1 /* 2 * Copyright 2016-2018 The OpenSSL Project Authors. All Rights Reserved. 3 * 4 * Licensed under the OpenSSL license (the "License"). You may not use 5 * this file except in compliance with the License. You can obtain a copy 6 * in the file LICENSE in the source distribution or at 7 * https://www.openssl.org/source/license.html 8 */ 9 10 #include <string.h> 11 #include "ec_lcl.h" 12 #include <openssl/sha.h> 13 14 #if defined(X25519_ASM) && (defined(__x86_64) || defined(__x86_64__) || \ 15 defined(_M_AMD64) || defined(_M_X64)) 16 17 # define BASE_2_64_IMPLEMENTED 18 19 typedef uint64_t fe64[4]; 20 21 int x25519_fe64_eligible(void); 22 23 /* 24 * Following subroutines perform corresponding operations modulo 25 * 2^256-38, i.e. double the curve modulus. However, inputs and 26 * outputs are permitted to be partially reduced, i.e. to remain 27 * in [0..2^256) range. It's all tied up in final fe64_tobytes 28 * that performs full reduction modulo 2^255-19. 29 * 30 * There are no reference C implementations for these. 31 */ 32 void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g); 33 void x25519_fe64_sqr(fe64 h, const fe64 f); 34 void x25519_fe64_mul121666(fe64 h, fe64 f); 35 void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g); 36 void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g); 37 void x25519_fe64_tobytes(uint8_t *s, const fe64 f); 38 # define fe64_mul x25519_fe64_mul 39 # define fe64_sqr x25519_fe64_sqr 40 # define fe64_mul121666 x25519_fe64_mul121666 41 # define fe64_add x25519_fe64_add 42 # define fe64_sub x25519_fe64_sub 43 # define fe64_tobytes x25519_fe64_tobytes 44 45 static uint64_t load_8(const uint8_t *in) 46 { 47 uint64_t result; 48 49 result = in[0]; 50 result |= ((uint64_t)in[1]) << 8; 51 result |= ((uint64_t)in[2]) << 16; 52 result |= ((uint64_t)in[3]) << 24; 53 result |= ((uint64_t)in[4]) << 32; 54 result |= ((uint64_t)in[5]) << 40; 55 result |= ((uint64_t)in[6]) << 48; 56 result |= ((uint64_t)in[7]) << 56; 57 58 return result; 59 } 60 61 static void fe64_frombytes(fe64 h, const uint8_t *s) 62 { 63 h[0] = load_8(s); 64 h[1] = load_8(s + 8); 65 h[2] = load_8(s + 16); 66 h[3] = load_8(s + 24) & 0x7fffffffffffffff; 67 } 68 69 static void fe64_0(fe64 h) 70 { 71 h[0] = 0; 72 h[1] = 0; 73 h[2] = 0; 74 h[3] = 0; 75 } 76 77 static void fe64_1(fe64 h) 78 { 79 h[0] = 1; 80 h[1] = 0; 81 h[2] = 0; 82 h[3] = 0; 83 } 84 85 static void fe64_copy(fe64 h, const fe64 f) 86 { 87 h[0] = f[0]; 88 h[1] = f[1]; 89 h[2] = f[2]; 90 h[3] = f[3]; 91 } 92 93 static void fe64_cswap(fe64 f, fe64 g, unsigned int b) 94 { 95 int i; 96 uint64_t mask = 0 - (uint64_t)b; 97 98 for (i = 0; i < 4; i++) { 99 uint64_t x = f[i] ^ g[i]; 100 x &= mask; 101 f[i] ^= x; 102 g[i] ^= x; 103 } 104 } 105 106 static void fe64_invert(fe64 out, const fe64 z) 107 { 108 fe64 t0; 109 fe64 t1; 110 fe64 t2; 111 fe64 t3; 112 int i; 113 114 /* 115 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as 116 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. 117 */ 118 119 /* t0 = z ** 2 */ 120 fe64_sqr(t0, z); 121 122 /* t1 = t0 ** (2 ** 2) = z ** 8 */ 123 fe64_sqr(t1, t0); 124 fe64_sqr(t1, t1); 125 126 /* t1 = z * t1 = z ** 9 */ 127 fe64_mul(t1, z, t1); 128 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ 129 fe64_mul(t0, t0, t1); 130 131 /* t2 = t0 ** 2 = z ** 22 */ 132 fe64_sqr(t2, t0); 133 134 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ 135 fe64_mul(t1, t1, t2); 136 137 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ 138 fe64_sqr(t2, t1); 139 for (i = 1; i < 5; ++i) 140 fe64_sqr(t2, t2); 141 142 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ 143 fe64_mul(t1, t2, t1); 144 145 /* Continuing similarly... */ 146 147 /* t2 = z ** (2 ** 20 - 1) */ 148 fe64_sqr(t2, t1); 149 for (i = 1; i < 10; ++i) 150 fe64_sqr(t2, t2); 151 152 fe64_mul(t2, t2, t1); 153 154 /* t2 = z ** (2 ** 40 - 1) */ 155 fe64_sqr(t3, t2); 156 for (i = 1; i < 20; ++i) 157 fe64_sqr(t3, t3); 158 159 fe64_mul(t2, t3, t2); 160 161 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ 162 for (i = 0; i < 10; ++i) 163 fe64_sqr(t2, t2); 164 165 /* t1 = z ** (2 ** 50 - 1) */ 166 fe64_mul(t1, t2, t1); 167 168 /* t2 = z ** (2 ** 100 - 1) */ 169 fe64_sqr(t2, t1); 170 for (i = 1; i < 50; ++i) 171 fe64_sqr(t2, t2); 172 173 fe64_mul(t2, t2, t1); 174 175 /* t2 = z ** (2 ** 200 - 1) */ 176 fe64_sqr(t3, t2); 177 for (i = 1; i < 100; ++i) 178 fe64_sqr(t3, t3); 179 180 fe64_mul(t2, t3, t2); 181 182 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ 183 for (i = 0; i < 50; ++i) 184 fe64_sqr(t2, t2); 185 186 /* t1 = z ** (2 ** 250 - 1) */ 187 fe64_mul(t1, t2, t1); 188 189 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ 190 for (i = 0; i < 5; ++i) 191 fe64_sqr(t1, t1); 192 193 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ 194 fe64_mul(out, t1, t0); 195 } 196 197 /* 198 * Duplicate of original x25519_scalar_mult_generic, but using 199 * fe64_* subroutines. 200 */ 201 static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32], 202 const uint8_t point[32]) 203 { 204 fe64 x1, x2, z2, x3, z3, tmp0, tmp1; 205 uint8_t e[32]; 206 unsigned swap = 0; 207 int pos; 208 209 memcpy(e, scalar, 32); 210 e[0] &= 0xf8; 211 e[31] &= 0x7f; 212 e[31] |= 0x40; 213 fe64_frombytes(x1, point); 214 fe64_1(x2); 215 fe64_0(z2); 216 fe64_copy(x3, x1); 217 fe64_1(z3); 218 219 for (pos = 254; pos >= 0; --pos) { 220 unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); 221 222 swap ^= b; 223 fe64_cswap(x2, x3, swap); 224 fe64_cswap(z2, z3, swap); 225 swap = b; 226 fe64_sub(tmp0, x3, z3); 227 fe64_sub(tmp1, x2, z2); 228 fe64_add(x2, x2, z2); 229 fe64_add(z2, x3, z3); 230 fe64_mul(z3, x2, tmp0); 231 fe64_mul(z2, z2, tmp1); 232 fe64_sqr(tmp0, tmp1); 233 fe64_sqr(tmp1, x2); 234 fe64_add(x3, z3, z2); 235 fe64_sub(z2, z3, z2); 236 fe64_mul(x2, tmp1, tmp0); 237 fe64_sub(tmp1, tmp1, tmp0); 238 fe64_sqr(z2, z2); 239 fe64_mul121666(z3, tmp1); 240 fe64_sqr(x3, x3); 241 fe64_add(tmp0, tmp0, z3); 242 fe64_mul(z3, x1, z2); 243 fe64_mul(z2, tmp1, tmp0); 244 } 245 246 fe64_invert(z2, z2); 247 fe64_mul(x2, x2, z2); 248 fe64_tobytes(out, x2); 249 250 OPENSSL_cleanse(e, sizeof(e)); 251 } 252 #endif 253 254 #if defined(X25519_ASM) \ 255 || ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \ 256 && !defined(__sparc__) \ 257 && !(defined(__ANDROID__) && !defined(__clang__)) ) 258 /* 259 * Base 2^51 implementation. It's virtually no different from reference 260 * base 2^25.5 implementation in respect to lax boundary conditions for 261 * intermediate values and even individual limbs. So that whatever you 262 * know about the reference, applies even here... 263 */ 264 # define BASE_2_51_IMPLEMENTED 265 266 typedef uint64_t fe51[5]; 267 268 static const uint64_t MASK51 = 0x7ffffffffffff; 269 270 static uint64_t load_7(const uint8_t *in) 271 { 272 uint64_t result; 273 274 result = in[0]; 275 result |= ((uint64_t)in[1]) << 8; 276 result |= ((uint64_t)in[2]) << 16; 277 result |= ((uint64_t)in[3]) << 24; 278 result |= ((uint64_t)in[4]) << 32; 279 result |= ((uint64_t)in[5]) << 40; 280 result |= ((uint64_t)in[6]) << 48; 281 282 return result; 283 } 284 285 static uint64_t load_6(const uint8_t *in) 286 { 287 uint64_t result; 288 289 result = in[0]; 290 result |= ((uint64_t)in[1]) << 8; 291 result |= ((uint64_t)in[2]) << 16; 292 result |= ((uint64_t)in[3]) << 24; 293 result |= ((uint64_t)in[4]) << 32; 294 result |= ((uint64_t)in[5]) << 40; 295 296 return result; 297 } 298 299 static void fe51_frombytes(fe51 h, const uint8_t *s) 300 { 301 uint64_t h0 = load_7(s); /* 56 bits */ 302 uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */ 303 uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */ 304 uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */ 305 uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */ 306 307 h1 |= h0 >> 51; h0 &= MASK51; 308 h2 |= h1 >> 51; h1 &= MASK51; 309 h3 |= h2 >> 51; h2 &= MASK51; 310 h4 |= h3 >> 51; h3 &= MASK51; 311 312 h[0] = h0; 313 h[1] = h1; 314 h[2] = h2; 315 h[3] = h3; 316 h[4] = h4; 317 } 318 319 static void fe51_tobytes(uint8_t *s, const fe51 h) 320 { 321 uint64_t h0 = h[0]; 322 uint64_t h1 = h[1]; 323 uint64_t h2 = h[2]; 324 uint64_t h3 = h[3]; 325 uint64_t h4 = h[4]; 326 uint64_t q; 327 328 /* compare to modulus */ 329 q = (h0 + 19) >> 51; 330 q = (h1 + q) >> 51; 331 q = (h2 + q) >> 51; 332 q = (h3 + q) >> 51; 333 q = (h4 + q) >> 51; 334 335 /* full reduce */ 336 h0 += 19 * q; 337 h1 += h0 >> 51; h0 &= MASK51; 338 h2 += h1 >> 51; h1 &= MASK51; 339 h3 += h2 >> 51; h2 &= MASK51; 340 h4 += h3 >> 51; h3 &= MASK51; 341 h4 &= MASK51; 342 343 /* smash */ 344 s[0] = (uint8_t)(h0 >> 0); 345 s[1] = (uint8_t)(h0 >> 8); 346 s[2] = (uint8_t)(h0 >> 16); 347 s[3] = (uint8_t)(h0 >> 24); 348 s[4] = (uint8_t)(h0 >> 32); 349 s[5] = (uint8_t)(h0 >> 40); 350 s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3)); 351 s[7] = (uint8_t)(h1 >> 5); 352 s[8] = (uint8_t)(h1 >> 13); 353 s[9] = (uint8_t)(h1 >> 21); 354 s[10] = (uint8_t)(h1 >> 29); 355 s[11] = (uint8_t)(h1 >> 37); 356 s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6)); 357 s[13] = (uint8_t)(h2 >> 2); 358 s[14] = (uint8_t)(h2 >> 10); 359 s[15] = (uint8_t)(h2 >> 18); 360 s[16] = (uint8_t)(h2 >> 26); 361 s[17] = (uint8_t)(h2 >> 34); 362 s[18] = (uint8_t)(h2 >> 42); 363 s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1)); 364 s[20] = (uint8_t)(h3 >> 7); 365 s[21] = (uint8_t)(h3 >> 15); 366 s[22] = (uint8_t)(h3 >> 23); 367 s[23] = (uint8_t)(h3 >> 31); 368 s[24] = (uint8_t)(h3 >> 39); 369 s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4)); 370 s[26] = (uint8_t)(h4 >> 4); 371 s[27] = (uint8_t)(h4 >> 12); 372 s[28] = (uint8_t)(h4 >> 20); 373 s[29] = (uint8_t)(h4 >> 28); 374 s[30] = (uint8_t)(h4 >> 36); 375 s[31] = (uint8_t)(h4 >> 44); 376 } 377 378 # if defined(X25519_ASM) 379 void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g); 380 void x25519_fe51_sqr(fe51 h, const fe51 f); 381 void x25519_fe51_mul121666(fe51 h, fe51 f); 382 # define fe51_mul x25519_fe51_mul 383 # define fe51_sq x25519_fe51_sqr 384 # define fe51_mul121666 x25519_fe51_mul121666 385 # else 386 387 typedef __uint128_t u128; 388 389 static void fe51_mul(fe51 h, const fe51 f, const fe51 g) 390 { 391 u128 h0, h1, h2, h3, h4; 392 uint64_t f_i, g0, g1, g2, g3, g4; 393 394 f_i = f[0]; 395 h0 = (u128)f_i * (g0 = g[0]); 396 h1 = (u128)f_i * (g1 = g[1]); 397 h2 = (u128)f_i * (g2 = g[2]); 398 h3 = (u128)f_i * (g3 = g[3]); 399 h4 = (u128)f_i * (g4 = g[4]); 400 401 f_i = f[1]; 402 h0 += (u128)f_i * (g4 *= 19); 403 h1 += (u128)f_i * g0; 404 h2 += (u128)f_i * g1; 405 h3 += (u128)f_i * g2; 406 h4 += (u128)f_i * g3; 407 408 f_i = f[2]; 409 h0 += (u128)f_i * (g3 *= 19); 410 h1 += (u128)f_i * g4; 411 h2 += (u128)f_i * g0; 412 h3 += (u128)f_i * g1; 413 h4 += (u128)f_i * g2; 414 415 f_i = f[3]; 416 h0 += (u128)f_i * (g2 *= 19); 417 h1 += (u128)f_i * g3; 418 h2 += (u128)f_i * g4; 419 h3 += (u128)f_i * g0; 420 h4 += (u128)f_i * g1; 421 422 f_i = f[4]; 423 h0 += (u128)f_i * (g1 *= 19); 424 h1 += (u128)f_i * g2; 425 h2 += (u128)f_i * g3; 426 h3 += (u128)f_i * g4; 427 h4 += (u128)f_i * g0; 428 429 /* partial [lazy] reduction */ 430 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; 431 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; 432 433 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; 434 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; 435 436 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; 437 g3 += g2 >> 51; g2 &= MASK51; 438 g1 += g0 >> 51; g0 &= MASK51; 439 440 h[0] = g0; 441 h[1] = g1; 442 h[2] = g2; 443 h[3] = g3; 444 h[4] = g4; 445 } 446 447 static void fe51_sq(fe51 h, const fe51 f) 448 { 449 # if defined(OPENSSL_SMALL_FOOTPRINT) 450 fe51_mul(h, f, f); 451 # else 452 /* dedicated squaring gives 16-25% overall improvement */ 453 uint64_t g0 = f[0]; 454 uint64_t g1 = f[1]; 455 uint64_t g2 = f[2]; 456 uint64_t g3 = f[3]; 457 uint64_t g4 = f[4]; 458 u128 h0, h1, h2, h3, h4; 459 460 h0 = (u128)g0 * g0; g0 *= 2; 461 h1 = (u128)g0 * g1; 462 h2 = (u128)g0 * g2; 463 h3 = (u128)g0 * g3; 464 h4 = (u128)g0 * g4; 465 466 g0 = g4; /* borrow g0 */ 467 h3 += (u128)g0 * (g4 *= 19); 468 469 h2 += (u128)g1 * g1; g1 *= 2; 470 h3 += (u128)g1 * g2; 471 h4 += (u128)g1 * g3; 472 h0 += (u128)g1 * g4; 473 474 g0 = g3; /* borrow g0 */ 475 h1 += (u128)g0 * (g3 *= 19); 476 h2 += (u128)(g0 * 2) * g4; 477 478 h4 += (u128)g2 * g2; g2 *= 2; 479 h0 += (u128)g2 * g3; 480 h1 += (u128)g2 * g4; 481 482 /* partial [lazy] reduction */ 483 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; 484 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; 485 486 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; 487 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; 488 489 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; 490 g3 += g2 >> 51; g2 &= MASK51; 491 g1 += g0 >> 51; g0 &= MASK51; 492 493 h[0] = g0; 494 h[1] = g1; 495 h[2] = g2; 496 h[3] = g3; 497 h[4] = g4; 498 # endif 499 } 500 501 static void fe51_mul121666(fe51 h, fe51 f) 502 { 503 u128 h0 = f[0] * (u128)121666; 504 u128 h1 = f[1] * (u128)121666; 505 u128 h2 = f[2] * (u128)121666; 506 u128 h3 = f[3] * (u128)121666; 507 u128 h4 = f[4] * (u128)121666; 508 uint64_t g0, g1, g2, g3, g4; 509 510 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; 511 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; 512 513 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; 514 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; 515 516 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; 517 g3 += g2 >> 51; g2 &= MASK51; 518 g1 += g0 >> 51; g0 &= MASK51; 519 520 h[0] = g0; 521 h[1] = g1; 522 h[2] = g2; 523 h[3] = g3; 524 h[4] = g4; 525 } 526 # endif 527 528 static void fe51_add(fe51 h, const fe51 f, const fe51 g) 529 { 530 h[0] = f[0] + g[0]; 531 h[1] = f[1] + g[1]; 532 h[2] = f[2] + g[2]; 533 h[3] = f[3] + g[3]; 534 h[4] = f[4] + g[4]; 535 } 536 537 static void fe51_sub(fe51 h, const fe51 f, const fe51 g) 538 { 539 /* 540 * Add 2*modulus to ensure that result remains positive 541 * even if subtrahend is partially reduced. 542 */ 543 h[0] = (f[0] + 0xfffffffffffda) - g[0]; 544 h[1] = (f[1] + 0xffffffffffffe) - g[1]; 545 h[2] = (f[2] + 0xffffffffffffe) - g[2]; 546 h[3] = (f[3] + 0xffffffffffffe) - g[3]; 547 h[4] = (f[4] + 0xffffffffffffe) - g[4]; 548 } 549 550 static void fe51_0(fe51 h) 551 { 552 h[0] = 0; 553 h[1] = 0; 554 h[2] = 0; 555 h[3] = 0; 556 h[4] = 0; 557 } 558 559 static void fe51_1(fe51 h) 560 { 561 h[0] = 1; 562 h[1] = 0; 563 h[2] = 0; 564 h[3] = 0; 565 h[4] = 0; 566 } 567 568 static void fe51_copy(fe51 h, const fe51 f) 569 { 570 h[0] = f[0]; 571 h[1] = f[1]; 572 h[2] = f[2]; 573 h[3] = f[3]; 574 h[4] = f[4]; 575 } 576 577 static void fe51_cswap(fe51 f, fe51 g, unsigned int b) 578 { 579 int i; 580 uint64_t mask = 0 - (uint64_t)b; 581 582 for (i = 0; i < 5; i++) { 583 int64_t x = f[i] ^ g[i]; 584 x &= mask; 585 f[i] ^= x; 586 g[i] ^= x; 587 } 588 } 589 590 static void fe51_invert(fe51 out, const fe51 z) 591 { 592 fe51 t0; 593 fe51 t1; 594 fe51 t2; 595 fe51 t3; 596 int i; 597 598 /* 599 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as 600 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. 601 */ 602 603 /* t0 = z ** 2 */ 604 fe51_sq(t0, z); 605 606 /* t1 = t0 ** (2 ** 2) = z ** 8 */ 607 fe51_sq(t1, t0); 608 fe51_sq(t1, t1); 609 610 /* t1 = z * t1 = z ** 9 */ 611 fe51_mul(t1, z, t1); 612 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ 613 fe51_mul(t0, t0, t1); 614 615 /* t2 = t0 ** 2 = z ** 22 */ 616 fe51_sq(t2, t0); 617 618 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ 619 fe51_mul(t1, t1, t2); 620 621 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ 622 fe51_sq(t2, t1); 623 for (i = 1; i < 5; ++i) 624 fe51_sq(t2, t2); 625 626 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ 627 fe51_mul(t1, t2, t1); 628 629 /* Continuing similarly... */ 630 631 /* t2 = z ** (2 ** 20 - 1) */ 632 fe51_sq(t2, t1); 633 for (i = 1; i < 10; ++i) 634 fe51_sq(t2, t2); 635 636 fe51_mul(t2, t2, t1); 637 638 /* t2 = z ** (2 ** 40 - 1) */ 639 fe51_sq(t3, t2); 640 for (i = 1; i < 20; ++i) 641 fe51_sq(t3, t3); 642 643 fe51_mul(t2, t3, t2); 644 645 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ 646 for (i = 0; i < 10; ++i) 647 fe51_sq(t2, t2); 648 649 /* t1 = z ** (2 ** 50 - 1) */ 650 fe51_mul(t1, t2, t1); 651 652 /* t2 = z ** (2 ** 100 - 1) */ 653 fe51_sq(t2, t1); 654 for (i = 1; i < 50; ++i) 655 fe51_sq(t2, t2); 656 657 fe51_mul(t2, t2, t1); 658 659 /* t2 = z ** (2 ** 200 - 1) */ 660 fe51_sq(t3, t2); 661 for (i = 1; i < 100; ++i) 662 fe51_sq(t3, t3); 663 664 fe51_mul(t2, t3, t2); 665 666 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ 667 for (i = 0; i < 50; ++i) 668 fe51_sq(t2, t2); 669 670 /* t1 = z ** (2 ** 250 - 1) */ 671 fe51_mul(t1, t2, t1); 672 673 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ 674 for (i = 0; i < 5; ++i) 675 fe51_sq(t1, t1); 676 677 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ 678 fe51_mul(out, t1, t0); 679 } 680 681 /* 682 * Duplicate of original x25519_scalar_mult_generic, but using 683 * fe51_* subroutines. 684 */ 685 static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], 686 const uint8_t point[32]) 687 { 688 fe51 x1, x2, z2, x3, z3, tmp0, tmp1; 689 uint8_t e[32]; 690 unsigned swap = 0; 691 int pos; 692 693 # ifdef BASE_2_64_IMPLEMENTED 694 if (x25519_fe64_eligible()) { 695 x25519_scalar_mulx(out, scalar, point); 696 return; 697 } 698 # endif 699 700 memcpy(e, scalar, 32); 701 e[0] &= 0xf8; 702 e[31] &= 0x7f; 703 e[31] |= 0x40; 704 fe51_frombytes(x1, point); 705 fe51_1(x2); 706 fe51_0(z2); 707 fe51_copy(x3, x1); 708 fe51_1(z3); 709 710 for (pos = 254; pos >= 0; --pos) { 711 unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); 712 713 swap ^= b; 714 fe51_cswap(x2, x3, swap); 715 fe51_cswap(z2, z3, swap); 716 swap = b; 717 fe51_sub(tmp0, x3, z3); 718 fe51_sub(tmp1, x2, z2); 719 fe51_add(x2, x2, z2); 720 fe51_add(z2, x3, z3); 721 fe51_mul(z3, tmp0, x2); 722 fe51_mul(z2, z2, tmp1); 723 fe51_sq(tmp0, tmp1); 724 fe51_sq(tmp1, x2); 725 fe51_add(x3, z3, z2); 726 fe51_sub(z2, z3, z2); 727 fe51_mul(x2, tmp1, tmp0); 728 fe51_sub(tmp1, tmp1, tmp0); 729 fe51_sq(z2, z2); 730 fe51_mul121666(z3, tmp1); 731 fe51_sq(x3, x3); 732 fe51_add(tmp0, tmp0, z3); 733 fe51_mul(z3, x1, z2); 734 fe51_mul(z2, tmp1, tmp0); 735 } 736 737 fe51_invert(z2, z2); 738 fe51_mul(x2, x2, z2); 739 fe51_tobytes(out, x2); 740 741 OPENSSL_cleanse(e, sizeof(e)); 742 } 743 #endif 744 745 /* 746 * Reference base 2^25.5 implementation. 747 */ 748 /* 749 * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP 750 * 20141124 (http://bench.cr.yp.to/supercop.html). 751 * 752 * The field functions are shared by Ed25519 and X25519 where possible. 753 */ 754 755 /* fe means field element. Here the field is \Z/(2^255-19). An element t, 756 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 757 * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on 758 * context. */ 759 typedef int32_t fe[10]; 760 761 static const int64_t kBottom25Bits = 0x1ffffffLL; 762 static const int64_t kBottom26Bits = 0x3ffffffLL; 763 static const int64_t kTop39Bits = 0xfffffffffe000000LL; 764 static const int64_t kTop38Bits = 0xfffffffffc000000LL; 765 766 static uint64_t load_3(const uint8_t *in) { 767 uint64_t result; 768 result = (uint64_t)in[0]; 769 result |= ((uint64_t)in[1]) << 8; 770 result |= ((uint64_t)in[2]) << 16; 771 return result; 772 } 773 774 static uint64_t load_4(const uint8_t *in) { 775 uint64_t result; 776 result = (uint64_t)in[0]; 777 result |= ((uint64_t)in[1]) << 8; 778 result |= ((uint64_t)in[2]) << 16; 779 result |= ((uint64_t)in[3]) << 24; 780 return result; 781 } 782 783 static void fe_frombytes(fe h, const uint8_t *s) { 784 /* Ignores top bit of h. */ 785 int64_t h0 = load_4(s); 786 int64_t h1 = load_3(s + 4) << 6; 787 int64_t h2 = load_3(s + 7) << 5; 788 int64_t h3 = load_3(s + 10) << 3; 789 int64_t h4 = load_3(s + 13) << 2; 790 int64_t h5 = load_4(s + 16); 791 int64_t h6 = load_3(s + 20) << 7; 792 int64_t h7 = load_3(s + 23) << 5; 793 int64_t h8 = load_3(s + 26) << 4; 794 int64_t h9 = (load_3(s + 29) & 8388607) << 2; 795 int64_t carry0; 796 int64_t carry1; 797 int64_t carry2; 798 int64_t carry3; 799 int64_t carry4; 800 int64_t carry5; 801 int64_t carry6; 802 int64_t carry7; 803 int64_t carry8; 804 int64_t carry9; 805 806 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; 807 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; 808 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; 809 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; 810 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; 811 812 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; 813 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; 814 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; 815 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; 816 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; 817 818 h[0] = (int32_t)h0; 819 h[1] = (int32_t)h1; 820 h[2] = (int32_t)h2; 821 h[3] = (int32_t)h3; 822 h[4] = (int32_t)h4; 823 h[5] = (int32_t)h5; 824 h[6] = (int32_t)h6; 825 h[7] = (int32_t)h7; 826 h[8] = (int32_t)h8; 827 h[9] = (int32_t)h9; 828 } 829 830 /* Preconditions: 831 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. 832 * 833 * Write p=2^255-19; q=floor(h/p). 834 * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). 835 * 836 * Proof: 837 * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. 838 * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. 839 * 840 * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). 841 * Then 0<y<1. 842 * 843 * Write r=h-pq. 844 * Have 0<=r<=p-1=2^255-20. 845 * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. 846 * 847 * Write x=r+19(2^-255)r+y. 848 * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. 849 * 850 * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) 851 * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ 852 static void fe_tobytes(uint8_t *s, const fe h) { 853 int32_t h0 = h[0]; 854 int32_t h1 = h[1]; 855 int32_t h2 = h[2]; 856 int32_t h3 = h[3]; 857 int32_t h4 = h[4]; 858 int32_t h5 = h[5]; 859 int32_t h6 = h[6]; 860 int32_t h7 = h[7]; 861 int32_t h8 = h[8]; 862 int32_t h9 = h[9]; 863 int32_t q; 864 865 q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; 866 q = (h0 + q) >> 26; 867 q = (h1 + q) >> 25; 868 q = (h2 + q) >> 26; 869 q = (h3 + q) >> 25; 870 q = (h4 + q) >> 26; 871 q = (h5 + q) >> 25; 872 q = (h6 + q) >> 26; 873 q = (h7 + q) >> 25; 874 q = (h8 + q) >> 26; 875 q = (h9 + q) >> 25; 876 877 /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ 878 h0 += 19 * q; 879 /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ 880 881 h1 += h0 >> 26; h0 &= kBottom26Bits; 882 h2 += h1 >> 25; h1 &= kBottom25Bits; 883 h3 += h2 >> 26; h2 &= kBottom26Bits; 884 h4 += h3 >> 25; h3 &= kBottom25Bits; 885 h5 += h4 >> 26; h4 &= kBottom26Bits; 886 h6 += h5 >> 25; h5 &= kBottom25Bits; 887 h7 += h6 >> 26; h6 &= kBottom26Bits; 888 h8 += h7 >> 25; h7 &= kBottom25Bits; 889 h9 += h8 >> 26; h8 &= kBottom26Bits; 890 h9 &= kBottom25Bits; 891 /* h10 = carry9 */ 892 893 /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. 894 * Have h0+...+2^230 h9 between 0 and 2^255-1; 895 * evidently 2^255 h10-2^255 q = 0. 896 * Goal: Output h0+...+2^230 h9. */ 897 898 s[0] = (uint8_t)(h0 >> 0); 899 s[1] = (uint8_t)(h0 >> 8); 900 s[2] = (uint8_t)(h0 >> 16); 901 s[3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2)); 902 s[4] = (uint8_t)(h1 >> 6); 903 s[5] = (uint8_t)(h1 >> 14); 904 s[6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3)); 905 s[7] = (uint8_t)(h2 >> 5); 906 s[8] = (uint8_t)(h2 >> 13); 907 s[9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5)); 908 s[10] = (uint8_t)(h3 >> 3); 909 s[11] = (uint8_t)(h3 >> 11); 910 s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6)); 911 s[13] = (uint8_t)(h4 >> 2); 912 s[14] = (uint8_t)(h4 >> 10); 913 s[15] = (uint8_t)(h4 >> 18); 914 s[16] = (uint8_t)(h5 >> 0); 915 s[17] = (uint8_t)(h5 >> 8); 916 s[18] = (uint8_t)(h5 >> 16); 917 s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1)); 918 s[20] = (uint8_t)(h6 >> 7); 919 s[21] = (uint8_t)(h6 >> 15); 920 s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3)); 921 s[23] = (uint8_t)(h7 >> 5); 922 s[24] = (uint8_t)(h7 >> 13); 923 s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4)); 924 s[26] = (uint8_t)(h8 >> 4); 925 s[27] = (uint8_t)(h8 >> 12); 926 s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6)); 927 s[29] = (uint8_t)(h9 >> 2); 928 s[30] = (uint8_t)(h9 >> 10); 929 s[31] = (uint8_t)(h9 >> 18); 930 } 931 932 /* h = f */ 933 static void fe_copy(fe h, const fe f) { 934 memmove(h, f, sizeof(int32_t) * 10); 935 } 936 937 /* h = 0 */ 938 static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } 939 940 /* h = 1 */ 941 static void fe_1(fe h) { 942 memset(h, 0, sizeof(int32_t) * 10); 943 h[0] = 1; 944 } 945 946 /* h = f + g 947 * Can overlap h with f or g. 948 * 949 * Preconditions: 950 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. 951 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. 952 * 953 * Postconditions: 954 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ 955 static void fe_add(fe h, const fe f, const fe g) { 956 unsigned i; 957 for (i = 0; i < 10; i++) { 958 h[i] = f[i] + g[i]; 959 } 960 } 961 962 /* h = f - g 963 * Can overlap h with f or g. 964 * 965 * Preconditions: 966 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. 967 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. 968 * 969 * Postconditions: 970 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ 971 static void fe_sub(fe h, const fe f, const fe g) { 972 unsigned i; 973 for (i = 0; i < 10; i++) { 974 h[i] = f[i] - g[i]; 975 } 976 } 977 978 /* h = f * g 979 * Can overlap h with f or g. 980 * 981 * Preconditions: 982 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. 983 * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. 984 * 985 * Postconditions: 986 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. 987 * 988 * Notes on implementation strategy: 989 * 990 * Using schoolbook multiplication. 991 * Karatsuba would save a little in some cost models. 992 * 993 * Most multiplications by 2 and 19 are 32-bit precomputations; 994 * cheaper than 64-bit postcomputations. 995 * 996 * There is one remaining multiplication by 19 in the carry chain; 997 * one *19 precomputation can be merged into this, 998 * but the resulting data flow is considerably less clean. 999 * 1000 * There are 12 carries below. 1001 * 10 of them are 2-way parallelizable and vectorizable. 1002 * Can get away with 11 carries, but then data flow is much deeper. 1003 * 1004 * With tighter constraints on inputs can squeeze carries into int32. */ 1005 static void fe_mul(fe h, const fe f, const fe g) { 1006 int32_t f0 = f[0]; 1007 int32_t f1 = f[1]; 1008 int32_t f2 = f[2]; 1009 int32_t f3 = f[3]; 1010 int32_t f4 = f[4]; 1011 int32_t f5 = f[5]; 1012 int32_t f6 = f[6]; 1013 int32_t f7 = f[7]; 1014 int32_t f8 = f[8]; 1015 int32_t f9 = f[9]; 1016 int32_t g0 = g[0]; 1017 int32_t g1 = g[1]; 1018 int32_t g2 = g[2]; 1019 int32_t g3 = g[3]; 1020 int32_t g4 = g[4]; 1021 int32_t g5 = g[5]; 1022 int32_t g6 = g[6]; 1023 int32_t g7 = g[7]; 1024 int32_t g8 = g[8]; 1025 int32_t g9 = g[9]; 1026 int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ 1027 int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ 1028 int32_t g3_19 = 19 * g3; 1029 int32_t g4_19 = 19 * g4; 1030 int32_t g5_19 = 19 * g5; 1031 int32_t g6_19 = 19 * g6; 1032 int32_t g7_19 = 19 * g7; 1033 int32_t g8_19 = 19 * g8; 1034 int32_t g9_19 = 19 * g9; 1035 int32_t f1_2 = 2 * f1; 1036 int32_t f3_2 = 2 * f3; 1037 int32_t f5_2 = 2 * f5; 1038 int32_t f7_2 = 2 * f7; 1039 int32_t f9_2 = 2 * f9; 1040 int64_t f0g0 = f0 * (int64_t) g0; 1041 int64_t f0g1 = f0 * (int64_t) g1; 1042 int64_t f0g2 = f0 * (int64_t) g2; 1043 int64_t f0g3 = f0 * (int64_t) g3; 1044 int64_t f0g4 = f0 * (int64_t) g4; 1045 int64_t f0g5 = f0 * (int64_t) g5; 1046 int64_t f0g6 = f0 * (int64_t) g6; 1047 int64_t f0g7 = f0 * (int64_t) g7; 1048 int64_t f0g8 = f0 * (int64_t) g8; 1049 int64_t f0g9 = f0 * (int64_t) g9; 1050 int64_t f1g0 = f1 * (int64_t) g0; 1051 int64_t f1g1_2 = f1_2 * (int64_t) g1; 1052 int64_t f1g2 = f1 * (int64_t) g2; 1053 int64_t f1g3_2 = f1_2 * (int64_t) g3; 1054 int64_t f1g4 = f1 * (int64_t) g4; 1055 int64_t f1g5_2 = f1_2 * (int64_t) g5; 1056 int64_t f1g6 = f1 * (int64_t) g6; 1057 int64_t f1g7_2 = f1_2 * (int64_t) g7; 1058 int64_t f1g8 = f1 * (int64_t) g8; 1059 int64_t f1g9_38 = f1_2 * (int64_t) g9_19; 1060 int64_t f2g0 = f2 * (int64_t) g0; 1061 int64_t f2g1 = f2 * (int64_t) g1; 1062 int64_t f2g2 = f2 * (int64_t) g2; 1063 int64_t f2g3 = f2 * (int64_t) g3; 1064 int64_t f2g4 = f2 * (int64_t) g4; 1065 int64_t f2g5 = f2 * (int64_t) g5; 1066 int64_t f2g6 = f2 * (int64_t) g6; 1067 int64_t f2g7 = f2 * (int64_t) g7; 1068 int64_t f2g8_19 = f2 * (int64_t) g8_19; 1069 int64_t f2g9_19 = f2 * (int64_t) g9_19; 1070 int64_t f3g0 = f3 * (int64_t) g0; 1071 int64_t f3g1_2 = f3_2 * (int64_t) g1; 1072 int64_t f3g2 = f3 * (int64_t) g2; 1073 int64_t f3g3_2 = f3_2 * (int64_t) g3; 1074 int64_t f3g4 = f3 * (int64_t) g4; 1075 int64_t f3g5_2 = f3_2 * (int64_t) g5; 1076 int64_t f3g6 = f3 * (int64_t) g6; 1077 int64_t f3g7_38 = f3_2 * (int64_t) g7_19; 1078 int64_t f3g8_19 = f3 * (int64_t) g8_19; 1079 int64_t f3g9_38 = f3_2 * (int64_t) g9_19; 1080 int64_t f4g0 = f4 * (int64_t) g0; 1081 int64_t f4g1 = f4 * (int64_t) g1; 1082 int64_t f4g2 = f4 * (int64_t) g2; 1083 int64_t f4g3 = f4 * (int64_t) g3; 1084 int64_t f4g4 = f4 * (int64_t) g4; 1085 int64_t f4g5 = f4 * (int64_t) g5; 1086 int64_t f4g6_19 = f4 * (int64_t) g6_19; 1087 int64_t f4g7_19 = f4 * (int64_t) g7_19; 1088 int64_t f4g8_19 = f4 * (int64_t) g8_19; 1089 int64_t f4g9_19 = f4 * (int64_t) g9_19; 1090 int64_t f5g0 = f5 * (int64_t) g0; 1091 int64_t f5g1_2 = f5_2 * (int64_t) g1; 1092 int64_t f5g2 = f5 * (int64_t) g2; 1093 int64_t f5g3_2 = f5_2 * (int64_t) g3; 1094 int64_t f5g4 = f5 * (int64_t) g4; 1095 int64_t f5g5_38 = f5_2 * (int64_t) g5_19; 1096 int64_t f5g6_19 = f5 * (int64_t) g6_19; 1097 int64_t f5g7_38 = f5_2 * (int64_t) g7_19; 1098 int64_t f5g8_19 = f5 * (int64_t) g8_19; 1099 int64_t f5g9_38 = f5_2 * (int64_t) g9_19; 1100 int64_t f6g0 = f6 * (int64_t) g0; 1101 int64_t f6g1 = f6 * (int64_t) g1; 1102 int64_t f6g2 = f6 * (int64_t) g2; 1103 int64_t f6g3 = f6 * (int64_t) g3; 1104 int64_t f6g4_19 = f6 * (int64_t) g4_19; 1105 int64_t f6g5_19 = f6 * (int64_t) g5_19; 1106 int64_t f6g6_19 = f6 * (int64_t) g6_19; 1107 int64_t f6g7_19 = f6 * (int64_t) g7_19; 1108 int64_t f6g8_19 = f6 * (int64_t) g8_19; 1109 int64_t f6g9_19 = f6 * (int64_t) g9_19; 1110 int64_t f7g0 = f7 * (int64_t) g0; 1111 int64_t f7g1_2 = f7_2 * (int64_t) g1; 1112 int64_t f7g2 = f7 * (int64_t) g2; 1113 int64_t f7g3_38 = f7_2 * (int64_t) g3_19; 1114 int64_t f7g4_19 = f7 * (int64_t) g4_19; 1115 int64_t f7g5_38 = f7_2 * (int64_t) g5_19; 1116 int64_t f7g6_19 = f7 * (int64_t) g6_19; 1117 int64_t f7g7_38 = f7_2 * (int64_t) g7_19; 1118 int64_t f7g8_19 = f7 * (int64_t) g8_19; 1119 int64_t f7g9_38 = f7_2 * (int64_t) g9_19; 1120 int64_t f8g0 = f8 * (int64_t) g0; 1121 int64_t f8g1 = f8 * (int64_t) g1; 1122 int64_t f8g2_19 = f8 * (int64_t) g2_19; 1123 int64_t f8g3_19 = f8 * (int64_t) g3_19; 1124 int64_t f8g4_19 = f8 * (int64_t) g4_19; 1125 int64_t f8g5_19 = f8 * (int64_t) g5_19; 1126 int64_t f8g6_19 = f8 * (int64_t) g6_19; 1127 int64_t f8g7_19 = f8 * (int64_t) g7_19; 1128 int64_t f8g8_19 = f8 * (int64_t) g8_19; 1129 int64_t f8g9_19 = f8 * (int64_t) g9_19; 1130 int64_t f9g0 = f9 * (int64_t) g0; 1131 int64_t f9g1_38 = f9_2 * (int64_t) g1_19; 1132 int64_t f9g2_19 = f9 * (int64_t) g2_19; 1133 int64_t f9g3_38 = f9_2 * (int64_t) g3_19; 1134 int64_t f9g4_19 = f9 * (int64_t) g4_19; 1135 int64_t f9g5_38 = f9_2 * (int64_t) g5_19; 1136 int64_t f9g6_19 = f9 * (int64_t) g6_19; 1137 int64_t f9g7_38 = f9_2 * (int64_t) g7_19; 1138 int64_t f9g8_19 = f9 * (int64_t) g8_19; 1139 int64_t f9g9_38 = f9_2 * (int64_t) g9_19; 1140 int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; 1141 int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; 1142 int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; 1143 int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; 1144 int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; 1145 int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; 1146 int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; 1147 int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; 1148 int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; 1149 int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; 1150 int64_t carry0; 1151 int64_t carry1; 1152 int64_t carry2; 1153 int64_t carry3; 1154 int64_t carry4; 1155 int64_t carry5; 1156 int64_t carry6; 1157 int64_t carry7; 1158 int64_t carry8; 1159 int64_t carry9; 1160 1161 /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) 1162 * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 1163 * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) 1164 * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ 1165 1166 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; 1167 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; 1168 /* |h0| <= 2^25 */ 1169 /* |h4| <= 2^25 */ 1170 /* |h1| <= 1.71*2^59 */ 1171 /* |h5| <= 1.71*2^59 */ 1172 1173 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; 1174 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; 1175 /* |h1| <= 2^24; from now on fits into int32 */ 1176 /* |h5| <= 2^24; from now on fits into int32 */ 1177 /* |h2| <= 1.41*2^60 */ 1178 /* |h6| <= 1.41*2^60 */ 1179 1180 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; 1181 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; 1182 /* |h2| <= 2^25; from now on fits into int32 unchanged */ 1183 /* |h6| <= 2^25; from now on fits into int32 unchanged */ 1184 /* |h3| <= 1.71*2^59 */ 1185 /* |h7| <= 1.71*2^59 */ 1186 1187 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; 1188 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; 1189 /* |h3| <= 2^24; from now on fits into int32 unchanged */ 1190 /* |h7| <= 2^24; from now on fits into int32 unchanged */ 1191 /* |h4| <= 1.72*2^34 */ 1192 /* |h8| <= 1.41*2^60 */ 1193 1194 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; 1195 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; 1196 /* |h4| <= 2^25; from now on fits into int32 unchanged */ 1197 /* |h8| <= 2^25; from now on fits into int32 unchanged */ 1198 /* |h5| <= 1.01*2^24 */ 1199 /* |h9| <= 1.71*2^59 */ 1200 1201 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; 1202 /* |h9| <= 2^24; from now on fits into int32 unchanged */ 1203 /* |h0| <= 1.1*2^39 */ 1204 1205 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; 1206 /* |h0| <= 2^25; from now on fits into int32 unchanged */ 1207 /* |h1| <= 1.01*2^24 */ 1208 1209 h[0] = (int32_t)h0; 1210 h[1] = (int32_t)h1; 1211 h[2] = (int32_t)h2; 1212 h[3] = (int32_t)h3; 1213 h[4] = (int32_t)h4; 1214 h[5] = (int32_t)h5; 1215 h[6] = (int32_t)h6; 1216 h[7] = (int32_t)h7; 1217 h[8] = (int32_t)h8; 1218 h[9] = (int32_t)h9; 1219 } 1220 1221 /* h = f * f 1222 * Can overlap h with f. 1223 * 1224 * Preconditions: 1225 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. 1226 * 1227 * Postconditions: 1228 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. 1229 * 1230 * See fe_mul.c for discussion of implementation strategy. */ 1231 static void fe_sq(fe h, const fe f) { 1232 int32_t f0 = f[0]; 1233 int32_t f1 = f[1]; 1234 int32_t f2 = f[2]; 1235 int32_t f3 = f[3]; 1236 int32_t f4 = f[4]; 1237 int32_t f5 = f[5]; 1238 int32_t f6 = f[6]; 1239 int32_t f7 = f[7]; 1240 int32_t f8 = f[8]; 1241 int32_t f9 = f[9]; 1242 int32_t f0_2 = 2 * f0; 1243 int32_t f1_2 = 2 * f1; 1244 int32_t f2_2 = 2 * f2; 1245 int32_t f3_2 = 2 * f3; 1246 int32_t f4_2 = 2 * f4; 1247 int32_t f5_2 = 2 * f5; 1248 int32_t f6_2 = 2 * f6; 1249 int32_t f7_2 = 2 * f7; 1250 int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ 1251 int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ 1252 int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ 1253 int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ 1254 int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ 1255 int64_t f0f0 = f0 * (int64_t) f0; 1256 int64_t f0f1_2 = f0_2 * (int64_t) f1; 1257 int64_t f0f2_2 = f0_2 * (int64_t) f2; 1258 int64_t f0f3_2 = f0_2 * (int64_t) f3; 1259 int64_t f0f4_2 = f0_2 * (int64_t) f4; 1260 int64_t f0f5_2 = f0_2 * (int64_t) f5; 1261 int64_t f0f6_2 = f0_2 * (int64_t) f6; 1262 int64_t f0f7_2 = f0_2 * (int64_t) f7; 1263 int64_t f0f8_2 = f0_2 * (int64_t) f8; 1264 int64_t f0f9_2 = f0_2 * (int64_t) f9; 1265 int64_t f1f1_2 = f1_2 * (int64_t) f1; 1266 int64_t f1f2_2 = f1_2 * (int64_t) f2; 1267 int64_t f1f3_4 = f1_2 * (int64_t) f3_2; 1268 int64_t f1f4_2 = f1_2 * (int64_t) f4; 1269 int64_t f1f5_4 = f1_2 * (int64_t) f5_2; 1270 int64_t f1f6_2 = f1_2 * (int64_t) f6; 1271 int64_t f1f7_4 = f1_2 * (int64_t) f7_2; 1272 int64_t f1f8_2 = f1_2 * (int64_t) f8; 1273 int64_t f1f9_76 = f1_2 * (int64_t) f9_38; 1274 int64_t f2f2 = f2 * (int64_t) f2; 1275 int64_t f2f3_2 = f2_2 * (int64_t) f3; 1276 int64_t f2f4_2 = f2_2 * (int64_t) f4; 1277 int64_t f2f5_2 = f2_2 * (int64_t) f5; 1278 int64_t f2f6_2 = f2_2 * (int64_t) f6; 1279 int64_t f2f7_2 = f2_2 * (int64_t) f7; 1280 int64_t f2f8_38 = f2_2 * (int64_t) f8_19; 1281 int64_t f2f9_38 = f2 * (int64_t) f9_38; 1282 int64_t f3f3_2 = f3_2 * (int64_t) f3; 1283 int64_t f3f4_2 = f3_2 * (int64_t) f4; 1284 int64_t f3f5_4 = f3_2 * (int64_t) f5_2; 1285 int64_t f3f6_2 = f3_2 * (int64_t) f6; 1286 int64_t f3f7_76 = f3_2 * (int64_t) f7_38; 1287 int64_t f3f8_38 = f3_2 * (int64_t) f8_19; 1288 int64_t f3f9_76 = f3_2 * (int64_t) f9_38; 1289 int64_t f4f4 = f4 * (int64_t) f4; 1290 int64_t f4f5_2 = f4_2 * (int64_t) f5; 1291 int64_t f4f6_38 = f4_2 * (int64_t) f6_19; 1292 int64_t f4f7_38 = f4 * (int64_t) f7_38; 1293 int64_t f4f8_38 = f4_2 * (int64_t) f8_19; 1294 int64_t f4f9_38 = f4 * (int64_t) f9_38; 1295 int64_t f5f5_38 = f5 * (int64_t) f5_38; 1296 int64_t f5f6_38 = f5_2 * (int64_t) f6_19; 1297 int64_t f5f7_76 = f5_2 * (int64_t) f7_38; 1298 int64_t f5f8_38 = f5_2 * (int64_t) f8_19; 1299 int64_t f5f9_76 = f5_2 * (int64_t) f9_38; 1300 int64_t f6f6_19 = f6 * (int64_t) f6_19; 1301 int64_t f6f7_38 = f6 * (int64_t) f7_38; 1302 int64_t f6f8_38 = f6_2 * (int64_t) f8_19; 1303 int64_t f6f9_38 = f6 * (int64_t) f9_38; 1304 int64_t f7f7_38 = f7 * (int64_t) f7_38; 1305 int64_t f7f8_38 = f7_2 * (int64_t) f8_19; 1306 int64_t f7f9_76 = f7_2 * (int64_t) f9_38; 1307 int64_t f8f8_19 = f8 * (int64_t) f8_19; 1308 int64_t f8f9_38 = f8 * (int64_t) f9_38; 1309 int64_t f9f9_38 = f9 * (int64_t) f9_38; 1310 int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; 1311 int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; 1312 int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; 1313 int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; 1314 int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; 1315 int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; 1316 int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; 1317 int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; 1318 int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; 1319 int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; 1320 int64_t carry0; 1321 int64_t carry1; 1322 int64_t carry2; 1323 int64_t carry3; 1324 int64_t carry4; 1325 int64_t carry5; 1326 int64_t carry6; 1327 int64_t carry7; 1328 int64_t carry8; 1329 int64_t carry9; 1330 1331 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; 1332 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; 1333 1334 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; 1335 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; 1336 1337 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; 1338 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; 1339 1340 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; 1341 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; 1342 1343 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; 1344 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; 1345 1346 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; 1347 1348 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; 1349 1350 h[0] = (int32_t)h0; 1351 h[1] = (int32_t)h1; 1352 h[2] = (int32_t)h2; 1353 h[3] = (int32_t)h3; 1354 h[4] = (int32_t)h4; 1355 h[5] = (int32_t)h5; 1356 h[6] = (int32_t)h6; 1357 h[7] = (int32_t)h7; 1358 h[8] = (int32_t)h8; 1359 h[9] = (int32_t)h9; 1360 } 1361 1362 static void fe_invert(fe out, const fe z) { 1363 fe t0; 1364 fe t1; 1365 fe t2; 1366 fe t3; 1367 int i; 1368 1369 /* 1370 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as 1371 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. 1372 */ 1373 1374 /* t0 = z ** 2 */ 1375 fe_sq(t0, z); 1376 1377 /* t1 = t0 ** (2 ** 2) = z ** 8 */ 1378 fe_sq(t1, t0); 1379 fe_sq(t1, t1); 1380 1381 /* t1 = z * t1 = z ** 9 */ 1382 fe_mul(t1, z, t1); 1383 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ 1384 fe_mul(t0, t0, t1); 1385 1386 /* t2 = t0 ** 2 = z ** 22 */ 1387 fe_sq(t2, t0); 1388 1389 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ 1390 fe_mul(t1, t1, t2); 1391 1392 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ 1393 fe_sq(t2, t1); 1394 for (i = 1; i < 5; ++i) { 1395 fe_sq(t2, t2); 1396 } 1397 1398 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ 1399 fe_mul(t1, t2, t1); 1400 1401 /* Continuing similarly... */ 1402 1403 /* t2 = z ** (2 ** 20 - 1) */ 1404 fe_sq(t2, t1); 1405 for (i = 1; i < 10; ++i) { 1406 fe_sq(t2, t2); 1407 } 1408 fe_mul(t2, t2, t1); 1409 1410 /* t2 = z ** (2 ** 40 - 1) */ 1411 fe_sq(t3, t2); 1412 for (i = 1; i < 20; ++i) { 1413 fe_sq(t3, t3); 1414 } 1415 fe_mul(t2, t3, t2); 1416 1417 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ 1418 for (i = 0; i < 10; ++i) { 1419 fe_sq(t2, t2); 1420 } 1421 /* t1 = z ** (2 ** 50 - 1) */ 1422 fe_mul(t1, t2, t1); 1423 1424 /* t2 = z ** (2 ** 100 - 1) */ 1425 fe_sq(t2, t1); 1426 for (i = 1; i < 50; ++i) { 1427 fe_sq(t2, t2); 1428 } 1429 fe_mul(t2, t2, t1); 1430 1431 /* t2 = z ** (2 ** 200 - 1) */ 1432 fe_sq(t3, t2); 1433 for (i = 1; i < 100; ++i) { 1434 fe_sq(t3, t3); 1435 } 1436 fe_mul(t2, t3, t2); 1437 1438 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ 1439 fe_sq(t2, t2); 1440 for (i = 1; i < 50; ++i) { 1441 fe_sq(t2, t2); 1442 } 1443 1444 /* t1 = z ** (2 ** 250 - 1) */ 1445 fe_mul(t1, t2, t1); 1446 1447 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ 1448 fe_sq(t1, t1); 1449 for (i = 1; i < 5; ++i) { 1450 fe_sq(t1, t1); 1451 } 1452 1453 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ 1454 fe_mul(out, t1, t0); 1455 } 1456 1457 /* h = -f 1458 * 1459 * Preconditions: 1460 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. 1461 * 1462 * Postconditions: 1463 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ 1464 static void fe_neg(fe h, const fe f) { 1465 unsigned i; 1466 for (i = 0; i < 10; i++) { 1467 h[i] = -f[i]; 1468 } 1469 } 1470 1471 /* Replace (f,g) with (g,g) if b == 1; 1472 * replace (f,g) with (f,g) if b == 0. 1473 * 1474 * Preconditions: b in {0,1}. */ 1475 static void fe_cmov(fe f, const fe g, unsigned b) { 1476 size_t i; 1477 b = 0-b; 1478 for (i = 0; i < 10; i++) { 1479 int32_t x = f[i] ^ g[i]; 1480 x &= b; 1481 f[i] ^= x; 1482 } 1483 } 1484 1485 /* return 0 if f == 0 1486 * return 1 if f != 0 1487 * 1488 * Preconditions: 1489 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ 1490 static int fe_isnonzero(const fe f) { 1491 uint8_t s[32]; 1492 static const uint8_t zero[32] = {0}; 1493 fe_tobytes(s, f); 1494 1495 return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; 1496 } 1497 1498 /* return 1 if f is in {1,3,5,...,q-2} 1499 * return 0 if f is in {0,2,4,...,q-1} 1500 * 1501 * Preconditions: 1502 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ 1503 static int fe_isnegative(const fe f) { 1504 uint8_t s[32]; 1505 fe_tobytes(s, f); 1506 return s[0] & 1; 1507 } 1508 1509 /* h = 2 * f * f 1510 * Can overlap h with f. 1511 * 1512 * Preconditions: 1513 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. 1514 * 1515 * Postconditions: 1516 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. 1517 * 1518 * See fe_mul.c for discussion of implementation strategy. */ 1519 static void fe_sq2(fe h, const fe f) { 1520 int32_t f0 = f[0]; 1521 int32_t f1 = f[1]; 1522 int32_t f2 = f[2]; 1523 int32_t f3 = f[3]; 1524 int32_t f4 = f[4]; 1525 int32_t f5 = f[5]; 1526 int32_t f6 = f[6]; 1527 int32_t f7 = f[7]; 1528 int32_t f8 = f[8]; 1529 int32_t f9 = f[9]; 1530 int32_t f0_2 = 2 * f0; 1531 int32_t f1_2 = 2 * f1; 1532 int32_t f2_2 = 2 * f2; 1533 int32_t f3_2 = 2 * f3; 1534 int32_t f4_2 = 2 * f4; 1535 int32_t f5_2 = 2 * f5; 1536 int32_t f6_2 = 2 * f6; 1537 int32_t f7_2 = 2 * f7; 1538 int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ 1539 int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ 1540 int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ 1541 int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ 1542 int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ 1543 int64_t f0f0 = f0 * (int64_t) f0; 1544 int64_t f0f1_2 = f0_2 * (int64_t) f1; 1545 int64_t f0f2_2 = f0_2 * (int64_t) f2; 1546 int64_t f0f3_2 = f0_2 * (int64_t) f3; 1547 int64_t f0f4_2 = f0_2 * (int64_t) f4; 1548 int64_t f0f5_2 = f0_2 * (int64_t) f5; 1549 int64_t f0f6_2 = f0_2 * (int64_t) f6; 1550 int64_t f0f7_2 = f0_2 * (int64_t) f7; 1551 int64_t f0f8_2 = f0_2 * (int64_t) f8; 1552 int64_t f0f9_2 = f0_2 * (int64_t) f9; 1553 int64_t f1f1_2 = f1_2 * (int64_t) f1; 1554 int64_t f1f2_2 = f1_2 * (int64_t) f2; 1555 int64_t f1f3_4 = f1_2 * (int64_t) f3_2; 1556 int64_t f1f4_2 = f1_2 * (int64_t) f4; 1557 int64_t f1f5_4 = f1_2 * (int64_t) f5_2; 1558 int64_t f1f6_2 = f1_2 * (int64_t) f6; 1559 int64_t f1f7_4 = f1_2 * (int64_t) f7_2; 1560 int64_t f1f8_2 = f1_2 * (int64_t) f8; 1561 int64_t f1f9_76 = f1_2 * (int64_t) f9_38; 1562 int64_t f2f2 = f2 * (int64_t) f2; 1563 int64_t f2f3_2 = f2_2 * (int64_t) f3; 1564 int64_t f2f4_2 = f2_2 * (int64_t) f4; 1565 int64_t f2f5_2 = f2_2 * (int64_t) f5; 1566 int64_t f2f6_2 = f2_2 * (int64_t) f6; 1567 int64_t f2f7_2 = f2_2 * (int64_t) f7; 1568 int64_t f2f8_38 = f2_2 * (int64_t) f8_19; 1569 int64_t f2f9_38 = f2 * (int64_t) f9_38; 1570 int64_t f3f3_2 = f3_2 * (int64_t) f3; 1571 int64_t f3f4_2 = f3_2 * (int64_t) f4; 1572 int64_t f3f5_4 = f3_2 * (int64_t) f5_2; 1573 int64_t f3f6_2 = f3_2 * (int64_t) f6; 1574 int64_t f3f7_76 = f3_2 * (int64_t) f7_38; 1575 int64_t f3f8_38 = f3_2 * (int64_t) f8_19; 1576 int64_t f3f9_76 = f3_2 * (int64_t) f9_38; 1577 int64_t f4f4 = f4 * (int64_t) f4; 1578 int64_t f4f5_2 = f4_2 * (int64_t) f5; 1579 int64_t f4f6_38 = f4_2 * (int64_t) f6_19; 1580 int64_t f4f7_38 = f4 * (int64_t) f7_38; 1581 int64_t f4f8_38 = f4_2 * (int64_t) f8_19; 1582 int64_t f4f9_38 = f4 * (int64_t) f9_38; 1583 int64_t f5f5_38 = f5 * (int64_t) f5_38; 1584 int64_t f5f6_38 = f5_2 * (int64_t) f6_19; 1585 int64_t f5f7_76 = f5_2 * (int64_t) f7_38; 1586 int64_t f5f8_38 = f5_2 * (int64_t) f8_19; 1587 int64_t f5f9_76 = f5_2 * (int64_t) f9_38; 1588 int64_t f6f6_19 = f6 * (int64_t) f6_19; 1589 int64_t f6f7_38 = f6 * (int64_t) f7_38; 1590 int64_t f6f8_38 = f6_2 * (int64_t) f8_19; 1591 int64_t f6f9_38 = f6 * (int64_t) f9_38; 1592 int64_t f7f7_38 = f7 * (int64_t) f7_38; 1593 int64_t f7f8_38 = f7_2 * (int64_t) f8_19; 1594 int64_t f7f9_76 = f7_2 * (int64_t) f9_38; 1595 int64_t f8f8_19 = f8 * (int64_t) f8_19; 1596 int64_t f8f9_38 = f8 * (int64_t) f9_38; 1597 int64_t f9f9_38 = f9 * (int64_t) f9_38; 1598 int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; 1599 int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; 1600 int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; 1601 int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; 1602 int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; 1603 int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; 1604 int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; 1605 int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; 1606 int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; 1607 int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; 1608 int64_t carry0; 1609 int64_t carry1; 1610 int64_t carry2; 1611 int64_t carry3; 1612 int64_t carry4; 1613 int64_t carry5; 1614 int64_t carry6; 1615 int64_t carry7; 1616 int64_t carry8; 1617 int64_t carry9; 1618 1619 h0 += h0; 1620 h1 += h1; 1621 h2 += h2; 1622 h3 += h3; 1623 h4 += h4; 1624 h5 += h5; 1625 h6 += h6; 1626 h7 += h7; 1627 h8 += h8; 1628 h9 += h9; 1629 1630 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; 1631 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; 1632 1633 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; 1634 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; 1635 1636 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; 1637 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; 1638 1639 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; 1640 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; 1641 1642 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; 1643 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; 1644 1645 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; 1646 1647 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; 1648 1649 h[0] = (int32_t)h0; 1650 h[1] = (int32_t)h1; 1651 h[2] = (int32_t)h2; 1652 h[3] = (int32_t)h3; 1653 h[4] = (int32_t)h4; 1654 h[5] = (int32_t)h5; 1655 h[6] = (int32_t)h6; 1656 h[7] = (int32_t)h7; 1657 h[8] = (int32_t)h8; 1658 h[9] = (int32_t)h9; 1659 } 1660 1661 static void fe_pow22523(fe out, const fe z) { 1662 fe t0; 1663 fe t1; 1664 fe t2; 1665 int i; 1666 1667 fe_sq(t0, z); 1668 fe_sq(t1, t0); 1669 for (i = 1; i < 2; ++i) { 1670 fe_sq(t1, t1); 1671 } 1672 fe_mul(t1, z, t1); 1673 fe_mul(t0, t0, t1); 1674 fe_sq(t0, t0); 1675 fe_mul(t0, t1, t0); 1676 fe_sq(t1, t0); 1677 for (i = 1; i < 5; ++i) { 1678 fe_sq(t1, t1); 1679 } 1680 fe_mul(t0, t1, t0); 1681 fe_sq(t1, t0); 1682 for (i = 1; i < 10; ++i) { 1683 fe_sq(t1, t1); 1684 } 1685 fe_mul(t1, t1, t0); 1686 fe_sq(t2, t1); 1687 for (i = 1; i < 20; ++i) { 1688 fe_sq(t2, t2); 1689 } 1690 fe_mul(t1, t2, t1); 1691 fe_sq(t1, t1); 1692 for (i = 1; i < 10; ++i) { 1693 fe_sq(t1, t1); 1694 } 1695 fe_mul(t0, t1, t0); 1696 fe_sq(t1, t0); 1697 for (i = 1; i < 50; ++i) { 1698 fe_sq(t1, t1); 1699 } 1700 fe_mul(t1, t1, t0); 1701 fe_sq(t2, t1); 1702 for (i = 1; i < 100; ++i) { 1703 fe_sq(t2, t2); 1704 } 1705 fe_mul(t1, t2, t1); 1706 fe_sq(t1, t1); 1707 for (i = 1; i < 50; ++i) { 1708 fe_sq(t1, t1); 1709 } 1710 fe_mul(t0, t1, t0); 1711 fe_sq(t0, t0); 1712 for (i = 1; i < 2; ++i) { 1713 fe_sq(t0, t0); 1714 } 1715 fe_mul(out, t0, z); 1716 } 1717 1718 /* ge means group element. 1719 1720 * Here the group is the set of pairs (x,y) of field elements (see fe.h) 1721 * satisfying -x^2 + y^2 = 1 + d x^2y^2 1722 * where d = -121665/121666. 1723 * 1724 * Representations: 1725 * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z 1726 * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT 1727 * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T 1728 * ge_precomp (Duif): (y+x,y-x,2dxy) */ 1729 1730 typedef struct { 1731 fe X; 1732 fe Y; 1733 fe Z; 1734 } ge_p2; 1735 1736 typedef struct { 1737 fe X; 1738 fe Y; 1739 fe Z; 1740 fe T; 1741 } ge_p3; 1742 1743 typedef struct { 1744 fe X; 1745 fe Y; 1746 fe Z; 1747 fe T; 1748 } ge_p1p1; 1749 1750 typedef struct { 1751 fe yplusx; 1752 fe yminusx; 1753 fe xy2d; 1754 } ge_precomp; 1755 1756 typedef struct { 1757 fe YplusX; 1758 fe YminusX; 1759 fe Z; 1760 fe T2d; 1761 } ge_cached; 1762 1763 static void ge_tobytes(uint8_t *s, const ge_p2 *h) { 1764 fe recip; 1765 fe x; 1766 fe y; 1767 1768 fe_invert(recip, h->Z); 1769 fe_mul(x, h->X, recip); 1770 fe_mul(y, h->Y, recip); 1771 fe_tobytes(s, y); 1772 s[31] ^= fe_isnegative(x) << 7; 1773 } 1774 1775 static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) { 1776 fe recip; 1777 fe x; 1778 fe y; 1779 1780 fe_invert(recip, h->Z); 1781 fe_mul(x, h->X, recip); 1782 fe_mul(y, h->Y, recip); 1783 fe_tobytes(s, y); 1784 s[31] ^= fe_isnegative(x) << 7; 1785 } 1786 1787 static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, 1788 -8787816, -6275908, -3247719, -18696448, -12055116}; 1789 1790 static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, 1791 -272473, -25146209, -2005654, 326686, 11406482}; 1792 1793 static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { 1794 fe u; 1795 fe v; 1796 fe v3; 1797 fe vxx; 1798 fe check; 1799 1800 fe_frombytes(h->Y, s); 1801 fe_1(h->Z); 1802 fe_sq(u, h->Y); 1803 fe_mul(v, u, d); 1804 fe_sub(u, u, h->Z); /* u = y^2-1 */ 1805 fe_add(v, v, h->Z); /* v = dy^2+1 */ 1806 1807 fe_sq(v3, v); 1808 fe_mul(v3, v3, v); /* v3 = v^3 */ 1809 fe_sq(h->X, v3); 1810 fe_mul(h->X, h->X, v); 1811 fe_mul(h->X, h->X, u); /* x = uv^7 */ 1812 1813 fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ 1814 fe_mul(h->X, h->X, v3); 1815 fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ 1816 1817 fe_sq(vxx, h->X); 1818 fe_mul(vxx, vxx, v); 1819 fe_sub(check, vxx, u); /* vx^2-u */ 1820 if (fe_isnonzero(check)) { 1821 fe_add(check, vxx, u); /* vx^2+u */ 1822 if (fe_isnonzero(check)) { 1823 return -1; 1824 } 1825 fe_mul(h->X, h->X, sqrtm1); 1826 } 1827 1828 if (fe_isnegative(h->X) != (s[31] >> 7)) { 1829 fe_neg(h->X, h->X); 1830 } 1831 1832 fe_mul(h->T, h->X, h->Y); 1833 return 0; 1834 } 1835 1836 static void ge_p2_0(ge_p2 *h) { 1837 fe_0(h->X); 1838 fe_1(h->Y); 1839 fe_1(h->Z); 1840 } 1841 1842 static void ge_p3_0(ge_p3 *h) { 1843 fe_0(h->X); 1844 fe_1(h->Y); 1845 fe_1(h->Z); 1846 fe_0(h->T); 1847 } 1848 1849 static void ge_precomp_0(ge_precomp *h) { 1850 fe_1(h->yplusx); 1851 fe_1(h->yminusx); 1852 fe_0(h->xy2d); 1853 } 1854 1855 /* r = p */ 1856 static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { 1857 fe_copy(r->X, p->X); 1858 fe_copy(r->Y, p->Y); 1859 fe_copy(r->Z, p->Z); 1860 } 1861 1862 static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, 1863 15978800, -12551817, -6495438, 29715968, 9444199}; 1864 1865 /* r = p */ 1866 static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { 1867 fe_add(r->YplusX, p->Y, p->X); 1868 fe_sub(r->YminusX, p->Y, p->X); 1869 fe_copy(r->Z, p->Z); 1870 fe_mul(r->T2d, p->T, d2); 1871 } 1872 1873 /* r = p */ 1874 static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { 1875 fe_mul(r->X, p->X, p->T); 1876 fe_mul(r->Y, p->Y, p->Z); 1877 fe_mul(r->Z, p->Z, p->T); 1878 } 1879 1880 /* r = p */ 1881 static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { 1882 fe_mul(r->X, p->X, p->T); 1883 fe_mul(r->Y, p->Y, p->Z); 1884 fe_mul(r->Z, p->Z, p->T); 1885 fe_mul(r->T, p->X, p->Y); 1886 } 1887 1888 /* r = 2 * p */ 1889 static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { 1890 fe t0; 1891 1892 fe_sq(r->X, p->X); 1893 fe_sq(r->Z, p->Y); 1894 fe_sq2(r->T, p->Z); 1895 fe_add(r->Y, p->X, p->Y); 1896 fe_sq(t0, r->Y); 1897 fe_add(r->Y, r->Z, r->X); 1898 fe_sub(r->Z, r->Z, r->X); 1899 fe_sub(r->X, t0, r->Y); 1900 fe_sub(r->T, r->T, r->Z); 1901 } 1902 1903 /* r = 2 * p */ 1904 static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { 1905 ge_p2 q; 1906 ge_p3_to_p2(&q, p); 1907 ge_p2_dbl(r, &q); 1908 } 1909 1910 /* r = p + q */ 1911 static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { 1912 fe t0; 1913 1914 fe_add(r->X, p->Y, p->X); 1915 fe_sub(r->Y, p->Y, p->X); 1916 fe_mul(r->Z, r->X, q->yplusx); 1917 fe_mul(r->Y, r->Y, q->yminusx); 1918 fe_mul(r->T, q->xy2d, p->T); 1919 fe_add(t0, p->Z, p->Z); 1920 fe_sub(r->X, r->Z, r->Y); 1921 fe_add(r->Y, r->Z, r->Y); 1922 fe_add(r->Z, t0, r->T); 1923 fe_sub(r->T, t0, r->T); 1924 } 1925 1926 /* r = p - q */ 1927 static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { 1928 fe t0; 1929 1930 fe_add(r->X, p->Y, p->X); 1931 fe_sub(r->Y, p->Y, p->X); 1932 fe_mul(r->Z, r->X, q->yminusx); 1933 fe_mul(r->Y, r->Y, q->yplusx); 1934 fe_mul(r->T, q->xy2d, p->T); 1935 fe_add(t0, p->Z, p->Z); 1936 fe_sub(r->X, r->Z, r->Y); 1937 fe_add(r->Y, r->Z, r->Y); 1938 fe_sub(r->Z, t0, r->T); 1939 fe_add(r->T, t0, r->T); 1940 } 1941 1942 /* r = p + q */ 1943 static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { 1944 fe t0; 1945 1946 fe_add(r->X, p->Y, p->X); 1947 fe_sub(r->Y, p->Y, p->X); 1948 fe_mul(r->Z, r->X, q->YplusX); 1949 fe_mul(r->Y, r->Y, q->YminusX); 1950 fe_mul(r->T, q->T2d, p->T); 1951 fe_mul(r->X, p->Z, q->Z); 1952 fe_add(t0, r->X, r->X); 1953 fe_sub(r->X, r->Z, r->Y); 1954 fe_add(r->Y, r->Z, r->Y); 1955 fe_add(r->Z, t0, r->T); 1956 fe_sub(r->T, t0, r->T); 1957 } 1958 1959 /* r = p - q */ 1960 static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { 1961 fe t0; 1962 1963 fe_add(r->X, p->Y, p->X); 1964 fe_sub(r->Y, p->Y, p->X); 1965 fe_mul(r->Z, r->X, q->YminusX); 1966 fe_mul(r->Y, r->Y, q->YplusX); 1967 fe_mul(r->T, q->T2d, p->T); 1968 fe_mul(r->X, p->Z, q->Z); 1969 fe_add(t0, r->X, r->X); 1970 fe_sub(r->X, r->Z, r->Y); 1971 fe_add(r->Y, r->Z, r->Y); 1972 fe_sub(r->Z, t0, r->T); 1973 fe_add(r->T, t0, r->T); 1974 } 1975 1976 static uint8_t equal(signed char b, signed char c) { 1977 uint8_t ub = b; 1978 uint8_t uc = c; 1979 uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ 1980 uint32_t y = x; /* 0: yes; 1..255: no */ 1981 y -= 1; /* 4294967295: yes; 0..254: no */ 1982 y >>= 31; /* 1: yes; 0: no */ 1983 return y; 1984 } 1985 1986 static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { 1987 fe_cmov(t->yplusx, u->yplusx, b); 1988 fe_cmov(t->yminusx, u->yminusx, b); 1989 fe_cmov(t->xy2d, u->xy2d, b); 1990 } 1991 1992 /* k25519Precomp[i][j] = (j+1)*256^i*B */ 1993 static const ge_precomp k25519Precomp[32][8] = { 1994 { 1995 { 1996 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 1997 27544626, -11754271, -6079156, 2047605}, 1998 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 1999 5043384, 19500929, -15469378}, 2000 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 2001 29287919, 11864899, -24514362, -4438546}, 2002 }, 2003 { 2004 {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, 2005 -11717903, -3814571, -358445, -10211303}, 2006 {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, 2007 -15616551, 11189268, -26829678, -5319081}, 2008 {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, 2009 -3128826, -9541118, -15472047, -4166697}, 2010 }, 2011 { 2012 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 2013 27787600, -14772189, 28944400, -1550024}, 2014 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 2015 16354577, -11775962, 7689662, 11199574}, 2016 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 2017 7512774, 10017326, -17749093, -9920357}, 2018 }, 2019 { 2020 {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, 2021 -28926210, 15006023, 3284568, -6276540}, 2022 {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 2023 7464579, 9656445, 13059162, 10374397}, 2024 {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, 2025 -3839045, -641708, -101325}, 2026 }, 2027 { 2028 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 2029 32867885, 14515107, -15438304, 10819380}, 2030 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 2031 12483688, -12668491, 5581306}, 2032 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 2033 28542350, 13850243, -23678021, -15815942}, 2034 }, 2035 { 2036 {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, 2037 -19188627, -15224819, -9818940, -12085777}, 2038 {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, 2039 -15689887, 1762328, 14866737}, 2040 {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, 2041 -28236412, 3959421, 27914454, 4383652}, 2042 }, 2043 { 2044 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 2045 5230134, -23952439, -15175766}, 2046 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 2047 20654025, 16520125, 30598449, 7715701}, 2048 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, 2049 -31400660, 1370708, 29794553, -1409300}, 2050 }, 2051 { 2052 {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 2053 30290735, 10876454, -33154098, 2381726}, 2054 {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, 2055 -6236617, 3696005, -32300832, 15351955}, 2056 {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, 2057 -32961401, -2970515, 29551813, 10109425}, 2058 }, 2059 }, 2060 { 2061 { 2062 {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, 2063 -2378284, -1627556, 10092783, -4764171}, 2064 {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, 2065 -32508754, 12005538, -17810127, 12803510}, 2066 {17228999, -15661624, -1233527, 300140, -1224870, -11714777, 2067 30364213, -9038194, 18016357, 4397660}, 2068 }, 2069 { 2070 {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, 2071 -26619106, 14544525, -17477504, 982639}, 2072 {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, 2073 -4120128, -21047696, 9934963}, 2074 {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, 2075 -14747930, 4559895, -30123922, -10897950}, 2076 }, 2077 { 2078 {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 2079 24191034, 4541697, -13338309, 5500568}, 2080 {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, 2081 -17430592, 12264343, 10874051, 13524335}, 2082 {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 2083 5080568, -22528059, 5376628}, 2084 }, 2085 { 2086 {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, 2087 -22321305, -9447443, 4535768, 1569007}, 2088 {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, 2089 -30494562, 3044290, 31848280, 12543772}, 2090 {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, 2091 -27377195, -2062731, 7718482, 14474653}, 2092 }, 2093 { 2094 {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, 2095 -7236665, 24316168, -5253567}, 2096 {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 2097 33040651, -13424532, -20729456, 8321686}, 2098 {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 2099 23845965, -11874838, -9984458, 608372}, 2100 }, 2101 { 2102 {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 2103 1123968, -6780577, 27229399, 23887}, 2104 {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 2105 12797024, -6440308, -1633405, 16678954}, 2106 {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, 2107 -1508144, -4795045, -17169265, 4904953}, 2108 }, 2109 { 2110 {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 2111 5169211, 16191880, 2128236, -4326833}, 2112 {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, 2113 -29806336, 916033, -6882542, -2986532}, 2114 {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 2115 285431, 2763829, 15736322, 4143876}, 2116 }, 2117 { 2118 {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, 2119 -14594663, 23527084, -16458268}, 2120 {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, 2121 -32625340, 4087881, -15188911, -14416214}, 2122 {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 2123 4357868, -4774191, -16323038}, 2124 }, 2125 }, 2126 { 2127 { 2128 {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 2129 23365147, -3949732, 7390890, 2759800}, 2130 {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, 2131 -4264057, 1244380, -12919645}, 2132 {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 2133 9208236, 15886429, 16489664}, 2134 }, 2135 { 2136 {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, 2137 -13693198, 398369, -30606455, -712933}, 2138 {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 2139 13348553, 12076947, -30836462, 5113182}, 2140 {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, 2141 -30341101, -7336386, 13847711, 5387222}, 2142 }, 2143 { 2144 {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 2145 8763061, 3617786, -19600662, 10370991}, 2146 {20246567, -14369378, 22358229, -543712, 18507283, -10413996, 2147 14554437, -8746092, 32232924, 16763880}, 2148 {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 2149 11094161, 15689506, 3140038, -16510092}, 2150 }, 2151 { 2152 {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, 2153 -27224800, 9448613, -28774454, 366295}, 2154 {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 2155 28344573, 8041113, 719605, 11671788}, 2156 {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, 2157 -15266516, 27000813, -10195553}, 2158 }, 2159 { 2160 {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 2161 5336097, 6750977, -14521026}, 2162 {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 2163 1695823, -8819122, 8169720, 16220347}, 2164 {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, 2165 -11144307, -2627664, -5990708, -14166033}, 2166 }, 2167 { 2168 {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 2169 27884329, 2847284, 2655861, 1738395}, 2170 {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 2171 21651608, -3239336, -19087449, -11005278}, 2172 {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 2173 5821408, 10478196, 8544890}, 2174 }, 2175 { 2176 {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 2177 19270449, 12217473, 17789017, -3395995}, 2178 {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 2179 15479401, -3853233, 30460520, 1052596}, 2180 {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 2181 27491595, -4612359, 3179268, -9478891}, 2182 }, 2183 { 2184 {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, 2185 -14756777, -16411740, 19072640, -9511060}, 2186 {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 2187 5977896, -5215017, 473099, 5040608}, 2188 {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 2189 28326862, 1721092, -19558642, -3131606}, 2190 }, 2191 }, 2192 { 2193 { 2194 {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 2195 8076149, -27868496, 11538389}, 2196 {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 2197 8754525, 7446702, -5676054, 5797016}, 2198 {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2199 2014099, -9050574, -2369172, -5877341}, 2200 }, 2201 { 2202 {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 2203 1192730, -3714199, 15123619, 10811505}, 2204 {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 2205 15776356, -28886779, -11974553}, 2206 {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, 2207 -20654173, -16484855, 4714547, -9600655}, 2208 }, 2209 { 2210 {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 2211 24611599, -4543832, -11745876, 12340220}, 2212 {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 2213 9613953, 8241152, 15370987, 9608631}, 2214 {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 2215 15866074, -28210621, -8814099}, 2216 }, 2217 { 2218 {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 2219 858697, 20571223, 8420556}, 2220 {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 2221 33531827, 12516406, -21574435, -12476749}, 2222 {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 2223 7256740, 8791136, 15069930}, 2224 }, 2225 { 2226 {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 2227 14711875, 4874229, -30663140, -2331391}, 2228 {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, 2229 -7912378, -33069337, 9234253}, 2230 {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 2231 31559055, -11609587, 18979186, 13396066}, 2232 }, 2233 { 2234 {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, 2235 -18816887, 13594782, 33514650, 7021958}, 2236 {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, 2237 -25948728, -3916677, -21480480, 12868082}, 2238 {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, 2239 -21446107, 2244500, -12455797, -8089383}, 2240 }, 2241 { 2242 {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 2243 33086546, 8957937, -15233648, 5540521}, 2244 {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, 2245 -23710744, -1568984, -16128528, -14962807}, 2246 {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 2247 892185, -11513277, -15205948}, 2248 }, 2249 { 2250 {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 2251 4763127, -19179614, 5867134}, 2252 {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 2253 27846559, 5931263, -29749703, -16108455}, 2254 {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 2255 7283490, -15148073, -19526700, 7734629}, 2256 }, 2257 }, 2258 { 2259 { 2260 {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 2261 7585295, -3176626, 18549497, 15302069}, 2262 {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 2263 10458790, -6418461, -8872242, 8424746}, 2264 {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 2265 19206234, 7134917, -11284482, -828919}, 2266 }, 2267 { 2268 {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 2269 10243738, -14685461, -5066034, 16498837}, 2270 {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, 2271 -14124238, 6536641, 10543906}, 2272 {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, 2273 -2669190, -16625574, -27235709, 8876771}, 2274 }, 2275 { 2276 {-25742899, -12566864, -15649966, -846607, -33026686, -796288, 2277 -33481822, 15824474, -604426, -9039817}, 2278 {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, 2279 -4890037, 1657394, 3084098}, 2280 {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 2281 31280319, 14396151, -30233575, 15272409}, 2282 }, 2283 { 2284 {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, 2285 -25173957, -12636138, -25014757, 1950504}, 2286 {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, 2287 -8384306, -8767532, 15341279, 8373727}, 2288 {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 2289 298136, -10232602, -2878207, 15190420}, 2290 }, 2291 { 2292 {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 2293 8669718, 2742393, -26033313, -6875003}, 2294 {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 2295 9291594, -16247779, -12154742, 6048605}, 2296 {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 2297 13934231, 5128323, 11213262, 9168384}, 2298 }, 2299 { 2300 {-26280513, 11007847, 19408960, -940758, -18592965, -4328580, 2301 -5088060, -11105150, 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17081145, -13406266, 21909293, -16067981, 4003 -15136294, -3765346, -21277997, 5473616}, 4004 {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, 4005 -7125085, 12469656, 29111212, -5451014}, 4006 }, 4007 { 4008 {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 4009 24367466, 6388839, -10295587, 452383}, 4010 {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, 4011 -24236251, -5915248, 15766062, 8407814}, 4012 {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, 4013 -8917023, -4388953, -8067909, 2276718}, 4014 }, 4015 { 4016 {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, 4017 -23827587, 5096219, 22740376, -7303417}, 4018 {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 4019 24051124, 13742383, -15637599, 13295222}, 4020 {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, 4021 -17720195, -4612972, -4451357, -14669444}, 4022 }, 4023 { 4024 {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, 4025 -2469266, -4141880, 7770569, 9620597}, 4026 {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, 4027 -1694323, -33502340, -14767970}, 4028 {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 4029 1220118, 30494170, -11440799}, 4030 }, 4031 { 4032 {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, 4033 -26739026, 926050, -1684339, -13333647}, 4034 {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 4035 9021034, 9078865, 3353509, 4033511}, 4036 {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 4037 23161163, 8839127, 27485041, 7356032}, 4038 }, 4039 }, 4040 { 4041 { 4042 {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 4043 2625015, 28431036, -16771834}, 4044 {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, 4045 -22545972, 14150565, 15970762, 4099461}, 4046 {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 4047 13617293, -9937143, 11465739, 8317062}, 4048 }, 4049 { 4050 {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 4051 14898637, 3848455, 20969334, -5157516}, 4052 {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, 4053 -21610826, -3649888, 11177095, 14989547}, 4054 {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 4055 13515641, 2581286, -28487508, 9930240}, 4056 }, 4057 { 4058 {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 4059 18345767, -13403753, 16291481, -5314038}, 4060 {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 4061 6957617, 4368891, 9788741}, 4062 {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, 4063 -21722536, -8613148, 16250552, -11111103}, 4064 }, 4065 { 4066 {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 4067 10604807, -30190403, 4782747}, 4068 {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, 4069 -9981571, 4383045, 22546403, 437323}, 4070 {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 4071 27343084, 2786261, -30633590, -14097016}, 4072 }, 4073 { 4074 {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, 4075 -19690631, 2355319, -19284671, -6114373}, 4076 {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 4077 18952177, 15496498, -29380133, 11754228}, 4078 {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 4079 7141596, 11724556, 22761615, -10134141}, 4080 }, 4081 { 4082 {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, 4083 -28741185, -12227393, 32851222, 11717399}, 4084 {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 4085 31474879, 3483633, -1193175, -4030831}, 4086 {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 4087 33142652, 6546660, -19985279, -3948376}, 4088 }, 4089 { 4090 {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, 4091 -8537131, -12833048, -30772034, -15486313}, 4092 {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, 4093 -31135347, -16049879, 10928917, 3011958}, 4094 {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, 4095 -30831056, -12805180, 18008031, 10258577}, 4096 }, 4097 { 4098 {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, 4099 -1853465, 1367120, 25127874, 6671743}, 4100 {29701166, -14373934, -10878120, 9279288, -17568, 13127210, 4101 21382910, 11042292, 25838796, 4642684}, 4102 {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 4103 30468147, -13900640, 18423289, 4177476}, 4104 }, 4105 }, 4106 }; 4107 4108 static uint8_t negative(signed char b) { 4109 uint32_t x = b; 4110 x >>= 31; /* 1: yes; 0: no */ 4111 return x; 4112 } 4113 4114 static void table_select(ge_precomp *t, int pos, signed char b) { 4115 ge_precomp minust; 4116 uint8_t bnegative = negative(b); 4117 uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); 4118 4119 ge_precomp_0(t); 4120 cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); 4121 cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); 4122 cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); 4123 cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); 4124 cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); 4125 cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); 4126 cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); 4127 cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); 4128 fe_copy(minust.yplusx, t->yminusx); 4129 fe_copy(minust.yminusx, t->yplusx); 4130 fe_neg(minust.xy2d, t->xy2d); 4131 cmov(t, &minust, bnegative); 4132 } 4133 4134 /* h = a * B 4135 * where a = a[0]+256*a[1]+...+256^31 a[31] 4136 * B is the Ed25519 base point (x,4/5) with x positive. 4137 * 4138 * Preconditions: 4139 * a[31] <= 127 */ 4140 static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { 4141 signed char e[64]; 4142 signed char carry; 4143 ge_p1p1 r; 4144 ge_p2 s; 4145 ge_precomp t; 4146 int i; 4147 4148 for (i = 0; i < 32; ++i) { 4149 e[2 * i + 0] = (a[i] >> 0) & 15; 4150 e[2 * i + 1] = (a[i] >> 4) & 15; 4151 } 4152 /* each e[i] is between 0 and 15 */ 4153 /* e[63] is between 0 and 7 */ 4154 4155 carry = 0; 4156 for (i = 0; i < 63; ++i) { 4157 e[i] += carry; 4158 carry = e[i] + 8; 4159 carry >>= 4; 4160 e[i] -= carry << 4; 4161 } 4162 e[63] += carry; 4163 /* each e[i] is between -8 and 8 */ 4164 4165 ge_p3_0(h); 4166 for (i = 1; i < 64; i += 2) { 4167 table_select(&t, i / 2, e[i]); 4168 ge_madd(&r, h, &t); 4169 ge_p1p1_to_p3(h, &r); 4170 } 4171 4172 ge_p3_dbl(&r, h); 4173 ge_p1p1_to_p2(&s, &r); 4174 ge_p2_dbl(&r, &s); 4175 ge_p1p1_to_p2(&s, &r); 4176 ge_p2_dbl(&r, &s); 4177 ge_p1p1_to_p2(&s, &r); 4178 ge_p2_dbl(&r, &s); 4179 ge_p1p1_to_p3(h, &r); 4180 4181 for (i = 0; i < 64; i += 2) { 4182 table_select(&t, i / 2, e[i]); 4183 ge_madd(&r, h, &t); 4184 ge_p1p1_to_p3(h, &r); 4185 } 4186 4187 OPENSSL_cleanse(e, sizeof(e)); 4188 } 4189 4190 #if !defined(BASE_2_51_IMPLEMENTED) 4191 /* Replace (f,g) with (g,f) if b == 1; 4192 * replace (f,g) with (f,g) if b == 0. 4193 * 4194 * Preconditions: b in {0,1}. */ 4195 static void fe_cswap(fe f, fe g, unsigned int b) { 4196 size_t i; 4197 b = 0-b; 4198 for (i = 0; i < 10; i++) { 4199 int32_t x = f[i] ^ g[i]; 4200 x &= b; 4201 f[i] ^= x; 4202 g[i] ^= x; 4203 } 4204 } 4205 4206 /* h = f * 121666 4207 * Can overlap h with f. 4208 * 4209 * Preconditions: 4210 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. 4211 * 4212 * Postconditions: 4213 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ 4214 static void fe_mul121666(fe h, fe f) { 4215 int32_t f0 = f[0]; 4216 int32_t f1 = f[1]; 4217 int32_t f2 = f[2]; 4218 int32_t f3 = f[3]; 4219 int32_t f4 = f[4]; 4220 int32_t f5 = f[5]; 4221 int32_t f6 = f[6]; 4222 int32_t f7 = f[7]; 4223 int32_t f8 = f[8]; 4224 int32_t f9 = f[9]; 4225 int64_t h0 = f0 * (int64_t) 121666; 4226 int64_t h1 = f1 * (int64_t) 121666; 4227 int64_t h2 = f2 * (int64_t) 121666; 4228 int64_t h3 = f3 * (int64_t) 121666; 4229 int64_t h4 = f4 * (int64_t) 121666; 4230 int64_t h5 = f5 * (int64_t) 121666; 4231 int64_t h6 = f6 * (int64_t) 121666; 4232 int64_t h7 = f7 * (int64_t) 121666; 4233 int64_t h8 = f8 * (int64_t) 121666; 4234 int64_t h9 = f9 * (int64_t) 121666; 4235 int64_t carry0; 4236 int64_t carry1; 4237 int64_t carry2; 4238 int64_t carry3; 4239 int64_t carry4; 4240 int64_t carry5; 4241 int64_t carry6; 4242 int64_t carry7; 4243 int64_t carry8; 4244 int64_t carry9; 4245 4246 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; 4247 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; 4248 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; 4249 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; 4250 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; 4251 4252 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; 4253 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; 4254 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; 4255 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; 4256 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; 4257 4258 h[0] = (int32_t)h0; 4259 h[1] = (int32_t)h1; 4260 h[2] = (int32_t)h2; 4261 h[3] = (int32_t)h3; 4262 h[4] = (int32_t)h4; 4263 h[5] = (int32_t)h5; 4264 h[6] = (int32_t)h6; 4265 h[7] = (int32_t)h7; 4266 h[8] = (int32_t)h8; 4267 h[9] = (int32_t)h9; 4268 } 4269 4270 static void x25519_scalar_mult_generic(uint8_t out[32], 4271 const uint8_t scalar[32], 4272 const uint8_t point[32]) { 4273 fe x1, x2, z2, x3, z3, tmp0, tmp1; 4274 uint8_t e[32]; 4275 unsigned swap = 0; 4276 int pos; 4277 4278 memcpy(e, scalar, 32); 4279 e[0] &= 248; 4280 e[31] &= 127; 4281 e[31] |= 64; 4282 fe_frombytes(x1, point); 4283 fe_1(x2); 4284 fe_0(z2); 4285 fe_copy(x3, x1); 4286 fe_1(z3); 4287 4288 for (pos = 254; pos >= 0; --pos) { 4289 unsigned b = 1 & (e[pos / 8] >> (pos & 7)); 4290 swap ^= b; 4291 fe_cswap(x2, x3, swap); 4292 fe_cswap(z2, z3, swap); 4293 swap = b; 4294 fe_sub(tmp0, x3, z3); 4295 fe_sub(tmp1, x2, z2); 4296 fe_add(x2, x2, z2); 4297 fe_add(z2, x3, z3); 4298 fe_mul(z3, tmp0, x2); 4299 fe_mul(z2, z2, tmp1); 4300 fe_sq(tmp0, tmp1); 4301 fe_sq(tmp1, x2); 4302 fe_add(x3, z3, z2); 4303 fe_sub(z2, z3, z2); 4304 fe_mul(x2, tmp1, tmp0); 4305 fe_sub(tmp1, tmp1, tmp0); 4306 fe_sq(z2, z2); 4307 fe_mul121666(z3, tmp1); 4308 fe_sq(x3, x3); 4309 fe_add(tmp0, tmp0, z3); 4310 fe_mul(z3, x1, z2); 4311 fe_mul(z2, tmp1, tmp0); 4312 } 4313 4314 fe_invert(z2, z2); 4315 fe_mul(x2, x2, z2); 4316 fe_tobytes(out, x2); 4317 4318 OPENSSL_cleanse(e, sizeof(e)); 4319 } 4320 4321 static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], 4322 const uint8_t point[32]) { 4323 x25519_scalar_mult_generic(out, scalar, point); 4324 } 4325 #endif 4326 4327 static void slide(signed char *r, const uint8_t *a) { 4328 int i; 4329 int b; 4330 int k; 4331 4332 for (i = 0; i < 256; ++i) { 4333 r[i] = 1 & (a[i >> 3] >> (i & 7)); 4334 } 4335 4336 for (i = 0; i < 256; ++i) { 4337 if (r[i]) { 4338 for (b = 1; b <= 6 && i + b < 256; ++b) { 4339 if (r[i + b]) { 4340 if (r[i] + (r[i + b] << b) <= 15) { 4341 r[i] += r[i + b] << b; 4342 r[i + b] = 0; 4343 } else if (r[i] - (r[i + b] << b) >= -15) { 4344 r[i] -= r[i + b] << b; 4345 for (k = i + b; k < 256; ++k) { 4346 if (!r[k]) { 4347 r[k] = 1; 4348 break; 4349 } 4350 r[k] = 0; 4351 } 4352 } else { 4353 break; 4354 } 4355 } 4356 } 4357 } 4358 } 4359 } 4360 4361 static const ge_precomp Bi[8] = { 4362 { 4363 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, 4364 -11754271, -6079156, 2047605}, 4365 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 4366 5043384, 19500929, -15469378}, 4367 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 4368 11864899, -24514362, -4438546}, 4369 }, 4370 { 4371 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, 4372 -14772189, 28944400, -1550024}, 4373 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, 4374 -11775962, 7689662, 11199574}, 4375 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 4376 10017326, -17749093, -9920357}, 4377 }, 4378 { 4379 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 4380 14515107, -15438304, 10819380}, 4381 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 4382 12483688, -12668491, 5581306}, 4383 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 4384 13850243, -23678021, -15815942}, 4385 }, 4386 { 4387 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 4388 5230134, -23952439, -15175766}, 4389 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 4390 16520125, 30598449, 7715701}, 4391 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 4392 1370708, 29794553, -1409300}, 4393 }, 4394 { 4395 {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, 4396 -1361450, -13062696, 13821877}, 4397 {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, 4398 -7212327, 18853322, -14220951}, 4399 {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, 4400 -10431137, 2207753, -3209784}, 4401 }, 4402 { 4403 {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, 4404 -663000, -31111463, -16132436}, 4405 {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 4406 15725684, 171356, 6466918}, 4407 {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, 4408 -14088058, -30714912, 16193877}, 4409 }, 4410 { 4411 {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4412 4729455, -18074513, 9256800}, 4413 {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 4414 9761698, -19827198, 630305}, 4415 {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, 4416 -15960994, -2449256, -14291300}, 4417 }, 4418 { 4419 {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 4420 15033784, 25105118, -7894876}, 4421 {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 4422 1573892, -2625887, 2198790, -15804619}, 4423 {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, 4424 -16236442, -32461234, -12290683}, 4425 }, 4426 }; 4427 4428 /* r = a * A + b * B 4429 * where a = a[0]+256*a[1]+...+256^31 a[31]. 4430 * and b = b[0]+256*b[1]+...+256^31 b[31]. 4431 * B is the Ed25519 base point (x,4/5) with x positive. */ 4432 static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, 4433 const ge_p3 *A, const uint8_t *b) { 4434 signed char aslide[256]; 4435 signed char bslide[256]; 4436 ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ 4437 ge_p1p1 t; 4438 ge_p3 u; 4439 ge_p3 A2; 4440 int i; 4441 4442 slide(aslide, a); 4443 slide(bslide, b); 4444 4445 ge_p3_to_cached(&Ai[0], A); 4446 ge_p3_dbl(&t, A); 4447 ge_p1p1_to_p3(&A2, &t); 4448 ge_add(&t, &A2, &Ai[0]); 4449 ge_p1p1_to_p3(&u, &t); 4450 ge_p3_to_cached(&Ai[1], &u); 4451 ge_add(&t, &A2, &Ai[1]); 4452 ge_p1p1_to_p3(&u, &t); 4453 ge_p3_to_cached(&Ai[2], &u); 4454 ge_add(&t, &A2, &Ai[2]); 4455 ge_p1p1_to_p3(&u, &t); 4456 ge_p3_to_cached(&Ai[3], &u); 4457 ge_add(&t, &A2, &Ai[3]); 4458 ge_p1p1_to_p3(&u, &t); 4459 ge_p3_to_cached(&Ai[4], &u); 4460 ge_add(&t, &A2, &Ai[4]); 4461 ge_p1p1_to_p3(&u, &t); 4462 ge_p3_to_cached(&Ai[5], &u); 4463 ge_add(&t, &A2, &Ai[5]); 4464 ge_p1p1_to_p3(&u, &t); 4465 ge_p3_to_cached(&Ai[6], &u); 4466 ge_add(&t, &A2, &Ai[6]); 4467 ge_p1p1_to_p3(&u, &t); 4468 ge_p3_to_cached(&Ai[7], &u); 4469 4470 ge_p2_0(r); 4471 4472 for (i = 255; i >= 0; --i) { 4473 if (aslide[i] || bslide[i]) { 4474 break; 4475 } 4476 } 4477 4478 for (; i >= 0; --i) { 4479 ge_p2_dbl(&t, r); 4480 4481 if (aslide[i] > 0) { 4482 ge_p1p1_to_p3(&u, &t); 4483 ge_add(&t, &u, &Ai[aslide[i] / 2]); 4484 } else if (aslide[i] < 0) { 4485 ge_p1p1_to_p3(&u, &t); 4486 ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); 4487 } 4488 4489 if (bslide[i] > 0) { 4490 ge_p1p1_to_p3(&u, &t); 4491 ge_madd(&t, &u, &Bi[bslide[i] / 2]); 4492 } else if (bslide[i] < 0) { 4493 ge_p1p1_to_p3(&u, &t); 4494 ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); 4495 } 4496 4497 ge_p1p1_to_p2(r, &t); 4498 } 4499 } 4500 4501 /* The set of scalars is \Z/l 4502 * where l = 2^252 + 27742317777372353535851937790883648493. */ 4503 4504 /* Input: 4505 * s[0]+256*s[1]+...+256^63*s[63] = s 4506 * 4507 * Output: 4508 * s[0]+256*s[1]+...+256^31*s[31] = s mod l 4509 * where l = 2^252 + 27742317777372353535851937790883648493. 4510 * Overwrites s in place. */ 4511 static void x25519_sc_reduce(uint8_t *s) { 4512 int64_t s0 = 2097151 & load_3(s); 4513 int64_t s1 = 2097151 & (load_4(s + 2) >> 5); 4514 int64_t s2 = 2097151 & (load_3(s + 5) >> 2); 4515 int64_t s3 = 2097151 & (load_4(s + 7) >> 7); 4516 int64_t s4 = 2097151 & (load_4(s + 10) >> 4); 4517 int64_t s5 = 2097151 & (load_3(s + 13) >> 1); 4518 int64_t s6 = 2097151 & (load_4(s + 15) >> 6); 4519 int64_t s7 = 2097151 & (load_3(s + 18) >> 3); 4520 int64_t s8 = 2097151 & load_3(s + 21); 4521 int64_t s9 = 2097151 & (load_4(s + 23) >> 5); 4522 int64_t s10 = 2097151 & (load_3(s + 26) >> 2); 4523 int64_t s11 = 2097151 & (load_4(s + 28) >> 7); 4524 int64_t s12 = 2097151 & (load_4(s + 31) >> 4); 4525 int64_t s13 = 2097151 & (load_3(s + 34) >> 1); 4526 int64_t s14 = 2097151 & (load_4(s + 36) >> 6); 4527 int64_t s15 = 2097151 & (load_3(s + 39) >> 3); 4528 int64_t s16 = 2097151 & load_3(s + 42); 4529 int64_t s17 = 2097151 & (load_4(s + 44) >> 5); 4530 int64_t s18 = 2097151 & (load_3(s + 47) >> 2); 4531 int64_t s19 = 2097151 & (load_4(s + 49) >> 7); 4532 int64_t s20 = 2097151 & (load_4(s + 52) >> 4); 4533 int64_t s21 = 2097151 & (load_3(s + 55) >> 1); 4534 int64_t s22 = 2097151 & (load_4(s + 57) >> 6); 4535 int64_t s23 = (load_4(s + 60) >> 3); 4536 int64_t carry0; 4537 int64_t carry1; 4538 int64_t carry2; 4539 int64_t carry3; 4540 int64_t carry4; 4541 int64_t carry5; 4542 int64_t carry6; 4543 int64_t carry7; 4544 int64_t carry8; 4545 int64_t carry9; 4546 int64_t carry10; 4547 int64_t carry11; 4548 int64_t carry12; 4549 int64_t carry13; 4550 int64_t carry14; 4551 int64_t carry15; 4552 int64_t carry16; 4553 4554 s11 += s23 * 666643; 4555 s12 += s23 * 470296; 4556 s13 += s23 * 654183; 4557 s14 -= s23 * 997805; 4558 s15 += s23 * 136657; 4559 s16 -= s23 * 683901; 4560 s23 = 0; 4561 4562 s10 += s22 * 666643; 4563 s11 += s22 * 470296; 4564 s12 += s22 * 654183; 4565 s13 -= s22 * 997805; 4566 s14 += s22 * 136657; 4567 s15 -= s22 * 683901; 4568 s22 = 0; 4569 4570 s9 += s21 * 666643; 4571 s10 += s21 * 470296; 4572 s11 += s21 * 654183; 4573 s12 -= s21 * 997805; 4574 s13 += s21 * 136657; 4575 s14 -= s21 * 683901; 4576 s21 = 0; 4577 4578 s8 += s20 * 666643; 4579 s9 += s20 * 470296; 4580 s10 += s20 * 654183; 4581 s11 -= s20 * 997805; 4582 s12 += s20 * 136657; 4583 s13 -= s20 * 683901; 4584 s20 = 0; 4585 4586 s7 += s19 * 666643; 4587 s8 += s19 * 470296; 4588 s9 += s19 * 654183; 4589 s10 -= s19 * 997805; 4590 s11 += s19 * 136657; 4591 s12 -= s19 * 683901; 4592 s19 = 0; 4593 4594 s6 += s18 * 666643; 4595 s7 += s18 * 470296; 4596 s8 += s18 * 654183; 4597 s9 -= s18 * 997805; 4598 s10 += s18 * 136657; 4599 s11 -= s18 * 683901; 4600 s18 = 0; 4601 4602 carry6 = (s6 + (1 << 20)) >> 21; 4603 s7 += carry6; 4604 s6 -= carry6 * (1 << 21); 4605 carry8 = (s8 + (1 << 20)) >> 21; 4606 s9 += carry8; 4607 s8 -= carry8 * (1 << 21); 4608 carry10 = (s10 + (1 << 20)) >> 21; 4609 s11 += carry10; 4610 s10 -= carry10 * (1 << 21); 4611 carry12 = (s12 + (1 << 20)) >> 21; 4612 s13 += carry12; 4613 s12 -= carry12 * (1 << 21); 4614 carry14 = (s14 + (1 << 20)) >> 21; 4615 s15 += carry14; 4616 s14 -= carry14 * (1 << 21); 4617 carry16 = (s16 + (1 << 20)) >> 21; 4618 s17 += carry16; 4619 s16 -= carry16 * (1 << 21); 4620 4621 carry7 = (s7 + (1 << 20)) >> 21; 4622 s8 += carry7; 4623 s7 -= carry7 * (1 << 21); 4624 carry9 = (s9 + (1 << 20)) >> 21; 4625 s10 += carry9; 4626 s9 -= carry9 * (1 << 21); 4627 carry11 = (s11 + (1 << 20)) >> 21; 4628 s12 += carry11; 4629 s11 -= carry11 * (1 << 21); 4630 carry13 = (s13 + (1 << 20)) >> 21; 4631 s14 += carry13; 4632 s13 -= carry13 * (1 << 21); 4633 carry15 = (s15 + (1 << 20)) >> 21; 4634 s16 += carry15; 4635 s15 -= carry15 * (1 << 21); 4636 4637 s5 += s17 * 666643; 4638 s6 += s17 * 470296; 4639 s7 += s17 * 654183; 4640 s8 -= s17 * 997805; 4641 s9 += s17 * 136657; 4642 s10 -= s17 * 683901; 4643 s17 = 0; 4644 4645 s4 += s16 * 666643; 4646 s5 += s16 * 470296; 4647 s6 += s16 * 654183; 4648 s7 -= s16 * 997805; 4649 s8 += s16 * 136657; 4650 s9 -= s16 * 683901; 4651 s16 = 0; 4652 4653 s3 += s15 * 666643; 4654 s4 += s15 * 470296; 4655 s5 += s15 * 654183; 4656 s6 -= s15 * 997805; 4657 s7 += s15 * 136657; 4658 s8 -= s15 * 683901; 4659 s15 = 0; 4660 4661 s2 += s14 * 666643; 4662 s3 += s14 * 470296; 4663 s4 += s14 * 654183; 4664 s5 -= s14 * 997805; 4665 s6 += s14 * 136657; 4666 s7 -= s14 * 683901; 4667 s14 = 0; 4668 4669 s1 += s13 * 666643; 4670 s2 += s13 * 470296; 4671 s3 += s13 * 654183; 4672 s4 -= s13 * 997805; 4673 s5 += s13 * 136657; 4674 s6 -= s13 * 683901; 4675 s13 = 0; 4676 4677 s0 += s12 * 666643; 4678 s1 += s12 * 470296; 4679 s2 += s12 * 654183; 4680 s3 -= s12 * 997805; 4681 s4 += s12 * 136657; 4682 s5 -= s12 * 683901; 4683 s12 = 0; 4684 4685 carry0 = (s0 + (1 << 20)) >> 21; 4686 s1 += carry0; 4687 s0 -= carry0 * (1 << 21); 4688 carry2 = (s2 + (1 << 20)) >> 21; 4689 s3 += carry2; 4690 s2 -= carry2 * (1 << 21); 4691 carry4 = (s4 + (1 << 20)) >> 21; 4692 s5 += carry4; 4693 s4 -= carry4 * (1 << 21); 4694 carry6 = (s6 + (1 << 20)) >> 21; 4695 s7 += carry6; 4696 s6 -= carry6 * (1 << 21); 4697 carry8 = (s8 + (1 << 20)) >> 21; 4698 s9 += carry8; 4699 s8 -= carry8 * (1 << 21); 4700 carry10 = (s10 + (1 << 20)) >> 21; 4701 s11 += carry10; 4702 s10 -= carry10 * (1 << 21); 4703 4704 carry1 = (s1 + (1 << 20)) >> 21; 4705 s2 += carry1; 4706 s1 -= carry1 * (1 << 21); 4707 carry3 = (s3 + (1 << 20)) >> 21; 4708 s4 += carry3; 4709 s3 -= carry3 * (1 << 21); 4710 carry5 = (s5 + (1 << 20)) >> 21; 4711 s6 += carry5; 4712 s5 -= carry5 * (1 << 21); 4713 carry7 = (s7 + (1 << 20)) >> 21; 4714 s8 += carry7; 4715 s7 -= carry7 * (1 << 21); 4716 carry9 = (s9 + (1 << 20)) >> 21; 4717 s10 += carry9; 4718 s9 -= carry9 * (1 << 21); 4719 carry11 = (s11 + (1 << 20)) >> 21; 4720 s12 += carry11; 4721 s11 -= carry11 * (1 << 21); 4722 4723 s0 += s12 * 666643; 4724 s1 += s12 * 470296; 4725 s2 += s12 * 654183; 4726 s3 -= s12 * 997805; 4727 s4 += s12 * 136657; 4728 s5 -= s12 * 683901; 4729 s12 = 0; 4730 4731 carry0 = s0 >> 21; 4732 s1 += carry0; 4733 s0 -= carry0 * (1 << 21); 4734 carry1 = s1 >> 21; 4735 s2 += carry1; 4736 s1 -= carry1 * (1 << 21); 4737 carry2 = s2 >> 21; 4738 s3 += carry2; 4739 s2 -= carry2 * (1 << 21); 4740 carry3 = s3 >> 21; 4741 s4 += carry3; 4742 s3 -= carry3 * (1 << 21); 4743 carry4 = s4 >> 21; 4744 s5 += carry4; 4745 s4 -= carry4 * (1 << 21); 4746 carry5 = s5 >> 21; 4747 s6 += carry5; 4748 s5 -= carry5 * (1 << 21); 4749 carry6 = s6 >> 21; 4750 s7 += carry6; 4751 s6 -= carry6 * (1 << 21); 4752 carry7 = s7 >> 21; 4753 s8 += carry7; 4754 s7 -= carry7 * (1 << 21); 4755 carry8 = s8 >> 21; 4756 s9 += carry8; 4757 s8 -= carry8 * (1 << 21); 4758 carry9 = s9 >> 21; 4759 s10 += carry9; 4760 s9 -= carry9 * (1 << 21); 4761 carry10 = s10 >> 21; 4762 s11 += carry10; 4763 s10 -= carry10 * (1 << 21); 4764 carry11 = s11 >> 21; 4765 s12 += carry11; 4766 s11 -= carry11 * (1 << 21); 4767 4768 s0 += s12 * 666643; 4769 s1 += s12 * 470296; 4770 s2 += s12 * 654183; 4771 s3 -= s12 * 997805; 4772 s4 += s12 * 136657; 4773 s5 -= s12 * 683901; 4774 s12 = 0; 4775 4776 carry0 = s0 >> 21; 4777 s1 += carry0; 4778 s0 -= carry0 * (1 << 21); 4779 carry1 = s1 >> 21; 4780 s2 += carry1; 4781 s1 -= carry1 * (1 << 21); 4782 carry2 = s2 >> 21; 4783 s3 += carry2; 4784 s2 -= carry2 * (1 << 21); 4785 carry3 = s3 >> 21; 4786 s4 += carry3; 4787 s3 -= carry3 * (1 << 21); 4788 carry4 = s4 >> 21; 4789 s5 += carry4; 4790 s4 -= carry4 * (1 << 21); 4791 carry5 = s5 >> 21; 4792 s6 += carry5; 4793 s5 -= carry5 * (1 << 21); 4794 carry6 = s6 >> 21; 4795 s7 += carry6; 4796 s6 -= carry6 * (1 << 21); 4797 carry7 = s7 >> 21; 4798 s8 += carry7; 4799 s7 -= carry7 * (1 << 21); 4800 carry8 = s8 >> 21; 4801 s9 += carry8; 4802 s8 -= carry8 * (1 << 21); 4803 carry9 = s9 >> 21; 4804 s10 += carry9; 4805 s9 -= carry9 * (1 << 21); 4806 carry10 = s10 >> 21; 4807 s11 += carry10; 4808 s10 -= carry10 * (1 << 21); 4809 4810 s[0] = (uint8_t)(s0 >> 0); 4811 s[1] = (uint8_t)(s0 >> 8); 4812 s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); 4813 s[3] = (uint8_t)(s1 >> 3); 4814 s[4] = (uint8_t)(s1 >> 11); 4815 s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); 4816 s[6] = (uint8_t)(s2 >> 6); 4817 s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); 4818 s[8] = (uint8_t)(s3 >> 1); 4819 s[9] = (uint8_t)(s3 >> 9); 4820 s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); 4821 s[11] = (uint8_t)(s4 >> 4); 4822 s[12] = (uint8_t)(s4 >> 12); 4823 s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); 4824 s[14] = (uint8_t)(s5 >> 7); 4825 s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); 4826 s[16] = (uint8_t)(s6 >> 2); 4827 s[17] = (uint8_t)(s6 >> 10); 4828 s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); 4829 s[19] = (uint8_t)(s7 >> 5); 4830 s[20] = (uint8_t)(s7 >> 13); 4831 s[21] = (uint8_t)(s8 >> 0); 4832 s[22] = (uint8_t)(s8 >> 8); 4833 s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); 4834 s[24] = (uint8_t)(s9 >> 3); 4835 s[25] = (uint8_t)(s9 >> 11); 4836 s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); 4837 s[27] = (uint8_t)(s10 >> 6); 4838 s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); 4839 s[29] = (uint8_t)(s11 >> 1); 4840 s[30] = (uint8_t)(s11 >> 9); 4841 s[31] = (uint8_t)(s11 >> 17); 4842 } 4843 4844 /* Input: 4845 * a[0]+256*a[1]+...+256^31*a[31] = a 4846 * b[0]+256*b[1]+...+256^31*b[31] = b 4847 * c[0]+256*c[1]+...+256^31*c[31] = c 4848 * 4849 * Output: 4850 * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l 4851 * where l = 2^252 + 27742317777372353535851937790883648493. */ 4852 static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, 4853 const uint8_t *c) { 4854 int64_t a0 = 2097151 & load_3(a); 4855 int64_t a1 = 2097151 & (load_4(a + 2) >> 5); 4856 int64_t a2 = 2097151 & (load_3(a + 5) >> 2); 4857 int64_t a3 = 2097151 & (load_4(a + 7) >> 7); 4858 int64_t a4 = 2097151 & (load_4(a + 10) >> 4); 4859 int64_t a5 = 2097151 & (load_3(a + 13) >> 1); 4860 int64_t a6 = 2097151 & (load_4(a + 15) >> 6); 4861 int64_t a7 = 2097151 & (load_3(a + 18) >> 3); 4862 int64_t a8 = 2097151 & load_3(a + 21); 4863 int64_t a9 = 2097151 & (load_4(a + 23) >> 5); 4864 int64_t a10 = 2097151 & (load_3(a + 26) >> 2); 4865 int64_t a11 = (load_4(a + 28) >> 7); 4866 int64_t b0 = 2097151 & load_3(b); 4867 int64_t b1 = 2097151 & (load_4(b + 2) >> 5); 4868 int64_t b2 = 2097151 & (load_3(b + 5) >> 2); 4869 int64_t b3 = 2097151 & (load_4(b + 7) >> 7); 4870 int64_t b4 = 2097151 & (load_4(b + 10) >> 4); 4871 int64_t b5 = 2097151 & (load_3(b + 13) >> 1); 4872 int64_t b6 = 2097151 & (load_4(b + 15) >> 6); 4873 int64_t b7 = 2097151 & (load_3(b + 18) >> 3); 4874 int64_t b8 = 2097151 & load_3(b + 21); 4875 int64_t b9 = 2097151 & (load_4(b + 23) >> 5); 4876 int64_t b10 = 2097151 & (load_3(b + 26) >> 2); 4877 int64_t b11 = (load_4(b + 28) >> 7); 4878 int64_t c0 = 2097151 & load_3(c); 4879 int64_t c1 = 2097151 & (load_4(c + 2) >> 5); 4880 int64_t c2 = 2097151 & (load_3(c + 5) >> 2); 4881 int64_t c3 = 2097151 & (load_4(c + 7) >> 7); 4882 int64_t c4 = 2097151 & (load_4(c + 10) >> 4); 4883 int64_t c5 = 2097151 & (load_3(c + 13) >> 1); 4884 int64_t c6 = 2097151 & (load_4(c + 15) >> 6); 4885 int64_t c7 = 2097151 & (load_3(c + 18) >> 3); 4886 int64_t c8 = 2097151 & load_3(c + 21); 4887 int64_t c9 = 2097151 & (load_4(c + 23) >> 5); 4888 int64_t c10 = 2097151 & (load_3(c + 26) >> 2); 4889 int64_t c11 = (load_4(c + 28) >> 7); 4890 int64_t s0; 4891 int64_t s1; 4892 int64_t s2; 4893 int64_t s3; 4894 int64_t s4; 4895 int64_t s5; 4896 int64_t s6; 4897 int64_t s7; 4898 int64_t s8; 4899 int64_t s9; 4900 int64_t s10; 4901 int64_t s11; 4902 int64_t s12; 4903 int64_t s13; 4904 int64_t s14; 4905 int64_t s15; 4906 int64_t s16; 4907 int64_t s17; 4908 int64_t s18; 4909 int64_t s19; 4910 int64_t s20; 4911 int64_t s21; 4912 int64_t s22; 4913 int64_t s23; 4914 int64_t carry0; 4915 int64_t carry1; 4916 int64_t carry2; 4917 int64_t carry3; 4918 int64_t carry4; 4919 int64_t carry5; 4920 int64_t carry6; 4921 int64_t carry7; 4922 int64_t carry8; 4923 int64_t carry9; 4924 int64_t carry10; 4925 int64_t carry11; 4926 int64_t carry12; 4927 int64_t carry13; 4928 int64_t carry14; 4929 int64_t carry15; 4930 int64_t carry16; 4931 int64_t carry17; 4932 int64_t carry18; 4933 int64_t carry19; 4934 int64_t carry20; 4935 int64_t carry21; 4936 int64_t carry22; 4937 4938 s0 = c0 + a0 * b0; 4939 s1 = c1 + a0 * b1 + a1 * b0; 4940 s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; 4941 s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; 4942 s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; 4943 s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; 4944 s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; 4945 s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + 4946 a6 * b1 + a7 * b0; 4947 s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + 4948 a6 * b2 + a7 * b1 + a8 * b0; 4949 s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + 4950 a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; 4951 s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + 4952 a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; 4953 s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + 4954 a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; 4955 s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + 4956 a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; 4957 s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + 4958 a9 * b4 + a10 * b3 + a11 * b2; 4959 s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + 4960 a10 * b4 + a11 * b3; 4961 s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + 4962 a11 * b4; 4963 s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; 4964 s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; 4965 s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; 4966 s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; 4967 s20 = a9 * b11 + a10 * b10 + a11 * b9; 4968 s21 = a10 * b11 + a11 * b10; 4969 s22 = a11 * b11; 4970 s23 = 0; 4971 4972 carry0 = (s0 + (1 << 20)) >> 21; 4973 s1 += carry0; 4974 s0 -= carry0 * (1 << 21); 4975 carry2 = (s2 + (1 << 20)) >> 21; 4976 s3 += carry2; 4977 s2 -= carry2 * (1 << 21); 4978 carry4 = (s4 + (1 << 20)) >> 21; 4979 s5 += carry4; 4980 s4 -= carry4 * (1 << 21); 4981 carry6 = (s6 + (1 << 20)) >> 21; 4982 s7 += carry6; 4983 s6 -= carry6 * (1 << 21); 4984 carry8 = (s8 + (1 << 20)) >> 21; 4985 s9 += carry8; 4986 s8 -= carry8 * (1 << 21); 4987 carry10 = (s10 + (1 << 20)) >> 21; 4988 s11 += carry10; 4989 s10 -= carry10 * (1 << 21); 4990 carry12 = (s12 + (1 << 20)) >> 21; 4991 s13 += carry12; 4992 s12 -= carry12 * (1 << 21); 4993 carry14 = (s14 + (1 << 20)) >> 21; 4994 s15 += carry14; 4995 s14 -= carry14 * (1 << 21); 4996 carry16 = (s16 + (1 << 20)) >> 21; 4997 s17 += carry16; 4998 s16 -= carry16 * (1 << 21); 4999 carry18 = (s18 + (1 << 20)) >> 21; 5000 s19 += carry18; 5001 s18 -= carry18 * (1 << 21); 5002 carry20 = (s20 + (1 << 20)) >> 21; 5003 s21 += carry20; 5004 s20 -= carry20 * (1 << 21); 5005 carry22 = (s22 + (1 << 20)) >> 21; 5006 s23 += carry22; 5007 s22 -= carry22 * (1 << 21); 5008 5009 carry1 = (s1 + (1 << 20)) >> 21; 5010 s2 += carry1; 5011 s1 -= carry1 * (1 << 21); 5012 carry3 = (s3 + (1 << 20)) >> 21; 5013 s4 += carry3; 5014 s3 -= carry3 * (1 << 21); 5015 carry5 = (s5 + (1 << 20)) >> 21; 5016 s6 += carry5; 5017 s5 -= carry5 * (1 << 21); 5018 carry7 = (s7 + (1 << 20)) >> 21; 5019 s8 += carry7; 5020 s7 -= carry7 * (1 << 21); 5021 carry9 = (s9 + (1 << 20)) >> 21; 5022 s10 += carry9; 5023 s9 -= carry9 * (1 << 21); 5024 carry11 = (s11 + (1 << 20)) >> 21; 5025 s12 += carry11; 5026 s11 -= carry11 * (1 << 21); 5027 carry13 = (s13 + (1 << 20)) >> 21; 5028 s14 += carry13; 5029 s13 -= carry13 * (1 << 21); 5030 carry15 = (s15 + (1 << 20)) >> 21; 5031 s16 += carry15; 5032 s15 -= carry15 * (1 << 21); 5033 carry17 = (s17 + (1 << 20)) >> 21; 5034 s18 += carry17; 5035 s17 -= carry17 * (1 << 21); 5036 carry19 = (s19 + (1 << 20)) >> 21; 5037 s20 += carry19; 5038 s19 -= carry19 * (1 << 21); 5039 carry21 = (s21 + (1 << 20)) >> 21; 5040 s22 += carry21; 5041 s21 -= carry21 * (1 << 21); 5042 5043 s11 += s23 * 666643; 5044 s12 += s23 * 470296; 5045 s13 += s23 * 654183; 5046 s14 -= s23 * 997805; 5047 s15 += s23 * 136657; 5048 s16 -= s23 * 683901; 5049 s23 = 0; 5050 5051 s10 += s22 * 666643; 5052 s11 += s22 * 470296; 5053 s12 += s22 * 654183; 5054 s13 -= s22 * 997805; 5055 s14 += s22 * 136657; 5056 s15 -= s22 * 683901; 5057 s22 = 0; 5058 5059 s9 += s21 * 666643; 5060 s10 += s21 * 470296; 5061 s11 += s21 * 654183; 5062 s12 -= s21 * 997805; 5063 s13 += s21 * 136657; 5064 s14 -= s21 * 683901; 5065 s21 = 0; 5066 5067 s8 += s20 * 666643; 5068 s9 += s20 * 470296; 5069 s10 += s20 * 654183; 5070 s11 -= s20 * 997805; 5071 s12 += s20 * 136657; 5072 s13 -= s20 * 683901; 5073 s20 = 0; 5074 5075 s7 += s19 * 666643; 5076 s8 += s19 * 470296; 5077 s9 += s19 * 654183; 5078 s10 -= s19 * 997805; 5079 s11 += s19 * 136657; 5080 s12 -= s19 * 683901; 5081 s19 = 0; 5082 5083 s6 += s18 * 666643; 5084 s7 += s18 * 470296; 5085 s8 += s18 * 654183; 5086 s9 -= s18 * 997805; 5087 s10 += s18 * 136657; 5088 s11 -= s18 * 683901; 5089 s18 = 0; 5090 5091 carry6 = (s6 + (1 << 20)) >> 21; 5092 s7 += carry6; 5093 s6 -= carry6 * (1 << 21); 5094 carry8 = (s8 + (1 << 20)) >> 21; 5095 s9 += carry8; 5096 s8 -= carry8 * (1 << 21); 5097 carry10 = (s10 + (1 << 20)) >> 21; 5098 s11 += carry10; 5099 s10 -= carry10 * (1 << 21); 5100 carry12 = (s12 + (1 << 20)) >> 21; 5101 s13 += carry12; 5102 s12 -= carry12 * (1 << 21); 5103 carry14 = (s14 + (1 << 20)) >> 21; 5104 s15 += carry14; 5105 s14 -= carry14 * (1 << 21); 5106 carry16 = (s16 + (1 << 20)) >> 21; 5107 s17 += carry16; 5108 s16 -= carry16 * (1 << 21); 5109 5110 carry7 = (s7 + (1 << 20)) >> 21; 5111 s8 += carry7; 5112 s7 -= carry7 * (1 << 21); 5113 carry9 = (s9 + (1 << 20)) >> 21; 5114 s10 += carry9; 5115 s9 -= carry9 * (1 << 21); 5116 carry11 = (s11 + (1 << 20)) >> 21; 5117 s12 += carry11; 5118 s11 -= carry11 * (1 << 21); 5119 carry13 = (s13 + (1 << 20)) >> 21; 5120 s14 += carry13; 5121 s13 -= carry13 * (1 << 21); 5122 carry15 = (s15 + (1 << 20)) >> 21; 5123 s16 += carry15; 5124 s15 -= carry15 * (1 << 21); 5125 5126 s5 += s17 * 666643; 5127 s6 += s17 * 470296; 5128 s7 += s17 * 654183; 5129 s8 -= s17 * 997805; 5130 s9 += s17 * 136657; 5131 s10 -= s17 * 683901; 5132 s17 = 0; 5133 5134 s4 += s16 * 666643; 5135 s5 += s16 * 470296; 5136 s6 += s16 * 654183; 5137 s7 -= s16 * 997805; 5138 s8 += s16 * 136657; 5139 s9 -= s16 * 683901; 5140 s16 = 0; 5141 5142 s3 += s15 * 666643; 5143 s4 += s15 * 470296; 5144 s5 += s15 * 654183; 5145 s6 -= s15 * 997805; 5146 s7 += s15 * 136657; 5147 s8 -= s15 * 683901; 5148 s15 = 0; 5149 5150 s2 += s14 * 666643; 5151 s3 += s14 * 470296; 5152 s4 += s14 * 654183; 5153 s5 -= s14 * 997805; 5154 s6 += s14 * 136657; 5155 s7 -= s14 * 683901; 5156 s14 = 0; 5157 5158 s1 += s13 * 666643; 5159 s2 += s13 * 470296; 5160 s3 += s13 * 654183; 5161 s4 -= s13 * 997805; 5162 s5 += s13 * 136657; 5163 s6 -= s13 * 683901; 5164 s13 = 0; 5165 5166 s0 += s12 * 666643; 5167 s1 += s12 * 470296; 5168 s2 += s12 * 654183; 5169 s3 -= s12 * 997805; 5170 s4 += s12 * 136657; 5171 s5 -= s12 * 683901; 5172 s12 = 0; 5173 5174 carry0 = (s0 + (1 << 20)) >> 21; 5175 s1 += carry0; 5176 s0 -= carry0 * (1 << 21); 5177 carry2 = (s2 + (1 << 20)) >> 21; 5178 s3 += carry2; 5179 s2 -= carry2 * (1 << 21); 5180 carry4 = (s4 + (1 << 20)) >> 21; 5181 s5 += carry4; 5182 s4 -= carry4 * (1 << 21); 5183 carry6 = (s6 + (1 << 20)) >> 21; 5184 s7 += carry6; 5185 s6 -= carry6 * (1 << 21); 5186 carry8 = (s8 + (1 << 20)) >> 21; 5187 s9 += carry8; 5188 s8 -= carry8 * (1 << 21); 5189 carry10 = (s10 + (1 << 20)) >> 21; 5190 s11 += carry10; 5191 s10 -= carry10 * (1 << 21); 5192 5193 carry1 = (s1 + (1 << 20)) >> 21; 5194 s2 += carry1; 5195 s1 -= carry1 * (1 << 21); 5196 carry3 = (s3 + (1 << 20)) >> 21; 5197 s4 += carry3; 5198 s3 -= carry3 * (1 << 21); 5199 carry5 = (s5 + (1 << 20)) >> 21; 5200 s6 += carry5; 5201 s5 -= carry5 * (1 << 21); 5202 carry7 = (s7 + (1 << 20)) >> 21; 5203 s8 += carry7; 5204 s7 -= carry7 * (1 << 21); 5205 carry9 = (s9 + (1 << 20)) >> 21; 5206 s10 += carry9; 5207 s9 -= carry9 * (1 << 21); 5208 carry11 = (s11 + (1 << 20)) >> 21; 5209 s12 += carry11; 5210 s11 -= carry11 * (1 << 21); 5211 5212 s0 += s12 * 666643; 5213 s1 += s12 * 470296; 5214 s2 += s12 * 654183; 5215 s3 -= s12 * 997805; 5216 s4 += s12 * 136657; 5217 s5 -= s12 * 683901; 5218 s12 = 0; 5219 5220 carry0 = s0 >> 21; 5221 s1 += carry0; 5222 s0 -= carry0 * (1 << 21); 5223 carry1 = s1 >> 21; 5224 s2 += carry1; 5225 s1 -= carry1 * (1 << 21); 5226 carry2 = s2 >> 21; 5227 s3 += carry2; 5228 s2 -= carry2 * (1 << 21); 5229 carry3 = s3 >> 21; 5230 s4 += carry3; 5231 s3 -= carry3 * (1 << 21); 5232 carry4 = s4 >> 21; 5233 s5 += carry4; 5234 s4 -= carry4 * (1 << 21); 5235 carry5 = s5 >> 21; 5236 s6 += carry5; 5237 s5 -= carry5 * (1 << 21); 5238 carry6 = s6 >> 21; 5239 s7 += carry6; 5240 s6 -= carry6 * (1 << 21); 5241 carry7 = s7 >> 21; 5242 s8 += carry7; 5243 s7 -= carry7 * (1 << 21); 5244 carry8 = s8 >> 21; 5245 s9 += carry8; 5246 s8 -= carry8 * (1 << 21); 5247 carry9 = s9 >> 21; 5248 s10 += carry9; 5249 s9 -= carry9 * (1 << 21); 5250 carry10 = s10 >> 21; 5251 s11 += carry10; 5252 s10 -= carry10 * (1 << 21); 5253 carry11 = s11 >> 21; 5254 s12 += carry11; 5255 s11 -= carry11 * (1 << 21); 5256 5257 s0 += s12 * 666643; 5258 s1 += s12 * 470296; 5259 s2 += s12 * 654183; 5260 s3 -= s12 * 997805; 5261 s4 += s12 * 136657; 5262 s5 -= s12 * 683901; 5263 s12 = 0; 5264 5265 carry0 = s0 >> 21; 5266 s1 += carry0; 5267 s0 -= carry0 * (1 << 21); 5268 carry1 = s1 >> 21; 5269 s2 += carry1; 5270 s1 -= carry1 * (1 << 21); 5271 carry2 = s2 >> 21; 5272 s3 += carry2; 5273 s2 -= carry2 * (1 << 21); 5274 carry3 = s3 >> 21; 5275 s4 += carry3; 5276 s3 -= carry3 * (1 << 21); 5277 carry4 = s4 >> 21; 5278 s5 += carry4; 5279 s4 -= carry4 * (1 << 21); 5280 carry5 = s5 >> 21; 5281 s6 += carry5; 5282 s5 -= carry5 * (1 << 21); 5283 carry6 = s6 >> 21; 5284 s7 += carry6; 5285 s6 -= carry6 * (1 << 21); 5286 carry7 = s7 >> 21; 5287 s8 += carry7; 5288 s7 -= carry7 * (1 << 21); 5289 carry8 = s8 >> 21; 5290 s9 += carry8; 5291 s8 -= carry8 * (1 << 21); 5292 carry9 = s9 >> 21; 5293 s10 += carry9; 5294 s9 -= carry9 * (1 << 21); 5295 carry10 = s10 >> 21; 5296 s11 += carry10; 5297 s10 -= carry10 * (1 << 21); 5298 5299 s[0] = (uint8_t)(s0 >> 0); 5300 s[1] = (uint8_t)(s0 >> 8); 5301 s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); 5302 s[3] = (uint8_t)(s1 >> 3); 5303 s[4] = (uint8_t)(s1 >> 11); 5304 s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); 5305 s[6] = (uint8_t)(s2 >> 6); 5306 s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); 5307 s[8] = (uint8_t)(s3 >> 1); 5308 s[9] = (uint8_t)(s3 >> 9); 5309 s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); 5310 s[11] = (uint8_t)(s4 >> 4); 5311 s[12] = (uint8_t)(s4 >> 12); 5312 s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); 5313 s[14] = (uint8_t)(s5 >> 7); 5314 s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); 5315 s[16] = (uint8_t)(s6 >> 2); 5316 s[17] = (uint8_t)(s6 >> 10); 5317 s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); 5318 s[19] = (uint8_t)(s7 >> 5); 5319 s[20] = (uint8_t)(s7 >> 13); 5320 s[21] = (uint8_t)(s8 >> 0); 5321 s[22] = (uint8_t)(s8 >> 8); 5322 s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); 5323 s[24] = (uint8_t)(s9 >> 3); 5324 s[25] = (uint8_t)(s9 >> 11); 5325 s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); 5326 s[27] = (uint8_t)(s10 >> 6); 5327 s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); 5328 s[29] = (uint8_t)(s11 >> 1); 5329 s[30] = (uint8_t)(s11 >> 9); 5330 s[31] = (uint8_t)(s11 >> 17); 5331 } 5332 5333 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, 5334 const uint8_t public_key[32], const uint8_t private_key[32]) { 5335 uint8_t az[SHA512_DIGEST_LENGTH]; 5336 uint8_t nonce[SHA512_DIGEST_LENGTH]; 5337 ge_p3 R; 5338 uint8_t hram[SHA512_DIGEST_LENGTH]; 5339 SHA512_CTX hash_ctx; 5340 5341 SHA512_Init(&hash_ctx); 5342 SHA512_Update(&hash_ctx, private_key, 32); 5343 SHA512_Final(az, &hash_ctx); 5344 5345 az[0] &= 248; 5346 az[31] &= 63; 5347 az[31] |= 64; 5348 5349 SHA512_Init(&hash_ctx); 5350 SHA512_Update(&hash_ctx, az + 32, 32); 5351 SHA512_Update(&hash_ctx, message, message_len); 5352 SHA512_Final(nonce, &hash_ctx); 5353 5354 x25519_sc_reduce(nonce); 5355 ge_scalarmult_base(&R, nonce); 5356 ge_p3_tobytes(out_sig, &R); 5357 5358 SHA512_Init(&hash_ctx); 5359 SHA512_Update(&hash_ctx, out_sig, 32); 5360 SHA512_Update(&hash_ctx, public_key, 32); 5361 SHA512_Update(&hash_ctx, message, message_len); 5362 SHA512_Final(hram, &hash_ctx); 5363 5364 x25519_sc_reduce(hram); 5365 sc_muladd(out_sig + 32, hram, az, nonce); 5366 5367 OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx)); 5368 OPENSSL_cleanse(nonce, sizeof(nonce)); 5369 OPENSSL_cleanse(az, sizeof(az)); 5370 5371 return 1; 5372 } 5373 5374 int ED25519_verify(const uint8_t *message, size_t message_len, 5375 const uint8_t signature[64], const uint8_t public_key[32]) { 5376 ge_p3 A; 5377 uint8_t rcopy[32]; 5378 uint8_t scopy[32]; 5379 SHA512_CTX hash_ctx; 5380 ge_p2 R; 5381 uint8_t rcheck[32]; 5382 uint8_t h[SHA512_DIGEST_LENGTH]; 5383 5384 if ((signature[63] & 224) != 0 || 5385 ge_frombytes_vartime(&A, public_key) != 0) { 5386 return 0; 5387 } 5388 5389 fe_neg(A.X, A.X); 5390 fe_neg(A.T, A.T); 5391 5392 memcpy(rcopy, signature, 32); 5393 memcpy(scopy, signature + 32, 32); 5394 5395 SHA512_Init(&hash_ctx); 5396 SHA512_Update(&hash_ctx, signature, 32); 5397 SHA512_Update(&hash_ctx, public_key, 32); 5398 SHA512_Update(&hash_ctx, message, message_len); 5399 SHA512_Final(h, &hash_ctx); 5400 5401 x25519_sc_reduce(h); 5402 5403 ge_double_scalarmult_vartime(&R, h, &A, scopy); 5404 5405 ge_tobytes(rcheck, &R); 5406 5407 return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0; 5408 } 5409 5410 void ED25519_public_from_private(uint8_t out_public_key[32], 5411 const uint8_t private_key[32]) { 5412 uint8_t az[SHA512_DIGEST_LENGTH]; 5413 ge_p3 A; 5414 5415 SHA512(private_key, 32, az); 5416 5417 az[0] &= 248; 5418 az[31] &= 63; 5419 az[31] |= 64; 5420 5421 ge_scalarmult_base(&A, az); 5422 ge_p3_tobytes(out_public_key, &A); 5423 5424 OPENSSL_cleanse(az, sizeof(az)); 5425 } 5426 5427 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], 5428 const uint8_t peer_public_value[32]) { 5429 static const uint8_t kZeros[32] = {0}; 5430 x25519_scalar_mult(out_shared_key, private_key, peer_public_value); 5431 /* The all-zero output results when the input is a point of small order. */ 5432 return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; 5433 } 5434 5435 void X25519_public_from_private(uint8_t out_public_value[32], 5436 const uint8_t private_key[32]) { 5437 uint8_t e[32]; 5438 ge_p3 A; 5439 fe zplusy, zminusy, zminusy_inv; 5440 5441 memcpy(e, private_key, 32); 5442 e[0] &= 248; 5443 e[31] &= 127; 5444 e[31] |= 64; 5445 5446 ge_scalarmult_base(&A, e); 5447 5448 /* We only need the u-coordinate of the curve25519 point. The map is 5449 * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ 5450 fe_add(zplusy, A.Z, A.Y); 5451 fe_sub(zminusy, A.Z, A.Y); 5452 fe_invert(zminusy_inv, zminusy); 5453 fe_mul(zplusy, zplusy, zminusy_inv); 5454 fe_tobytes(out_public_value, zplusy); 5455 5456 OPENSSL_cleanse(e, sizeof(e)); 5457 } 5458