Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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. |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 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> |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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 | // |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 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 | // |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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 | // |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 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 | // |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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) { |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1072 | // z2z2 = z2**2 |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1073 | fe z2z2; fe_sqr(z2z2, z2); |
| 1074 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1075 | // u1 = x1*z2z2 |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1084 | // s1 = y1 * z2**3 |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1090 | // u1 = x1*z2z2 |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1091 | fe_copy(u1, x1); |
| 1092 | // two_z1z2 = 2z1z2 |
| 1093 | fe_add(two_z1z2, z1, z1); |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1094 | // s1 = y1 * z2**3 |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1095 | fe_copy(s1, y1); |
| 1096 | } |
| 1097 | |
| 1098 | // u2 = x2*z1z1 |
| 1099 | fe u2; fe_mul(u2, x2, z1z1); |
| 1100 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1101 | // h = u2 - u1 |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1112 | // s2 = y2 * z1**3 |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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) { |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 1123 | point_double(x3, y3, z3, x1, y1, z1); |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1124 | return; |
| 1125 | } |
| 1126 | |
| 1127 | // I = (2h)**2 |
| 1128 | fe i; |
| 1129 | fe_add(i, h, h); |
| 1130 | fe_sqr(i, i); |
| 1131 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1132 | // J = h * I |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1133 | fe j; fe_mul(j, h, i); |
| 1134 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 1135 | // V = U1 * I |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 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 | |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1653 | if (x_out != NULL) { |
| 1654 | fe_mul(x, x, z1); |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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); |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 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 | |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 1721 | static int ec_GFp_nistp256_point_mul_public(const EC_GROUP *group, EC_POINT *r, |
| 1722 | const EC_SCALAR *g_scalar, |
| 1723 | const EC_POINT *p, |
| 1724 | const EC_SCALAR *p_scalar, |
| 1725 | BN_CTX *unused_ctx) { |
| 1726 | #define P256_WSIZE_PUBLIC 4 |
| 1727 | // Precompute multiples of |p|. p_pre_comp[i] is (2*i+1) * |p|. |
| 1728 | fe p_pre_comp[1 << (P256_WSIZE_PUBLIC-1)][3]; |
| 1729 | if (!BN_to_fe(p_pre_comp[0][0], &p->X) || |
| 1730 | !BN_to_fe(p_pre_comp[0][1], &p->Y) || |
| 1731 | !BN_to_fe(p_pre_comp[0][2], &p->Z)) { |
| 1732 | return 0; |
| 1733 | } |
| 1734 | fe p2[3]; |
| 1735 | point_double(p2[0], p2[1], p2[2], p_pre_comp[0][0], p_pre_comp[0][1], |
| 1736 | p_pre_comp[0][2]); |
| 1737 | for (size_t i = 1; i < OPENSSL_ARRAY_SIZE(p_pre_comp); i++) { |
| 1738 | point_add(p_pre_comp[i][0], p_pre_comp[i][1], p_pre_comp[i][2], |
| 1739 | p_pre_comp[i - 1][0], p_pre_comp[i - 1][1], p_pre_comp[i - 1][2], |
| 1740 | 0 /* not mixed */, p2[0], p2[1], p2[2]); |
| 1741 | } |
| 1742 | |
| 1743 | // Set up the coefficients for |p_scalar|. |
| 1744 | int8_t p_wNAF[257]; |
| 1745 | if (!ec_compute_wNAF(group, p_wNAF, p_scalar, 256, P256_WSIZE_PUBLIC)) { |
| 1746 | return 0; |
| 1747 | } |
| 1748 | |
| 1749 | // Set |ret| to the point at infinity. |
| 1750 | int skip = 1; // Save some point operations. |
| 1751 | fe ret[3] = {{0},{0},{0}}; |
| 1752 | for (int i = 256; i >= 0; i--) { |
| 1753 | if (!skip) { |
| 1754 | point_double(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2]); |
| 1755 | } |
| 1756 | |
| 1757 | // For the |g_scalar|, we use the precomputed table without the |
| 1758 | // constant-time lookup. |
| 1759 | if (i <= 31) { |
| 1760 | // First, look 32 bits upwards. |
| 1761 | uint64_t bits = get_bit(g_scalar->bytes, i + 224) << 3; |
| 1762 | bits |= get_bit(g_scalar->bytes, i + 160) << 2; |
| 1763 | bits |= get_bit(g_scalar->bytes, i + 96) << 1; |
| 1764 | bits |= get_bit(g_scalar->bytes, i + 32); |
| 1765 | point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], 1 /* mixed */, |
| 1766 | g_pre_comp[1][bits][0], g_pre_comp[1][bits][1], |
| 1767 | g_pre_comp[1][bits][2]); |
| 1768 | skip = 0; |
| 1769 | |
| 1770 | // Second, look at the current position. |
| 1771 | bits = get_bit(g_scalar->bytes, i + 192) << 3; |
| 1772 | bits |= get_bit(g_scalar->bytes, i + 128) << 2; |
| 1773 | bits |= get_bit(g_scalar->bytes, i + 64) << 1; |
| 1774 | bits |= get_bit(g_scalar->bytes, i); |
| 1775 | point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], 1 /* mixed */, |
| 1776 | g_pre_comp[0][bits][0], g_pre_comp[0][bits][1], |
| 1777 | g_pre_comp[0][bits][2]); |
| 1778 | } |
| 1779 | |
| 1780 | int digit = p_wNAF[i]; |
| 1781 | if (digit != 0) { |
| 1782 | assert(digit & 1); |
| 1783 | int idx = digit < 0 ? (-digit) >> 1 : digit >> 1; |
| 1784 | fe *y = &p_pre_comp[idx][1], tmp; |
| 1785 | if (digit < 0) { |
| 1786 | fe_opp(tmp, p_pre_comp[idx][1]); |
| 1787 | y = &tmp; |
| 1788 | } |
| 1789 | if (!skip) { |
| 1790 | point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], |
| 1791 | 0 /* not mixed */, p_pre_comp[idx][0], *y, p_pre_comp[idx][2]); |
| 1792 | } else { |
| 1793 | fe_copy(ret[0], p_pre_comp[idx][0]); |
| 1794 | fe_copy(ret[1], *y); |
| 1795 | fe_copy(ret[2], p_pre_comp[idx][2]); |
| 1796 | skip = 0; |
| 1797 | } |
| 1798 | } |
| 1799 | } |
| 1800 | |
| 1801 | if (!fe_to_BN(&r->X, ret[0]) || |
| 1802 | !fe_to_BN(&r->Y, ret[1]) || |
| 1803 | !fe_to_BN(&r->Z, ret[2])) { |
| 1804 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| 1805 | return 0; |
| 1806 | } |
| 1807 | return 1; |
| 1808 | } |
| 1809 | |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1810 | DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistp256_method) { |
| 1811 | out->group_init = ec_GFp_mont_group_init; |
| 1812 | out->group_finish = ec_GFp_mont_group_finish; |
| 1813 | out->group_set_curve = ec_GFp_mont_group_set_curve; |
| 1814 | out->point_get_affine_coordinates = |
| 1815 | ec_GFp_nistp256_point_get_affine_coordinates; |
| 1816 | out->mul = ec_GFp_nistp256_points_mul; |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 1817 | out->mul_public = ec_GFp_nistp256_point_mul_public; |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1818 | out->field_mul = ec_GFp_mont_field_mul; |
| 1819 | out->field_sqr = ec_GFp_mont_field_sqr; |
| 1820 | out->field_encode = ec_GFp_mont_field_encode; |
| 1821 | out->field_decode = ec_GFp_mont_field_decode; |
| 1822 | }; |
| 1823 | |
| 1824 | #undef BORINGSSL_NISTP256_64BIT |