// The MIT License (MIT) // // Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file). // // Permission is hereby granted, free of charge, to any person obtaining a copy // of this software and associated documentation files (the "Software"), to deal // in the Software without restriction, including without limitation the rights // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell // copies of the Software, and to permit persons to whom the Software is // furnished to do so, subject to the following conditions: // // The above copyright notice and this permission notice shall be included in all // copies or substantial portions of the Software. // // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE // SOFTWARE. // The field arithmetic code is generated by Fiat // (https://github.com/mit-plv/fiat-crypto), which is MIT licensed. // // An implementation of the NIST P-256 elliptic curve point multiplication. // 256-bit Montgomery form, generated using fiat-crypto, for 64 and 32-bit. // Field operations with inputs in [0,p) return outputs in [0,p). #include #include #include #include #include #include #include "../../crypto/fipsmodule/delocate.h" #include "../../crypto/fipsmodule/ec/internal.h" #include "../../crypto/internal.h" // MSVC does not implement uint128_t, and crashes with intrinsics #if defined(BORINGSSL_HAS_UINT128) #define BORINGSSL_NISTP256_64BIT 1 #endif // "intrinsics" #if defined(BORINGSSL_NISTP256_64BIT) static uint64_t mulx_u64(uint64_t a, uint64_t b, uint64_t *high) { uint128_t x = (uint128_t)a * b; *high = (uint64_t) (x >> 64); return (uint64_t) x; } static uint64_t addcarryx_u64(uint8_t c, uint64_t a, uint64_t b, uint64_t *low) { uint128_t x = (uint128_t)a + b + c; *low = (uint64_t) x; return (uint64_t) (x>>64); } static uint64_t subborrow_u64(uint8_t c, uint64_t a, uint64_t b, uint64_t *low) { uint128_t t = ((uint128_t) b + c); uint128_t x = a-t; *low = (uint64_t) x; return (uint8_t) (x>>127); } static uint64_t cmovznz_u64(uint64_t t, uint64_t z, uint64_t nz) { t = -!!t; // all set if nonzero, 0 if 0 return (t&nz) | ((~t)&z); } #else static uint32_t mulx_u32(uint32_t a, uint32_t b, uint32_t *high) { uint64_t x = (uint64_t)a * b; *high = (uint32_t) (x >> 32); return (uint32_t) x; } static uint32_t addcarryx_u32(uint8_t c, uint32_t a, uint32_t b, uint32_t *low) { uint64_t x = (uint64_t)a + b + c; *low = (uint32_t) x; return (uint32_t) (x>>32); } static uint32_t subborrow_u32(uint8_t c, uint32_t a, uint32_t b, uint32_t *low) { uint64_t t = ((uint64_t) b + c); uint64_t x = a-t; *low = (uint32_t) x; return (uint8_t) (x>>63); } static uint32_t cmovznz_u32(uint32_t t, uint32_t z, uint32_t nz) { t = -!!t; // all set if nonzero, 0 if 0 return (t&nz) | ((~t)&z); } #endif // fiat-crypto generated code #if defined(BORINGSSL_NISTP256_64BIT) static void fe_add(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { { const uint64_t x8 = in1[3]; { const uint64_t x9 = in1[2]; { const uint64_t x7 = in1[1]; { const uint64_t x5 = in1[0]; { const uint64_t x14 = in2[3]; { const uint64_t x15 = in2[2]; { const uint64_t x13 = in2[1]; { const uint64_t x11 = in2[0]; { uint64_t x17; uint8_t x18 = addcarryx_u64(0x0, x5, x11, &x17); { uint64_t x20; uint8_t x21 = addcarryx_u64(x18, x7, x13, &x20); { uint64_t x23; uint8_t x24 = addcarryx_u64(x21, x9, x15, &x23); { uint64_t x26; uint8_t x27 = addcarryx_u64(x24, x8, x14, &x26); { uint64_t x29; uint8_t x30 = subborrow_u64(0x0, x17, 0xffffffffffffffffL, &x29); { uint64_t x32; uint8_t x33 = subborrow_u64(x30, x20, 0xffffffff, &x32); { uint64_t x35; uint8_t x36 = subborrow_u64(x33, x23, 0x0, &x35); { uint64_t x38; uint8_t x39 = subborrow_u64(x36, x26, 0xffffffff00000001L, &x38); { uint64_t _1; uint8_t x42 = subborrow_u64(x39, x27, 0x0, &_1); { uint64_t x43 = cmovznz_u64(x42, x38, x26); { uint64_t x44 = cmovznz_u64(x42, x35, x23); { uint64_t x45 = cmovznz_u64(x42, x32, x20); { uint64_t x46 = cmovznz_u64(x42, x29, x17); out[0] = x46; out[1] = x45; out[2] = x44; out[3] = x43; }}}}}}}}}}}}}}}}}}}}} } // fe_op sets out = -in static void fe_opp(uint64_t out[4], const uint64_t in1[4]) { const uint64_t x5 = in1[3]; const uint64_t x6 = in1[2]; const uint64_t x4 = in1[1]; const uint64_t x2 = in1[0]; uint64_t x8; uint8_t x9 = subborrow_u64(0x0, 0x0, x2, &x8); uint64_t x11; uint8_t x12 = subborrow_u64(x9, 0x0, x4, &x11); uint64_t x14; uint8_t x15 = subborrow_u64(x12, 0x0, x6, &x14); uint64_t x17; uint8_t x18 = subborrow_u64(x15, 0x0, x5, &x17); uint64_t x19 = (uint64_t)cmovznz_u64(x18, 0x0, 0xffffffffffffffffL); uint64_t x20 = (x19 & 0xffffffffffffffffL); uint64_t x22; uint8_t x23 = addcarryx_u64(0x0, x8, x20, &x22); uint64_t x24 = (x19 & 0xffffffff); uint64_t x26; uint8_t x27 = addcarryx_u64(x23, x11, x24, &x26); uint64_t x29; uint8_t x30 = addcarryx_u64(x27, x14, 0x0, &x29); uint64_t x31 = (x19 & 0xffffffff00000001L); uint64_t x33; addcarryx_u64(x30, x17, x31, &x33); out[0] = x22; out[1] = x26; out[2] = x29; out[3] = x33; } static void fe_mul(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { const uint64_t x8 = in1[3]; const uint64_t x9 = in1[2]; const uint64_t x7 = in1[1]; const uint64_t x5 = in1[0]; const uint64_t x14 = in2[3]; const uint64_t x15 = in2[2]; const uint64_t x13 = in2[1]; const uint64_t x11 = in2[0]; uint64_t x18; uint64_t x17 = mulx_u64(x5, x11, &x18); uint64_t x21; uint64_t x20 = mulx_u64(x5, x13, &x21); uint64_t x24; uint64_t x23 = mulx_u64(x5, x15, &x24); uint64_t x27; uint64_t x26 = mulx_u64(x5, x14, &x27); uint64_t x29; uint8_t x30 = addcarryx_u64(0x0, x18, x20, &x29); uint64_t x32; uint8_t x33 = addcarryx_u64(x30, x21, x23, &x32); uint64_t x35; uint8_t x36 = addcarryx_u64(x33, x24, x26, &x35); uint64_t x38; addcarryx_u64(0x0, x36, x27, &x38); uint64_t x42; uint64_t x41 = mulx_u64(x17, 0xffffffffffffffffL, &x42); uint64_t x45; uint64_t x44 = mulx_u64(x17, 0xffffffff, &x45); uint64_t x48; uint64_t x47 = mulx_u64(x17, 0xffffffff00000001L, &x48); uint64_t x50; uint8_t x51 = addcarryx_u64(0x0, x42, x44, &x50); uint64_t x53; uint8_t x54 = addcarryx_u64(x51, x45, 0x0, &x53); uint64_t x56; uint8_t x57 = addcarryx_u64(x54, 0x0, x47, &x56); uint64_t x59; addcarryx_u64(0x0, x57, x48, &x59); uint64_t _2; uint8_t x63 = addcarryx_u64(0x0, x17, x41, &_2); uint64_t x65; uint8_t x66 = addcarryx_u64(x63, x29, x50, &x65); uint64_t x68; uint8_t x69 = addcarryx_u64(x66, x32, x53, &x68); uint64_t x71; uint8_t x72 = addcarryx_u64(x69, x35, x56, &x71); uint64_t x74; uint8_t x75 = addcarryx_u64(x72, x38, x59, &x74); uint64_t x78; uint64_t x77 = mulx_u64(x7, x11, &x78); uint64_t x81; uint64_t x80 = mulx_u64(x7, x13, &x81); uint64_t x84; uint64_t x83 = mulx_u64(x7, x15, &x84); uint64_t x87; uint64_t x86 = mulx_u64(x7, x14, &x87); uint64_t x89; uint8_t x90 = addcarryx_u64(0x0, x78, x80, &x89); uint64_t x92; uint8_t x93 = addcarryx_u64(x90, x81, x83, &x92); uint64_t x95; uint8_t x96 = addcarryx_u64(x93, x84, x86, &x95); uint64_t x98; addcarryx_u64(0x0, x96, x87, &x98); uint64_t x101; uint8_t x102 = addcarryx_u64(0x0, x65, x77, &x101); uint64_t x104; uint8_t x105 = addcarryx_u64(x102, x68, x89, &x104); uint64_t x107; uint8_t x108 = addcarryx_u64(x105, x71, x92, &x107); uint64_t x110; uint8_t x111 = addcarryx_u64(x108, x74, x95, &x110); uint64_t x113; uint8_t x114 = addcarryx_u64(x111, x75, x98, &x113); uint64_t x117; uint64_t x116 = mulx_u64(x101, 0xffffffffffffffffL, &x117); uint64_t x120; uint64_t x119 = mulx_u64(x101, 0xffffffff, &x120); uint64_t x123; uint64_t x122 = mulx_u64(x101, 0xffffffff00000001L, &x123); uint64_t x125; uint8_t x126 = addcarryx_u64(0x0, x117, x119, &x125); uint64_t x128; uint8_t x129 = addcarryx_u64(x126, x120, 0x0, &x128); uint64_t x131; uint8_t x132 = addcarryx_u64(x129, 0x0, x122, &x131); uint64_t x134; addcarryx_u64(0x0, x132, x123, &x134); uint64_t _3; uint8_t x138 = addcarryx_u64(0x0, x101, x116, &_3); uint64_t x140; uint8_t x141 = addcarryx_u64(x138, x104, x125, &x140); uint64_t x143; uint8_t x144 = addcarryx_u64(x141, x107, x128, &x143); uint64_t x146; uint8_t x147 = addcarryx_u64(x144, x110, x131, &x146); uint64_t x149; uint8_t x150 = addcarryx_u64(x147, x113, x134, &x149); uint8_t x151 = (x150 + x114); uint64_t x154; uint64_t x153 = mulx_u64(x9, x11, &x154); uint64_t x157; uint64_t x156 = mulx_u64(x9, x13, &x157); uint64_t x160; uint64_t x159 = mulx_u64(x9, x15, &x160); uint64_t x163; uint64_t x162 = mulx_u64(x9, x14, &x163); uint64_t x165; uint8_t x166 = addcarryx_u64(0x0, x154, x156, &x165); uint64_t x168; uint8_t x169 = addcarryx_u64(x166, x157, x159, &x168); uint64_t x171; uint8_t x172 = addcarryx_u64(x169, x160, x162, &x171); uint64_t x174; addcarryx_u64(0x0, x172, x163, &x174); uint64_t x177; uint8_t x178 = addcarryx_u64(0x0, x140, x153, &x177); uint64_t x180; uint8_t x181 = addcarryx_u64(x178, x143, x165, &x180); uint64_t x183; uint8_t x184 = addcarryx_u64(x181, x146, x168, &x183); uint64_t x186; uint8_t x187 = addcarryx_u64(x184, x149, x171, &x186); uint64_t x189; uint8_t x190 = addcarryx_u64(x187, x151, x174, &x189); uint64_t x193; uint64_t x192 = mulx_u64(x177, 0xffffffffffffffffL, &x193); uint64_t x196; uint64_t x195 = mulx_u64(x177, 0xffffffff, &x196); uint64_t x199; uint64_t x198 = mulx_u64(x177, 0xffffffff00000001L, &x199); uint64_t x201; uint8_t x202 = addcarryx_u64(0x0, x193, x195, &x201); uint64_t x204; uint8_t x205 = addcarryx_u64(x202, x196, 0x0, &x204); uint64_t x207; uint8_t x208 = addcarryx_u64(x205, 0x0, x198, &x207); uint64_t x210; addcarryx_u64(0x0, x208, x199, &x210); uint64_t _4; uint8_t x214 = addcarryx_u64(0x0, x177, x192, &_4); uint64_t x216; uint8_t x217 = addcarryx_u64(x214, x180, x201, &x216); uint64_t x219; uint8_t x220 = addcarryx_u64(x217, x183, x204, &x219); uint64_t x222; uint8_t x223 = addcarryx_u64(x220, x186, x207, &x222); uint64_t x225; uint8_t x226 = addcarryx_u64(x223, x189, x210, &x225); uint8_t x227 = (x226 + x190); uint64_t x230; uint64_t x229 = mulx_u64(x8, x11, &x230); uint64_t x233; uint64_t x232 = mulx_u64(x8, x13, &x233); uint64_t x236; uint64_t x235 = mulx_u64(x8, x15, &x236); uint64_t x239; uint64_t x238 = mulx_u64(x8, x14, &x239); uint64_t x241; uint8_t x242 = addcarryx_u64(0x0, x230, x232, &x241); uint64_t x244; uint8_t x245 = addcarryx_u64(x242, x233, x235, &x244); uint64_t x247; uint8_t x248 = addcarryx_u64(x245, x236, x238, &x247); uint64_t x250; addcarryx_u64(0x0, x248, x239, &x250); uint64_t x253; uint8_t x254 = addcarryx_u64(0x0, x216, x229, &x253); uint64_t x256; uint8_t x257 = addcarryx_u64(x254, x219, x241, &x256); uint64_t x259; uint8_t x260 = addcarryx_u64(x257, x222, x244, &x259); uint64_t x262; uint8_t x263 = addcarryx_u64(x260, x225, x247, &x262); uint64_t x265; uint8_t x266 = addcarryx_u64(x263, x227, x250, &x265); uint64_t x269; uint64_t x268 = mulx_u64(x253, 0xffffffffffffffffL, &x269); uint64_t x272; uint64_t x271 = mulx_u64(x253, 0xffffffff, &x272); uint64_t x275; uint64_t x274 = mulx_u64(x253, 0xffffffff00000001L, &x275); uint64_t x277; uint8_t x278 = addcarryx_u64(0x0, x269, x271, &x277); uint64_t x280; uint8_t x281 = addcarryx_u64(x278, x272, 0x0, &x280); uint64_t x283; uint8_t x284 = addcarryx_u64(x281, 0x0, x274, &x283); uint64_t x286; addcarryx_u64(0x0, x284, x275, &x286); uint64_t _5; uint8_t x290 = addcarryx_u64(0x0, x253, x268, &_5); uint64_t x292; uint8_t x293 = addcarryx_u64(x290, x256, x277, &x292); uint64_t x295; uint8_t x296 = addcarryx_u64(x293, x259, x280, &x295); uint64_t x298; uint8_t x299 = addcarryx_u64(x296, x262, x283, &x298); uint64_t x301; uint8_t x302 = addcarryx_u64(x299, x265, x286, &x301); uint8_t x303 = (x302 + x266); uint64_t x305; uint8_t x306 = subborrow_u64(0x0, x292, 0xffffffffffffffffL, &x305); uint64_t x308; uint8_t x309 = subborrow_u64(x306, x295, 0xffffffff, &x308); uint64_t x311; uint8_t x312 = subborrow_u64(x309, x298, 0x0, &x311); uint64_t x314; uint8_t x315 = subborrow_u64(x312, x301, 0xffffffff00000001L, &x314); uint64_t _6; uint8_t x318 = subborrow_u64(x315, x303, 0x0, &_6); uint64_t x319 = cmovznz_u64(x318, x314, x301); uint64_t x320 = cmovznz_u64(x318, x311, x298); uint64_t x321 = cmovznz_u64(x318, x308, x295); uint64_t x322 = cmovznz_u64(x318, x305, x292); out[0] = x322; out[1] = x321; out[2] = x320; out[3] = x319; } static void fe_sub(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { const uint64_t x8 = in1[3]; const uint64_t x9 = in1[2]; const uint64_t x7 = in1[1]; const uint64_t x5 = in1[0]; const uint64_t x14 = in2[3]; const uint64_t x15 = in2[2]; const uint64_t x13 = in2[1]; const uint64_t x11 = in2[0]; uint64_t x17; uint8_t x18 = subborrow_u64(0x0, x5, x11, &x17); uint64_t x20; uint8_t x21 = subborrow_u64(x18, x7, x13, &x20); uint64_t x23; uint8_t x24 = subborrow_u64(x21, x9, x15, &x23); uint64_t x26; uint8_t x27 = subborrow_u64(x24, x8, x14, &x26); uint64_t x28 = (uint64_t)cmovznz_u64(x27, 0x0, 0xffffffffffffffffL); uint64_t x29 = (x28 & 0xffffffffffffffffL); uint64_t x31; uint8_t x32 = addcarryx_u64(0x0, x17, x29, &x31); uint64_t x33 = (x28 & 0xffffffff); uint64_t x35; uint8_t x36 = addcarryx_u64(x32, x20, x33, &x35); uint64_t x38; uint8_t x39 = addcarryx_u64(x36, x23, 0x0, &x38); uint64_t x40 = (x28 & 0xffffffff00000001L); uint64_t x42; addcarryx_u64(x39, x26, x40, &x42); out[0] = x31; out[1] = x35; out[2] = x38; out[3] = x42; } #else // 64BIT, else 32BIT static void fe_add(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { const uint32_t x16 = in1[7]; const uint32_t x17 = in1[6]; const uint32_t x15 = in1[5]; const uint32_t x13 = in1[4]; const uint32_t x11 = in1[3]; const uint32_t x9 = in1[2]; const uint32_t x7 = in1[1]; const uint32_t x5 = in1[0]; const uint32_t x30 = in2[7]; const uint32_t x31 = in2[6]; const uint32_t x29 = in2[5]; const uint32_t x27 = in2[4]; const uint32_t x25 = in2[3]; const uint32_t x23 = in2[2]; const uint32_t x21 = in2[1]; const uint32_t x19 = in2[0]; uint32_t x33; uint8_t x34 = addcarryx_u32(0x0, x5, x19, &x33); uint32_t x36; uint8_t x37 = addcarryx_u32(x34, x7, x21, &x36); uint32_t x39; uint8_t x40 = addcarryx_u32(x37, x9, x23, &x39); uint32_t x42; uint8_t x43 = addcarryx_u32(x40, x11, x25, &x42); uint32_t x45; uint8_t x46 = addcarryx_u32(x43, x13, x27, &x45); uint32_t x48; uint8_t x49 = addcarryx_u32(x46, x15, x29, &x48); uint32_t x51; uint8_t x52 = addcarryx_u32(x49, x17, x31, &x51); uint32_t x54; uint8_t x55 = addcarryx_u32(x52, x16, x30, &x54); uint32_t x57; uint8_t x58 = subborrow_u32(0x0, x33, 0xffffffff, &x57); uint32_t x60; uint8_t x61 = subborrow_u32(x58, x36, 0xffffffff, &x60); uint32_t x63; uint8_t x64 = subborrow_u32(x61, x39, 0xffffffff, &x63); uint32_t x66; uint8_t x67 = subborrow_u32(x64, x42, 0x0, &x66); uint32_t x69; uint8_t x70 = subborrow_u32(x67, x45, 0x0, &x69); uint32_t x72; uint8_t x73 = subborrow_u32(x70, x48, 0x0, &x72); uint32_t x75; uint8_t x76 = subborrow_u32(x73, x51, 0x1, &x75); uint32_t x78; uint8_t x79 = subborrow_u32(x76, x54, 0xffffffff, &x78); uint32_t _; uint8_t x82 = subborrow_u32(x79, x55, 0x0, &_); uint32_t x83 = cmovznz_u32(x82, x78, x54); uint32_t x84 = cmovznz_u32(x82, x75, x51); uint32_t x85 = cmovznz_u32(x82, x72, x48); uint32_t x86 = cmovznz_u32(x82, x69, x45); uint32_t x87 = cmovznz_u32(x82, x66, x42); uint32_t x88 = cmovznz_u32(x82, x63, x39); uint32_t x89 = cmovznz_u32(x82, x60, x36); uint32_t x90 = cmovznz_u32(x82, x57, x33); out[0] = x90; out[1] = x89; out[2] = x88; out[3] = x87; out[4] = x86; out[5] = x85; out[6] = x84; out[7] = x83; } static void fe_mul(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { const uint32_t x16 = in1[7]; const uint32_t x17 = in1[6]; const uint32_t x15 = in1[5]; const uint32_t x13 = in1[4]; const uint32_t x11 = in1[3]; const uint32_t x9 = in1[2]; const uint32_t x7 = in1[1]; const uint32_t x5 = in1[0]; const uint32_t x30 = in2[7]; const uint32_t x31 = in2[6]; const uint32_t x29 = in2[5]; const uint32_t x27 = in2[4]; const uint32_t x25 = in2[3]; const uint32_t x23 = in2[2]; const uint32_t x21 = in2[1]; const uint32_t x19 = in2[0]; uint32_t x34; uint32_t x33 = mulx_u32(x5, x19, &x34); uint32_t x37; uint32_t x36 = mulx_u32(x5, x21, &x37); uint32_t x40; uint32_t x39 = mulx_u32(x5, x23, &x40); uint32_t x43; uint32_t x42 = mulx_u32(x5, x25, &x43); uint32_t x46; uint32_t x45 = mulx_u32(x5, x27, &x46); uint32_t x49; uint32_t x48 = mulx_u32(x5, x29, &x49); uint32_t x52; uint32_t x51 = mulx_u32(x5, x31, &x52); uint32_t x55; uint32_t x54 = mulx_u32(x5, x30, &x55); uint32_t x57; uint8_t x58 = addcarryx_u32(0x0, x34, x36, &x57); uint32_t x60; uint8_t x61 = addcarryx_u32(x58, x37, x39, &x60); uint32_t x63; uint8_t x64 = addcarryx_u32(x61, x40, x42, &x63); uint32_t x66; uint8_t x67 = addcarryx_u32(x64, x43, x45, &x66); uint32_t x69; uint8_t x70 = addcarryx_u32(x67, x46, x48, &x69); uint32_t x72; uint8_t x73 = addcarryx_u32(x70, x49, x51, &x72); uint32_t x75; uint8_t x76 = addcarryx_u32(x73, x52, x54, &x75); uint32_t x78; addcarryx_u32(0x0, x76, x55, &x78); uint32_t x82; uint32_t x81 = mulx_u32(x33, 0xffffffff, &x82); uint32_t x85; uint32_t x84 = mulx_u32(x33, 0xffffffff, &x85); uint32_t x88; uint32_t x87 = mulx_u32(x33, 0xffffffff, &x88); uint32_t x91; uint32_t x90 = mulx_u32(x33, 0xffffffff, &x91); uint32_t x93; uint8_t x94 = addcarryx_u32(0x0, x82, x84, &x93); uint32_t x96; uint8_t x97 = addcarryx_u32(x94, x85, x87, &x96); uint32_t x99; uint8_t x100 = addcarryx_u32(x97, x88, 0x0, &x99); uint8_t x101 = (0x0 + 0x0); uint32_t _1; uint8_t x104 = addcarryx_u32(0x0, x33, x81, &_1); uint32_t x106; uint8_t x107 = addcarryx_u32(x104, x57, x93, &x106); uint32_t x109; uint8_t x110 = addcarryx_u32(x107, x60, x96, &x109); uint32_t x112; uint8_t x113 = addcarryx_u32(x110, x63, x99, &x112); uint32_t x115; uint8_t x116 = addcarryx_u32(x113, x66, x100, &x115); uint32_t x118; uint8_t x119 = addcarryx_u32(x116, x69, x101, &x118); uint32_t x121; uint8_t x122 = addcarryx_u32(x119, x72, x33, &x121); uint32_t x124; uint8_t x125 = addcarryx_u32(x122, x75, x90, &x124); uint32_t x127; uint8_t x128 = addcarryx_u32(x125, x78, x91, &x127); uint8_t x129 = (x128 + 0x0); uint32_t x132; uint32_t x131 = mulx_u32(x7, x19, &x132); uint32_t x135; uint32_t x134 = mulx_u32(x7, x21, &x135); uint32_t x138; uint32_t x137 = mulx_u32(x7, x23, &x138); uint32_t x141; uint32_t x140 = mulx_u32(x7, x25, &x141); uint32_t x144; uint32_t x143 = mulx_u32(x7, x27, &x144); uint32_t x147; uint32_t x146 = mulx_u32(x7, x29, &x147); uint32_t x150; uint32_t x149 = mulx_u32(x7, x31, &x150); uint32_t x153; uint32_t x152 = mulx_u32(x7, x30, &x153); uint32_t x155; uint8_t x156 = addcarryx_u32(0x0, x132, x134, &x155); uint32_t x158; uint8_t x159 = addcarryx_u32(x156, x135, x137, &x158); uint32_t x161; uint8_t x162 = addcarryx_u32(x159, x138, x140, &x161); uint32_t x164; uint8_t x165 = addcarryx_u32(x162, x141, x143, &x164); uint32_t x167; uint8_t x168 = addcarryx_u32(x165, x144, x146, &x167); uint32_t x170; uint8_t x171 = addcarryx_u32(x168, x147, x149, &x170); uint32_t x173; uint8_t x174 = addcarryx_u32(x171, x150, x152, &x173); uint32_t x176; addcarryx_u32(0x0, x174, x153, &x176); uint32_t x179; uint8_t x180 = addcarryx_u32(0x0, x106, x131, &x179); uint32_t x182; uint8_t x183 = addcarryx_u32(x180, x109, x155, &x182); uint32_t x185; uint8_t x186 = addcarryx_u32(x183, x112, x158, &x185); uint32_t x188; uint8_t x189 = addcarryx_u32(x186, x115, x161, &x188); uint32_t x191; uint8_t x192 = addcarryx_u32(x189, x118, x164, &x191); uint32_t x194; uint8_t x195 = addcarryx_u32(x192, x121, x167, &x194); uint32_t x197; uint8_t x198 = addcarryx_u32(x195, x124, x170, &x197); uint32_t x200; uint8_t x201 = addcarryx_u32(x198, x127, x173, &x200); uint32_t x203; uint8_t x204 = addcarryx_u32(x201, x129, x176, &x203); uint32_t x207; uint32_t x206 = mulx_u32(x179, 0xffffffff, &x207); uint32_t x210; uint32_t x209 = mulx_u32(x179, 0xffffffff, &x210); uint32_t x213; uint32_t x212 = mulx_u32(x179, 0xffffffff, &x213); uint32_t x216; uint32_t x215 = mulx_u32(x179, 0xffffffff, &x216); uint32_t x218; uint8_t x219 = addcarryx_u32(0x0, x207, x209, &x218); uint32_t x221; uint8_t x222 = addcarryx_u32(x219, x210, x212, &x221); uint32_t x224; uint8_t x225 = addcarryx_u32(x222, x213, 0x0, &x224); uint8_t x226 = (0x0 + 0x0); uint32_t _2; uint8_t x229 = addcarryx_u32(0x0, x179, x206, &_2); uint32_t x231; uint8_t x232 = addcarryx_u32(x229, x182, x218, &x231); uint32_t x234; uint8_t x235 = addcarryx_u32(x232, x185, x221, &x234); uint32_t x237; uint8_t x238 = addcarryx_u32(x235, x188, x224, &x237); uint32_t x240; uint8_t x241 = addcarryx_u32(x238, x191, x225, &x240); uint32_t x243; uint8_t x244 = addcarryx_u32(x241, x194, x226, &x243); uint32_t x246; uint8_t x247 = addcarryx_u32(x244, x197, x179, &x246); uint32_t x249; uint8_t x250 = addcarryx_u32(x247, x200, x215, &x249); uint32_t x252; uint8_t x253 = addcarryx_u32(x250, x203, x216, &x252); uint8_t x254 = (x253 + x204); uint32_t x257; uint32_t x256 = mulx_u32(x9, x19, &x257); uint32_t x260; uint32_t x259 = mulx_u32(x9, x21, &x260); uint32_t x263; uint32_t x262 = mulx_u32(x9, x23, &x263); uint32_t x266; uint32_t x265 = mulx_u32(x9, x25, &x266); uint32_t x269; uint32_t x268 = mulx_u32(x9, x27, &x269); uint32_t x272; uint32_t x271 = mulx_u32(x9, x29, &x272); uint32_t x275; uint32_t x274 = mulx_u32(x9, x31, &x275); uint32_t x278; uint32_t x277 = mulx_u32(x9, x30, &x278); uint32_t x280; uint8_t x281 = addcarryx_u32(0x0, x257, x259, &x280); uint32_t x283; uint8_t x284 = addcarryx_u32(x281, x260, x262, &x283); uint32_t x286; uint8_t x287 = addcarryx_u32(x284, x263, x265, &x286); uint32_t x289; uint8_t x290 = addcarryx_u32(x287, x266, x268, &x289); uint32_t x292; uint8_t x293 = addcarryx_u32(x290, x269, x271, &x292); uint32_t x295; uint8_t x296 = addcarryx_u32(x293, x272, x274, &x295); uint32_t x298; uint8_t x299 = addcarryx_u32(x296, x275, x277, &x298); uint32_t x301; addcarryx_u32(0x0, x299, x278, &x301); uint32_t x304; uint8_t x305 = addcarryx_u32(0x0, x231, x256, &x304); uint32_t x307; uint8_t x308 = addcarryx_u32(x305, x234, x280, &x307); uint32_t x310; uint8_t x311 = addcarryx_u32(x308, x237, x283, &x310); uint32_t x313; uint8_t x314 = addcarryx_u32(x311, x240, x286, &x313); uint32_t x316; uint8_t x317 = addcarryx_u32(x314, x243, x289, &x316); uint32_t x319; uint8_t x320 = addcarryx_u32(x317, x246, x292, &x319); uint32_t x322; uint8_t x323 = addcarryx_u32(x320, x249, x295, &x322); uint32_t x325; uint8_t x326 = addcarryx_u32(x323, x252, x298, &x325); uint32_t x328; uint8_t x329 = addcarryx_u32(x326, x254, x301, &x328); uint32_t x332; uint32_t x331 = mulx_u32(x304, 0xffffffff, &x332); uint32_t x335; uint32_t x334 = mulx_u32(x304, 0xffffffff, &x335); uint32_t x338; uint32_t x337 = mulx_u32(x304, 0xffffffff, &x338); uint32_t x341; uint32_t x340 = mulx_u32(x304, 0xffffffff, &x341); uint32_t x343; uint8_t x344 = addcarryx_u32(0x0, x332, x334, &x343); uint32_t x346; uint8_t x347 = addcarryx_u32(x344, x335, x337, &x346); uint32_t x349; uint8_t x350 = addcarryx_u32(x347, x338, 0x0, &x349); uint8_t x351 = (0x0 + 0x0); uint32_t _3; uint8_t x354 = addcarryx_u32(0x0, x304, x331, &_3); uint32_t x356; uint8_t x357 = addcarryx_u32(x354, x307, x343, &x356); uint32_t x359; uint8_t x360 = addcarryx_u32(x357, x310, x346, &x359); uint32_t x362; uint8_t x363 = addcarryx_u32(x360, x313, x349, &x362); uint32_t x365; uint8_t x366 = addcarryx_u32(x363, x316, x350, &x365); uint32_t x368; uint8_t x369 = addcarryx_u32(x366, x319, x351, &x368); uint32_t x371; uint8_t x372 = addcarryx_u32(x369, x322, x304, &x371); uint32_t x374; uint8_t x375 = addcarryx_u32(x372, x325, x340, &x374); uint32_t x377; uint8_t x378 = addcarryx_u32(x375, x328, x341, &x377); uint8_t x379 = (x378 + x329); uint32_t x382; uint32_t x381 = mulx_u32(x11, x19, &x382); uint32_t x385; uint32_t x384 = mulx_u32(x11, x21, &x385); uint32_t x388; uint32_t x387 = mulx_u32(x11, x23, &x388); uint32_t x391; uint32_t x390 = mulx_u32(x11, x25, &x391); uint32_t x394; uint32_t x393 = mulx_u32(x11, x27, &x394); uint32_t x397; uint32_t x396 = mulx_u32(x11, x29, &x397); uint32_t x400; uint32_t x399 = mulx_u32(x11, x31, &x400); uint32_t x403; uint32_t x402 = mulx_u32(x11, x30, &x403); uint32_t x405; uint8_t x406 = addcarryx_u32(0x0, x382, x384, &x405); uint32_t x408; uint8_t x409 = addcarryx_u32(x406, x385, x387, &x408); uint32_t x411; uint8_t x412 = addcarryx_u32(x409, x388, x390, &x411); uint32_t x414; uint8_t x415 = addcarryx_u32(x412, x391, x393, &x414); uint32_t x417; uint8_t x418 = addcarryx_u32(x415, x394, x396, &x417); uint32_t x420; uint8_t x421 = addcarryx_u32(x418, x397, x399, &x420); uint32_t x423; uint8_t x424 = addcarryx_u32(x421, x400, x402, &x423); uint32_t x426; addcarryx_u32(0x0, x424, x403, &x426); uint32_t x429; uint8_t x430 = addcarryx_u32(0x0, x356, x381, &x429); uint32_t x432; uint8_t x433 = addcarryx_u32(x430, x359, x405, &x432); uint32_t x435; uint8_t x436 = addcarryx_u32(x433, x362, x408, &x435); uint32_t x438; uint8_t x439 = addcarryx_u32(x436, x365, x411, &x438); uint32_t x441; uint8_t x442 = addcarryx_u32(x439, x368, x414, &x441); uint32_t x444; uint8_t x445 = addcarryx_u32(x442, x371, x417, &x444); uint32_t x447; uint8_t x448 = addcarryx_u32(x445, x374, x420, &x447); uint32_t x450; uint8_t x451 = addcarryx_u32(x448, x377, x423, &x450); uint32_t x453; uint8_t x454 = addcarryx_u32(x451, x379, x426, &x453); uint32_t x457; uint32_t x456 = mulx_u32(x429, 0xffffffff, &x457); uint32_t x460; uint32_t x459 = mulx_u32(x429, 0xffffffff, &x460); uint32_t x463; uint32_t x462 = mulx_u32(x429, 0xffffffff, &x463); uint32_t x466; uint32_t x465 = mulx_u32(x429, 0xffffffff, &x466); uint32_t x468; uint8_t x469 = addcarryx_u32(0x0, x457, x459, &x468); uint32_t x471; uint8_t x472 = addcarryx_u32(x469, x460, x462, &x471); uint32_t x474; uint8_t x475 = addcarryx_u32(x472, x463, 0x0, &x474); uint8_t x476 = (0x0 + 0x0); uint32_t _4; uint8_t x479 = addcarryx_u32(0x0, x429, x456, &_4); uint32_t x481; uint8_t x482 = addcarryx_u32(x479, x432, x468, &x481); uint32_t x484; uint8_t x485 = addcarryx_u32(x482, x435, x471, &x484); uint32_t x487; uint8_t x488 = addcarryx_u32(x485, x438, x474, &x487); uint32_t x490; uint8_t x491 = addcarryx_u32(x488, x441, x475, &x490); uint32_t x493; uint8_t x494 = addcarryx_u32(x491, x444, x476, &x493); uint32_t x496; uint8_t x497 = addcarryx_u32(x494, x447, x429, &x496); uint32_t x499; uint8_t x500 = addcarryx_u32(x497, x450, x465, &x499); uint32_t x502; uint8_t x503 = addcarryx_u32(x500, x453, x466, &x502); uint8_t x504 = (x503 + x454); uint32_t x507; uint32_t x506 = mulx_u32(x13, x19, &x507); uint32_t x510; uint32_t x509 = mulx_u32(x13, x21, &x510); uint32_t x513; uint32_t x512 = mulx_u32(x13, x23, &x513); uint32_t x516; uint32_t x515 = mulx_u32(x13, x25, &x516); uint32_t x519; uint32_t x518 = mulx_u32(x13, x27, &x519); uint32_t x522; uint32_t x521 = mulx_u32(x13, x29, &x522); uint32_t x525; uint32_t x524 = mulx_u32(x13, x31, &x525); uint32_t x528; uint32_t x527 = mulx_u32(x13, x30, &x528); uint32_t x530; uint8_t x531 = addcarryx_u32(0x0, x507, x509, &x530); uint32_t x533; uint8_t x534 = addcarryx_u32(x531, x510, x512, &x533); uint32_t x536; uint8_t x537 = addcarryx_u32(x534, x513, x515, &x536); uint32_t x539; uint8_t x540 = addcarryx_u32(x537, x516, x518, &x539); uint32_t x542; uint8_t x543 = addcarryx_u32(x540, x519, x521, &x542); uint32_t x545; uint8_t x546 = addcarryx_u32(x543, x522, x524, &x545); uint32_t x548; uint8_t x549 = addcarryx_u32(x546, x525, x527, &x548); uint32_t x551; addcarryx_u32(0x0, x549, x528, &x551); uint32_t x554; uint8_t x555 = addcarryx_u32(0x0, x481, x506, &x554); uint32_t x557; uint8_t x558 = addcarryx_u32(x555, x484, x530, &x557); uint32_t x560; uint8_t x561 = addcarryx_u32(x558, x487, x533, &x560); uint32_t x563; uint8_t x564 = addcarryx_u32(x561, x490, x536, &x563); uint32_t x566; uint8_t x567 = addcarryx_u32(x564, x493, x539, &x566); uint32_t x569; uint8_t x570 = addcarryx_u32(x567, x496, x542, &x569); uint32_t x572; uint8_t x573 = addcarryx_u32(x570, x499, x545, &x572); uint32_t x575; uint8_t x576 = addcarryx_u32(x573, x502, x548, &x575); uint32_t x578; uint8_t x579 = addcarryx_u32(x576, x504, x551, &x578); uint32_t x582; uint32_t x581 = mulx_u32(x554, 0xffffffff, &x582); uint32_t x585; uint32_t x584 = mulx_u32(x554, 0xffffffff, &x585); uint32_t x588; uint32_t x587 = mulx_u32(x554, 0xffffffff, &x588); uint32_t x591; uint32_t x590 = mulx_u32(x554, 0xffffffff, &x591); uint32_t x593; uint8_t x594 = addcarryx_u32(0x0, x582, x584, &x593); uint32_t x596; uint8_t x597 = addcarryx_u32(x594, x585, x587, &x596); uint32_t x599; uint8_t x600 = addcarryx_u32(x597, x588, 0x0, &x599); uint8_t x601 = (0x0 + 0x0); uint32_t _5; uint8_t x604 = addcarryx_u32(0x0, x554, x581, &_5); uint32_t x606; uint8_t x607 = addcarryx_u32(x604, x557, x593, &x606); uint32_t x609; uint8_t x610 = addcarryx_u32(x607, x560, x596, &x609); uint32_t x612; uint8_t x613 = addcarryx_u32(x610, x563, x599, &x612); uint32_t x615; uint8_t x616 = addcarryx_u32(x613, x566, x600, &x615); uint32_t x618; uint8_t x619 = addcarryx_u32(x616, x569, x601, &x618); uint32_t x621; uint8_t x622 = addcarryx_u32(x619, x572, x554, &x621); uint32_t x624; uint8_t x625 = addcarryx_u32(x622, x575, x590, &x624); uint32_t x627; uint8_t x628 = addcarryx_u32(x625, x578, x591, &x627); uint8_t x629 = (x628 + x579); uint32_t x632; uint32_t x631 = mulx_u32(x15, x19, &x632); uint32_t x635; uint32_t x634 = mulx_u32(x15, x21, &x635); uint32_t x638; uint32_t x637 = mulx_u32(x15, x23, &x638); uint32_t x641; uint32_t x640 = mulx_u32(x15, x25, &x641); uint32_t x644; uint32_t x643 = mulx_u32(x15, x27, &x644); uint32_t x647; uint32_t x646 = mulx_u32(x15, x29, &x647); uint32_t x650; uint32_t x649 = mulx_u32(x15, x31, &x650); uint32_t x653; uint32_t x652 = mulx_u32(x15, x30, &x653); uint32_t x655; uint8_t x656 = addcarryx_u32(0x0, x632, x634, &x655); uint32_t x658; uint8_t x659 = addcarryx_u32(x656, x635, x637, &x658); uint32_t x661; uint8_t x662 = addcarryx_u32(x659, x638, x640, &x661); uint32_t x664; uint8_t x665 = addcarryx_u32(x662, x641, x643, &x664); uint32_t x667; uint8_t x668 = addcarryx_u32(x665, x644, x646, &x667); uint32_t x670; uint8_t x671 = addcarryx_u32(x668, x647, x649, &x670); uint32_t x673; uint8_t x674 = addcarryx_u32(x671, x650, x652, &x673); uint32_t x676; addcarryx_u32(0x0, x674, x653, &x676); uint32_t x679; uint8_t x680 = addcarryx_u32(0x0, x606, x631, &x679); uint32_t x682; uint8_t x683 = addcarryx_u32(x680, x609, x655, &x682); uint32_t x685; uint8_t x686 = addcarryx_u32(x683, x612, x658, &x685); uint32_t x688; uint8_t x689 = addcarryx_u32(x686, x615, x661, &x688); uint32_t x691; uint8_t x692 = addcarryx_u32(x689, x618, x664, &x691); uint32_t x694; uint8_t x695 = addcarryx_u32(x692, x621, x667, &x694); uint32_t x697; uint8_t x698 = addcarryx_u32(x695, x624, x670, &x697); uint32_t x700; uint8_t x701 = addcarryx_u32(x698, x627, x673, &x700); uint32_t x703; uint8_t x704 = addcarryx_u32(x701, x629, x676, &x703); uint32_t x707; uint32_t x706 = mulx_u32(x679, 0xffffffff, &x707); uint32_t x710; uint32_t x709 = mulx_u32(x679, 0xffffffff, &x710); uint32_t x713; uint32_t x712 = mulx_u32(x679, 0xffffffff, &x713); uint32_t x716; uint32_t x715 = mulx_u32(x679, 0xffffffff, &x716); uint32_t x718; uint8_t x719 = addcarryx_u32(0x0, x707, x709, &x718); uint32_t x721; uint8_t x722 = addcarryx_u32(x719, x710, x712, &x721); uint32_t x724; uint8_t x725 = addcarryx_u32(x722, x713, 0x0, &x724); uint8_t x726 = (0x0 + 0x0); uint32_t _6; uint8_t x729 = addcarryx_u32(0x0, x679, x706, &_6); uint32_t x731; uint8_t x732 = addcarryx_u32(x729, x682, x718, &x731); uint32_t x734; uint8_t x735 = addcarryx_u32(x732, x685, x721, &x734); uint32_t x737; uint8_t x738 = addcarryx_u32(x735, x688, x724, &x737); uint32_t x740; uint8_t x741 = addcarryx_u32(x738, x691, x725, &x740); uint32_t x743; uint8_t x744 = addcarryx_u32(x741, x694, x726, &x743); uint32_t x746; uint8_t x747 = addcarryx_u32(x744, x697, x679, &x746); uint32_t x749; uint8_t x750 = addcarryx_u32(x747, x700, x715, &x749); uint32_t x752; uint8_t x753 = addcarryx_u32(x750, x703, x716, &x752); uint8_t x754 = (x753 + x704); uint32_t x757; uint32_t x756 = mulx_u32(x17, x19, &x757); uint32_t x760; uint32_t x759 = mulx_u32(x17, x21, &x760); uint32_t x763; uint32_t x762 = mulx_u32(x17, x23, &x763); uint32_t x766; uint32_t x765 = mulx_u32(x17, x25, &x766); uint32_t x769; uint32_t x768 = mulx_u32(x17, x27, &x769); uint32_t x772; uint32_t x771 = mulx_u32(x17, x29, &x772); uint32_t x775; uint32_t x774 = mulx_u32(x17, x31, &x775); uint32_t x778; uint32_t x777 = mulx_u32(x17, x30, &x778); uint32_t x780; uint8_t x781 = addcarryx_u32(0x0, x757, x759, &x780); uint32_t x783; uint8_t x784 = addcarryx_u32(x781, x760, x762, &x783); uint32_t x786; uint8_t x787 = addcarryx_u32(x784, x763, x765, &x786); uint32_t x789; uint8_t x790 = addcarryx_u32(x787, x766, x768, &x789); uint32_t x792; uint8_t x793 = addcarryx_u32(x790, x769, x771, &x792); uint32_t x795; uint8_t x796 = addcarryx_u32(x793, x772, x774, &x795); uint32_t x798; uint8_t x799 = addcarryx_u32(x796, x775, x777, &x798); uint32_t x801; addcarryx_u32(0x0, x799, x778, &x801); uint32_t x804; uint8_t x805 = addcarryx_u32(0x0, x731, x756, &x804); uint32_t x807; uint8_t x808 = addcarryx_u32(x805, x734, x780, &x807); uint32_t x810; uint8_t x811 = addcarryx_u32(x808, x737, x783, &x810); uint32_t x813; uint8_t x814 = addcarryx_u32(x811, x740, x786, &x813); uint32_t x816; uint8_t x817 = addcarryx_u32(x814, x743, x789, &x816); uint32_t x819; uint8_t x820 = addcarryx_u32(x817, x746, x792, &x819); uint32_t x822; uint8_t x823 = addcarryx_u32(x820, x749, x795, &x822); uint32_t x825; uint8_t x826 = addcarryx_u32(x823, x752, x798, &x825); uint32_t x828; uint8_t x829 = addcarryx_u32(x826, x754, x801, &x828); uint32_t x832; uint32_t x831 = mulx_u32(x804, 0xffffffff, &x832); uint32_t x835; uint32_t x834 = mulx_u32(x804, 0xffffffff, &x835); uint32_t x838; uint32_t x837 = mulx_u32(x804, 0xffffffff, &x838); uint32_t x841; uint32_t x840 = mulx_u32(x804, 0xffffffff, &x841); uint32_t x843; uint8_t x844 = addcarryx_u32(0x0, x832, x834, &x843); uint32_t x846; uint8_t x847 = addcarryx_u32(x844, x835, x837, &x846); uint32_t x849; uint8_t x850 = addcarryx_u32(x847, x838, 0x0, &x849); uint8_t x851 = (0x0 + 0x0); uint32_t _7; uint8_t x854 = addcarryx_u32(0x0, x804, x831, &_7); uint32_t x856; uint8_t x857 = addcarryx_u32(x854, x807, x843, &x856); uint32_t x859; uint8_t x860 = addcarryx_u32(x857, x810, x846, &x859); uint32_t x862; uint8_t x863 = addcarryx_u32(x860, x813, x849, &x862); uint32_t x865; uint8_t x866 = addcarryx_u32(x863, x816, x850, &x865); uint32_t x868; uint8_t x869 = addcarryx_u32(x866, x819, x851, &x868); uint32_t x871; uint8_t x872 = addcarryx_u32(x869, x822, x804, &x871); uint32_t x874; uint8_t x875 = addcarryx_u32(x872, x825, x840, &x874); uint32_t x877; uint8_t x878 = addcarryx_u32(x875, x828, x841, &x877); uint8_t x879 = (x878 + x829); uint32_t x882; uint32_t x881 = mulx_u32(x16, x19, &x882); uint32_t x885; uint32_t x884 = mulx_u32(x16, x21, &x885); uint32_t x888; uint32_t x887 = mulx_u32(x16, x23, &x888); uint32_t x891; uint32_t x890 = mulx_u32(x16, x25, &x891); uint32_t x894; uint32_t x893 = mulx_u32(x16, x27, &x894); uint32_t x897; uint32_t x896 = mulx_u32(x16, x29, &x897); uint32_t x900; uint32_t x899 = mulx_u32(x16, x31, &x900); uint32_t x903; uint32_t x902 = mulx_u32(x16, x30, &x903); uint32_t x905; uint8_t x906 = addcarryx_u32(0x0, x882, x884, &x905); uint32_t x908; uint8_t x909 = addcarryx_u32(x906, x885, x887, &x908); uint32_t x911; uint8_t x912 = addcarryx_u32(x909, x888, x890, &x911); uint32_t x914; uint8_t x915 = addcarryx_u32(x912, x891, x893, &x914); uint32_t x917; uint8_t x918 = addcarryx_u32(x915, x894, x896, &x917); uint32_t x920; uint8_t x921 = addcarryx_u32(x918, x897, x899, &x920); uint32_t x923; uint8_t x924 = addcarryx_u32(x921, x900, x902, &x923); uint32_t x926; addcarryx_u32(0x0, x924, x903, &x926); uint32_t x929; uint8_t x930 = addcarryx_u32(0x0, x856, x881, &x929); uint32_t x932; uint8_t x933 = addcarryx_u32(x930, x859, x905, &x932); uint32_t x935; uint8_t x936 = addcarryx_u32(x933, x862, x908, &x935); uint32_t x938; uint8_t x939 = addcarryx_u32(x936, x865, x911, &x938); uint32_t x941; uint8_t x942 = addcarryx_u32(x939, x868, x914, &x941); uint32_t x944; uint8_t x945 = addcarryx_u32(x942, x871, x917, &x944); uint32_t x947; uint8_t x948 = addcarryx_u32(x945, x874, x920, &x947); uint32_t x950; uint8_t x951 = addcarryx_u32(x948, x877, x923, &x950); uint32_t x953; uint8_t x954 = addcarryx_u32(x951, x879, x926, &x953); uint32_t x957; uint32_t x956 = mulx_u32(x929, 0xffffffff, &x957); uint32_t x960; uint32_t x959 = mulx_u32(x929, 0xffffffff, &x960); uint32_t x963; uint32_t x962 = mulx_u32(x929, 0xffffffff, &x963); uint32_t x966; uint32_t x965 = mulx_u32(x929, 0xffffffff, &x966); uint32_t x968; uint8_t x969 = addcarryx_u32(0x0, x957, x959, &x968); uint32_t x971; uint8_t x972 = addcarryx_u32(x969, x960, x962, &x971); uint32_t x974; uint8_t x975 = addcarryx_u32(x972, x963, 0x0, &x974); uint8_t x976 = (0x0 + 0x0); uint32_t _8; uint8_t x979 = addcarryx_u32(0x0, x929, x956, &_8); uint32_t x981; uint8_t x982 = addcarryx_u32(x979, x932, x968, &x981); uint32_t x984; uint8_t x985 = addcarryx_u32(x982, x935, x971, &x984); uint32_t x987; uint8_t x988 = addcarryx_u32(x985, x938, x974, &x987); uint32_t x990; uint8_t x991 = addcarryx_u32(x988, x941, x975, &x990); uint32_t x993; uint8_t x994 = addcarryx_u32(x991, x944, x976, &x993); uint32_t x996; uint8_t x997 = addcarryx_u32(x994, x947, x929, &x996); uint32_t x999; uint8_t x1000 = addcarryx_u32(x997, x950, x965, &x999); uint32_t x1002; uint8_t x1003 = addcarryx_u32(x1000, x953, x966, &x1002); uint8_t x1004 = (x1003 + x954); uint32_t x1006; uint8_t x1007 = subborrow_u32(0x0, x981, 0xffffffff, &x1006); uint32_t x1009; uint8_t x1010 = subborrow_u32(x1007, x984, 0xffffffff, &x1009); uint32_t x1012; uint8_t x1013 = subborrow_u32(x1010, x987, 0xffffffff, &x1012); uint32_t x1015; uint8_t x1016 = subborrow_u32(x1013, x990, 0x0, &x1015); uint32_t x1018; uint8_t x1019 = subborrow_u32(x1016, x993, 0x0, &x1018); uint32_t x1021; uint8_t x1022 = subborrow_u32(x1019, x996, 0x0, &x1021); uint32_t x1024; uint8_t x1025 = subborrow_u32(x1022, x999, 0x1, &x1024); uint32_t x1027; uint8_t x1028 = subborrow_u32(x1025, x1002, 0xffffffff, &x1027); uint32_t _9; uint8_t x1031 = subborrow_u32(x1028, x1004, 0x0, &_9); uint32_t x1032 = cmovznz_u32(x1031, x1027, x1002); uint32_t x1033 = cmovznz_u32(x1031, x1024, x999); uint32_t x1034 = cmovznz_u32(x1031, x1021, x996); uint32_t x1035 = cmovznz_u32(x1031, x1018, x993); uint32_t x1036 = cmovznz_u32(x1031, x1015, x990); uint32_t x1037 = cmovznz_u32(x1031, x1012, x987); uint32_t x1038 = cmovznz_u32(x1031, x1009, x984); uint32_t x1039 = cmovznz_u32(x1031, x1006, x981); out[0] = x1039; out[1] = x1038; out[2] = x1037; out[3] = x1036; out[4] = x1035; out[5] = x1034; out[6] = x1033; out[7] = x1032; } // NOTE: the following functions are generated from fiat-crypto, from the same // template as their 64-bit counterparts above, but the correctness proof of // the template was not composed with the correctness proof of the // specialization pipeline. This is because Coq unexplainedly loops on trying // to synthesize opp and sub using the normal pipeline. static void fe_sub(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { const uint32_t x14 = in1[7]; const uint32_t x15 = in1[6]; const uint32_t x13 = in1[5]; const uint32_t x11 = in1[4]; const uint32_t x9 = in1[3]; const uint32_t x7 = in1[2]; const uint32_t x5 = in1[1]; const uint32_t x3 = in1[0]; const uint32_t x28 = in2[7]; const uint32_t x29 = in2[6]; const uint32_t x27 = in2[5]; const uint32_t x25 = in2[4]; const uint32_t x23 = in2[3]; const uint32_t x21 = in2[2]; const uint32_t x19 = in2[1]; const uint32_t x17 = in2[0]; uint32_t x31; uint8_t x32 = subborrow_u32(0x0, x3, x17, &x31); uint32_t x34; uint8_t x35 = subborrow_u32(x32, x5, x19, &x34); uint32_t x37; uint8_t x38 = subborrow_u32(x35, x7, x21, &x37); uint32_t x40; uint8_t x41 = subborrow_u32(x38, x9, x23, &x40); uint32_t x43; uint8_t x44 = subborrow_u32(x41, x11, x25, &x43); uint32_t x46; uint8_t x47 = subborrow_u32(x44, x13, x27, &x46); uint32_t x49; uint8_t x50 = subborrow_u32(x47, x15, x29, &x49); uint32_t x52; uint8_t x53 = subborrow_u32(x50, x14, x28, &x52); uint32_t x54 = cmovznz_u32(x53, 0x0, 0xffffffff); uint32_t x56; uint8_t x57 = addcarryx_u32(0x0, x31, (x54 & 0xffffffff), &x56); uint32_t x59; uint8_t x60 = addcarryx_u32(x57, x34, (x54 & 0xffffffff), &x59); uint32_t x62; uint8_t x63 = addcarryx_u32(x60, x37, (x54 & 0xffffffff), &x62); uint32_t x65; uint8_t x66 = addcarryx_u32(x63, x40, 0x0, &x65); uint32_t x68; uint8_t x69 = addcarryx_u32(x66, x43, 0x0, &x68); uint32_t x71; uint8_t x72 = addcarryx_u32(x69, x46, 0x0, &x71); uint32_t x74; uint8_t x75 = addcarryx_u32(x72, x49, ((uint8_t)x54 & 0x1), &x74); uint32_t x77; addcarryx_u32(x75, x52, (x54 & 0xffffffff), &x77); out[0] = x56; out[1] = x59; out[2] = x62; out[3] = x65; out[4] = x68; out[5] = x71; out[6] = x74; out[7] = x77; } // fe_op sets out = -in static void fe_opp(uint32_t out[8], const uint32_t in1[8]) { const uint32_t x12 = in1[7]; const uint32_t x13 = in1[6]; const uint32_t x11 = in1[5]; const uint32_t x9 = in1[4]; const uint32_t x7 = in1[3]; const uint32_t x5 = in1[2]; const uint32_t x3 = in1[1]; const uint32_t x1 = in1[0]; uint32_t x15; uint8_t x16 = subborrow_u32(0x0, 0x0, x1, &x15); uint32_t x18; uint8_t x19 = subborrow_u32(x16, 0x0, x3, &x18); uint32_t x21; uint8_t x22 = subborrow_u32(x19, 0x0, x5, &x21); uint32_t x24; uint8_t x25 = subborrow_u32(x22, 0x0, x7, &x24); uint32_t x27; uint8_t x28 = subborrow_u32(x25, 0x0, x9, &x27); uint32_t x30; uint8_t x31 = subborrow_u32(x28, 0x0, x11, &x30); uint32_t x33; uint8_t x34 = subborrow_u32(x31, 0x0, x13, &x33); uint32_t x36; uint8_t x37 = subborrow_u32(x34, 0x0, x12, &x36); uint32_t x38 = cmovznz_u32(x37, 0x0, 0xffffffff); uint32_t x40; uint8_t x41 = addcarryx_u32(0x0, x15, (x38 & 0xffffffff), &x40); uint32_t x43; uint8_t x44 = addcarryx_u32(x41, x18, (x38 & 0xffffffff), &x43); uint32_t x46; uint8_t x47 = addcarryx_u32(x44, x21, (x38 & 0xffffffff), &x46); uint32_t x49; uint8_t x50 = addcarryx_u32(x47, x24, 0x0, &x49); uint32_t x52; uint8_t x53 = addcarryx_u32(x50, x27, 0x0, &x52); uint32_t x55; uint8_t x56 = addcarryx_u32(x53, x30, 0x0, &x55); uint32_t x58; uint8_t x59 = addcarryx_u32(x56, x33, ((uint8_t)x38 & 0x1), &x58); uint32_t x61; addcarryx_u32(x59, x36, (x38 & 0xffffffff), &x61); out[0] = x40; out[1] = x43; out[2] = x46; out[3] = x49; out[4] = x52; out[5] = x55; out[6] = x58; out[7] = x61; } #endif // utility functions, handwritten #define NBYTES 32 #if defined(BORINGSSL_NISTP256_64BIT) #define NLIMBS 4 typedef uint64_t limb_t; #define cmovznz_limb cmovznz_u64 typedef uint64_t fe[NLIMBS]; #else // 64BIT; else 32BIT #define NLIMBS 8 typedef uint32_t limb_t; #define cmovznz_limb cmovznz_u32 typedef uint32_t fe[NLIMBS]; #endif // 64BIT static limb_t fe_nz(const limb_t in1[NLIMBS]) { limb_t ret = 0; for (int i = 0; i < NLIMBS; i++) { ret |= in1[i]; } return ret; } static void fe_copy(limb_t out[NLIMBS], const limb_t in1[NLIMBS]) { for (int i = 0; i < NLIMBS; i++) { out[i] = in1[i]; } } static void fe_cmovznz(limb_t out[NLIMBS], limb_t t, const limb_t z[NLIMBS], const limb_t nz[NLIMBS]) { for (int i = 0; i < NLIMBS; i++) { out[i] = cmovznz_limb(t, z[i], nz[i]); } } static void fe_sqr(fe out, const fe in) { fe_mul(out, in, in); } static void fe_tobytes(uint8_t out[NBYTES], const fe in) { for (int i = 0; i> (8*(i%sizeof(in[0])))); } } static void fe_frombytes(fe out, const uint8_t in[NBYTES]) { for (int i = 0; i // As a sanity check, a proof that these points form a commutative group: // // point_double calculates 2*(x_in, y_in, z_in) // // The method is taken from: // http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b // // Coq transcription and correctness proof: // // // // Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. // while x_out == y_in is not (maybe this works, but it's not tested). static void point_double(fe x_out, fe y_out, fe z_out, const fe x_in, const fe y_in, const fe z_in) { fe delta, gamma, beta, ftmp, ftmp2, tmptmp, alpha, fourbeta; // delta = z^2 fe_sqr(delta, z_in); // gamma = y^2 fe_sqr(gamma, y_in); // beta = x*gamma fe_mul(beta, x_in, gamma); // alpha = 3*(x-delta)*(x+delta) fe_sub(ftmp, x_in, delta); fe_add(ftmp2, x_in, delta); fe_add(tmptmp, ftmp2, ftmp2); fe_add(ftmp2, ftmp2, tmptmp); fe_mul(alpha, ftmp, ftmp2); // x' = alpha^2 - 8*beta fe_sqr(x_out, alpha); fe_add(fourbeta, beta, beta); fe_add(fourbeta, fourbeta, fourbeta); fe_add(tmptmp, fourbeta, fourbeta); fe_sub(x_out, x_out, tmptmp); // z' = (y + z)^2 - gamma - delta fe_add(delta, gamma, delta); fe_add(ftmp, y_in, z_in); fe_sqr(z_out, ftmp); fe_sub(z_out, z_out, delta); // y' = alpha*(4*beta - x') - 8*gamma^2 fe_sub(y_out, fourbeta, x_out); fe_add(gamma, gamma, gamma); fe_sqr(gamma, gamma); fe_mul(y_out, alpha, y_out); fe_add(gamma, gamma, gamma); fe_sub(y_out, y_out, gamma); } // point_add calcuates (x1, y1, z1) + (x2, y2, z2) // // The method is taken from: // http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, // adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). // // Coq transcription and correctness proof: // // // // This function includes a branch for checking whether the two input points // are equal, (while not equal to the point at infinity). This case never // happens during single point multiplication, so there is no timing leak for // ECDH or ECDSA signing. static void point_add(fe x3, fe y3, fe z3, const fe x1, const fe y1, const fe z1, const int mixed, const fe x2, const fe y2, const fe z2) { fe x_out, y_out, z_out; limb_t z1nz = fe_nz(z1); limb_t z2nz = fe_nz(z2); // z1z1 = z1z1 = z1**2 fe z1z1; fe_sqr(z1z1, z1); fe u1, s1, two_z1z2; if (!mixed) { // z2z2 = z2**2 fe z2z2; fe_sqr(z2z2, z2); // u1 = x1*z2z2 fe_mul(u1, x1, z2z2); // two_z1z2 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 fe_add(two_z1z2, z1, z2); fe_sqr(two_z1z2, two_z1z2); fe_sub(two_z1z2, two_z1z2, z1z1); fe_sub(two_z1z2, two_z1z2, z2z2); // s1 = y1 * z2**3 fe_mul(s1, z2, z2z2); fe_mul(s1, s1, y1); } else { // We'll assume z2 = 1 (special case z2 = 0 is handled later). // u1 = x1*z2z2 fe_copy(u1, x1); // two_z1z2 = 2z1z2 fe_add(two_z1z2, z1, z1); // s1 = y1 * z2**3 fe_copy(s1, y1); } // u2 = x2*z1z1 fe u2; fe_mul(u2, x2, z1z1); // h = u2 - u1 fe h; fe_sub(h, u2, u1); limb_t xneq = fe_nz(h); // z_out = two_z1z2 * h fe_mul(z_out, h, two_z1z2); // z1z1z1 = z1 * z1z1 fe z1z1z1; fe_mul(z1z1z1, z1, z1z1); // s2 = y2 * z1**3 fe s2; fe_mul(s2, y2, z1z1z1); // r = (s2 - s1)*2 fe r; fe_sub(r, s2, s1); fe_add(r, r, r); limb_t yneq = fe_nz(r); if (!xneq && !yneq && z1nz && z2nz) { point_double(x3, y3, z3, x1, y1, z1); return; } // I = (2h)**2 fe i; fe_add(i, h, h); fe_sqr(i, i); // J = h * I fe j; fe_mul(j, h, i); // V = U1 * I fe v; fe_mul(v, u1, i); // x_out = r**2 - J - 2V fe_sqr(x_out, r); fe_sub(x_out, x_out, j); fe_sub(x_out, x_out, v); fe_sub(x_out, x_out, v); // y_out = r(V-x_out) - 2 * s1 * J fe_sub(y_out, v, x_out); fe_mul(y_out, y_out, r); fe s1j; fe_mul(s1j, s1, j); fe_sub(y_out, y_out, s1j); fe_sub(y_out, y_out, s1j); fe_cmovznz(x_out, z1nz, x2, x_out); fe_cmovznz(x3, z2nz, x1, x_out); fe_cmovznz(y_out, z1nz, y2, y_out); fe_cmovznz(y3, z2nz, y1, y_out); fe_cmovznz(z_out, z1nz, z2, z_out); fe_cmovznz(z3, z2nz, z1, z_out); } // 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. // g_pre_comp is the table of precomputed base points #if defined(BORINGSSL_NISTP256_64BIT) static const fe g_pre_comp[2][16][3] = { {{{0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}}, {{0x79e730d418a9143c, 0x75ba95fc5fedb601, 0x79fb732b77622510, 0x18905f76a53755c6}, {0xddf25357ce95560a, 0x8b4ab8e4ba19e45c, 0xd2e88688dd21f325, 0x8571ff1825885d85}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x4f922fc516a0d2bb, 0xd5cc16c1a623499, 0x9241cf3a57c62c8b, 0x2f5e6961fd1b667f}, {0x5c15c70bf5a01797, 0x3d20b44d60956192, 0x4911b37071fdb52, 0xf648f9168d6f0f7b}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x9e566847e137bbbc, 0xe434469e8a6a0bec, 0xb1c4276179d73463, 0x5abe0285133d0015}, {0x92aa837cc04c7dab, 0x573d9f4c43260c07, 0xc93156278e6cc37, 0x94bb725b6b6f7383}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x62a8c244bfe20925, 0x91c19ac38fdce867, 0x5a96a5d5dd387063, 0x61d587d421d324f6}, {0xe87673a2a37173ea, 0x2384800853778b65, 0x10f8441e05bab43e, 0xfa11fe124621efbe}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x1c891f2b2cb19ffd, 0x1ba8d5bb1923c23, 0xb6d03d678ac5ca8e, 0x586eb04c1f13bedc}, {0xc35c6e527e8ed09, 0x1e81a33c1819ede2, 0x278fd6c056c652fa, 0x19d5ac0870864f11}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x62577734d2b533d5, 0x673b8af6a1bdddc0, 0x577e7c9aa79ec293, 0xbb6de651c3b266b1}, {0xe7e9303ab65259b3, 0xd6a0afd3d03a7480, 0xc5ac83d19b3cfc27, 0x60b4619a5d18b99b}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xbd6a38e11ae5aa1c, 0xb8b7652b49e73658, 0xb130014ee5f87ed, 0x9d0f27b2aeebffcd}, {0xca9246317a730a55, 0x9c955b2fddbbc83a, 0x7c1dfe0ac019a71, 0x244a566d356ec48d}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x56f8410ef4f8b16a, 0x97241afec47b266a, 0xa406b8e6d9c87c1, 0x803f3e02cd42ab1b}, {0x7f0309a804dbec69, 0xa83b85f73bbad05f, 0xc6097273ad8e197f, 0xc097440e5067adc1}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x846a56f2c379ab34, 0xa8ee068b841df8d1, 0x20314459176c68ef, 0xf1af32d5915f1f30}, {0x99c375315d75bd50, 0x837cffbaf72f67bc, 0x613a41848d7723f, 0x23d0f130e2d41c8b}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xed93e225d5be5a2b, 0x6fe799835934f3c6, 0x4314092622626ffc, 0x50bbb4d97990216a}, {0x378191c6e57ec63e, 0x65422c40181dcdb2, 0x41a8099b0236e0f6, 0x2b10011801fe49c3}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xfc68b5c59b391593, 0xc385f5a2598270fc, 0x7144f3aad19adcbb, 0xdd55899983fbae0c}, {0x93b88b8e74b82ff4, 0xd2e03c4071e734c9, 0x9a7a9eaf43c0322a, 0xe6e4c551149d6041}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x5fe14bfe80ec21fe, 0xf6ce116ac255be82, 0x98bc5a072f4a5d67, 0xfad27148db7e63af}, {0x90c0b6ac29ab05b3, 0x37a9a83c4e251ae6, 0xa7dc875c2aade7d, 0x77387de39f0e1a84}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x1e9ecc49a56c0dd7, 0xa5cffcd846086c74, 0x8f7a1408f505aece, 0xb37b85c0bef0c47e}, {0x3596b6e4cc0e6a8f, 0xfd6d4bbf6b388f23, 0xaba453fac39cef4e, 0x9c135ac8f9f628d5}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xa1c729495c8f8be, 0x2961c4803bf362bf, 0x9e418403df63d4ac, 0xc109f9cb91ece900}, {0xc2d095d058945705, 0xb9083d96ddeb85c0, 0x84692b8d7a40449b, 0x9bc3344f2eee1ee1}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xd5ae35642913074, 0x55491b2748a542b1, 0x469ca665b310732a, 0x29591d525f1a4cc1}, {0xe76f5b6bb84f983f, 0xbe7eef419f5f84e1, 0x1200d49680baa189, 0x6376551f18ef332c}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}}, {{{0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}}, {{0x202886024147519a, 0xd0981eac26b372f0, 0xa9d4a7caa785ebc8, 0xd953c50ddbdf58e9}, {0x9d6361ccfd590f8f, 0x72e9626b44e6c917, 0x7fd9611022eb64cf, 0x863ebb7e9eb288f3}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x4fe7ee31b0e63d34, 0xf4600572a9e54fab, 0xc0493334d5e7b5a4, 0x8589fb9206d54831}, {0xaa70f5cc6583553a, 0x879094ae25649e5, 0xcc90450710044652, 0xebb0696d02541c4f}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xabbaa0c03b89da99, 0xa6f2d79eb8284022, 0x27847862b81c05e8, 0x337a4b5905e54d63}, {0x3c67500d21f7794a, 0x207005b77d6d7f61, 0xa5a378104cfd6e8, 0xd65e0d5f4c2fbd6}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xd433e50f6d3549cf, 0x6f33696ffacd665e, 0x695bfdacce11fcb4, 0x810ee252af7c9860}, {0x65450fe17159bb2c, 0xf7dfbebe758b357b, 0x2b057e74d69fea72, 0xd485717a92731745}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xce1f69bbe83f7669, 0x9f8ae8272877d6b, 0x9548ae543244278d, 0x207755dee3c2c19c}, {0x87bd61d96fef1945, 0x18813cefb12d28c3, 0x9fbcd1d672df64aa, 0x48dc5ee57154b00d}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xef0f469ef49a3154, 0x3e85a5956e2b2e9a, 0x45aaec1eaa924a9c, 0xaa12dfc8a09e4719}, {0x26f272274df69f1d, 0xe0e4c82ca2ff5e73, 0xb9d8ce73b7a9dd44, 0x6c036e73e48ca901}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xe1e421e1a47153f0, 0xb86c3b79920418c9, 0x93bdce87705d7672, 0xf25ae793cab79a77}, {0x1f3194a36d869d0c, 0x9d55c8824986c264, 0x49fb5ea3096e945e, 0x39b8e65313db0a3e}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xe3417bc035d0b34a, 0x440b386b8327c0a7, 0x8fb7262dac0362d1, 0x2c41114ce0cdf943}, {0x2ba5cef1ad95a0b1, 0xc09b37a867d54362, 0x26d6cdd201e486c9, 0x20477abf42ff9297}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xf121b41bc0a67d2, 0x62d4760a444d248a, 0xe044f1d659b4737, 0x8fde365250bb4a8}, {0xaceec3da848bf287, 0xc2a62182d3369d6e, 0x3582dfdc92449482, 0x2f7e2fd2565d6cd7}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xa0122b5178a876b, 0x51ff96ff085104b4, 0x50b31ab14f29f76, 0x84abb28b5f87d4e6}, {0xd5ed439f8270790a, 0x2d6cb59d85e3f46b, 0x75f55c1b6c1e2212, 0xe5436f6717655640}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xc2965ecc9aeb596d, 0x1ea03e7023c92b4, 0x4704b4b62e013961, 0xca8fd3f905ea367}, {0x92523a42551b2b61, 0x1eb7a89c390fcd06, 0xe7f1d2be0392a63e, 0x96dca2644ddb0c33}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x231c210e15339848, 0xe87a28e870778c8d, 0x9d1de6616956e170, 0x4ac3c9382bb09c0b}, {0x19be05516998987d, 0x8b2376c4ae09f4d6, 0x1de0b7651a3f933d, 0x380d94c7e39705f4}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x3685954b8c31c31d, 0x68533d005bf21a0c, 0xbd7626e75c79ec9, 0xca17754742c69d54}, {0xcc6edafff6d2dbb2, 0xfd0d8cbd174a9d18, 0x875e8793aa4578e8, 0xa976a7139cab2ce6}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0xce37ab11b43ea1db, 0xa7ff1a95259d292, 0x851b02218f84f186, 0xa7222beadefaad13}, {0xa2ac78ec2b0a9144, 0x5a024051f2fa59c5, 0x91d1eca56147ce38, 0xbe94d523bc2ac690}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, {{0x2d8daefd79ec1a0f, 0x3bbcd6fdceb39c97, 0xf5575ffc58f61a95, 0xdbd986c4adf7b420}, {0x81aa881415f39eb7, 0x6ee2fcf5b98d976c, 0x5465475dcf2f717d, 0x8e24d3c46860bbd0}, {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}}}; #else static const fe g_pre_comp[2][16][3] = { {{{0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}}, {{0x18a9143c,0x79e730d4, 0x5fedb601,0x75ba95fc, 0x77622510,0x79fb732b, 0xa53755c6,0x18905f76}, {0xce95560a,0xddf25357, 0xba19e45c,0x8b4ab8e4, 0xdd21f325,0xd2e88688, 0x25885d85,0x8571ff18}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x16a0d2bb,0x4f922fc5, 0x1a623499,0xd5cc16c, 0x57c62c8b,0x9241cf3a, 0xfd1b667f,0x2f5e6961}, {0xf5a01797,0x5c15c70b, 0x60956192,0x3d20b44d, 0x71fdb52,0x4911b37, 0x8d6f0f7b,0xf648f916}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xe137bbbc,0x9e566847, 0x8a6a0bec,0xe434469e, 0x79d73463,0xb1c42761, 0x133d0015,0x5abe0285}, {0xc04c7dab,0x92aa837c, 0x43260c07,0x573d9f4c, 0x78e6cc37,0xc931562, 0x6b6f7383,0x94bb725b}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xbfe20925,0x62a8c244, 0x8fdce867,0x91c19ac3, 0xdd387063,0x5a96a5d5, 0x21d324f6,0x61d587d4}, {0xa37173ea,0xe87673a2, 0x53778b65,0x23848008, 0x5bab43e,0x10f8441e, 0x4621efbe,0xfa11fe12}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x2cb19ffd,0x1c891f2b, 0xb1923c23,0x1ba8d5b, 0x8ac5ca8e,0xb6d03d67, 0x1f13bedc,0x586eb04c}, {0x27e8ed09,0xc35c6e5, 0x1819ede2,0x1e81a33c, 0x56c652fa,0x278fd6c0, 0x70864f11,0x19d5ac08}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xd2b533d5,0x62577734, 0xa1bdddc0,0x673b8af6, 0xa79ec293,0x577e7c9a, 0xc3b266b1,0xbb6de651}, {0xb65259b3,0xe7e9303a, 0xd03a7480,0xd6a0afd3, 0x9b3cfc27,0xc5ac83d1, 0x5d18b99b,0x60b4619a}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x1ae5aa1c,0xbd6a38e1, 0x49e73658,0xb8b7652b, 0xee5f87ed,0xb130014, 0xaeebffcd,0x9d0f27b2}, {0x7a730a55,0xca924631, 0xddbbc83a,0x9c955b2f, 0xac019a71,0x7c1dfe0, 0x356ec48d,0x244a566d}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xf4f8b16a,0x56f8410e, 0xc47b266a,0x97241afe, 0x6d9c87c1,0xa406b8e, 0xcd42ab1b,0x803f3e02}, {0x4dbec69,0x7f0309a8, 0x3bbad05f,0xa83b85f7, 0xad8e197f,0xc6097273, 0x5067adc1,0xc097440e}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xc379ab34,0x846a56f2, 0x841df8d1,0xa8ee068b, 0x176c68ef,0x20314459, 0x915f1f30,0xf1af32d5}, {0x5d75bd50,0x99c37531, 0xf72f67bc,0x837cffba, 0x48d7723f,0x613a418, 0xe2d41c8b,0x23d0f130}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xd5be5a2b,0xed93e225, 0x5934f3c6,0x6fe79983, 0x22626ffc,0x43140926, 0x7990216a,0x50bbb4d9}, {0xe57ec63e,0x378191c6, 0x181dcdb2,0x65422c40, 0x236e0f6,0x41a8099b, 0x1fe49c3,0x2b100118}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x9b391593,0xfc68b5c5, 0x598270fc,0xc385f5a2, 0xd19adcbb,0x7144f3aa, 0x83fbae0c,0xdd558999}, {0x74b82ff4,0x93b88b8e, 0x71e734c9,0xd2e03c40, 0x43c0322a,0x9a7a9eaf, 0x149d6041,0xe6e4c551}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x80ec21fe,0x5fe14bfe, 0xc255be82,0xf6ce116a, 0x2f4a5d67,0x98bc5a07, 0xdb7e63af,0xfad27148}, {0x29ab05b3,0x90c0b6ac, 0x4e251ae6,0x37a9a83c, 0xc2aade7d,0xa7dc875, 0x9f0e1a84,0x77387de3}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xa56c0dd7,0x1e9ecc49, 0x46086c74,0xa5cffcd8, 0xf505aece,0x8f7a1408, 0xbef0c47e,0xb37b85c0}, {0xcc0e6a8f,0x3596b6e4, 0x6b388f23,0xfd6d4bbf, 0xc39cef4e,0xaba453fa, 0xf9f628d5,0x9c135ac8}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x95c8f8be,0xa1c7294, 0x3bf362bf,0x2961c480, 0xdf63d4ac,0x9e418403, 0x91ece900,0xc109f9cb}, {0x58945705,0xc2d095d0, 0xddeb85c0,0xb9083d96, 0x7a40449b,0x84692b8d, 0x2eee1ee1,0x9bc3344f}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x42913074,0xd5ae356, 0x48a542b1,0x55491b27, 0xb310732a,0x469ca665, 0x5f1a4cc1,0x29591d52}, {0xb84f983f,0xe76f5b6b, 0x9f5f84e1,0xbe7eef41, 0x80baa189,0x1200d496, 0x18ef332c,0x6376551f}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}}, {{{0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}}, {{0x4147519a,0x20288602, 0x26b372f0,0xd0981eac, 0xa785ebc8,0xa9d4a7ca, 0xdbdf58e9,0xd953c50d}, {0xfd590f8f,0x9d6361cc, 0x44e6c917,0x72e9626b, 0x22eb64cf,0x7fd96110, 0x9eb288f3,0x863ebb7e}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xb0e63d34,0x4fe7ee31, 0xa9e54fab,0xf4600572, 0xd5e7b5a4,0xc0493334, 0x6d54831,0x8589fb92}, {0x6583553a,0xaa70f5cc, 0xe25649e5,0x879094a, 0x10044652,0xcc904507, 0x2541c4f,0xebb0696d}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x3b89da99,0xabbaa0c0, 0xb8284022,0xa6f2d79e, 0xb81c05e8,0x27847862, 0x5e54d63,0x337a4b59}, {0x21f7794a,0x3c67500d, 0x7d6d7f61,0x207005b7, 0x4cfd6e8,0xa5a3781, 0xf4c2fbd6,0xd65e0d5}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x6d3549cf,0xd433e50f, 0xfacd665e,0x6f33696f, 0xce11fcb4,0x695bfdac, 0xaf7c9860,0x810ee252}, {0x7159bb2c,0x65450fe1, 0x758b357b,0xf7dfbebe, 0xd69fea72,0x2b057e74, 0x92731745,0xd485717a}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xe83f7669,0xce1f69bb, 0x72877d6b,0x9f8ae82, 0x3244278d,0x9548ae54, 0xe3c2c19c,0x207755de}, {0x6fef1945,0x87bd61d9, 0xb12d28c3,0x18813cef, 0x72df64aa,0x9fbcd1d6, 0x7154b00d,0x48dc5ee5}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xf49a3154,0xef0f469e, 0x6e2b2e9a,0x3e85a595, 0xaa924a9c,0x45aaec1e, 0xa09e4719,0xaa12dfc8}, {0x4df69f1d,0x26f27227, 0xa2ff5e73,0xe0e4c82c, 0xb7a9dd44,0xb9d8ce73, 0xe48ca901,0x6c036e73}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xa47153f0,0xe1e421e1, 0x920418c9,0xb86c3b79, 0x705d7672,0x93bdce87, 0xcab79a77,0xf25ae793}, {0x6d869d0c,0x1f3194a3, 0x4986c264,0x9d55c882, 0x96e945e,0x49fb5ea3, 0x13db0a3e,0x39b8e653}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x35d0b34a,0xe3417bc0, 0x8327c0a7,0x440b386b, 0xac0362d1,0x8fb7262d, 0xe0cdf943,0x2c41114c}, {0xad95a0b1,0x2ba5cef1, 0x67d54362,0xc09b37a8, 0x1e486c9,0x26d6cdd2, 0x42ff9297,0x20477abf}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xbc0a67d2,0xf121b41, 0x444d248a,0x62d4760a, 0x659b4737,0xe044f1d, 0x250bb4a8,0x8fde365}, {0x848bf287,0xaceec3da, 0xd3369d6e,0xc2a62182, 0x92449482,0x3582dfdc, 0x565d6cd7,0x2f7e2fd2}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x178a876b,0xa0122b5, 0x85104b4,0x51ff96ff, 0x14f29f76,0x50b31ab, 0x5f87d4e6,0x84abb28b}, {0x8270790a,0xd5ed439f, 0x85e3f46b,0x2d6cb59d, 0x6c1e2212,0x75f55c1b, 0x17655640,0xe5436f67}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x9aeb596d,0xc2965ecc, 0x23c92b4,0x1ea03e7, 0x2e013961,0x4704b4b6, 0x905ea367,0xca8fd3f}, {0x551b2b61,0x92523a42, 0x390fcd06,0x1eb7a89c, 0x392a63e,0xe7f1d2be, 0x4ddb0c33,0x96dca264}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x15339848,0x231c210e, 0x70778c8d,0xe87a28e8, 0x6956e170,0x9d1de661, 0x2bb09c0b,0x4ac3c938}, {0x6998987d,0x19be0551, 0xae09f4d6,0x8b2376c4, 0x1a3f933d,0x1de0b765, 0xe39705f4,0x380d94c7}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x8c31c31d,0x3685954b, 0x5bf21a0c,0x68533d00, 0x75c79ec9,0xbd7626e, 0x42c69d54,0xca177547}, {0xf6d2dbb2,0xcc6edaff, 0x174a9d18,0xfd0d8cbd, 0xaa4578e8,0x875e8793, 0x9cab2ce6,0xa976a713}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0xb43ea1db,0xce37ab11, 0x5259d292,0xa7ff1a9, 0x8f84f186,0x851b0221, 0xdefaad13,0xa7222bea}, {0x2b0a9144,0xa2ac78ec, 0xf2fa59c5,0x5a024051, 0x6147ce38,0x91d1eca5, 0xbc2ac690,0xbe94d523}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, {{0x79ec1a0f,0x2d8daefd, 0xceb39c97,0x3bbcd6fd, 0x58f61a95,0xf5575ffc, 0xadf7b420,0xdbd986c4}, {0x15f39eb7,0x81aa8814, 0xb98d976c,0x6ee2fcf5, 0xcf2f717d,0x5465475d, 0x6860bbd0,0x8e24d3c4}, {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}}}; #endif // select_point selects the |idx|th point from a precomputation table and // copies it to out. static void select_point(const limb_t idx, size_t size, const fe pre_comp[/*size*/][3], fe out[3]) { OPENSSL_memset(out, 0, sizeof(fe) * 3); for (size_t i = 0; i < size; i++) { limb_t mismatch = i ^ idx; fe_cmovznz(out[0], mismatch, pre_comp[i][0], out[0]); fe_cmovznz(out[1], mismatch, pre_comp[i][1], out[1]); fe_cmovznz(out[2], mismatch, pre_comp[i][2], out[2]); } } // get_bit returns the |i|th bit in |in| static char get_bit(const uint8_t *in, int i) { if (i < 0 || i >= 256) { return 0; } return (in[i >> 3] >> (i & 7)) & 1; } // Interleaved point multiplication using precomputed point multiples: The // small point multiples 0*P, 1*P, ..., 17*P are in p_pre_comp, the scalar // in p_scalar, if non-NULL. If g_scalar is non-NULL, we also add this multiple // of the generator, using certain (large) precomputed multiples in g_pre_comp. // Output point (X, Y, Z) is stored in x_out, y_out, z_out. static void batch_mul(fe x_out, fe y_out, fe z_out, const uint8_t *p_scalar, const uint8_t *g_scalar, const fe p_pre_comp[17][3]) { // set nq to the point at infinity fe nq[3] = {{0},{0},{0}}, ftmp, tmp[3]; uint64_t bits; uint8_t sign, digit; // Loop over both scalars msb-to-lsb, interleaving additions of multiples // of the generator (two in each of the last 32 rounds) and additions of p // (every 5th round). int skip = 1; // save two point operations in the first round size_t i = p_scalar != NULL ? 255 : 31; for (;;) { // double if (!skip) { point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); } // add multiples of the generator if (g_scalar != NULL && i <= 31) { // first, look 32 bits upwards bits = get_bit(g_scalar, i + 224) << 3; bits |= get_bit(g_scalar, i + 160) << 2; bits |= get_bit(g_scalar, i + 96) << 1; bits |= get_bit(g_scalar, i + 32); // select the point to add, in constant time select_point(bits, 16, g_pre_comp[1], tmp); if (!skip) { point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, tmp[0], tmp[1], tmp[2]); } else { fe_copy(nq[0], tmp[0]); fe_copy(nq[1], tmp[1]); fe_copy(nq[2], tmp[2]); skip = 0; } // second, look at the current position bits = get_bit(g_scalar, i + 192) << 3; bits |= get_bit(g_scalar, i + 128) << 2; bits |= get_bit(g_scalar, i + 64) << 1; bits |= get_bit(g_scalar, i); // select the point to add, in constant time select_point(bits, 16, g_pre_comp[0], tmp); point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, tmp[0], tmp[1], tmp[2]); } // do other additions every 5 doublings if (p_scalar != NULL && i % 5 == 0) { bits = get_bit(p_scalar, i + 4) << 5; bits |= get_bit(p_scalar, i + 3) << 4; bits |= get_bit(p_scalar, i + 2) << 3; bits |= get_bit(p_scalar, i + 1) << 2; bits |= get_bit(p_scalar, i) << 1; bits |= get_bit(p_scalar, i - 1); ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); // select the point to add or subtract, in constant time. select_point(digit, 17, p_pre_comp, tmp); fe_opp(ftmp, tmp[1]); // (X, -Y, Z) is the negative point. fe_cmovznz(tmp[1], sign, tmp[1], ftmp); if (!skip) { point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */, tmp[0], tmp[1], tmp[2]); } else { fe_copy(nq[0], tmp[0]); fe_copy(nq[1], tmp[1]); fe_copy(nq[2], tmp[2]); skip = 0; } } if (i == 0) { break; } --i; } fe_copy(x_out, nq[0]); fe_copy(y_out, nq[1]); fe_copy(z_out, nq[2]); } // OPENSSL EC_METHOD FUNCTIONS // Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = // (X/Z^2, Y/Z^3). static int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x_out, BIGNUM *y_out, BN_CTX *ctx) { fe x, y, z1, z2; if (EC_POINT_is_at_infinity(group, point)) { OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); return 0; } if (!BN_to_fe(x, &point->X) || !BN_to_fe(y, &point->Y) || !BN_to_fe(z1, &point->Z)) { return 0; } fe_inv(z2, z1); fe_sqr(z1, z2); // Instead of using |fe_from_montgomery| to convert the |x| coordinate and // then calling |fe_from_montgomery| again to convert the |y| coordinate // below, convert the common factor |z1| once now, saving one reduction. fe_from_montgomery(z1); if (x_out != NULL) { fe_mul(x, x, z1); if (!fe_to_BN(x_out, x)) { OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); return 0; } } if (y_out != NULL) { fe_mul(z1, z1, z2); fe_mul(y, y, z1); if (!fe_to_BN(y_out, y)) { OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); return 0; } } return 1; } static int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar, const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *unused_ctx) { fe p_pre_comp[17][3]; fe x_out, y_out, z_out; if (p != NULL && p_scalar != NULL) { // We treat NULL scalars as 0, and NULL points as points at infinity, i.e., // they contribute nothing to the linear combination. OPENSSL_memset(&p_pre_comp, 0, sizeof(p_pre_comp)); // Precompute multiples. if (!BN_to_fe(p_pre_comp[1][0], &p->X) || !BN_to_fe(p_pre_comp[1][1], &p->Y) || !BN_to_fe(p_pre_comp[1][2], &p->Z)) { return 0; } for (size_t j = 2; j <= 16; ++j) { if (j & 1) { point_add(p_pre_comp[j][0], p_pre_comp[j][1], p_pre_comp[j][2], p_pre_comp[1][0], p_pre_comp[1][1], p_pre_comp[1][2], 0, p_pre_comp[j - 1][0], p_pre_comp[j - 1][1], p_pre_comp[j - 1][2]); } else { point_double(p_pre_comp[j][0], p_pre_comp[j][1], p_pre_comp[j][2], p_pre_comp[j / 2][0], p_pre_comp[j / 2][1], p_pre_comp[j / 2][2]); } } } batch_mul(x_out, y_out, z_out, (p != NULL && p_scalar != NULL) ? p_scalar->bytes : NULL, g_scalar != NULL ? g_scalar->bytes : NULL, (const fe (*) [3])p_pre_comp); if (!fe_to_BN(&r->X, x_out) || !fe_to_BN(&r->Y, y_out) || !fe_to_BN(&r->Z, z_out)) { OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); return 0; } return 1; } static int ec_GFp_nistp256_point_mul_public(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar, const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *unused_ctx) { #define P256_WSIZE_PUBLIC 4 // Precompute multiples of |p|. p_pre_comp[i] is (2*i+1) * |p|. fe p_pre_comp[1 << (P256_WSIZE_PUBLIC-1)][3]; if (!BN_to_fe(p_pre_comp[0][0], &p->X) || !BN_to_fe(p_pre_comp[0][1], &p->Y) || !BN_to_fe(p_pre_comp[0][2], &p->Z)) { return 0; } fe p2[3]; point_double(p2[0], p2[1], p2[2], p_pre_comp[0][0], p_pre_comp[0][1], p_pre_comp[0][2]); for (size_t i = 1; i < OPENSSL_ARRAY_SIZE(p_pre_comp); i++) { point_add(p_pre_comp[i][0], p_pre_comp[i][1], p_pre_comp[i][2], p_pre_comp[i - 1][0], p_pre_comp[i - 1][1], p_pre_comp[i - 1][2], 0 /* not mixed */, p2[0], p2[1], p2[2]); } // Set up the coefficients for |p_scalar|. int8_t p_wNAF[257]; if (!ec_compute_wNAF(group, p_wNAF, p_scalar, 256, P256_WSIZE_PUBLIC)) { return 0; } // Set |ret| to the point at infinity. int skip = 1; // Save some point operations. fe ret[3] = {{0},{0},{0}}; for (int i = 256; i >= 0; i--) { if (!skip) { point_double(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2]); } // For the |g_scalar|, we use the precomputed table without the // constant-time lookup. if (i <= 31) { // First, look 32 bits upwards. uint64_t bits = get_bit(g_scalar->bytes, i + 224) << 3; bits |= get_bit(g_scalar->bytes, i + 160) << 2; bits |= get_bit(g_scalar->bytes, i + 96) << 1; bits |= get_bit(g_scalar->bytes, i + 32); point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], 1 /* mixed */, g_pre_comp[1][bits][0], g_pre_comp[1][bits][1], g_pre_comp[1][bits][2]); skip = 0; // Second, look at the current position. bits = get_bit(g_scalar->bytes, i + 192) << 3; bits |= get_bit(g_scalar->bytes, i + 128) << 2; bits |= get_bit(g_scalar->bytes, i + 64) << 1; bits |= get_bit(g_scalar->bytes, i); point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], 1 /* mixed */, g_pre_comp[0][bits][0], g_pre_comp[0][bits][1], g_pre_comp[0][bits][2]); } int digit = p_wNAF[i]; if (digit != 0) { assert(digit & 1); int idx = digit < 0 ? (-digit) >> 1 : digit >> 1; fe *y = &p_pre_comp[idx][1], tmp; if (digit < 0) { fe_opp(tmp, p_pre_comp[idx][1]); y = &tmp; } if (!skip) { point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], 0 /* not mixed */, p_pre_comp[idx][0], *y, p_pre_comp[idx][2]); } else { fe_copy(ret[0], p_pre_comp[idx][0]); fe_copy(ret[1], *y); fe_copy(ret[2], p_pre_comp[idx][2]); skip = 0; } } } if (!fe_to_BN(&r->X, ret[0]) || !fe_to_BN(&r->Y, ret[1]) || !fe_to_BN(&r->Z, ret[2])) { OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); return 0; } return 1; } DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistp256_method) { out->group_init = ec_GFp_mont_group_init; out->group_finish = ec_GFp_mont_group_finish; out->group_set_curve = ec_GFp_mont_group_set_curve; out->point_get_affine_coordinates = ec_GFp_nistp256_point_get_affine_coordinates; out->mul = ec_GFp_nistp256_points_mul; out->mul_public = ec_GFp_nistp256_point_mul_public; out->field_mul = ec_GFp_mont_field_mul; out->field_sqr = ec_GFp_mont_field_sqr; out->field_encode = ec_GFp_mont_field_encode; out->field_decode = ec_GFp_mont_field_decode; }; #undef BORINGSSL_NISTP256_64BIT