1 // The MIT License (MIT) 2 // 3 // Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file). 4 // 5 // Permission is hereby granted, free of charge, to any person obtaining a copy 6 // of this software and associated documentation files (the "Software"), to deal 7 // in the Software without restriction, including without limitation the rights 8 // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 // copies of the Software, and to permit persons to whom the Software is 10 // furnished to do so, subject to the following conditions: 11 // 12 // The above copyright notice and this permission notice shall be included in all 13 // copies or substantial portions of the Software. 14 // 15 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 // SOFTWARE. 22 23 // The field arithmetic code is generated by Fiat 24 // (https://github.com/mit-plv/fiat-crypto), which is MIT licensed. 25 // 26 // An implementation of the NIST P-256 elliptic curve point multiplication. 27 // 256-bit Montgomery form, generated using fiat-crypto, for 64 and 32-bit. 28 // Field operations with inputs in [0,p) return outputs in [0,p). 29 30 #include <openssl/base.h> 31 32 #include <openssl/bn.h> 33 #include <openssl/ec.h> 34 #include <openssl/err.h> 35 #include <openssl/mem.h> 36 37 #include <string.h> 38 39 #include "../../crypto/fipsmodule/delocate.h" 40 #include "../../crypto/fipsmodule/ec/internal.h" 41 #include "../../crypto/internal.h" 42 43 44 // MSVC does not implement uint128_t, and crashes with intrinsics 45 #if defined(BORINGSSL_HAS_UINT128) 46 #define BORINGSSL_NISTP256_64BIT 1 47 #endif 48 49 // "intrinsics" 50 51 #if defined(BORINGSSL_NISTP256_64BIT) 52 53 static uint64_t mulx_u64(uint64_t a, uint64_t b, uint64_t *high) { 54 uint128_t x = (uint128_t)a * b; 55 *high = (uint64_t) (x >> 64); 56 return (uint64_t) x; 57 } 58 59 static uint64_t addcarryx_u64(uint8_t c, uint64_t a, uint64_t b, uint64_t *low) { 60 uint128_t x = (uint128_t)a + b + c; 61 *low = (uint64_t) x; 62 return (uint64_t) (x>>64); 63 } 64 65 static uint64_t subborrow_u64(uint8_t c, uint64_t a, uint64_t b, uint64_t *low) { 66 uint128_t t = ((uint128_t) b + c); 67 uint128_t x = a-t; 68 *low = (uint64_t) x; 69 return (uint8_t) (x>>127); 70 } 71 72 static uint64_t cmovznz_u64(uint64_t t, uint64_t z, uint64_t nz) { 73 t = -!!t; // all set if nonzero, 0 if 0 74 return (t&nz) | ((~t)&z); 75 } 76 77 #else 78 79 static uint32_t mulx_u32(uint32_t a, uint32_t b, uint32_t *high) { 80 uint64_t x = (uint64_t)a * b; 81 *high = (uint32_t) (x >> 32); 82 return (uint32_t) x; 83 } 84 85 static uint32_t addcarryx_u32(uint8_t c, uint32_t a, uint32_t b, uint32_t *low) { 86 uint64_t x = (uint64_t)a + b + c; 87 *low = (uint32_t) x; 88 return (uint32_t) (x>>32); 89 } 90 91 static uint32_t subborrow_u32(uint8_t c, uint32_t a, uint32_t b, uint32_t *low) { 92 uint64_t t = ((uint64_t) b + c); 93 uint64_t x = a-t; 94 *low = (uint32_t) x; 95 return (uint8_t) (x>>63); 96 } 97 98 static uint32_t cmovznz_u32(uint32_t t, uint32_t z, uint32_t nz) { 99 t = -!!t; // all set if nonzero, 0 if 0 100 return (t&nz) | ((~t)&z); 101 } 102 103 #endif 104 105 // fiat-crypto generated code 106 107 #if defined(BORINGSSL_NISTP256_64BIT) 108 109 static void fe_add(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { 110 { const uint64_t x8 = in1[3]; 111 { const uint64_t x9 = in1[2]; 112 { const uint64_t x7 = in1[1]; 113 { const uint64_t x5 = in1[0]; 114 { const uint64_t x14 = in2[3]; 115 { const uint64_t x15 = in2[2]; 116 { const uint64_t x13 = in2[1]; 117 { const uint64_t x11 = in2[0]; 118 { uint64_t x17; uint8_t x18 = addcarryx_u64(0x0, x5, x11, &x17); 119 { uint64_t x20; uint8_t x21 = addcarryx_u64(x18, x7, x13, &x20); 120 { uint64_t x23; uint8_t x24 = addcarryx_u64(x21, x9, x15, &x23); 121 { uint64_t x26; uint8_t x27 = addcarryx_u64(x24, x8, x14, &x26); 122 { uint64_t x29; uint8_t x30 = subborrow_u64(0x0, x17, 0xffffffffffffffffL, &x29); 123 { uint64_t x32; uint8_t x33 = subborrow_u64(x30, x20, 0xffffffff, &x32); 124 { uint64_t x35; uint8_t x36 = subborrow_u64(x33, x23, 0x0, &x35); 125 { uint64_t x38; uint8_t x39 = subborrow_u64(x36, x26, 0xffffffff00000001L, &x38); 126 { uint64_t _1; uint8_t x42 = subborrow_u64(x39, x27, 0x0, &_1); 127 { uint64_t x43 = cmovznz_u64(x42, x38, x26); 128 { uint64_t x44 = cmovznz_u64(x42, x35, x23); 129 { uint64_t x45 = cmovznz_u64(x42, x32, x20); 130 { uint64_t x46 = cmovznz_u64(x42, x29, x17); 131 out[0] = x46; 132 out[1] = x45; 133 out[2] = x44; 134 out[3] = x43; 135 }}}}}}}}}}}}}}}}}}}}} 136 } 137 138 // fe_op sets out = -in 139 static void fe_opp(uint64_t out[4], const uint64_t in1[4]) { 140 const uint64_t x5 = in1[3]; 141 const uint64_t x6 = in1[2]; 142 const uint64_t x4 = in1[1]; 143 const uint64_t x2 = in1[0]; 144 uint64_t x8; uint8_t x9 = subborrow_u64(0x0, 0x0, x2, &x8); 145 uint64_t x11; uint8_t x12 = subborrow_u64(x9, 0x0, x4, &x11); 146 uint64_t x14; uint8_t x15 = subborrow_u64(x12, 0x0, x6, &x14); 147 uint64_t x17; uint8_t x18 = subborrow_u64(x15, 0x0, x5, &x17); 148 uint64_t x19 = (uint64_t)cmovznz_u64(x18, 0x0, 0xffffffffffffffffL); 149 uint64_t x20 = (x19 & 0xffffffffffffffffL); 150 uint64_t x22; uint8_t x23 = addcarryx_u64(0x0, x8, x20, &x22); 151 uint64_t x24 = (x19 & 0xffffffff); 152 uint64_t x26; uint8_t x27 = addcarryx_u64(x23, x11, x24, &x26); 153 uint64_t x29; uint8_t x30 = addcarryx_u64(x27, x14, 0x0, &x29); 154 uint64_t x31 = (x19 & 0xffffffff00000001L); 155 uint64_t x33; addcarryx_u64(x30, x17, x31, &x33); 156 out[0] = x22; 157 out[1] = x26; 158 out[2] = x29; 159 out[3] = x33; 160 } 161 162 static void fe_mul(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { 163 const uint64_t x8 = in1[3]; 164 const uint64_t x9 = in1[2]; 165 const uint64_t x7 = in1[1]; 166 const uint64_t x5 = in1[0]; 167 const uint64_t x14 = in2[3]; 168 const uint64_t x15 = in2[2]; 169 const uint64_t x13 = in2[1]; 170 const uint64_t x11 = in2[0]; 171 uint64_t x18; uint64_t x17 = mulx_u64(x5, x11, &x18); 172 uint64_t x21; uint64_t x20 = mulx_u64(x5, x13, &x21); 173 uint64_t x24; uint64_t x23 = mulx_u64(x5, x15, &x24); 174 uint64_t x27; uint64_t x26 = mulx_u64(x5, x14, &x27); 175 uint64_t x29; uint8_t x30 = addcarryx_u64(0x0, x18, x20, &x29); 176 uint64_t x32; uint8_t x33 = addcarryx_u64(x30, x21, x23, &x32); 177 uint64_t x35; uint8_t x36 = addcarryx_u64(x33, x24, x26, &x35); 178 uint64_t x38; addcarryx_u64(0x0, x36, x27, &x38); 179 uint64_t x42; uint64_t x41 = mulx_u64(x17, 0xffffffffffffffffL, &x42); 180 uint64_t x45; uint64_t x44 = mulx_u64(x17, 0xffffffff, &x45); 181 uint64_t x48; uint64_t x47 = mulx_u64(x17, 0xffffffff00000001L, &x48); 182 uint64_t x50; uint8_t x51 = addcarryx_u64(0x0, x42, x44, &x50); 183 uint64_t x53; uint8_t x54 = addcarryx_u64(x51, x45, 0x0, &x53); 184 uint64_t x56; uint8_t x57 = addcarryx_u64(x54, 0x0, x47, &x56); 185 uint64_t x59; addcarryx_u64(0x0, x57, x48, &x59); 186 uint64_t _2; uint8_t x63 = addcarryx_u64(0x0, x17, x41, &_2); 187 uint64_t x65; uint8_t x66 = addcarryx_u64(x63, x29, x50, &x65); 188 uint64_t x68; uint8_t x69 = addcarryx_u64(x66, x32, x53, &x68); 189 uint64_t x71; uint8_t x72 = addcarryx_u64(x69, x35, x56, &x71); 190 uint64_t x74; uint8_t x75 = addcarryx_u64(x72, x38, x59, &x74); 191 uint64_t x78; uint64_t x77 = mulx_u64(x7, x11, &x78); 192 uint64_t x81; uint64_t x80 = mulx_u64(x7, x13, &x81); 193 uint64_t x84; uint64_t x83 = mulx_u64(x7, x15, &x84); 194 uint64_t x87; uint64_t x86 = mulx_u64(x7, x14, &x87); 195 uint64_t x89; uint8_t x90 = addcarryx_u64(0x0, x78, x80, &x89); 196 uint64_t x92; uint8_t x93 = addcarryx_u64(x90, x81, x83, &x92); 197 uint64_t x95; uint8_t x96 = addcarryx_u64(x93, x84, x86, &x95); 198 uint64_t x98; addcarryx_u64(0x0, x96, x87, &x98); 199 uint64_t x101; uint8_t x102 = addcarryx_u64(0x0, x65, x77, &x101); 200 uint64_t x104; uint8_t x105 = addcarryx_u64(x102, x68, x89, &x104); 201 uint64_t x107; uint8_t x108 = addcarryx_u64(x105, x71, x92, &x107); 202 uint64_t x110; uint8_t x111 = addcarryx_u64(x108, x74, x95, &x110); 203 uint64_t x113; uint8_t x114 = addcarryx_u64(x111, x75, x98, &x113); 204 uint64_t x117; uint64_t x116 = mulx_u64(x101, 0xffffffffffffffffL, &x117); 205 uint64_t x120; uint64_t x119 = mulx_u64(x101, 0xffffffff, &x120); 206 uint64_t x123; uint64_t x122 = mulx_u64(x101, 0xffffffff00000001L, &x123); 207 uint64_t x125; uint8_t x126 = addcarryx_u64(0x0, x117, x119, &x125); 208 uint64_t x128; uint8_t x129 = addcarryx_u64(x126, x120, 0x0, &x128); 209 uint64_t x131; uint8_t x132 = addcarryx_u64(x129, 0x0, x122, &x131); 210 uint64_t x134; addcarryx_u64(0x0, x132, x123, &x134); 211 uint64_t _3; uint8_t x138 = addcarryx_u64(0x0, x101, x116, &_3); 212 uint64_t x140; uint8_t x141 = addcarryx_u64(x138, x104, x125, &x140); 213 uint64_t x143; uint8_t x144 = addcarryx_u64(x141, x107, x128, &x143); 214 uint64_t x146; uint8_t x147 = addcarryx_u64(x144, x110, x131, &x146); 215 uint64_t x149; uint8_t x150 = addcarryx_u64(x147, x113, x134, &x149); 216 uint8_t x151 = (x150 + x114); 217 uint64_t x154; uint64_t x153 = mulx_u64(x9, x11, &x154); 218 uint64_t x157; uint64_t x156 = mulx_u64(x9, x13, &x157); 219 uint64_t x160; uint64_t x159 = mulx_u64(x9, x15, &x160); 220 uint64_t x163; uint64_t x162 = mulx_u64(x9, x14, &x163); 221 uint64_t x165; uint8_t x166 = addcarryx_u64(0x0, x154, x156, &x165); 222 uint64_t x168; uint8_t x169 = addcarryx_u64(x166, x157, x159, &x168); 223 uint64_t x171; uint8_t x172 = addcarryx_u64(x169, x160, x162, &x171); 224 uint64_t x174; addcarryx_u64(0x0, x172, x163, &x174); 225 uint64_t x177; uint8_t x178 = addcarryx_u64(0x0, x140, x153, &x177); 226 uint64_t x180; uint8_t x181 = addcarryx_u64(x178, x143, x165, &x180); 227 uint64_t x183; uint8_t x184 = addcarryx_u64(x181, x146, x168, &x183); 228 uint64_t x186; uint8_t x187 = addcarryx_u64(x184, x149, x171, &x186); 229 uint64_t x189; uint8_t x190 = addcarryx_u64(x187, x151, x174, &x189); 230 uint64_t x193; uint64_t x192 = mulx_u64(x177, 0xffffffffffffffffL, &x193); 231 uint64_t x196; uint64_t x195 = mulx_u64(x177, 0xffffffff, &x196); 232 uint64_t x199; uint64_t x198 = mulx_u64(x177, 0xffffffff00000001L, &x199); 233 uint64_t x201; uint8_t x202 = addcarryx_u64(0x0, x193, x195, &x201); 234 uint64_t x204; uint8_t x205 = addcarryx_u64(x202, x196, 0x0, &x204); 235 uint64_t x207; uint8_t x208 = addcarryx_u64(x205, 0x0, x198, &x207); 236 uint64_t x210; addcarryx_u64(0x0, x208, x199, &x210); 237 uint64_t _4; uint8_t x214 = addcarryx_u64(0x0, x177, x192, &_4); 238 uint64_t x216; uint8_t x217 = addcarryx_u64(x214, x180, x201, &x216); 239 uint64_t x219; uint8_t x220 = addcarryx_u64(x217, x183, x204, &x219); 240 uint64_t x222; uint8_t x223 = addcarryx_u64(x220, x186, x207, &x222); 241 uint64_t x225; uint8_t x226 = addcarryx_u64(x223, x189, x210, &x225); 242 uint8_t x227 = (x226 + x190); 243 uint64_t x230; uint64_t x229 = mulx_u64(x8, x11, &x230); 244 uint64_t x233; uint64_t x232 = mulx_u64(x8, x13, &x233); 245 uint64_t x236; uint64_t x235 = mulx_u64(x8, x15, &x236); 246 uint64_t x239; uint64_t x238 = mulx_u64(x8, x14, &x239); 247 uint64_t x241; uint8_t x242 = addcarryx_u64(0x0, x230, x232, &x241); 248 uint64_t x244; uint8_t x245 = addcarryx_u64(x242, x233, x235, &x244); 249 uint64_t x247; uint8_t x248 = addcarryx_u64(x245, x236, x238, &x247); 250 uint64_t x250; addcarryx_u64(0x0, x248, x239, &x250); 251 uint64_t x253; uint8_t x254 = addcarryx_u64(0x0, x216, x229, &x253); 252 uint64_t x256; uint8_t x257 = addcarryx_u64(x254, x219, x241, &x256); 253 uint64_t x259; uint8_t x260 = addcarryx_u64(x257, x222, x244, &x259); 254 uint64_t x262; uint8_t x263 = addcarryx_u64(x260, x225, x247, &x262); 255 uint64_t x265; uint8_t x266 = addcarryx_u64(x263, x227, x250, &x265); 256 uint64_t x269; uint64_t x268 = mulx_u64(x253, 0xffffffffffffffffL, &x269); 257 uint64_t x272; uint64_t x271 = mulx_u64(x253, 0xffffffff, &x272); 258 uint64_t x275; uint64_t x274 = mulx_u64(x253, 0xffffffff00000001L, &x275); 259 uint64_t x277; uint8_t x278 = addcarryx_u64(0x0, x269, x271, &x277); 260 uint64_t x280; uint8_t x281 = addcarryx_u64(x278, x272, 0x0, &x280); 261 uint64_t x283; uint8_t x284 = addcarryx_u64(x281, 0x0, x274, &x283); 262 uint64_t x286; addcarryx_u64(0x0, x284, x275, &x286); 263 uint64_t _5; uint8_t x290 = addcarryx_u64(0x0, x253, x268, &_5); 264 uint64_t x292; uint8_t x293 = addcarryx_u64(x290, x256, x277, &x292); 265 uint64_t x295; uint8_t x296 = addcarryx_u64(x293, x259, x280, &x295); 266 uint64_t x298; uint8_t x299 = addcarryx_u64(x296, x262, x283, &x298); 267 uint64_t x301; uint8_t x302 = addcarryx_u64(x299, x265, x286, &x301); 268 uint8_t x303 = (x302 + x266); 269 uint64_t x305; uint8_t x306 = subborrow_u64(0x0, x292, 0xffffffffffffffffL, &x305); 270 uint64_t x308; uint8_t x309 = subborrow_u64(x306, x295, 0xffffffff, &x308); 271 uint64_t x311; uint8_t x312 = subborrow_u64(x309, x298, 0x0, &x311); 272 uint64_t x314; uint8_t x315 = subborrow_u64(x312, x301, 0xffffffff00000001L, &x314); 273 uint64_t _6; uint8_t x318 = subborrow_u64(x315, x303, 0x0, &_6); 274 uint64_t x319 = cmovznz_u64(x318, x314, x301); 275 uint64_t x320 = cmovznz_u64(x318, x311, x298); 276 uint64_t x321 = cmovznz_u64(x318, x308, x295); 277 uint64_t x322 = cmovznz_u64(x318, x305, x292); 278 out[0] = x322; 279 out[1] = x321; 280 out[2] = x320; 281 out[3] = x319; 282 } 283 284 static void fe_sub(uint64_t out[4], const uint64_t in1[4], const uint64_t in2[4]) { 285 const uint64_t x8 = in1[3]; 286 const uint64_t x9 = in1[2]; 287 const uint64_t x7 = in1[1]; 288 const uint64_t x5 = in1[0]; 289 const uint64_t x14 = in2[3]; 290 const uint64_t x15 = in2[2]; 291 const uint64_t x13 = in2[1]; 292 const uint64_t x11 = in2[0]; 293 uint64_t x17; uint8_t x18 = subborrow_u64(0x0, x5, x11, &x17); 294 uint64_t x20; uint8_t x21 = subborrow_u64(x18, x7, x13, &x20); 295 uint64_t x23; uint8_t x24 = subborrow_u64(x21, x9, x15, &x23); 296 uint64_t x26; uint8_t x27 = subborrow_u64(x24, x8, x14, &x26); 297 uint64_t x28 = (uint64_t)cmovznz_u64(x27, 0x0, 0xffffffffffffffffL); 298 uint64_t x29 = (x28 & 0xffffffffffffffffL); 299 uint64_t x31; uint8_t x32 = addcarryx_u64(0x0, x17, x29, &x31); 300 uint64_t x33 = (x28 & 0xffffffff); 301 uint64_t x35; uint8_t x36 = addcarryx_u64(x32, x20, x33, &x35); 302 uint64_t x38; uint8_t x39 = addcarryx_u64(x36, x23, 0x0, &x38); 303 uint64_t x40 = (x28 & 0xffffffff00000001L); 304 uint64_t x42; addcarryx_u64(x39, x26, x40, &x42); 305 out[0] = x31; 306 out[1] = x35; 307 out[2] = x38; 308 out[3] = x42; 309 } 310 311 #else // 64BIT, else 32BIT 312 313 static void fe_add(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { 314 const uint32_t x16 = in1[7]; 315 const uint32_t x17 = in1[6]; 316 const uint32_t x15 = in1[5]; 317 const uint32_t x13 = in1[4]; 318 const uint32_t x11 = in1[3]; 319 const uint32_t x9 = in1[2]; 320 const uint32_t x7 = in1[1]; 321 const uint32_t x5 = in1[0]; 322 const uint32_t x30 = in2[7]; 323 const uint32_t x31 = in2[6]; 324 const uint32_t x29 = in2[5]; 325 const uint32_t x27 = in2[4]; 326 const uint32_t x25 = in2[3]; 327 const uint32_t x23 = in2[2]; 328 const uint32_t x21 = in2[1]; 329 const uint32_t x19 = in2[0]; 330 uint32_t x33; uint8_t x34 = addcarryx_u32(0x0, x5, x19, &x33); 331 uint32_t x36; uint8_t x37 = addcarryx_u32(x34, x7, x21, &x36); 332 uint32_t x39; uint8_t x40 = addcarryx_u32(x37, x9, x23, &x39); 333 uint32_t x42; uint8_t x43 = addcarryx_u32(x40, x11, x25, &x42); 334 uint32_t x45; uint8_t x46 = addcarryx_u32(x43, x13, x27, &x45); 335 uint32_t x48; uint8_t x49 = addcarryx_u32(x46, x15, x29, &x48); 336 uint32_t x51; uint8_t x52 = addcarryx_u32(x49, x17, x31, &x51); 337 uint32_t x54; uint8_t x55 = addcarryx_u32(x52, x16, x30, &x54); 338 uint32_t x57; uint8_t x58 = subborrow_u32(0x0, x33, 0xffffffff, &x57); 339 uint32_t x60; uint8_t x61 = subborrow_u32(x58, x36, 0xffffffff, &x60); 340 uint32_t x63; uint8_t x64 = subborrow_u32(x61, x39, 0xffffffff, &x63); 341 uint32_t x66; uint8_t x67 = subborrow_u32(x64, x42, 0x0, &x66); 342 uint32_t x69; uint8_t x70 = subborrow_u32(x67, x45, 0x0, &x69); 343 uint32_t x72; uint8_t x73 = subborrow_u32(x70, x48, 0x0, &x72); 344 uint32_t x75; uint8_t x76 = subborrow_u32(x73, x51, 0x1, &x75); 345 uint32_t x78; uint8_t x79 = subborrow_u32(x76, x54, 0xffffffff, &x78); 346 uint32_t _; uint8_t x82 = subborrow_u32(x79, x55, 0x0, &_); 347 uint32_t x83 = cmovznz_u32(x82, x78, x54); 348 uint32_t x84 = cmovznz_u32(x82, x75, x51); 349 uint32_t x85 = cmovznz_u32(x82, x72, x48); 350 uint32_t x86 = cmovznz_u32(x82, x69, x45); 351 uint32_t x87 = cmovznz_u32(x82, x66, x42); 352 uint32_t x88 = cmovznz_u32(x82, x63, x39); 353 uint32_t x89 = cmovznz_u32(x82, x60, x36); 354 uint32_t x90 = cmovznz_u32(x82, x57, x33); 355 out[0] = x90; 356 out[1] = x89; 357 out[2] = x88; 358 out[3] = x87; 359 out[4] = x86; 360 out[5] = x85; 361 out[6] = x84; 362 out[7] = x83; 363 } 364 365 static void fe_mul(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { 366 const uint32_t x16 = in1[7]; 367 const uint32_t x17 = in1[6]; 368 const uint32_t x15 = in1[5]; 369 const uint32_t x13 = in1[4]; 370 const uint32_t x11 = in1[3]; 371 const uint32_t x9 = in1[2]; 372 const uint32_t x7 = in1[1]; 373 const uint32_t x5 = in1[0]; 374 const uint32_t x30 = in2[7]; 375 const uint32_t x31 = in2[6]; 376 const uint32_t x29 = in2[5]; 377 const uint32_t x27 = in2[4]; 378 const uint32_t x25 = in2[3]; 379 const uint32_t x23 = in2[2]; 380 const uint32_t x21 = in2[1]; 381 const uint32_t x19 = in2[0]; 382 uint32_t x34; uint32_t x33 = mulx_u32(x5, x19, &x34); 383 uint32_t x37; uint32_t x36 = mulx_u32(x5, x21, &x37); 384 uint32_t x40; uint32_t x39 = mulx_u32(x5, x23, &x40); 385 uint32_t x43; uint32_t x42 = mulx_u32(x5, x25, &x43); 386 uint32_t x46; uint32_t x45 = mulx_u32(x5, x27, &x46); 387 uint32_t x49; uint32_t x48 = mulx_u32(x5, x29, &x49); 388 uint32_t x52; uint32_t x51 = mulx_u32(x5, x31, &x52); 389 uint32_t x55; uint32_t x54 = mulx_u32(x5, x30, &x55); 390 uint32_t x57; uint8_t x58 = addcarryx_u32(0x0, x34, x36, &x57); 391 uint32_t x60; uint8_t x61 = addcarryx_u32(x58, x37, x39, &x60); 392 uint32_t x63; uint8_t x64 = addcarryx_u32(x61, x40, x42, &x63); 393 uint32_t x66; uint8_t x67 = addcarryx_u32(x64, x43, x45, &x66); 394 uint32_t x69; uint8_t x70 = addcarryx_u32(x67, x46, x48, &x69); 395 uint32_t x72; uint8_t x73 = addcarryx_u32(x70, x49, x51, &x72); 396 uint32_t x75; uint8_t x76 = addcarryx_u32(x73, x52, x54, &x75); 397 uint32_t x78; addcarryx_u32(0x0, x76, x55, &x78); 398 uint32_t x82; uint32_t x81 = mulx_u32(x33, 0xffffffff, &x82); 399 uint32_t x85; uint32_t x84 = mulx_u32(x33, 0xffffffff, &x85); 400 uint32_t x88; uint32_t x87 = mulx_u32(x33, 0xffffffff, &x88); 401 uint32_t x91; uint32_t x90 = mulx_u32(x33, 0xffffffff, &x91); 402 uint32_t x93; uint8_t x94 = addcarryx_u32(0x0, x82, x84, &x93); 403 uint32_t x96; uint8_t x97 = addcarryx_u32(x94, x85, x87, &x96); 404 uint32_t x99; uint8_t x100 = addcarryx_u32(x97, x88, 0x0, &x99); 405 uint8_t x101 = (0x0 + 0x0); 406 uint32_t _1; uint8_t x104 = addcarryx_u32(0x0, x33, x81, &_1); 407 uint32_t x106; uint8_t x107 = addcarryx_u32(x104, x57, x93, &x106); 408 uint32_t x109; uint8_t x110 = addcarryx_u32(x107, x60, x96, &x109); 409 uint32_t x112; uint8_t x113 = addcarryx_u32(x110, x63, x99, &x112); 410 uint32_t x115; uint8_t x116 = addcarryx_u32(x113, x66, x100, &x115); 411 uint32_t x118; uint8_t x119 = addcarryx_u32(x116, x69, x101, &x118); 412 uint32_t x121; uint8_t x122 = addcarryx_u32(x119, x72, x33, &x121); 413 uint32_t x124; uint8_t x125 = addcarryx_u32(x122, x75, x90, &x124); 414 uint32_t x127; uint8_t x128 = addcarryx_u32(x125, x78, x91, &x127); 415 uint8_t x129 = (x128 + 0x0); 416 uint32_t x132; uint32_t x131 = mulx_u32(x7, x19, &x132); 417 uint32_t x135; uint32_t x134 = mulx_u32(x7, x21, &x135); 418 uint32_t x138; uint32_t x137 = mulx_u32(x7, x23, &x138); 419 uint32_t x141; uint32_t x140 = mulx_u32(x7, x25, &x141); 420 uint32_t x144; uint32_t x143 = mulx_u32(x7, x27, &x144); 421 uint32_t x147; uint32_t x146 = mulx_u32(x7, x29, &x147); 422 uint32_t x150; uint32_t x149 = mulx_u32(x7, x31, &x150); 423 uint32_t x153; uint32_t x152 = mulx_u32(x7, x30, &x153); 424 uint32_t x155; uint8_t x156 = addcarryx_u32(0x0, x132, x134, &x155); 425 uint32_t x158; uint8_t x159 = addcarryx_u32(x156, x135, x137, &x158); 426 uint32_t x161; uint8_t x162 = addcarryx_u32(x159, x138, x140, &x161); 427 uint32_t x164; uint8_t x165 = addcarryx_u32(x162, x141, x143, &x164); 428 uint32_t x167; uint8_t x168 = addcarryx_u32(x165, x144, x146, &x167); 429 uint32_t x170; uint8_t x171 = addcarryx_u32(x168, x147, x149, &x170); 430 uint32_t x173; uint8_t x174 = addcarryx_u32(x171, x150, x152, &x173); 431 uint32_t x176; addcarryx_u32(0x0, x174, x153, &x176); 432 uint32_t x179; uint8_t x180 = addcarryx_u32(0x0, x106, x131, &x179); 433 uint32_t x182; uint8_t x183 = addcarryx_u32(x180, x109, x155, &x182); 434 uint32_t x185; uint8_t x186 = addcarryx_u32(x183, x112, x158, &x185); 435 uint32_t x188; uint8_t x189 = addcarryx_u32(x186, x115, x161, &x188); 436 uint32_t x191; uint8_t x192 = addcarryx_u32(x189, x118, x164, &x191); 437 uint32_t x194; uint8_t x195 = addcarryx_u32(x192, x121, x167, &x194); 438 uint32_t x197; uint8_t x198 = addcarryx_u32(x195, x124, x170, &x197); 439 uint32_t x200; uint8_t x201 = addcarryx_u32(x198, x127, x173, &x200); 440 uint32_t x203; uint8_t x204 = addcarryx_u32(x201, x129, x176, &x203); 441 uint32_t x207; uint32_t x206 = mulx_u32(x179, 0xffffffff, &x207); 442 uint32_t x210; uint32_t x209 = mulx_u32(x179, 0xffffffff, &x210); 443 uint32_t x213; uint32_t x212 = mulx_u32(x179, 0xffffffff, &x213); 444 uint32_t x216; uint32_t x215 = mulx_u32(x179, 0xffffffff, &x216); 445 uint32_t x218; uint8_t x219 = addcarryx_u32(0x0, x207, x209, &x218); 446 uint32_t x221; uint8_t x222 = addcarryx_u32(x219, x210, x212, &x221); 447 uint32_t x224; uint8_t x225 = addcarryx_u32(x222, x213, 0x0, &x224); 448 uint8_t x226 = (0x0 + 0x0); 449 uint32_t _2; uint8_t x229 = addcarryx_u32(0x0, x179, x206, &_2); 450 uint32_t x231; uint8_t x232 = addcarryx_u32(x229, x182, x218, &x231); 451 uint32_t x234; uint8_t x235 = addcarryx_u32(x232, x185, x221, &x234); 452 uint32_t x237; uint8_t x238 = addcarryx_u32(x235, x188, x224, &x237); 453 uint32_t x240; uint8_t x241 = addcarryx_u32(x238, x191, x225, &x240); 454 uint32_t x243; uint8_t x244 = addcarryx_u32(x241, x194, x226, &x243); 455 uint32_t x246; uint8_t x247 = addcarryx_u32(x244, x197, x179, &x246); 456 uint32_t x249; uint8_t x250 = addcarryx_u32(x247, x200, x215, &x249); 457 uint32_t x252; uint8_t x253 = addcarryx_u32(x250, x203, x216, &x252); 458 uint8_t x254 = (x253 + x204); 459 uint32_t x257; uint32_t x256 = mulx_u32(x9, x19, &x257); 460 uint32_t x260; uint32_t x259 = mulx_u32(x9, x21, &x260); 461 uint32_t x263; uint32_t x262 = mulx_u32(x9, x23, &x263); 462 uint32_t x266; uint32_t x265 = mulx_u32(x9, x25, &x266); 463 uint32_t x269; uint32_t x268 = mulx_u32(x9, x27, &x269); 464 uint32_t x272; uint32_t x271 = mulx_u32(x9, x29, &x272); 465 uint32_t x275; uint32_t x274 = mulx_u32(x9, x31, &x275); 466 uint32_t x278; uint32_t x277 = mulx_u32(x9, x30, &x278); 467 uint32_t x280; uint8_t x281 = addcarryx_u32(0x0, x257, x259, &x280); 468 uint32_t x283; uint8_t x284 = addcarryx_u32(x281, x260, x262, &x283); 469 uint32_t x286; uint8_t x287 = addcarryx_u32(x284, x263, x265, &x286); 470 uint32_t x289; uint8_t x290 = addcarryx_u32(x287, x266, x268, &x289); 471 uint32_t x292; uint8_t x293 = addcarryx_u32(x290, x269, x271, &x292); 472 uint32_t x295; uint8_t x296 = addcarryx_u32(x293, x272, x274, &x295); 473 uint32_t x298; uint8_t x299 = addcarryx_u32(x296, x275, x277, &x298); 474 uint32_t x301; addcarryx_u32(0x0, x299, x278, &x301); 475 uint32_t x304; uint8_t x305 = addcarryx_u32(0x0, x231, x256, &x304); 476 uint32_t x307; uint8_t x308 = addcarryx_u32(x305, x234, x280, &x307); 477 uint32_t x310; uint8_t x311 = addcarryx_u32(x308, x237, x283, &x310); 478 uint32_t x313; uint8_t x314 = addcarryx_u32(x311, x240, x286, &x313); 479 uint32_t x316; uint8_t x317 = addcarryx_u32(x314, x243, x289, &x316); 480 uint32_t x319; uint8_t x320 = addcarryx_u32(x317, x246, x292, &x319); 481 uint32_t x322; uint8_t x323 = addcarryx_u32(x320, x249, x295, &x322); 482 uint32_t x325; uint8_t x326 = addcarryx_u32(x323, x252, x298, &x325); 483 uint32_t x328; uint8_t x329 = addcarryx_u32(x326, x254, x301, &x328); 484 uint32_t x332; uint32_t x331 = mulx_u32(x304, 0xffffffff, &x332); 485 uint32_t x335; uint32_t x334 = mulx_u32(x304, 0xffffffff, &x335); 486 uint32_t x338; uint32_t x337 = mulx_u32(x304, 0xffffffff, &x338); 487 uint32_t x341; uint32_t x340 = mulx_u32(x304, 0xffffffff, &x341); 488 uint32_t x343; uint8_t x344 = addcarryx_u32(0x0, x332, x334, &x343); 489 uint32_t x346; uint8_t x347 = addcarryx_u32(x344, x335, x337, &x346); 490 uint32_t x349; uint8_t x350 = addcarryx_u32(x347, x338, 0x0, &x349); 491 uint8_t x351 = (0x0 + 0x0); 492 uint32_t _3; uint8_t x354 = addcarryx_u32(0x0, x304, x331, &_3); 493 uint32_t x356; uint8_t x357 = addcarryx_u32(x354, x307, x343, &x356); 494 uint32_t x359; uint8_t x360 = addcarryx_u32(x357, x310, x346, &x359); 495 uint32_t x362; uint8_t x363 = addcarryx_u32(x360, x313, x349, &x362); 496 uint32_t x365; uint8_t x366 = addcarryx_u32(x363, x316, x350, &x365); 497 uint32_t x368; uint8_t x369 = addcarryx_u32(x366, x319, x351, &x368); 498 uint32_t x371; uint8_t x372 = addcarryx_u32(x369, x322, x304, &x371); 499 uint32_t x374; uint8_t x375 = addcarryx_u32(x372, x325, x340, &x374); 500 uint32_t x377; uint8_t x378 = addcarryx_u32(x375, x328, x341, &x377); 501 uint8_t x379 = (x378 + x329); 502 uint32_t x382; uint32_t x381 = mulx_u32(x11, x19, &x382); 503 uint32_t x385; uint32_t x384 = mulx_u32(x11, x21, &x385); 504 uint32_t x388; uint32_t x387 = mulx_u32(x11, x23, &x388); 505 uint32_t x391; uint32_t x390 = mulx_u32(x11, x25, &x391); 506 uint32_t x394; uint32_t x393 = mulx_u32(x11, x27, &x394); 507 uint32_t x397; uint32_t x396 = mulx_u32(x11, x29, &x397); 508 uint32_t x400; uint32_t x399 = mulx_u32(x11, x31, &x400); 509 uint32_t x403; uint32_t x402 = mulx_u32(x11, x30, &x403); 510 uint32_t x405; uint8_t x406 = addcarryx_u32(0x0, x382, x384, &x405); 511 uint32_t x408; uint8_t x409 = addcarryx_u32(x406, x385, x387, &x408); 512 uint32_t x411; uint8_t x412 = addcarryx_u32(x409, x388, x390, &x411); 513 uint32_t x414; uint8_t x415 = addcarryx_u32(x412, x391, x393, &x414); 514 uint32_t x417; uint8_t x418 = addcarryx_u32(x415, x394, x396, &x417); 515 uint32_t x420; uint8_t x421 = addcarryx_u32(x418, x397, x399, &x420); 516 uint32_t x423; uint8_t x424 = addcarryx_u32(x421, x400, x402, &x423); 517 uint32_t x426; addcarryx_u32(0x0, x424, x403, &x426); 518 uint32_t x429; uint8_t x430 = addcarryx_u32(0x0, x356, x381, &x429); 519 uint32_t x432; uint8_t x433 = addcarryx_u32(x430, x359, x405, &x432); 520 uint32_t x435; uint8_t x436 = addcarryx_u32(x433, x362, x408, &x435); 521 uint32_t x438; uint8_t x439 = addcarryx_u32(x436, x365, x411, &x438); 522 uint32_t x441; uint8_t x442 = addcarryx_u32(x439, x368, x414, &x441); 523 uint32_t x444; uint8_t x445 = addcarryx_u32(x442, x371, x417, &x444); 524 uint32_t x447; uint8_t x448 = addcarryx_u32(x445, x374, x420, &x447); 525 uint32_t x450; uint8_t x451 = addcarryx_u32(x448, x377, x423, &x450); 526 uint32_t x453; uint8_t x454 = addcarryx_u32(x451, x379, x426, &x453); 527 uint32_t x457; uint32_t x456 = mulx_u32(x429, 0xffffffff, &x457); 528 uint32_t x460; uint32_t x459 = mulx_u32(x429, 0xffffffff, &x460); 529 uint32_t x463; uint32_t x462 = mulx_u32(x429, 0xffffffff, &x463); 530 uint32_t x466; uint32_t x465 = mulx_u32(x429, 0xffffffff, &x466); 531 uint32_t x468; uint8_t x469 = addcarryx_u32(0x0, x457, x459, &x468); 532 uint32_t x471; uint8_t x472 = addcarryx_u32(x469, x460, x462, &x471); 533 uint32_t x474; uint8_t x475 = addcarryx_u32(x472, x463, 0x0, &x474); 534 uint8_t x476 = (0x0 + 0x0); 535 uint32_t _4; uint8_t x479 = addcarryx_u32(0x0, x429, x456, &_4); 536 uint32_t x481; uint8_t x482 = addcarryx_u32(x479, x432, x468, &x481); 537 uint32_t x484; uint8_t x485 = addcarryx_u32(x482, x435, x471, &x484); 538 uint32_t x487; uint8_t x488 = addcarryx_u32(x485, x438, x474, &x487); 539 uint32_t x490; uint8_t x491 = addcarryx_u32(x488, x441, x475, &x490); 540 uint32_t x493; uint8_t x494 = addcarryx_u32(x491, x444, x476, &x493); 541 uint32_t x496; uint8_t x497 = addcarryx_u32(x494, x447, x429, &x496); 542 uint32_t x499; uint8_t x500 = addcarryx_u32(x497, x450, x465, &x499); 543 uint32_t x502; uint8_t x503 = addcarryx_u32(x500, x453, x466, &x502); 544 uint8_t x504 = (x503 + x454); 545 uint32_t x507; uint32_t x506 = mulx_u32(x13, x19, &x507); 546 uint32_t x510; uint32_t x509 = mulx_u32(x13, x21, &x510); 547 uint32_t x513; uint32_t x512 = mulx_u32(x13, x23, &x513); 548 uint32_t x516; uint32_t x515 = mulx_u32(x13, x25, &x516); 549 uint32_t x519; uint32_t x518 = mulx_u32(x13, x27, &x519); 550 uint32_t x522; uint32_t x521 = mulx_u32(x13, x29, &x522); 551 uint32_t x525; uint32_t x524 = mulx_u32(x13, x31, &x525); 552 uint32_t x528; uint32_t x527 = mulx_u32(x13, x30, &x528); 553 uint32_t x530; uint8_t x531 = addcarryx_u32(0x0, x507, x509, &x530); 554 uint32_t x533; uint8_t x534 = addcarryx_u32(x531, x510, x512, &x533); 555 uint32_t x536; uint8_t x537 = addcarryx_u32(x534, x513, x515, &x536); 556 uint32_t x539; uint8_t x540 = addcarryx_u32(x537, x516, x518, &x539); 557 uint32_t x542; uint8_t x543 = addcarryx_u32(x540, x519, x521, &x542); 558 uint32_t x545; uint8_t x546 = addcarryx_u32(x543, x522, x524, &x545); 559 uint32_t x548; uint8_t x549 = addcarryx_u32(x546, x525, x527, &x548); 560 uint32_t x551; addcarryx_u32(0x0, x549, x528, &x551); 561 uint32_t x554; uint8_t x555 = addcarryx_u32(0x0, x481, x506, &x554); 562 uint32_t x557; uint8_t x558 = addcarryx_u32(x555, x484, x530, &x557); 563 uint32_t x560; uint8_t x561 = addcarryx_u32(x558, x487, x533, &x560); 564 uint32_t x563; uint8_t x564 = addcarryx_u32(x561, x490, x536, &x563); 565 uint32_t x566; uint8_t x567 = addcarryx_u32(x564, x493, x539, &x566); 566 uint32_t x569; uint8_t x570 = addcarryx_u32(x567, x496, x542, &x569); 567 uint32_t x572; uint8_t x573 = addcarryx_u32(x570, x499, x545, &x572); 568 uint32_t x575; uint8_t x576 = addcarryx_u32(x573, x502, x548, &x575); 569 uint32_t x578; uint8_t x579 = addcarryx_u32(x576, x504, x551, &x578); 570 uint32_t x582; uint32_t x581 = mulx_u32(x554, 0xffffffff, &x582); 571 uint32_t x585; uint32_t x584 = mulx_u32(x554, 0xffffffff, &x585); 572 uint32_t x588; uint32_t x587 = mulx_u32(x554, 0xffffffff, &x588); 573 uint32_t x591; uint32_t x590 = mulx_u32(x554, 0xffffffff, &x591); 574 uint32_t x593; uint8_t x594 = addcarryx_u32(0x0, x582, x584, &x593); 575 uint32_t x596; uint8_t x597 = addcarryx_u32(x594, x585, x587, &x596); 576 uint32_t x599; uint8_t x600 = addcarryx_u32(x597, x588, 0x0, &x599); 577 uint8_t x601 = (0x0 + 0x0); 578 uint32_t _5; uint8_t x604 = addcarryx_u32(0x0, x554, x581, &_5); 579 uint32_t x606; uint8_t x607 = addcarryx_u32(x604, x557, x593, &x606); 580 uint32_t x609; uint8_t x610 = addcarryx_u32(x607, x560, x596, &x609); 581 uint32_t x612; uint8_t x613 = addcarryx_u32(x610, x563, x599, &x612); 582 uint32_t x615; uint8_t x616 = addcarryx_u32(x613, x566, x600, &x615); 583 uint32_t x618; uint8_t x619 = addcarryx_u32(x616, x569, x601, &x618); 584 uint32_t x621; uint8_t x622 = addcarryx_u32(x619, x572, x554, &x621); 585 uint32_t x624; uint8_t x625 = addcarryx_u32(x622, x575, x590, &x624); 586 uint32_t x627; uint8_t x628 = addcarryx_u32(x625, x578, x591, &x627); 587 uint8_t x629 = (x628 + x579); 588 uint32_t x632; uint32_t x631 = mulx_u32(x15, x19, &x632); 589 uint32_t x635; uint32_t x634 = mulx_u32(x15, x21, &x635); 590 uint32_t x638; uint32_t x637 = mulx_u32(x15, x23, &x638); 591 uint32_t x641; uint32_t x640 = mulx_u32(x15, x25, &x641); 592 uint32_t x644; uint32_t x643 = mulx_u32(x15, x27, &x644); 593 uint32_t x647; uint32_t x646 = mulx_u32(x15, x29, &x647); 594 uint32_t x650; uint32_t x649 = mulx_u32(x15, x31, &x650); 595 uint32_t x653; uint32_t x652 = mulx_u32(x15, x30, &x653); 596 uint32_t x655; uint8_t x656 = addcarryx_u32(0x0, x632, x634, &x655); 597 uint32_t x658; uint8_t x659 = addcarryx_u32(x656, x635, x637, &x658); 598 uint32_t x661; uint8_t x662 = addcarryx_u32(x659, x638, x640, &x661); 599 uint32_t x664; uint8_t x665 = addcarryx_u32(x662, x641, x643, &x664); 600 uint32_t x667; uint8_t x668 = addcarryx_u32(x665, x644, x646, &x667); 601 uint32_t x670; uint8_t x671 = addcarryx_u32(x668, x647, x649, &x670); 602 uint32_t x673; uint8_t x674 = addcarryx_u32(x671, x650, x652, &x673); 603 uint32_t x676; addcarryx_u32(0x0, x674, x653, &x676); 604 uint32_t x679; uint8_t x680 = addcarryx_u32(0x0, x606, x631, &x679); 605 uint32_t x682; uint8_t x683 = addcarryx_u32(x680, x609, x655, &x682); 606 uint32_t x685; uint8_t x686 = addcarryx_u32(x683, x612, x658, &x685); 607 uint32_t x688; uint8_t x689 = addcarryx_u32(x686, x615, x661, &x688); 608 uint32_t x691; uint8_t x692 = addcarryx_u32(x689, x618, x664, &x691); 609 uint32_t x694; uint8_t x695 = addcarryx_u32(x692, x621, x667, &x694); 610 uint32_t x697; uint8_t x698 = addcarryx_u32(x695, x624, x670, &x697); 611 uint32_t x700; uint8_t x701 = addcarryx_u32(x698, x627, x673, &x700); 612 uint32_t x703; uint8_t x704 = addcarryx_u32(x701, x629, x676, &x703); 613 uint32_t x707; uint32_t x706 = mulx_u32(x679, 0xffffffff, &x707); 614 uint32_t x710; uint32_t x709 = mulx_u32(x679, 0xffffffff, &x710); 615 uint32_t x713; uint32_t x712 = mulx_u32(x679, 0xffffffff, &x713); 616 uint32_t x716; uint32_t x715 = mulx_u32(x679, 0xffffffff, &x716); 617 uint32_t x718; uint8_t x719 = addcarryx_u32(0x0, x707, x709, &x718); 618 uint32_t x721; uint8_t x722 = addcarryx_u32(x719, x710, x712, &x721); 619 uint32_t x724; uint8_t x725 = addcarryx_u32(x722, x713, 0x0, &x724); 620 uint8_t x726 = (0x0 + 0x0); 621 uint32_t _6; uint8_t x729 = addcarryx_u32(0x0, x679, x706, &_6); 622 uint32_t x731; uint8_t x732 = addcarryx_u32(x729, x682, x718, &x731); 623 uint32_t x734; uint8_t x735 = addcarryx_u32(x732, x685, x721, &x734); 624 uint32_t x737; uint8_t x738 = addcarryx_u32(x735, x688, x724, &x737); 625 uint32_t x740; uint8_t x741 = addcarryx_u32(x738, x691, x725, &x740); 626 uint32_t x743; uint8_t x744 = addcarryx_u32(x741, x694, x726, &x743); 627 uint32_t x746; uint8_t x747 = addcarryx_u32(x744, x697, x679, &x746); 628 uint32_t x749; uint8_t x750 = addcarryx_u32(x747, x700, x715, &x749); 629 uint32_t x752; uint8_t x753 = addcarryx_u32(x750, x703, x716, &x752); 630 uint8_t x754 = (x753 + x704); 631 uint32_t x757; uint32_t x756 = mulx_u32(x17, x19, &x757); 632 uint32_t x760; uint32_t x759 = mulx_u32(x17, x21, &x760); 633 uint32_t x763; uint32_t x762 = mulx_u32(x17, x23, &x763); 634 uint32_t x766; uint32_t x765 = mulx_u32(x17, x25, &x766); 635 uint32_t x769; uint32_t x768 = mulx_u32(x17, x27, &x769); 636 uint32_t x772; uint32_t x771 = mulx_u32(x17, x29, &x772); 637 uint32_t x775; uint32_t x774 = mulx_u32(x17, x31, &x775); 638 uint32_t x778; uint32_t x777 = mulx_u32(x17, x30, &x778); 639 uint32_t x780; uint8_t x781 = addcarryx_u32(0x0, x757, x759, &x780); 640 uint32_t x783; uint8_t x784 = addcarryx_u32(x781, x760, x762, &x783); 641 uint32_t x786; uint8_t x787 = addcarryx_u32(x784, x763, x765, &x786); 642 uint32_t x789; uint8_t x790 = addcarryx_u32(x787, x766, x768, &x789); 643 uint32_t x792; uint8_t x793 = addcarryx_u32(x790, x769, x771, &x792); 644 uint32_t x795; uint8_t x796 = addcarryx_u32(x793, x772, x774, &x795); 645 uint32_t x798; uint8_t x799 = addcarryx_u32(x796, x775, x777, &x798); 646 uint32_t x801; addcarryx_u32(0x0, x799, x778, &x801); 647 uint32_t x804; uint8_t x805 = addcarryx_u32(0x0, x731, x756, &x804); 648 uint32_t x807; uint8_t x808 = addcarryx_u32(x805, x734, x780, &x807); 649 uint32_t x810; uint8_t x811 = addcarryx_u32(x808, x737, x783, &x810); 650 uint32_t x813; uint8_t x814 = addcarryx_u32(x811, x740, x786, &x813); 651 uint32_t x816; uint8_t x817 = addcarryx_u32(x814, x743, x789, &x816); 652 uint32_t x819; uint8_t x820 = addcarryx_u32(x817, x746, x792, &x819); 653 uint32_t x822; uint8_t x823 = addcarryx_u32(x820, x749, x795, &x822); 654 uint32_t x825; uint8_t x826 = addcarryx_u32(x823, x752, x798, &x825); 655 uint32_t x828; uint8_t x829 = addcarryx_u32(x826, x754, x801, &x828); 656 uint32_t x832; uint32_t x831 = mulx_u32(x804, 0xffffffff, &x832); 657 uint32_t x835; uint32_t x834 = mulx_u32(x804, 0xffffffff, &x835); 658 uint32_t x838; uint32_t x837 = mulx_u32(x804, 0xffffffff, &x838); 659 uint32_t x841; uint32_t x840 = mulx_u32(x804, 0xffffffff, &x841); 660 uint32_t x843; uint8_t x844 = addcarryx_u32(0x0, x832, x834, &x843); 661 uint32_t x846; uint8_t x847 = addcarryx_u32(x844, x835, x837, &x846); 662 uint32_t x849; uint8_t x850 = addcarryx_u32(x847, x838, 0x0, &x849); 663 uint8_t x851 = (0x0 + 0x0); 664 uint32_t _7; uint8_t x854 = addcarryx_u32(0x0, x804, x831, &_7); 665 uint32_t x856; uint8_t x857 = addcarryx_u32(x854, x807, x843, &x856); 666 uint32_t x859; uint8_t x860 = addcarryx_u32(x857, x810, x846, &x859); 667 uint32_t x862; uint8_t x863 = addcarryx_u32(x860, x813, x849, &x862); 668 uint32_t x865; uint8_t x866 = addcarryx_u32(x863, x816, x850, &x865); 669 uint32_t x868; uint8_t x869 = addcarryx_u32(x866, x819, x851, &x868); 670 uint32_t x871; uint8_t x872 = addcarryx_u32(x869, x822, x804, &x871); 671 uint32_t x874; uint8_t x875 = addcarryx_u32(x872, x825, x840, &x874); 672 uint32_t x877; uint8_t x878 = addcarryx_u32(x875, x828, x841, &x877); 673 uint8_t x879 = (x878 + x829); 674 uint32_t x882; uint32_t x881 = mulx_u32(x16, x19, &x882); 675 uint32_t x885; uint32_t x884 = mulx_u32(x16, x21, &x885); 676 uint32_t x888; uint32_t x887 = mulx_u32(x16, x23, &x888); 677 uint32_t x891; uint32_t x890 = mulx_u32(x16, x25, &x891); 678 uint32_t x894; uint32_t x893 = mulx_u32(x16, x27, &x894); 679 uint32_t x897; uint32_t x896 = mulx_u32(x16, x29, &x897); 680 uint32_t x900; uint32_t x899 = mulx_u32(x16, x31, &x900); 681 uint32_t x903; uint32_t x902 = mulx_u32(x16, x30, &x903); 682 uint32_t x905; uint8_t x906 = addcarryx_u32(0x0, x882, x884, &x905); 683 uint32_t x908; uint8_t x909 = addcarryx_u32(x906, x885, x887, &x908); 684 uint32_t x911; uint8_t x912 = addcarryx_u32(x909, x888, x890, &x911); 685 uint32_t x914; uint8_t x915 = addcarryx_u32(x912, x891, x893, &x914); 686 uint32_t x917; uint8_t x918 = addcarryx_u32(x915, x894, x896, &x917); 687 uint32_t x920; uint8_t x921 = addcarryx_u32(x918, x897, x899, &x920); 688 uint32_t x923; uint8_t x924 = addcarryx_u32(x921, x900, x902, &x923); 689 uint32_t x926; addcarryx_u32(0x0, x924, x903, &x926); 690 uint32_t x929; uint8_t x930 = addcarryx_u32(0x0, x856, x881, &x929); 691 uint32_t x932; uint8_t x933 = addcarryx_u32(x930, x859, x905, &x932); 692 uint32_t x935; uint8_t x936 = addcarryx_u32(x933, x862, x908, &x935); 693 uint32_t x938; uint8_t x939 = addcarryx_u32(x936, x865, x911, &x938); 694 uint32_t x941; uint8_t x942 = addcarryx_u32(x939, x868, x914, &x941); 695 uint32_t x944; uint8_t x945 = addcarryx_u32(x942, x871, x917, &x944); 696 uint32_t x947; uint8_t x948 = addcarryx_u32(x945, x874, x920, &x947); 697 uint32_t x950; uint8_t x951 = addcarryx_u32(x948, x877, x923, &x950); 698 uint32_t x953; uint8_t x954 = addcarryx_u32(x951, x879, x926, &x953); 699 uint32_t x957; uint32_t x956 = mulx_u32(x929, 0xffffffff, &x957); 700 uint32_t x960; uint32_t x959 = mulx_u32(x929, 0xffffffff, &x960); 701 uint32_t x963; uint32_t x962 = mulx_u32(x929, 0xffffffff, &x963); 702 uint32_t x966; uint32_t x965 = mulx_u32(x929, 0xffffffff, &x966); 703 uint32_t x968; uint8_t x969 = addcarryx_u32(0x0, x957, x959, &x968); 704 uint32_t x971; uint8_t x972 = addcarryx_u32(x969, x960, x962, &x971); 705 uint32_t x974; uint8_t x975 = addcarryx_u32(x972, x963, 0x0, &x974); 706 uint8_t x976 = (0x0 + 0x0); 707 uint32_t _8; uint8_t x979 = addcarryx_u32(0x0, x929, x956, &_8); 708 uint32_t x981; uint8_t x982 = addcarryx_u32(x979, x932, x968, &x981); 709 uint32_t x984; uint8_t x985 = addcarryx_u32(x982, x935, x971, &x984); 710 uint32_t x987; uint8_t x988 = addcarryx_u32(x985, x938, x974, &x987); 711 uint32_t x990; uint8_t x991 = addcarryx_u32(x988, x941, x975, &x990); 712 uint32_t x993; uint8_t x994 = addcarryx_u32(x991, x944, x976, &x993); 713 uint32_t x996; uint8_t x997 = addcarryx_u32(x994, x947, x929, &x996); 714 uint32_t x999; uint8_t x1000 = addcarryx_u32(x997, x950, x965, &x999); 715 uint32_t x1002; uint8_t x1003 = addcarryx_u32(x1000, x953, x966, &x1002); 716 uint8_t x1004 = (x1003 + x954); 717 uint32_t x1006; uint8_t x1007 = subborrow_u32(0x0, x981, 0xffffffff, &x1006); 718 uint32_t x1009; uint8_t x1010 = subborrow_u32(x1007, x984, 0xffffffff, &x1009); 719 uint32_t x1012; uint8_t x1013 = subborrow_u32(x1010, x987, 0xffffffff, &x1012); 720 uint32_t x1015; uint8_t x1016 = subborrow_u32(x1013, x990, 0x0, &x1015); 721 uint32_t x1018; uint8_t x1019 = subborrow_u32(x1016, x993, 0x0, &x1018); 722 uint32_t x1021; uint8_t x1022 = subborrow_u32(x1019, x996, 0x0, &x1021); 723 uint32_t x1024; uint8_t x1025 = subborrow_u32(x1022, x999, 0x1, &x1024); 724 uint32_t x1027; uint8_t x1028 = subborrow_u32(x1025, x1002, 0xffffffff, &x1027); 725 uint32_t _9; uint8_t x1031 = subborrow_u32(x1028, x1004, 0x0, &_9); 726 uint32_t x1032 = cmovznz_u32(x1031, x1027, x1002); 727 uint32_t x1033 = cmovznz_u32(x1031, x1024, x999); 728 uint32_t x1034 = cmovznz_u32(x1031, x1021, x996); 729 uint32_t x1035 = cmovznz_u32(x1031, x1018, x993); 730 uint32_t x1036 = cmovznz_u32(x1031, x1015, x990); 731 uint32_t x1037 = cmovznz_u32(x1031, x1012, x987); 732 uint32_t x1038 = cmovznz_u32(x1031, x1009, x984); 733 uint32_t x1039 = cmovznz_u32(x1031, x1006, x981); 734 out[0] = x1039; 735 out[1] = x1038; 736 out[2] = x1037; 737 out[3] = x1036; 738 out[4] = x1035; 739 out[5] = x1034; 740 out[6] = x1033; 741 out[7] = x1032; 742 } 743 744 // NOTE: the following functions are generated from fiat-crypto, from the same 745 // template as their 64-bit counterparts above, but the correctness proof of 746 // the template was not composed with the correctness proof of the 747 // specialization pipeline. This is because Coq unexplainedly loops on trying 748 // to synthesize opp and sub using the normal pipeline. 749 750 static void fe_sub(uint32_t out[8], const uint32_t in1[8], const uint32_t in2[8]) { 751 const uint32_t x14 = in1[7]; 752 const uint32_t x15 = in1[6]; 753 const uint32_t x13 = in1[5]; 754 const uint32_t x11 = in1[4]; 755 const uint32_t x9 = in1[3]; 756 const uint32_t x7 = in1[2]; 757 const uint32_t x5 = in1[1]; 758 const uint32_t x3 = in1[0]; 759 const uint32_t x28 = in2[7]; 760 const uint32_t x29 = in2[6]; 761 const uint32_t x27 = in2[5]; 762 const uint32_t x25 = in2[4]; 763 const uint32_t x23 = in2[3]; 764 const uint32_t x21 = in2[2]; 765 const uint32_t x19 = in2[1]; 766 const uint32_t x17 = in2[0]; 767 uint32_t x31; uint8_t x32 = subborrow_u32(0x0, x3, x17, &x31); 768 uint32_t x34; uint8_t x35 = subborrow_u32(x32, x5, x19, &x34); 769 uint32_t x37; uint8_t x38 = subborrow_u32(x35, x7, x21, &x37); 770 uint32_t x40; uint8_t x41 = subborrow_u32(x38, x9, x23, &x40); 771 uint32_t x43; uint8_t x44 = subborrow_u32(x41, x11, x25, &x43); 772 uint32_t x46; uint8_t x47 = subborrow_u32(x44, x13, x27, &x46); 773 uint32_t x49; uint8_t x50 = subborrow_u32(x47, x15, x29, &x49); 774 uint32_t x52; uint8_t x53 = subborrow_u32(x50, x14, x28, &x52); 775 uint32_t x54 = cmovznz_u32(x53, 0x0, 0xffffffff); 776 uint32_t x56; uint8_t x57 = addcarryx_u32(0x0, x31, (x54 & 0xffffffff), &x56); 777 uint32_t x59; uint8_t x60 = addcarryx_u32(x57, x34, (x54 & 0xffffffff), &x59); 778 uint32_t x62; uint8_t x63 = addcarryx_u32(x60, x37, (x54 & 0xffffffff), &x62); 779 uint32_t x65; uint8_t x66 = addcarryx_u32(x63, x40, 0x0, &x65); 780 uint32_t x68; uint8_t x69 = addcarryx_u32(x66, x43, 0x0, &x68); 781 uint32_t x71; uint8_t x72 = addcarryx_u32(x69, x46, 0x0, &x71); 782 uint32_t x74; uint8_t x75 = addcarryx_u32(x72, x49, ((uint8_t)x54 & 0x1), &x74); 783 uint32_t x77; addcarryx_u32(x75, x52, (x54 & 0xffffffff), &x77); 784 out[0] = x56; 785 out[1] = x59; 786 out[2] = x62; 787 out[3] = x65; 788 out[4] = x68; 789 out[5] = x71; 790 out[6] = x74; 791 out[7] = x77; 792 } 793 794 // fe_op sets out = -in 795 static void fe_opp(uint32_t out[8], const uint32_t in1[8]) { 796 const uint32_t x12 = in1[7]; 797 const uint32_t x13 = in1[6]; 798 const uint32_t x11 = in1[5]; 799 const uint32_t x9 = in1[4]; 800 const uint32_t x7 = in1[3]; 801 const uint32_t x5 = in1[2]; 802 const uint32_t x3 = in1[1]; 803 const uint32_t x1 = in1[0]; 804 uint32_t x15; uint8_t x16 = subborrow_u32(0x0, 0x0, x1, &x15); 805 uint32_t x18; uint8_t x19 = subborrow_u32(x16, 0x0, x3, &x18); 806 uint32_t x21; uint8_t x22 = subborrow_u32(x19, 0x0, x5, &x21); 807 uint32_t x24; uint8_t x25 = subborrow_u32(x22, 0x0, x7, &x24); 808 uint32_t x27; uint8_t x28 = subborrow_u32(x25, 0x0, x9, &x27); 809 uint32_t x30; uint8_t x31 = subborrow_u32(x28, 0x0, x11, &x30); 810 uint32_t x33; uint8_t x34 = subborrow_u32(x31, 0x0, x13, &x33); 811 uint32_t x36; uint8_t x37 = subborrow_u32(x34, 0x0, x12, &x36); 812 uint32_t x38 = cmovznz_u32(x37, 0x0, 0xffffffff); 813 uint32_t x40; uint8_t x41 = addcarryx_u32(0x0, x15, (x38 & 0xffffffff), &x40); 814 uint32_t x43; uint8_t x44 = addcarryx_u32(x41, x18, (x38 & 0xffffffff), &x43); 815 uint32_t x46; uint8_t x47 = addcarryx_u32(x44, x21, (x38 & 0xffffffff), &x46); 816 uint32_t x49; uint8_t x50 = addcarryx_u32(x47, x24, 0x0, &x49); 817 uint32_t x52; uint8_t x53 = addcarryx_u32(x50, x27, 0x0, &x52); 818 uint32_t x55; uint8_t x56 = addcarryx_u32(x53, x30, 0x0, &x55); 819 uint32_t x58; uint8_t x59 = addcarryx_u32(x56, x33, ((uint8_t)x38 & 0x1), &x58); 820 uint32_t x61; addcarryx_u32(x59, x36, (x38 & 0xffffffff), &x61); 821 out[0] = x40; 822 out[1] = x43; 823 out[2] = x46; 824 out[3] = x49; 825 out[4] = x52; 826 out[5] = x55; 827 out[6] = x58; 828 out[7] = x61; 829 } 830 831 #endif 832 833 // utility functions, handwritten 834 835 #define NBYTES 32 836 837 #if defined(BORINGSSL_NISTP256_64BIT) 838 839 #define NLIMBS 4 840 typedef uint64_t limb_t; 841 #define cmovznz_limb cmovznz_u64 842 typedef uint64_t fe[NLIMBS]; 843 #else // 64BIT; else 32BIT 844 845 #define NLIMBS 8 846 typedef uint32_t limb_t; 847 #define cmovznz_limb cmovznz_u32 848 typedef uint32_t fe[NLIMBS]; 849 850 #endif // 64BIT 851 852 static limb_t fe_nz(const limb_t in1[NLIMBS]) { 853 limb_t ret = 0; 854 for (int i = 0; i < NLIMBS; i++) { 855 ret |= in1[i]; 856 } 857 return ret; 858 } 859 860 static void fe_copy(limb_t out[NLIMBS], const limb_t in1[NLIMBS]) { 861 for (int i = 0; i < NLIMBS; i++) { 862 out[i] = in1[i]; 863 } 864 } 865 866 static void fe_cmovznz(limb_t out[NLIMBS], limb_t t, const limb_t z[NLIMBS], 867 const limb_t nz[NLIMBS]) { 868 for (int i = 0; i < NLIMBS; i++) { 869 out[i] = cmovznz_limb(t, z[i], nz[i]); 870 } 871 } 872 873 static void fe_sqr(fe out, const fe in) { 874 fe_mul(out, in, in); 875 } 876 877 static void fe_tobytes(uint8_t out[NBYTES], const fe in) { 878 for (int i = 0; i<NBYTES; i++) { 879 out[i] = (uint8_t)(in[i/sizeof(in[0])] >> (8*(i%sizeof(in[0])))); 880 } 881 } 882 883 static void fe_frombytes(fe out, const uint8_t in[NBYTES]) { 884 for (int i = 0; i<NLIMBS; i++) { 885 out[i] = 0; 886 } 887 for (int i = 0; i<NBYTES; i++) { 888 out[i/sizeof(out[0])] |= ((limb_t)in[i]) << (8*(i%sizeof(out[0]))); 889 } 890 } 891 892 static void fe_from_montgomery(fe x) { 893 static const limb_t kOne[NLIMBS] = {1, 0}; 894 fe_mul(x, x, kOne); 895 } 896 897 // BN_* compatability wrappers 898 899 static int BN_to_fe(fe out, const BIGNUM *bn) { 900 uint8_t tmp[NBYTES]; 901 if (!BN_bn2le_padded(tmp, NBYTES, bn)) { 902 return 0; 903 } 904 fe_frombytes(out, tmp); 905 return 1; 906 } 907 908 static BIGNUM *fe_to_BN(BIGNUM *out, const fe in) { 909 uint8_t tmp[NBYTES]; 910 fe_tobytes(tmp, in); 911 return BN_le2bn(tmp, NBYTES, out); 912 } 913 914 // fe_inv calculates |out| = |in|^{-1} 915 // 916 // Based on Fermat's Little Theorem: 917 // a^p = a (mod p) 918 // a^{p-1} = 1 (mod p) 919 // a^{p-2} = a^{-1} (mod p) 920 static void fe_inv(fe out, const fe in) { 921 fe ftmp, ftmp2; 922 // each e_I will hold |in|^{2^I - 1} 923 fe e2, e4, e8, e16, e32, e64; 924 925 fe_sqr(ftmp, in); // 2^1 926 fe_mul(ftmp, in, ftmp); // 2^2 - 2^0 927 fe_copy(e2, ftmp); 928 fe_sqr(ftmp, ftmp); // 2^3 - 2^1 929 fe_sqr(ftmp, ftmp); // 2^4 - 2^2 930 fe_mul(ftmp, ftmp, e2); // 2^4 - 2^0 931 fe_copy(e4, ftmp); 932 fe_sqr(ftmp, ftmp); // 2^5 - 2^1 933 fe_sqr(ftmp, ftmp); // 2^6 - 2^2 934 fe_sqr(ftmp, ftmp); // 2^7 - 2^3 935 fe_sqr(ftmp, ftmp); // 2^8 - 2^4 936 fe_mul(ftmp, ftmp, e4); // 2^8 - 2^0 937 fe_copy(e8, ftmp); 938 for (size_t i = 0; i < 8; i++) { 939 fe_sqr(ftmp, ftmp); 940 } // 2^16 - 2^8 941 fe_mul(ftmp, ftmp, e8); // 2^16 - 2^0 942 fe_copy(e16, ftmp); 943 for (size_t i = 0; i < 16; i++) { 944 fe_sqr(ftmp, ftmp); 945 } // 2^32 - 2^16 946 fe_mul(ftmp, ftmp, e16); // 2^32 - 2^0 947 fe_copy(e32, ftmp); 948 for (size_t i = 0; i < 32; i++) { 949 fe_sqr(ftmp, ftmp); 950 } // 2^64 - 2^32 951 fe_copy(e64, ftmp); 952 fe_mul(ftmp, ftmp, in); // 2^64 - 2^32 + 2^0 953 for (size_t i = 0; i < 192; i++) { 954 fe_sqr(ftmp, ftmp); 955 } // 2^256 - 2^224 + 2^192 956 957 fe_mul(ftmp2, e64, e32); // 2^64 - 2^0 958 for (size_t i = 0; i < 16; i++) { 959 fe_sqr(ftmp2, ftmp2); 960 } // 2^80 - 2^16 961 fe_mul(ftmp2, ftmp2, e16); // 2^80 - 2^0 962 for (size_t i = 0; i < 8; i++) { 963 fe_sqr(ftmp2, ftmp2); 964 } // 2^88 - 2^8 965 fe_mul(ftmp2, ftmp2, e8); // 2^88 - 2^0 966 for (size_t i = 0; i < 4; i++) { 967 fe_sqr(ftmp2, ftmp2); 968 } // 2^92 - 2^4 969 fe_mul(ftmp2, ftmp2, e4); // 2^92 - 2^0 970 fe_sqr(ftmp2, ftmp2); // 2^93 - 2^1 971 fe_sqr(ftmp2, ftmp2); // 2^94 - 2^2 972 fe_mul(ftmp2, ftmp2, e2); // 2^94 - 2^0 973 fe_sqr(ftmp2, ftmp2); // 2^95 - 2^1 974 fe_sqr(ftmp2, ftmp2); // 2^96 - 2^2 975 fe_mul(ftmp2, ftmp2, in); // 2^96 - 3 976 977 fe_mul(out, ftmp2, ftmp); // 2^256 - 2^224 + 2^192 + 2^96 - 3 978 } 979 980 // Group operations 981 // ---------------- 982 // 983 // Building on top of the field operations we have the operations on the 984 // elliptic curve group itself. Points on the curve are represented in Jacobian 985 // coordinates. 986 // 987 // Both operations were transcribed to Coq and proven to correspond to naive 988 // implementations using Affine coordinates, for all suitable fields. In the 989 // Coq proofs, issues of constant-time execution and memory layout (aliasing) 990 // conventions were not considered. Specification of affine coordinates: 991 // <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Spec/WeierstrassCurve.v#L28> 992 // As a sanity check, a proof that these points form a commutative group: 993 // <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/AffineProofs.v#L33> 994 995 // point_double calculates 2*(x_in, y_in, z_in) 996 // 997 // The method is taken from: 998 // http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b 999 // 1000 // Coq transcription and correctness proof: 1001 // <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L93> 1002 // <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L201> 1003 // 1004 // Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. 1005 // while x_out == y_in is not (maybe this works, but it's not tested). 1006 static void point_double(fe x_out, fe y_out, fe z_out, 1007 const fe x_in, const fe y_in, const fe z_in) { 1008 fe delta, gamma, beta, ftmp, ftmp2, tmptmp, alpha, fourbeta; 1009 // delta = z^2 1010 fe_sqr(delta, z_in); 1011 // gamma = y^2 1012 fe_sqr(gamma, y_in); 1013 // beta = x*gamma 1014 fe_mul(beta, x_in, gamma); 1015 1016 // alpha = 3*(x-delta)*(x+delta) 1017 fe_sub(ftmp, x_in, delta); 1018 fe_add(ftmp2, x_in, delta); 1019 1020 fe_add(tmptmp, ftmp2, ftmp2); 1021 fe_add(ftmp2, ftmp2, tmptmp); 1022 fe_mul(alpha, ftmp, ftmp2); 1023 1024 // x' = alpha^2 - 8*beta 1025 fe_sqr(x_out, alpha); 1026 fe_add(fourbeta, beta, beta); 1027 fe_add(fourbeta, fourbeta, fourbeta); 1028 fe_add(tmptmp, fourbeta, fourbeta); 1029 fe_sub(x_out, x_out, tmptmp); 1030 1031 // z' = (y + z)^2 - gamma - delta 1032 fe_add(delta, gamma, delta); 1033 fe_add(ftmp, y_in, z_in); 1034 fe_sqr(z_out, ftmp); 1035 fe_sub(z_out, z_out, delta); 1036 1037 // y' = alpha*(4*beta - x') - 8*gamma^2 1038 fe_sub(y_out, fourbeta, x_out); 1039 fe_add(gamma, gamma, gamma); 1040 fe_sqr(gamma, gamma); 1041 fe_mul(y_out, alpha, y_out); 1042 fe_add(gamma, gamma, gamma); 1043 fe_sub(y_out, y_out, gamma); 1044 } 1045 1046 // point_add calcuates (x1, y1, z1) + (x2, y2, z2) 1047 // 1048 // The method is taken from: 1049 // http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, 1050 // adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). 1051 // 1052 // Coq transcription and correctness proof: 1053 // <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L135> 1054 // <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L205> 1055 // 1056 // This function includes a branch for checking whether the two input points 1057 // are equal, (while not equal to the point at infinity). This case never 1058 // happens during single point multiplication, so there is no timing leak for 1059 // ECDH or ECDSA signing. 1060 static void point_add(fe x3, fe y3, fe z3, const fe x1, 1061 const fe y1, const fe z1, const int mixed, 1062 const fe x2, const fe y2, const fe z2) { 1063 fe x_out, y_out, z_out; 1064 limb_t z1nz = fe_nz(z1); 1065 limb_t z2nz = fe_nz(z2); 1066 1067 // z1z1 = z1z1 = z1**2 1068 fe z1z1; fe_sqr(z1z1, z1); 1069 1070 fe u1, s1, two_z1z2; 1071 if (!mixed) { 1072 // z2z2 = z2**2 1073 fe z2z2; fe_sqr(z2z2, z2); 1074 1075 // u1 = x1*z2z2 1076 fe_mul(u1, x1, z2z2); 1077 1078 // two_z1z2 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 1079 fe_add(two_z1z2, z1, z2); 1080 fe_sqr(two_z1z2, two_z1z2); 1081 fe_sub(two_z1z2, two_z1z2, z1z1); 1082 fe_sub(two_z1z2, two_z1z2, z2z2); 1083 1084 // s1 = y1 * z2**3 1085 fe_mul(s1, z2, z2z2); 1086 fe_mul(s1, s1, y1); 1087 } else { 1088 // We'll assume z2 = 1 (special case z2 = 0 is handled later). 1089 1090 // u1 = x1*z2z2 1091 fe_copy(u1, x1); 1092 // two_z1z2 = 2z1z2 1093 fe_add(two_z1z2, z1, z1); 1094 // s1 = y1 * z2**3 1095 fe_copy(s1, y1); 1096 } 1097 1098 // u2 = x2*z1z1 1099 fe u2; fe_mul(u2, x2, z1z1); 1100 1101 // h = u2 - u1 1102 fe h; fe_sub(h, u2, u1); 1103 1104 limb_t xneq = fe_nz(h); 1105 1106 // z_out = two_z1z2 * h 1107 fe_mul(z_out, h, two_z1z2); 1108 1109 // z1z1z1 = z1 * z1z1 1110 fe z1z1z1; fe_mul(z1z1z1, z1, z1z1); 1111 1112 // s2 = y2 * z1**3 1113 fe s2; fe_mul(s2, y2, z1z1z1); 1114 1115 // r = (s2 - s1)*2 1116 fe r; 1117 fe_sub(r, s2, s1); 1118 fe_add(r, r, r); 1119 1120 limb_t yneq = fe_nz(r); 1121 1122 if (!xneq && !yneq && z1nz && z2nz) { 1123 point_double(x3, y3, z3, x1, y1, z1); 1124 return; 1125 } 1126 1127 // I = (2h)**2 1128 fe i; 1129 fe_add(i, h, h); 1130 fe_sqr(i, i); 1131 1132 // J = h * I 1133 fe j; fe_mul(j, h, i); 1134 1135 // V = U1 * I 1136 fe v; fe_mul(v, u1, i); 1137 1138 // x_out = r**2 - J - 2V 1139 fe_sqr(x_out, r); 1140 fe_sub(x_out, x_out, j); 1141 fe_sub(x_out, x_out, v); 1142 fe_sub(x_out, x_out, v); 1143 1144 // y_out = r(V-x_out) - 2 * s1 * J 1145 fe_sub(y_out, v, x_out); 1146 fe_mul(y_out, y_out, r); 1147 fe s1j; 1148 fe_mul(s1j, s1, j); 1149 fe_sub(y_out, y_out, s1j); 1150 fe_sub(y_out, y_out, s1j); 1151 1152 fe_cmovznz(x_out, z1nz, x2, x_out); 1153 fe_cmovznz(x3, z2nz, x1, x_out); 1154 fe_cmovznz(y_out, z1nz, y2, y_out); 1155 fe_cmovznz(y3, z2nz, y1, y_out); 1156 fe_cmovznz(z_out, z1nz, z2, z_out); 1157 fe_cmovznz(z3, z2nz, z1, z_out); 1158 } 1159 1160 // Base point pre computation 1161 // -------------------------- 1162 // 1163 // Two different sorts of precomputed tables are used in the following code. 1164 // Each contain various points on the curve, where each point is three field 1165 // elements (x, y, z). 1166 // 1167 // For the base point table, z is usually 1 (0 for the point at infinity). 1168 // This table has 2 * 16 elements, starting with the following: 1169 // index | bits | point 1170 // ------+---------+------------------------------ 1171 // 0 | 0 0 0 0 | 0G 1172 // 1 | 0 0 0 1 | 1G 1173 // 2 | 0 0 1 0 | 2^64G 1174 // 3 | 0 0 1 1 | (2^64 + 1)G 1175 // 4 | 0 1 0 0 | 2^128G 1176 // 5 | 0 1 0 1 | (2^128 + 1)G 1177 // 6 | 0 1 1 0 | (2^128 + 2^64)G 1178 // 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G 1179 // 8 | 1 0 0 0 | 2^192G 1180 // 9 | 1 0 0 1 | (2^192 + 1)G 1181 // 10 | 1 0 1 0 | (2^192 + 2^64)G 1182 // 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G 1183 // 12 | 1 1 0 0 | (2^192 + 2^128)G 1184 // 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G 1185 // 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G 1186 // 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G 1187 // followed by a copy of this with each element multiplied by 2^32. 1188 // 1189 // The reason for this is so that we can clock bits into four different 1190 // locations when doing simple scalar multiplies against the base point, 1191 // and then another four locations using the second 16 elements. 1192 // 1193 // Tables for other points have table[i] = iG for i in 0 .. 16. 1194 1195 // g_pre_comp is the table of precomputed base points 1196 #if defined(BORINGSSL_NISTP256_64BIT) 1197 static const fe g_pre_comp[2][16][3] = { 1198 {{{0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}}, 1199 {{0x79e730d418a9143c, 0x75ba95fc5fedb601, 0x79fb732b77622510, 1200 0x18905f76a53755c6}, 1201 {0xddf25357ce95560a, 0x8b4ab8e4ba19e45c, 0xd2e88688dd21f325, 1202 0x8571ff1825885d85}, 1203 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1204 {{0x4f922fc516a0d2bb, 0xd5cc16c1a623499, 0x9241cf3a57c62c8b, 1205 0x2f5e6961fd1b667f}, 1206 {0x5c15c70bf5a01797, 0x3d20b44d60956192, 0x4911b37071fdb52, 1207 0xf648f9168d6f0f7b}, 1208 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1209 {{0x9e566847e137bbbc, 0xe434469e8a6a0bec, 0xb1c4276179d73463, 1210 0x5abe0285133d0015}, 1211 {0x92aa837cc04c7dab, 0x573d9f4c43260c07, 0xc93156278e6cc37, 1212 0x94bb725b6b6f7383}, 1213 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1214 {{0x62a8c244bfe20925, 0x91c19ac38fdce867, 0x5a96a5d5dd387063, 1215 0x61d587d421d324f6}, 1216 {0xe87673a2a37173ea, 0x2384800853778b65, 0x10f8441e05bab43e, 1217 0xfa11fe124621efbe}, 1218 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1219 {{0x1c891f2b2cb19ffd, 0x1ba8d5bb1923c23, 0xb6d03d678ac5ca8e, 1220 0x586eb04c1f13bedc}, 1221 {0xc35c6e527e8ed09, 0x1e81a33c1819ede2, 0x278fd6c056c652fa, 1222 0x19d5ac0870864f11}, 1223 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1224 {{0x62577734d2b533d5, 0x673b8af6a1bdddc0, 0x577e7c9aa79ec293, 1225 0xbb6de651c3b266b1}, 1226 {0xe7e9303ab65259b3, 0xd6a0afd3d03a7480, 0xc5ac83d19b3cfc27, 1227 0x60b4619a5d18b99b}, 1228 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1229 {{0xbd6a38e11ae5aa1c, 0xb8b7652b49e73658, 0xb130014ee5f87ed, 1230 0x9d0f27b2aeebffcd}, 1231 {0xca9246317a730a55, 0x9c955b2fddbbc83a, 0x7c1dfe0ac019a71, 1232 0x244a566d356ec48d}, 1233 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1234 {{0x56f8410ef4f8b16a, 0x97241afec47b266a, 0xa406b8e6d9c87c1, 1235 0x803f3e02cd42ab1b}, 1236 {0x7f0309a804dbec69, 0xa83b85f73bbad05f, 0xc6097273ad8e197f, 1237 0xc097440e5067adc1}, 1238 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1239 {{0x846a56f2c379ab34, 0xa8ee068b841df8d1, 0x20314459176c68ef, 1240 0xf1af32d5915f1f30}, 1241 {0x99c375315d75bd50, 0x837cffbaf72f67bc, 0x613a41848d7723f, 1242 0x23d0f130e2d41c8b}, 1243 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1244 {{0xed93e225d5be5a2b, 0x6fe799835934f3c6, 0x4314092622626ffc, 1245 0x50bbb4d97990216a}, 1246 {0x378191c6e57ec63e, 0x65422c40181dcdb2, 0x41a8099b0236e0f6, 1247 0x2b10011801fe49c3}, 1248 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1249 {{0xfc68b5c59b391593, 0xc385f5a2598270fc, 0x7144f3aad19adcbb, 1250 0xdd55899983fbae0c}, 1251 {0x93b88b8e74b82ff4, 0xd2e03c4071e734c9, 0x9a7a9eaf43c0322a, 1252 0xe6e4c551149d6041}, 1253 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1254 {{0x5fe14bfe80ec21fe, 0xf6ce116ac255be82, 0x98bc5a072f4a5d67, 1255 0xfad27148db7e63af}, 1256 {0x90c0b6ac29ab05b3, 0x37a9a83c4e251ae6, 0xa7dc875c2aade7d, 1257 0x77387de39f0e1a84}, 1258 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1259 {{0x1e9ecc49a56c0dd7, 0xa5cffcd846086c74, 0x8f7a1408f505aece, 1260 0xb37b85c0bef0c47e}, 1261 {0x3596b6e4cc0e6a8f, 0xfd6d4bbf6b388f23, 0xaba453fac39cef4e, 1262 0x9c135ac8f9f628d5}, 1263 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1264 {{0xa1c729495c8f8be, 0x2961c4803bf362bf, 0x9e418403df63d4ac, 1265 0xc109f9cb91ece900}, 1266 {0xc2d095d058945705, 0xb9083d96ddeb85c0, 0x84692b8d7a40449b, 1267 0x9bc3344f2eee1ee1}, 1268 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1269 {{0xd5ae35642913074, 0x55491b2748a542b1, 0x469ca665b310732a, 1270 0x29591d525f1a4cc1}, 1271 {0xe76f5b6bb84f983f, 0xbe7eef419f5f84e1, 0x1200d49680baa189, 1272 0x6376551f18ef332c}, 1273 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}}, 1274 {{{0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}, {0x0, 0x0, 0x0, 0x0}}, 1275 {{0x202886024147519a, 0xd0981eac26b372f0, 0xa9d4a7caa785ebc8, 1276 0xd953c50ddbdf58e9}, 1277 {0x9d6361ccfd590f8f, 0x72e9626b44e6c917, 0x7fd9611022eb64cf, 1278 0x863ebb7e9eb288f3}, 1279 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1280 {{0x4fe7ee31b0e63d34, 0xf4600572a9e54fab, 0xc0493334d5e7b5a4, 1281 0x8589fb9206d54831}, 1282 {0xaa70f5cc6583553a, 0x879094ae25649e5, 0xcc90450710044652, 1283 0xebb0696d02541c4f}, 1284 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1285 {{0xabbaa0c03b89da99, 0xa6f2d79eb8284022, 0x27847862b81c05e8, 1286 0x337a4b5905e54d63}, 1287 {0x3c67500d21f7794a, 0x207005b77d6d7f61, 0xa5a378104cfd6e8, 1288 0xd65e0d5f4c2fbd6}, 1289 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1290 {{0xd433e50f6d3549cf, 0x6f33696ffacd665e, 0x695bfdacce11fcb4, 1291 0x810ee252af7c9860}, 1292 {0x65450fe17159bb2c, 0xf7dfbebe758b357b, 0x2b057e74d69fea72, 1293 0xd485717a92731745}, 1294 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1295 {{0xce1f69bbe83f7669, 0x9f8ae8272877d6b, 0x9548ae543244278d, 1296 0x207755dee3c2c19c}, 1297 {0x87bd61d96fef1945, 0x18813cefb12d28c3, 0x9fbcd1d672df64aa, 1298 0x48dc5ee57154b00d}, 1299 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1300 {{0xef0f469ef49a3154, 0x3e85a5956e2b2e9a, 0x45aaec1eaa924a9c, 1301 0xaa12dfc8a09e4719}, 1302 {0x26f272274df69f1d, 0xe0e4c82ca2ff5e73, 0xb9d8ce73b7a9dd44, 1303 0x6c036e73e48ca901}, 1304 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1305 {{0xe1e421e1a47153f0, 0xb86c3b79920418c9, 0x93bdce87705d7672, 1306 0xf25ae793cab79a77}, 1307 {0x1f3194a36d869d0c, 0x9d55c8824986c264, 0x49fb5ea3096e945e, 1308 0x39b8e65313db0a3e}, 1309 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1310 {{0xe3417bc035d0b34a, 0x440b386b8327c0a7, 0x8fb7262dac0362d1, 1311 0x2c41114ce0cdf943}, 1312 {0x2ba5cef1ad95a0b1, 0xc09b37a867d54362, 0x26d6cdd201e486c9, 1313 0x20477abf42ff9297}, 1314 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1315 {{0xf121b41bc0a67d2, 0x62d4760a444d248a, 0xe044f1d659b4737, 1316 0x8fde365250bb4a8}, 1317 {0xaceec3da848bf287, 0xc2a62182d3369d6e, 0x3582dfdc92449482, 1318 0x2f7e2fd2565d6cd7}, 1319 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1320 {{0xa0122b5178a876b, 0x51ff96ff085104b4, 0x50b31ab14f29f76, 1321 0x84abb28b5f87d4e6}, 1322 {0xd5ed439f8270790a, 0x2d6cb59d85e3f46b, 0x75f55c1b6c1e2212, 1323 0xe5436f6717655640}, 1324 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1325 {{0xc2965ecc9aeb596d, 0x1ea03e7023c92b4, 0x4704b4b62e013961, 1326 0xca8fd3f905ea367}, 1327 {0x92523a42551b2b61, 0x1eb7a89c390fcd06, 0xe7f1d2be0392a63e, 1328 0x96dca2644ddb0c33}, 1329 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1330 {{0x231c210e15339848, 0xe87a28e870778c8d, 0x9d1de6616956e170, 1331 0x4ac3c9382bb09c0b}, 1332 {0x19be05516998987d, 0x8b2376c4ae09f4d6, 0x1de0b7651a3f933d, 1333 0x380d94c7e39705f4}, 1334 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1335 {{0x3685954b8c31c31d, 0x68533d005bf21a0c, 0xbd7626e75c79ec9, 1336 0xca17754742c69d54}, 1337 {0xcc6edafff6d2dbb2, 0xfd0d8cbd174a9d18, 0x875e8793aa4578e8, 1338 0xa976a7139cab2ce6}, 1339 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1340 {{0xce37ab11b43ea1db, 0xa7ff1a95259d292, 0x851b02218f84f186, 1341 0xa7222beadefaad13}, 1342 {0xa2ac78ec2b0a9144, 0x5a024051f2fa59c5, 0x91d1eca56147ce38, 1343 0xbe94d523bc2ac690}, 1344 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}, 1345 {{0x2d8daefd79ec1a0f, 0x3bbcd6fdceb39c97, 0xf5575ffc58f61a95, 1346 0xdbd986c4adf7b420}, 1347 {0x81aa881415f39eb7, 0x6ee2fcf5b98d976c, 0x5465475dcf2f717d, 1348 0x8e24d3c46860bbd0}, 1349 {0x1, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffe}}}}; 1350 #else 1351 static const fe g_pre_comp[2][16][3] = { 1352 {{{0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, 1353 {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, 1354 {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}}, 1355 {{0x18a9143c,0x79e730d4, 0x5fedb601,0x75ba95fc, 0x77622510,0x79fb732b, 1356 0xa53755c6,0x18905f76}, 1357 {0xce95560a,0xddf25357, 0xba19e45c,0x8b4ab8e4, 0xdd21f325,0xd2e88688, 1358 0x25885d85,0x8571ff18}, 1359 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1360 {{0x16a0d2bb,0x4f922fc5, 0x1a623499,0xd5cc16c, 0x57c62c8b,0x9241cf3a, 1361 0xfd1b667f,0x2f5e6961}, 1362 {0xf5a01797,0x5c15c70b, 0x60956192,0x3d20b44d, 0x71fdb52,0x4911b37, 1363 0x8d6f0f7b,0xf648f916}, 1364 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1365 {{0xe137bbbc,0x9e566847, 0x8a6a0bec,0xe434469e, 0x79d73463,0xb1c42761, 1366 0x133d0015,0x5abe0285}, 1367 {0xc04c7dab,0x92aa837c, 0x43260c07,0x573d9f4c, 0x78e6cc37,0xc931562, 1368 0x6b6f7383,0x94bb725b}, 1369 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1370 {{0xbfe20925,0x62a8c244, 0x8fdce867,0x91c19ac3, 0xdd387063,0x5a96a5d5, 1371 0x21d324f6,0x61d587d4}, 1372 {0xa37173ea,0xe87673a2, 0x53778b65,0x23848008, 0x5bab43e,0x10f8441e, 1373 0x4621efbe,0xfa11fe12}, 1374 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1375 {{0x2cb19ffd,0x1c891f2b, 0xb1923c23,0x1ba8d5b, 0x8ac5ca8e,0xb6d03d67, 1376 0x1f13bedc,0x586eb04c}, 1377 {0x27e8ed09,0xc35c6e5, 0x1819ede2,0x1e81a33c, 0x56c652fa,0x278fd6c0, 1378 0x70864f11,0x19d5ac08}, 1379 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1380 {{0xd2b533d5,0x62577734, 0xa1bdddc0,0x673b8af6, 0xa79ec293,0x577e7c9a, 1381 0xc3b266b1,0xbb6de651}, 1382 {0xb65259b3,0xe7e9303a, 0xd03a7480,0xd6a0afd3, 0x9b3cfc27,0xc5ac83d1, 1383 0x5d18b99b,0x60b4619a}, 1384 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1385 {{0x1ae5aa1c,0xbd6a38e1, 0x49e73658,0xb8b7652b, 0xee5f87ed,0xb130014, 1386 0xaeebffcd,0x9d0f27b2}, 1387 {0x7a730a55,0xca924631, 0xddbbc83a,0x9c955b2f, 0xac019a71,0x7c1dfe0, 1388 0x356ec48d,0x244a566d}, 1389 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1390 {{0xf4f8b16a,0x56f8410e, 0xc47b266a,0x97241afe, 0x6d9c87c1,0xa406b8e, 1391 0xcd42ab1b,0x803f3e02}, 1392 {0x4dbec69,0x7f0309a8, 0x3bbad05f,0xa83b85f7, 0xad8e197f,0xc6097273, 1393 0x5067adc1,0xc097440e}, 1394 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1395 {{0xc379ab34,0x846a56f2, 0x841df8d1,0xa8ee068b, 0x176c68ef,0x20314459, 1396 0x915f1f30,0xf1af32d5}, 1397 {0x5d75bd50,0x99c37531, 0xf72f67bc,0x837cffba, 0x48d7723f,0x613a418, 1398 0xe2d41c8b,0x23d0f130}, 1399 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1400 {{0xd5be5a2b,0xed93e225, 0x5934f3c6,0x6fe79983, 0x22626ffc,0x43140926, 1401 0x7990216a,0x50bbb4d9}, 1402 {0xe57ec63e,0x378191c6, 0x181dcdb2,0x65422c40, 0x236e0f6,0x41a8099b, 1403 0x1fe49c3,0x2b100118}, 1404 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1405 {{0x9b391593,0xfc68b5c5, 0x598270fc,0xc385f5a2, 0xd19adcbb,0x7144f3aa, 1406 0x83fbae0c,0xdd558999}, 1407 {0x74b82ff4,0x93b88b8e, 0x71e734c9,0xd2e03c40, 0x43c0322a,0x9a7a9eaf, 1408 0x149d6041,0xe6e4c551}, 1409 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1410 {{0x80ec21fe,0x5fe14bfe, 0xc255be82,0xf6ce116a, 0x2f4a5d67,0x98bc5a07, 1411 0xdb7e63af,0xfad27148}, 1412 {0x29ab05b3,0x90c0b6ac, 0x4e251ae6,0x37a9a83c, 0xc2aade7d,0xa7dc875, 1413 0x9f0e1a84,0x77387de3}, 1414 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1415 {{0xa56c0dd7,0x1e9ecc49, 0x46086c74,0xa5cffcd8, 0xf505aece,0x8f7a1408, 1416 0xbef0c47e,0xb37b85c0}, 1417 {0xcc0e6a8f,0x3596b6e4, 0x6b388f23,0xfd6d4bbf, 0xc39cef4e,0xaba453fa, 1418 0xf9f628d5,0x9c135ac8}, 1419 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1420 {{0x95c8f8be,0xa1c7294, 0x3bf362bf,0x2961c480, 0xdf63d4ac,0x9e418403, 1421 0x91ece900,0xc109f9cb}, 1422 {0x58945705,0xc2d095d0, 0xddeb85c0,0xb9083d96, 0x7a40449b,0x84692b8d, 1423 0x2eee1ee1,0x9bc3344f}, 1424 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1425 {{0x42913074,0xd5ae356, 0x48a542b1,0x55491b27, 0xb310732a,0x469ca665, 1426 0x5f1a4cc1,0x29591d52}, 1427 {0xb84f983f,0xe76f5b6b, 0x9f5f84e1,0xbe7eef41, 0x80baa189,0x1200d496, 1428 0x18ef332c,0x6376551f}, 1429 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}}, 1430 {{{0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, 1431 {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}, 1432 {0x0,0x0, 0x0,0x0, 0x0,0x0, 0x0,0x0}}, 1433 {{0x4147519a,0x20288602, 0x26b372f0,0xd0981eac, 0xa785ebc8,0xa9d4a7ca, 1434 0xdbdf58e9,0xd953c50d}, 1435 {0xfd590f8f,0x9d6361cc, 0x44e6c917,0x72e9626b, 0x22eb64cf,0x7fd96110, 1436 0x9eb288f3,0x863ebb7e}, 1437 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1438 {{0xb0e63d34,0x4fe7ee31, 0xa9e54fab,0xf4600572, 0xd5e7b5a4,0xc0493334, 1439 0x6d54831,0x8589fb92}, 1440 {0x6583553a,0xaa70f5cc, 0xe25649e5,0x879094a, 0x10044652,0xcc904507, 1441 0x2541c4f,0xebb0696d}, 1442 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1443 {{0x3b89da99,0xabbaa0c0, 0xb8284022,0xa6f2d79e, 0xb81c05e8,0x27847862, 1444 0x5e54d63,0x337a4b59}, 1445 {0x21f7794a,0x3c67500d, 0x7d6d7f61,0x207005b7, 0x4cfd6e8,0xa5a3781, 1446 0xf4c2fbd6,0xd65e0d5}, 1447 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1448 {{0x6d3549cf,0xd433e50f, 0xfacd665e,0x6f33696f, 0xce11fcb4,0x695bfdac, 1449 0xaf7c9860,0x810ee252}, 1450 {0x7159bb2c,0x65450fe1, 0x758b357b,0xf7dfbebe, 0xd69fea72,0x2b057e74, 1451 0x92731745,0xd485717a}, 1452 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1453 {{0xe83f7669,0xce1f69bb, 0x72877d6b,0x9f8ae82, 0x3244278d,0x9548ae54, 1454 0xe3c2c19c,0x207755de}, 1455 {0x6fef1945,0x87bd61d9, 0xb12d28c3,0x18813cef, 0x72df64aa,0x9fbcd1d6, 1456 0x7154b00d,0x48dc5ee5}, 1457 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1458 {{0xf49a3154,0xef0f469e, 0x6e2b2e9a,0x3e85a595, 0xaa924a9c,0x45aaec1e, 1459 0xa09e4719,0xaa12dfc8}, 1460 {0x4df69f1d,0x26f27227, 0xa2ff5e73,0xe0e4c82c, 0xb7a9dd44,0xb9d8ce73, 1461 0xe48ca901,0x6c036e73}, 1462 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1463 {{0xa47153f0,0xe1e421e1, 0x920418c9,0xb86c3b79, 0x705d7672,0x93bdce87, 1464 0xcab79a77,0xf25ae793}, 1465 {0x6d869d0c,0x1f3194a3, 0x4986c264,0x9d55c882, 0x96e945e,0x49fb5ea3, 1466 0x13db0a3e,0x39b8e653}, 1467 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1468 {{0x35d0b34a,0xe3417bc0, 0x8327c0a7,0x440b386b, 0xac0362d1,0x8fb7262d, 1469 0xe0cdf943,0x2c41114c}, 1470 {0xad95a0b1,0x2ba5cef1, 0x67d54362,0xc09b37a8, 0x1e486c9,0x26d6cdd2, 1471 0x42ff9297,0x20477abf}, 1472 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1473 {{0xbc0a67d2,0xf121b41, 0x444d248a,0x62d4760a, 0x659b4737,0xe044f1d, 1474 0x250bb4a8,0x8fde365}, 1475 {0x848bf287,0xaceec3da, 0xd3369d6e,0xc2a62182, 0x92449482,0x3582dfdc, 1476 0x565d6cd7,0x2f7e2fd2}, 1477 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1478 {{0x178a876b,0xa0122b5, 0x85104b4,0x51ff96ff, 0x14f29f76,0x50b31ab, 1479 0x5f87d4e6,0x84abb28b}, 1480 {0x8270790a,0xd5ed439f, 0x85e3f46b,0x2d6cb59d, 0x6c1e2212,0x75f55c1b, 1481 0x17655640,0xe5436f67}, 1482 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1483 {{0x9aeb596d,0xc2965ecc, 0x23c92b4,0x1ea03e7, 0x2e013961,0x4704b4b6, 1484 0x905ea367,0xca8fd3f}, 1485 {0x551b2b61,0x92523a42, 0x390fcd06,0x1eb7a89c, 0x392a63e,0xe7f1d2be, 1486 0x4ddb0c33,0x96dca264}, 1487 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1488 {{0x15339848,0x231c210e, 0x70778c8d,0xe87a28e8, 0x6956e170,0x9d1de661, 1489 0x2bb09c0b,0x4ac3c938}, 1490 {0x6998987d,0x19be0551, 0xae09f4d6,0x8b2376c4, 0x1a3f933d,0x1de0b765, 1491 0xe39705f4,0x380d94c7}, 1492 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1493 {{0x8c31c31d,0x3685954b, 0x5bf21a0c,0x68533d00, 0x75c79ec9,0xbd7626e, 1494 0x42c69d54,0xca177547}, 1495 {0xf6d2dbb2,0xcc6edaff, 0x174a9d18,0xfd0d8cbd, 0xaa4578e8,0x875e8793, 1496 0x9cab2ce6,0xa976a713}, 1497 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1498 {{0xb43ea1db,0xce37ab11, 0x5259d292,0xa7ff1a9, 0x8f84f186,0x851b0221, 1499 0xdefaad13,0xa7222bea}, 1500 {0x2b0a9144,0xa2ac78ec, 0xf2fa59c5,0x5a024051, 0x6147ce38,0x91d1eca5, 1501 0xbc2ac690,0xbe94d523}, 1502 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}, 1503 {{0x79ec1a0f,0x2d8daefd, 0xceb39c97,0x3bbcd6fd, 0x58f61a95,0xf5575ffc, 1504 0xadf7b420,0xdbd986c4}, 1505 {0x15f39eb7,0x81aa8814, 0xb98d976c,0x6ee2fcf5, 0xcf2f717d,0x5465475d, 1506 0x6860bbd0,0x8e24d3c4}, 1507 {0x1,0x0, 0x0,0xffffffff, 0xffffffff,0xffffffff, 0xfffffffe,0x0}}}}; 1508 #endif 1509 1510 // select_point selects the |idx|th point from a precomputation table and 1511 // copies it to out. 1512 static void select_point(const limb_t idx, size_t size, 1513 const fe pre_comp[/*size*/][3], 1514 fe out[3]) { 1515 OPENSSL_memset(out, 0, sizeof(fe) * 3); 1516 for (size_t i = 0; i < size; i++) { 1517 limb_t mismatch = i ^ idx; 1518 fe_cmovznz(out[0], mismatch, pre_comp[i][0], out[0]); 1519 fe_cmovznz(out[1], mismatch, pre_comp[i][1], out[1]); 1520 fe_cmovznz(out[2], mismatch, pre_comp[i][2], out[2]); 1521 } 1522 } 1523 1524 // get_bit returns the |i|th bit in |in| 1525 static char get_bit(const uint8_t *in, int i) { 1526 if (i < 0 || i >= 256) { 1527 return 0; 1528 } 1529 return (in[i >> 3] >> (i & 7)) & 1; 1530 } 1531 1532 // Interleaved point multiplication using precomputed point multiples: The 1533 // small point multiples 0*P, 1*P, ..., 17*P are in p_pre_comp, the scalar 1534 // in p_scalar, if non-NULL. If g_scalar is non-NULL, we also add this multiple 1535 // of the generator, using certain (large) precomputed multiples in g_pre_comp. 1536 // Output point (X, Y, Z) is stored in x_out, y_out, z_out. 1537 static void batch_mul(fe x_out, fe y_out, fe z_out, 1538 const uint8_t *p_scalar, const uint8_t *g_scalar, 1539 const fe p_pre_comp[17][3]) { 1540 // set nq to the point at infinity 1541 fe nq[3] = {{0},{0},{0}}, ftmp, tmp[3]; 1542 uint64_t bits; 1543 uint8_t sign, digit; 1544 1545 // Loop over both scalars msb-to-lsb, interleaving additions of multiples 1546 // of the generator (two in each of the last 32 rounds) and additions of p 1547 // (every 5th round). 1548 1549 int skip = 1; // save two point operations in the first round 1550 size_t i = p_scalar != NULL ? 255 : 31; 1551 for (;;) { 1552 // double 1553 if (!skip) { 1554 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); 1555 } 1556 1557 // add multiples of the generator 1558 if (g_scalar != NULL && i <= 31) { 1559 // first, look 32 bits upwards 1560 bits = get_bit(g_scalar, i + 224) << 3; 1561 bits |= get_bit(g_scalar, i + 160) << 2; 1562 bits |= get_bit(g_scalar, i + 96) << 1; 1563 bits |= get_bit(g_scalar, i + 32); 1564 // select the point to add, in constant time 1565 select_point(bits, 16, g_pre_comp[1], tmp); 1566 1567 if (!skip) { 1568 point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, 1569 tmp[0], tmp[1], tmp[2]); 1570 } else { 1571 fe_copy(nq[0], tmp[0]); 1572 fe_copy(nq[1], tmp[1]); 1573 fe_copy(nq[2], tmp[2]); 1574 skip = 0; 1575 } 1576 1577 // second, look at the current position 1578 bits = get_bit(g_scalar, i + 192) << 3; 1579 bits |= get_bit(g_scalar, i + 128) << 2; 1580 bits |= get_bit(g_scalar, i + 64) << 1; 1581 bits |= get_bit(g_scalar, i); 1582 // select the point to add, in constant time 1583 select_point(bits, 16, g_pre_comp[0], tmp); 1584 point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, tmp[0], 1585 tmp[1], tmp[2]); 1586 } 1587 1588 // do other additions every 5 doublings 1589 if (p_scalar != NULL && i % 5 == 0) { 1590 bits = get_bit(p_scalar, i + 4) << 5; 1591 bits |= get_bit(p_scalar, i + 3) << 4; 1592 bits |= get_bit(p_scalar, i + 2) << 3; 1593 bits |= get_bit(p_scalar, i + 1) << 2; 1594 bits |= get_bit(p_scalar, i) << 1; 1595 bits |= get_bit(p_scalar, i - 1); 1596 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); 1597 1598 // select the point to add or subtract, in constant time. 1599 select_point(digit, 17, p_pre_comp, tmp); 1600 fe_opp(ftmp, tmp[1]); // (X, -Y, Z) is the negative point. 1601 fe_cmovznz(tmp[1], sign, tmp[1], ftmp); 1602 1603 if (!skip) { 1604 point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */, 1605 tmp[0], tmp[1], tmp[2]); 1606 } else { 1607 fe_copy(nq[0], tmp[0]); 1608 fe_copy(nq[1], tmp[1]); 1609 fe_copy(nq[2], tmp[2]); 1610 skip = 0; 1611 } 1612 } 1613 1614 if (i == 0) { 1615 break; 1616 } 1617 --i; 1618 } 1619 fe_copy(x_out, nq[0]); 1620 fe_copy(y_out, nq[1]); 1621 fe_copy(z_out, nq[2]); 1622 } 1623 1624 // OPENSSL EC_METHOD FUNCTIONS 1625 1626 // Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = 1627 // (X/Z^2, Y/Z^3). 1628 static int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, 1629 const EC_POINT *point, 1630 BIGNUM *x_out, 1631 BIGNUM *y_out, 1632 BN_CTX *ctx) { 1633 fe x, y, z1, z2; 1634 1635 if (EC_POINT_is_at_infinity(group, point)) { 1636 OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); 1637 return 0; 1638 } 1639 if (!BN_to_fe(x, &point->X) || 1640 !BN_to_fe(y, &point->Y) || 1641 !BN_to_fe(z1, &point->Z)) { 1642 return 0; 1643 } 1644 1645 fe_inv(z2, z1); 1646 fe_sqr(z1, z2); 1647 1648 // Instead of using |fe_from_montgomery| to convert the |x| coordinate and 1649 // then calling |fe_from_montgomery| again to convert the |y| coordinate 1650 // below, convert the common factor |z1| once now, saving one reduction. 1651 fe_from_montgomery(z1); 1652 1653 if (x_out != NULL) { 1654 fe_mul(x, x, z1); 1655 if (!fe_to_BN(x_out, x)) { 1656 OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); 1657 return 0; 1658 } 1659 } 1660 1661 if (y_out != NULL) { 1662 fe_mul(z1, z1, z2); 1663 fe_mul(y, y, z1); 1664 if (!fe_to_BN(y_out, y)) { 1665 OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); 1666 return 0; 1667 } 1668 } 1669 1670 return 1; 1671 } 1672 1673 static int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, 1674 const EC_SCALAR *g_scalar, 1675 const EC_POINT *p, 1676 const EC_SCALAR *p_scalar, 1677 BN_CTX *unused_ctx) { 1678 fe p_pre_comp[17][3]; 1679 fe x_out, y_out, z_out; 1680 1681 if (p != NULL && p_scalar != NULL) { 1682 // We treat NULL scalars as 0, and NULL points as points at infinity, i.e., 1683 // they contribute nothing to the linear combination. 1684 OPENSSL_memset(&p_pre_comp, 0, sizeof(p_pre_comp)); 1685 // Precompute multiples. 1686 if (!BN_to_fe(p_pre_comp[1][0], &p->X) || 1687 !BN_to_fe(p_pre_comp[1][1], &p->Y) || 1688 !BN_to_fe(p_pre_comp[1][2], &p->Z)) { 1689 return 0; 1690 } 1691 for (size_t j = 2; j <= 16; ++j) { 1692 if (j & 1) { 1693 point_add(p_pre_comp[j][0], p_pre_comp[j][1], 1694 p_pre_comp[j][2], p_pre_comp[1][0], 1695 p_pre_comp[1][1], p_pre_comp[1][2], 1696 0, 1697 p_pre_comp[j - 1][0], p_pre_comp[j - 1][1], 1698 p_pre_comp[j - 1][2]); 1699 } else { 1700 point_double(p_pre_comp[j][0], p_pre_comp[j][1], 1701 p_pre_comp[j][2], p_pre_comp[j / 2][0], 1702 p_pre_comp[j / 2][1], p_pre_comp[j / 2][2]); 1703 } 1704 } 1705 } 1706 1707 batch_mul(x_out, y_out, z_out, 1708 (p != NULL && p_scalar != NULL) ? p_scalar->bytes : NULL, 1709 g_scalar != NULL ? g_scalar->bytes : NULL, 1710 (const fe (*) [3])p_pre_comp); 1711 1712 if (!fe_to_BN(&r->X, x_out) || 1713 !fe_to_BN(&r->Y, y_out) || 1714 !fe_to_BN(&r->Z, z_out)) { 1715 OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); 1716 return 0; 1717 } 1718 return 1; 1719 } 1720 1721 DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistp256_method) { 1722 out->group_init = ec_GFp_mont_group_init; 1723 out->group_finish = ec_GFp_mont_group_finish; 1724 out->group_set_curve = ec_GFp_mont_group_set_curve; 1725 out->point_get_affine_coordinates = 1726 ec_GFp_nistp256_point_get_affine_coordinates; 1727 out->mul = ec_GFp_nistp256_points_mul; 1728 // The variable-time wNAF point multiplication uses fewer field operations than 1729 // the constant-time implementation here, but the 64-bit field arithmetic in 1730 // this file is much faster than the generic BIGNUM-based field arithmetic used 1731 // by wNAF. For 32-bit, the wNAF code is overall ~60% faster on non-precomputed 1732 // points, so we use it for public inputs. 1733 #if defined(BORINGSSL_NISTP256_64BIT) 1734 out->mul_public = ec_GFp_nistp256_points_mul; 1735 #else 1736 out->mul_public = ec_wNAF_mul; 1737 #endif 1738 out->field_mul = ec_GFp_mont_field_mul; 1739 out->field_sqr = ec_GFp_mont_field_sqr; 1740 out->field_encode = ec_GFp_mont_field_encode; 1741 out->field_decode = ec_GFp_mont_field_decode; 1742 }; 1743 1744 #undef BORINGSSL_NISTP256_64BIT 1745
