| /* Copyright (c) 2020, Google Inc. |
| * |
| * Permission to use, copy, modify, and/or distribute this software for any |
| * purpose with or without fee is hereby granted, provided that the above |
| * copyright notice and this permission notice appear in all copies. |
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| |
| // This file is generated by make_tables.go. |
| |
| // Base point pre computation |
| // -------------------------- |
| // |
| // Two different sorts of precomputed tables are used in the following code. |
| // Each contain various points on the curve, where each point is three field |
| // elements (x, y, z). |
| // |
| // For the base point table, z is usually 1 (0 for the point at infinity). |
| // This table has 2 * 16 elements, starting with the following: |
| // index | bits | point |
| // ------+---------+------------------------------ |
| // 0 | 0 0 0 0 | 0G |
| // 1 | 0 0 0 1 | 1G |
| // 2 | 0 0 1 0 | 2^64G |
| // 3 | 0 0 1 1 | (2^64 + 1)G |
| // 4 | 0 1 0 0 | 2^128G |
| // 5 | 0 1 0 1 | (2^128 + 1)G |
| // 6 | 0 1 1 0 | (2^128 + 2^64)G |
| // 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G |
| // 8 | 1 0 0 0 | 2^192G |
| // 9 | 1 0 0 1 | (2^192 + 1)G |
| // 10 | 1 0 1 0 | (2^192 + 2^64)G |
| // 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G |
| // 12 | 1 1 0 0 | (2^192 + 2^128)G |
| // 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G |
| // 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G |
| // 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G |
| // followed by a copy of this with each element multiplied by 2^32. |
| // |
| // The reason for this is so that we can clock bits into four different |
| // locations when doing simple scalar multiplies against the base point, |
| // and then another four locations using the second 16 elements. |
| // |
| // Tables for other points have table[i] = iG for i in 0 .. 16. |
| |
| // fiat_p256_g_pre_comp is the table of precomputed base points |
| #if defined(OPENSSL_64_BIT) |
| static const fiat_p256_felem fiat_p256_g_pre_comp[2][15][2] = { |
| {{{0x79e730d418a9143c, 0x75ba95fc5fedb601, 0x79fb732b77622510, |
| 0x18905f76a53755c6}, |
| {0xddf25357ce95560a, 0x8b4ab8e4ba19e45c, 0xd2e88688dd21f325, |
| 0x8571ff1825885d85}}, |
| {{0x4f922fc516a0d2bb, 0x0d5cc16c1a623499, 0x9241cf3a57c62c8b, |
| 0x2f5e6961fd1b667f}, |
| {0x5c15c70bf5a01797, 0x3d20b44d60956192, 0x04911b37071fdb52, |
| 0xf648f9168d6f0f7b}}, |
| {{0x9e566847e137bbbc, 0xe434469e8a6a0bec, 0xb1c4276179d73463, |
| 0x5abe0285133d0015}, |
| {0x92aa837cc04c7dab, 0x573d9f4c43260c07, 0x0c93156278e6cc37, |
| 0x94bb725b6b6f7383}}, |
| {{0x62a8c244bfe20925, 0x91c19ac38fdce867, 0x5a96a5d5dd387063, |
| 0x61d587d421d324f6}, |
| {0xe87673a2a37173ea, 0x2384800853778b65, 0x10f8441e05bab43e, |
| 0xfa11fe124621efbe}}, |
| {{0x1c891f2b2cb19ffd, 0x01ba8d5bb1923c23, 0xb6d03d678ac5ca8e, |
| 0x586eb04c1f13bedc}, |
| {0x0c35c6e527e8ed09, 0x1e81a33c1819ede2, 0x278fd6c056c652fa, |
| 0x19d5ac0870864f11}}, |
| {{0x62577734d2b533d5, 0x673b8af6a1bdddc0, 0x577e7c9aa79ec293, |
| 0xbb6de651c3b266b1}, |
| {0xe7e9303ab65259b3, 0xd6a0afd3d03a7480, 0xc5ac83d19b3cfc27, |
| 0x60b4619a5d18b99b}}, |
| {{0xbd6a38e11ae5aa1c, 0xb8b7652b49e73658, 0x0b130014ee5f87ed, |
| 0x9d0f27b2aeebffcd}, |
| {0xca9246317a730a55, 0x9c955b2fddbbc83a, 0x07c1dfe0ac019a71, |
| 0x244a566d356ec48d}}, |
| {{0x56f8410ef4f8b16a, 0x97241afec47b266a, 0x0a406b8e6d9c87c1, |
| 0x803f3e02cd42ab1b}, |
| {0x7f0309a804dbec69, 0xa83b85f73bbad05f, 0xc6097273ad8e197f, |
| 0xc097440e5067adc1}}, |
| {{0x846a56f2c379ab34, 0xa8ee068b841df8d1, 0x20314459176c68ef, |
| 0xf1af32d5915f1f30}, |
| {0x99c375315d75bd50, 0x837cffbaf72f67bc, 0x0613a41848d7723f, |
| 0x23d0f130e2d41c8b}}, |
| {{0xed93e225d5be5a2b, 0x6fe799835934f3c6, 0x4314092622626ffc, |
| 0x50bbb4d97990216a}, |
| {0x378191c6e57ec63e, 0x65422c40181dcdb2, 0x41a8099b0236e0f6, |
| 0x2b10011801fe49c3}}, |
| {{0xfc68b5c59b391593, 0xc385f5a2598270fc, 0x7144f3aad19adcbb, |
| 0xdd55899983fbae0c}, |
| {0x93b88b8e74b82ff4, 0xd2e03c4071e734c9, 0x9a7a9eaf43c0322a, |
| 0xe6e4c551149d6041}}, |
| {{0x5fe14bfe80ec21fe, 0xf6ce116ac255be82, 0x98bc5a072f4a5d67, |
| 0xfad27148db7e63af}, |
| {0x90c0b6ac29ab05b3, 0x37a9a83c4e251ae6, 0x0a7dc875c2aade7d, |
| 0x77387de39f0e1a84}}, |
| {{0x1e9ecc49a56c0dd7, 0xa5cffcd846086c74, 0x8f7a1408f505aece, |
| 0xb37b85c0bef0c47e}, |
| {0x3596b6e4cc0e6a8f, 0xfd6d4bbf6b388f23, 0xaba453fac39cef4e, |
| 0x9c135ac8f9f628d5}}, |
| {{0x0a1c729495c8f8be, 0x2961c4803bf362bf, 0x9e418403df63d4ac, |
| 0xc109f9cb91ece900}, |
| {0xc2d095d058945705, 0xb9083d96ddeb85c0, 0x84692b8d7a40449b, |
| 0x9bc3344f2eee1ee1}}, |
| {{0x0d5ae35642913074, 0x55491b2748a542b1, 0x469ca665b310732a, |
| 0x29591d525f1a4cc1}, |
| {0xe76f5b6bb84f983f, 0xbe7eef419f5f84e1, 0x1200d49680baa189, |
| 0x6376551f18ef332c}}}, |
| {{{0x202886024147519a, 0xd0981eac26b372f0, 0xa9d4a7caa785ebc8, |
| 0xd953c50ddbdf58e9}, |
| {0x9d6361ccfd590f8f, 0x72e9626b44e6c917, 0x7fd9611022eb64cf, |
| 0x863ebb7e9eb288f3}}, |
| {{0x4fe7ee31b0e63d34, 0xf4600572a9e54fab, 0xc0493334d5e7b5a4, |
| 0x8589fb9206d54831}, |
| {0xaa70f5cc6583553a, 0x0879094ae25649e5, 0xcc90450710044652, |
| 0xebb0696d02541c4f}}, |
| {{0xabbaa0c03b89da99, 0xa6f2d79eb8284022, 0x27847862b81c05e8, |
| 0x337a4b5905e54d63}, |
| {0x3c67500d21f7794a, 0x207005b77d6d7f61, 0x0a5a378104cfd6e8, |
| 0x0d65e0d5f4c2fbd6}}, |
| {{0xd433e50f6d3549cf, 0x6f33696ffacd665e, 0x695bfdacce11fcb4, |
| 0x810ee252af7c9860}, |
| {0x65450fe17159bb2c, 0xf7dfbebe758b357b, 0x2b057e74d69fea72, |
| 0xd485717a92731745}}, |
| {{0xce1f69bbe83f7669, 0x09f8ae8272877d6b, 0x9548ae543244278d, |
| 0x207755dee3c2c19c}, |
| {0x87bd61d96fef1945, 0x18813cefb12d28c3, 0x9fbcd1d672df64aa, |
| 0x48dc5ee57154b00d}}, |
| {{0xef0f469ef49a3154, 0x3e85a5956e2b2e9a, 0x45aaec1eaa924a9c, |
| 0xaa12dfc8a09e4719}, |
| {0x26f272274df69f1d, 0xe0e4c82ca2ff5e73, 0xb9d8ce73b7a9dd44, |
| 0x6c036e73e48ca901}}, |
| {{0xe1e421e1a47153f0, 0xb86c3b79920418c9, 0x93bdce87705d7672, |
| 0xf25ae793cab79a77}, |
| {0x1f3194a36d869d0c, 0x9d55c8824986c264, 0x49fb5ea3096e945e, |
| 0x39b8e65313db0a3e}}, |
| {{0xe3417bc035d0b34a, 0x440b386b8327c0a7, 0x8fb7262dac0362d1, |
| 0x2c41114ce0cdf943}, |
| {0x2ba5cef1ad95a0b1, 0xc09b37a867d54362, 0x26d6cdd201e486c9, |
| 0x20477abf42ff9297}}, |
| {{0x0f121b41bc0a67d2, 0x62d4760a444d248a, 0x0e044f1d659b4737, |
| 0x08fde365250bb4a8}, |
| {0xaceec3da848bf287, 0xc2a62182d3369d6e, 0x3582dfdc92449482, |
| 0x2f7e2fd2565d6cd7}}, |
| {{0x0a0122b5178a876b, 0x51ff96ff085104b4, 0x050b31ab14f29f76, |
| 0x84abb28b5f87d4e6}, |
| {0xd5ed439f8270790a, 0x2d6cb59d85e3f46b, 0x75f55c1b6c1e2212, |
| 0xe5436f6717655640}}, |
| {{0xc2965ecc9aeb596d, 0x01ea03e7023c92b4, 0x4704b4b62e013961, |
| 0x0ca8fd3f905ea367}, |
| {0x92523a42551b2b61, 0x1eb7a89c390fcd06, 0xe7f1d2be0392a63e, |
| 0x96dca2644ddb0c33}}, |
| {{0x231c210e15339848, 0xe87a28e870778c8d, 0x9d1de6616956e170, |
| 0x4ac3c9382bb09c0b}, |
| {0x19be05516998987d, 0x8b2376c4ae09f4d6, 0x1de0b7651a3f933d, |
| 0x380d94c7e39705f4}}, |
| {{0x3685954b8c31c31d, 0x68533d005bf21a0c, 0x0bd7626e75c79ec9, |
| 0xca17754742c69d54}, |
| {0xcc6edafff6d2dbb2, 0xfd0d8cbd174a9d18, 0x875e8793aa4578e8, |
| 0xa976a7139cab2ce6}}, |
| {{0xce37ab11b43ea1db, 0x0a7ff1a95259d292, 0x851b02218f84f186, |
| 0xa7222beadefaad13}, |
| {0xa2ac78ec2b0a9144, 0x5a024051f2fa59c5, 0x91d1eca56147ce38, |
| 0xbe94d523bc2ac690}}, |
| {{0x2d8daefd79ec1a0f, 0x3bbcd6fdceb39c97, 0xf5575ffc58f61a95, |
| 0xdbd986c4adf7b420}, |
| {0x81aa881415f39eb7, 0x6ee2fcf5b98d976c, 0x5465475dcf2f717d, |
| 0x8e24d3c46860bbd0}}}}; |
| #else |
| static const fiat_p256_felem fiat_p256_g_pre_comp[2][15][2] = { |
| {{{0x18a9143c, 0x79e730d4, 0x5fedb601, 0x75ba95fc, 0x77622510, 0x79fb732b, |
| 0xa53755c6, 0x18905f76}, |
| {0xce95560a, 0xddf25357, 0xba19e45c, 0x8b4ab8e4, 0xdd21f325, 0xd2e88688, |
| 0x25885d85, 0x8571ff18}}, |
| {{0x16a0d2bb, 0x4f922fc5, 0x1a623499, 0x0d5cc16c, 0x57c62c8b, 0x9241cf3a, |
| 0xfd1b667f, 0x2f5e6961}, |
| {0xf5a01797, 0x5c15c70b, 0x60956192, 0x3d20b44d, 0x071fdb52, 0x04911b37, |
| 0x8d6f0f7b, 0xf648f916}}, |
| {{0xe137bbbc, 0x9e566847, 0x8a6a0bec, 0xe434469e, 0x79d73463, 0xb1c42761, |
| 0x133d0015, 0x5abe0285}, |
| {0xc04c7dab, 0x92aa837c, 0x43260c07, 0x573d9f4c, 0x78e6cc37, 0x0c931562, |
| 0x6b6f7383, 0x94bb725b}}, |
| {{0xbfe20925, 0x62a8c244, 0x8fdce867, 0x91c19ac3, 0xdd387063, 0x5a96a5d5, |
| 0x21d324f6, 0x61d587d4}, |
| {0xa37173ea, 0xe87673a2, 0x53778b65, 0x23848008, 0x05bab43e, 0x10f8441e, |
| 0x4621efbe, 0xfa11fe12}}, |
| {{0x2cb19ffd, 0x1c891f2b, 0xb1923c23, 0x01ba8d5b, 0x8ac5ca8e, 0xb6d03d67, |
| 0x1f13bedc, 0x586eb04c}, |
| {0x27e8ed09, 0x0c35c6e5, 0x1819ede2, 0x1e81a33c, 0x56c652fa, 0x278fd6c0, |
| 0x70864f11, 0x19d5ac08}}, |
| {{0xd2b533d5, 0x62577734, 0xa1bdddc0, 0x673b8af6, 0xa79ec293, 0x577e7c9a, |
| 0xc3b266b1, 0xbb6de651}, |
| {0xb65259b3, 0xe7e9303a, 0xd03a7480, 0xd6a0afd3, 0x9b3cfc27, 0xc5ac83d1, |
| 0x5d18b99b, 0x60b4619a}}, |
| {{0x1ae5aa1c, 0xbd6a38e1, 0x49e73658, 0xb8b7652b, 0xee5f87ed, 0x0b130014, |
| 0xaeebffcd, 0x9d0f27b2}, |
| {0x7a730a55, 0xca924631, 0xddbbc83a, 0x9c955b2f, 0xac019a71, 0x07c1dfe0, |
| 0x356ec48d, 0x244a566d}}, |
| {{0xf4f8b16a, 0x56f8410e, 0xc47b266a, 0x97241afe, 0x6d9c87c1, 0x0a406b8e, |
| 0xcd42ab1b, 0x803f3e02}, |
| {0x04dbec69, 0x7f0309a8, 0x3bbad05f, 0xa83b85f7, 0xad8e197f, 0xc6097273, |
| 0x5067adc1, 0xc097440e}}, |
| {{0xc379ab34, 0x846a56f2, 0x841df8d1, 0xa8ee068b, 0x176c68ef, 0x20314459, |
| 0x915f1f30, 0xf1af32d5}, |
| {0x5d75bd50, 0x99c37531, 0xf72f67bc, 0x837cffba, 0x48d7723f, 0x0613a418, |
| 0xe2d41c8b, 0x23d0f130}}, |
| {{0xd5be5a2b, 0xed93e225, 0x5934f3c6, 0x6fe79983, 0x22626ffc, 0x43140926, |
| 0x7990216a, 0x50bbb4d9}, |
| {0xe57ec63e, 0x378191c6, 0x181dcdb2, 0x65422c40, 0x0236e0f6, 0x41a8099b, |
| 0x01fe49c3, 0x2b100118}}, |
| {{0x9b391593, 0xfc68b5c5, 0x598270fc, 0xc385f5a2, 0xd19adcbb, 0x7144f3aa, |
| 0x83fbae0c, 0xdd558999}, |
| {0x74b82ff4, 0x93b88b8e, 0x71e734c9, 0xd2e03c40, 0x43c0322a, 0x9a7a9eaf, |
| 0x149d6041, 0xe6e4c551}}, |
| {{0x80ec21fe, 0x5fe14bfe, 0xc255be82, 0xf6ce116a, 0x2f4a5d67, 0x98bc5a07, |
| 0xdb7e63af, 0xfad27148}, |
| {0x29ab05b3, 0x90c0b6ac, 0x4e251ae6, 0x37a9a83c, 0xc2aade7d, 0x0a7dc875, |
| 0x9f0e1a84, 0x77387de3}}, |
| {{0xa56c0dd7, 0x1e9ecc49, 0x46086c74, 0xa5cffcd8, 0xf505aece, 0x8f7a1408, |
| 0xbef0c47e, 0xb37b85c0}, |
| {0xcc0e6a8f, 0x3596b6e4, 0x6b388f23, 0xfd6d4bbf, 0xc39cef4e, 0xaba453fa, |
| 0xf9f628d5, 0x9c135ac8}}, |
| {{0x95c8f8be, 0x0a1c7294, 0x3bf362bf, 0x2961c480, 0xdf63d4ac, 0x9e418403, |
| 0x91ece900, 0xc109f9cb}, |
| {0x58945705, 0xc2d095d0, 0xddeb85c0, 0xb9083d96, 0x7a40449b, 0x84692b8d, |
| 0x2eee1ee1, 0x9bc3344f}}, |
| {{0x42913074, 0x0d5ae356, 0x48a542b1, 0x55491b27, 0xb310732a, 0x469ca665, |
| 0x5f1a4cc1, 0x29591d52}, |
| {0xb84f983f, 0xe76f5b6b, 0x9f5f84e1, 0xbe7eef41, 0x80baa189, 0x1200d496, |
| 0x18ef332c, 0x6376551f}}}, |
| {{{0x4147519a, 0x20288602, 0x26b372f0, 0xd0981eac, 0xa785ebc8, 0xa9d4a7ca, |
| 0xdbdf58e9, 0xd953c50d}, |
| {0xfd590f8f, 0x9d6361cc, 0x44e6c917, 0x72e9626b, 0x22eb64cf, 0x7fd96110, |
| 0x9eb288f3, 0x863ebb7e}}, |
| {{0xb0e63d34, 0x4fe7ee31, 0xa9e54fab, 0xf4600572, 0xd5e7b5a4, 0xc0493334, |
| 0x06d54831, 0x8589fb92}, |
| {0x6583553a, 0xaa70f5cc, 0xe25649e5, 0x0879094a, 0x10044652, 0xcc904507, |
| 0x02541c4f, 0xebb0696d}}, |
| {{0x3b89da99, 0xabbaa0c0, 0xb8284022, 0xa6f2d79e, 0xb81c05e8, 0x27847862, |
| 0x05e54d63, 0x337a4b59}, |
| {0x21f7794a, 0x3c67500d, 0x7d6d7f61, 0x207005b7, 0x04cfd6e8, 0x0a5a3781, |
| 0xf4c2fbd6, 0x0d65e0d5}}, |
| {{0x6d3549cf, 0xd433e50f, 0xfacd665e, 0x6f33696f, 0xce11fcb4, 0x695bfdac, |
| 0xaf7c9860, 0x810ee252}, |
| {0x7159bb2c, 0x65450fe1, 0x758b357b, 0xf7dfbebe, 0xd69fea72, 0x2b057e74, |
| 0x92731745, 0xd485717a}}, |
| {{0xe83f7669, 0xce1f69bb, 0x72877d6b, 0x09f8ae82, 0x3244278d, 0x9548ae54, |
| 0xe3c2c19c, 0x207755de}, |
| {0x6fef1945, 0x87bd61d9, 0xb12d28c3, 0x18813cef, 0x72df64aa, 0x9fbcd1d6, |
| 0x7154b00d, 0x48dc5ee5}}, |
| {{0xf49a3154, 0xef0f469e, 0x6e2b2e9a, 0x3e85a595, 0xaa924a9c, 0x45aaec1e, |
| 0xa09e4719, 0xaa12dfc8}, |
| {0x4df69f1d, 0x26f27227, 0xa2ff5e73, 0xe0e4c82c, 0xb7a9dd44, 0xb9d8ce73, |
| 0xe48ca901, 0x6c036e73}}, |
| {{0xa47153f0, 0xe1e421e1, 0x920418c9, 0xb86c3b79, 0x705d7672, 0x93bdce87, |
| 0xcab79a77, 0xf25ae793}, |
| {0x6d869d0c, 0x1f3194a3, 0x4986c264, 0x9d55c882, 0x096e945e, 0x49fb5ea3, |
| 0x13db0a3e, 0x39b8e653}}, |
| {{0x35d0b34a, 0xe3417bc0, 0x8327c0a7, 0x440b386b, 0xac0362d1, 0x8fb7262d, |
| 0xe0cdf943, 0x2c41114c}, |
| {0xad95a0b1, 0x2ba5cef1, 0x67d54362, 0xc09b37a8, 0x01e486c9, 0x26d6cdd2, |
| 0x42ff9297, 0x20477abf}}, |
| {{0xbc0a67d2, 0x0f121b41, 0x444d248a, 0x62d4760a, 0x659b4737, 0x0e044f1d, |
| 0x250bb4a8, 0x08fde365}, |
| {0x848bf287, 0xaceec3da, 0xd3369d6e, 0xc2a62182, 0x92449482, 0x3582dfdc, |
| 0x565d6cd7, 0x2f7e2fd2}}, |
| {{0x178a876b, 0x0a0122b5, 0x085104b4, 0x51ff96ff, 0x14f29f76, 0x050b31ab, |
| 0x5f87d4e6, 0x84abb28b}, |
| {0x8270790a, 0xd5ed439f, 0x85e3f46b, 0x2d6cb59d, 0x6c1e2212, 0x75f55c1b, |
| 0x17655640, 0xe5436f67}}, |
| {{0x9aeb596d, 0xc2965ecc, 0x023c92b4, 0x01ea03e7, 0x2e013961, 0x4704b4b6, |
| 0x905ea367, 0x0ca8fd3f}, |
| {0x551b2b61, 0x92523a42, 0x390fcd06, 0x1eb7a89c, 0x0392a63e, 0xe7f1d2be, |
| 0x4ddb0c33, 0x96dca264}}, |
| {{0x15339848, 0x231c210e, 0x70778c8d, 0xe87a28e8, 0x6956e170, 0x9d1de661, |
| 0x2bb09c0b, 0x4ac3c938}, |
| {0x6998987d, 0x19be0551, 0xae09f4d6, 0x8b2376c4, 0x1a3f933d, 0x1de0b765, |
| 0xe39705f4, 0x380d94c7}}, |
| {{0x8c31c31d, 0x3685954b, 0x5bf21a0c, 0x68533d00, 0x75c79ec9, 0x0bd7626e, |
| 0x42c69d54, 0xca177547}, |
| {0xf6d2dbb2, 0xcc6edaff, 0x174a9d18, 0xfd0d8cbd, 0xaa4578e8, 0x875e8793, |
| 0x9cab2ce6, 0xa976a713}}, |
| {{0xb43ea1db, 0xce37ab11, 0x5259d292, 0x0a7ff1a9, 0x8f84f186, 0x851b0221, |
| 0xdefaad13, 0xa7222bea}, |
| {0x2b0a9144, 0xa2ac78ec, 0xf2fa59c5, 0x5a024051, 0x6147ce38, 0x91d1eca5, |
| 0xbc2ac690, 0xbe94d523}}, |
| {{0x79ec1a0f, 0x2d8daefd, 0xceb39c97, 0x3bbcd6fd, 0x58f61a95, 0xf5575ffc, |
| 0xadf7b420, 0xdbd986c4}, |
| {0x15f39eb7, 0x81aa8814, 0xb98d976c, 0x6ee2fcf5, 0xcf2f717d, 0x5465475d, |
| 0x6860bbd0, 0x8e24d3c4}}}}; |
| #endif |
