEC == COMPRESSION) { - fp2add(A, x, y2); // y2 = x + A - fp2mul_mont(y2, x, y2); // y2 = x*(x + A) - fpadd(y2[0], one_fp, y2[0]); // y2 = x(x + A) + 1 - fp2mul_mont(x, y2, y2); // y2 = x*(x^2 + Ax + 1); - fpsqr_mont(y2[0], a2); - fpsqr_mont(y2[1], b2); - fpadd(a2, b2, N); // N := norm(y2); - - fpcopy(N, temp0); - for (i = 0; i < OALICE_BITS - 2; i++) { - fpsqr_mont(temp0, temp0); - } - for (i = 0; i < OBOB_EXPON; i++) { - fpsqr_mont(temp0, temp1); - fpmul_mont(temp0, temp1, temp0); - } - fpsqr_mont(temp0, temp1); // z = N^((p + 1) div 4); - fpcorrection(temp1); - fpcorrection(N); - if (memcmp(temp1, N, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { - fp2neg(x); - fp2sub(x, A, x); // x = -x - A; - if (COMPorDEC == COMPRESSION) - *bit = 1; - } - } else { - if (*bit) { - fp2neg(x); - fp2sub(x,A,x); // x = -x - A; - } - } -} - - -static void make_positive(f2elm_t x) -{ - unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); - felm_t zero = {0}; - - from_fp2mont(x, x); - if (memcmp(x[0], zero, (size_t)nbytes) != 0) { - if ((x[0][0] & 1) == 1) - fp2neg(x); - } else { - if ((x[1][0] & 1) == 1) - fp2neg(x); - } - to_fp2mont(x, x); -} - - -static void BiQuad_affine(const f2elm_t a24, const f2elm_t x0, const f2elm_t x1, point_proj_t R) -{ - f2elm_t Ap2, aa, bb, cc, t0, t1; - - fp2add(a24, a24, Ap2); - fp2add(Ap2, Ap2, Ap2); // Ap2 = a+2 = 4*a24 - - fp2sub(x0, x1, aa); - fp2sqr_mont(aa, aa); - - fp2mul_mont(x0, x1, cc); - fpsub(cc[0], (digit_t*)Montgomery_one, cc[0]); - fp2sqr_mont(cc, cc); - - fpsub(x0[0], (digit_t*)Montgomery_one, bb[0]); - fpcopy(x0[1], bb[1]); - fp2sqr_mont(bb, bb); - fp2mul_mont(Ap2, x0, t0); - fp2add(bb, t0, bb); - fp2mul_mont(x1, bb, bb); - fpsub(x1[0], (digit_t*)Montgomery_one, t0[0]); - fpcopy(x1[1], t0[1]); - fp2sqr_mont(t0, t0); - fp2mul_mont(Ap2, x1, t1); - fp2add(t0, t1, t0); - fp2mul_mont(x0, t0, t0); - fp2add(bb, t0, bb); - fp2add(bb, bb, bb); - - fp2sqr_mont(bb, t0); - fp2mul_mont(aa, cc, t1); - fp2add(t1, t1, t1); - fp2add(t1, t1, t1); - fp2sub(t0, t1, t0); - sqrt_Fp2(t0, t0); - make_positive(t0); // Make the sqrt "positive" - fp2add(bb, t0, R->X); - fp2add(aa, aa, R->Z); -} - - -static void get_4_isog_dual(const point_proj_t P, f2elm_t A24, f2elm_t C24, f2elm_t* coeff) -{ - fp2sub(P->X, P->Z, coeff[1]); - fp2add(P->X, P->Z, coeff[2]); - fp2sqr_mont(P->Z, coeff[4]); - fp2add(coeff[4], coeff[4], coeff[0]); - fp2sqr_mont(coeff[0], C24); - fp2add(coeff[0], coeff[0], coeff[0]); - fp2sqr_mont(P->X, coeff[3]); - fp2add(coeff[3], coeff[3], A24); - fp2sqr_mont(A24, A24); -} - -#if (OALICE_BITS % 2 == 1) - -static void eval_dual_2_isog(const f2elm_t X2, const f2elm_t Z2, point_proj_t P) -{ - f2elm_t t0; - - fp2add(P->X, P->Z, t0); - fp2sub(P->X, P->Z, P->Z); - fp2sqr_mont(t0, t0); - fp2sqr_mont(P->Z, P->Z); - fp2sub(t0, P->Z, P->Z); - fp2mul_mont(X2, P->Z, P->Z); - fp2mul_mont(Z2, t0, P->X); -} - -#endif - -static void eval_final_dual_2_isog(point_proj_t P) -{ - f2elm_t t0, t1; - felm_t t2; - - fp2add(P->X, P->Z, t0); - fp2mul_mont(P->X, P->Z, t1); - fp2sqr_mont(t0, P->X); - fpcopy((P->X)[0], t2); - fpcopy((P->X)[1], (P->X)[0]); - fpcopy(t2, (P->X)[1]); - fpneg((P->X)[1]); - fp2add(t1, t1, P->Z); - fp2add(P->Z, P->Z, P->Z); -} - - -static void eval_dual_4_isog_shared(const f2elm_t X4pZ4, const f2elm_t X42, const f2elm_t Z42, f2elm_t* coeff) -{ - fp2sub(X42, Z42, coeff[0]); - fp2add(X42, Z42, coeff[1]); - fp2sqr_mont(X4pZ4, coeff[2]); - fp2sub(coeff[2], coeff[1], coeff[2]); -} - - -static void eval_dual_4_isog(const f2elm_t A24, const f2elm_t C24, const f2elm_t* coeff, point_proj_t P) -{ - f2elm_t t0, t1, t2, t3; - - fp2add(P->X, P->Z, t0); - fp2sub(P->X, P->Z, t1); - fp2sqr_mont(t0, t0); - fp2sqr_mont(t1, t1); - fp2sub(t0, t1, t2); - fp2sub(C24, A24, t3); - fp2mul_mont(t2, t3, t3); - fp2mul_mont(C24, t0, t2); - fp2sub(t2, t3, t2); - fp2mul_mont(t2, t0, P->X); - fp2mul_mont(t3, t1, P->Z); - fp2mul_mont(coeff[0], P->X, P->X); - fp2mul_mont(coeff[1], P->Z, t0); - fp2add(P->X, t0, P->X); - fp2mul_mont(coeff[2], P->Z, P->Z); -} - - -static void eval_full_dual_4_isog(const f2elm_t As[][5], point_proj_t P) -{ - // First all 4-isogenies - for(unsigned int i = 0; i < MAX_Alice; i++) { - eval_dual_4_isog(As[MAX_Alice-i][0], As[MAX_Alice-i][1], *(As+MAX_Alice-i-1)+2, P); - } -#if (OALICE_BITS % 2 == 1) - eval_dual_2_isog(As[MAX_Alice][2], As[MAX_Alice][3], P); -#endif - eval_final_dual_2_isog(P); // to A = 0 -} - - -static void TripleAndParabola_proj(const point_full_proj_t R, f2elm_t l1x, f2elm_t l1z) -{ - fp2sqr_mont(R->X, l1z); - fp2add(l1z, l1z, l1x); - fp2add(l1x, l1z, l1x); - fpadd(l1x[0], (digit_t*)&Montgomery_one, l1x[0]); - fp2add(R->Y, R->Y, l1z); -} - - -static void Tate3_proj(const point_full_proj_t P, const point_full_proj_t Q, f2elm_t gX, f2elm_t gZ) -{ - f2elm_t t0, l1x; - - TripleAndParabola_proj(P, l1x, gZ); - fp2sub(Q->X, P->X, gX); - fp2mul_mont(l1x, gX, gX); - fp2sub(P->Y, Q->Y, t0); - fp2mul_mont(gZ, t0, t0); - fp2add(gX, t0, gX); -} - - -static void FinalExpo3(f2elm_t gX, f2elm_t gZ) -{ - unsigned int i; - f2elm_t f_; - - fp2copy(gZ, f_); - fpneg(f_[1]); - fp2mul_mont(gX, f_, f_); - fp2inv_mont_bingcd(f_); - fpneg(gX[1]); - fp2mul_mont(gX,gZ, gX); - fp2mul_mont(gX,f_, gX); - for(i = 0; i < OALICE_BITS; i++) - fp2sqr_mont(gX, gX); - for(i = 0; i < OBOB_EXPON-1; i++) - cube_Fp2_cycl(gX, (digit_t*)Montgomery_one); -} - - -static void FinalExpo3_2way(f2elm_t *gX, f2elm_t *gZ) -{ - unsigned int i, j; - f2elm_t f_[2], finv[2]; - - for(i = 0; i < 2; i++) { - fp2copy(gZ[i], f_[i]); - fpneg(f_[i][1]); // Conjugate - fp2mul_mont(gX[i], f_[i], f_[i]); - } - mont_n_way_inv(f_,2,finv); - for(i = 0; i < 2; i++) { - fpneg(gX[i][1]); - fp2mul_mont(gX[i], gZ[i], gX[i]); - fp2mul_mont(gX[i], finv[i], gX[i]); - for(j = 0; j < OALICE_BITS; j++) - fp2sqr_mont(gX[i], gX[i]); - for(j = 0; j < OBOB_EXPON-1; j++) - cube_Fp2_cycl(gX[i], (digit_t*)&Montgomery_one); - } -} - - -static bool FirstPoint_dual(const point_proj_t P, point_full_proj_t R, unsigned char *ind) -{ - point_full_proj_t R3,S3; - f2elm_t gX[2],gZ[2]; - felm_t zero = {0}; - unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); - unsigned char alpha,beta; - - fpcopy((digit_t*)B_gen_3_tors + 0*NWORDS_FIELD, (R3->X)[0]); - fpcopy((digit_t*)B_gen_3_tors + 1*NWORDS_FIELD, (R3->X)[1]); - fpcopy((digit_t*)B_gen_3_tors + 2*NWORDS_FIELD, (R3->Y)[0]); - fpcopy((digit_t*)B_gen_3_tors + 3*NWORDS_FIELD, (R3->Y)[1]); - fpcopy((digit_t*)B_gen_3_tors + 4*NWORDS_FIELD, (S3->X)[0]); - fpcopy((digit_t*)B_gen_3_tors + 5*NWORDS_FIELD, (S3->X)[1]); - fpcopy((digit_t*)B_gen_3_tors + 6*NWORDS_FIELD, (S3->Y)[0]); - fpcopy((digit_t*)B_gen_3_tors + 7*NWORDS_FIELD, (S3->Y)[1]); - - CompletePoint(P,R); - Tate3_proj(R3,R,gX[0],gZ[0]); - Tate3_proj(S3,R,gX[1],gZ[1]); - FinalExpo3_2way(gX,gZ); - - // Do small DLog with respect to g_R3_S3 - fp2correction(gX[0]); - fp2correction(gX[1]); - if (memcmp(gX[0][1], zero, (size_t)nbytes) == 0) // = 1 - alpha = 0; - else if (memcmp(gX[0][1], (digit_t*)g_R_S_im, (size_t)nbytes) == 0) // = g_R3_S3 - alpha = 1; - else // = g_R3_S3^2 - alpha = 2; - - if (memcmp(gX[1][1], zero, (size_t)nbytes) == 0) // = 1 - beta = 0; - else if (memcmp(gX[1][1], (digit_t*)g_R_S_im, (size_t)nbytes) == 0) // = g_R3_S3 - beta = 1; - else // = g_R3_S3^2 - beta = 2; - - if (alpha == 0 && beta == 0) // Not full order - return false; - - // Return the 3-torsion point that R lies above - if (alpha == 0) // Lies above R3 - *ind = 0; - else if (beta == 0) // Lies above S3 - *ind = 1; - else if (alpha + beta == 3) // Lies above R3+S3 - *ind = 3; - else // Lies above R3-S3 - *ind = 2; - - return true; -} - - -static bool SecondPoint_dual(const point_proj_t P, point_full_proj_t R, unsigned char ind) -{ - point_full_proj_t RS3; - f2elm_t gX, gZ; - felm_t zero = {0}; - unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); - - // Pair with 3-torsion point determined by first point - fpcopy((digit_t*)B_gen_3_tors + (4*ind + 0)*NWORDS_FIELD, (RS3->X)[0]); - fpcopy((digit_t*)B_gen_3_tors + (4*ind + 1)*NWORDS_FIELD, (RS3->X)[1]); - fpcopy((digit_t*)B_gen_3_tors + (4*ind + 2)*NWORDS_FIELD, (RS3->Y)[0]); - fpcopy((digit_t*)B_gen_3_tors + (4*ind + 3)*NWORDS_FIELD, (RS3->Y)[1]); - - CompletePoint(P, R); - Tate3_proj(RS3, R, gX, gZ); - FinalExpo3(gX, gZ); - - fp2correction(gX); - if (memcmp(gX[1], zero, (size_t)nbytes) != 0) // Not equal to 1 - return true; - else - return false; -} - - -static void FirstPoint3n(const f2elm_t a24, const f2elm_t As[][5], f2elm_t x, point_full_proj_t R, unsigned int *r, unsigned char *ind, unsigned char *bitEll) -{ - bool b = false; - point_proj_t P; - felm_t zero = {0}; - *r = 0; - - while (!b) { - *bitEll = 0; - Elligator2(a24, *r, x, bitEll, COMPRESSION); // Get x-coordinate on curve a24 - - fp2copy(x, P->X); - fpcopy((digit_t*)&Montgomery_one, (P->Z)[0]); - fpcopy(zero, (P->Z)[1]); - eval_full_dual_4_isog(As, P); // Move x over to A = 0 - - b = FirstPoint_dual(P, R, ind); // Compute DLog with 3-torsion points - *r = *r + 1; - } -} - - -static void SecondPoint3n(const f2elm_t a24, const f2elm_t As[][5], f2elm_t x, point_full_proj_t R, unsigned int *r, unsigned char ind, unsigned char *bitEll) -{ - bool b = false; - point_proj_t P; - felm_t zero = {0}; - - while (!b) { - *bitEll = 0; - Elligator2(a24, *r, x, bitEll, COMPRESSION); - - fp2copy(x, P->X); - fpcopy((digit_t*)&Montgomery_one, (P->Z)[0]); - fpcopy(zero, (P->Z)[1]); - eval_full_dual_4_isog(As, P); // Move x over to A = 0 - - b = SecondPoint_dual(P, R, ind); - *r = *r + 1; - } -} - - -static void makeDiff(const point_full_proj_t R, point_full_proj_t S, const point_proj_t D) -{ - f2elm_t t0, t1, t2; - unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); - - fp2sub(R->X, S->X, t0); - fp2sub(R->Y, S->Y, t1); - fp2sqr_mont(t0, t0); - fp2sqr_mont(t1, t1); - fp2add(R->X, S->X, t2); - fp2mul_mont(t0, t2, t2); - fp2sub(t1, t2, t1); - fp2mul_mont(D->Z, t1, t1); - fp2mul_mont(D->X, t0, t0); - fp2correction(t0); - fp2correction(t1); - if (memcmp(t0[0], t1[0], (size_t)nbytes) == 0 && memcmp(t0[1], t1[1], (size_t)nbytes) == 0) - fp2neg(S->Y); -} - - -static void BuildOrdinary3nBasis_dual(const f2elm_t a24, const f2elm_t As[][5], point_full_proj_t *R, unsigned int *r, unsigned int *bitsEll) -{ - point_proj_t D; - f2elm_t xs[2]; - unsigned char ind, bit; - - FirstPoint3n(a24, As, xs[0], R[0], r, &ind, &bit); - *bitsEll = (unsigned int)bit; - *(r+1) = *r; - SecondPoint3n(a24, As, xs[1], R[1], r+1, ind, &bit); - *bitsEll |= ((unsigned int)bit << 1); - - // Get x-coordinate of difference - BiQuad_affine(a24, xs[0], xs[1], D); - eval_full_dual_4_isog(As, D); // Move x over to A = 0 - makeDiff(R[0], R[1], D); -} - - static void FullIsogeny_A_dual(unsigned char* PrivateKeyA, f2elm_t As[][5], f2elm_t a24, unsigned int sike) { // Input: a private key PrivateKeyA in the range [0, 2^eA - 1]. @@ -604,21 +137,6 @@ static void Dlogs3_dual(const f2elm_t *f, int *D, digit_t *d0, digit_t *c0, digi } -static void BuildOrdinary3nBasis_Decomp_dual(const f2elm_t A24, point_proj_t *Rs, unsigned char *r, const unsigned char bitsEll) -{ - unsigned char bitEll[2]; - - bitEll[0] = bitsEll & 0x1; - bitEll[1] = (bitsEll >> 1) & 0x1; - - // Elligator2 both x-coordinates - Elligator2(A24, (unsigned int)r[0]-1, Rs[0]->X, &bitEll[0], DECOMPRESSION); - Elligator2(A24, (unsigned int)r[1]-1, Rs[1]->X, &bitEll[1], DECOMPRESSION); - // Get x-coordinate of difference - BiQuad_affine(A24, Rs[0]->X, Rs[1]->X, Rs[2]); -} - - static void PKADecompression_dual(const unsigned char* SecretKeyB, const unsigned char* CompressedPKA, point_proj_t R, f2elm_t A) { unsigned char bit, rs[3]; @@ -820,120 +338,6 @@ int EphemeralSecretAgreement_B(const unsigned char* PrivateKeyB, const unsigned } -static void BuildEntangledXonly(const f2elm_t A, point_proj_t *R, unsigned char *qnr, unsigned char *ind) -{ - felm_t s; - f2elm_t *t_ptr, r, t; - - // Select the correct table - if (is_sqr_fp2(A, s)) { - t_ptr = (f2elm_t *)table_v_qnr; - *qnr = 1; - } else { - t_ptr = (f2elm_t *)table_v_qr; - *qnr = 0; - } - - // Get x0 - *ind = 0; - do { - fp2mul_mont(A, (felm_t *)*t_ptr++, R[0]->X); // R[0]->X = A*v - fp2neg(R[0]->X); // R[0]->X = -A*v - fp2add(R[0]->X, A, t); - fp2mul_mont(R[0]->X, t, t); - fpadd(t[0], (digit_t*)Montgomery_one, t[0]); - fp2mul_mont(R[0]->X, t, t); // t = R[0]->X^3 + A*R[0]->X^2 + R[0]->X - *ind += 1; - } while (!is_sqr_fp2(t, s)); - *ind -= 1; - - if (*qnr) - fpcopy((digit_t*)table_r_qnr[*ind], r[0]); - else - fpcopy((digit_t*)table_r_qr[*ind], r[0]); - - // Get x1 - fp2add(R[0]->X, A, R[1]->X); - fp2neg(R[1]->X); // R[1]->X = -R[0]->X-A - - // Get difference x2, z2 - fp2sub(R[0]->X, R[1]->X, R[2]->Z); - fp2sqr_mont(R[2]->Z, R[2]->Z); - - fpcopy(r[0], r[1]); // (1+i)*ind - fpadd((digit_t*)Montgomery_one, r[0], r[0]); - fp2sqr_mont(r, r); - fp2mul_mont(t, r, R[2]->X); -} - - -static void RecoverY(const f2elm_t A, const point_proj_t *xs, point_full_proj_t *Rs) -{ - f2elm_t t0, t1, t2, t3, t4; - - fp2mul_mont(xs[2]->X, xs[1]->Z, t0); - fp2mul_mont(xs[1]->X, xs[2]->Z, t1); - fp2mul_mont(xs[1]->X, xs[2]->X, t2); - fp2mul_mont(xs[1]->Z, xs[2]->Z, t3); - fp2sqr_mont(xs[1]->X, t4); - fp2sqr_mont(xs[1]->Z, Rs[1]->X); - fp2sub(t2, t3, Rs[1]->Y); - fp2mul_mont(xs[1]->X, Rs[1]->Y, Rs[1]->Y); - fp2add(t4, Rs[1]->X, t4); - fp2mul_mont(xs[2]->Z, t4, t4); - fp2mul_mont(A, t1, Rs[1]->X); - fp2sub(t0, t1, Rs[1]->Z); - - fp2mul_mont(Rs[0]->X, Rs[1]->Z, t0); - fp2add(t2, Rs[1]->X, t1); - fp2add(t1, t1, t1); - fp2sub(t0, t1, t0); - fp2mul_mont(xs[1]->Z, t0, t0); - fp2sub(t0, t4, t0); - fp2mul_mont(Rs[0]->X, t0, t0); - fp2add(t0, Rs[1]->Y, Rs[1]->Y); - fp2mul_mont(Rs[0]->Y, t3, t0); - fp2mul_mont(xs[1]->X, t0, Rs[1]->X); - fp2add(Rs[1]->X, Rs[1]->X, Rs[1]->X); - fp2mul_mont(xs[1]->Z, t0, Rs[1]->Z); - fp2add(Rs[1]->Z, Rs[1]->Z, Rs[1]->Z); - - fp2inv_mont_bingcd(Rs[1]->Z); - fp2mul_mont(Rs[1]->X, Rs[1]->Z, Rs[1]->X); - fp2mul_mont(Rs[1]->Y, Rs[1]->Z, Rs[1]->Y); -} - - -static void BuildOrdinary2nBasis_dual(const f2elm_t A, const f2elm_t Ds[][2], point_full_proj_t *Rs, unsigned char *qnr, unsigned char *ind) -{ - unsigned int i; - felm_t t0; - f2elm_t A6 = {0}; - point_proj_t xs[3] = {0}; - - // Generate x-only entangled basis - BuildEntangledXonly(A, xs, qnr, ind); - fpcopy((digit_t*)Montgomery_one, (xs[0]->Z)[0]); - fpcopy((digit_t*)Montgomery_one, (xs[1]->Z)[0]); - - // Move them back to A = 6 - for(i = 0; i < MAX_Bob; i++) { - eval_3_isog(xs[0], Ds[MAX_Bob-1-i]); - eval_3_isog(xs[1], Ds[MAX_Bob-1-i]); - eval_3_isog(xs[2], Ds[MAX_Bob-1-i]); - } - - // Recover y-coordinates with a single sqrt on A = 6 - fpcopy((digit_t*)Montgomery_one, A6[0]); - fpadd(A6[0], A6[0], t0); - fpadd(t0, t0, A6[0]); - fpadd(A6[0], t0, A6[0]); // A6 = 6 - - CompleteMPoint(A6, xs[0], Rs[0]); - RecoverY(A6, xs, Rs); -} - - static void FullIsogeny_B_dual(const unsigned char* PrivateKeyB, f2elm_t Ds[][2], f2elm_t A) { // Bob's ephemeral public key generation // Input: a private key PrivateKeyB in the range [0, 2^Floor(Log(2,oB)) - 1]. @@ -1008,46 +412,6 @@ static void Dlogs2_dual(const f2elm_t *f, int *D, digit_t *d0, digit_t *c0, digi } -static void BuildEntangledXonly_Decomp(const f2elm_t A, point_proj_t *R, unsigned char qnr, unsigned char ind) -{ - f2elm_t *t_ptr, r, t; - - // Select the correct table - if ( qnr == 1 ) - t_ptr = (f2elm_t *)table_v_qnr; - else - t_ptr = (f2elm_t *)table_v_qr; - - if (ind >= TABLE_V_LEN/2) - ind = 0; - // Get x0 - fp2mul_mont(A, t_ptr[ind], R[0]->X); // x1 = A*v - fp2neg(R[0]->X); // R[0]->X = -A*v - fp2add(R[0]->X, A, t); - fp2mul_mont(R[0]->X, t, t); - fpadd(t[0], (digit_t*)Montgomery_one, t[0]); - fp2mul_mont(R[0]->X, t, t); // t = R[0]->X^3 + A*R[0]->X^2 + R[0]->X - - if (qnr == 1) - fpcopy((digit_t*)table_r_qnr[ind], r[0]); - else - fpcopy((digit_t*)table_r_qr[ind], r[0]); - - // Get x1 - fp2add(R[0]->X, A, R[1]->X); - fp2neg(R[1]->X); // R[1]->X = -R[0]->X-A - - // Get difference x2,z2 - fp2sub(R[0]->X, R[1]->X, R[2]->Z); - fp2sqr_mont(R[2]->Z, R[2]->Z); - - fpcopy(r[0],r[1]); // (1+i)*ind - fpadd((digit_t*)Montgomery_one, r[0], r[0]); - fp2sqr_mont(r, r); - fp2mul_mont(t, r, R[2]->X); -} - - static void PKBDecompression_extended(const unsigned char* SecretKeyA, const unsigned char* CompressedPKB, point_proj_t R, f2elm_t A, unsigned char* tphiBKA_t) { // Bob's PK decompression -- SIKE protocol uint64_t mask = (digit_t)(-1); @@ -1377,20 +741,19 @@ int8_t validate_ciphertext(const unsigned char* ephemeralsk_, const unsigned cha { // If ct validation passes returns 0, otherwise returns -1. point_proj_t phis[3] = {0}, R, S, pts[MAX_INT_POINTS_BOB]; f2elm_t XPB, XQB, XRB, coeff[3], A24plus = {0}, A24minus = {0}, A = {0}, comp1 = {0}, comp2 = {0}, one = {0}; + digit_t temp[NWORDS_ORDER] = {0}, sk[NWORDS_ORDER] = {0}; unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0; - digit_t temp[NWORDS_ORDER] = {0}; - digit_t sk[NWORDS_ORDER] = {0}; - + fpcopy((digit_t*)&Montgomery_one, one[0]); // Initialize basis points init_basis((digit_t*)B_gen, XPB, XQB, XRB); fp2_decode(xKA, phis[0]->X); - fpcopy((digit_t*)&Montgomery_one, phis[0]->Z[0]); // phi[0] <- PA + skA*QA + fpcopy(one[0], phis[0]->Z[0]); // phis[0] <- PA + skA*QA // Initialize constants: A24minus = A-2C, A24plus = A+2C, where A=6, C=1 - fpcopy((digit_t*)&Montgomery_one, A24plus[0]); + fpcopy(one[0], A24plus[0]); fp2add(A24plus, A24plus, A24plus); fp2add(A24plus, A24plus, A24minus); // A24minus = 4 fp2add(A24plus, A24minus, A); // A = 6 @@ -1432,7 +795,7 @@ int8_t validate_ciphertext(const unsigned char* ephemeralsk_, const unsigned cha fp2_decode(tphiBKA_t, S->X); fp2_decode(&tphiBKA_t[FP2_ENCODED_BYTES], S->Z); // Recover t*3^n*((a0+skA*a1)*S1 + (b0+skA*b1)*S2) decode_to_digits(&tphiBKA_t[2*FP2_ENCODED_BYTES], temp, ORDER_A_ENCODED_BYTES, NWORDS_ORDER); - Ladder(phis[0], temp, A, OALICE_BITS, R); // t*(phiP + skA*phiQ) + Ladder(phis[0], temp, A, OALICE_BITS, R); // R <- t*(phiP + skA*phiQ), t in {(a0+skA*a1)^-1, (b0+skA*b1)^-1} fp2mul_mont(R->X, S->Z, comp1); fp2mul_mont(R->Z, S->X, comp2); diff --git a/src/compression/torsion_basis.c b/src/compression/torsion_basis.c index 1225e19..af54ef8 100644 --- a/src/compression/torsion_basis.c +++ b/src/compression/torsion_basis.c @@ -5,404 +5,479 @@ *********************************************************************************************/ -void get_2_torsion_entangled_basis_compression(const f2elm_t A, point_t S1, point_t S2, unsigned char *bit, unsigned char *entry) -{ // Build an entangled basis for E[2^m]. - // At first glance this is similar to the Elligator 2 technique, but the field element u is a *square* here, not a non-square. - unsigned int i, index, isSqrA = 0; - felm_t r = {0}, s, z, alpha, twoalphainv, beta; - f2elm_t t, u, u0, one = {0}, *t_ptr; - felm_t *x1 = (felm_t*) S1->x, *y1 = (felm_t*) S1->y, *x2 = (felm_t*) S2->x, *y2 = (felm_t*) S2->y; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - copy_words((const digit_t *)u0_entang, u0[0], 2*NWORDS_FIELD); - copy_words((const digit_t *)u_entang, u[0], 2*NWORDS_FIELD); +#define COMPRESSION 0 +#define DECOMPRESSION 1 - // Select the correct table - if (is_sqr_fp2(A, s)) { - t_ptr = (f2elm_t *)table_v_qnr; - isSqrA = 1; - } else { - t_ptr = (f2elm_t *)table_v_qr; - } - *bit = (unsigned char)isSqrA; // This bit is transmitted along with the PK to speedup decompression - index = 0; - do { - fp2mul_mont(A, (felm_t *)*t_ptr++, x1); // x1 = A*v - fp2neg(x1); // x1 = -A*v - fp2add(x1, A, t); - fp2mul_mont(x1, t, t); - fpadd(t[0], one[0], t[0]); - fp2mul_mont(x1, t, t); // t = x1^3 + A*x1^2 + x1 = x1(x1(x1 + A) + 1) - index += 2; - } while (!is_sqr_fp2(t, s)); - *entry = ((unsigned char)index - 2)/2; // This table entry will also be transmitted along with the PubKey to speedup decompression - - if (isSqrA) - copy_words((const digit_t *)table_r_qnr[(index-2)/2], r, NWORDS_FIELD); - else - copy_words((const digit_t *)table_r_qr[(index-2)/2], r, NWORDS_FIELD); +static void Elligator2(const f2elm_t a24, const unsigned int r, f2elm_t x, unsigned char *bit, const unsigned char COMPorDEC) +{ // Generate an x-coordinate of a point on curve with (affine) coefficient a24 + // Use the counter r + int i; + felm_t one_fp, a2, b2, N, temp0, temp1; + f2elm_t A, y2, *t_ptr; + + fpcopy((digit_t*)&Montgomery_one, one_fp); + fp2add(a24, a24, A); + fpsub(A[0], one_fp, A[0]); + fp2add(A, A, A); // A = 4*a24-2 + + // Elligator computation + t_ptr = (f2elm_t *)&v_3_torsion[r]; + fp2mul_mont(A, (felm_t*)t_ptr, x); // x = A*v; v := 1/(1 + U*r^2) table lookup + fp2neg(x); // x = -A*v; - // Finish sqrt computation for y1 = sqrt(x1^3+A*x1^2+x1) - fpadd(t[0],s,z); - fpdiv2(z,z); - fpcopy(z,alpha); - for (i = 0; i < OALICE_BITS - 2; i++) { - fpsqr_mont(alpha, alpha); - } - for (i = 0; i < OBOB_EXPON; i++) { - fpsqr_mont(alpha, s); - fpmul_mont(alpha, s, alpha); // alpha = z^((p+1)/4) - } + if (COMPorDEC == COMPRESSION) { + fp2add(A, x, y2); // y2 = x + A + fp2mul_mont(y2, x, y2); // y2 = x*(x + A) + fpadd(y2[0], one_fp, y2[0]); // y2 = x(x + A) + 1 + fp2mul_mont(x, y2, y2); // y2 = x*(x^2 + Ax + 1); + fpsqr_mont(y2[0], a2); + fpsqr_mont(y2[1], b2); + fpadd(a2, b2, N); // N := norm(y2); - fpadd(alpha,alpha,twoalphainv); - fpinv_mont_bingcd(twoalphainv); - fpmul_mont(t[1],twoalphainv,beta); - fpsqr_mont(alpha, twoalphainv); - fpcorrection(twoalphainv); - fpcorrection(z); - if (memcmp(twoalphainv, z, NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { - fpcopy(alpha,y1[0]); - fpcopy(beta,y1[1]); + fpcopy(N, temp0); + for (i = 0; i < OALICE_BITS - 2; i++) { + fpsqr_mont(temp0, temp0); + } + for (i = 0; i < OBOB_EXPON; i++) { + fpsqr_mont(temp0, temp1); + fpmul_mont(temp0, temp1, temp0); + } + fpsqr_mont(temp0, temp1); // z = N^((p + 1) div 4); + fpcorrection(temp1); + fpcorrection(N); + if (memcmp(temp1, N, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + fp2neg(x); + fp2sub(x, A, x); // x = -x - A; + if (COMPorDEC == COMPRESSION) + *bit = 1; + } } else { - fpneg(beta); - fpcopy(beta,y1[0]); - fpneg(alpha); - fpcopy(alpha,y1[1]); - } - fp2add(x1, A, x2); - fp2neg(x2); // x2 = A*v - A - fp2mul_mont(u0,y1,y2); - fpmul_mont(r,y2[0],y2[0]); - fpmul_mont(r,y2[1],y2[1]); // y2 = u0*r*y1 + if (*bit) { + fp2neg(x); + fp2sub(x,A,x); // x = -x - A; + } + } } -void get_2_torsion_entangled_basis_decompression(const f2elm_t A, point_t S1, point_t S2, unsigned char isASqr, unsigned char entry) -{ // Build an entangled basis for E[2^m] during decompression using the the entry and table already computed during compression - unsigned int i; - felm_t r = {0}, s, z, alpha, twoalphainv, beta; - f2elm_t t, u, u0, one = {0}, *t_ptr; - felm_t *x1 = (felm_t*) S1->x, *y1 = (felm_t*) S1->y, *x2 = (felm_t*) S2->x, *y2 = (felm_t*) S2->y; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - - copy_words((const digit_t *)u0_entang, u0[0], 2*NWORDS_FIELD); - copy_words((const digit_t *)u_entang, u[0], 2*NWORDS_FIELD); - - // Select the table - t_ptr = isASqr ? (f2elm_t *)table_v_qnr : (f2elm_t *)table_v_qr; - - fp2mul_mont(A, t_ptr[entry], x1); // x1 = A*v - fp2neg(x1); // x1 = -A*v - fp2add(x1, A, t); - fp2mul_mont(x1, t, t); - fpadd(t[0], one[0], t[0]); - fp2mul_mont(x1, t, t); // t = x1^3 + A*x1^2 + x1 = x1(x1(x1 + A) + 1) - is_sqr_fp2(t, s); - - if (isASqr) - copy_words((const digit_t *)table_r_qnr[entry], r, NWORDS_FIELD); - else - copy_words((const digit_t *)table_r_qr[entry], r, NWORDS_FIELD); - - // Finish sqrt computation for y1 = sqrt(x1^3+A*x1^2+x1) - fpadd(t[0],s,z); - fpdiv2(z,z); - fpcopy(z,alpha); - for (i = 0; i < OALICE_BITS - 2; i++) { - fpsqr_mont(alpha, alpha); +static void TripleAndParabola_proj(const point_full_proj_t R, f2elm_t l1x, f2elm_t l1z) +{ + fp2sqr_mont(R->X, l1z); + fp2add(l1z, l1z, l1x); + fp2add(l1x, l1z, l1x); + fpadd(l1x[0], (digit_t*)&Montgomery_one, l1x[0]); + fp2add(R->Y, R->Y, l1z); +} + + +static void Tate3_proj(const point_full_proj_t P, const point_full_proj_t Q, f2elm_t gX, f2elm_t gZ) +{ + f2elm_t t0, l1x; + + TripleAndParabola_proj(P, l1x, gZ); + fp2sub(Q->X, P->X, gX); + fp2mul_mont(l1x, gX, gX); + fp2sub(P->Y, Q->Y, t0); + fp2mul_mont(gZ, t0, t0); + fp2add(gX, t0, gX); +} + + +static void FinalExpo3_2way(f2elm_t *gX, f2elm_t *gZ) +{ + unsigned int i, j; + f2elm_t f_[2], finv[2]; + + for(i = 0; i < 2; i++) { + fp2copy(gZ[i], f_[i]); + fpneg(f_[i][1]); // Conjugate + fp2mul_mont(gX[i], f_[i], f_[i]); } - for (i = 0; i < OBOB_EXPON; i++) { - fpsqr_mont(alpha, s); - fpmul_mont(alpha, s, alpha); // alpha = z^((p+1)/4) + mont_n_way_inv(f_,2,finv); + for(i = 0; i < 2; i++) { + fpneg(gX[i][1]); + fp2mul_mont(gX[i], gZ[i], gX[i]); + fp2mul_mont(gX[i], finv[i], gX[i]); + for(j = 0; j < OALICE_BITS; j++) + fp2sqr_mont(gX[i], gX[i]); + for(j = 0; j < OBOB_EXPON-1; j++) + cube_Fp2_cycl(gX[i], (digit_t*)&Montgomery_one); } +} + + +static void FinalExpo3(f2elm_t gX, f2elm_t gZ) +{ + unsigned int i; + f2elm_t f_; + + fp2copy(gZ, f_); + fpneg(f_[1]); + fp2mul_mont(gX, f_, f_); + fp2inv_mont_bingcd(f_); + fpneg(gX[1]); + fp2mul_mont(gX,gZ, gX); + fp2mul_mont(gX,f_, gX); + for(i = 0; i < OALICE_BITS; i++) + fp2sqr_mont(gX, gX); + for(i = 0; i < OBOB_EXPON-1; i++) + cube_Fp2_cycl(gX, (digit_t*)Montgomery_one); +} + + +static void make_positive(f2elm_t x) +{ + unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); + felm_t zero = {0}; - fpadd(alpha,alpha,twoalphainv); - fpinv_mont_bingcd(twoalphainv); - fpmul_mont(t[1],twoalphainv,beta); - fpsqr_mont(alpha, twoalphainv); - fpcorrection(twoalphainv); - fpcorrection(z); - if (memcmp((unsigned char*)twoalphainv, (unsigned char*)z, NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { - fpcopy(alpha,y1[0]); - fpcopy(beta,y1[1]); + from_fp2mont(x, x); + if (memcmp(x[0], zero, (size_t)nbytes) != 0) { + if ((x[0][0] & 1) == 1) + fp2neg(x); } else { - fpneg(beta); - fpcopy(beta,y1[0]); - fpneg(alpha); - fpcopy(alpha,y1[1]); + if ((x[1][0] & 1) == 1) + fp2neg(x); } - fp2add(x1, A, x2); - fp2neg(x2); // x2 = A*v - A - fp2mul_mont(u0,y1,y2); - fpmul_mont(r,y2[0],y2[0]); - fpmul_mont(r,y2[1],y2[1]); // y2 = u0*r*y1 + to_fp2mont(x, x); } -void sqrtinv2(const f2elm_t v, const f2elm_t z, f2elm_t s, f2elm_t invz) -{ // Compute the square root of a field element v in F_{p^2} and invert a field element z. - int j; - felm_t az, bz, av, bv, Nz, Nv, av2, bv2, r, t, x, y, kk; - f2elm_t conjz, zero = {0}; - - fpsqr_mont(z[0],az); - fpsqr_mont(z[1],bz); - fpadd(az,bz,Nz); - fpcopy(v[0],av); - fpcopy(v[1],bv); - - if (memcmp(bv,zero[0],NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { - fpsqr_mont(av,av2); - fpsqr_mont(bv,bv2); - fpadd(av2,bv2,Nv); - - fpcopy(Nv,r); - for (j = 0; j < OALICE_BITS - 2; j++) - fpsqr_mont(r,r); - for (j = 0; j < OBOB_EXPON; j++) { - fpsqr_mont(r,t); - fpmul_mont(r,t,r); - } - fpsqr_mont(r,t); - fpcorrection(t); - fpcorrection(Nv); - if (memcmp(t,Nv,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { - mp_add(av,r,r,NWORDS_FIELD); - - if ((r[0] & 0x01) != 0) - mp_add(r,(digit_t*)&PRIME,r,NWORDS_FIELD); - - mp_shiftr1(r,NWORDS_FIELD); - - fpcopy(r,x); - for (j = 0; j < OALICE_BITS - 2; j++) - fpsqr_mont(x,x); - for (j = 0; j < OBOB_EXPON; j++) { - fpsqr_mont(x,t); - fpmul_mont(x,t,x); - } - - if (memcmp(Nz,zero[0],NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { - fpmul_mont(x,Nz,t); - fpadd(t,t,t); - fpinv_mont_bingcd(t); - fpcopy(t,kk); - fpmul_mont(bv,Nz,y); - fpmul_mont(y,kk,y); - - fpsqr_mont(x,t); - fpcorrection(t); - fpcorrection(r); - if (memcmp(t,r,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { - fpcopy(x,s[0]); - fpcopy(y,s[1]); - } else { - fpcopy(y,s[0]); - fpcopy(x,s[1]); - } - fp2_conj(z,conjz); - fpmul_mont(x,kk,t); - fpadd(t,t,t); - fpmul_mont(t,conjz[0],invz[0]); - fpmul_mont(t,conjz[1],invz[1]); - } else { - fpadd(x,x,t); - fpinv_mont_bingcd(t); - fpmul_mont(bv,t,y); - fpsqr_mont(x,t); - if (memcmp(t,r,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { - fpcopy(x,s[0]); - fpcopy(y,s[1]); - } else { - fpcopy(y,s[0]); - fpcopy(x,s[1]); - } - fp2copy(zero,invz); - } - - } else { - fp2copy(zero,s); - if (memcmp(Nz,zero[0],NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { - fpinv_mont_bingcd(Nz); - fp2_conj(z,conjz); - fpmul_mont(Nz,conjz[0],invz[0]); - fpmul_mont(Nz,conjz[1],invz[1]); - } else { - fp2copy(zero,invz); - } - } - } else { - fpcopy(av,r); - for (j = 0; j < OALICE_BITS - 2; j++) - fpsqr_mont(r,r); - for (j = 0; j < OBOB_EXPON; j++) { - fpsqr_mont(r,t); - fpmul_mont(r,t,r); - } - fpsqr_mont(r,t); - if (memcmp(t,av,NBITS_TO_NBYTES(NBITS_FIELD)) == 0) { - fpcopy(r,s[0]); - fpcopy(zero[0],s[1]); - } else { - fpcopy(zero[0],s[0]); - fpcopy(r,s[1]); - } +static bool FirstPoint_dual(const point_proj_t P, point_full_proj_t R, unsigned char *ind) +{ + point_full_proj_t R3,S3; + f2elm_t gX[2],gZ[2]; + felm_t zero = {0}; + unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); + unsigned char alpha,beta; - if (memcmp(Nz,zero[0],NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { - fp2_conj(z,conjz); - fpinv_mont_bingcd(Nz); - fpmul_mont(Nz,conjz[0],invz[0]); - fpmul_mont(Nz,conjz[1],invz[1]); - } else { - fp2copy(zero,invz); - } - } + fpcopy((digit_t*)B_gen_3_tors + 0*NWORDS_FIELD, (R3->X)[0]); + fpcopy((digit_t*)B_gen_3_tors + 1*NWORDS_FIELD, (R3->X)[1]); + fpcopy((digit_t*)B_gen_3_tors + 2*NWORDS_FIELD, (R3->Y)[0]); + fpcopy((digit_t*)B_gen_3_tors + 3*NWORDS_FIELD, (R3->Y)[1]); + fpcopy((digit_t*)B_gen_3_tors + 4*NWORDS_FIELD, (S3->X)[0]); + fpcopy((digit_t*)B_gen_3_tors + 5*NWORDS_FIELD, (S3->X)[1]); + fpcopy((digit_t*)B_gen_3_tors + 6*NWORDS_FIELD, (S3->Y)[0]); + fpcopy((digit_t*)B_gen_3_tors + 7*NWORDS_FIELD, (S3->Y)[1]); + + CompletePoint(P,R); + Tate3_proj(R3,R,gX[0],gZ[0]); + Tate3_proj(S3,R,gX[1],gZ[1]); + FinalExpo3_2way(gX,gZ); + + // Do small DLog with respect to g_R3_S3 + fp2correction(gX[0]); + fp2correction(gX[1]); + if (memcmp(gX[0][1], zero, (size_t)nbytes) == 0) // = 1 + alpha = 0; + else if (memcmp(gX[0][1], g_R_S_im, (size_t)nbytes) == 0) // = g_R3_S3 + alpha = 1; + else // = g_R3_S3^2 + alpha = 2; + + if (memcmp(gX[1][1], zero, (size_t)nbytes) == 0) // = 1 + beta = 0; + else if (memcmp(gX[1][1], g_R_S_im, (size_t)nbytes) == 0) // = g_R3_S3 + beta = 1; + else // = g_R3_S3^2 + beta = 2; + + if (alpha == 0 && beta == 0) // Not full order + return false; + + // Return the 3-torsion point that R lies above + if (alpha == 0) // Lies above R3 + *ind = 0; + else if (beta == 0) // Lies above S3 + *ind = 1; + else if (alpha + beta == 3) // Lies above R3+S3 + *ind = 3; + else // Lies above R3-S3 + *ind = 2; + + return true; } -void BasePoint3n(f2elm_t A, unsigned int *r, point_proj_t P, point_proj_t Q) -{ // xz-only construction of a point of order 3^n in the Montgomery curve y^2 = x^3 + A*x^2 + x from base counter r. - // This is essentially the Elligator 2 technique coupled with cofactor multiplication and LI checking. - int i; - felm_t a2, b2, N, temp0, temp1; - f2elm_t A2, A24, two = {0}, x, y2, one_fp2 = {0}, *t_ptr; - point_proj_t S; - - fpcopy((digit_t*)&Montgomery_one, one_fp2[0]); - fp2div2(A,A2); - fpcopy(one_fp2[0],two[0]); - fpadd(two[0], two[0], two[0]); - fp2add(A,two,A24); - fp2div2(A24,A24); - fp2div2(A24,A24); - - t_ptr = (f2elm_t *)&v_3_torsion[*r]; - do { - *r += 1; - fp2mul_mont(A,(felm_t*)t_ptr++,x); // x = A*v; v := 1/(1 + U*r^2) table lookup - fp2neg(x); // x = -A*v; - fp2add(A,x,y2); // y2 = x + A - fp2mul_mont(y2, x, y2); // y2 = x*(x + A) - fpadd(y2[0], one_fp2[0], y2[0]); // y2 = x(x + A) + 1 - fp2mul_mont(x,y2,y2); // y2 = x*(x^2 + Ax + 1); - fpsqr_mont(y2[0],a2); - fpsqr_mont(y2[1],b2); - fpadd(a2,b2,N); // N := norm(y2); - - fpcopy(N,temp0); - for (i = 0; i < OALICE_BITS - 2; i++) { - fpsqr_mont(temp0, temp0); - } - for (i = 0; i < OBOB_EXPON; i++) { - fpsqr_mont(temp0, temp1); - fpmul_mont(temp0, temp1, temp0); - } - fpsqr_mont(temp0,temp1); // z = N^((p + 1) div 4); - fpcorrection(temp1); - fpcorrection(N); - if (memcmp(temp1,N,NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { - fp2neg(x); - fp2sub(x,A,x); // x = -x - A; - } - fp2copy(x,S->X); - fp2copy(one_fp2,S->Z); - Double(S,P,A24,OALICE_BITS); // x, z := Double(A24, x, 1, eA); - xTPLe_fast(P,Q,A2,OBOB_EXPON-1); // t, w := Triple(A_2, x, z, eB-1); - fp2correction(Q->X); - fp2correction(Q->Z); - } while (is_felm_zero(Q->Z[0]) && is_felm_zero(Q->Z[1])); +static bool SecondPoint_dual(const point_proj_t P, point_full_proj_t R, unsigned char ind) +{ + point_full_proj_t RS3; + f2elm_t gX, gZ; + felm_t zero = {0}; + unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); + + // Pair with 3-torsion point determined by first point + fpcopy((digit_t*)B_gen_3_tors + (4*ind + 0)*NWORDS_FIELD, (RS3->X)[0]); + fpcopy((digit_t*)B_gen_3_tors + (4*ind + 1)*NWORDS_FIELD, (RS3->X)[1]); + fpcopy((digit_t*)B_gen_3_tors + (4*ind + 2)*NWORDS_FIELD, (RS3->Y)[0]); + fpcopy((digit_t*)B_gen_3_tors + (4*ind + 3)*NWORDS_FIELD, (RS3->Y)[1]); + + CompletePoint(P, R); + Tate3_proj(RS3, R, gX, gZ); + FinalExpo3(gX, gZ); + + fp2correction(gX); + if (memcmp(gX[1], zero, (size_t)nbytes) != 0) // Not equal to 1 + return true; + else + return false; } -void BasePoint3n_decompression(f2elm_t A, const unsigned char r, point_proj_t P) -{ // Deterministic xz-only construction of a point of order 3^n in the Montgomery curve y^2 = x^3 + A*x^2 + x from counter r1. - // Notice that the Elligator 2 counter r was generated beforehand during key compression without linear independence testing - int i; - felm_t a2, b2, N, temp0, temp1; - f2elm_t A2, A24, two = {0}, x, y2, one_fp2 = {0}; - point_proj_t S; - - fpcopy((digit_t*)&Montgomery_one, one_fp2[0]); - fp2div2(A,A2); - fpcopy((digit_t*)&Montgomery_one,two[0]); - fpadd(two[0], two[0], two[0]); - fp2add(A,two,A24); - fp2div2(A24,A24); - fp2div2(A24,A24); - - if ( (r-1) < TABLE_V3_LEN) - fp2mul_mont(A, (felm_t*)&v_3_torsion[r-1], x); // x = A*v; - else // If the index r is out of range, just use a default (0) - fp2mul_mont(A, (felm_t*)&v_3_torsion[0], x); // x = A*v0; - fp2neg(x); // x = -A*v; - fp2add(x,A,y2); // y2 = x + A - fp2mul_mont(x,y2,y2); // y2 = x*(x + A) - fpadd(y2[0], one_fp2[0], y2[0]); // y2 = x(x + A) + 1 - fp2mul_mont(x, y2, y2); // y2 = x*(x^2 + A*x + 1); - fpsqr_mont(y2[0],a2); - fpsqr_mont(y2[1],b2); - fpadd(a2,b2,N); // N := Fp!norm(y2); - - fpcopy(N,temp0); - for (i = 0; i < OALICE_BITS - 2; i++) { - fpsqr_mont(temp0, temp0); - } - for (i = 0; i < OBOB_EXPON; i++) { - fpsqr_mont(temp0, temp1); - fpmul_mont(temp0, temp1, temp0); +static void FirstPoint3n(const f2elm_t a24, const f2elm_t As[][5], f2elm_t x, point_full_proj_t R, unsigned int *r, unsigned char *ind, unsigned char *bitEll) +{ + bool b = false; + point_proj_t P; + felm_t zero = {0}; + *r = 0; + + while (!b) { + *bitEll = 0; + Elligator2(a24, *r, x, bitEll, COMPRESSION); // Get x-coordinate on curve a24 + + fp2copy(x, P->X); + fpcopy((digit_t*)&Montgomery_one, (P->Z)[0]); + fpcopy(zero, (P->Z)[1]); + eval_full_dual_4_isog(As, P); // Move x over to A = 0 + + b = FirstPoint_dual(P, R, ind); // Compute DLog with 3-torsion points + *r = *r + 1; } - fpsqr_mont(temp0,temp1); // z = N^((p + 1) div 4); - fpcorrection(temp1); - fpcorrection(N); - if (memcmp(temp1,N,NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { - fp2neg(x); - fp2sub(x,A,x); // x = -x - A; +} + + +static void SecondPoint3n(const f2elm_t a24, const f2elm_t As[][5], f2elm_t x, point_full_proj_t R, unsigned int *r, unsigned char ind, unsigned char *bitEll) +{ + bool b = false; + point_proj_t P; + felm_t zero = {0}; + + while (!b) { + *bitEll = 0; + Elligator2(a24, *r, x, bitEll, COMPRESSION); + + fp2copy(x, P->X); + fpcopy((digit_t*)&Montgomery_one, (P->Z)[0]); + fpcopy(zero, (P->Z)[1]); + eval_full_dual_4_isog(As, P); // Move x over to A = 0 + + b = SecondPoint_dual(P, R, ind); + *r = *r + 1; } - fp2copy(x,S->X); - fp2copy(one_fp2,S->Z); - Double(S,P,A24,OALICE_BITS); // x, z := Double(A24, x, 1, eA); } -void BuildOrdinaryE3nBasis(f2elm_t A, point_full_proj_t R1, point_full_proj_t R2, unsigned int rs[2]) -{ // Generate a basis for the 3^eB torsion - unsigned int r = 0; - f2elm_t t2w1, t1w2; - point_proj_t P, Q, R, S; +static void makeDiff(const point_full_proj_t R, point_full_proj_t S, const point_proj_t D) +{ + f2elm_t t0, t1, t2; + unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD); + + fp2sub(R->X, S->X, t0); + fp2sub(R->Y, S->Y, t1); + fp2sqr_mont(t0, t0); + fp2sqr_mont(t1, t1); + fp2add(R->X, S->X, t2); + fp2mul_mont(t0, t2, t2); + fp2sub(t1, t2, t1); + fp2mul_mont(D->Z, t1, t1); + fp2mul_mont(D->X, t0, t0); + fp2correction(t0); + fp2correction(t1); + if (memcmp(t0[0], t1[0], (size_t)nbytes) == 0 && memcmp(t0[1], t1[1], (size_t)nbytes) == 0) + fp2neg(S->Y); +} + + +static void BiQuad_affine(const f2elm_t a24, const f2elm_t x0, const f2elm_t x1, point_proj_t R) +{ + f2elm_t Ap2, aa, bb, cc, t0, t1; + + fp2add(a24, a24, Ap2); + fp2add(Ap2, Ap2, Ap2); // Ap2 = a+2 = 4*a24 + + fp2sub(x0, x1, aa); + fp2sqr_mont(aa, aa); + + fp2mul_mont(x0, x1, cc); + fpsub(cc[0], (digit_t*)Montgomery_one, cc[0]); + fp2sqr_mont(cc, cc); + + fpsub(x0[0], (digit_t*)Montgomery_one, bb[0]); + fpcopy(x0[1], bb[1]); + fp2sqr_mont(bb, bb); + fp2mul_mont(Ap2, x0, t0); + fp2add(bb, t0, bb); + fp2mul_mont(x1, bb, bb); + fpsub(x1[0], (digit_t*)Montgomery_one, t0[0]); + fpcopy(x1[1], t0[1]); + fp2sqr_mont(t0, t0); + fp2mul_mont(Ap2, x1, t1); + fp2add(t0, t1, t0); + fp2mul_mont(x0, t0, t0); + fp2add(bb, t0, bb); + fp2add(bb, bb, bb); + + fp2sqr_mont(bb, t0); + fp2mul_mont(aa, cc, t1); + fp2add(t1, t1, t1); + fp2add(t1, t1, t1); + fp2sub(t0, t1, t0); + sqrt_Fp2(t0, t0); + make_positive(t0); // Make the sqrt "positive" + fp2add(bb, t0, R->X); + fp2add(aa, aa, R->Z); +} + + +static void BuildOrdinary3nBasis_dual(const f2elm_t a24, const f2elm_t As[][5], point_full_proj_t *R, unsigned int *r, unsigned int *bitsEll) +{ + point_proj_t D; + f2elm_t xs[2]; + unsigned char ind, bit; + + FirstPoint3n(a24, As, xs[0], R[0], r, &ind, &bit); + *bitsEll = (unsigned int)bit; + *(r+1) = *r; + SecondPoint3n(a24, As, xs[1], R[1], r+1, ind, &bit); + *bitsEll |= ((unsigned int)bit << 1); + + // Get x-coordinate of difference + BiQuad_affine(a24, xs[0], xs[1], D); + eval_full_dual_4_isog(As, D); // Move x over to A = 0 + makeDiff(R[0], R[1], D); +} + + +static void BuildOrdinary3nBasis_Decomp_dual(const f2elm_t A24, point_proj_t *Rs, unsigned char *r, const unsigned char bitsEll) +{ + unsigned char bitEll[2]; - // 1st basis point: - BasePoint3n(A,&r,P,Q); - rs[0] = r; + bitEll[0] = bitsEll & 0x1; + bitEll[1] = (bitsEll >> 1) & 0x1; - // 2nd basis point: + // Elligator2 both x-coordinates + Elligator2(A24, (unsigned int)r[0]-1, Rs[0]->X, &bitEll[0], DECOMPRESSION); + Elligator2(A24, (unsigned int)r[1]-1, Rs[1]->X, &bitEll[1], DECOMPRESSION); + // Get x-coordinate of difference + BiQuad_affine(A24, Rs[0]->X, Rs[1]->X, Rs[2]); +} + + + +static void BuildEntangledXonly(const f2elm_t A, point_proj_t *R, unsigned char *qnr, unsigned char *ind) +{ + felm_t s; + f2elm_t *t_ptr, r, t; + + // Select the correct table + if (is_sqr_fp2(A, s)) { + t_ptr = (f2elm_t *)table_v_qnr; + *qnr = 1; + } else { + t_ptr = (f2elm_t *)table_v_qr; + *qnr = 0; + } + + // Get x0 + *ind = 0; do { - BasePoint3n(A,&r,R,S); - fp2mul_mont(S->X,Q->Z,t2w1); - fp2mul_mont(Q->X,S->Z,t1w2); - fp2correction(t2w1); - fp2correction(t1w2); - } while (memcmp(t2w1[0],t1w2[0],NBITS_TO_NBYTES(NBITS_FIELD)) == 0 && memcmp(t2w1[1],t1w2[1],NBITS_TO_NBYTES(NBITS_FIELD)) == 0); // Pr[t2/w2 == t1/w1] = 1/4: E[loop length] = 4/3 - rs[1] = r; - - // NB: ideally the following point completions could share one inversion at the cost of 3 products, but this is not implemented here. - CompleteMPoint(A,P,R1); - CompleteMPoint(A,R,R2); + fp2mul_mont(A, (felm_t *)*t_ptr++, R[0]->X); // R[0]->X = A*v + fp2neg(R[0]->X); // R[0]->X = -A*v + fp2add(R[0]->X, A, t); + fp2mul_mont(R[0]->X, t, t); + fpadd(t[0], (digit_t*)Montgomery_one, t[0]); + fp2mul_mont(R[0]->X, t, t); // t = R[0]->X^3 + A*R[0]->X^2 + R[0]->X + *ind += 1; + } while (!is_sqr_fp2(t, s)); + *ind -= 1; + + if (*qnr) + fpcopy((digit_t*)table_r_qnr[*ind], r[0]); + else + fpcopy((digit_t*)table_r_qr[*ind], r[0]); + + // Get x1 + fp2add(R[0]->X, A, R[1]->X); + fp2neg(R[1]->X); // R[1]->X = -R[0]->X-A + + // Get difference x2, z2 + fp2sub(R[0]->X, R[1]->X, R[2]->Z); + fp2sqr_mont(R[2]->Z, R[2]->Z); + + fpcopy(r[0], r[1]); // (1+i)*ind + fpadd((digit_t*)Montgomery_one, r[0], r[0]); + fp2sqr_mont(r, r); + fp2mul_mont(t, r, R[2]->X); } -void BuildOrdinaryE3nBasis_decompression(f2elm_t A, point_full_proj_t R1, point_full_proj_t R2, const unsigned char r1, const unsigned char r2) -{ // Generate a basis for the 3^eB torsion using shared information - point_proj_t P, R; - - // 1st basis point: - BasePoint3n_decompression(A,r1,P); - // 2nd basis point: - BasePoint3n_decompression(A,r2,R); + +static void BuildOrdinary2nBasis_dual(const f2elm_t A, const f2elm_t Ds[][2], point_full_proj_t *Rs, unsigned char *qnr, unsigned char *ind) +{ + unsigned int i; + felm_t t0; + f2elm_t A6 = {0}; + point_proj_t xs[3] = {0}; + + // Generate x-only entangled basis + BuildEntangledXonly(A, xs, qnr, ind); + fpcopy((digit_t*)Montgomery_one, (xs[0]->Z)[0]); + fpcopy((digit_t*)Montgomery_one, (xs[1]->Z)[0]); + + // Move them back to A = 6 + for(i = 0; i < MAX_Bob; i++) { + eval_3_isog(xs[0], Ds[MAX_Bob-1-i]); + eval_3_isog(xs[1], Ds[MAX_Bob-1-i]); + eval_3_isog(xs[2], Ds[MAX_Bob-1-i]); + } + + // Recover y-coordinates with a single sqrt on A = 6 + fpcopy((digit_t*)Montgomery_one, A6[0]); + fpadd(A6[0], A6[0], t0); + fpadd(t0, t0, A6[0]); + fpadd(A6[0], t0, A6[0]); + + CompleteMPoint(A6, xs[0], Rs[0]); + RecoverY(A6, xs, Rs); +} + + + +static void BuildEntangledXonly_Decomp(const f2elm_t A, point_proj_t *R, unsigned char qnr, unsigned char ind) +{ + f2elm_t *t_ptr, r, t; - // NB: ideally the following point completions could share one inversion at the cost of 3 products, but this is not implemented here. - CompleteMPoint(A,P,R1); - CompleteMPoint(A,R,R2); + // Select the correct table + if ( qnr == 1 ) + t_ptr = (f2elm_t *)table_v_qnr; + else + t_ptr = (f2elm_t *)table_v_qr; + + if (ind >= TABLE_V_LEN/2) + ind = 0; + // Get x0 + fp2mul_mont(A, t_ptr[ind], R[0]->X); // x1 = A*v + fp2neg(R[0]->X); // R[0]->X = -A*v + fp2add(R[0]->X, A, t); + fp2mul_mont(R[0]->X, t, t); + fpadd(t[0], (digit_t*)Montgomery_one, t[0]); + fp2mul_mont(R[0]->X, t, t); // t = R[0]->X^3 + A*R[0]->X^2 + R[0]->X + + if (qnr == 1) + fpcopy((digit_t*)table_r_qnr[ind], r[0]); + else + fpcopy((digit_t*)table_r_qr[ind], r[0]); + + // Get x1 + fp2add(R[0]->X, A, R[1]->X); + fp2neg(R[1]->X); // R[1]->X = -R[0]->X-A + + // Get difference x2,z2 + fp2sub(R[0]->X, R[1]->X, R[2]->Z); + fp2sqr_mont(R[2]->Z, R[2]->Z); + + fpcopy(r[0],r[1]); // (1+i)*ind + fpadd((digit_t*)Montgomery_one, r[0], r[0]); + fp2sqr_mont(r, r); + fp2mul_mont(t, r, R[2]->X); } - diff --git a/src/ec_isogeny.c b/src/ec_isogeny.c index e0f23a5..42ecd66 100644 --- a/src/ec_isogeny.c +++ b/src/ec_isogeny.c @@ -267,33 +267,36 @@ void j_inv(const f2elm_t A, const f2elm_t C, f2elm_t jinv) } -void xDBLADD(point_proj_t P, point_proj_t Q, const f2elm_t xPQ, const f2elm_t A24) +void xDBLADD(point_proj_t P, point_proj_t Q, const f2elm_t XPQ, const f2elm_t ZPQ, const f2elm_t A24) { // Simultaneous doubling and differential addition. // Input: projective Montgomery points P=(XP:ZP) and Q=(XQ:ZQ) such that xP=XP/ZP and xQ=XQ/ZQ, affine difference xPQ=x(P-Q) and Montgomery curve constant A24=(A+2)/4. // Output: projective Montgomery points P <- 2*P = (X2P:Z2P) such that x(2P)=X2P/Z2P, and Q <- P+Q = (XQP:ZQP) such that = x(Q+P)=XQP/ZQP. f2elm_t t0, t1, t2; - mp2_add(P->X, P->Z, t0); // t0 = XP+ZP - mp2_sub_p2(P->X, P->Z, t1); // t1 = XP-ZP - fp2sqr_mont(t0, P->X); // XP = (XP+ZP)^2 - mp2_sub_p2(Q->X, Q->Z, t2); // t2 = XQ-ZQ - mp2_add(Q->X, Q->Z, Q->X); // XQ = XQ+ZQ - fp2mul_mont(t0, t2, t0); // t0 = (XP+ZP)*(XQ-ZQ) - fp2sqr_mont(t1, P->Z); // ZP = (XP-ZP)^2 - fp2mul_mont(t1, Q->X, t1); // t1 = (XP-ZP)*(XQ+ZQ) - mp2_sub_p2(P->X, P->Z, t2); // t2 = (XP+ZP)^2-(XP-ZP)^2 - fp2mul_mont(P->X, P->Z, P->X); // XP = (XP+ZP)^2*(XP-ZP)^2 - fp2mul_mont(A24, t2, Q->X); // XQ = A24*[(XP+ZP)^2-(XP-ZP)^2] - mp2_sub_p2(t0, t1, Q->Z); // ZQ = (XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ) - mp2_add(Q->X, P->Z, P->Z); // ZP = A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2 - mp2_add(t0, t1, Q->X); // XQ = (XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ) - fp2mul_mont(P->Z, t2, P->Z); // ZP = [A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2]*[(XP+ZP)^2-(XP-ZP)^2] - fp2sqr_mont(Q->Z, Q->Z); // ZQ = [(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2 - fp2sqr_mont(Q->X, Q->X); // XQ = [(XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)]^2 - fp2mul_mont(Q->Z, xPQ, Q->Z); // ZQ = xPQ*[(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2 + fp2add(P->X, P->Z, t0); // t0 = XP+ZP + fp2sub(P->X, P->Z, t1); // t1 = XP-ZP + fp2sqr_mont(t0, P->X); // XP = (XP+ZP)^2 + fp2sub(Q->X, Q->Z, t2); // t2 = XQ-ZQ + fp2correction(t2); + fp2add(Q->X, Q->Z, Q->X); // XQ = XQ+ZQ + fp2mul_mont(t0, t2, t0); // t0 = (XP+ZP)*(XQ-ZQ) + fp2sqr_mont(t1, P->Z); // ZP = (XP-ZP)^2 + fp2mul_mont(t1, Q->X, t1); // t1 = (XP-ZP)*(XQ+ZQ) + fp2sub(P->X, P->Z, t2); // t2 = (XP+ZP)^2-(XP-ZP)^2 + fp2mul_mont(P->X, P->Z, P->X); // XP = (XP+ZP)^2*(XP-ZP)^2 + fp2mul_mont(t2, A24, Q->X); // XQ = A24*[(XP+ZP)^2-(XP-ZP)^2] + fp2sub(t0, t1, Q->Z); // ZQ = (XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ) + fp2add(Q->X, P->Z, P->Z); // ZP = A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2 + fp2add(t0, t1, Q->X); // XQ = (XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ) + fp2mul_mont(P->Z, t2, P->Z); // ZP = [A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2]*[(XP+ZP)^2-(XP-ZP)^2] + fp2sqr_mont(Q->Z, Q->Z); // ZQ = [(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2 + fp2sqr_mont(Q->X, Q->X); // XQ = [(XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)]^2 + fp2mul_mont(Q->X, ZPQ, Q->X); // XQ = ZPQ*[(XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)]^2 + fp2mul_mont(Q->Z, XPQ, Q->Z); // ZQ = XPQ*[(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2 } + static void swap_points(point_proj_t P, point_proj_t Q, const digit_t option) { // Swap points. // If option = 0 then P <- P and Q <- Q, else if option = 0xFF...FF then P <- Q and Q <- P @@ -354,8 +357,7 @@ static void LADDER3PT(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xPQ, con mask = 0 - (digit_t)swap; swap_points(R, R2, mask); - xDBLADD(R0, R2, R->X, A24); - fp2mul_mont(R2->X, R->Z, R2->X); + xDBLADD(R0, R2, R->X, R->Z, A24); } swap = 0 ^ prevbit; mask = 0 - (digit_t)swap; @@ -364,6 +366,44 @@ static void LADDER3PT(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xPQ, con #ifdef COMPRESS + +static void RecoverY(const f2elm_t A, const point_proj_t *xs, point_full_proj_t *Rs) +{ + f2elm_t t0, t1, t2, t3, t4; + + fp2mul_mont(xs[2]->X, xs[1]->Z, t0); + fp2mul_mont(xs[1]->X, xs[2]->Z, t1); + fp2mul_mont(xs[1]->X, xs[2]->X, t2); + fp2mul_mont(xs[1]->Z, xs[2]->Z, t3); + fp2sqr_mont(xs[1]->X, t4); + fp2sqr_mont(xs[1]->Z, Rs[1]->X); + fp2sub(t2, t3, Rs[1]->Y); + fp2mul_mont(xs[1]->X, Rs[1]->Y, Rs[1]->Y); + fp2add(t4, Rs[1]->X, t4); + fp2mul_mont(xs[2]->Z, t4, t4); + fp2mul_mont(A, t1, Rs[1]->X); + fp2sub(t0, t1, Rs[1]->Z); + + fp2mul_mont(Rs[0]->X, Rs[1]->Z, t0); + fp2add(t2, Rs[1]->X, t1); + fp2add(t1, t1, t1); + fp2sub(t0, t1, t0); + fp2mul_mont(xs[1]->Z, t0, t0); + fp2sub(t0, t4, t0); + fp2mul_mont(Rs[0]->X, t0, t0); + fp2add(t0, Rs[1]->Y, Rs[1]->Y); + fp2mul_mont(Rs[0]->Y, t3, t0); + fp2mul_mont(xs[1]->X, t0, Rs[1]->X); + fp2add(Rs[1]->X, Rs[1]->X, Rs[1]->X); + fp2mul_mont(xs[1]->Z, t0, Rs[1]->Z); + fp2add(Rs[1]->Z, Rs[1]->Z, Rs[1]->Z); + + fp2inv_mont_bingcd(Rs[1]->Z); + fp2mul_mont(Rs[1]->X, Rs[1]->Z, Rs[1]->X); + fp2mul_mont(Rs[1]->Y, Rs[1]->Z, Rs[1]->Y); +} + + static void CompletePoint(const point_proj_t P, point_full_proj_t R) { // Complete point on A = 0 curve f2elm_t xz, s2, r2, yz, invz, t0, t1, one = {0}; @@ -391,7 +431,7 @@ void CompleteMPoint(const f2elm_t A, point_proj_t P, point_full_proj_t R) f2elm_t zero = {0}, one = {0}, xz, yz, s2, r2, invz, temp0, temp1; fpcopy((digit_t*)&Montgomery_one, one[0]); - if (memcmp(P->Z[0], zero,NBITS_TO_NBYTES(NBITS_FIELD)) != 0 || memcmp(P->Z[1], zero, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { + if (memcmp(P->Z[0], zero, NBITS_TO_NBYTES(NBITS_FIELD)) != 0 || memcmp(P->Z[1], zero, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) { fp2mul_mont(P->X, P->Z, xz); // xz = x*z; fpsub(P->X[0], P->Z[1], temp0[0]); fpadd(P->X[1], P->Z[0], temp0[1]); @@ -482,136 +522,6 @@ void xTPLe_fast(point_proj_t P, point_proj_t Q, const f2elm_t A2, int e) } -void ADD(const point_full_proj_t P, const f2elm_t QX, const f2elm_t QY, const f2elm_t QZ, const f2elm_t A, point_full_proj_t R) -{ // General addition. - // Input: projective Montgomery points P=(XP:YP:ZP) and Q=(XQ:YQ:ZQ). - // Output: projective Montgomery point R <- P+Q = (XQP:YQP:ZQP). - f2elm_t t0 = {0}, t1 = {0}, t2 = {0}, t3 = {0}, t4 = {0}, t5 = {0}, t6 = {0}, t7 = {0}; - - fp2mul_mont(QX, P->Z, t0); // t0 = x2*Z1 - fp2mul_mont(P->X, QZ, t1); // t1 = X1*z2 - fp2add(t0, t1, t2); // t2 = t0 + t1 - fp2sub(t1, t0, t3); // t3 = t1 - t0 - fp2mul_mont(QX, P->X, t0); // t0 = x2*X1 - fp2mul_mont(P->Z, QZ, t1); // t1 = Z1*z2 - fp2add(t0, t1, t4); // t4 = t0 + t1 - fp2mul_mont(t0, A, t0); // t0 = t0*A - fp2mul_mont(QY, P->Y, t5); // t5 = y2*Y1 - fp2sub(t0, t5, t0); // t0 = t0 - t5 - fp2mul_mont(t0, t1, t0); // t0 = t0*t1 - fp2add(t0, t0, t0); // t0 = t0 + t0 - fp2mul_mont(t2, t4, t5); // t5 = t2*t4 - fp2add(t5, t0, t5); // t5 = t5 + t0 - fp2sqr_mont(P->X, t0); // t0 = X1 ^ 2 - fp2sqr_mont(P->Z, t6); // t6 = Z1 ^ 2 - fp2add(t0, t6, t0); // t0 = t0 + t6 - fp2add(t1, t1, t1); // t1 = t1 + t1 - fp2mul_mont(QY, P->X, t7); // t7 = y2*X1 - fp2mul_mont(QX, P->Y, t6); // t6 = x2*Y1 - fp2sub(t7, t6, t7); // t7 = t7 - t6 - fp2mul_mont(t1, t7, t1); // t1 = t1*t7 - fp2mul_mont(A, t2, t7); // t7 = A*t2 - fp2add(t7, t4, t4); // t4 = t4 + t7 - fp2mul_mont(t1, t4, t4); // t4 = t1*t4 - fp2mul_mont(QY, QZ, t1); // t1 = y2*z2 - fp2mul_mont(t0, t1, t0); // t0 = t0*t1 - fp2sqr_mont(QZ, t1); // t1 = z2 ^ 2 - fp2sqr_mont(QX, t6); // t6 = x2 ^ 2 - fp2add(t1, t6, t1); // t1 = t1 + t6 - fp2mul_mont(P->Z, P->Y, t6); // t6 = Z1*Y1 - fp2mul_mont(t1, t6, t1); // t1 = t1*t6 - fp2sub(t0, t1, t0); // t0 = t0 - t1 - fp2mul_mont(t2, t0, t0); // t0 = t2*t0 - fp2mul_mont(t5, t3, R->X); // X3 = t5*t3 - fp2add(t4, t0, R->Y); // Y3 = t4 + t0 - fp2sqr_mont(t3, t0); // t0 = t3 ^ 2 - fp2mul_mont(t3, t0, R->Z); // Z3 = t3*t0 -} - - -void Mont_ladder(const f2elm_t x, const digit_t* m, point_proj_t P, point_proj_t Q, const f2elm_t A24, const unsigned int order_bits, const unsigned int order_fullbits) -{ // The Montgomery ladder - // Inputs: the affine x-coordinate of a point P on E: B*y^2=x^3+A*x^2+x, - // scalar m - // curve constant A24 = (A+2)/4 - // order_bits = subgroup order bitlength - // order_fullbits = smallest multiple of 32 larger than the order bitlength - // Output: P = m*(x:1) - unsigned int bit = 0, owords = NBITS_TO_NWORDS(order_fullbits); - digit_t mask, scalar[NWORDS_ORDER]; - int i; - - // Initializing with the points (1:0) and (x:1) - fpcopy((digit_t*)&Montgomery_one, (digit_t*)P->X[0]); - fpzero(P->X[1]); - fp2zero(P->Z); - - fp2copy(x, Q->X); - fpcopy((digit_t*)&Montgomery_one, (digit_t*)Q->Z[0]); - fpzero(Q->Z[1]); - - for (i = NWORDS_ORDER-1; i >= 0; i--) { - scalar[i] = m[i]; - } - - for (i = order_fullbits-order_bits; i > 0; i--) { - mp_shiftl1(scalar, owords); - } - - for (i = order_bits; i > 0; i--) { - bit = (unsigned int)(scalar[owords-1] >> (RADIX-1)); - mp_shiftl1(scalar, owords); - mask = 0-(digit_t)bit; - - swap_points(P, Q, mask); - xDBLADD(P, Q, x, A24); // If bit=0 then P <- 2*P and Q <- P+Q, - swap_points(P, Q, mask); // else if bit=1 then Q <- 2*Q and P <- P+Q - } -} - - -void mont_twodim_scalarmult(digit_t* a, const point_t R, const point_t S, const f2elm_t A, const f2elm_t A24, point_full_proj_t P, const unsigned int order_bits) -{ // Computes P = R + [a]S - point_proj_t P0 = {0}, P1 = {0}; - point_full_proj_t P2 = {0}; - f2elm_t one = {0}; - - fpcopy((digit_t*)&Montgomery_one, one[0]); - Mont_ladder(S->x, a, P0, P1, A24, order_bits, MAXBITS_ORDER); - recover_os(P0->X, P0->Z, P1->X, P1->Z, S->x, S->y, A, P2->X, P2->Y, P2->Z); - ADD(P2, R->x, R->y, one, A, P); -} - - -void xDBLADD_proj(point_proj_t P, point_proj_t Q, const f2elm_t XPQ, const f2elm_t ZPQ, const f2elm_t A24) -{ // Simultaneous doubling and differential addition. - // Input: projective Montgomery points P=(XP:ZP) and Q=(XQ:ZQ) such that xP=XP/ZP and xQ=XQ/ZQ, affine difference xPQ=x(P-Q) and Montgomery curve constant A24=(A+2)/4. - // Output: projective Montgomery points P <- 2*P = (X2P:Z2P) such that x(2P)=X2P/Z2P, and Q <- P+Q = (XQP:ZQP) such that = x(Q+P)=XQP/ZQP. - f2elm_t t0, t1, t2; - - fp2add(P->X, P->Z, t0); // t0 = XP+ZP - fp2sub(P->X, P->Z, t1); // t1 = XP-ZP - fp2sqr_mont(t0, P->X); // XP = (XP+ZP)^2 - fp2sub(Q->X, Q->Z, t2); // t2 = XQ-ZQ - fp2correction(t2); - fp2add(Q->X, Q->Z, Q->X); // XQ = XQ+ZQ - fp2mul_mont(t0, t2, t0); // t0 = (XP+ZP)*(XQ-ZQ) - fp2sqr_mont(t1, P->Z); // ZP = (XP-ZP)^2 - fp2mul_mont(t1, Q->X, t1); // t1 = (XP-ZP)*(XQ+ZQ) - fp2sub(P->X, P->Z, t2); // t2 = (XP+ZP)^2-(XP-ZP)^2 - fp2mul_mont(P->X, P->Z, P->X); // XP = (XP+ZP)^2*(XP-ZP)^2 - fp2mul_mont(t2, A24, Q->X); // XQ = A24*[(XP+ZP)^2-(XP-ZP)^2] - fp2sub(t0, t1, Q->Z); // ZQ = (XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ) - fp2add(Q->X, P->Z, P->Z); // ZP = A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2 - fp2add(t0, t1, Q->X); // XQ = (XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ) - fp2mul_mont(P->Z, t2, P->Z); // ZP = [A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2]*[(XP+ZP)^2-(XP-ZP)^2] - fp2sqr_mont(Q->Z, Q->Z); // ZQ = [(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2 - fp2sqr_mont(Q->X, Q->X); // XQ = [(XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)]^2 - fp2mul_mont(Q->X, ZPQ, Q->X); // XQ = ZPQ*[(XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)]^2 - fp2mul_mont(Q->Z, XPQ, Q->Z); // ZQ = XPQ*[(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2 -} - - void xDBL_e(const point_proj_t P, point_proj_t Q, const f2elm_t A24, const int e) { // Doubling of a Montgomery point in projective coordinates (X:Z) over affine curve coefficient A. // Input: projective Montgomery x-coordinates P = (X1:Z1), where x1=X1/Z1 and Montgomery curve constants (A+2)/4. @@ -635,13 +545,110 @@ void xDBL_e(const point_proj_t P, point_proj_t Q, const f2elm_t A24, const int e } -void Ladder(const point_proj_t P, const digit_t* m, const f2elm_t A, const unsigned int order_bits, point_proj_t R) +static void eval_dual_4_isog_shared(const f2elm_t X4pZ4, const f2elm_t X42, const f2elm_t Z42, f2elm_t* coeff) +{ + fp2sub(X42, Z42, coeff[0]); + fp2add(X42, Z42, coeff[1]); + fp2sqr_mont(X4pZ4, coeff[2]); + fp2sub(coeff[2], coeff[1], coeff[2]); +} + + +static void eval_dual_4_isog(const f2elm_t A24, const f2elm_t C24, const f2elm_t* coeff, point_proj_t P) +{ + f2elm_t t0, t1, t2, t3; + + fp2add(P->X, P->Z, t0); + fp2sub(P->X, P->Z, t1); + fp2sqr_mont(t0, t0); + fp2sqr_mont(t1, t1); + fp2sub(t0, t1, t2); + fp2sub(C24, A24, t3); + fp2mul_mont(t2, t3, t3); + fp2mul_mont(C24, t0, t2); + fp2sub(t2, t3, t2); + fp2mul_mont(t2, t0, P->X); + fp2mul_mont(t3, t1, P->Z); + fp2mul_mont(coeff[0], P->X, P->X); + fp2mul_mont(coeff[1], P->Z, t0); + fp2add(P->X, t0, P->X); + fp2mul_mont(coeff[2], P->Z, P->Z); +} + + +static void get_4_isog_dual(const point_proj_t P, f2elm_t A24, f2elm_t C24, f2elm_t* coeff) { + fp2sub(P->X, P->Z, coeff[1]); + fp2add(P->X, P->Z, coeff[2]); + fp2sqr_mont(P->Z, coeff[4]); + fp2add(coeff[4], coeff[4], coeff[0]); + fp2sqr_mont(coeff[0], C24); + fp2add(coeff[0], coeff[0], coeff[0]); + fp2sqr_mont(P->X, coeff[3]); + fp2add(coeff[3], coeff[3], A24); + fp2sqr_mont(A24, A24); +} + + +#if (OALICE_BITS % 2 == 1) + +static void eval_dual_2_isog(const f2elm_t X2, const f2elm_t Z2, point_proj_t P) +{ + f2elm_t t0; + + fp2add(P->X, P->Z, t0); + fp2sub(P->X, P->Z, P->Z); + fp2sqr_mont(t0, t0); + fp2sqr_mont(P->Z, P->Z); + fp2sub(t0, P->Z, P->Z); + fp2mul_mont(X2, P->Z, P->Z); + fp2mul_mont(Z2, t0, P->X); +} + +#endif + + +static void eval_final_dual_2_isog(point_proj_t P) +{ + f2elm_t t0, t1; + felm_t t2; + + fp2add(P->X, P->Z, t0); + fp2mul_mont(P->X, P->Z, t1); + fp2sqr_mont(t0, P->X); + fpcopy((P->X)[0], t2); + fpcopy((P->X)[1], (P->X)[0]); + fpcopy(t2, (P->X)[1]); + fpneg((P->X)[1]); + fp2add(t1, t1, P->Z); + fp2add(P->Z, P->Z, P->Z); +} + + +static void eval_full_dual_4_isog(const f2elm_t As[][5], point_proj_t P) +{ + // First all 4-isogenies + for(unsigned int i = 0; i < MAX_Alice; i++) { + eval_dual_4_isog(As[MAX_Alice-i][0], As[MAX_Alice-i][1], *(As+MAX_Alice-i-1)+2, P); + } +#if (OALICE_BITS % 2 == 1) + eval_dual_2_isog(As[MAX_Alice][2], As[MAX_Alice][3], P); +#endif + eval_final_dual_2_isog(P); // to A = 0 +} + + +void Ladder(const point_proj_t P, const digit_t* m, const f2elm_t A, const unsigned int order_bits, point_proj_t R) +{ // The Montgomery ladder + // Inputs: a projective point P=[X:Z] on E: B*y^2=x^3+A*x^2+x, + // scalar m + // curve coefficient A + // order_bits = subgroup order bitlength + // Output: R = m*(X:Z) point_proj_t R0, R1; f2elm_t A24 = {0}; - unsigned int bit = 0; digit_t mask; - int j, swap, prevbit = 0; + unsigned int bit = 0, prevbit = 0, j, swap; fpcopy((digit_t*)&Montgomery_one, A24[0]); fpadd(A24[0], A24[0], A24[0]); @@ -651,10 +658,6 @@ void Ladder(const point_proj_t P, const digit_t* m, const f2elm_t A, const unsig j = order_bits - 1; bit = (m[j >> LOG2RADIX] >> (j & (RADIX-1))) & 1; - while (bit == 0) { - j--; - bit = (m[j >> LOG2RADIX] >> (j & (RADIX-1))) & 1; - } // R0 <- P, R1 <- 2P fp2copy(P->X, R0->X); @@ -662,14 +665,14 @@ void Ladder(const point_proj_t P, const digit_t* m, const f2elm_t A, const unsig xDBL_e(P, R1, A24, 1); // Main loop - for (int i = j - 1; i >= 0; i--) { + for (int i = j; i >= 0; i--) { bit = (m[i >> LOG2RADIX] >> (i & (RADIX-1))) & 1; swap = bit ^ prevbit; prevbit = bit; mask = 0 - (digit_t)swap; swap_points(R0, R1, mask); - xDBLADD_proj(R0, R1, P->X, P->Z, A24); + xDBLADD(R0, R1, P->X, P->Z, A24); } swap = 0 ^ prevbit; mask = 0 - (digit_t)swap; @@ -679,4 +682,39 @@ void Ladder(const point_proj_t P, const digit_t* m, const f2elm_t A, const unsig fp2copy(R0->Z, R->Z); } + +static void Ladder3pt_dual(const point_proj_t *Rs, const digit_t* m, const unsigned int AliceOrBob, point_proj_t R, const f2elm_t A24) +{ // Project 3-point ladder + point_proj_t R0 = {0}, R2 = {0}; + digit_t mask; + int i, nbits, bit, swap, prevbit = 0; + + if (AliceOrBob == ALICE) { + nbits = OALICE_BITS; + } else { + nbits = OBOB_BITS; + } + + fp2copy(Rs[1]->X, R0->X); + fp2copy(Rs[1]->Z, R0->Z); + fp2copy(Rs[2]->X, R2->X); + fp2copy(Rs[2]->Z, R2->Z); + fp2copy(Rs[0]->X, R->X); + fp2copy(Rs[0]->Z, R->Z); + + // Main loop + for (i = 0; i < nbits; i++) { + bit = (m[i >> LOG2RADIX] >> (i & (RADIX-1))) & 1; + swap = bit ^ prevbit; + prevbit = bit; + mask = 0 - (digit_t)swap; + + swap_points(R, R2, mask); + xDBLADD(R0, R2, R->X, R->Z, A24); + } + swap = 0 ^ prevbit; + mask = 0 - (digit_t)swap; + swap_points(R, R2, mask); +} + #endif \ No newline at end of file diff --git a/src/fpx.c b/src/fpx.c index 58a39bb..72629f8 100644 --- a/src/fpx.c +++ b/src/fpx.c @@ -969,7 +969,7 @@ unsigned char is_sqr_fp2(const f2elm_t a, felm_t s) fpsqr_mont(s,temp); // s = z^((p+1)/4) fpcorrection(temp); fpcorrection(z); - if (memcmp((unsigned char*)temp, (unsigned char*)z, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) // s^2 !=? z + if (memcmp(temp, z, NBITS_TO_NBYTES(NBITS_FIELD)) != 0) // s^2 !=? z return 0; return 1; @@ -1483,4 +1483,114 @@ void recover_os(const f2elm_t X1, const f2elm_t Z1, const f2elm_t X2, const f2el fp2sub(t0, t1, Y3); // Y3 = Z2*[(X1+x*Z1+2*A*Z1)*(X1*x+Z1)-2*A*Z1^2] - (X1-x*Z1)^2*X2 } // Closing COMPRESSED +#endif + + +#ifdef ELL2_TORUS + +int mod(int a, unsigned int b) +{ + unsigned int r; + if (b == 0) return 0; // avoid invalid operation + r = a % b; + while (r < 0) r += b; + return r; +} + + +int highest_2t(const int n) +{ // Find largest power 2^t dividing n + return (n & (~(n - 1))); +} + + +int highest_t(const int n) +{ // Find largest t s.t. 2^t divides n and 2^(t+1) does not + int t = 0, power2t = highest_2t(n); + + while (power2t > 1) { + power2t >>= 1; + t++; + } + return t; +} + + +void toproj(const f2elm_t a, felm_t *b) { + fpadd(a[0], (digit_t*)&Montgomery_one, b[0]); + fpcopy(a[1], b[1]); +} + + +void fromproj(const felm_t *a, felm_t *b) { + felm_t x, xx, y, yy, tmp1, tmp2; + + fpcopy(a[0],x); + fpcopy(a[1],y); + fpsqr_mont(x,xx); + fpsqr_mont(y,yy); + fpsub(xx,yy,tmp1); + fpadd(xx,yy,tmp2); + fpinv_mont(tmp2); + fpmul_mont(tmp1,tmp2,b[0]); + fpmul_mont(x,y,tmp1); + fpadd(tmp1,tmp1,tmp1); + fpmul_mont(tmp1,tmp2,b[1]); + fpcorrection(b[0]); + fpcorrection(b[1]); +} + + +void inv_Fp2_cycl_proj(felm_t *proja) +{ // Given an Fp2 element a in the cyclotomic subgroup, compute a^-1 + if (!is_felm_zero(proja[1])) { + fpneg(proja[0]); + fpcorrection(proja[0]); + } +} + + +int reverse_bits(int t, unsigned int nbits) +{ // Given t = b_{n-1}2^(n-1) + ... + b_{1}2 + b_{0}, return b_{0}2^(n-1) + ... + b{n-2}2 + b_{n-1} + int x = t, r = 0, bits=0; + while (x > 0) { + r = (r << 1) + (x%2); + x >>= 1; + bits++; + } + while (bits < nbits) { + r <<= 1; + bits++; + } + return r; +} + + +void sqr_Fp2_cycl_proj(felm_t *proja) +{ // Cyclotomic squaring on projective elements of norm 1, using a^(p+1) = 1. + felm_t t0, t1, xy; + + fpadd(proja[0],proja[1],t0); + fpsub(proja[0],proja[1],t1); + fpmul_mont(proja[0],proja[1],xy); + fpmul_mont(t0,t1,proja[0]); + fpadd(xy,xy,proja[1]); +} + + +void mulmixed_montproj(const felm_t *proja, const felm_t alpha, felm_t *projc) +{ // [x,y] * [alpha, 1] + felm_t t0, x, y; + + fpcopy(proja[0], x); + fpcopy(proja[1], y); + fpmul_mont(x,alpha,t0); + fpsub(t0, y, projc[0]); // x*alpha - y + fpmul_mont(y, alpha, t0); + fpadd(x, t0, projc[1]); // x + y*alpha + + fpcorrection(projc[0]); + fpcorrection(projc[1]); +} + #endif \ No newline at end of file diff --git a/src/internal.h b/src/internal.h index 7d0ceec..924f246 100644 --- a/src/internal.h +++ b/src/internal.h @@ -70,7 +70,7 @@ void mont_n_way_inv(const f2elm_t* vec, const int n, f2elm_t* out); void j_inv(const f2elm_t A, const f2elm_t C, f2elm_t jinv); // Simultaneous doubling and differential addition. -void xDBLADD(point_proj_t P, point_proj_t Q, const f2elm_t xPQ, const f2elm_t A24); +void xDBLADD(point_proj_t P, point_proj_t Q, const f2elm_t XPQ, const f2elm_t ZPQ, const f2elm_t A24); // Doubling of a Montgomery point in projective coordinates (X:Z). void xDBL(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24);