Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -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 | // Some of this code is taken from the ref10 version of Ed25519 in SUPERCOP |
| 24 | // 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as |
| 25 | // public domain but parts have been replaced with code generated by Fiat |
| 26 | // (https://github.com/mit-plv/fiat-crypto), which is MIT licensed. |
| 27 | // |
| 28 | // The field functions are shared by Ed25519 and X25519 where possible. |
| 29 | |
| 30 | #include <openssl/curve25519.h> |
| 31 | |
| 32 | #include <assert.h> |
| 33 | #include <string.h> |
| 34 | |
| 35 | #include <openssl/cpu.h> |
| 36 | #include <openssl/mem.h> |
| 37 | #include <openssl/rand.h> |
| 38 | #include <openssl/sha.h> |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 39 | #include <openssl/type_check.h> |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 40 | |
| 41 | #include "internal.h" |
| 42 | #include "../../crypto/internal.h" |
| 43 | |
| 44 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 45 | // Various pre-computed constants. |
| 46 | #include "./curve25519_tables.h" |
| 47 | |
| 48 | |
| 49 | // Low-level intrinsic operations (hand-written). |
| 50 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 51 | static uint64_t load_3(const uint8_t *in) { |
| 52 | uint64_t result; |
| 53 | result = (uint64_t)in[0]; |
| 54 | result |= ((uint64_t)in[1]) << 8; |
| 55 | result |= ((uint64_t)in[2]) << 16; |
| 56 | return result; |
| 57 | } |
| 58 | |
| 59 | static uint64_t load_4(const uint8_t *in) { |
| 60 | uint64_t result; |
| 61 | result = (uint64_t)in[0]; |
| 62 | result |= ((uint64_t)in[1]) << 8; |
| 63 | result |= ((uint64_t)in[2]) << 16; |
| 64 | result |= ((uint64_t)in[3]) << 24; |
| 65 | return result; |
| 66 | } |
| 67 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 68 | #if defined(BORINGSSL_CURVE25519_64BIT) |
| 69 | static uint64_t load_8(const uint8_t *in) { |
| 70 | uint64_t result; |
| 71 | result = (uint64_t)in[0]; |
| 72 | result |= ((uint64_t)in[1]) << 8; |
| 73 | result |= ((uint64_t)in[2]) << 16; |
| 74 | result |= ((uint64_t)in[3]) << 24; |
| 75 | result |= ((uint64_t)in[4]) << 32; |
| 76 | result |= ((uint64_t)in[5]) << 40; |
| 77 | result |= ((uint64_t)in[6]) << 48; |
| 78 | result |= ((uint64_t)in[7]) << 56; |
| 79 | return result; |
| 80 | } |
| 81 | |
| 82 | static uint8_t /*bool*/ addcarryx_u51(uint8_t /*bool*/ c, uint64_t a, |
| 83 | uint64_t b, uint64_t *low) { |
| 84 | // This function extracts 51 bits of result and 1 bit of carry (52 total), so |
| 85 | // a 64-bit intermediate is sufficient. |
| 86 | uint64_t x = a + b + c; |
| 87 | *low = x & ((UINT64_C(1) << 51) - 1); |
| 88 | return (x >> 51) & 1; |
| 89 | } |
| 90 | |
| 91 | static uint8_t /*bool*/ subborrow_u51(uint8_t /*bool*/ c, uint64_t a, |
| 92 | uint64_t b, uint64_t *low) { |
| 93 | // This function extracts 51 bits of result and 1 bit of borrow (52 total), so |
| 94 | // a 64-bit intermediate is sufficient. |
| 95 | uint64_t x = a - b - c; |
| 96 | *low = x & ((UINT64_C(1) << 51) - 1); |
| 97 | return x >> 63; |
| 98 | } |
| 99 | |
| 100 | static uint64_t cmovznz64(uint64_t t, uint64_t z, uint64_t nz) { |
| 101 | t = -!!t; // all set if nonzero, 0 if 0 |
| 102 | return (t&nz) | ((~t)&z); |
| 103 | } |
| 104 | |
| 105 | #else |
| 106 | |
| 107 | static uint8_t /*bool*/ addcarryx_u25(uint8_t /*bool*/ c, uint32_t a, |
| 108 | uint32_t b, uint32_t *low) { |
| 109 | // This function extracts 25 bits of result and 1 bit of carry (26 total), so |
| 110 | // a 32-bit intermediate is sufficient. |
| 111 | uint32_t x = a + b + c; |
| 112 | *low = x & ((1 << 25) - 1); |
| 113 | return (x >> 25) & 1; |
| 114 | } |
| 115 | |
| 116 | static uint8_t /*bool*/ addcarryx_u26(uint8_t /*bool*/ c, uint32_t a, |
| 117 | uint32_t b, uint32_t *low) { |
| 118 | // This function extracts 26 bits of result and 1 bit of carry (27 total), so |
| 119 | // a 32-bit intermediate is sufficient. |
| 120 | uint32_t x = a + b + c; |
| 121 | *low = x & ((1 << 26) - 1); |
| 122 | return (x >> 26) & 1; |
| 123 | } |
| 124 | |
| 125 | static uint8_t /*bool*/ subborrow_u25(uint8_t /*bool*/ c, uint32_t a, |
| 126 | uint32_t b, uint32_t *low) { |
| 127 | // This function extracts 25 bits of result and 1 bit of borrow (26 total), so |
| 128 | // a 32-bit intermediate is sufficient. |
| 129 | uint32_t x = a - b - c; |
| 130 | *low = x & ((1 << 25) - 1); |
| 131 | return x >> 31; |
| 132 | } |
| 133 | |
| 134 | static uint8_t /*bool*/ subborrow_u26(uint8_t /*bool*/ c, uint32_t a, |
| 135 | uint32_t b, uint32_t *low) { |
| 136 | // This function extracts 26 bits of result and 1 bit of borrow (27 total), so |
| 137 | // a 32-bit intermediate is sufficient. |
| 138 | uint32_t x = a - b - c; |
| 139 | *low = x & ((1 << 26) - 1); |
| 140 | return x >> 31; |
| 141 | } |
| 142 | |
| 143 | static uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz) { |
| 144 | t = -!!t; // all set if nonzero, 0 if 0 |
| 145 | return (t&nz) | ((~t)&z); |
| 146 | } |
| 147 | |
| 148 | #endif |
| 149 | |
| 150 | |
| 151 | // Field operations. |
| 152 | |
| 153 | #if defined(BORINGSSL_CURVE25519_64BIT) |
| 154 | |
| 155 | #define assert_fe(f) do { \ |
| 156 | for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \ |
| 157 | assert(f[_assert_fe_i] < 1.125*(UINT64_C(1)<<51)); \ |
| 158 | } \ |
| 159 | } while (0) |
| 160 | |
| 161 | #define assert_fe_loose(f) do { \ |
| 162 | for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \ |
| 163 | assert(f[_assert_fe_i] < 3.375*(UINT64_C(1)<<51)); \ |
| 164 | } \ |
| 165 | } while (0) |
| 166 | |
| 167 | #define assert_fe_frozen(f) do { \ |
| 168 | for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \ |
| 169 | assert(f[_assert_fe_i] < (UINT64_C(1)<<51)); \ |
| 170 | } \ |
| 171 | } while (0) |
| 172 | |
| 173 | static void fe_frombytes_impl(uint64_t h[5], const uint8_t *s) { |
| 174 | // Ignores top bit of s. |
| 175 | uint64_t a0 = load_8(s); |
| 176 | uint64_t a1 = load_8(s+8); |
| 177 | uint64_t a2 = load_8(s+16); |
| 178 | uint64_t a3 = load_8(s+24); |
| 179 | // Use 51 bits, 64-51 = 13 left. |
| 180 | h[0] = a0 & ((UINT64_C(1) << 51) - 1); |
| 181 | // (64-51) + 38 = 13 + 38 = 51 |
| 182 | h[1] = (a0 >> 51) | ((a1 & ((UINT64_C(1) << 38) - 1)) << 13); |
| 183 | // (64-38) + 25 = 26 + 25 = 51 |
| 184 | h[2] = (a1 >> 38) | ((a2 & ((UINT64_C(1) << 25) - 1)) << 26); |
| 185 | // (64-25) + 12 = 39 + 12 = 51 |
| 186 | h[3] = (a2 >> 25) | ((a3 & ((UINT64_C(1) << 12) - 1)) << 39); |
| 187 | // (64-12) = 52, ignore top bit |
| 188 | h[4] = (a3 >> 12) & ((UINT64_C(1) << 51) - 1); |
| 189 | assert_fe(h); |
| 190 | } |
| 191 | |
| 192 | static void fe_frombytes(fe *h, const uint8_t *s) { |
| 193 | fe_frombytes_impl(h->v, s); |
| 194 | } |
| 195 | |
| 196 | static void fe_freeze(uint64_t out[5], const uint64_t in1[5]) { |
| 197 | { const uint64_t x7 = in1[4]; |
| 198 | { const uint64_t x8 = in1[3]; |
| 199 | { const uint64_t x6 = in1[2]; |
| 200 | { const uint64_t x4 = in1[1]; |
| 201 | { const uint64_t x2 = in1[0]; |
| 202 | { uint64_t x10; uint8_t/*bool*/ x11 = subborrow_u51(0x0, x2, 0x7ffffffffffed, &x10); |
| 203 | { uint64_t x13; uint8_t/*bool*/ x14 = subborrow_u51(x11, x4, 0x7ffffffffffff, &x13); |
| 204 | { uint64_t x16; uint8_t/*bool*/ x17 = subborrow_u51(x14, x6, 0x7ffffffffffff, &x16); |
| 205 | { uint64_t x19; uint8_t/*bool*/ x20 = subborrow_u51(x17, x8, 0x7ffffffffffff, &x19); |
| 206 | { uint64_t x22; uint8_t/*bool*/ x23 = subborrow_u51(x20, x7, 0x7ffffffffffff, &x22); |
| 207 | { uint64_t x24 = cmovznz64(x23, 0x0, 0xffffffffffffffffL); |
| 208 | { uint64_t x25 = (x24 & 0x7ffffffffffed); |
| 209 | { uint64_t x27; uint8_t/*bool*/ x28 = addcarryx_u51(0x0, x10, x25, &x27); |
| 210 | { uint64_t x29 = (x24 & 0x7ffffffffffff); |
| 211 | { uint64_t x31; uint8_t/*bool*/ x32 = addcarryx_u51(x28, x13, x29, &x31); |
| 212 | { uint64_t x33 = (x24 & 0x7ffffffffffff); |
| 213 | { uint64_t x35; uint8_t/*bool*/ x36 = addcarryx_u51(x32, x16, x33, &x35); |
| 214 | { uint64_t x37 = (x24 & 0x7ffffffffffff); |
| 215 | { uint64_t x39; uint8_t/*bool*/ x40 = addcarryx_u51(x36, x19, x37, &x39); |
| 216 | { uint64_t x41 = (x24 & 0x7ffffffffffff); |
| 217 | { uint64_t x43; addcarryx_u51(x40, x22, x41, &x43); |
| 218 | out[0] = x27; |
| 219 | out[1] = x31; |
| 220 | out[2] = x35; |
| 221 | out[3] = x39; |
| 222 | out[4] = x43; |
| 223 | }}}}}}}}}}}}}}}}}}}}} |
| 224 | } |
| 225 | |
| 226 | static void fe_tobytes(uint8_t s[32], const fe *f) { |
| 227 | assert_fe(f->v); |
| 228 | uint64_t h[5]; |
| 229 | fe_freeze(h, f->v); |
| 230 | assert_fe_frozen(h); |
| 231 | |
| 232 | s[0] = h[0] >> 0; |
| 233 | s[1] = h[0] >> 8; |
| 234 | s[2] = h[0] >> 16; |
| 235 | s[3] = h[0] >> 24; |
| 236 | s[4] = h[0] >> 32; |
| 237 | s[5] = h[0] >> 40; |
| 238 | s[6] = (h[0] >> 48) | (h[1] << 3); |
| 239 | s[7] = h[1] >> 5; |
| 240 | s[8] = h[1] >> 13; |
| 241 | s[9] = h[1] >> 21; |
| 242 | s[10] = h[1] >> 29; |
| 243 | s[11] = h[1] >> 37; |
| 244 | s[12] = (h[1] >> 45) | (h[2] << 6); |
| 245 | s[13] = h[2] >> 2; |
| 246 | s[14] = h[2] >> 10; |
| 247 | s[15] = h[2] >> 18; |
| 248 | s[16] = h[2] >> 26; |
| 249 | s[17] = h[2] >> 34; |
| 250 | s[18] = h[2] >> 42; |
| 251 | s[19] = (h[2] >> 50) | (h[3] << 1); |
| 252 | s[20] = h[3] >> 7; |
| 253 | s[21] = h[3] >> 15; |
| 254 | s[22] = h[3] >> 23; |
| 255 | s[23] = h[3] >> 31; |
| 256 | s[24] = h[3] >> 39; |
| 257 | s[25] = (h[3] >> 47) | (h[4] << 4); |
| 258 | s[26] = h[4] >> 4; |
| 259 | s[27] = h[4] >> 12; |
| 260 | s[28] = h[4] >> 20; |
| 261 | s[29] = h[4] >> 28; |
| 262 | s[30] = h[4] >> 36; |
| 263 | s[31] = h[4] >> 44; |
| 264 | } |
| 265 | |
| 266 | // h = 0 |
| 267 | static void fe_0(fe *h) { |
| 268 | OPENSSL_memset(h, 0, sizeof(fe)); |
| 269 | } |
| 270 | |
| 271 | static void fe_loose_0(fe_loose *h) { |
| 272 | OPENSSL_memset(h, 0, sizeof(fe_loose)); |
| 273 | } |
| 274 | |
| 275 | // h = 1 |
| 276 | static void fe_1(fe *h) { |
| 277 | OPENSSL_memset(h, 0, sizeof(fe)); |
| 278 | h->v[0] = 1; |
| 279 | } |
| 280 | |
| 281 | static void fe_loose_1(fe_loose *h) { |
| 282 | OPENSSL_memset(h, 0, sizeof(fe_loose)); |
| 283 | h->v[0] = 1; |
| 284 | } |
| 285 | |
| 286 | static void fe_add_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) { |
| 287 | { const uint64_t x10 = in1[4]; |
| 288 | { const uint64_t x11 = in1[3]; |
| 289 | { const uint64_t x9 = in1[2]; |
| 290 | { const uint64_t x7 = in1[1]; |
| 291 | { const uint64_t x5 = in1[0]; |
| 292 | { const uint64_t x18 = in2[4]; |
| 293 | { const uint64_t x19 = in2[3]; |
| 294 | { const uint64_t x17 = in2[2]; |
| 295 | { const uint64_t x15 = in2[1]; |
| 296 | { const uint64_t x13 = in2[0]; |
| 297 | out[0] = (x5 + x13); |
| 298 | out[1] = (x7 + x15); |
| 299 | out[2] = (x9 + x17); |
| 300 | out[3] = (x11 + x19); |
| 301 | out[4] = (x10 + x18); |
| 302 | }}}}}}}}}} |
| 303 | } |
| 304 | |
| 305 | // h = f + g |
| 306 | // Can overlap h with f or g. |
| 307 | static void fe_add(fe_loose *h, const fe *f, const fe *g) { |
| 308 | assert_fe(f->v); |
| 309 | assert_fe(g->v); |
| 310 | fe_add_impl(h->v, f->v, g->v); |
| 311 | assert_fe_loose(h->v); |
| 312 | } |
| 313 | |
| 314 | static void fe_sub_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) { |
| 315 | { const uint64_t x10 = in1[4]; |
| 316 | { const uint64_t x11 = in1[3]; |
| 317 | { const uint64_t x9 = in1[2]; |
| 318 | { const uint64_t x7 = in1[1]; |
| 319 | { const uint64_t x5 = in1[0]; |
| 320 | { const uint64_t x18 = in2[4]; |
| 321 | { const uint64_t x19 = in2[3]; |
| 322 | { const uint64_t x17 = in2[2]; |
| 323 | { const uint64_t x15 = in2[1]; |
| 324 | { const uint64_t x13 = in2[0]; |
| 325 | out[0] = ((0xfffffffffffda + x5) - x13); |
| 326 | out[1] = ((0xffffffffffffe + x7) - x15); |
| 327 | out[2] = ((0xffffffffffffe + x9) - x17); |
| 328 | out[3] = ((0xffffffffffffe + x11) - x19); |
| 329 | out[4] = ((0xffffffffffffe + x10) - x18); |
| 330 | }}}}}}}}}} |
| 331 | } |
| 332 | |
| 333 | // h = f - g |
| 334 | // Can overlap h with f or g. |
| 335 | static void fe_sub(fe_loose *h, const fe *f, const fe *g) { |
| 336 | assert_fe(f->v); |
| 337 | assert_fe(g->v); |
| 338 | fe_sub_impl(h->v, f->v, g->v); |
| 339 | assert_fe_loose(h->v); |
| 340 | } |
| 341 | |
| 342 | static void fe_carry_impl(uint64_t out[5], const uint64_t in1[5]) { |
| 343 | { const uint64_t x7 = in1[4]; |
| 344 | { const uint64_t x8 = in1[3]; |
| 345 | { const uint64_t x6 = in1[2]; |
| 346 | { const uint64_t x4 = in1[1]; |
| 347 | { const uint64_t x2 = in1[0]; |
| 348 | { uint64_t x9 = (x2 >> 0x33); |
| 349 | { uint64_t x10 = (x2 & 0x7ffffffffffff); |
| 350 | { uint64_t x11 = (x9 + x4); |
| 351 | { uint64_t x12 = (x11 >> 0x33); |
| 352 | { uint64_t x13 = (x11 & 0x7ffffffffffff); |
| 353 | { uint64_t x14 = (x12 + x6); |
| 354 | { uint64_t x15 = (x14 >> 0x33); |
| 355 | { uint64_t x16 = (x14 & 0x7ffffffffffff); |
| 356 | { uint64_t x17 = (x15 + x8); |
| 357 | { uint64_t x18 = (x17 >> 0x33); |
| 358 | { uint64_t x19 = (x17 & 0x7ffffffffffff); |
| 359 | { uint64_t x20 = (x18 + x7); |
| 360 | { uint64_t x21 = (x20 >> 0x33); |
| 361 | { uint64_t x22 = (x20 & 0x7ffffffffffff); |
| 362 | { uint64_t x23 = (x10 + (0x13 * x21)); |
| 363 | { uint64_t x24 = (x23 >> 0x33); |
| 364 | { uint64_t x25 = (x23 & 0x7ffffffffffff); |
| 365 | { uint64_t x26 = (x24 + x13); |
| 366 | { uint64_t x27 = (x26 >> 0x33); |
| 367 | { uint64_t x28 = (x26 & 0x7ffffffffffff); |
| 368 | out[0] = x25; |
| 369 | out[1] = x28; |
| 370 | out[2] = (x27 + x16); |
| 371 | out[3] = x19; |
| 372 | out[4] = x22; |
| 373 | }}}}}}}}}}}}}}}}}}}}}}}}} |
| 374 | } |
| 375 | |
| 376 | static void fe_carry(fe *h, const fe_loose* f) { |
| 377 | assert_fe_loose(f->v); |
| 378 | fe_carry_impl(h->v, f->v); |
| 379 | assert_fe(h->v); |
| 380 | } |
| 381 | |
| 382 | static void fe_mul_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) { |
| 383 | assert_fe_loose(in1); |
| 384 | assert_fe_loose(in2); |
| 385 | { const uint64_t x10 = in1[4]; |
| 386 | { const uint64_t x11 = in1[3]; |
| 387 | { const uint64_t x9 = in1[2]; |
| 388 | { const uint64_t x7 = in1[1]; |
| 389 | { const uint64_t x5 = in1[0]; |
| 390 | { const uint64_t x18 = in2[4]; |
| 391 | { const uint64_t x19 = in2[3]; |
| 392 | { const uint64_t x17 = in2[2]; |
| 393 | { const uint64_t x15 = in2[1]; |
| 394 | { const uint64_t x13 = in2[0]; |
| 395 | { uint128_t x20 = ((uint128_t)x5 * x13); |
| 396 | { uint128_t x21 = (((uint128_t)x5 * x15) + ((uint128_t)x7 * x13)); |
| 397 | { uint128_t x22 = ((((uint128_t)x5 * x17) + ((uint128_t)x9 * x13)) + ((uint128_t)x7 * x15)); |
| 398 | { uint128_t x23 = (((((uint128_t)x5 * x19) + ((uint128_t)x11 * x13)) + ((uint128_t)x7 * x17)) + ((uint128_t)x9 * x15)); |
| 399 | { uint128_t x24 = ((((((uint128_t)x5 * x18) + ((uint128_t)x10 * x13)) + ((uint128_t)x11 * x15)) + ((uint128_t)x7 * x19)) + ((uint128_t)x9 * x17)); |
| 400 | { uint64_t x25 = (x10 * 0x13); |
| 401 | { uint64_t x26 = (x7 * 0x13); |
| 402 | { uint64_t x27 = (x9 * 0x13); |
| 403 | { uint64_t x28 = (x11 * 0x13); |
| 404 | { uint128_t x29 = ((((x20 + ((uint128_t)x25 * x15)) + ((uint128_t)x26 * x18)) + ((uint128_t)x27 * x19)) + ((uint128_t)x28 * x17)); |
| 405 | { uint128_t x30 = (((x21 + ((uint128_t)x25 * x17)) + ((uint128_t)x27 * x18)) + ((uint128_t)x28 * x19)); |
| 406 | { uint128_t x31 = ((x22 + ((uint128_t)x25 * x19)) + ((uint128_t)x28 * x18)); |
| 407 | { uint128_t x32 = (x23 + ((uint128_t)x25 * x18)); |
| 408 | { uint64_t x33 = (uint64_t) (x29 >> 0x33); |
| 409 | { uint64_t x34 = ((uint64_t)x29 & 0x7ffffffffffff); |
| 410 | { uint128_t x35 = (x33 + x30); |
| 411 | { uint64_t x36 = (uint64_t) (x35 >> 0x33); |
| 412 | { uint64_t x37 = ((uint64_t)x35 & 0x7ffffffffffff); |
| 413 | { uint128_t x38 = (x36 + x31); |
| 414 | { uint64_t x39 = (uint64_t) (x38 >> 0x33); |
| 415 | { uint64_t x40 = ((uint64_t)x38 & 0x7ffffffffffff); |
| 416 | { uint128_t x41 = (x39 + x32); |
| 417 | { uint64_t x42 = (uint64_t) (x41 >> 0x33); |
| 418 | { uint64_t x43 = ((uint64_t)x41 & 0x7ffffffffffff); |
| 419 | { uint128_t x44 = (x42 + x24); |
| 420 | { uint64_t x45 = (uint64_t) (x44 >> 0x33); |
| 421 | { uint64_t x46 = ((uint64_t)x44 & 0x7ffffffffffff); |
| 422 | { uint64_t x47 = (x34 + (0x13 * x45)); |
| 423 | { uint64_t x48 = (x47 >> 0x33); |
| 424 | { uint64_t x49 = (x47 & 0x7ffffffffffff); |
| 425 | { uint64_t x50 = (x48 + x37); |
| 426 | { uint64_t x51 = (x50 >> 0x33); |
| 427 | { uint64_t x52 = (x50 & 0x7ffffffffffff); |
| 428 | out[0] = x49; |
| 429 | out[1] = x52; |
| 430 | out[2] = (x51 + x40); |
| 431 | out[3] = x43; |
| 432 | out[4] = x46; |
| 433 | }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| 434 | assert_fe(out); |
| 435 | } |
| 436 | |
| 437 | static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) { |
| 438 | fe_mul_impl(h->v, f->v, g->v); |
| 439 | } |
| 440 | |
| 441 | static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) { |
| 442 | fe_mul_impl(h->v, f->v, g->v); |
| 443 | } |
| 444 | |
| 445 | static void fe_mul_ttt(fe *h, const fe *f, const fe *g) { |
| 446 | fe_mul_impl(h->v, f->v, g->v); |
| 447 | } |
| 448 | |
| 449 | static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) { |
| 450 | fe_mul_impl(h->v, f->v, g->v); |
| 451 | } |
| 452 | |
| 453 | static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) { |
| 454 | fe_mul_impl(h->v, f->v, g->v); |
| 455 | } |
| 456 | |
| 457 | static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) { |
| 458 | fe_mul_impl(h->v, f->v, g->v); |
| 459 | } |
| 460 | |
| 461 | static void fe_sqr_impl(uint64_t out[5], const uint64_t in1[5]) { |
| 462 | assert_fe_loose(in1); |
| 463 | { const uint64_t x7 = in1[4]; |
| 464 | { const uint64_t x8 = in1[3]; |
| 465 | { const uint64_t x6 = in1[2]; |
| 466 | { const uint64_t x4 = in1[1]; |
| 467 | { const uint64_t x2 = in1[0]; |
| 468 | { uint64_t x9 = (x2 * 0x2); |
| 469 | { uint64_t x10 = (x4 * 0x2); |
| 470 | { uint64_t x11 = ((x6 * 0x2) * 0x13); |
| 471 | { uint64_t x12 = (x7 * 0x13); |
| 472 | { uint64_t x13 = (x12 * 0x2); |
| 473 | { uint128_t x14 = ((((uint128_t)x2 * x2) + ((uint128_t)x13 * x4)) + ((uint128_t)x11 * x8)); |
| 474 | { uint128_t x15 = ((((uint128_t)x9 * x4) + ((uint128_t)x13 * x6)) + ((uint128_t)x8 * (x8 * 0x13))); |
| 475 | { uint128_t x16 = ((((uint128_t)x9 * x6) + ((uint128_t)x4 * x4)) + ((uint128_t)x13 * x8)); |
| 476 | { uint128_t x17 = ((((uint128_t)x9 * x8) + ((uint128_t)x10 * x6)) + ((uint128_t)x7 * x12)); |
| 477 | { uint128_t x18 = ((((uint128_t)x9 * x7) + ((uint128_t)x10 * x8)) + ((uint128_t)x6 * x6)); |
| 478 | { uint64_t x19 = (uint64_t) (x14 >> 0x33); |
| 479 | { uint64_t x20 = ((uint64_t)x14 & 0x7ffffffffffff); |
| 480 | { uint128_t x21 = (x19 + x15); |
| 481 | { uint64_t x22 = (uint64_t) (x21 >> 0x33); |
| 482 | { uint64_t x23 = ((uint64_t)x21 & 0x7ffffffffffff); |
| 483 | { uint128_t x24 = (x22 + x16); |
| 484 | { uint64_t x25 = (uint64_t) (x24 >> 0x33); |
| 485 | { uint64_t x26 = ((uint64_t)x24 & 0x7ffffffffffff); |
| 486 | { uint128_t x27 = (x25 + x17); |
| 487 | { uint64_t x28 = (uint64_t) (x27 >> 0x33); |
| 488 | { uint64_t x29 = ((uint64_t)x27 & 0x7ffffffffffff); |
| 489 | { uint128_t x30 = (x28 + x18); |
| 490 | { uint64_t x31 = (uint64_t) (x30 >> 0x33); |
| 491 | { uint64_t x32 = ((uint64_t)x30 & 0x7ffffffffffff); |
| 492 | { uint64_t x33 = (x20 + (0x13 * x31)); |
| 493 | { uint64_t x34 = (x33 >> 0x33); |
| 494 | { uint64_t x35 = (x33 & 0x7ffffffffffff); |
| 495 | { uint64_t x36 = (x34 + x23); |
| 496 | { uint64_t x37 = (x36 >> 0x33); |
| 497 | { uint64_t x38 = (x36 & 0x7ffffffffffff); |
| 498 | out[0] = x35; |
| 499 | out[1] = x38; |
| 500 | out[2] = (x37 + x26); |
| 501 | out[3] = x29; |
| 502 | out[4] = x32; |
| 503 | }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| 504 | assert_fe(out); |
| 505 | } |
| 506 | |
| 507 | static void fe_sq_tl(fe *h, const fe_loose *f) { |
| 508 | fe_sqr_impl(h->v, f->v); |
| 509 | } |
| 510 | |
| 511 | static void fe_sq_tt(fe *h, const fe *f) { |
| 512 | fe_sqr_impl(h->v, f->v); |
| 513 | } |
| 514 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 515 | // Replace (f,g) with (g,f) if b == 1; |
| 516 | // replace (f,g) with (f,g) if b == 0. |
| 517 | // |
| 518 | // Preconditions: b in {0,1}. |
| 519 | static void fe_cswap(fe *f, fe *g, uint64_t b) { |
| 520 | b = 0-b; |
| 521 | for (unsigned i = 0; i < 5; i++) { |
| 522 | uint64_t x = f->v[i] ^ g->v[i]; |
| 523 | x &= b; |
| 524 | f->v[i] ^= x; |
| 525 | g->v[i] ^= x; |
| 526 | } |
| 527 | } |
| 528 | |
| 529 | // NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.. |
| 530 | static void fe_mul_121666_impl(uint64_t out[5], const uint64_t in1[5]) { |
| 531 | assert_fe_loose(in1); |
| 532 | { const uint64_t x10 = in1[4]; |
| 533 | { const uint64_t x11 = in1[3]; |
| 534 | { const uint64_t x9 = in1[2]; |
| 535 | { const uint64_t x7 = in1[1]; |
| 536 | { const uint64_t x5 = in1[0]; |
| 537 | { const uint64_t x18 = 0; |
| 538 | { const uint64_t x19 = 0; |
| 539 | { const uint64_t x17 = 0; |
| 540 | { const uint64_t x15 = 0; |
| 541 | { const uint64_t x13 = 121666; |
| 542 | { uint128_t x20 = ((uint128_t)x5 * x13); |
| 543 | { uint128_t x21 = (((uint128_t)x5 * x15) + ((uint128_t)x7 * x13)); |
| 544 | { uint128_t x22 = ((((uint128_t)x5 * x17) + ((uint128_t)x9 * x13)) + ((uint128_t)x7 * x15)); |
| 545 | { uint128_t x23 = (((((uint128_t)x5 * x19) + ((uint128_t)x11 * x13)) + ((uint128_t)x7 * x17)) + ((uint128_t)x9 * x15)); |
| 546 | { uint128_t x24 = ((((((uint128_t)x5 * x18) + ((uint128_t)x10 * x13)) + ((uint128_t)x11 * x15)) + ((uint128_t)x7 * x19)) + ((uint128_t)x9 * x17)); |
| 547 | { uint64_t x25 = (x10 * 0x13); |
| 548 | { uint64_t x26 = (x7 * 0x13); |
| 549 | { uint64_t x27 = (x9 * 0x13); |
| 550 | { uint64_t x28 = (x11 * 0x13); |
| 551 | { uint128_t x29 = ((((x20 + ((uint128_t)x25 * x15)) + ((uint128_t)x26 * x18)) + ((uint128_t)x27 * x19)) + ((uint128_t)x28 * x17)); |
| 552 | { uint128_t x30 = (((x21 + ((uint128_t)x25 * x17)) + ((uint128_t)x27 * x18)) + ((uint128_t)x28 * x19)); |
| 553 | { uint128_t x31 = ((x22 + ((uint128_t)x25 * x19)) + ((uint128_t)x28 * x18)); |
| 554 | { uint128_t x32 = (x23 + ((uint128_t)x25 * x18)); |
| 555 | { uint64_t x33 = (uint64_t) (x29 >> 0x33); |
| 556 | { uint64_t x34 = ((uint64_t)x29 & 0x7ffffffffffff); |
| 557 | { uint128_t x35 = (x33 + x30); |
| 558 | { uint64_t x36 = (uint64_t) (x35 >> 0x33); |
| 559 | { uint64_t x37 = ((uint64_t)x35 & 0x7ffffffffffff); |
| 560 | { uint128_t x38 = (x36 + x31); |
| 561 | { uint64_t x39 = (uint64_t) (x38 >> 0x33); |
| 562 | { uint64_t x40 = ((uint64_t)x38 & 0x7ffffffffffff); |
| 563 | { uint128_t x41 = (x39 + x32); |
| 564 | { uint64_t x42 = (uint64_t) (x41 >> 0x33); |
| 565 | { uint64_t x43 = ((uint64_t)x41 & 0x7ffffffffffff); |
| 566 | { uint128_t x44 = (x42 + x24); |
| 567 | { uint64_t x45 = (uint64_t) (x44 >> 0x33); |
| 568 | { uint64_t x46 = ((uint64_t)x44 & 0x7ffffffffffff); |
| 569 | { uint64_t x47 = (x34 + (0x13 * x45)); |
| 570 | { uint64_t x48 = (x47 >> 0x33); |
| 571 | { uint64_t x49 = (x47 & 0x7ffffffffffff); |
| 572 | { uint64_t x50 = (x48 + x37); |
| 573 | { uint64_t x51 = (x50 >> 0x33); |
| 574 | { uint64_t x52 = (x50 & 0x7ffffffffffff); |
| 575 | out[0] = x49; |
| 576 | out[1] = x52; |
| 577 | out[2] = (x51 + x40); |
| 578 | out[3] = x43; |
| 579 | out[4] = x46; |
| 580 | }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| 581 | assert_fe(out); |
| 582 | } |
| 583 | |
| 584 | static void fe_mul121666(fe *h, const fe_loose *f) { |
| 585 | assert_fe_loose(f->v); |
| 586 | fe_mul_121666_impl(h->v, f->v); |
| 587 | assert_fe(h->v); |
| 588 | } |
| 589 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 590 | // Adapted from Fiat-synthesized |fe_sub_impl| with |out| = 0. |
| 591 | static void fe_neg_impl(uint64_t out[5], const uint64_t in2[5]) { |
| 592 | { const uint64_t x10 = 0; |
| 593 | { const uint64_t x11 = 0; |
| 594 | { const uint64_t x9 = 0; |
| 595 | { const uint64_t x7 = 0; |
| 596 | { const uint64_t x5 = 0; |
| 597 | { const uint64_t x18 = in2[4]; |
| 598 | { const uint64_t x19 = in2[3]; |
| 599 | { const uint64_t x17 = in2[2]; |
| 600 | { const uint64_t x15 = in2[1]; |
| 601 | { const uint64_t x13 = in2[0]; |
| 602 | out[0] = ((0xfffffffffffda + x5) - x13); |
| 603 | out[1] = ((0xffffffffffffe + x7) - x15); |
| 604 | out[2] = ((0xffffffffffffe + x9) - x17); |
| 605 | out[3] = ((0xffffffffffffe + x11) - x19); |
| 606 | out[4] = ((0xffffffffffffe + x10) - x18); |
| 607 | }}}}}}}}}} |
| 608 | } |
| 609 | |
| 610 | // h = -f |
| 611 | static void fe_neg(fe_loose *h, const fe *f) { |
| 612 | assert_fe(f->v); |
| 613 | fe_neg_impl(h->v, f->v); |
| 614 | assert_fe_loose(h->v); |
| 615 | } |
| 616 | |
| 617 | // Replace (f,g) with (g,g) if b == 1; |
| 618 | // replace (f,g) with (f,g) if b == 0. |
| 619 | // |
| 620 | // Preconditions: b in {0,1}. |
| 621 | static void fe_cmov(fe_loose *f, const fe_loose *g, uint64_t b) { |
| 622 | b = 0-b; |
| 623 | for (unsigned i = 0; i < 5; i++) { |
| 624 | uint64_t x = f->v[i] ^ g->v[i]; |
| 625 | x &= b; |
| 626 | f->v[i] ^= x; |
| 627 | } |
| 628 | } |
| 629 | |
| 630 | #else |
| 631 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 632 | #define assert_fe(f) do { \ |
| 633 | for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \ |
| 634 | assert(f[_assert_fe_i] < 1.125*(1<<(26-(_assert_fe_i&1)))); \ |
| 635 | } \ |
| 636 | } while (0) |
| 637 | |
| 638 | #define assert_fe_loose(f) do { \ |
| 639 | for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \ |
| 640 | assert(f[_assert_fe_i] < 3.375*(1<<(26-(_assert_fe_i&1)))); \ |
| 641 | } \ |
| 642 | } while (0) |
| 643 | |
Robert Sloan | a450c92 | 2018-01-08 10:35:32 -0800 | [diff] [blame] | 644 | #define assert_fe_frozen(f) do { \ |
| 645 | for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \ |
| 646 | assert(f[_assert_fe_i] < (1u<<(26-(_assert_fe_i&1)))); \ |
| 647 | } \ |
| 648 | } while (0) |
| 649 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 650 | static void fe_frombytes_impl(uint32_t h[10], const uint8_t *s) { |
| 651 | // Ignores top bit of s. |
| 652 | uint32_t a0 = load_4(s); |
| 653 | uint32_t a1 = load_4(s+4); |
| 654 | uint32_t a2 = load_4(s+8); |
| 655 | uint32_t a3 = load_4(s+12); |
| 656 | uint32_t a4 = load_4(s+16); |
| 657 | uint32_t a5 = load_4(s+20); |
| 658 | uint32_t a6 = load_4(s+24); |
| 659 | uint32_t a7 = load_4(s+28); |
| 660 | h[0] = a0&((1<<26)-1); // 26 used, 32-26 left. 26 |
| 661 | h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); // (32-26) + 19 = 6+19 = 25 |
| 662 | h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); // (32-19) + 13 = 13+13 = 26 |
| 663 | h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); // (32-13) + 6 = 19+ 6 = 25 |
| 664 | h[4] = (a3>> 6); // (32- 6) = 26 |
| 665 | h[5] = a4&((1<<25)-1); // 25 |
| 666 | h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); // (32-25) + 19 = 7+19 = 26 |
| 667 | h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); // (32-19) + 12 = 13+12 = 25 |
| 668 | h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); // (32-12) + 6 = 20+ 6 = 26 |
| 669 | h[9] = (a7>> 6)&((1<<25)-1); // 25 |
| 670 | assert_fe(h); |
| 671 | } |
| 672 | |
| 673 | static void fe_frombytes(fe *h, const uint8_t *s) { |
| 674 | fe_frombytes_impl(h->v, s); |
| 675 | } |
| 676 | |
Robert Sloan | a450c92 | 2018-01-08 10:35:32 -0800 | [diff] [blame] | 677 | static void fe_freeze(uint32_t out[10], const uint32_t in1[10]) { |
| 678 | { const uint32_t x17 = in1[9]; |
| 679 | { const uint32_t x18 = in1[8]; |
| 680 | { const uint32_t x16 = in1[7]; |
| 681 | { const uint32_t x14 = in1[6]; |
| 682 | { const uint32_t x12 = in1[5]; |
| 683 | { const uint32_t x10 = in1[4]; |
| 684 | { const uint32_t x8 = in1[3]; |
| 685 | { const uint32_t x6 = in1[2]; |
| 686 | { const uint32_t x4 = in1[1]; |
| 687 | { const uint32_t x2 = in1[0]; |
| 688 | { uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20); |
| 689 | { uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23); |
| 690 | { uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26); |
| 691 | { uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29); |
| 692 | { uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32); |
| 693 | { uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35); |
| 694 | { uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38); |
| 695 | { uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41); |
| 696 | { uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44); |
| 697 | { uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47); |
| 698 | { uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff); |
| 699 | { uint32_t x50 = (x49 & 0x3ffffed); |
| 700 | { uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52); |
| 701 | { uint32_t x54 = (x49 & 0x1ffffff); |
| 702 | { uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56); |
| 703 | { uint32_t x58 = (x49 & 0x3ffffff); |
| 704 | { uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60); |
| 705 | { uint32_t x62 = (x49 & 0x1ffffff); |
| 706 | { uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64); |
| 707 | { uint32_t x66 = (x49 & 0x3ffffff); |
| 708 | { uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68); |
| 709 | { uint32_t x70 = (x49 & 0x1ffffff); |
| 710 | { uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72); |
| 711 | { uint32_t x74 = (x49 & 0x3ffffff); |
| 712 | { uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76); |
| 713 | { uint32_t x78 = (x49 & 0x1ffffff); |
| 714 | { uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80); |
| 715 | { uint32_t x82 = (x49 & 0x3ffffff); |
| 716 | { uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84); |
| 717 | { uint32_t x86 = (x49 & 0x1ffffff); |
| 718 | { uint32_t x88; addcarryx_u25(x85, x47, x86, &x88); |
| 719 | out[0] = x52; |
| 720 | out[1] = x56; |
| 721 | out[2] = x60; |
| 722 | out[3] = x64; |
| 723 | out[4] = x68; |
| 724 | out[5] = x72; |
| 725 | out[6] = x76; |
| 726 | out[7] = x80; |
| 727 | out[8] = x84; |
| 728 | out[9] = x88; |
| 729 | }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| 730 | } |
| 731 | |
| 732 | static void fe_tobytes(uint8_t s[32], const fe *f) { |
| 733 | assert_fe(f->v); |
| 734 | uint32_t h[10]; |
| 735 | fe_freeze(h, f->v); |
| 736 | assert_fe_frozen(h); |
| 737 | |
| 738 | s[0] = h[0] >> 0; |
| 739 | s[1] = h[0] >> 8; |
| 740 | s[2] = h[0] >> 16; |
| 741 | s[3] = (h[0] >> 24) | (h[1] << 2); |
| 742 | s[4] = h[1] >> 6; |
| 743 | s[5] = h[1] >> 14; |
| 744 | s[6] = (h[1] >> 22) | (h[2] << 3); |
| 745 | s[7] = h[2] >> 5; |
| 746 | s[8] = h[2] >> 13; |
| 747 | s[9] = (h[2] >> 21) | (h[3] << 5); |
| 748 | s[10] = h[3] >> 3; |
| 749 | s[11] = h[3] >> 11; |
| 750 | s[12] = (h[3] >> 19) | (h[4] << 6); |
| 751 | s[13] = h[4] >> 2; |
| 752 | s[14] = h[4] >> 10; |
| 753 | s[15] = h[4] >> 18; |
| 754 | s[16] = h[5] >> 0; |
| 755 | s[17] = h[5] >> 8; |
| 756 | s[18] = h[5] >> 16; |
| 757 | s[19] = (h[5] >> 24) | (h[6] << 1); |
| 758 | s[20] = h[6] >> 7; |
| 759 | s[21] = h[6] >> 15; |
| 760 | s[22] = (h[6] >> 23) | (h[7] << 3); |
| 761 | s[23] = h[7] >> 5; |
| 762 | s[24] = h[7] >> 13; |
| 763 | s[25] = (h[7] >> 21) | (h[8] << 4); |
| 764 | s[26] = h[8] >> 4; |
| 765 | s[27] = h[8] >> 12; |
| 766 | s[28] = (h[8] >> 20) | (h[9] << 6); |
| 767 | s[29] = h[9] >> 2; |
| 768 | s[30] = h[9] >> 10; |
| 769 | s[31] = h[9] >> 18; |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 770 | } |
| 771 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 772 | // h = 0 |
| 773 | static void fe_0(fe *h) { |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 774 | OPENSSL_memset(h, 0, sizeof(fe)); |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 775 | } |
| 776 | |
| 777 | static void fe_loose_0(fe_loose *h) { |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 778 | OPENSSL_memset(h, 0, sizeof(fe_loose)); |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 779 | } |
| 780 | |
| 781 | // h = 1 |
| 782 | static void fe_1(fe *h) { |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 783 | OPENSSL_memset(h, 0, sizeof(fe)); |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 784 | h->v[0] = 1; |
| 785 | } |
| 786 | |
| 787 | static void fe_loose_1(fe_loose *h) { |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 788 | OPENSSL_memset(h, 0, sizeof(fe_loose)); |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 789 | h->v[0] = 1; |
| 790 | } |
| 791 | |
| 792 | static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) { |
| 793 | { const uint32_t x20 = in1[9]; |
| 794 | { const uint32_t x21 = in1[8]; |
| 795 | { const uint32_t x19 = in1[7]; |
| 796 | { const uint32_t x17 = in1[6]; |
| 797 | { const uint32_t x15 = in1[5]; |
| 798 | { const uint32_t x13 = in1[4]; |
| 799 | { const uint32_t x11 = in1[3]; |
| 800 | { const uint32_t x9 = in1[2]; |
| 801 | { const uint32_t x7 = in1[1]; |
| 802 | { const uint32_t x5 = in1[0]; |
| 803 | { const uint32_t x38 = in2[9]; |
| 804 | { const uint32_t x39 = in2[8]; |
| 805 | { const uint32_t x37 = in2[7]; |
| 806 | { const uint32_t x35 = in2[6]; |
| 807 | { const uint32_t x33 = in2[5]; |
| 808 | { const uint32_t x31 = in2[4]; |
| 809 | { const uint32_t x29 = in2[3]; |
| 810 | { const uint32_t x27 = in2[2]; |
| 811 | { const uint32_t x25 = in2[1]; |
| 812 | { const uint32_t x23 = in2[0]; |
| 813 | out[0] = (x5 + x23); |
| 814 | out[1] = (x7 + x25); |
| 815 | out[2] = (x9 + x27); |
| 816 | out[3] = (x11 + x29); |
| 817 | out[4] = (x13 + x31); |
| 818 | out[5] = (x15 + x33); |
| 819 | out[6] = (x17 + x35); |
| 820 | out[7] = (x19 + x37); |
| 821 | out[8] = (x21 + x39); |
| 822 | out[9] = (x20 + x38); |
| 823 | }}}}}}}}}}}}}}}}}}}} |
| 824 | } |
| 825 | |
| 826 | // h = f + g |
| 827 | // Can overlap h with f or g. |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 828 | static void fe_add(fe_loose *h, const fe *f, const fe *g) { |
| 829 | assert_fe(f->v); |
| 830 | assert_fe(g->v); |
| 831 | fe_add_impl(h->v, f->v, g->v); |
| 832 | assert_fe_loose(h->v); |
| 833 | } |
| 834 | |
| 835 | static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) { |
| 836 | { const uint32_t x20 = in1[9]; |
| 837 | { const uint32_t x21 = in1[8]; |
| 838 | { const uint32_t x19 = in1[7]; |
| 839 | { const uint32_t x17 = in1[6]; |
| 840 | { const uint32_t x15 = in1[5]; |
| 841 | { const uint32_t x13 = in1[4]; |
| 842 | { const uint32_t x11 = in1[3]; |
| 843 | { const uint32_t x9 = in1[2]; |
| 844 | { const uint32_t x7 = in1[1]; |
| 845 | { const uint32_t x5 = in1[0]; |
| 846 | { const uint32_t x38 = in2[9]; |
| 847 | { const uint32_t x39 = in2[8]; |
| 848 | { const uint32_t x37 = in2[7]; |
| 849 | { const uint32_t x35 = in2[6]; |
| 850 | { const uint32_t x33 = in2[5]; |
| 851 | { const uint32_t x31 = in2[4]; |
| 852 | { const uint32_t x29 = in2[3]; |
| 853 | { const uint32_t x27 = in2[2]; |
| 854 | { const uint32_t x25 = in2[1]; |
| 855 | { const uint32_t x23 = in2[0]; |
| 856 | out[0] = ((0x7ffffda + x5) - x23); |
| 857 | out[1] = ((0x3fffffe + x7) - x25); |
| 858 | out[2] = ((0x7fffffe + x9) - x27); |
| 859 | out[3] = ((0x3fffffe + x11) - x29); |
| 860 | out[4] = ((0x7fffffe + x13) - x31); |
| 861 | out[5] = ((0x3fffffe + x15) - x33); |
| 862 | out[6] = ((0x7fffffe + x17) - x35); |
| 863 | out[7] = ((0x3fffffe + x19) - x37); |
| 864 | out[8] = ((0x7fffffe + x21) - x39); |
| 865 | out[9] = ((0x3fffffe + x20) - x38); |
| 866 | }}}}}}}}}}}}}}}}}}}} |
| 867 | } |
| 868 | |
| 869 | // h = f - g |
| 870 | // Can overlap h with f or g. |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 871 | static void fe_sub(fe_loose *h, const fe *f, const fe *g) { |
| 872 | assert_fe(f->v); |
| 873 | assert_fe(g->v); |
| 874 | fe_sub_impl(h->v, f->v, g->v); |
| 875 | assert_fe_loose(h->v); |
| 876 | } |
| 877 | |
| 878 | static void fe_carry_impl(uint32_t out[10], const uint32_t in1[10]) { |
| 879 | { const uint32_t x17 = in1[9]; |
| 880 | { const uint32_t x18 = in1[8]; |
| 881 | { const uint32_t x16 = in1[7]; |
| 882 | { const uint32_t x14 = in1[6]; |
| 883 | { const uint32_t x12 = in1[5]; |
| 884 | { const uint32_t x10 = in1[4]; |
| 885 | { const uint32_t x8 = in1[3]; |
| 886 | { const uint32_t x6 = in1[2]; |
| 887 | { const uint32_t x4 = in1[1]; |
| 888 | { const uint32_t x2 = in1[0]; |
| 889 | { uint32_t x19 = (x2 >> 0x1a); |
| 890 | { uint32_t x20 = (x2 & 0x3ffffff); |
| 891 | { uint32_t x21 = (x19 + x4); |
| 892 | { uint32_t x22 = (x21 >> 0x19); |
| 893 | { uint32_t x23 = (x21 & 0x1ffffff); |
| 894 | { uint32_t x24 = (x22 + x6); |
| 895 | { uint32_t x25 = (x24 >> 0x1a); |
| 896 | { uint32_t x26 = (x24 & 0x3ffffff); |
| 897 | { uint32_t x27 = (x25 + x8); |
| 898 | { uint32_t x28 = (x27 >> 0x19); |
| 899 | { uint32_t x29 = (x27 & 0x1ffffff); |
| 900 | { uint32_t x30 = (x28 + x10); |
| 901 | { uint32_t x31 = (x30 >> 0x1a); |
| 902 | { uint32_t x32 = (x30 & 0x3ffffff); |
| 903 | { uint32_t x33 = (x31 + x12); |
| 904 | { uint32_t x34 = (x33 >> 0x19); |
| 905 | { uint32_t x35 = (x33 & 0x1ffffff); |
| 906 | { uint32_t x36 = (x34 + x14); |
| 907 | { uint32_t x37 = (x36 >> 0x1a); |
| 908 | { uint32_t x38 = (x36 & 0x3ffffff); |
| 909 | { uint32_t x39 = (x37 + x16); |
| 910 | { uint32_t x40 = (x39 >> 0x19); |
| 911 | { uint32_t x41 = (x39 & 0x1ffffff); |
| 912 | { uint32_t x42 = (x40 + x18); |
| 913 | { uint32_t x43 = (x42 >> 0x1a); |
| 914 | { uint32_t x44 = (x42 & 0x3ffffff); |
| 915 | { uint32_t x45 = (x43 + x17); |
| 916 | { uint32_t x46 = (x45 >> 0x19); |
| 917 | { uint32_t x47 = (x45 & 0x1ffffff); |
| 918 | { uint32_t x48 = (x20 + (0x13 * x46)); |
| 919 | { uint32_t x49 = (x48 >> 0x1a); |
| 920 | { uint32_t x50 = (x48 & 0x3ffffff); |
| 921 | { uint32_t x51 = (x49 + x23); |
| 922 | { uint32_t x52 = (x51 >> 0x19); |
| 923 | { uint32_t x53 = (x51 & 0x1ffffff); |
| 924 | out[0] = x50; |
| 925 | out[1] = x53; |
| 926 | out[2] = (x52 + x26); |
| 927 | out[3] = x29; |
| 928 | out[4] = x32; |
| 929 | out[5] = x35; |
| 930 | out[6] = x38; |
| 931 | out[7] = x41; |
| 932 | out[8] = x44; |
| 933 | out[9] = x47; |
| 934 | }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| 935 | } |
| 936 | |
| 937 | static void fe_carry(fe *h, const fe_loose* f) { |
| 938 | assert_fe_loose(f->v); |
| 939 | fe_carry_impl(h->v, f->v); |
| 940 | assert_fe(h->v); |
| 941 | } |
| 942 | |
| 943 | static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) { |
| 944 | assert_fe_loose(in1); |
| 945 | assert_fe_loose(in2); |
| 946 | { const uint32_t x20 = in1[9]; |
| 947 | { const uint32_t x21 = in1[8]; |
| 948 | { const uint32_t x19 = in1[7]; |
| 949 | { const uint32_t x17 = in1[6]; |
| 950 | { const uint32_t x15 = in1[5]; |
| 951 | { const uint32_t x13 = in1[4]; |
| 952 | { const uint32_t x11 = in1[3]; |
| 953 | { const uint32_t x9 = in1[2]; |
| 954 | { const uint32_t x7 = in1[1]; |
| 955 | { const uint32_t x5 = in1[0]; |
| 956 | { const uint32_t x38 = in2[9]; |
| 957 | { const uint32_t x39 = in2[8]; |
| 958 | { const uint32_t x37 = in2[7]; |
| 959 | { const uint32_t x35 = in2[6]; |
| 960 | { const uint32_t x33 = in2[5]; |
| 961 | { const uint32_t x31 = in2[4]; |
| 962 | { const uint32_t x29 = in2[3]; |
| 963 | { const uint32_t x27 = in2[2]; |
| 964 | { const uint32_t x25 = in2[1]; |
| 965 | { const uint32_t x23 = in2[0]; |
| 966 | { uint64_t x40 = ((uint64_t)x23 * x5); |
| 967 | { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); |
| 968 | { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); |
| 969 | { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); |
| 970 | { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); |
| 971 | { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); |
| 972 | { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); |
| 973 | { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); |
| 974 | { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); |
| 975 | { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); |
| 976 | { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); |
| 977 | { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); |
| 978 | { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); |
| 979 | { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); |
| 980 | { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17)); |
| 981 | { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); |
| 982 | { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); |
| 983 | { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); |
| 984 | { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); |
| 985 | { uint64_t x59 = (x48 + (x58 << 0x4)); |
| 986 | { uint64_t x60 = (x59 + (x58 << 0x1)); |
| 987 | { uint64_t x61 = (x60 + x58); |
| 988 | { uint64_t x62 = (x47 + (x57 << 0x4)); |
| 989 | { uint64_t x63 = (x62 + (x57 << 0x1)); |
| 990 | { uint64_t x64 = (x63 + x57); |
| 991 | { uint64_t x65 = (x46 + (x56 << 0x4)); |
| 992 | { uint64_t x66 = (x65 + (x56 << 0x1)); |
| 993 | { uint64_t x67 = (x66 + x56); |
| 994 | { uint64_t x68 = (x45 + (x55 << 0x4)); |
| 995 | { uint64_t x69 = (x68 + (x55 << 0x1)); |
| 996 | { uint64_t x70 = (x69 + x55); |
| 997 | { uint64_t x71 = (x44 + (x54 << 0x4)); |
| 998 | { uint64_t x72 = (x71 + (x54 << 0x1)); |
| 999 | { uint64_t x73 = (x72 + x54); |
| 1000 | { uint64_t x74 = (x43 + (x53 << 0x4)); |
| 1001 | { uint64_t x75 = (x74 + (x53 << 0x1)); |
| 1002 | { uint64_t x76 = (x75 + x53); |
| 1003 | { uint64_t x77 = (x42 + (x52 << 0x4)); |
| 1004 | { uint64_t x78 = (x77 + (x52 << 0x1)); |
| 1005 | { uint64_t x79 = (x78 + x52); |
| 1006 | { uint64_t x80 = (x41 + (x51 << 0x4)); |
| 1007 | { uint64_t x81 = (x80 + (x51 << 0x1)); |
| 1008 | { uint64_t x82 = (x81 + x51); |
| 1009 | { uint64_t x83 = (x40 + (x50 << 0x4)); |
| 1010 | { uint64_t x84 = (x83 + (x50 << 0x1)); |
| 1011 | { uint64_t x85 = (x84 + x50); |
| 1012 | { uint64_t x86 = (x85 >> 0x1a); |
| 1013 | { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); |
| 1014 | { uint64_t x88 = (x86 + x82); |
| 1015 | { uint64_t x89 = (x88 >> 0x19); |
| 1016 | { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); |
| 1017 | { uint64_t x91 = (x89 + x79); |
| 1018 | { uint64_t x92 = (x91 >> 0x1a); |
| 1019 | { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); |
| 1020 | { uint64_t x94 = (x92 + x76); |
| 1021 | { uint64_t x95 = (x94 >> 0x19); |
| 1022 | { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); |
| 1023 | { uint64_t x97 = (x95 + x73); |
| 1024 | { uint64_t x98 = (x97 >> 0x1a); |
| 1025 | { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); |
| 1026 | { uint64_t x100 = (x98 + x70); |
| 1027 | { uint64_t x101 = (x100 >> 0x19); |
| 1028 | { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); |
| 1029 | { uint64_t x103 = (x101 + x67); |
| 1030 | { uint64_t x104 = (x103 >> 0x1a); |
| 1031 | { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); |
| 1032 | { uint64_t x106 = (x104 + x64); |
| 1033 | { uint64_t x107 = (x106 >> 0x19); |
| 1034 | { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); |
| 1035 | { uint64_t x109 = (x107 + x61); |
| 1036 | { uint64_t x110 = (x109 >> 0x1a); |
| 1037 | { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); |
| 1038 | { uint64_t x112 = (x110 + x49); |
| 1039 | { uint64_t x113 = (x112 >> 0x19); |
| 1040 | { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); |
| 1041 | { uint64_t x115 = (x87 + (0x13 * x113)); |
| 1042 | { uint32_t x116 = (uint32_t) (x115 >> 0x1a); |
| 1043 | { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); |
| 1044 | { uint32_t x118 = (x116 + x90); |
| 1045 | { uint32_t x119 = (x118 >> 0x19); |
| 1046 | { uint32_t x120 = (x118 & 0x1ffffff); |
| 1047 | out[0] = x117; |
| 1048 | out[1] = x120; |
| 1049 | out[2] = (x119 + x93); |
| 1050 | out[3] = x96; |
| 1051 | out[4] = x99; |
| 1052 | out[5] = x102; |
| 1053 | out[6] = x105; |
| 1054 | out[7] = x108; |
| 1055 | out[8] = x111; |
| 1056 | out[9] = x114; |
| 1057 | }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| 1058 | assert_fe(out); |
| 1059 | } |
| 1060 | |
| 1061 | static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) { |
| 1062 | fe_mul_impl(h->v, f->v, g->v); |
| 1063 | } |
| 1064 | |
| 1065 | static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) { |
| 1066 | fe_mul_impl(h->v, f->v, g->v); |
| 1067 | } |
| 1068 | |
| 1069 | static void fe_mul_ttt(fe *h, const fe *f, const fe *g) { |
| 1070 | fe_mul_impl(h->v, f->v, g->v); |
| 1071 | } |
| 1072 | |
| 1073 | static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) { |
| 1074 | fe_mul_impl(h->v, f->v, g->v); |
| 1075 | } |
| 1076 | |
| 1077 | static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) { |
| 1078 | fe_mul_impl(h->v, f->v, g->v); |
| 1079 | } |
| 1080 | |
| 1081 | static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) { |
| 1082 | fe_mul_impl(h->v, f->v, g->v); |
| 1083 | } |
| 1084 | |
| 1085 | static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) { |
| 1086 | assert_fe_loose(in1); |
| 1087 | { const uint32_t x17 = in1[9]; |
| 1088 | { const uint32_t x18 = in1[8]; |
| 1089 | { const uint32_t x16 = in1[7]; |
| 1090 | { const uint32_t x14 = in1[6]; |
| 1091 | { const uint32_t x12 = in1[5]; |
| 1092 | { const uint32_t x10 = in1[4]; |
| 1093 | { const uint32_t x8 = in1[3]; |
| 1094 | { const uint32_t x6 = in1[2]; |
| 1095 | { const uint32_t x4 = in1[1]; |
| 1096 | { const uint32_t x2 = in1[0]; |
| 1097 | { uint64_t x19 = ((uint64_t)x2 * x2); |
| 1098 | { uint64_t x20 = ((uint64_t)(0x2 * x2) * x4); |
| 1099 | { uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6))); |
| 1100 | { uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8))); |
| 1101 | { uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10)); |
| 1102 | { uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12))); |
| 1103 | { uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12))); |
| 1104 | { uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16))); |
| 1105 | { uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12)))))); |
| 1106 | { uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17))); |
| 1107 | { uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17))))); |
| 1108 | { uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17))); |
| 1109 | { uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17)))))); |
| 1110 | { uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17))); |
| 1111 | { uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17))); |
| 1112 | { uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17))); |
| 1113 | { uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17)); |
| 1114 | { uint64_t x36 = ((uint64_t)(0x2 * x18) * x17); |
| 1115 | { uint64_t x37 = ((uint64_t)(0x2 * x17) * x17); |
| 1116 | { uint64_t x38 = (x27 + (x37 << 0x4)); |
| 1117 | { uint64_t x39 = (x38 + (x37 << 0x1)); |
| 1118 | { uint64_t x40 = (x39 + x37); |
| 1119 | { uint64_t x41 = (x26 + (x36 << 0x4)); |
| 1120 | { uint64_t x42 = (x41 + (x36 << 0x1)); |
| 1121 | { uint64_t x43 = (x42 + x36); |
| 1122 | { uint64_t x44 = (x25 + (x35 << 0x4)); |
| 1123 | { uint64_t x45 = (x44 + (x35 << 0x1)); |
| 1124 | { uint64_t x46 = (x45 + x35); |
| 1125 | { uint64_t x47 = (x24 + (x34 << 0x4)); |
| 1126 | { uint64_t x48 = (x47 + (x34 << 0x1)); |
| 1127 | { uint64_t x49 = (x48 + x34); |
| 1128 | { uint64_t x50 = (x23 + (x33 << 0x4)); |
| 1129 | { uint64_t x51 = (x50 + (x33 << 0x1)); |
| 1130 | { uint64_t x52 = (x51 + x33); |
| 1131 | { uint64_t x53 = (x22 + (x32 << 0x4)); |
| 1132 | { uint64_t x54 = (x53 + (x32 << 0x1)); |
| 1133 | { uint64_t x55 = (x54 + x32); |
| 1134 | { uint64_t x56 = (x21 + (x31 << 0x4)); |
| 1135 | { uint64_t x57 = (x56 + (x31 << 0x1)); |
| 1136 | { uint64_t x58 = (x57 + x31); |
| 1137 | { uint64_t x59 = (x20 + (x30 << 0x4)); |
| 1138 | { uint64_t x60 = (x59 + (x30 << 0x1)); |
| 1139 | { uint64_t x61 = (x60 + x30); |
| 1140 | { uint64_t x62 = (x19 + (x29 << 0x4)); |
| 1141 | { uint64_t x63 = (x62 + (x29 << 0x1)); |
| 1142 | { uint64_t x64 = (x63 + x29); |
| 1143 | { uint64_t x65 = (x64 >> 0x1a); |
| 1144 | { uint32_t x66 = ((uint32_t)x64 & 0x3ffffff); |
| 1145 | { uint64_t x67 = (x65 + x61); |
| 1146 | { uint64_t x68 = (x67 >> 0x19); |
| 1147 | { uint32_t x69 = ((uint32_t)x67 & 0x1ffffff); |
| 1148 | { uint64_t x70 = (x68 + x58); |
| 1149 | { uint64_t x71 = (x70 >> 0x1a); |
| 1150 | { uint32_t x72 = ((uint32_t)x70 & 0x3ffffff); |
| 1151 | { uint64_t x73 = (x71 + x55); |
| 1152 | { uint64_t x74 = (x73 >> 0x19); |
| 1153 | { uint32_t x75 = ((uint32_t)x73 & 0x1ffffff); |
| 1154 | { uint64_t x76 = (x74 + x52); |
| 1155 | { uint64_t x77 = (x76 >> 0x1a); |
| 1156 | { uint32_t x78 = ((uint32_t)x76 & 0x3ffffff); |
| 1157 | { uint64_t x79 = (x77 + x49); |
| 1158 | { uint64_t x80 = (x79 >> 0x19); |
| 1159 | { uint32_t x81 = ((uint32_t)x79 & 0x1ffffff); |
| 1160 | { uint64_t x82 = (x80 + x46); |
| 1161 | { uint64_t x83 = (x82 >> 0x1a); |
| 1162 | { uint32_t x84 = ((uint32_t)x82 & 0x3ffffff); |
| 1163 | { uint64_t x85 = (x83 + x43); |
| 1164 | { uint64_t x86 = (x85 >> 0x19); |
| 1165 | { uint32_t x87 = ((uint32_t)x85 & 0x1ffffff); |
| 1166 | { uint64_t x88 = (x86 + x40); |
| 1167 | { uint64_t x89 = (x88 >> 0x1a); |
| 1168 | { uint32_t x90 = ((uint32_t)x88 & 0x3ffffff); |
| 1169 | { uint64_t x91 = (x89 + x28); |
| 1170 | { uint64_t x92 = (x91 >> 0x19); |
| 1171 | { uint32_t x93 = ((uint32_t)x91 & 0x1ffffff); |
| 1172 | { uint64_t x94 = (x66 + (0x13 * x92)); |
| 1173 | { uint32_t x95 = (uint32_t) (x94 >> 0x1a); |
| 1174 | { uint32_t x96 = ((uint32_t)x94 & 0x3ffffff); |
| 1175 | { uint32_t x97 = (x95 + x69); |
| 1176 | { uint32_t x98 = (x97 >> 0x19); |
| 1177 | { uint32_t x99 = (x97 & 0x1ffffff); |
| 1178 | out[0] = x96; |
| 1179 | out[1] = x99; |
| 1180 | out[2] = (x98 + x72); |
| 1181 | out[3] = x75; |
| 1182 | out[4] = x78; |
| 1183 | out[5] = x81; |
| 1184 | out[6] = x84; |
| 1185 | out[7] = x87; |
| 1186 | out[8] = x90; |
| 1187 | out[9] = x93; |
| 1188 | }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| 1189 | assert_fe(out); |
| 1190 | } |
| 1191 | |
| 1192 | static void fe_sq_tl(fe *h, const fe_loose *f) { |
| 1193 | fe_sqr_impl(h->v, f->v); |
| 1194 | } |
| 1195 | |
| 1196 | static void fe_sq_tt(fe *h, const fe *f) { |
| 1197 | fe_sqr_impl(h->v, f->v); |
| 1198 | } |
| 1199 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1200 | // Replace (f,g) with (g,f) if b == 1; |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1201 | // replace (f,g) with (f,g) if b == 0. |
| 1202 | // |
| 1203 | // Preconditions: b in {0,1}. |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1204 | static void fe_cswap(fe *f, fe *g, unsigned int b) { |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1205 | b = 0-b; |
| 1206 | unsigned i; |
| 1207 | for (i = 0; i < 10; i++) { |
| 1208 | uint32_t x = f->v[i] ^ g->v[i]; |
| 1209 | x &= b; |
| 1210 | f->v[i] ^= x; |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1211 | g->v[i] ^= x; |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1212 | } |
| 1213 | } |
| 1214 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1215 | // NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.. |
| 1216 | static void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) { |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1217 | assert_fe_loose(in1); |
| 1218 | { const uint32_t x20 = in1[9]; |
| 1219 | { const uint32_t x21 = in1[8]; |
| 1220 | { const uint32_t x19 = in1[7]; |
| 1221 | { const uint32_t x17 = in1[6]; |
| 1222 | { const uint32_t x15 = in1[5]; |
| 1223 | { const uint32_t x13 = in1[4]; |
| 1224 | { const uint32_t x11 = in1[3]; |
| 1225 | { const uint32_t x9 = in1[2]; |
| 1226 | { const uint32_t x7 = in1[1]; |
| 1227 | { const uint32_t x5 = in1[0]; |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1228 | { const uint32_t x38 = 0; |
| 1229 | { const uint32_t x39 = 0; |
| 1230 | { const uint32_t x37 = 0; |
| 1231 | { const uint32_t x35 = 0; |
| 1232 | { const uint32_t x33 = 0; |
| 1233 | { const uint32_t x31 = 0; |
| 1234 | { const uint32_t x29 = 0; |
| 1235 | { const uint32_t x27 = 0; |
| 1236 | { const uint32_t x25 = 0; |
| 1237 | { const uint32_t x23 = 121666; |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1238 | { uint64_t x40 = ((uint64_t)x23 * x5); |
| 1239 | { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); |
| 1240 | { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); |
| 1241 | { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); |
| 1242 | { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); |
| 1243 | { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); |
| 1244 | { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); |
| 1245 | { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); |
| 1246 | { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); |
| 1247 | { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); |
| 1248 | { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); |
| 1249 | { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); |
| 1250 | { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); |
| 1251 | { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); |
| 1252 | { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17)); |
| 1253 | { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); |
| 1254 | { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); |
| 1255 | { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); |
| 1256 | { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); |
| 1257 | { uint64_t x59 = (x48 + (x58 << 0x4)); |
| 1258 | { uint64_t x60 = (x59 + (x58 << 0x1)); |
| 1259 | { uint64_t x61 = (x60 + x58); |
| 1260 | { uint64_t x62 = (x47 + (x57 << 0x4)); |
| 1261 | { uint64_t x63 = (x62 + (x57 << 0x1)); |
| 1262 | { uint64_t x64 = (x63 + x57); |
| 1263 | { uint64_t x65 = (x46 + (x56 << 0x4)); |
| 1264 | { uint64_t x66 = (x65 + (x56 << 0x1)); |
| 1265 | { uint64_t x67 = (x66 + x56); |
| 1266 | { uint64_t x68 = (x45 + (x55 << 0x4)); |
| 1267 | { uint64_t x69 = (x68 + (x55 << 0x1)); |
| 1268 | { uint64_t x70 = (x69 + x55); |
| 1269 | { uint64_t x71 = (x44 + (x54 << 0x4)); |
| 1270 | { uint64_t x72 = (x71 + (x54 << 0x1)); |
| 1271 | { uint64_t x73 = (x72 + x54); |
| 1272 | { uint64_t x74 = (x43 + (x53 << 0x4)); |
| 1273 | { uint64_t x75 = (x74 + (x53 << 0x1)); |
| 1274 | { uint64_t x76 = (x75 + x53); |
| 1275 | { uint64_t x77 = (x42 + (x52 << 0x4)); |
| 1276 | { uint64_t x78 = (x77 + (x52 << 0x1)); |
| 1277 | { uint64_t x79 = (x78 + x52); |
| 1278 | { uint64_t x80 = (x41 + (x51 << 0x4)); |
| 1279 | { uint64_t x81 = (x80 + (x51 << 0x1)); |
| 1280 | { uint64_t x82 = (x81 + x51); |
| 1281 | { uint64_t x83 = (x40 + (x50 << 0x4)); |
| 1282 | { uint64_t x84 = (x83 + (x50 << 0x1)); |
| 1283 | { uint64_t x85 = (x84 + x50); |
| 1284 | { uint64_t x86 = (x85 >> 0x1a); |
| 1285 | { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); |
| 1286 | { uint64_t x88 = (x86 + x82); |
| 1287 | { uint64_t x89 = (x88 >> 0x19); |
| 1288 | { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); |
| 1289 | { uint64_t x91 = (x89 + x79); |
| 1290 | { uint64_t x92 = (x91 >> 0x1a); |
| 1291 | { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); |
| 1292 | { uint64_t x94 = (x92 + x76); |
| 1293 | { uint64_t x95 = (x94 >> 0x19); |
| 1294 | { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); |
| 1295 | { uint64_t x97 = (x95 + x73); |
| 1296 | { uint64_t x98 = (x97 >> 0x1a); |
| 1297 | { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); |
| 1298 | { uint64_t x100 = (x98 + x70); |
| 1299 | { uint64_t x101 = (x100 >> 0x19); |
| 1300 | { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); |
| 1301 | { uint64_t x103 = (x101 + x67); |
| 1302 | { uint64_t x104 = (x103 >> 0x1a); |
| 1303 | { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); |
| 1304 | { uint64_t x106 = (x104 + x64); |
| 1305 | { uint64_t x107 = (x106 >> 0x19); |
| 1306 | { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); |
| 1307 | { uint64_t x109 = (x107 + x61); |
| 1308 | { uint64_t x110 = (x109 >> 0x1a); |
| 1309 | { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); |
| 1310 | { uint64_t x112 = (x110 + x49); |
| 1311 | { uint64_t x113 = (x112 >> 0x19); |
| 1312 | { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); |
| 1313 | { uint64_t x115 = (x87 + (0x13 * x113)); |
| 1314 | { uint32_t x116 = (uint32_t) (x115 >> 0x1a); |
| 1315 | { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); |
| 1316 | { uint32_t x118 = (x116 + x90); |
| 1317 | { uint32_t x119 = (x118 >> 0x19); |
| 1318 | { uint32_t x120 = (x118 & 0x1ffffff); |
| 1319 | out[0] = x117; |
| 1320 | out[1] = x120; |
| 1321 | out[2] = (x119 + x93); |
| 1322 | out[3] = x96; |
| 1323 | out[4] = x99; |
| 1324 | out[5] = x102; |
| 1325 | out[6] = x105; |
| 1326 | out[7] = x108; |
| 1327 | out[8] = x111; |
| 1328 | out[9] = x114; |
| 1329 | }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| 1330 | assert_fe(out); |
| 1331 | } |
| 1332 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1333 | static void fe_mul121666(fe *h, const fe_loose *f) { |
| 1334 | assert_fe_loose(f->v); |
| 1335 | fe_mul_121666_impl(h->v, f->v); |
| 1336 | assert_fe(h->v); |
| 1337 | } |
| 1338 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1339 | // Adapted from Fiat-synthesized |fe_sub_impl| with |out| = 0. |
| 1340 | static void fe_neg_impl(uint32_t out[10], const uint32_t in2[10]) { |
| 1341 | { const uint32_t x20 = 0; |
| 1342 | { const uint32_t x21 = 0; |
| 1343 | { const uint32_t x19 = 0; |
| 1344 | { const uint32_t x17 = 0; |
| 1345 | { const uint32_t x15 = 0; |
| 1346 | { const uint32_t x13 = 0; |
| 1347 | { const uint32_t x11 = 0; |
| 1348 | { const uint32_t x9 = 0; |
| 1349 | { const uint32_t x7 = 0; |
| 1350 | { const uint32_t x5 = 0; |
| 1351 | { const uint32_t x38 = in2[9]; |
| 1352 | { const uint32_t x39 = in2[8]; |
| 1353 | { const uint32_t x37 = in2[7]; |
| 1354 | { const uint32_t x35 = in2[6]; |
| 1355 | { const uint32_t x33 = in2[5]; |
| 1356 | { const uint32_t x31 = in2[4]; |
| 1357 | { const uint32_t x29 = in2[3]; |
| 1358 | { const uint32_t x27 = in2[2]; |
| 1359 | { const uint32_t x25 = in2[1]; |
| 1360 | { const uint32_t x23 = in2[0]; |
| 1361 | out[0] = ((0x7ffffda + x5) - x23); |
| 1362 | out[1] = ((0x3fffffe + x7) - x25); |
| 1363 | out[2] = ((0x7fffffe + x9) - x27); |
| 1364 | out[3] = ((0x3fffffe + x11) - x29); |
| 1365 | out[4] = ((0x7fffffe + x13) - x31); |
| 1366 | out[5] = ((0x3fffffe + x15) - x33); |
| 1367 | out[6] = ((0x7fffffe + x17) - x35); |
| 1368 | out[7] = ((0x3fffffe + x19) - x37); |
| 1369 | out[8] = ((0x7fffffe + x21) - x39); |
| 1370 | out[9] = ((0x3fffffe + x20) - x38); |
| 1371 | }}}}}}}}}}}}}}}}}}}} |
| 1372 | } |
| 1373 | |
| 1374 | // h = -f |
| 1375 | static void fe_neg(fe_loose *h, const fe *f) { |
| 1376 | assert_fe(f->v); |
| 1377 | fe_neg_impl(h->v, f->v); |
| 1378 | assert_fe_loose(h->v); |
| 1379 | } |
| 1380 | |
| 1381 | // Replace (f,g) with (g,g) if b == 1; |
| 1382 | // replace (f,g) with (f,g) if b == 0. |
| 1383 | // |
| 1384 | // Preconditions: b in {0,1}. |
| 1385 | static void fe_cmov(fe_loose *f, const fe_loose *g, unsigned b) { |
| 1386 | b = 0-b; |
| 1387 | unsigned i; |
| 1388 | for (i = 0; i < 10; i++) { |
| 1389 | uint32_t x = f->v[i] ^ g->v[i]; |
| 1390 | x &= b; |
| 1391 | f->v[i] ^= x; |
| 1392 | } |
| 1393 | } |
| 1394 | |
| 1395 | #endif // BORINGSSL_CURVE25519_64BIT |
| 1396 | |
| 1397 | // h = f |
| 1398 | static void fe_copy(fe *h, const fe *f) { |
| 1399 | OPENSSL_memmove(h, f, sizeof(fe)); |
| 1400 | } |
| 1401 | |
| 1402 | static void fe_copy_lt(fe_loose *h, const fe *f) { |
| 1403 | OPENSSL_COMPILE_ASSERT(sizeof(fe_loose) == sizeof(fe), |
| 1404 | fe_and_fe_loose_mismatch); |
| 1405 | OPENSSL_memmove(h, f, sizeof(fe)); |
| 1406 | } |
| 1407 | #if !defined(OPENSSL_SMALL) |
| 1408 | static void fe_copy_ll(fe_loose *h, const fe_loose *f) { |
| 1409 | OPENSSL_memmove(h, f, sizeof(fe_loose)); |
| 1410 | } |
| 1411 | #endif // !defined(OPENSSL_SMALL) |
| 1412 | |
| 1413 | static void fe_loose_invert(fe *out, const fe_loose *z) { |
| 1414 | fe t0; |
| 1415 | fe t1; |
| 1416 | fe t2; |
| 1417 | fe t3; |
| 1418 | int i; |
| 1419 | |
| 1420 | fe_sq_tl(&t0, z); |
| 1421 | fe_sq_tt(&t1, &t0); |
| 1422 | for (i = 1; i < 2; ++i) { |
| 1423 | fe_sq_tt(&t1, &t1); |
| 1424 | } |
| 1425 | fe_mul_tlt(&t1, z, &t1); |
| 1426 | fe_mul_ttt(&t0, &t0, &t1); |
| 1427 | fe_sq_tt(&t2, &t0); |
| 1428 | fe_mul_ttt(&t1, &t1, &t2); |
| 1429 | fe_sq_tt(&t2, &t1); |
| 1430 | for (i = 1; i < 5; ++i) { |
| 1431 | fe_sq_tt(&t2, &t2); |
| 1432 | } |
| 1433 | fe_mul_ttt(&t1, &t2, &t1); |
| 1434 | fe_sq_tt(&t2, &t1); |
| 1435 | for (i = 1; i < 10; ++i) { |
| 1436 | fe_sq_tt(&t2, &t2); |
| 1437 | } |
| 1438 | fe_mul_ttt(&t2, &t2, &t1); |
| 1439 | fe_sq_tt(&t3, &t2); |
| 1440 | for (i = 1; i < 20; ++i) { |
| 1441 | fe_sq_tt(&t3, &t3); |
| 1442 | } |
| 1443 | fe_mul_ttt(&t2, &t3, &t2); |
| 1444 | fe_sq_tt(&t2, &t2); |
| 1445 | for (i = 1; i < 10; ++i) { |
| 1446 | fe_sq_tt(&t2, &t2); |
| 1447 | } |
| 1448 | fe_mul_ttt(&t1, &t2, &t1); |
| 1449 | fe_sq_tt(&t2, &t1); |
| 1450 | for (i = 1; i < 50; ++i) { |
| 1451 | fe_sq_tt(&t2, &t2); |
| 1452 | } |
| 1453 | fe_mul_ttt(&t2, &t2, &t1); |
| 1454 | fe_sq_tt(&t3, &t2); |
| 1455 | for (i = 1; i < 100; ++i) { |
| 1456 | fe_sq_tt(&t3, &t3); |
| 1457 | } |
| 1458 | fe_mul_ttt(&t2, &t3, &t2); |
| 1459 | fe_sq_tt(&t2, &t2); |
| 1460 | for (i = 1; i < 50; ++i) { |
| 1461 | fe_sq_tt(&t2, &t2); |
| 1462 | } |
| 1463 | fe_mul_ttt(&t1, &t2, &t1); |
| 1464 | fe_sq_tt(&t1, &t1); |
| 1465 | for (i = 1; i < 5; ++i) { |
| 1466 | fe_sq_tt(&t1, &t1); |
| 1467 | } |
| 1468 | fe_mul_ttt(out, &t1, &t0); |
| 1469 | } |
| 1470 | |
| 1471 | static void fe_invert(fe *out, const fe *z) { |
| 1472 | fe_loose l; |
| 1473 | fe_copy_lt(&l, z); |
| 1474 | fe_loose_invert(out, &l); |
| 1475 | } |
| 1476 | |
| 1477 | // return 0 if f == 0 |
| 1478 | // return 1 if f != 0 |
| 1479 | static int fe_isnonzero(const fe_loose *f) { |
| 1480 | fe tight; |
| 1481 | fe_carry(&tight, f); |
| 1482 | uint8_t s[32]; |
| 1483 | fe_tobytes(s, &tight); |
| 1484 | |
| 1485 | static const uint8_t zero[32] = {0}; |
| 1486 | return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; |
| 1487 | } |
| 1488 | |
| 1489 | // return 1 if f is in {1,3,5,...,q-2} |
| 1490 | // return 0 if f is in {0,2,4,...,q-1} |
| 1491 | static int fe_isnegative(const fe *f) { |
| 1492 | uint8_t s[32]; |
| 1493 | fe_tobytes(s, f); |
| 1494 | return s[0] & 1; |
| 1495 | } |
| 1496 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1497 | static void fe_sq2_tt(fe *h, const fe *f) { |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1498 | // h = f^2 |
| 1499 | fe_sq_tt(h, f); |
| 1500 | |
| 1501 | // h = h + h |
| 1502 | fe_loose tmp; |
| 1503 | fe_add(&tmp, h, h); |
| 1504 | fe_carry(h, &tmp); |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1505 | } |
| 1506 | |
| 1507 | static void fe_pow22523(fe *out, const fe *z) { |
| 1508 | fe t0; |
| 1509 | fe t1; |
| 1510 | fe t2; |
| 1511 | int i; |
| 1512 | |
| 1513 | fe_sq_tt(&t0, z); |
| 1514 | fe_sq_tt(&t1, &t0); |
| 1515 | for (i = 1; i < 2; ++i) { |
| 1516 | fe_sq_tt(&t1, &t1); |
| 1517 | } |
| 1518 | fe_mul_ttt(&t1, z, &t1); |
| 1519 | fe_mul_ttt(&t0, &t0, &t1); |
| 1520 | fe_sq_tt(&t0, &t0); |
| 1521 | fe_mul_ttt(&t0, &t1, &t0); |
| 1522 | fe_sq_tt(&t1, &t0); |
| 1523 | for (i = 1; i < 5; ++i) { |
| 1524 | fe_sq_tt(&t1, &t1); |
| 1525 | } |
| 1526 | fe_mul_ttt(&t0, &t1, &t0); |
| 1527 | fe_sq_tt(&t1, &t0); |
| 1528 | for (i = 1; i < 10; ++i) { |
| 1529 | fe_sq_tt(&t1, &t1); |
| 1530 | } |
| 1531 | fe_mul_ttt(&t1, &t1, &t0); |
| 1532 | fe_sq_tt(&t2, &t1); |
| 1533 | for (i = 1; i < 20; ++i) { |
| 1534 | fe_sq_tt(&t2, &t2); |
| 1535 | } |
| 1536 | fe_mul_ttt(&t1, &t2, &t1); |
| 1537 | fe_sq_tt(&t1, &t1); |
| 1538 | for (i = 1; i < 10; ++i) { |
| 1539 | fe_sq_tt(&t1, &t1); |
| 1540 | } |
| 1541 | fe_mul_ttt(&t0, &t1, &t0); |
| 1542 | fe_sq_tt(&t1, &t0); |
| 1543 | for (i = 1; i < 50; ++i) { |
| 1544 | fe_sq_tt(&t1, &t1); |
| 1545 | } |
| 1546 | fe_mul_ttt(&t1, &t1, &t0); |
| 1547 | fe_sq_tt(&t2, &t1); |
| 1548 | for (i = 1; i < 100; ++i) { |
| 1549 | fe_sq_tt(&t2, &t2); |
| 1550 | } |
| 1551 | fe_mul_ttt(&t1, &t2, &t1); |
| 1552 | fe_sq_tt(&t1, &t1); |
| 1553 | for (i = 1; i < 50; ++i) { |
| 1554 | fe_sq_tt(&t1, &t1); |
| 1555 | } |
| 1556 | fe_mul_ttt(&t0, &t1, &t0); |
| 1557 | fe_sq_tt(&t0, &t0); |
| 1558 | for (i = 1; i < 2; ++i) { |
| 1559 | fe_sq_tt(&t0, &t0); |
| 1560 | } |
| 1561 | fe_mul_ttt(out, &t0, z); |
| 1562 | } |
| 1563 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1564 | |
| 1565 | // Group operations. |
| 1566 | |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 1567 | void x25519_ge_tobytes(uint8_t s[32], const ge_p2 *h) { |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1568 | fe recip; |
| 1569 | fe x; |
| 1570 | fe y; |
| 1571 | |
| 1572 | fe_invert(&recip, &h->Z); |
| 1573 | fe_mul_ttt(&x, &h->X, &recip); |
| 1574 | fe_mul_ttt(&y, &h->Y, &recip); |
| 1575 | fe_tobytes(s, &y); |
| 1576 | s[31] ^= fe_isnegative(&x) << 7; |
| 1577 | } |
| 1578 | |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 1579 | static void ge_p3_tobytes(uint8_t s[32], const ge_p3 *h) { |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1580 | fe recip; |
| 1581 | fe x; |
| 1582 | fe y; |
| 1583 | |
| 1584 | fe_invert(&recip, &h->Z); |
| 1585 | fe_mul_ttt(&x, &h->X, &recip); |
| 1586 | fe_mul_ttt(&y, &h->Y, &recip); |
| 1587 | fe_tobytes(s, &y); |
| 1588 | s[31] ^= fe_isnegative(&x) << 7; |
| 1589 | } |
| 1590 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1591 | int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { |
| 1592 | fe u; |
| 1593 | fe_loose v; |
| 1594 | fe v3; |
| 1595 | fe vxx; |
| 1596 | fe_loose check; |
| 1597 | |
| 1598 | fe_frombytes(&h->Y, s); |
| 1599 | fe_1(&h->Z); |
| 1600 | fe_sq_tt(&v3, &h->Y); |
| 1601 | fe_mul_ttt(&vxx, &v3, &d); |
| 1602 | fe_sub(&v, &v3, &h->Z); // u = y^2-1 |
| 1603 | fe_carry(&u, &v); |
| 1604 | fe_add(&v, &vxx, &h->Z); // v = dy^2+1 |
| 1605 | |
| 1606 | fe_sq_tl(&v3, &v); |
| 1607 | fe_mul_ttl(&v3, &v3, &v); // v3 = v^3 |
| 1608 | fe_sq_tt(&h->X, &v3); |
| 1609 | fe_mul_ttl(&h->X, &h->X, &v); |
| 1610 | fe_mul_ttt(&h->X, &h->X, &u); // x = uv^7 |
| 1611 | |
| 1612 | fe_pow22523(&h->X, &h->X); // x = (uv^7)^((q-5)/8) |
| 1613 | fe_mul_ttt(&h->X, &h->X, &v3); |
| 1614 | fe_mul_ttt(&h->X, &h->X, &u); // x = uv^3(uv^7)^((q-5)/8) |
| 1615 | |
| 1616 | fe_sq_tt(&vxx, &h->X); |
| 1617 | fe_mul_ttl(&vxx, &vxx, &v); |
| 1618 | fe_sub(&check, &vxx, &u); |
| 1619 | if (fe_isnonzero(&check)) { |
| 1620 | fe_add(&check, &vxx, &u); |
| 1621 | if (fe_isnonzero(&check)) { |
| 1622 | return -1; |
| 1623 | } |
| 1624 | fe_mul_ttt(&h->X, &h->X, &sqrtm1); |
| 1625 | } |
| 1626 | |
| 1627 | if (fe_isnegative(&h->X) != (s[31] >> 7)) { |
| 1628 | fe_loose t; |
| 1629 | fe_neg(&t, &h->X); |
| 1630 | fe_carry(&h->X, &t); |
| 1631 | } |
| 1632 | |
| 1633 | fe_mul_ttt(&h->T, &h->X, &h->Y); |
| 1634 | return 0; |
| 1635 | } |
| 1636 | |
| 1637 | static void ge_p2_0(ge_p2 *h) { |
| 1638 | fe_0(&h->X); |
| 1639 | fe_1(&h->Y); |
| 1640 | fe_1(&h->Z); |
| 1641 | } |
| 1642 | |
| 1643 | static void ge_p3_0(ge_p3 *h) { |
| 1644 | fe_0(&h->X); |
| 1645 | fe_1(&h->Y); |
| 1646 | fe_1(&h->Z); |
| 1647 | fe_0(&h->T); |
| 1648 | } |
| 1649 | |
| 1650 | static void ge_cached_0(ge_cached *h) { |
| 1651 | fe_loose_1(&h->YplusX); |
| 1652 | fe_loose_1(&h->YminusX); |
| 1653 | fe_loose_1(&h->Z); |
| 1654 | fe_loose_0(&h->T2d); |
| 1655 | } |
| 1656 | |
| 1657 | static void ge_precomp_0(ge_precomp *h) { |
| 1658 | fe_loose_1(&h->yplusx); |
| 1659 | fe_loose_1(&h->yminusx); |
| 1660 | fe_loose_0(&h->xy2d); |
| 1661 | } |
| 1662 | |
| 1663 | // r = p |
| 1664 | static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { |
| 1665 | fe_copy(&r->X, &p->X); |
| 1666 | fe_copy(&r->Y, &p->Y); |
| 1667 | fe_copy(&r->Z, &p->Z); |
| 1668 | } |
| 1669 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1670 | // r = p |
| 1671 | void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { |
| 1672 | fe_add(&r->YplusX, &p->Y, &p->X); |
| 1673 | fe_sub(&r->YminusX, &p->Y, &p->X); |
| 1674 | fe_copy_lt(&r->Z, &p->Z); |
| 1675 | fe_mul_ltt(&r->T2d, &p->T, &d2); |
| 1676 | } |
| 1677 | |
| 1678 | // r = p |
| 1679 | void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { |
| 1680 | fe_mul_tll(&r->X, &p->X, &p->T); |
| 1681 | fe_mul_tll(&r->Y, &p->Y, &p->Z); |
| 1682 | fe_mul_tll(&r->Z, &p->Z, &p->T); |
| 1683 | } |
| 1684 | |
| 1685 | // r = p |
| 1686 | void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { |
| 1687 | fe_mul_tll(&r->X, &p->X, &p->T); |
| 1688 | fe_mul_tll(&r->Y, &p->Y, &p->Z); |
| 1689 | fe_mul_tll(&r->Z, &p->Z, &p->T); |
| 1690 | fe_mul_tll(&r->T, &p->X, &p->Y); |
| 1691 | } |
| 1692 | |
| 1693 | // r = p |
| 1694 | static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) { |
| 1695 | ge_p3 t; |
| 1696 | x25519_ge_p1p1_to_p3(&t, p); |
| 1697 | x25519_ge_p3_to_cached(r, &t); |
| 1698 | } |
| 1699 | |
| 1700 | // r = 2 * p |
| 1701 | static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { |
| 1702 | fe trX, trZ, trT; |
| 1703 | fe t0; |
| 1704 | |
| 1705 | fe_sq_tt(&trX, &p->X); |
| 1706 | fe_sq_tt(&trZ, &p->Y); |
| 1707 | fe_sq2_tt(&trT, &p->Z); |
| 1708 | fe_add(&r->Y, &p->X, &p->Y); |
| 1709 | fe_sq_tl(&t0, &r->Y); |
| 1710 | |
| 1711 | fe_add(&r->Y, &trZ, &trX); |
| 1712 | fe_sub(&r->Z, &trZ, &trX); |
| 1713 | fe_carry(&trZ, &r->Y); |
| 1714 | fe_sub(&r->X, &t0, &trZ); |
| 1715 | fe_carry(&trZ, &r->Z); |
| 1716 | fe_sub(&r->T, &trT, &trZ); |
| 1717 | } |
| 1718 | |
| 1719 | // r = 2 * p |
| 1720 | static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { |
| 1721 | ge_p2 q; |
| 1722 | ge_p3_to_p2(&q, p); |
| 1723 | ge_p2_dbl(r, &q); |
| 1724 | } |
| 1725 | |
| 1726 | // r = p + q |
| 1727 | static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
| 1728 | fe trY, trZ, trT; |
| 1729 | |
| 1730 | fe_add(&r->X, &p->Y, &p->X); |
| 1731 | fe_sub(&r->Y, &p->Y, &p->X); |
| 1732 | fe_mul_tll(&trZ, &r->X, &q->yplusx); |
| 1733 | fe_mul_tll(&trY, &r->Y, &q->yminusx); |
| 1734 | fe_mul_tlt(&trT, &q->xy2d, &p->T); |
| 1735 | fe_add(&r->T, &p->Z, &p->Z); |
| 1736 | fe_sub(&r->X, &trZ, &trY); |
| 1737 | fe_add(&r->Y, &trZ, &trY); |
| 1738 | fe_carry(&trZ, &r->T); |
| 1739 | fe_add(&r->Z, &trZ, &trT); |
| 1740 | fe_sub(&r->T, &trZ, &trT); |
| 1741 | } |
| 1742 | |
| 1743 | // r = p - q |
| 1744 | static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
| 1745 | fe trY, trZ, trT; |
| 1746 | |
| 1747 | fe_add(&r->X, &p->Y, &p->X); |
| 1748 | fe_sub(&r->Y, &p->Y, &p->X); |
| 1749 | fe_mul_tll(&trZ, &r->X, &q->yminusx); |
| 1750 | fe_mul_tll(&trY, &r->Y, &q->yplusx); |
| 1751 | fe_mul_tlt(&trT, &q->xy2d, &p->T); |
| 1752 | fe_add(&r->T, &p->Z, &p->Z); |
| 1753 | fe_sub(&r->X, &trZ, &trY); |
| 1754 | fe_add(&r->Y, &trZ, &trY); |
| 1755 | fe_carry(&trZ, &r->T); |
| 1756 | fe_sub(&r->Z, &trZ, &trT); |
| 1757 | fe_add(&r->T, &trZ, &trT); |
| 1758 | } |
| 1759 | |
| 1760 | // r = p + q |
| 1761 | void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
| 1762 | fe trX, trY, trZ, trT; |
| 1763 | |
| 1764 | fe_add(&r->X, &p->Y, &p->X); |
| 1765 | fe_sub(&r->Y, &p->Y, &p->X); |
| 1766 | fe_mul_tll(&trZ, &r->X, &q->YplusX); |
| 1767 | fe_mul_tll(&trY, &r->Y, &q->YminusX); |
| 1768 | fe_mul_tlt(&trT, &q->T2d, &p->T); |
| 1769 | fe_mul_ttl(&trX, &p->Z, &q->Z); |
| 1770 | fe_add(&r->T, &trX, &trX); |
| 1771 | fe_sub(&r->X, &trZ, &trY); |
| 1772 | fe_add(&r->Y, &trZ, &trY); |
| 1773 | fe_carry(&trZ, &r->T); |
| 1774 | fe_add(&r->Z, &trZ, &trT); |
| 1775 | fe_sub(&r->T, &trZ, &trT); |
| 1776 | } |
| 1777 | |
| 1778 | // r = p - q |
| 1779 | void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
| 1780 | fe trX, trY, trZ, trT; |
| 1781 | |
| 1782 | fe_add(&r->X, &p->Y, &p->X); |
| 1783 | fe_sub(&r->Y, &p->Y, &p->X); |
| 1784 | fe_mul_tll(&trZ, &r->X, &q->YminusX); |
| 1785 | fe_mul_tll(&trY, &r->Y, &q->YplusX); |
| 1786 | fe_mul_tlt(&trT, &q->T2d, &p->T); |
| 1787 | fe_mul_ttl(&trX, &p->Z, &q->Z); |
| 1788 | fe_add(&r->T, &trX, &trX); |
| 1789 | fe_sub(&r->X, &trZ, &trY); |
| 1790 | fe_add(&r->Y, &trZ, &trY); |
| 1791 | fe_carry(&trZ, &r->T); |
| 1792 | fe_sub(&r->Z, &trZ, &trT); |
| 1793 | fe_add(&r->T, &trZ, &trT); |
| 1794 | } |
| 1795 | |
| 1796 | static uint8_t equal(signed char b, signed char c) { |
| 1797 | uint8_t ub = b; |
| 1798 | uint8_t uc = c; |
| 1799 | uint8_t x = ub ^ uc; // 0: yes; 1..255: no |
| 1800 | uint32_t y = x; // 0: yes; 1..255: no |
| 1801 | y -= 1; // 4294967295: yes; 0..254: no |
| 1802 | y >>= 31; // 1: yes; 0: no |
| 1803 | return y; |
| 1804 | } |
| 1805 | |
| 1806 | static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { |
| 1807 | fe_cmov(&t->yplusx, &u->yplusx, b); |
| 1808 | fe_cmov(&t->yminusx, &u->yminusx, b); |
| 1809 | fe_cmov(&t->xy2d, &u->xy2d, b); |
| 1810 | } |
| 1811 | |
| 1812 | void x25519_ge_scalarmult_small_precomp( |
| 1813 | ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) { |
| 1814 | // precomp_table is first expanded into matching |ge_precomp| |
| 1815 | // elements. |
| 1816 | ge_precomp multiples[15]; |
| 1817 | |
| 1818 | unsigned i; |
| 1819 | for (i = 0; i < 15; i++) { |
| 1820 | const uint8_t *bytes = &precomp_table[i*(2 * 32)]; |
| 1821 | fe x, y; |
| 1822 | fe_frombytes(&x, bytes); |
| 1823 | fe_frombytes(&y, bytes + 32); |
| 1824 | |
| 1825 | ge_precomp *out = &multiples[i]; |
| 1826 | fe_add(&out->yplusx, &y, &x); |
| 1827 | fe_sub(&out->yminusx, &y, &x); |
| 1828 | fe_mul_ltt(&out->xy2d, &x, &y); |
| 1829 | fe_mul_llt(&out->xy2d, &out->xy2d, &d2); |
| 1830 | } |
| 1831 | |
| 1832 | // See the comment above |k25519SmallPrecomp| about the structure of the |
| 1833 | // precomputed elements. This loop does 64 additions and 64 doublings to |
| 1834 | // calculate the result. |
| 1835 | ge_p3_0(h); |
| 1836 | |
| 1837 | for (i = 63; i < 64; i--) { |
| 1838 | unsigned j; |
| 1839 | signed char index = 0; |
| 1840 | |
| 1841 | for (j = 0; j < 4; j++) { |
| 1842 | const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7)); |
| 1843 | index |= (bit << j); |
| 1844 | } |
| 1845 | |
| 1846 | ge_precomp e; |
| 1847 | ge_precomp_0(&e); |
| 1848 | |
| 1849 | for (j = 1; j < 16; j++) { |
| 1850 | cmov(&e, &multiples[j-1], equal(index, j)); |
| 1851 | } |
| 1852 | |
| 1853 | ge_cached cached; |
| 1854 | ge_p1p1 r; |
| 1855 | x25519_ge_p3_to_cached(&cached, h); |
| 1856 | x25519_ge_add(&r, h, &cached); |
| 1857 | x25519_ge_p1p1_to_p3(h, &r); |
| 1858 | |
| 1859 | ge_madd(&r, h, &e); |
| 1860 | x25519_ge_p1p1_to_p3(h, &r); |
| 1861 | } |
| 1862 | } |
| 1863 | |
| 1864 | #if defined(OPENSSL_SMALL) |
| 1865 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1866 | void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { |
| 1867 | x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp); |
| 1868 | } |
| 1869 | |
| 1870 | #else |
| 1871 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1872 | static uint8_t negative(signed char b) { |
| 1873 | uint32_t x = b; |
| 1874 | x >>= 31; // 1: yes; 0: no |
| 1875 | return x; |
| 1876 | } |
| 1877 | |
| 1878 | static void table_select(ge_precomp *t, int pos, signed char b) { |
| 1879 | ge_precomp minust; |
| 1880 | uint8_t bnegative = negative(b); |
| 1881 | uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); |
| 1882 | |
| 1883 | ge_precomp_0(t); |
| 1884 | cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); |
| 1885 | cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); |
| 1886 | cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); |
| 1887 | cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); |
| 1888 | cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); |
| 1889 | cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); |
| 1890 | cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); |
| 1891 | cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); |
| 1892 | fe_copy_ll(&minust.yplusx, &t->yminusx); |
| 1893 | fe_copy_ll(&minust.yminusx, &t->yplusx); |
| 1894 | |
| 1895 | // NOTE: the input table is canonical, but types don't encode it |
| 1896 | fe tmp; |
| 1897 | fe_carry(&tmp, &t->xy2d); |
| 1898 | fe_neg(&minust.xy2d, &tmp); |
| 1899 | |
| 1900 | cmov(t, &minust, bnegative); |
| 1901 | } |
| 1902 | |
| 1903 | // h = a * B |
| 1904 | // where a = a[0]+256*a[1]+...+256^31 a[31] |
| 1905 | // B is the Ed25519 base point (x,4/5) with x positive. |
| 1906 | // |
| 1907 | // Preconditions: |
| 1908 | // a[31] <= 127 |
| 1909 | void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { |
| 1910 | signed char e[64]; |
| 1911 | signed char carry; |
| 1912 | ge_p1p1 r; |
| 1913 | ge_p2 s; |
| 1914 | ge_precomp t; |
| 1915 | int i; |
| 1916 | |
| 1917 | for (i = 0; i < 32; ++i) { |
| 1918 | e[2 * i + 0] = (a[i] >> 0) & 15; |
| 1919 | e[2 * i + 1] = (a[i] >> 4) & 15; |
| 1920 | } |
| 1921 | // each e[i] is between 0 and 15 |
| 1922 | // e[63] is between 0 and 7 |
| 1923 | |
| 1924 | carry = 0; |
| 1925 | for (i = 0; i < 63; ++i) { |
| 1926 | e[i] += carry; |
| 1927 | carry = e[i] + 8; |
| 1928 | carry >>= 4; |
| 1929 | e[i] -= carry << 4; |
| 1930 | } |
| 1931 | e[63] += carry; |
| 1932 | // each e[i] is between -8 and 8 |
| 1933 | |
| 1934 | ge_p3_0(h); |
| 1935 | for (i = 1; i < 64; i += 2) { |
| 1936 | table_select(&t, i / 2, e[i]); |
| 1937 | ge_madd(&r, h, &t); |
| 1938 | x25519_ge_p1p1_to_p3(h, &r); |
| 1939 | } |
| 1940 | |
| 1941 | ge_p3_dbl(&r, h); |
| 1942 | x25519_ge_p1p1_to_p2(&s, &r); |
| 1943 | ge_p2_dbl(&r, &s); |
| 1944 | x25519_ge_p1p1_to_p2(&s, &r); |
| 1945 | ge_p2_dbl(&r, &s); |
| 1946 | x25519_ge_p1p1_to_p2(&s, &r); |
| 1947 | ge_p2_dbl(&r, &s); |
| 1948 | x25519_ge_p1p1_to_p3(h, &r); |
| 1949 | |
| 1950 | for (i = 0; i < 64; i += 2) { |
| 1951 | table_select(&t, i / 2, e[i]); |
| 1952 | ge_madd(&r, h, &t); |
| 1953 | x25519_ge_p1p1_to_p3(h, &r); |
| 1954 | } |
| 1955 | } |
| 1956 | |
| 1957 | #endif |
| 1958 | |
| 1959 | static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) { |
| 1960 | fe_cmov(&t->YplusX, &u->YplusX, b); |
| 1961 | fe_cmov(&t->YminusX, &u->YminusX, b); |
| 1962 | fe_cmov(&t->Z, &u->Z, b); |
| 1963 | fe_cmov(&t->T2d, &u->T2d, b); |
| 1964 | } |
| 1965 | |
| 1966 | // r = scalar * A. |
| 1967 | // where a = a[0]+256*a[1]+...+256^31 a[31]. |
| 1968 | void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) { |
| 1969 | ge_p2 Ai_p2[8]; |
| 1970 | ge_cached Ai[16]; |
| 1971 | ge_p1p1 t; |
| 1972 | |
| 1973 | ge_cached_0(&Ai[0]); |
| 1974 | x25519_ge_p3_to_cached(&Ai[1], A); |
| 1975 | ge_p3_to_p2(&Ai_p2[1], A); |
| 1976 | |
| 1977 | unsigned i; |
| 1978 | for (i = 2; i < 16; i += 2) { |
| 1979 | ge_p2_dbl(&t, &Ai_p2[i / 2]); |
| 1980 | ge_p1p1_to_cached(&Ai[i], &t); |
| 1981 | if (i < 8) { |
| 1982 | x25519_ge_p1p1_to_p2(&Ai_p2[i], &t); |
| 1983 | } |
| 1984 | x25519_ge_add(&t, A, &Ai[i]); |
| 1985 | ge_p1p1_to_cached(&Ai[i + 1], &t); |
| 1986 | if (i < 7) { |
| 1987 | x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t); |
| 1988 | } |
| 1989 | } |
| 1990 | |
| 1991 | ge_p2_0(r); |
| 1992 | ge_p3 u; |
| 1993 | |
| 1994 | for (i = 0; i < 256; i += 4) { |
| 1995 | ge_p2_dbl(&t, r); |
| 1996 | x25519_ge_p1p1_to_p2(r, &t); |
| 1997 | ge_p2_dbl(&t, r); |
| 1998 | x25519_ge_p1p1_to_p2(r, &t); |
| 1999 | ge_p2_dbl(&t, r); |
| 2000 | x25519_ge_p1p1_to_p2(r, &t); |
| 2001 | ge_p2_dbl(&t, r); |
| 2002 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2003 | |
| 2004 | uint8_t index = scalar[31 - i/8]; |
| 2005 | index >>= 4 - (i & 4); |
| 2006 | index &= 0xf; |
| 2007 | |
| 2008 | unsigned j; |
| 2009 | ge_cached selected; |
| 2010 | ge_cached_0(&selected); |
| 2011 | for (j = 0; j < 16; j++) { |
| 2012 | cmov_cached(&selected, &Ai[j], equal(j, index)); |
| 2013 | } |
| 2014 | |
| 2015 | x25519_ge_add(&t, &u, &selected); |
| 2016 | x25519_ge_p1p1_to_p2(r, &t); |
| 2017 | } |
| 2018 | } |
| 2019 | |
| 2020 | static void slide(signed char *r, const uint8_t *a) { |
| 2021 | int i; |
| 2022 | int b; |
| 2023 | int k; |
| 2024 | |
| 2025 | for (i = 0; i < 256; ++i) { |
| 2026 | r[i] = 1 & (a[i >> 3] >> (i & 7)); |
| 2027 | } |
| 2028 | |
| 2029 | for (i = 0; i < 256; ++i) { |
| 2030 | if (r[i]) { |
| 2031 | for (b = 1; b <= 6 && i + b < 256; ++b) { |
| 2032 | if (r[i + b]) { |
| 2033 | if (r[i] + (r[i + b] << b) <= 15) { |
| 2034 | r[i] += r[i + b] << b; |
| 2035 | r[i + b] = 0; |
| 2036 | } else if (r[i] - (r[i + b] << b) >= -15) { |
| 2037 | r[i] -= r[i + b] << b; |
| 2038 | for (k = i + b; k < 256; ++k) { |
| 2039 | if (!r[k]) { |
| 2040 | r[k] = 1; |
| 2041 | break; |
| 2042 | } |
| 2043 | r[k] = 0; |
| 2044 | } |
| 2045 | } else { |
| 2046 | break; |
| 2047 | } |
| 2048 | } |
| 2049 | } |
| 2050 | } |
| 2051 | } |
| 2052 | } |
| 2053 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 2054 | // r = a * A + b * B |
| 2055 | // where a = a[0]+256*a[1]+...+256^31 a[31]. |
| 2056 | // and b = b[0]+256*b[1]+...+256^31 b[31]. |
| 2057 | // B is the Ed25519 base point (x,4/5) with x positive. |
| 2058 | static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, |
| 2059 | const ge_p3 *A, const uint8_t *b) { |
| 2060 | signed char aslide[256]; |
| 2061 | signed char bslide[256]; |
| 2062 | ge_cached Ai[8]; // A,3A,5A,7A,9A,11A,13A,15A |
| 2063 | ge_p1p1 t; |
| 2064 | ge_p3 u; |
| 2065 | ge_p3 A2; |
| 2066 | int i; |
| 2067 | |
| 2068 | slide(aslide, a); |
| 2069 | slide(bslide, b); |
| 2070 | |
| 2071 | x25519_ge_p3_to_cached(&Ai[0], A); |
| 2072 | ge_p3_dbl(&t, A); |
| 2073 | x25519_ge_p1p1_to_p3(&A2, &t); |
| 2074 | x25519_ge_add(&t, &A2, &Ai[0]); |
| 2075 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2076 | x25519_ge_p3_to_cached(&Ai[1], &u); |
| 2077 | x25519_ge_add(&t, &A2, &Ai[1]); |
| 2078 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2079 | x25519_ge_p3_to_cached(&Ai[2], &u); |
| 2080 | x25519_ge_add(&t, &A2, &Ai[2]); |
| 2081 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2082 | x25519_ge_p3_to_cached(&Ai[3], &u); |
| 2083 | x25519_ge_add(&t, &A2, &Ai[3]); |
| 2084 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2085 | x25519_ge_p3_to_cached(&Ai[4], &u); |
| 2086 | x25519_ge_add(&t, &A2, &Ai[4]); |
| 2087 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2088 | x25519_ge_p3_to_cached(&Ai[5], &u); |
| 2089 | x25519_ge_add(&t, &A2, &Ai[5]); |
| 2090 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2091 | x25519_ge_p3_to_cached(&Ai[6], &u); |
| 2092 | x25519_ge_add(&t, &A2, &Ai[6]); |
| 2093 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2094 | x25519_ge_p3_to_cached(&Ai[7], &u); |
| 2095 | |
| 2096 | ge_p2_0(r); |
| 2097 | |
| 2098 | for (i = 255; i >= 0; --i) { |
| 2099 | if (aslide[i] || bslide[i]) { |
| 2100 | break; |
| 2101 | } |
| 2102 | } |
| 2103 | |
| 2104 | for (; i >= 0; --i) { |
| 2105 | ge_p2_dbl(&t, r); |
| 2106 | |
| 2107 | if (aslide[i] > 0) { |
| 2108 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2109 | x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]); |
| 2110 | } else if (aslide[i] < 0) { |
| 2111 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2112 | x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); |
| 2113 | } |
| 2114 | |
| 2115 | if (bslide[i] > 0) { |
| 2116 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2117 | ge_madd(&t, &u, &Bi[bslide[i] / 2]); |
| 2118 | } else if (bslide[i] < 0) { |
| 2119 | x25519_ge_p1p1_to_p3(&u, &t); |
| 2120 | ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); |
| 2121 | } |
| 2122 | |
| 2123 | x25519_ge_p1p1_to_p2(r, &t); |
| 2124 | } |
| 2125 | } |
| 2126 | |
| 2127 | // The set of scalars is \Z/l |
| 2128 | // where l = 2^252 + 27742317777372353535851937790883648493. |
| 2129 | |
| 2130 | // Input: |
| 2131 | // s[0]+256*s[1]+...+256^63*s[63] = s |
| 2132 | // |
| 2133 | // Output: |
| 2134 | // s[0]+256*s[1]+...+256^31*s[31] = s mod l |
| 2135 | // where l = 2^252 + 27742317777372353535851937790883648493. |
| 2136 | // Overwrites s in place. |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 2137 | void x25519_sc_reduce(uint8_t s[64]) { |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 2138 | int64_t s0 = 2097151 & load_3(s); |
| 2139 | int64_t s1 = 2097151 & (load_4(s + 2) >> 5); |
| 2140 | int64_t s2 = 2097151 & (load_3(s + 5) >> 2); |
| 2141 | int64_t s3 = 2097151 & (load_4(s + 7) >> 7); |
| 2142 | int64_t s4 = 2097151 & (load_4(s + 10) >> 4); |
| 2143 | int64_t s5 = 2097151 & (load_3(s + 13) >> 1); |
| 2144 | int64_t s6 = 2097151 & (load_4(s + 15) >> 6); |
| 2145 | int64_t s7 = 2097151 & (load_3(s + 18) >> 3); |
| 2146 | int64_t s8 = 2097151 & load_3(s + 21); |
| 2147 | int64_t s9 = 2097151 & (load_4(s + 23) >> 5); |
| 2148 | int64_t s10 = 2097151 & (load_3(s + 26) >> 2); |
| 2149 | int64_t s11 = 2097151 & (load_4(s + 28) >> 7); |
| 2150 | int64_t s12 = 2097151 & (load_4(s + 31) >> 4); |
| 2151 | int64_t s13 = 2097151 & (load_3(s + 34) >> 1); |
| 2152 | int64_t s14 = 2097151 & (load_4(s + 36) >> 6); |
| 2153 | int64_t s15 = 2097151 & (load_3(s + 39) >> 3); |
| 2154 | int64_t s16 = 2097151 & load_3(s + 42); |
| 2155 | int64_t s17 = 2097151 & (load_4(s + 44) >> 5); |
| 2156 | int64_t s18 = 2097151 & (load_3(s + 47) >> 2); |
| 2157 | int64_t s19 = 2097151 & (load_4(s + 49) >> 7); |
| 2158 | int64_t s20 = 2097151 & (load_4(s + 52) >> 4); |
| 2159 | int64_t s21 = 2097151 & (load_3(s + 55) >> 1); |
| 2160 | int64_t s22 = 2097151 & (load_4(s + 57) >> 6); |
| 2161 | int64_t s23 = (load_4(s + 60) >> 3); |
| 2162 | int64_t carry0; |
| 2163 | int64_t carry1; |
| 2164 | int64_t carry2; |
| 2165 | int64_t carry3; |
| 2166 | int64_t carry4; |
| 2167 | int64_t carry5; |
| 2168 | int64_t carry6; |
| 2169 | int64_t carry7; |
| 2170 | int64_t carry8; |
| 2171 | int64_t carry9; |
| 2172 | int64_t carry10; |
| 2173 | int64_t carry11; |
| 2174 | int64_t carry12; |
| 2175 | int64_t carry13; |
| 2176 | int64_t carry14; |
| 2177 | int64_t carry15; |
| 2178 | int64_t carry16; |
| 2179 | |
| 2180 | s11 += s23 * 666643; |
| 2181 | s12 += s23 * 470296; |
| 2182 | s13 += s23 * 654183; |
| 2183 | s14 -= s23 * 997805; |
| 2184 | s15 += s23 * 136657; |
| 2185 | s16 -= s23 * 683901; |
| 2186 | s23 = 0; |
| 2187 | |
| 2188 | s10 += s22 * 666643; |
| 2189 | s11 += s22 * 470296; |
| 2190 | s12 += s22 * 654183; |
| 2191 | s13 -= s22 * 997805; |
| 2192 | s14 += s22 * 136657; |
| 2193 | s15 -= s22 * 683901; |
| 2194 | s22 = 0; |
| 2195 | |
| 2196 | s9 += s21 * 666643; |
| 2197 | s10 += s21 * 470296; |
| 2198 | s11 += s21 * 654183; |
| 2199 | s12 -= s21 * 997805; |
| 2200 | s13 += s21 * 136657; |
| 2201 | s14 -= s21 * 683901; |
| 2202 | s21 = 0; |
| 2203 | |
| 2204 | s8 += s20 * 666643; |
| 2205 | s9 += s20 * 470296; |
| 2206 | s10 += s20 * 654183; |
| 2207 | s11 -= s20 * 997805; |
| 2208 | s12 += s20 * 136657; |
| 2209 | s13 -= s20 * 683901; |
| 2210 | s20 = 0; |
| 2211 | |
| 2212 | s7 += s19 * 666643; |
| 2213 | s8 += s19 * 470296; |
| 2214 | s9 += s19 * 654183; |
| 2215 | s10 -= s19 * 997805; |
| 2216 | s11 += s19 * 136657; |
| 2217 | s12 -= s19 * 683901; |
| 2218 | s19 = 0; |
| 2219 | |
| 2220 | s6 += s18 * 666643; |
| 2221 | s7 += s18 * 470296; |
| 2222 | s8 += s18 * 654183; |
| 2223 | s9 -= s18 * 997805; |
| 2224 | s10 += s18 * 136657; |
| 2225 | s11 -= s18 * 683901; |
| 2226 | s18 = 0; |
| 2227 | |
| 2228 | carry6 = (s6 + (1 << 20)) >> 21; |
| 2229 | s7 += carry6; |
| 2230 | s6 -= carry6 << 21; |
| 2231 | carry8 = (s8 + (1 << 20)) >> 21; |
| 2232 | s9 += carry8; |
| 2233 | s8 -= carry8 << 21; |
| 2234 | carry10 = (s10 + (1 << 20)) >> 21; |
| 2235 | s11 += carry10; |
| 2236 | s10 -= carry10 << 21; |
| 2237 | carry12 = (s12 + (1 << 20)) >> 21; |
| 2238 | s13 += carry12; |
| 2239 | s12 -= carry12 << 21; |
| 2240 | carry14 = (s14 + (1 << 20)) >> 21; |
| 2241 | s15 += carry14; |
| 2242 | s14 -= carry14 << 21; |
| 2243 | carry16 = (s16 + (1 << 20)) >> 21; |
| 2244 | s17 += carry16; |
| 2245 | s16 -= carry16 << 21; |
| 2246 | |
| 2247 | carry7 = (s7 + (1 << 20)) >> 21; |
| 2248 | s8 += carry7; |
| 2249 | s7 -= carry7 << 21; |
| 2250 | carry9 = (s9 + (1 << 20)) >> 21; |
| 2251 | s10 += carry9; |
| 2252 | s9 -= carry9 << 21; |
| 2253 | carry11 = (s11 + (1 << 20)) >> 21; |
| 2254 | s12 += carry11; |
| 2255 | s11 -= carry11 << 21; |
| 2256 | carry13 = (s13 + (1 << 20)) >> 21; |
| 2257 | s14 += carry13; |
| 2258 | s13 -= carry13 << 21; |
| 2259 | carry15 = (s15 + (1 << 20)) >> 21; |
| 2260 | s16 += carry15; |
| 2261 | s15 -= carry15 << 21; |
| 2262 | |
| 2263 | s5 += s17 * 666643; |
| 2264 | s6 += s17 * 470296; |
| 2265 | s7 += s17 * 654183; |
| 2266 | s8 -= s17 * 997805; |
| 2267 | s9 += s17 * 136657; |
| 2268 | s10 -= s17 * 683901; |
| 2269 | s17 = 0; |
| 2270 | |
| 2271 | s4 += s16 * 666643; |
| 2272 | s5 += s16 * 470296; |
| 2273 | s6 += s16 * 654183; |
| 2274 | s7 -= s16 * 997805; |
| 2275 | s8 += s16 * 136657; |
| 2276 | s9 -= s16 * 683901; |
| 2277 | s16 = 0; |
| 2278 | |
| 2279 | s3 += s15 * 666643; |
| 2280 | s4 += s15 * 470296; |
| 2281 | s5 += s15 * 654183; |
| 2282 | s6 -= s15 * 997805; |
| 2283 | s7 += s15 * 136657; |
| 2284 | s8 -= s15 * 683901; |
| 2285 | s15 = 0; |
| 2286 | |
| 2287 | s2 += s14 * 666643; |
| 2288 | s3 += s14 * 470296; |
| 2289 | s4 += s14 * 654183; |
| 2290 | s5 -= s14 * 997805; |
| 2291 | s6 += s14 * 136657; |
| 2292 | s7 -= s14 * 683901; |
| 2293 | s14 = 0; |
| 2294 | |
| 2295 | s1 += s13 * 666643; |
| 2296 | s2 += s13 * 470296; |
| 2297 | s3 += s13 * 654183; |
| 2298 | s4 -= s13 * 997805; |
| 2299 | s5 += s13 * 136657; |
| 2300 | s6 -= s13 * 683901; |
| 2301 | s13 = 0; |
| 2302 | |
| 2303 | s0 += s12 * 666643; |
| 2304 | s1 += s12 * 470296; |
| 2305 | s2 += s12 * 654183; |
| 2306 | s3 -= s12 * 997805; |
| 2307 | s4 += s12 * 136657; |
| 2308 | s5 -= s12 * 683901; |
| 2309 | s12 = 0; |
| 2310 | |
| 2311 | carry0 = (s0 + (1 << 20)) >> 21; |
| 2312 | s1 += carry0; |
| 2313 | s0 -= carry0 << 21; |
| 2314 | carry2 = (s2 + (1 << 20)) >> 21; |
| 2315 | s3 += carry2; |
| 2316 | s2 -= carry2 << 21; |
| 2317 | carry4 = (s4 + (1 << 20)) >> 21; |
| 2318 | s5 += carry4; |
| 2319 | s4 -= carry4 << 21; |
| 2320 | carry6 = (s6 + (1 << 20)) >> 21; |
| 2321 | s7 += carry6; |
| 2322 | s6 -= carry6 << 21; |
| 2323 | carry8 = (s8 + (1 << 20)) >> 21; |
| 2324 | s9 += carry8; |
| 2325 | s8 -= carry8 << 21; |
| 2326 | carry10 = (s10 + (1 << 20)) >> 21; |
| 2327 | s11 += carry10; |
| 2328 | s10 -= carry10 << 21; |
| 2329 | |
| 2330 | carry1 = (s1 + (1 << 20)) >> 21; |
| 2331 | s2 += carry1; |
| 2332 | s1 -= carry1 << 21; |
| 2333 | carry3 = (s3 + (1 << 20)) >> 21; |
| 2334 | s4 += carry3; |
| 2335 | s3 -= carry3 << 21; |
| 2336 | carry5 = (s5 + (1 << 20)) >> 21; |
| 2337 | s6 += carry5; |
| 2338 | s5 -= carry5 << 21; |
| 2339 | carry7 = (s7 + (1 << 20)) >> 21; |
| 2340 | s8 += carry7; |
| 2341 | s7 -= carry7 << 21; |
| 2342 | carry9 = (s9 + (1 << 20)) >> 21; |
| 2343 | s10 += carry9; |
| 2344 | s9 -= carry9 << 21; |
| 2345 | carry11 = (s11 + (1 << 20)) >> 21; |
| 2346 | s12 += carry11; |
| 2347 | s11 -= carry11 << 21; |
| 2348 | |
| 2349 | s0 += s12 * 666643; |
| 2350 | s1 += s12 * 470296; |
| 2351 | s2 += s12 * 654183; |
| 2352 | s3 -= s12 * 997805; |
| 2353 | s4 += s12 * 136657; |
| 2354 | s5 -= s12 * 683901; |
| 2355 | s12 = 0; |
| 2356 | |
| 2357 | carry0 = s0 >> 21; |
| 2358 | s1 += carry0; |
| 2359 | s0 -= carry0 << 21; |
| 2360 | carry1 = s1 >> 21; |
| 2361 | s2 += carry1; |
| 2362 | s1 -= carry1 << 21; |
| 2363 | carry2 = s2 >> 21; |
| 2364 | s3 += carry2; |
| 2365 | s2 -= carry2 << 21; |
| 2366 | carry3 = s3 >> 21; |
| 2367 | s4 += carry3; |
| 2368 | s3 -= carry3 << 21; |
| 2369 | carry4 = s4 >> 21; |
| 2370 | s5 += carry4; |
| 2371 | s4 -= carry4 << 21; |
| 2372 | carry5 = s5 >> 21; |
| 2373 | s6 += carry5; |
| 2374 | s5 -= carry5 << 21; |
| 2375 | carry6 = s6 >> 21; |
| 2376 | s7 += carry6; |
| 2377 | s6 -= carry6 << 21; |
| 2378 | carry7 = s7 >> 21; |
| 2379 | s8 += carry7; |
| 2380 | s7 -= carry7 << 21; |
| 2381 | carry8 = s8 >> 21; |
| 2382 | s9 += carry8; |
| 2383 | s8 -= carry8 << 21; |
| 2384 | carry9 = s9 >> 21; |
| 2385 | s10 += carry9; |
| 2386 | s9 -= carry9 << 21; |
| 2387 | carry10 = s10 >> 21; |
| 2388 | s11 += carry10; |
| 2389 | s10 -= carry10 << 21; |
| 2390 | carry11 = s11 >> 21; |
| 2391 | s12 += carry11; |
| 2392 | s11 -= carry11 << 21; |
| 2393 | |
| 2394 | s0 += s12 * 666643; |
| 2395 | s1 += s12 * 470296; |
| 2396 | s2 += s12 * 654183; |
| 2397 | s3 -= s12 * 997805; |
| 2398 | s4 += s12 * 136657; |
| 2399 | s5 -= s12 * 683901; |
| 2400 | s12 = 0; |
| 2401 | |
| 2402 | carry0 = s0 >> 21; |
| 2403 | s1 += carry0; |
| 2404 | s0 -= carry0 << 21; |
| 2405 | carry1 = s1 >> 21; |
| 2406 | s2 += carry1; |
| 2407 | s1 -= carry1 << 21; |
| 2408 | carry2 = s2 >> 21; |
| 2409 | s3 += carry2; |
| 2410 | s2 -= carry2 << 21; |
| 2411 | carry3 = s3 >> 21; |
| 2412 | s4 += carry3; |
| 2413 | s3 -= carry3 << 21; |
| 2414 | carry4 = s4 >> 21; |
| 2415 | s5 += carry4; |
| 2416 | s4 -= carry4 << 21; |
| 2417 | carry5 = s5 >> 21; |
| 2418 | s6 += carry5; |
| 2419 | s5 -= carry5 << 21; |
| 2420 | carry6 = s6 >> 21; |
| 2421 | s7 += carry6; |
| 2422 | s6 -= carry6 << 21; |
| 2423 | carry7 = s7 >> 21; |
| 2424 | s8 += carry7; |
| 2425 | s7 -= carry7 << 21; |
| 2426 | carry8 = s8 >> 21; |
| 2427 | s9 += carry8; |
| 2428 | s8 -= carry8 << 21; |
| 2429 | carry9 = s9 >> 21; |
| 2430 | s10 += carry9; |
| 2431 | s9 -= carry9 << 21; |
| 2432 | carry10 = s10 >> 21; |
| 2433 | s11 += carry10; |
| 2434 | s10 -= carry10 << 21; |
| 2435 | |
| 2436 | s[0] = s0 >> 0; |
| 2437 | s[1] = s0 >> 8; |
| 2438 | s[2] = (s0 >> 16) | (s1 << 5); |
| 2439 | s[3] = s1 >> 3; |
| 2440 | s[4] = s1 >> 11; |
| 2441 | s[5] = (s1 >> 19) | (s2 << 2); |
| 2442 | s[6] = s2 >> 6; |
| 2443 | s[7] = (s2 >> 14) | (s3 << 7); |
| 2444 | s[8] = s3 >> 1; |
| 2445 | s[9] = s3 >> 9; |
| 2446 | s[10] = (s3 >> 17) | (s4 << 4); |
| 2447 | s[11] = s4 >> 4; |
| 2448 | s[12] = s4 >> 12; |
| 2449 | s[13] = (s4 >> 20) | (s5 << 1); |
| 2450 | s[14] = s5 >> 7; |
| 2451 | s[15] = (s5 >> 15) | (s6 << 6); |
| 2452 | s[16] = s6 >> 2; |
| 2453 | s[17] = s6 >> 10; |
| 2454 | s[18] = (s6 >> 18) | (s7 << 3); |
| 2455 | s[19] = s7 >> 5; |
| 2456 | s[20] = s7 >> 13; |
| 2457 | s[21] = s8 >> 0; |
| 2458 | s[22] = s8 >> 8; |
| 2459 | s[23] = (s8 >> 16) | (s9 << 5); |
| 2460 | s[24] = s9 >> 3; |
| 2461 | s[25] = s9 >> 11; |
| 2462 | s[26] = (s9 >> 19) | (s10 << 2); |
| 2463 | s[27] = s10 >> 6; |
| 2464 | s[28] = (s10 >> 14) | (s11 << 7); |
| 2465 | s[29] = s11 >> 1; |
| 2466 | s[30] = s11 >> 9; |
| 2467 | s[31] = s11 >> 17; |
| 2468 | } |
| 2469 | |
| 2470 | // Input: |
| 2471 | // a[0]+256*a[1]+...+256^31*a[31] = a |
| 2472 | // b[0]+256*b[1]+...+256^31*b[31] = b |
| 2473 | // c[0]+256*c[1]+...+256^31*c[31] = c |
| 2474 | // |
| 2475 | // Output: |
| 2476 | // s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l |
| 2477 | // where l = 2^252 + 27742317777372353535851937790883648493. |
| 2478 | static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, |
| 2479 | const uint8_t *c) { |
| 2480 | int64_t a0 = 2097151 & load_3(a); |
| 2481 | int64_t a1 = 2097151 & (load_4(a + 2) >> 5); |
| 2482 | int64_t a2 = 2097151 & (load_3(a + 5) >> 2); |
| 2483 | int64_t a3 = 2097151 & (load_4(a + 7) >> 7); |
| 2484 | int64_t a4 = 2097151 & (load_4(a + 10) >> 4); |
| 2485 | int64_t a5 = 2097151 & (load_3(a + 13) >> 1); |
| 2486 | int64_t a6 = 2097151 & (load_4(a + 15) >> 6); |
| 2487 | int64_t a7 = 2097151 & (load_3(a + 18) >> 3); |
| 2488 | int64_t a8 = 2097151 & load_3(a + 21); |
| 2489 | int64_t a9 = 2097151 & (load_4(a + 23) >> 5); |
| 2490 | int64_t a10 = 2097151 & (load_3(a + 26) >> 2); |
| 2491 | int64_t a11 = (load_4(a + 28) >> 7); |
| 2492 | int64_t b0 = 2097151 & load_3(b); |
| 2493 | int64_t b1 = 2097151 & (load_4(b + 2) >> 5); |
| 2494 | int64_t b2 = 2097151 & (load_3(b + 5) >> 2); |
| 2495 | int64_t b3 = 2097151 & (load_4(b + 7) >> 7); |
| 2496 | int64_t b4 = 2097151 & (load_4(b + 10) >> 4); |
| 2497 | int64_t b5 = 2097151 & (load_3(b + 13) >> 1); |
| 2498 | int64_t b6 = 2097151 & (load_4(b + 15) >> 6); |
| 2499 | int64_t b7 = 2097151 & (load_3(b + 18) >> 3); |
| 2500 | int64_t b8 = 2097151 & load_3(b + 21); |
| 2501 | int64_t b9 = 2097151 & (load_4(b + 23) >> 5); |
| 2502 | int64_t b10 = 2097151 & (load_3(b + 26) >> 2); |
| 2503 | int64_t b11 = (load_4(b + 28) >> 7); |
| 2504 | int64_t c0 = 2097151 & load_3(c); |
| 2505 | int64_t c1 = 2097151 & (load_4(c + 2) >> 5); |
| 2506 | int64_t c2 = 2097151 & (load_3(c + 5) >> 2); |
| 2507 | int64_t c3 = 2097151 & (load_4(c + 7) >> 7); |
| 2508 | int64_t c4 = 2097151 & (load_4(c + 10) >> 4); |
| 2509 | int64_t c5 = 2097151 & (load_3(c + 13) >> 1); |
| 2510 | int64_t c6 = 2097151 & (load_4(c + 15) >> 6); |
| 2511 | int64_t c7 = 2097151 & (load_3(c + 18) >> 3); |
| 2512 | int64_t c8 = 2097151 & load_3(c + 21); |
| 2513 | int64_t c9 = 2097151 & (load_4(c + 23) >> 5); |
| 2514 | int64_t c10 = 2097151 & (load_3(c + 26) >> 2); |
| 2515 | int64_t c11 = (load_4(c + 28) >> 7); |
| 2516 | int64_t s0; |
| 2517 | int64_t s1; |
| 2518 | int64_t s2; |
| 2519 | int64_t s3; |
| 2520 | int64_t s4; |
| 2521 | int64_t s5; |
| 2522 | int64_t s6; |
| 2523 | int64_t s7; |
| 2524 | int64_t s8; |
| 2525 | int64_t s9; |
| 2526 | int64_t s10; |
| 2527 | int64_t s11; |
| 2528 | int64_t s12; |
| 2529 | int64_t s13; |
| 2530 | int64_t s14; |
| 2531 | int64_t s15; |
| 2532 | int64_t s16; |
| 2533 | int64_t s17; |
| 2534 | int64_t s18; |
| 2535 | int64_t s19; |
| 2536 | int64_t s20; |
| 2537 | int64_t s21; |
| 2538 | int64_t s22; |
| 2539 | int64_t s23; |
| 2540 | int64_t carry0; |
| 2541 | int64_t carry1; |
| 2542 | int64_t carry2; |
| 2543 | int64_t carry3; |
| 2544 | int64_t carry4; |
| 2545 | int64_t carry5; |
| 2546 | int64_t carry6; |
| 2547 | int64_t carry7; |
| 2548 | int64_t carry8; |
| 2549 | int64_t carry9; |
| 2550 | int64_t carry10; |
| 2551 | int64_t carry11; |
| 2552 | int64_t carry12; |
| 2553 | int64_t carry13; |
| 2554 | int64_t carry14; |
| 2555 | int64_t carry15; |
| 2556 | int64_t carry16; |
| 2557 | int64_t carry17; |
| 2558 | int64_t carry18; |
| 2559 | int64_t carry19; |
| 2560 | int64_t carry20; |
| 2561 | int64_t carry21; |
| 2562 | int64_t carry22; |
| 2563 | |
| 2564 | s0 = c0 + a0 * b0; |
| 2565 | s1 = c1 + a0 * b1 + a1 * b0; |
| 2566 | s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; |
| 2567 | s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; |
| 2568 | s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; |
| 2569 | s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; |
| 2570 | s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; |
| 2571 | s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + |
| 2572 | a6 * b1 + a7 * b0; |
| 2573 | s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + |
| 2574 | a6 * b2 + a7 * b1 + a8 * b0; |
| 2575 | s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + |
| 2576 | a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; |
| 2577 | s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + |
| 2578 | a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; |
| 2579 | s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + |
| 2580 | a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; |
| 2581 | s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + |
| 2582 | a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; |
| 2583 | s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + |
| 2584 | a9 * b4 + a10 * b3 + a11 * b2; |
| 2585 | s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + |
| 2586 | a10 * b4 + a11 * b3; |
| 2587 | s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + |
| 2588 | a11 * b4; |
| 2589 | s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; |
| 2590 | s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; |
| 2591 | s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; |
| 2592 | s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; |
| 2593 | s20 = a9 * b11 + a10 * b10 + a11 * b9; |
| 2594 | s21 = a10 * b11 + a11 * b10; |
| 2595 | s22 = a11 * b11; |
| 2596 | s23 = 0; |
| 2597 | |
| 2598 | carry0 = (s0 + (1 << 20)) >> 21; |
| 2599 | s1 += carry0; |
| 2600 | s0 -= carry0 << 21; |
| 2601 | carry2 = (s2 + (1 << 20)) >> 21; |
| 2602 | s3 += carry2; |
| 2603 | s2 -= carry2 << 21; |
| 2604 | carry4 = (s4 + (1 << 20)) >> 21; |
| 2605 | s5 += carry4; |
| 2606 | s4 -= carry4 << 21; |
| 2607 | carry6 = (s6 + (1 << 20)) >> 21; |
| 2608 | s7 += carry6; |
| 2609 | s6 -= carry6 << 21; |
| 2610 | carry8 = (s8 + (1 << 20)) >> 21; |
| 2611 | s9 += carry8; |
| 2612 | s8 -= carry8 << 21; |
| 2613 | carry10 = (s10 + (1 << 20)) >> 21; |
| 2614 | s11 += carry10; |
| 2615 | s10 -= carry10 << 21; |
| 2616 | carry12 = (s12 + (1 << 20)) >> 21; |
| 2617 | s13 += carry12; |
| 2618 | s12 -= carry12 << 21; |
| 2619 | carry14 = (s14 + (1 << 20)) >> 21; |
| 2620 | s15 += carry14; |
| 2621 | s14 -= carry14 << 21; |
| 2622 | carry16 = (s16 + (1 << 20)) >> 21; |
| 2623 | s17 += carry16; |
| 2624 | s16 -= carry16 << 21; |
| 2625 | carry18 = (s18 + (1 << 20)) >> 21; |
| 2626 | s19 += carry18; |
| 2627 | s18 -= carry18 << 21; |
| 2628 | carry20 = (s20 + (1 << 20)) >> 21; |
| 2629 | s21 += carry20; |
| 2630 | s20 -= carry20 << 21; |
| 2631 | carry22 = (s22 + (1 << 20)) >> 21; |
| 2632 | s23 += carry22; |
| 2633 | s22 -= carry22 << 21; |
| 2634 | |
| 2635 | carry1 = (s1 + (1 << 20)) >> 21; |
| 2636 | s2 += carry1; |
| 2637 | s1 -= carry1 << 21; |
| 2638 | carry3 = (s3 + (1 << 20)) >> 21; |
| 2639 | s4 += carry3; |
| 2640 | s3 -= carry3 << 21; |
| 2641 | carry5 = (s5 + (1 << 20)) >> 21; |
| 2642 | s6 += carry5; |
| 2643 | s5 -= carry5 << 21; |
| 2644 | carry7 = (s7 + (1 << 20)) >> 21; |
| 2645 | s8 += carry7; |
| 2646 | s7 -= carry7 << 21; |
| 2647 | carry9 = (s9 + (1 << 20)) >> 21; |
| 2648 | s10 += carry9; |
| 2649 | s9 -= carry9 << 21; |
| 2650 | carry11 = (s11 + (1 << 20)) >> 21; |
| 2651 | s12 += carry11; |
| 2652 | s11 -= carry11 << 21; |
| 2653 | carry13 = (s13 + (1 << 20)) >> 21; |
| 2654 | s14 += carry13; |
| 2655 | s13 -= carry13 << 21; |
| 2656 | carry15 = (s15 + (1 << 20)) >> 21; |
| 2657 | s16 += carry15; |
| 2658 | s15 -= carry15 << 21; |
| 2659 | carry17 = (s17 + (1 << 20)) >> 21; |
| 2660 | s18 += carry17; |
| 2661 | s17 -= carry17 << 21; |
| 2662 | carry19 = (s19 + (1 << 20)) >> 21; |
| 2663 | s20 += carry19; |
| 2664 | s19 -= carry19 << 21; |
| 2665 | carry21 = (s21 + (1 << 20)) >> 21; |
| 2666 | s22 += carry21; |
| 2667 | s21 -= carry21 << 21; |
| 2668 | |
| 2669 | s11 += s23 * 666643; |
| 2670 | s12 += s23 * 470296; |
| 2671 | s13 += s23 * 654183; |
| 2672 | s14 -= s23 * 997805; |
| 2673 | s15 += s23 * 136657; |
| 2674 | s16 -= s23 * 683901; |
| 2675 | s23 = 0; |
| 2676 | |
| 2677 | s10 += s22 * 666643; |
| 2678 | s11 += s22 * 470296; |
| 2679 | s12 += s22 * 654183; |
| 2680 | s13 -= s22 * 997805; |
| 2681 | s14 += s22 * 136657; |
| 2682 | s15 -= s22 * 683901; |
| 2683 | s22 = 0; |
| 2684 | |
| 2685 | s9 += s21 * 666643; |
| 2686 | s10 += s21 * 470296; |
| 2687 | s11 += s21 * 654183; |
| 2688 | s12 -= s21 * 997805; |
| 2689 | s13 += s21 * 136657; |
| 2690 | s14 -= s21 * 683901; |
| 2691 | s21 = 0; |
| 2692 | |
| 2693 | s8 += s20 * 666643; |
| 2694 | s9 += s20 * 470296; |
| 2695 | s10 += s20 * 654183; |
| 2696 | s11 -= s20 * 997805; |
| 2697 | s12 += s20 * 136657; |
| 2698 | s13 -= s20 * 683901; |
| 2699 | s20 = 0; |
| 2700 | |
| 2701 | s7 += s19 * 666643; |
| 2702 | s8 += s19 * 470296; |
| 2703 | s9 += s19 * 654183; |
| 2704 | s10 -= s19 * 997805; |
| 2705 | s11 += s19 * 136657; |
| 2706 | s12 -= s19 * 683901; |
| 2707 | s19 = 0; |
| 2708 | |
| 2709 | s6 += s18 * 666643; |
| 2710 | s7 += s18 * 470296; |
| 2711 | s8 += s18 * 654183; |
| 2712 | s9 -= s18 * 997805; |
| 2713 | s10 += s18 * 136657; |
| 2714 | s11 -= s18 * 683901; |
| 2715 | s18 = 0; |
| 2716 | |
| 2717 | carry6 = (s6 + (1 << 20)) >> 21; |
| 2718 | s7 += carry6; |
| 2719 | s6 -= carry6 << 21; |
| 2720 | carry8 = (s8 + (1 << 20)) >> 21; |
| 2721 | s9 += carry8; |
| 2722 | s8 -= carry8 << 21; |
| 2723 | carry10 = (s10 + (1 << 20)) >> 21; |
| 2724 | s11 += carry10; |
| 2725 | s10 -= carry10 << 21; |
| 2726 | carry12 = (s12 + (1 << 20)) >> 21; |
| 2727 | s13 += carry12; |
| 2728 | s12 -= carry12 << 21; |
| 2729 | carry14 = (s14 + (1 << 20)) >> 21; |
| 2730 | s15 += carry14; |
| 2731 | s14 -= carry14 << 21; |
| 2732 | carry16 = (s16 + (1 << 20)) >> 21; |
| 2733 | s17 += carry16; |
| 2734 | s16 -= carry16 << 21; |
| 2735 | |
| 2736 | carry7 = (s7 + (1 << 20)) >> 21; |
| 2737 | s8 += carry7; |
| 2738 | s7 -= carry7 << 21; |
| 2739 | carry9 = (s9 + (1 << 20)) >> 21; |
| 2740 | s10 += carry9; |
| 2741 | s9 -= carry9 << 21; |
| 2742 | carry11 = (s11 + (1 << 20)) >> 21; |
| 2743 | s12 += carry11; |
| 2744 | s11 -= carry11 << 21; |
| 2745 | carry13 = (s13 + (1 << 20)) >> 21; |
| 2746 | s14 += carry13; |
| 2747 | s13 -= carry13 << 21; |
| 2748 | carry15 = (s15 + (1 << 20)) >> 21; |
| 2749 | s16 += carry15; |
| 2750 | s15 -= carry15 << 21; |
| 2751 | |
| 2752 | s5 += s17 * 666643; |
| 2753 | s6 += s17 * 470296; |
| 2754 | s7 += s17 * 654183; |
| 2755 | s8 -= s17 * 997805; |
| 2756 | s9 += s17 * 136657; |
| 2757 | s10 -= s17 * 683901; |
| 2758 | s17 = 0; |
| 2759 | |
| 2760 | s4 += s16 * 666643; |
| 2761 | s5 += s16 * 470296; |
| 2762 | s6 += s16 * 654183; |
| 2763 | s7 -= s16 * 997805; |
| 2764 | s8 += s16 * 136657; |
| 2765 | s9 -= s16 * 683901; |
| 2766 | s16 = 0; |
| 2767 | |
| 2768 | s3 += s15 * 666643; |
| 2769 | s4 += s15 * 470296; |
| 2770 | s5 += s15 * 654183; |
| 2771 | s6 -= s15 * 997805; |
| 2772 | s7 += s15 * 136657; |
| 2773 | s8 -= s15 * 683901; |
| 2774 | s15 = 0; |
| 2775 | |
| 2776 | s2 += s14 * 666643; |
| 2777 | s3 += s14 * 470296; |
| 2778 | s4 += s14 * 654183; |
| 2779 | s5 -= s14 * 997805; |
| 2780 | s6 += s14 * 136657; |
| 2781 | s7 -= s14 * 683901; |
| 2782 | s14 = 0; |
| 2783 | |
| 2784 | s1 += s13 * 666643; |
| 2785 | s2 += s13 * 470296; |
| 2786 | s3 += s13 * 654183; |
| 2787 | s4 -= s13 * 997805; |
| 2788 | s5 += s13 * 136657; |
| 2789 | s6 -= s13 * 683901; |
| 2790 | s13 = 0; |
| 2791 | |
| 2792 | s0 += s12 * 666643; |
| 2793 | s1 += s12 * 470296; |
| 2794 | s2 += s12 * 654183; |
| 2795 | s3 -= s12 * 997805; |
| 2796 | s4 += s12 * 136657; |
| 2797 | s5 -= s12 * 683901; |
| 2798 | s12 = 0; |
| 2799 | |
| 2800 | carry0 = (s0 + (1 << 20)) >> 21; |
| 2801 | s1 += carry0; |
| 2802 | s0 -= carry0 << 21; |
| 2803 | carry2 = (s2 + (1 << 20)) >> 21; |
| 2804 | s3 += carry2; |
| 2805 | s2 -= carry2 << 21; |
| 2806 | carry4 = (s4 + (1 << 20)) >> 21; |
| 2807 | s5 += carry4; |
| 2808 | s4 -= carry4 << 21; |
| 2809 | carry6 = (s6 + (1 << 20)) >> 21; |
| 2810 | s7 += carry6; |
| 2811 | s6 -= carry6 << 21; |
| 2812 | carry8 = (s8 + (1 << 20)) >> 21; |
| 2813 | s9 += carry8; |
| 2814 | s8 -= carry8 << 21; |
| 2815 | carry10 = (s10 + (1 << 20)) >> 21; |
| 2816 | s11 += carry10; |
| 2817 | s10 -= carry10 << 21; |
| 2818 | |
| 2819 | carry1 = (s1 + (1 << 20)) >> 21; |
| 2820 | s2 += carry1; |
| 2821 | s1 -= carry1 << 21; |
| 2822 | carry3 = (s3 + (1 << 20)) >> 21; |
| 2823 | s4 += carry3; |
| 2824 | s3 -= carry3 << 21; |
| 2825 | carry5 = (s5 + (1 << 20)) >> 21; |
| 2826 | s6 += carry5; |
| 2827 | s5 -= carry5 << 21; |
| 2828 | carry7 = (s7 + (1 << 20)) >> 21; |
| 2829 | s8 += carry7; |
| 2830 | s7 -= carry7 << 21; |
| 2831 | carry9 = (s9 + (1 << 20)) >> 21; |
| 2832 | s10 += carry9; |
| 2833 | s9 -= carry9 << 21; |
| 2834 | carry11 = (s11 + (1 << 20)) >> 21; |
| 2835 | s12 += carry11; |
| 2836 | s11 -= carry11 << 21; |
| 2837 | |
| 2838 | s0 += s12 * 666643; |
| 2839 | s1 += s12 * 470296; |
| 2840 | s2 += s12 * 654183; |
| 2841 | s3 -= s12 * 997805; |
| 2842 | s4 += s12 * 136657; |
| 2843 | s5 -= s12 * 683901; |
| 2844 | s12 = 0; |
| 2845 | |
| 2846 | carry0 = s0 >> 21; |
| 2847 | s1 += carry0; |
| 2848 | s0 -= carry0 << 21; |
| 2849 | carry1 = s1 >> 21; |
| 2850 | s2 += carry1; |
| 2851 | s1 -= carry1 << 21; |
| 2852 | carry2 = s2 >> 21; |
| 2853 | s3 += carry2; |
| 2854 | s2 -= carry2 << 21; |
| 2855 | carry3 = s3 >> 21; |
| 2856 | s4 += carry3; |
| 2857 | s3 -= carry3 << 21; |
| 2858 | carry4 = s4 >> 21; |
| 2859 | s5 += carry4; |
| 2860 | s4 -= carry4 << 21; |
| 2861 | carry5 = s5 >> 21; |
| 2862 | s6 += carry5; |
| 2863 | s5 -= carry5 << 21; |
| 2864 | carry6 = s6 >> 21; |
| 2865 | s7 += carry6; |
| 2866 | s6 -= carry6 << 21; |
| 2867 | carry7 = s7 >> 21; |
| 2868 | s8 += carry7; |
| 2869 | s7 -= carry7 << 21; |
| 2870 | carry8 = s8 >> 21; |
| 2871 | s9 += carry8; |
| 2872 | s8 -= carry8 << 21; |
| 2873 | carry9 = s9 >> 21; |
| 2874 | s10 += carry9; |
| 2875 | s9 -= carry9 << 21; |
| 2876 | carry10 = s10 >> 21; |
| 2877 | s11 += carry10; |
| 2878 | s10 -= carry10 << 21; |
| 2879 | carry11 = s11 >> 21; |
| 2880 | s12 += carry11; |
| 2881 | s11 -= carry11 << 21; |
| 2882 | |
| 2883 | s0 += s12 * 666643; |
| 2884 | s1 += s12 * 470296; |
| 2885 | s2 += s12 * 654183; |
| 2886 | s3 -= s12 * 997805; |
| 2887 | s4 += s12 * 136657; |
| 2888 | s5 -= s12 * 683901; |
| 2889 | s12 = 0; |
| 2890 | |
| 2891 | carry0 = s0 >> 21; |
| 2892 | s1 += carry0; |
| 2893 | s0 -= carry0 << 21; |
| 2894 | carry1 = s1 >> 21; |
| 2895 | s2 += carry1; |
| 2896 | s1 -= carry1 << 21; |
| 2897 | carry2 = s2 >> 21; |
| 2898 | s3 += carry2; |
| 2899 | s2 -= carry2 << 21; |
| 2900 | carry3 = s3 >> 21; |
| 2901 | s4 += carry3; |
| 2902 | s3 -= carry3 << 21; |
| 2903 | carry4 = s4 >> 21; |
| 2904 | s5 += carry4; |
| 2905 | s4 -= carry4 << 21; |
| 2906 | carry5 = s5 >> 21; |
| 2907 | s6 += carry5; |
| 2908 | s5 -= carry5 << 21; |
| 2909 | carry6 = s6 >> 21; |
| 2910 | s7 += carry6; |
| 2911 | s6 -= carry6 << 21; |
| 2912 | carry7 = s7 >> 21; |
| 2913 | s8 += carry7; |
| 2914 | s7 -= carry7 << 21; |
| 2915 | carry8 = s8 >> 21; |
| 2916 | s9 += carry8; |
| 2917 | s8 -= carry8 << 21; |
| 2918 | carry9 = s9 >> 21; |
| 2919 | s10 += carry9; |
| 2920 | s9 -= carry9 << 21; |
| 2921 | carry10 = s10 >> 21; |
| 2922 | s11 += carry10; |
| 2923 | s10 -= carry10 << 21; |
| 2924 | |
| 2925 | s[0] = s0 >> 0; |
| 2926 | s[1] = s0 >> 8; |
| 2927 | s[2] = (s0 >> 16) | (s1 << 5); |
| 2928 | s[3] = s1 >> 3; |
| 2929 | s[4] = s1 >> 11; |
| 2930 | s[5] = (s1 >> 19) | (s2 << 2); |
| 2931 | s[6] = s2 >> 6; |
| 2932 | s[7] = (s2 >> 14) | (s3 << 7); |
| 2933 | s[8] = s3 >> 1; |
| 2934 | s[9] = s3 >> 9; |
| 2935 | s[10] = (s3 >> 17) | (s4 << 4); |
| 2936 | s[11] = s4 >> 4; |
| 2937 | s[12] = s4 >> 12; |
| 2938 | s[13] = (s4 >> 20) | (s5 << 1); |
| 2939 | s[14] = s5 >> 7; |
| 2940 | s[15] = (s5 >> 15) | (s6 << 6); |
| 2941 | s[16] = s6 >> 2; |
| 2942 | s[17] = s6 >> 10; |
| 2943 | s[18] = (s6 >> 18) | (s7 << 3); |
| 2944 | s[19] = s7 >> 5; |
| 2945 | s[20] = s7 >> 13; |
| 2946 | s[21] = s8 >> 0; |
| 2947 | s[22] = s8 >> 8; |
| 2948 | s[23] = (s8 >> 16) | (s9 << 5); |
| 2949 | s[24] = s9 >> 3; |
| 2950 | s[25] = s9 >> 11; |
| 2951 | s[26] = (s9 >> 19) | (s10 << 2); |
| 2952 | s[27] = s10 >> 6; |
| 2953 | s[28] = (s10 >> 14) | (s11 << 7); |
| 2954 | s[29] = s11 >> 1; |
| 2955 | s[30] = s11 >> 9; |
| 2956 | s[31] = s11 >> 17; |
| 2957 | } |
| 2958 | |
| 2959 | void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) { |
| 2960 | uint8_t seed[32]; |
| 2961 | RAND_bytes(seed, 32); |
| 2962 | ED25519_keypair_from_seed(out_public_key, out_private_key, seed); |
| 2963 | } |
| 2964 | |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 2965 | int ED25519_sign(uint8_t out_sig[64], const uint8_t *message, |
| 2966 | size_t message_len, const uint8_t private_key[64]) { |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 2967 | uint8_t az[SHA512_DIGEST_LENGTH]; |
| 2968 | SHA512(private_key, 32, az); |
| 2969 | |
| 2970 | az[0] &= 248; |
| 2971 | az[31] &= 63; |
| 2972 | az[31] |= 64; |
| 2973 | |
| 2974 | SHA512_CTX hash_ctx; |
| 2975 | SHA512_Init(&hash_ctx); |
| 2976 | SHA512_Update(&hash_ctx, az + 32, 32); |
| 2977 | SHA512_Update(&hash_ctx, message, message_len); |
| 2978 | uint8_t nonce[SHA512_DIGEST_LENGTH]; |
| 2979 | SHA512_Final(nonce, &hash_ctx); |
| 2980 | |
| 2981 | x25519_sc_reduce(nonce); |
| 2982 | ge_p3 R; |
| 2983 | x25519_ge_scalarmult_base(&R, nonce); |
| 2984 | ge_p3_tobytes(out_sig, &R); |
| 2985 | |
| 2986 | SHA512_Init(&hash_ctx); |
| 2987 | SHA512_Update(&hash_ctx, out_sig, 32); |
| 2988 | SHA512_Update(&hash_ctx, private_key + 32, 32); |
| 2989 | SHA512_Update(&hash_ctx, message, message_len); |
| 2990 | uint8_t hram[SHA512_DIGEST_LENGTH]; |
| 2991 | SHA512_Final(hram, &hash_ctx); |
| 2992 | |
| 2993 | x25519_sc_reduce(hram); |
| 2994 | sc_muladd(out_sig + 32, hram, az, nonce); |
| 2995 | |
| 2996 | return 1; |
| 2997 | } |
| 2998 | |
| 2999 | int ED25519_verify(const uint8_t *message, size_t message_len, |
| 3000 | const uint8_t signature[64], const uint8_t public_key[32]) { |
| 3001 | ge_p3 A; |
| 3002 | if ((signature[63] & 224) != 0 || |
| 3003 | x25519_ge_frombytes_vartime(&A, public_key) != 0) { |
| 3004 | return 0; |
| 3005 | } |
| 3006 | |
| 3007 | fe_loose t; |
| 3008 | fe_neg(&t, &A.X); |
| 3009 | fe_carry(&A.X, &t); |
| 3010 | fe_neg(&t, &A.T); |
| 3011 | fe_carry(&A.T, &t); |
| 3012 | |
| 3013 | uint8_t pkcopy[32]; |
| 3014 | OPENSSL_memcpy(pkcopy, public_key, 32); |
| 3015 | uint8_t rcopy[32]; |
| 3016 | OPENSSL_memcpy(rcopy, signature, 32); |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 3017 | union { |
| 3018 | uint64_t u64[4]; |
| 3019 | uint8_t u8[32]; |
| 3020 | } scopy; |
| 3021 | OPENSSL_memcpy(&scopy.u8[0], signature + 32, 32); |
| 3022 | |
| 3023 | // https://tools.ietf.org/html/rfc8032#section-5.1.7 requires that s be in |
| 3024 | // the range [0, order) in order to prevent signature malleability. |
| 3025 | |
| 3026 | // kOrder is the order of Curve25519 in little-endian form. |
| 3027 | static const uint64_t kOrder[4] = { |
| 3028 | UINT64_C(0x5812631a5cf5d3ed), |
| 3029 | UINT64_C(0x14def9dea2f79cd6), |
| 3030 | 0, |
| 3031 | UINT64_C(0x1000000000000000), |
| 3032 | }; |
| 3033 | for (size_t i = 3;; i--) { |
| 3034 | if (scopy.u64[i] > kOrder[i]) { |
| 3035 | return 0; |
| 3036 | } else if (scopy.u64[i] < kOrder[i]) { |
| 3037 | break; |
| 3038 | } else if (i == 0) { |
| 3039 | return 0; |
| 3040 | } |
| 3041 | } |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3042 | |
| 3043 | SHA512_CTX hash_ctx; |
| 3044 | SHA512_Init(&hash_ctx); |
| 3045 | SHA512_Update(&hash_ctx, signature, 32); |
| 3046 | SHA512_Update(&hash_ctx, public_key, 32); |
| 3047 | SHA512_Update(&hash_ctx, message, message_len); |
| 3048 | uint8_t h[SHA512_DIGEST_LENGTH]; |
| 3049 | SHA512_Final(h, &hash_ctx); |
| 3050 | |
| 3051 | x25519_sc_reduce(h); |
| 3052 | |
| 3053 | ge_p2 R; |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 3054 | ge_double_scalarmult_vartime(&R, h, &A, scopy.u8); |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3055 | |
| 3056 | uint8_t rcheck[32]; |
| 3057 | x25519_ge_tobytes(rcheck, &R); |
| 3058 | |
| 3059 | return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0; |
| 3060 | } |
| 3061 | |
| 3062 | void ED25519_keypair_from_seed(uint8_t out_public_key[32], |
| 3063 | uint8_t out_private_key[64], |
| 3064 | const uint8_t seed[32]) { |
| 3065 | uint8_t az[SHA512_DIGEST_LENGTH]; |
| 3066 | SHA512(seed, 32, az); |
| 3067 | |
| 3068 | az[0] &= 248; |
| 3069 | az[31] &= 63; |
| 3070 | az[31] |= 64; |
| 3071 | |
| 3072 | ge_p3 A; |
| 3073 | x25519_ge_scalarmult_base(&A, az); |
| 3074 | ge_p3_tobytes(out_public_key, &A); |
| 3075 | |
| 3076 | OPENSSL_memcpy(out_private_key, seed, 32); |
| 3077 | OPENSSL_memcpy(out_private_key + 32, out_public_key, 32); |
| 3078 | } |
| 3079 | |
| 3080 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3081 | static void x25519_scalar_mult_generic(uint8_t out[32], |
| 3082 | const uint8_t scalar[32], |
| 3083 | const uint8_t point[32]) { |
| 3084 | fe x1, x2, z2, x3, z3, tmp0, tmp1; |
| 3085 | fe_loose x2l, z2l, x3l, tmp0l, tmp1l; |
| 3086 | |
| 3087 | uint8_t e[32]; |
| 3088 | OPENSSL_memcpy(e, scalar, 32); |
| 3089 | e[0] &= 248; |
| 3090 | e[31] &= 127; |
| 3091 | e[31] |= 64; |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 3092 | |
| 3093 | // The following implementation was transcribed to Coq and proven to |
| 3094 | // correspond to unary scalar multiplication in affine coordinates given that |
| 3095 | // x1 != 0 is the x coordinate of some point on the curve. It was also checked |
| 3096 | // in Coq that doing a ladderstep with x1 = x3 = 0 gives z2' = z3' = 0, and z2 |
| 3097 | // = z3 = 0 gives z2' = z3' = 0. The statement was quantified over the |
| 3098 | // underlying field, so it applies to Curve25519 itself and the quadratic |
| 3099 | // twist of Curve25519. It was not proven in Coq that prime-field arithmetic |
| 3100 | // correctly simulates extension-field arithmetic on prime-field values. |
| 3101 | // The decoding of the byte array representation of e was not considered. |
| 3102 | // Specification of Montgomery curves in affine coordinates: |
| 3103 | // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27> |
| 3104 | // Proof that these form a group that is isomorphic to a Weierstrass curve: |
| 3105 | // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35> |
| 3106 | // Coq transcription and correctness proof of the loop (where scalarbits=255): |
| 3107 | // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118> |
| 3108 | // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278> |
| 3109 | // preconditions: 0 <= e < 2^255 (not necessarily e < order), fe_invert(0) = 0 |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3110 | fe_frombytes(&x1, point); |
| 3111 | fe_1(&x2); |
| 3112 | fe_0(&z2); |
| 3113 | fe_copy(&x3, &x1); |
| 3114 | fe_1(&z3); |
| 3115 | |
| 3116 | unsigned swap = 0; |
| 3117 | int pos; |
| 3118 | for (pos = 254; pos >= 0; --pos) { |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 3119 | // loop invariant as of right before the test, for the case where x1 != 0: |
| 3120 | // pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 is nonzero |
| 3121 | // let r := e >> (pos+1) in the following equalities of projective points: |
| 3122 | // to_xz (r*P) === if swap then (x3, z3) else (x2, z2) |
| 3123 | // to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3) |
| 3124 | // x1 is the nonzero x coordinate of the nonzero point (r*P-(r+1)*P) |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3125 | unsigned b = 1 & (e[pos / 8] >> (pos & 7)); |
| 3126 | swap ^= b; |
| 3127 | fe_cswap(&x2, &x3, swap); |
| 3128 | fe_cswap(&z2, &z3, swap); |
| 3129 | swap = b; |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 3130 | // Coq transcription of ladderstep formula (called from transcribed loop): |
| 3131 | // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89> |
| 3132 | // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131> |
| 3133 | // x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217> |
| 3134 | // x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147> |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3135 | fe_sub(&tmp0l, &x3, &z3); |
| 3136 | fe_sub(&tmp1l, &x2, &z2); |
| 3137 | fe_add(&x2l, &x2, &z2); |
| 3138 | fe_add(&z2l, &x3, &z3); |
| 3139 | fe_mul_tll(&z3, &tmp0l, &x2l); |
| 3140 | fe_mul_tll(&z2, &z2l, &tmp1l); |
| 3141 | fe_sq_tl(&tmp0, &tmp1l); |
| 3142 | fe_sq_tl(&tmp1, &x2l); |
| 3143 | fe_add(&x3l, &z3, &z2); |
| 3144 | fe_sub(&z2l, &z3, &z2); |
| 3145 | fe_mul_ttt(&x2, &tmp1, &tmp0); |
| 3146 | fe_sub(&tmp1l, &tmp1, &tmp0); |
| 3147 | fe_sq_tl(&z2, &z2l); |
| 3148 | fe_mul121666(&z3, &tmp1l); |
| 3149 | fe_sq_tl(&x3, &x3l); |
| 3150 | fe_add(&tmp0l, &tmp0, &z3); |
| 3151 | fe_mul_ttt(&z3, &x1, &z2); |
| 3152 | fe_mul_tll(&z2, &tmp1l, &tmp0l); |
| 3153 | } |
Robert Sloan | 0da4395 | 2018-01-03 15:13:14 -0800 | [diff] [blame] | 3154 | // here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) else (x2, z2) |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3155 | fe_cswap(&x2, &x3, swap); |
| 3156 | fe_cswap(&z2, &z3, swap); |
| 3157 | |
| 3158 | fe_invert(&z2, &z2); |
| 3159 | fe_mul_ttt(&x2, &x2, &z2); |
| 3160 | fe_tobytes(out, &x2); |
| 3161 | } |
| 3162 | |
| 3163 | static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], |
| 3164 | const uint8_t point[32]) { |
| 3165 | #if defined(BORINGSSL_X25519_NEON) |
| 3166 | if (CRYPTO_is_NEON_capable()) { |
| 3167 | x25519_NEON(out, scalar, point); |
| 3168 | return; |
| 3169 | } |
| 3170 | #endif |
| 3171 | |
| 3172 | x25519_scalar_mult_generic(out, scalar, point); |
| 3173 | } |
| 3174 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3175 | void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) { |
| 3176 | RAND_bytes(out_private_key, 32); |
| 3177 | |
| 3178 | // All X25519 implementations should decode scalars correctly (see |
| 3179 | // https://tools.ietf.org/html/rfc7748#section-5). However, if an |
| 3180 | // implementation doesn't then it might interoperate with random keys a |
| 3181 | // fraction of the time because they'll, randomly, happen to be correctly |
| 3182 | // formed. |
| 3183 | // |
| 3184 | // Thus we do the opposite of the masking here to make sure that our private |
| 3185 | // keys are never correctly masked and so, hopefully, any incorrect |
| 3186 | // implementations are deterministically broken. |
| 3187 | // |
| 3188 | // This does not affect security because, although we're throwing away |
| 3189 | // entropy, a valid implementation of scalarmult should throw away the exact |
| 3190 | // same bits anyway. |
| 3191 | out_private_key[0] |= 7; |
| 3192 | out_private_key[31] &= 63; |
| 3193 | out_private_key[31] |= 128; |
| 3194 | |
| 3195 | X25519_public_from_private(out_public_value, out_private_key); |
| 3196 | } |
| 3197 | |
| 3198 | int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], |
| 3199 | const uint8_t peer_public_value[32]) { |
| 3200 | static const uint8_t kZeros[32] = {0}; |
| 3201 | x25519_scalar_mult(out_shared_key, private_key, peer_public_value); |
| 3202 | // The all-zero output results when the input is a point of small order. |
| 3203 | return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; |
| 3204 | } |
| 3205 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 3206 | void X25519_public_from_private(uint8_t out_public_value[32], |
| 3207 | const uint8_t private_key[32]) { |
| 3208 | #if defined(BORINGSSL_X25519_NEON) |
| 3209 | if (CRYPTO_is_NEON_capable()) { |
| 3210 | static const uint8_t kMongomeryBasePoint[32] = {9}; |
| 3211 | x25519_NEON(out_public_value, private_key, kMongomeryBasePoint); |
| 3212 | return; |
| 3213 | } |
| 3214 | #endif |
| 3215 | |
| 3216 | uint8_t e[32]; |
| 3217 | OPENSSL_memcpy(e, private_key, 32); |
| 3218 | e[0] &= 248; |
| 3219 | e[31] &= 127; |
| 3220 | e[31] |= 64; |
| 3221 | |
| 3222 | ge_p3 A; |
| 3223 | x25519_ge_scalarmult_base(&A, e); |
| 3224 | |
| 3225 | // We only need the u-coordinate of the curve25519 point. The map is |
| 3226 | // u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). |
| 3227 | fe_loose zplusy, zminusy; |
| 3228 | fe zminusy_inv; |
| 3229 | fe_add(&zplusy, &A.Z, &A.Y); |
| 3230 | fe_sub(&zminusy, &A.Z, &A.Y); |
| 3231 | fe_loose_invert(&zminusy_inv, &zminusy); |
| 3232 | fe_mul_tlt(&zminusy_inv, &zplusy, &zminusy_inv); |
| 3233 | fe_tobytes(out_public_value, &zminusy_inv); |
| 3234 | } |