| File: | out/../deps/openssl/openssl/crypto/ec/curve25519.c |
| Warning: | line 5372, column 5 Value stored to 's12' is never read |
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| 1 | /* |
| 2 | * Copyright 2016-2021 The OpenSSL Project Authors. All Rights Reserved. |
| 3 | * |
| 4 | * Licensed under the Apache License 2.0 (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 | /* |
| 11 | * ECDSA low level APIs are deprecated for public use, but still ok for |
| 12 | * internal use. |
| 13 | */ |
| 14 | #include "internal/deprecated.h" |
| 15 | |
| 16 | #include <string.h> |
| 17 | #include "crypto/ecx.h" |
| 18 | #include "ec_local.h" |
| 19 | #include <openssl/evp.h> |
| 20 | #include <openssl/sha.h> |
| 21 | |
| 22 | #include "internal/numbers.h" |
| 23 | |
| 24 | #if defined(X25519_ASM1) && (defined(__x86_641) || defined(__x86_64__1) || \ |
| 25 | defined(_M_AMD64) || defined(_M_X64)) |
| 26 | |
| 27 | # define BASE_2_64_IMPLEMENTED |
| 28 | |
| 29 | typedef uint64_t fe64[4]; |
| 30 | |
| 31 | int x25519_fe64_eligible(void); |
| 32 | |
| 33 | /* |
| 34 | * Following subroutines perform corresponding operations modulo |
| 35 | * 2^256-38, i.e. double the curve modulus. However, inputs and |
| 36 | * outputs are permitted to be partially reduced, i.e. to remain |
| 37 | * in [0..2^256) range. It's all tied up in final fe64_tobytes |
| 38 | * that performs full reduction modulo 2^255-19. |
| 39 | * |
| 40 | * There are no reference C implementations for these. |
| 41 | */ |
| 42 | void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g); |
| 43 | void x25519_fe64_sqr(fe64 h, const fe64 f); |
| 44 | void x25519_fe64_mul121666(fe64 h, fe64 f); |
| 45 | void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g); |
| 46 | void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g); |
| 47 | void x25519_fe64_tobytes(uint8_t *s, const fe64 f); |
| 48 | # define fe64_mulx25519_fe64_mul x25519_fe64_mul |
| 49 | # define fe64_sqrx25519_fe64_sqr x25519_fe64_sqr |
| 50 | # define fe64_mul121666x25519_fe64_mul121666 x25519_fe64_mul121666 |
| 51 | # define fe64_addx25519_fe64_add x25519_fe64_add |
| 52 | # define fe64_subx25519_fe64_sub x25519_fe64_sub |
| 53 | # define fe64_tobytesx25519_fe64_tobytes x25519_fe64_tobytes |
| 54 | |
| 55 | static uint64_t load_8(const uint8_t *in) |
| 56 | { |
| 57 | uint64_t result; |
| 58 | |
| 59 | result = in[0]; |
| 60 | result |= ((uint64_t)in[1]) << 8; |
| 61 | result |= ((uint64_t)in[2]) << 16; |
| 62 | result |= ((uint64_t)in[3]) << 24; |
| 63 | result |= ((uint64_t)in[4]) << 32; |
| 64 | result |= ((uint64_t)in[5]) << 40; |
| 65 | result |= ((uint64_t)in[6]) << 48; |
| 66 | result |= ((uint64_t)in[7]) << 56; |
| 67 | |
| 68 | return result; |
| 69 | } |
| 70 | |
| 71 | static void fe64_frombytes(fe64 h, const uint8_t *s) |
| 72 | { |
| 73 | h[0] = load_8(s); |
| 74 | h[1] = load_8(s + 8); |
| 75 | h[2] = load_8(s + 16); |
| 76 | h[3] = load_8(s + 24) & 0x7fffffffffffffff; |
| 77 | } |
| 78 | |
| 79 | static void fe64_0(fe64 h) |
| 80 | { |
| 81 | h[0] = 0; |
| 82 | h[1] = 0; |
| 83 | h[2] = 0; |
| 84 | h[3] = 0; |
| 85 | } |
| 86 | |
| 87 | static void fe64_1(fe64 h) |
| 88 | { |
| 89 | h[0] = 1; |
| 90 | h[1] = 0; |
| 91 | h[2] = 0; |
| 92 | h[3] = 0; |
| 93 | } |
| 94 | |
| 95 | static void fe64_copy(fe64 h, const fe64 f) |
| 96 | { |
| 97 | h[0] = f[0]; |
| 98 | h[1] = f[1]; |
| 99 | h[2] = f[2]; |
| 100 | h[3] = f[3]; |
| 101 | } |
| 102 | |
| 103 | static void fe64_cswap(fe64 f, fe64 g, unsigned int b) |
| 104 | { |
| 105 | int i; |
| 106 | uint64_t mask = 0 - (uint64_t)b; |
| 107 | |
| 108 | for (i = 0; i < 4; i++) { |
| 109 | uint64_t x = f[i] ^ g[i]; |
| 110 | x &= mask; |
| 111 | f[i] ^= x; |
| 112 | g[i] ^= x; |
| 113 | } |
| 114 | } |
| 115 | |
| 116 | static void fe64_invert(fe64 out, const fe64 z) |
| 117 | { |
| 118 | fe64 t0; |
| 119 | fe64 t1; |
| 120 | fe64 t2; |
| 121 | fe64 t3; |
| 122 | int i; |
| 123 | |
| 124 | /* |
| 125 | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as |
| 126 | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. |
| 127 | */ |
| 128 | |
| 129 | /* t0 = z ** 2 */ |
| 130 | fe64_sqrx25519_fe64_sqr(t0, z); |
| 131 | |
| 132 | /* t1 = t0 ** (2 ** 2) = z ** 8 */ |
| 133 | fe64_sqrx25519_fe64_sqr(t1, t0); |
| 134 | fe64_sqrx25519_fe64_sqr(t1, t1); |
| 135 | |
| 136 | /* t1 = z * t1 = z ** 9 */ |
| 137 | fe64_mulx25519_fe64_mul(t1, z, t1); |
| 138 | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ |
| 139 | fe64_mulx25519_fe64_mul(t0, t0, t1); |
| 140 | |
| 141 | /* t2 = t0 ** 2 = z ** 22 */ |
| 142 | fe64_sqrx25519_fe64_sqr(t2, t0); |
| 143 | |
| 144 | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ |
| 145 | fe64_mulx25519_fe64_mul(t1, t1, t2); |
| 146 | |
| 147 | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ |
| 148 | fe64_sqrx25519_fe64_sqr(t2, t1); |
| 149 | for (i = 1; i < 5; ++i) |
| 150 | fe64_sqrx25519_fe64_sqr(t2, t2); |
| 151 | |
| 152 | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ |
| 153 | fe64_mulx25519_fe64_mul(t1, t2, t1); |
| 154 | |
| 155 | /* Continuing similarly... */ |
| 156 | |
| 157 | /* t2 = z ** (2 ** 20 - 1) */ |
| 158 | fe64_sqrx25519_fe64_sqr(t2, t1); |
| 159 | for (i = 1; i < 10; ++i) |
| 160 | fe64_sqrx25519_fe64_sqr(t2, t2); |
| 161 | |
| 162 | fe64_mulx25519_fe64_mul(t2, t2, t1); |
| 163 | |
| 164 | /* t2 = z ** (2 ** 40 - 1) */ |
| 165 | fe64_sqrx25519_fe64_sqr(t3, t2); |
| 166 | for (i = 1; i < 20; ++i) |
| 167 | fe64_sqrx25519_fe64_sqr(t3, t3); |
| 168 | |
| 169 | fe64_mulx25519_fe64_mul(t2, t3, t2); |
| 170 | |
| 171 | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ |
| 172 | for (i = 0; i < 10; ++i) |
| 173 | fe64_sqrx25519_fe64_sqr(t2, t2); |
| 174 | |
| 175 | /* t1 = z ** (2 ** 50 - 1) */ |
| 176 | fe64_mulx25519_fe64_mul(t1, t2, t1); |
| 177 | |
| 178 | /* t2 = z ** (2 ** 100 - 1) */ |
| 179 | fe64_sqrx25519_fe64_sqr(t2, t1); |
| 180 | for (i = 1; i < 50; ++i) |
| 181 | fe64_sqrx25519_fe64_sqr(t2, t2); |
| 182 | |
| 183 | fe64_mulx25519_fe64_mul(t2, t2, t1); |
| 184 | |
| 185 | /* t2 = z ** (2 ** 200 - 1) */ |
| 186 | fe64_sqrx25519_fe64_sqr(t3, t2); |
| 187 | for (i = 1; i < 100; ++i) |
| 188 | fe64_sqrx25519_fe64_sqr(t3, t3); |
| 189 | |
| 190 | fe64_mulx25519_fe64_mul(t2, t3, t2); |
| 191 | |
| 192 | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ |
| 193 | for (i = 0; i < 50; ++i) |
| 194 | fe64_sqrx25519_fe64_sqr(t2, t2); |
| 195 | |
| 196 | /* t1 = z ** (2 ** 250 - 1) */ |
| 197 | fe64_mulx25519_fe64_mul(t1, t2, t1); |
| 198 | |
| 199 | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ |
| 200 | for (i = 0; i < 5; ++i) |
| 201 | fe64_sqrx25519_fe64_sqr(t1, t1); |
| 202 | |
| 203 | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ |
| 204 | fe64_mulx25519_fe64_mul(out, t1, t0); |
| 205 | } |
| 206 | |
| 207 | /* |
| 208 | * Duplicate of original x25519_scalar_mult_generic, but using |
| 209 | * fe64_* subroutines. |
| 210 | */ |
| 211 | static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32], |
| 212 | const uint8_t point[32]) |
| 213 | { |
| 214 | fe64 x1, x2, z2, x3, z3, tmp0, tmp1; |
| 215 | uint8_t e[32]; |
| 216 | unsigned swap = 0; |
| 217 | int pos; |
| 218 | |
| 219 | memcpy(e, scalar, 32); |
| 220 | e[0] &= 0xf8; |
| 221 | e[31] &= 0x7f; |
| 222 | e[31] |= 0x40; |
| 223 | fe64_frombytes(x1, point); |
| 224 | fe64_1(x2); |
| 225 | fe64_0(z2); |
| 226 | fe64_copy(x3, x1); |
| 227 | fe64_1(z3); |
| 228 | |
| 229 | for (pos = 254; pos >= 0; --pos) { |
| 230 | unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); |
| 231 | |
| 232 | swap ^= b; |
| 233 | fe64_cswap(x2, x3, swap); |
| 234 | fe64_cswap(z2, z3, swap); |
| 235 | swap = b; |
| 236 | fe64_subx25519_fe64_sub(tmp0, x3, z3); |
| 237 | fe64_subx25519_fe64_sub(tmp1, x2, z2); |
| 238 | fe64_addx25519_fe64_add(x2, x2, z2); |
| 239 | fe64_addx25519_fe64_add(z2, x3, z3); |
| 240 | fe64_mulx25519_fe64_mul(z3, x2, tmp0); |
| 241 | fe64_mulx25519_fe64_mul(z2, z2, tmp1); |
| 242 | fe64_sqrx25519_fe64_sqr(tmp0, tmp1); |
| 243 | fe64_sqrx25519_fe64_sqr(tmp1, x2); |
| 244 | fe64_addx25519_fe64_add(x3, z3, z2); |
| 245 | fe64_subx25519_fe64_sub(z2, z3, z2); |
| 246 | fe64_mulx25519_fe64_mul(x2, tmp1, tmp0); |
| 247 | fe64_subx25519_fe64_sub(tmp1, tmp1, tmp0); |
| 248 | fe64_sqrx25519_fe64_sqr(z2, z2); |
| 249 | fe64_mul121666x25519_fe64_mul121666(z3, tmp1); |
| 250 | fe64_sqrx25519_fe64_sqr(x3, x3); |
| 251 | fe64_addx25519_fe64_add(tmp0, tmp0, z3); |
| 252 | fe64_mulx25519_fe64_mul(z3, x1, z2); |
| 253 | fe64_mulx25519_fe64_mul(z2, tmp1, tmp0); |
| 254 | } |
| 255 | |
| 256 | fe64_invert(z2, z2); |
| 257 | fe64_mulx25519_fe64_mul(x2, x2, z2); |
| 258 | fe64_tobytesx25519_fe64_tobytes(out, x2); |
| 259 | |
| 260 | OPENSSL_cleanse(e, sizeof(e)); |
| 261 | } |
| 262 | #endif |
| 263 | |
| 264 | #if defined(X25519_ASM1) \ |
| 265 | || ( defined(INT128_MAX((int128_t) ((((int128_t) 1) << ((sizeof(int128_t) * 8) - 1)) ^ ((int128_t) -1)))) \ |
| 266 | && !defined(__sparc__) \ |
| 267 | && (!defined(__SIZEOF_LONG__8) || (__SIZEOF_LONG__8 == 8)) \ |
| 268 | && !(defined(__ANDROID__) && !defined(__clang__1)) ) |
| 269 | /* |
| 270 | * Base 2^51 implementation. It's virtually no different from reference |
| 271 | * base 2^25.5 implementation in respect to lax boundary conditions for |
| 272 | * intermediate values and even individual limbs. So that whatever you |
| 273 | * know about the reference, applies even here... |
| 274 | */ |
| 275 | # define BASE_2_51_IMPLEMENTED |
| 276 | |
| 277 | typedef uint64_t fe51[5]; |
| 278 | |
| 279 | static const uint64_t MASK51 = 0x7ffffffffffff; |
| 280 | |
| 281 | static uint64_t load_7(const uint8_t *in) |
| 282 | { |
| 283 | uint64_t result; |
| 284 | |
| 285 | result = in[0]; |
| 286 | result |= ((uint64_t)in[1]) << 8; |
| 287 | result |= ((uint64_t)in[2]) << 16; |
| 288 | result |= ((uint64_t)in[3]) << 24; |
| 289 | result |= ((uint64_t)in[4]) << 32; |
| 290 | result |= ((uint64_t)in[5]) << 40; |
| 291 | result |= ((uint64_t)in[6]) << 48; |
| 292 | |
| 293 | return result; |
| 294 | } |
| 295 | |
| 296 | static uint64_t load_6(const uint8_t *in) |
| 297 | { |
| 298 | uint64_t result; |
| 299 | |
| 300 | result = in[0]; |
| 301 | result |= ((uint64_t)in[1]) << 8; |
| 302 | result |= ((uint64_t)in[2]) << 16; |
| 303 | result |= ((uint64_t)in[3]) << 24; |
| 304 | result |= ((uint64_t)in[4]) << 32; |
| 305 | result |= ((uint64_t)in[5]) << 40; |
| 306 | |
| 307 | return result; |
| 308 | } |
| 309 | |
| 310 | static void fe51_frombytes(fe51 h, const uint8_t *s) |
| 311 | { |
| 312 | uint64_t h0 = load_7(s); /* 56 bits */ |
| 313 | uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */ |
| 314 | uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */ |
| 315 | uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */ |
| 316 | uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */ |
| 317 | |
| 318 | h1 |= h0 >> 51; h0 &= MASK51; |
| 319 | h2 |= h1 >> 51; h1 &= MASK51; |
| 320 | h3 |= h2 >> 51; h2 &= MASK51; |
| 321 | h4 |= h3 >> 51; h3 &= MASK51; |
| 322 | |
| 323 | h[0] = h0; |
| 324 | h[1] = h1; |
| 325 | h[2] = h2; |
| 326 | h[3] = h3; |
| 327 | h[4] = h4; |
| 328 | } |
| 329 | |
| 330 | static void fe51_tobytes(uint8_t *s, const fe51 h) |
| 331 | { |
| 332 | uint64_t h0 = h[0]; |
| 333 | uint64_t h1 = h[1]; |
| 334 | uint64_t h2 = h[2]; |
| 335 | uint64_t h3 = h[3]; |
| 336 | uint64_t h4 = h[4]; |
| 337 | uint64_t q; |
| 338 | |
| 339 | /* compare to modulus */ |
| 340 | q = (h0 + 19) >> 51; |
| 341 | q = (h1 + q) >> 51; |
| 342 | q = (h2 + q) >> 51; |
| 343 | q = (h3 + q) >> 51; |
| 344 | q = (h4 + q) >> 51; |
| 345 | |
| 346 | /* full reduce */ |
| 347 | h0 += 19 * q; |
| 348 | h1 += h0 >> 51; h0 &= MASK51; |
| 349 | h2 += h1 >> 51; h1 &= MASK51; |
| 350 | h3 += h2 >> 51; h2 &= MASK51; |
| 351 | h4 += h3 >> 51; h3 &= MASK51; |
| 352 | h4 &= MASK51; |
| 353 | |
| 354 | /* smash */ |
| 355 | s[0] = (uint8_t)(h0 >> 0); |
| 356 | s[1] = (uint8_t)(h0 >> 8); |
| 357 | s[2] = (uint8_t)(h0 >> 16); |
| 358 | s[3] = (uint8_t)(h0 >> 24); |
| 359 | s[4] = (uint8_t)(h0 >> 32); |
| 360 | s[5] = (uint8_t)(h0 >> 40); |
| 361 | s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3)); |
| 362 | s[7] = (uint8_t)(h1 >> 5); |
| 363 | s[8] = (uint8_t)(h1 >> 13); |
| 364 | s[9] = (uint8_t)(h1 >> 21); |
| 365 | s[10] = (uint8_t)(h1 >> 29); |
| 366 | s[11] = (uint8_t)(h1 >> 37); |
| 367 | s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6)); |
| 368 | s[13] = (uint8_t)(h2 >> 2); |
| 369 | s[14] = (uint8_t)(h2 >> 10); |
| 370 | s[15] = (uint8_t)(h2 >> 18); |
| 371 | s[16] = (uint8_t)(h2 >> 26); |
| 372 | s[17] = (uint8_t)(h2 >> 34); |
| 373 | s[18] = (uint8_t)(h2 >> 42); |
| 374 | s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1)); |
| 375 | s[20] = (uint8_t)(h3 >> 7); |
| 376 | s[21] = (uint8_t)(h3 >> 15); |
| 377 | s[22] = (uint8_t)(h3 >> 23); |
| 378 | s[23] = (uint8_t)(h3 >> 31); |
| 379 | s[24] = (uint8_t)(h3 >> 39); |
| 380 | s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4)); |
| 381 | s[26] = (uint8_t)(h4 >> 4); |
| 382 | s[27] = (uint8_t)(h4 >> 12); |
| 383 | s[28] = (uint8_t)(h4 >> 20); |
| 384 | s[29] = (uint8_t)(h4 >> 28); |
| 385 | s[30] = (uint8_t)(h4 >> 36); |
| 386 | s[31] = (uint8_t)(h4 >> 44); |
| 387 | } |
| 388 | |
| 389 | # if defined(X25519_ASM1) |
| 390 | void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g); |
| 391 | void x25519_fe51_sqr(fe51 h, const fe51 f); |
| 392 | void x25519_fe51_mul121666(fe51 h, fe51 f); |
| 393 | # define fe51_mulx25519_fe51_mul x25519_fe51_mul |
| 394 | # define fe51_sqx25519_fe51_sqr x25519_fe51_sqr |
| 395 | # define fe51_mul121666x25519_fe51_mul121666 x25519_fe51_mul121666 |
| 396 | # else |
| 397 | |
| 398 | typedef uint128_t u128; |
| 399 | |
| 400 | static void fe51_mulx25519_fe51_mul(fe51 h, const fe51 f, const fe51 g) |
| 401 | { |
| 402 | u128 h0, h1, h2, h3, h4; |
| 403 | uint64_t f_i, g0, g1, g2, g3, g4; |
| 404 | |
| 405 | f_i = f[0]; |
| 406 | h0 = (u128)f_i * (g0 = g[0]); |
| 407 | h1 = (u128)f_i * (g1 = g[1]); |
| 408 | h2 = (u128)f_i * (g2 = g[2]); |
| 409 | h3 = (u128)f_i * (g3 = g[3]); |
| 410 | h4 = (u128)f_i * (g4 = g[4]); |
| 411 | |
| 412 | f_i = f[1]; |
| 413 | h0 += (u128)f_i * (g4 *= 19); |
| 414 | h1 += (u128)f_i * g0; |
| 415 | h2 += (u128)f_i * g1; |
| 416 | h3 += (u128)f_i * g2; |
| 417 | h4 += (u128)f_i * g3; |
| 418 | |
| 419 | f_i = f[2]; |
| 420 | h0 += (u128)f_i * (g3 *= 19); |
| 421 | h1 += (u128)f_i * g4; |
| 422 | h2 += (u128)f_i * g0; |
| 423 | h3 += (u128)f_i * g1; |
| 424 | h4 += (u128)f_i * g2; |
| 425 | |
| 426 | f_i = f[3]; |
| 427 | h0 += (u128)f_i * (g2 *= 19); |
| 428 | h1 += (u128)f_i * g3; |
| 429 | h2 += (u128)f_i * g4; |
| 430 | h3 += (u128)f_i * g0; |
| 431 | h4 += (u128)f_i * g1; |
| 432 | |
| 433 | f_i = f[4]; |
| 434 | h0 += (u128)f_i * (g1 *= 19); |
| 435 | h1 += (u128)f_i * g2; |
| 436 | h2 += (u128)f_i * g3; |
| 437 | h3 += (u128)f_i * g4; |
| 438 | h4 += (u128)f_i * g0; |
| 439 | |
| 440 | /* partial [lazy] reduction */ |
| 441 | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; |
| 442 | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; |
| 443 | |
| 444 | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; |
| 445 | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; |
| 446 | |
| 447 | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; |
| 448 | g3 += g2 >> 51; g2 &= MASK51; |
| 449 | g1 += g0 >> 51; g0 &= MASK51; |
| 450 | |
| 451 | h[0] = g0; |
| 452 | h[1] = g1; |
| 453 | h[2] = g2; |
| 454 | h[3] = g3; |
| 455 | h[4] = g4; |
| 456 | } |
| 457 | |
| 458 | static void fe51_sqx25519_fe51_sqr(fe51 h, const fe51 f) |
| 459 | { |
| 460 | # if defined(OPENSSL_SMALL_FOOTPRINT) |
| 461 | fe51_mulx25519_fe51_mul(h, f, f); |
| 462 | # else |
| 463 | /* dedicated squaring gives 16-25% overall improvement */ |
| 464 | uint64_t g0 = f[0]; |
| 465 | uint64_t g1 = f[1]; |
| 466 | uint64_t g2 = f[2]; |
| 467 | uint64_t g3 = f[3]; |
| 468 | uint64_t g4 = f[4]; |
| 469 | u128 h0, h1, h2, h3, h4; |
| 470 | |
| 471 | h0 = (u128)g0 * g0; g0 *= 2; |
| 472 | h1 = (u128)g0 * g1; |
| 473 | h2 = (u128)g0 * g2; |
| 474 | h3 = (u128)g0 * g3; |
| 475 | h4 = (u128)g0 * g4; |
| 476 | |
| 477 | g0 = g4; /* borrow g0 */ |
| 478 | h3 += (u128)g0 * (g4 *= 19); |
| 479 | |
| 480 | h2 += (u128)g1 * g1; g1 *= 2; |
| 481 | h3 += (u128)g1 * g2; |
| 482 | h4 += (u128)g1 * g3; |
| 483 | h0 += (u128)g1 * g4; |
| 484 | |
| 485 | g0 = g3; /* borrow g0 */ |
| 486 | h1 += (u128)g0 * (g3 *= 19); |
| 487 | h2 += (u128)(g0 * 2) * g4; |
| 488 | |
| 489 | h4 += (u128)g2 * g2; g2 *= 2; |
| 490 | h0 += (u128)g2 * g3; |
| 491 | h1 += (u128)g2 * g4; |
| 492 | |
| 493 | /* partial [lazy] reduction */ |
| 494 | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; |
| 495 | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; |
| 496 | |
| 497 | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; |
| 498 | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; |
| 499 | |
| 500 | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; |
| 501 | g3 += g2 >> 51; g2 &= MASK51; |
| 502 | g1 += g0 >> 51; g0 &= MASK51; |
| 503 | |
| 504 | h[0] = g0; |
| 505 | h[1] = g1; |
| 506 | h[2] = g2; |
| 507 | h[3] = g3; |
| 508 | h[4] = g4; |
| 509 | # endif |
| 510 | } |
| 511 | |
| 512 | static void fe51_mul121666x25519_fe51_mul121666(fe51 h, fe51 f) |
| 513 | { |
| 514 | u128 h0 = f[0] * (u128)121666; |
| 515 | u128 h1 = f[1] * (u128)121666; |
| 516 | u128 h2 = f[2] * (u128)121666; |
| 517 | u128 h3 = f[3] * (u128)121666; |
| 518 | u128 h4 = f[4] * (u128)121666; |
| 519 | uint64_t g0, g1, g2, g3, g4; |
| 520 | |
| 521 | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; |
| 522 | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; |
| 523 | |
| 524 | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; |
| 525 | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; |
| 526 | |
| 527 | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; |
| 528 | g3 += g2 >> 51; g2 &= MASK51; |
| 529 | g1 += g0 >> 51; g0 &= MASK51; |
| 530 | |
| 531 | h[0] = g0; |
| 532 | h[1] = g1; |
| 533 | h[2] = g2; |
| 534 | h[3] = g3; |
| 535 | h[4] = g4; |
| 536 | } |
| 537 | # endif |
| 538 | |
| 539 | static void fe51_add(fe51 h, const fe51 f, const fe51 g) |
| 540 | { |
| 541 | h[0] = f[0] + g[0]; |
| 542 | h[1] = f[1] + g[1]; |
| 543 | h[2] = f[2] + g[2]; |
| 544 | h[3] = f[3] + g[3]; |
| 545 | h[4] = f[4] + g[4]; |
| 546 | } |
| 547 | |
| 548 | static void fe51_sub(fe51 h, const fe51 f, const fe51 g) |
| 549 | { |
| 550 | /* |
| 551 | * Add 2*modulus to ensure that result remains positive |
| 552 | * even if subtrahend is partially reduced. |
| 553 | */ |
| 554 | h[0] = (f[0] + 0xfffffffffffda) - g[0]; |
| 555 | h[1] = (f[1] + 0xffffffffffffe) - g[1]; |
| 556 | h[2] = (f[2] + 0xffffffffffffe) - g[2]; |
| 557 | h[3] = (f[3] + 0xffffffffffffe) - g[3]; |
| 558 | h[4] = (f[4] + 0xffffffffffffe) - g[4]; |
| 559 | } |
| 560 | |
| 561 | static void fe51_0(fe51 h) |
| 562 | { |
| 563 | h[0] = 0; |
| 564 | h[1] = 0; |
| 565 | h[2] = 0; |
| 566 | h[3] = 0; |
| 567 | h[4] = 0; |
| 568 | } |
| 569 | |
| 570 | static void fe51_1(fe51 h) |
| 571 | { |
| 572 | h[0] = 1; |
| 573 | h[1] = 0; |
| 574 | h[2] = 0; |
| 575 | h[3] = 0; |
| 576 | h[4] = 0; |
| 577 | } |
| 578 | |
| 579 | static void fe51_copy(fe51 h, const fe51 f) |
| 580 | { |
| 581 | h[0] = f[0]; |
| 582 | h[1] = f[1]; |
| 583 | h[2] = f[2]; |
| 584 | h[3] = f[3]; |
| 585 | h[4] = f[4]; |
| 586 | } |
| 587 | |
| 588 | static void fe51_cswap(fe51 f, fe51 g, unsigned int b) |
| 589 | { |
| 590 | int i; |
| 591 | uint64_t mask = 0 - (uint64_t)b; |
| 592 | |
| 593 | for (i = 0; i < 5; i++) { |
| 594 | int64_t x = f[i] ^ g[i]; |
| 595 | x &= mask; |
| 596 | f[i] ^= x; |
| 597 | g[i] ^= x; |
| 598 | } |
| 599 | } |
| 600 | |
| 601 | static void fe51_invert(fe51 out, const fe51 z) |
| 602 | { |
| 603 | fe51 t0; |
| 604 | fe51 t1; |
| 605 | fe51 t2; |
| 606 | fe51 t3; |
| 607 | int i; |
| 608 | |
| 609 | /* |
| 610 | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as |
| 611 | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. |
| 612 | */ |
| 613 | |
| 614 | /* t0 = z ** 2 */ |
| 615 | fe51_sqx25519_fe51_sqr(t0, z); |
| 616 | |
| 617 | /* t1 = t0 ** (2 ** 2) = z ** 8 */ |
| 618 | fe51_sqx25519_fe51_sqr(t1, t0); |
| 619 | fe51_sqx25519_fe51_sqr(t1, t1); |
| 620 | |
| 621 | /* t1 = z * t1 = z ** 9 */ |
| 622 | fe51_mulx25519_fe51_mul(t1, z, t1); |
| 623 | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ |
| 624 | fe51_mulx25519_fe51_mul(t0, t0, t1); |
| 625 | |
| 626 | /* t2 = t0 ** 2 = z ** 22 */ |
| 627 | fe51_sqx25519_fe51_sqr(t2, t0); |
| 628 | |
| 629 | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ |
| 630 | fe51_mulx25519_fe51_mul(t1, t1, t2); |
| 631 | |
| 632 | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ |
| 633 | fe51_sqx25519_fe51_sqr(t2, t1); |
| 634 | for (i = 1; i < 5; ++i) |
| 635 | fe51_sqx25519_fe51_sqr(t2, t2); |
| 636 | |
| 637 | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ |
| 638 | fe51_mulx25519_fe51_mul(t1, t2, t1); |
| 639 | |
| 640 | /* Continuing similarly... */ |
| 641 | |
| 642 | /* t2 = z ** (2 ** 20 - 1) */ |
| 643 | fe51_sqx25519_fe51_sqr(t2, t1); |
| 644 | for (i = 1; i < 10; ++i) |
| 645 | fe51_sqx25519_fe51_sqr(t2, t2); |
| 646 | |
| 647 | fe51_mulx25519_fe51_mul(t2, t2, t1); |
| 648 | |
| 649 | /* t2 = z ** (2 ** 40 - 1) */ |
| 650 | fe51_sqx25519_fe51_sqr(t3, t2); |
| 651 | for (i = 1; i < 20; ++i) |
| 652 | fe51_sqx25519_fe51_sqr(t3, t3); |
| 653 | |
| 654 | fe51_mulx25519_fe51_mul(t2, t3, t2); |
| 655 | |
| 656 | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ |
| 657 | for (i = 0; i < 10; ++i) |
| 658 | fe51_sqx25519_fe51_sqr(t2, t2); |
| 659 | |
| 660 | /* t1 = z ** (2 ** 50 - 1) */ |
| 661 | fe51_mulx25519_fe51_mul(t1, t2, t1); |
| 662 | |
| 663 | /* t2 = z ** (2 ** 100 - 1) */ |
| 664 | fe51_sqx25519_fe51_sqr(t2, t1); |
| 665 | for (i = 1; i < 50; ++i) |
| 666 | fe51_sqx25519_fe51_sqr(t2, t2); |
| 667 | |
| 668 | fe51_mulx25519_fe51_mul(t2, t2, t1); |
| 669 | |
| 670 | /* t2 = z ** (2 ** 200 - 1) */ |
| 671 | fe51_sqx25519_fe51_sqr(t3, t2); |
| 672 | for (i = 1; i < 100; ++i) |
| 673 | fe51_sqx25519_fe51_sqr(t3, t3); |
| 674 | |
| 675 | fe51_mulx25519_fe51_mul(t2, t3, t2); |
| 676 | |
| 677 | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ |
| 678 | for (i = 0; i < 50; ++i) |
| 679 | fe51_sqx25519_fe51_sqr(t2, t2); |
| 680 | |
| 681 | /* t1 = z ** (2 ** 250 - 1) */ |
| 682 | fe51_mulx25519_fe51_mul(t1, t2, t1); |
| 683 | |
| 684 | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ |
| 685 | for (i = 0; i < 5; ++i) |
| 686 | fe51_sqx25519_fe51_sqr(t1, t1); |
| 687 | |
| 688 | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ |
| 689 | fe51_mulx25519_fe51_mul(out, t1, t0); |
| 690 | } |
| 691 | |
| 692 | /* |
| 693 | * Duplicate of original x25519_scalar_mult_generic, but using |
| 694 | * fe51_* subroutines. |
| 695 | */ |
| 696 | static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], |
| 697 | const uint8_t point[32]) |
| 698 | { |
| 699 | fe51 x1, x2, z2, x3, z3, tmp0, tmp1; |
| 700 | uint8_t e[32]; |
| 701 | unsigned swap = 0; |
| 702 | int pos; |
| 703 | |
| 704 | # ifdef BASE_2_64_IMPLEMENTED |
| 705 | if (x25519_fe64_eligible()) { |
| 706 | x25519_scalar_mulx(out, scalar, point); |
| 707 | return; |
| 708 | } |
| 709 | # endif |
| 710 | |
| 711 | memcpy(e, scalar, 32); |
| 712 | e[0] &= 0xf8; |
| 713 | e[31] &= 0x7f; |
| 714 | e[31] |= 0x40; |
| 715 | fe51_frombytes(x1, point); |
| 716 | fe51_1(x2); |
| 717 | fe51_0(z2); |
| 718 | fe51_copy(x3, x1); |
| 719 | fe51_1(z3); |
| 720 | |
| 721 | for (pos = 254; pos >= 0; --pos) { |
| 722 | unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); |
| 723 | |
| 724 | swap ^= b; |
| 725 | fe51_cswap(x2, x3, swap); |
| 726 | fe51_cswap(z2, z3, swap); |
| 727 | swap = b; |
| 728 | fe51_sub(tmp0, x3, z3); |
| 729 | fe51_sub(tmp1, x2, z2); |
| 730 | fe51_add(x2, x2, z2); |
| 731 | fe51_add(z2, x3, z3); |
| 732 | fe51_mulx25519_fe51_mul(z3, tmp0, x2); |
| 733 | fe51_mulx25519_fe51_mul(z2, z2, tmp1); |
| 734 | fe51_sqx25519_fe51_sqr(tmp0, tmp1); |
| 735 | fe51_sqx25519_fe51_sqr(tmp1, x2); |
| 736 | fe51_add(x3, z3, z2); |
| 737 | fe51_sub(z2, z3, z2); |
| 738 | fe51_mulx25519_fe51_mul(x2, tmp1, tmp0); |
| 739 | fe51_sub(tmp1, tmp1, tmp0); |
| 740 | fe51_sqx25519_fe51_sqr(z2, z2); |
| 741 | fe51_mul121666x25519_fe51_mul121666(z3, tmp1); |
| 742 | fe51_sqx25519_fe51_sqr(x3, x3); |
| 743 | fe51_add(tmp0, tmp0, z3); |
| 744 | fe51_mulx25519_fe51_mul(z3, x1, z2); |
| 745 | fe51_mulx25519_fe51_mul(z2, tmp1, tmp0); |
| 746 | } |
| 747 | |
| 748 | fe51_invert(z2, z2); |
| 749 | fe51_mulx25519_fe51_mul(x2, x2, z2); |
| 750 | fe51_tobytes(out, x2); |
| 751 | |
| 752 | OPENSSL_cleanse(e, sizeof(e)); |
| 753 | } |
| 754 | #endif |
| 755 | |
| 756 | /* |
| 757 | * Reference base 2^25.5 implementation. |
| 758 | * |
| 759 | * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP |
| 760 | * 20141124 (http://bench.cr.yp.to/supercop.html). |
| 761 | * |
| 762 | * The field functions are shared by Ed25519 and X25519 where possible. |
| 763 | */ |
| 764 | |
| 765 | /* |
| 766 | * fe means field element. Here the field is \Z/(2^255-19). An element t, |
| 767 | * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 |
| 768 | * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on |
| 769 | * context. |
| 770 | */ |
| 771 | typedef int32_t fe[10]; |
| 772 | |
| 773 | static const int64_t kBottom21Bits = 0x1fffffLL; |
| 774 | static const int64_t kBottom25Bits = 0x1ffffffLL; |
| 775 | static const int64_t kBottom26Bits = 0x3ffffffLL; |
| 776 | static const int64_t kTop39Bits = 0xfffffffffe000000LL; |
| 777 | static const int64_t kTop38Bits = 0xfffffffffc000000LL; |
| 778 | |
| 779 | static uint64_t load_3(const uint8_t *in) |
| 780 | { |
| 781 | uint64_t result; |
| 782 | |
| 783 | result = ((uint64_t)in[0]); |
| 784 | result |= ((uint64_t)in[1]) << 8; |
| 785 | result |= ((uint64_t)in[2]) << 16; |
| 786 | return result; |
| 787 | } |
| 788 | |
| 789 | static uint64_t load_4(const uint8_t *in) |
| 790 | { |
| 791 | uint64_t result; |
| 792 | |
| 793 | result = ((uint64_t)in[0]); |
| 794 | result |= ((uint64_t)in[1]) << 8; |
| 795 | result |= ((uint64_t)in[2]) << 16; |
| 796 | result |= ((uint64_t)in[3]) << 24; |
| 797 | return result; |
| 798 | } |
| 799 | |
| 800 | static void fe_frombytes(fe h, const uint8_t *s) |
| 801 | { |
| 802 | /* Ignores top bit of h. */ |
| 803 | int64_t h0 = load_4(s); |
| 804 | int64_t h1 = load_3(s + 4) << 6; |
| 805 | int64_t h2 = load_3(s + 7) << 5; |
| 806 | int64_t h3 = load_3(s + 10) << 3; |
| 807 | int64_t h4 = load_3(s + 13) << 2; |
| 808 | int64_t h5 = load_4(s + 16); |
| 809 | int64_t h6 = load_3(s + 20) << 7; |
| 810 | int64_t h7 = load_3(s + 23) << 5; |
| 811 | int64_t h8 = load_3(s + 26) << 4; |
| 812 | int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2; |
| 813 | int64_t carry0; |
| 814 | int64_t carry1; |
| 815 | int64_t carry2; |
| 816 | int64_t carry3; |
| 817 | int64_t carry4; |
| 818 | int64_t carry5; |
| 819 | int64_t carry6; |
| 820 | int64_t carry7; |
| 821 | int64_t carry8; |
| 822 | int64_t carry9; |
| 823 | |
| 824 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 825 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 826 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 827 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 828 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 829 | |
| 830 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 831 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 832 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 833 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 834 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 835 | |
| 836 | h[0] = (int32_t)h0; |
| 837 | h[1] = (int32_t)h1; |
| 838 | h[2] = (int32_t)h2; |
| 839 | h[3] = (int32_t)h3; |
| 840 | h[4] = (int32_t)h4; |
| 841 | h[5] = (int32_t)h5; |
| 842 | h[6] = (int32_t)h6; |
| 843 | h[7] = (int32_t)h7; |
| 844 | h[8] = (int32_t)h8; |
| 845 | h[9] = (int32_t)h9; |
| 846 | } |
| 847 | |
| 848 | /* |
| 849 | * Preconditions: |
| 850 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
| 851 | * |
| 852 | * Write p=2^255-19; q=floor(h/p). |
| 853 | * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). |
| 854 | * |
| 855 | * Proof: |
| 856 | * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. |
| 857 | * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. |
| 858 | * |
| 859 | * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). |
| 860 | * Then 0<y<1. |
| 861 | * |
| 862 | * Write r=h-pq. |
| 863 | * Have 0<=r<=p-1=2^255-20. |
| 864 | * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. |
| 865 | * |
| 866 | * Write x=r+19(2^-255)r+y. |
| 867 | * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. |
| 868 | * |
| 869 | * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) |
| 870 | * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. |
| 871 | */ |
| 872 | static void fe_tobytes(uint8_t *s, const fe h) |
| 873 | { |
| 874 | int32_t h0 = h[0]; |
| 875 | int32_t h1 = h[1]; |
| 876 | int32_t h2 = h[2]; |
| 877 | int32_t h3 = h[3]; |
| 878 | int32_t h4 = h[4]; |
| 879 | int32_t h5 = h[5]; |
| 880 | int32_t h6 = h[6]; |
| 881 | int32_t h7 = h[7]; |
| 882 | int32_t h8 = h[8]; |
| 883 | int32_t h9 = h[9]; |
| 884 | int32_t q; |
| 885 | |
| 886 | q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; |
| 887 | q = (h0 + q) >> 26; |
| 888 | q = (h1 + q) >> 25; |
| 889 | q = (h2 + q) >> 26; |
| 890 | q = (h3 + q) >> 25; |
| 891 | q = (h4 + q) >> 26; |
| 892 | q = (h5 + q) >> 25; |
| 893 | q = (h6 + q) >> 26; |
| 894 | q = (h7 + q) >> 25; |
| 895 | q = (h8 + q) >> 26; |
| 896 | q = (h9 + q) >> 25; |
| 897 | |
| 898 | /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ |
| 899 | h0 += 19 * q; |
| 900 | /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ |
| 901 | |
| 902 | h1 += h0 >> 26; h0 &= kBottom26Bits; |
| 903 | h2 += h1 >> 25; h1 &= kBottom25Bits; |
| 904 | h3 += h2 >> 26; h2 &= kBottom26Bits; |
| 905 | h4 += h3 >> 25; h3 &= kBottom25Bits; |
| 906 | h5 += h4 >> 26; h4 &= kBottom26Bits; |
| 907 | h6 += h5 >> 25; h5 &= kBottom25Bits; |
| 908 | h7 += h6 >> 26; h6 &= kBottom26Bits; |
| 909 | h8 += h7 >> 25; h7 &= kBottom25Bits; |
| 910 | h9 += h8 >> 26; h8 &= kBottom26Bits; |
| 911 | h9 &= kBottom25Bits; |
| 912 | /* h10 = carry9 */ |
| 913 | |
| 914 | /* |
| 915 | * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. |
| 916 | * Have h0+...+2^230 h9 between 0 and 2^255-1; |
| 917 | * evidently 2^255 h10-2^255 q = 0. |
| 918 | * Goal: Output h0+...+2^230 h9. |
| 919 | */ |
| 920 | s[ 0] = (uint8_t) (h0 >> 0); |
| 921 | s[ 1] = (uint8_t) (h0 >> 8); |
| 922 | s[ 2] = (uint8_t) (h0 >> 16); |
| 923 | s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2)); |
| 924 | s[ 4] = (uint8_t) (h1 >> 6); |
| 925 | s[ 5] = (uint8_t) (h1 >> 14); |
| 926 | s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3)); |
| 927 | s[ 7] = (uint8_t) (h2 >> 5); |
| 928 | s[ 8] = (uint8_t) (h2 >> 13); |
| 929 | s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5)); |
| 930 | s[10] = (uint8_t) (h3 >> 3); |
| 931 | s[11] = (uint8_t) (h3 >> 11); |
| 932 | s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6)); |
| 933 | s[13] = (uint8_t) (h4 >> 2); |
| 934 | s[14] = (uint8_t) (h4 >> 10); |
| 935 | s[15] = (uint8_t) (h4 >> 18); |
| 936 | s[16] = (uint8_t) (h5 >> 0); |
| 937 | s[17] = (uint8_t) (h5 >> 8); |
| 938 | s[18] = (uint8_t) (h5 >> 16); |
| 939 | s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1)); |
| 940 | s[20] = (uint8_t) (h6 >> 7); |
| 941 | s[21] = (uint8_t) (h6 >> 15); |
| 942 | s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3)); |
| 943 | s[23] = (uint8_t) (h7 >> 5); |
| 944 | s[24] = (uint8_t) (h7 >> 13); |
| 945 | s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4)); |
| 946 | s[26] = (uint8_t) (h8 >> 4); |
| 947 | s[27] = (uint8_t) (h8 >> 12); |
| 948 | s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6)); |
| 949 | s[29] = (uint8_t) (h9 >> 2); |
| 950 | s[30] = (uint8_t) (h9 >> 10); |
| 951 | s[31] = (uint8_t) (h9 >> 18); |
| 952 | } |
| 953 | |
| 954 | /* h = f */ |
| 955 | static void fe_copy(fe h, const fe f) |
| 956 | { |
| 957 | memmove(h, f, sizeof(int32_t) * 10); |
| 958 | } |
| 959 | |
| 960 | /* h = 0 */ |
| 961 | static void fe_0(fe h) |
| 962 | { |
| 963 | memset(h, 0, sizeof(int32_t) * 10); |
| 964 | } |
| 965 | |
| 966 | /* h = 1 */ |
| 967 | static void fe_1(fe h) |
| 968 | { |
| 969 | memset(h, 0, sizeof(int32_t) * 10); |
| 970 | h[0] = 1; |
| 971 | } |
| 972 | |
| 973 | /* |
| 974 | * h = f + g |
| 975 | * |
| 976 | * Can overlap h with f or g. |
| 977 | * |
| 978 | * Preconditions: |
| 979 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 980 | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 981 | * |
| 982 | * Postconditions: |
| 983 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
| 984 | */ |
| 985 | static void fe_add(fe h, const fe f, const fe g) |
| 986 | { |
| 987 | unsigned i; |
| 988 | |
| 989 | for (i = 0; i < 10; i++) { |
| 990 | h[i] = f[i] + g[i]; |
| 991 | } |
| 992 | } |
| 993 | |
| 994 | /* |
| 995 | * h = f - g |
| 996 | * |
| 997 | * Can overlap h with f or g. |
| 998 | * |
| 999 | * Preconditions: |
| 1000 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 1001 | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 1002 | * |
| 1003 | * Postconditions: |
| 1004 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
| 1005 | */ |
| 1006 | static void fe_sub(fe h, const fe f, const fe g) |
| 1007 | { |
| 1008 | unsigned i; |
| 1009 | |
| 1010 | for (i = 0; i < 10; i++) { |
| 1011 | h[i] = f[i] - g[i]; |
| 1012 | } |
| 1013 | } |
| 1014 | |
| 1015 | /* |
| 1016 | * h = f * g |
| 1017 | * |
| 1018 | * Can overlap h with f or g. |
| 1019 | * |
| 1020 | * Preconditions: |
| 1021 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
| 1022 | * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
| 1023 | * |
| 1024 | * Postconditions: |
| 1025 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
| 1026 | * |
| 1027 | * Notes on implementation strategy: |
| 1028 | * |
| 1029 | * Using schoolbook multiplication. |
| 1030 | * Karatsuba would save a little in some cost models. |
| 1031 | * |
| 1032 | * Most multiplications by 2 and 19 are 32-bit precomputations; |
| 1033 | * cheaper than 64-bit postcomputations. |
| 1034 | * |
| 1035 | * There is one remaining multiplication by 19 in the carry chain; |
| 1036 | * one *19 precomputation can be merged into this, |
| 1037 | * but the resulting data flow is considerably less clean. |
| 1038 | * |
| 1039 | * There are 12 carries below. |
| 1040 | * 10 of them are 2-way parallelizable and vectorizable. |
| 1041 | * Can get away with 11 carries, but then data flow is much deeper. |
| 1042 | * |
| 1043 | * With tighter constraints on inputs can squeeze carries into int32. |
| 1044 | */ |
| 1045 | static void fe_mul(fe h, const fe f, const fe g) |
| 1046 | { |
| 1047 | int32_t f0 = f[0]; |
| 1048 | int32_t f1 = f[1]; |
| 1049 | int32_t f2 = f[2]; |
| 1050 | int32_t f3 = f[3]; |
| 1051 | int32_t f4 = f[4]; |
| 1052 | int32_t f5 = f[5]; |
| 1053 | int32_t f6 = f[6]; |
| 1054 | int32_t f7 = f[7]; |
| 1055 | int32_t f8 = f[8]; |
| 1056 | int32_t f9 = f[9]; |
| 1057 | int32_t g0 = g[0]; |
| 1058 | int32_t g1 = g[1]; |
| 1059 | int32_t g2 = g[2]; |
| 1060 | int32_t g3 = g[3]; |
| 1061 | int32_t g4 = g[4]; |
| 1062 | int32_t g5 = g[5]; |
| 1063 | int32_t g6 = g[6]; |
| 1064 | int32_t g7 = g[7]; |
| 1065 | int32_t g8 = g[8]; |
| 1066 | int32_t g9 = g[9]; |
| 1067 | int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ |
| 1068 | int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ |
| 1069 | int32_t g3_19 = 19 * g3; |
| 1070 | int32_t g4_19 = 19 * g4; |
| 1071 | int32_t g5_19 = 19 * g5; |
| 1072 | int32_t g6_19 = 19 * g6; |
| 1073 | int32_t g7_19 = 19 * g7; |
| 1074 | int32_t g8_19 = 19 * g8; |
| 1075 | int32_t g9_19 = 19 * g9; |
| 1076 | int32_t f1_2 = 2 * f1; |
| 1077 | int32_t f3_2 = 2 * f3; |
| 1078 | int32_t f5_2 = 2 * f5; |
| 1079 | int32_t f7_2 = 2 * f7; |
| 1080 | int32_t f9_2 = 2 * f9; |
| 1081 | int64_t f0g0 = f0 * (int64_t) g0; |
| 1082 | int64_t f0g1 = f0 * (int64_t) g1; |
| 1083 | int64_t f0g2 = f0 * (int64_t) g2; |
| 1084 | int64_t f0g3 = f0 * (int64_t) g3; |
| 1085 | int64_t f0g4 = f0 * (int64_t) g4; |
| 1086 | int64_t f0g5 = f0 * (int64_t) g5; |
| 1087 | int64_t f0g6 = f0 * (int64_t) g6; |
| 1088 | int64_t f0g7 = f0 * (int64_t) g7; |
| 1089 | int64_t f0g8 = f0 * (int64_t) g8; |
| 1090 | int64_t f0g9 = f0 * (int64_t) g9; |
| 1091 | int64_t f1g0 = f1 * (int64_t) g0; |
| 1092 | int64_t f1g1_2 = f1_2 * (int64_t) g1; |
| 1093 | int64_t f1g2 = f1 * (int64_t) g2; |
| 1094 | int64_t f1g3_2 = f1_2 * (int64_t) g3; |
| 1095 | int64_t f1g4 = f1 * (int64_t) g4; |
| 1096 | int64_t f1g5_2 = f1_2 * (int64_t) g5; |
| 1097 | int64_t f1g6 = f1 * (int64_t) g6; |
| 1098 | int64_t f1g7_2 = f1_2 * (int64_t) g7; |
| 1099 | int64_t f1g8 = f1 * (int64_t) g8; |
| 1100 | int64_t f1g9_38 = f1_2 * (int64_t) g9_19; |
| 1101 | int64_t f2g0 = f2 * (int64_t) g0; |
| 1102 | int64_t f2g1 = f2 * (int64_t) g1; |
| 1103 | int64_t f2g2 = f2 * (int64_t) g2; |
| 1104 | int64_t f2g3 = f2 * (int64_t) g3; |
| 1105 | int64_t f2g4 = f2 * (int64_t) g4; |
| 1106 | int64_t f2g5 = f2 * (int64_t) g5; |
| 1107 | int64_t f2g6 = f2 * (int64_t) g6; |
| 1108 | int64_t f2g7 = f2 * (int64_t) g7; |
| 1109 | int64_t f2g8_19 = f2 * (int64_t) g8_19; |
| 1110 | int64_t f2g9_19 = f2 * (int64_t) g9_19; |
| 1111 | int64_t f3g0 = f3 * (int64_t) g0; |
| 1112 | int64_t f3g1_2 = f3_2 * (int64_t) g1; |
| 1113 | int64_t f3g2 = f3 * (int64_t) g2; |
| 1114 | int64_t f3g3_2 = f3_2 * (int64_t) g3; |
| 1115 | int64_t f3g4 = f3 * (int64_t) g4; |
| 1116 | int64_t f3g5_2 = f3_2 * (int64_t) g5; |
| 1117 | int64_t f3g6 = f3 * (int64_t) g6; |
| 1118 | int64_t f3g7_38 = f3_2 * (int64_t) g7_19; |
| 1119 | int64_t f3g8_19 = f3 * (int64_t) g8_19; |
| 1120 | int64_t f3g9_38 = f3_2 * (int64_t) g9_19; |
| 1121 | int64_t f4g0 = f4 * (int64_t) g0; |
| 1122 | int64_t f4g1 = f4 * (int64_t) g1; |
| 1123 | int64_t f4g2 = f4 * (int64_t) g2; |
| 1124 | int64_t f4g3 = f4 * (int64_t) g3; |
| 1125 | int64_t f4g4 = f4 * (int64_t) g4; |
| 1126 | int64_t f4g5 = f4 * (int64_t) g5; |
| 1127 | int64_t f4g6_19 = f4 * (int64_t) g6_19; |
| 1128 | int64_t f4g7_19 = f4 * (int64_t) g7_19; |
| 1129 | int64_t f4g8_19 = f4 * (int64_t) g8_19; |
| 1130 | int64_t f4g9_19 = f4 * (int64_t) g9_19; |
| 1131 | int64_t f5g0 = f5 * (int64_t) g0; |
| 1132 | int64_t f5g1_2 = f5_2 * (int64_t) g1; |
| 1133 | int64_t f5g2 = f5 * (int64_t) g2; |
| 1134 | int64_t f5g3_2 = f5_2 * (int64_t) g3; |
| 1135 | int64_t f5g4 = f5 * (int64_t) g4; |
| 1136 | int64_t f5g5_38 = f5_2 * (int64_t) g5_19; |
| 1137 | int64_t f5g6_19 = f5 * (int64_t) g6_19; |
| 1138 | int64_t f5g7_38 = f5_2 * (int64_t) g7_19; |
| 1139 | int64_t f5g8_19 = f5 * (int64_t) g8_19; |
| 1140 | int64_t f5g9_38 = f5_2 * (int64_t) g9_19; |
| 1141 | int64_t f6g0 = f6 * (int64_t) g0; |
| 1142 | int64_t f6g1 = f6 * (int64_t) g1; |
| 1143 | int64_t f6g2 = f6 * (int64_t) g2; |
| 1144 | int64_t f6g3 = f6 * (int64_t) g3; |
| 1145 | int64_t f6g4_19 = f6 * (int64_t) g4_19; |
| 1146 | int64_t f6g5_19 = f6 * (int64_t) g5_19; |
| 1147 | int64_t f6g6_19 = f6 * (int64_t) g6_19; |
| 1148 | int64_t f6g7_19 = f6 * (int64_t) g7_19; |
| 1149 | int64_t f6g8_19 = f6 * (int64_t) g8_19; |
| 1150 | int64_t f6g9_19 = f6 * (int64_t) g9_19; |
| 1151 | int64_t f7g0 = f7 * (int64_t) g0; |
| 1152 | int64_t f7g1_2 = f7_2 * (int64_t) g1; |
| 1153 | int64_t f7g2 = f7 * (int64_t) g2; |
| 1154 | int64_t f7g3_38 = f7_2 * (int64_t) g3_19; |
| 1155 | int64_t f7g4_19 = f7 * (int64_t) g4_19; |
| 1156 | int64_t f7g5_38 = f7_2 * (int64_t) g5_19; |
| 1157 | int64_t f7g6_19 = f7 * (int64_t) g6_19; |
| 1158 | int64_t f7g7_38 = f7_2 * (int64_t) g7_19; |
| 1159 | int64_t f7g8_19 = f7 * (int64_t) g8_19; |
| 1160 | int64_t f7g9_38 = f7_2 * (int64_t) g9_19; |
| 1161 | int64_t f8g0 = f8 * (int64_t) g0; |
| 1162 | int64_t f8g1 = f8 * (int64_t) g1; |
| 1163 | int64_t f8g2_19 = f8 * (int64_t) g2_19; |
| 1164 | int64_t f8g3_19 = f8 * (int64_t) g3_19; |
| 1165 | int64_t f8g4_19 = f8 * (int64_t) g4_19; |
| 1166 | int64_t f8g5_19 = f8 * (int64_t) g5_19; |
| 1167 | int64_t f8g6_19 = f8 * (int64_t) g6_19; |
| 1168 | int64_t f8g7_19 = f8 * (int64_t) g7_19; |
| 1169 | int64_t f8g8_19 = f8 * (int64_t) g8_19; |
| 1170 | int64_t f8g9_19 = f8 * (int64_t) g9_19; |
| 1171 | int64_t f9g0 = f9 * (int64_t) g0; |
| 1172 | int64_t f9g1_38 = f9_2 * (int64_t) g1_19; |
| 1173 | int64_t f9g2_19 = f9 * (int64_t) g2_19; |
| 1174 | int64_t f9g3_38 = f9_2 * (int64_t) g3_19; |
| 1175 | int64_t f9g4_19 = f9 * (int64_t) g4_19; |
| 1176 | int64_t f9g5_38 = f9_2 * (int64_t) g5_19; |
| 1177 | int64_t f9g6_19 = f9 * (int64_t) g6_19; |
| 1178 | int64_t f9g7_38 = f9_2 * (int64_t) g7_19; |
| 1179 | int64_t f9g8_19 = f9 * (int64_t) g8_19; |
| 1180 | int64_t f9g9_38 = f9_2 * (int64_t) g9_19; |
| 1181 | int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; |
| 1182 | int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19; |
| 1183 | int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38; |
| 1184 | int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; |
| 1185 | int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; |
| 1186 | int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; |
| 1187 | int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; |
| 1188 | int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; |
| 1189 | int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; |
| 1190 | int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ; |
| 1191 | int64_t carry0; |
| 1192 | int64_t carry1; |
| 1193 | int64_t carry2; |
| 1194 | int64_t carry3; |
| 1195 | int64_t carry4; |
| 1196 | int64_t carry5; |
| 1197 | int64_t carry6; |
| 1198 | int64_t carry7; |
| 1199 | int64_t carry8; |
| 1200 | int64_t carry9; |
| 1201 | |
| 1202 | /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) |
| 1203 | * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 |
| 1204 | * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) |
| 1205 | * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ |
| 1206 | |
| 1207 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 1208 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 1209 | /* |h0| <= 2^25 */ |
| 1210 | /* |h4| <= 2^25 */ |
| 1211 | /* |h1| <= 1.71*2^59 */ |
| 1212 | /* |h5| <= 1.71*2^59 */ |
| 1213 | |
| 1214 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 1215 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 1216 | /* |h1| <= 2^24; from now on fits into int32 */ |
| 1217 | /* |h5| <= 2^24; from now on fits into int32 */ |
| 1218 | /* |h2| <= 1.41*2^60 */ |
| 1219 | /* |h6| <= 1.41*2^60 */ |
| 1220 | |
| 1221 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 1222 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 1223 | /* |h2| <= 2^25; from now on fits into int32 unchanged */ |
| 1224 | /* |h6| <= 2^25; from now on fits into int32 unchanged */ |
| 1225 | /* |h3| <= 1.71*2^59 */ |
| 1226 | /* |h7| <= 1.71*2^59 */ |
| 1227 | |
| 1228 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 1229 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 1230 | /* |h3| <= 2^24; from now on fits into int32 unchanged */ |
| 1231 | /* |h7| <= 2^24; from now on fits into int32 unchanged */ |
| 1232 | /* |h4| <= 1.72*2^34 */ |
| 1233 | /* |h8| <= 1.41*2^60 */ |
| 1234 | |
| 1235 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 1236 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 1237 | /* |h4| <= 2^25; from now on fits into int32 unchanged */ |
| 1238 | /* |h8| <= 2^25; from now on fits into int32 unchanged */ |
| 1239 | /* |h5| <= 1.01*2^24 */ |
| 1240 | /* |h9| <= 1.71*2^59 */ |
| 1241 | |
| 1242 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 1243 | /* |h9| <= 2^24; from now on fits into int32 unchanged */ |
| 1244 | /* |h0| <= 1.1*2^39 */ |
| 1245 | |
| 1246 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 1247 | /* |h0| <= 2^25; from now on fits into int32 unchanged */ |
| 1248 | /* |h1| <= 1.01*2^24 */ |
| 1249 | |
| 1250 | h[0] = (int32_t)h0; |
| 1251 | h[1] = (int32_t)h1; |
| 1252 | h[2] = (int32_t)h2; |
| 1253 | h[3] = (int32_t)h3; |
| 1254 | h[4] = (int32_t)h4; |
| 1255 | h[5] = (int32_t)h5; |
| 1256 | h[6] = (int32_t)h6; |
| 1257 | h[7] = (int32_t)h7; |
| 1258 | h[8] = (int32_t)h8; |
| 1259 | h[9] = (int32_t)h9; |
| 1260 | } |
| 1261 | |
| 1262 | /* |
| 1263 | * h = f * f |
| 1264 | * |
| 1265 | * Can overlap h with f. |
| 1266 | * |
| 1267 | * Preconditions: |
| 1268 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
| 1269 | * |
| 1270 | * Postconditions: |
| 1271 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
| 1272 | * |
| 1273 | * See fe_mul.c for discussion of implementation strategy. |
| 1274 | */ |
| 1275 | static void fe_sq(fe h, const fe f) |
| 1276 | { |
| 1277 | int32_t f0 = f[0]; |
| 1278 | int32_t f1 = f[1]; |
| 1279 | int32_t f2 = f[2]; |
| 1280 | int32_t f3 = f[3]; |
| 1281 | int32_t f4 = f[4]; |
| 1282 | int32_t f5 = f[5]; |
| 1283 | int32_t f6 = f[6]; |
| 1284 | int32_t f7 = f[7]; |
| 1285 | int32_t f8 = f[8]; |
| 1286 | int32_t f9 = f[9]; |
| 1287 | int32_t f0_2 = 2 * f0; |
| 1288 | int32_t f1_2 = 2 * f1; |
| 1289 | int32_t f2_2 = 2 * f2; |
| 1290 | int32_t f3_2 = 2 * f3; |
| 1291 | int32_t f4_2 = 2 * f4; |
| 1292 | int32_t f5_2 = 2 * f5; |
| 1293 | int32_t f6_2 = 2 * f6; |
| 1294 | int32_t f7_2 = 2 * f7; |
| 1295 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ |
| 1296 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ |
| 1297 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ |
| 1298 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ |
| 1299 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ |
| 1300 | int64_t f0f0 = f0 * (int64_t) f0; |
| 1301 | int64_t f0f1_2 = f0_2 * (int64_t) f1; |
| 1302 | int64_t f0f2_2 = f0_2 * (int64_t) f2; |
| 1303 | int64_t f0f3_2 = f0_2 * (int64_t) f3; |
| 1304 | int64_t f0f4_2 = f0_2 * (int64_t) f4; |
| 1305 | int64_t f0f5_2 = f0_2 * (int64_t) f5; |
| 1306 | int64_t f0f6_2 = f0_2 * (int64_t) f6; |
| 1307 | int64_t f0f7_2 = f0_2 * (int64_t) f7; |
| 1308 | int64_t f0f8_2 = f0_2 * (int64_t) f8; |
| 1309 | int64_t f0f9_2 = f0_2 * (int64_t) f9; |
| 1310 | int64_t f1f1_2 = f1_2 * (int64_t) f1; |
| 1311 | int64_t f1f2_2 = f1_2 * (int64_t) f2; |
| 1312 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; |
| 1313 | int64_t f1f4_2 = f1_2 * (int64_t) f4; |
| 1314 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; |
| 1315 | int64_t f1f6_2 = f1_2 * (int64_t) f6; |
| 1316 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; |
| 1317 | int64_t f1f8_2 = f1_2 * (int64_t) f8; |
| 1318 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; |
| 1319 | int64_t f2f2 = f2 * (int64_t) f2; |
| 1320 | int64_t f2f3_2 = f2_2 * (int64_t) f3; |
| 1321 | int64_t f2f4_2 = f2_2 * (int64_t) f4; |
| 1322 | int64_t f2f5_2 = f2_2 * (int64_t) f5; |
| 1323 | int64_t f2f6_2 = f2_2 * (int64_t) f6; |
| 1324 | int64_t f2f7_2 = f2_2 * (int64_t) f7; |
| 1325 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; |
| 1326 | int64_t f2f9_38 = f2 * (int64_t) f9_38; |
| 1327 | int64_t f3f3_2 = f3_2 * (int64_t) f3; |
| 1328 | int64_t f3f4_2 = f3_2 * (int64_t) f4; |
| 1329 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; |
| 1330 | int64_t f3f6_2 = f3_2 * (int64_t) f6; |
| 1331 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; |
| 1332 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; |
| 1333 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; |
| 1334 | int64_t f4f4 = f4 * (int64_t) f4; |
| 1335 | int64_t f4f5_2 = f4_2 * (int64_t) f5; |
| 1336 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; |
| 1337 | int64_t f4f7_38 = f4 * (int64_t) f7_38; |
| 1338 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; |
| 1339 | int64_t f4f9_38 = f4 * (int64_t) f9_38; |
| 1340 | int64_t f5f5_38 = f5 * (int64_t) f5_38; |
| 1341 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; |
| 1342 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; |
| 1343 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; |
| 1344 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; |
| 1345 | int64_t f6f6_19 = f6 * (int64_t) f6_19; |
| 1346 | int64_t f6f7_38 = f6 * (int64_t) f7_38; |
| 1347 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; |
| 1348 | int64_t f6f9_38 = f6 * (int64_t) f9_38; |
| 1349 | int64_t f7f7_38 = f7 * (int64_t) f7_38; |
| 1350 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; |
| 1351 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; |
| 1352 | int64_t f8f8_19 = f8 * (int64_t) f8_19; |
| 1353 | int64_t f8f9_38 = f8 * (int64_t) f9_38; |
| 1354 | int64_t f9f9_38 = f9 * (int64_t) f9_38; |
| 1355 | int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; |
| 1356 | int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; |
| 1357 | int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; |
| 1358 | int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; |
| 1359 | int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; |
| 1360 | int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; |
| 1361 | int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; |
| 1362 | int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; |
| 1363 | int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; |
| 1364 | int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; |
| 1365 | int64_t carry0; |
| 1366 | int64_t carry1; |
| 1367 | int64_t carry2; |
| 1368 | int64_t carry3; |
| 1369 | int64_t carry4; |
| 1370 | int64_t carry5; |
| 1371 | int64_t carry6; |
| 1372 | int64_t carry7; |
| 1373 | int64_t carry8; |
| 1374 | int64_t carry9; |
| 1375 | |
| 1376 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 1377 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 1378 | |
| 1379 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 1380 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 1381 | |
| 1382 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 1383 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 1384 | |
| 1385 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 1386 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 1387 | |
| 1388 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 1389 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 1390 | |
| 1391 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 1392 | |
| 1393 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 1394 | |
| 1395 | h[0] = (int32_t)h0; |
| 1396 | h[1] = (int32_t)h1; |
| 1397 | h[2] = (int32_t)h2; |
| 1398 | h[3] = (int32_t)h3; |
| 1399 | h[4] = (int32_t)h4; |
| 1400 | h[5] = (int32_t)h5; |
| 1401 | h[6] = (int32_t)h6; |
| 1402 | h[7] = (int32_t)h7; |
| 1403 | h[8] = (int32_t)h8; |
| 1404 | h[9] = (int32_t)h9; |
| 1405 | } |
| 1406 | |
| 1407 | static void fe_invert(fe out, const fe z) |
| 1408 | { |
| 1409 | fe t0; |
| 1410 | fe t1; |
| 1411 | fe t2; |
| 1412 | fe t3; |
| 1413 | int i; |
| 1414 | |
| 1415 | /* |
| 1416 | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as |
| 1417 | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. |
| 1418 | */ |
| 1419 | |
| 1420 | /* t0 = z ** 2 */ |
| 1421 | fe_sq(t0, z); |
| 1422 | |
| 1423 | /* t1 = t0 ** (2 ** 2) = z ** 8 */ |
| 1424 | fe_sq(t1, t0); |
| 1425 | fe_sq(t1, t1); |
| 1426 | |
| 1427 | /* t1 = z * t1 = z ** 9 */ |
| 1428 | fe_mul(t1, z, t1); |
| 1429 | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ |
| 1430 | fe_mul(t0, t0, t1); |
| 1431 | |
| 1432 | /* t2 = t0 ** 2 = z ** 22 */ |
| 1433 | fe_sq(t2, t0); |
| 1434 | |
| 1435 | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ |
| 1436 | fe_mul(t1, t1, t2); |
| 1437 | |
| 1438 | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ |
| 1439 | fe_sq(t2, t1); |
| 1440 | for (i = 1; i < 5; ++i) { |
| 1441 | fe_sq(t2, t2); |
| 1442 | } |
| 1443 | |
| 1444 | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ |
| 1445 | fe_mul(t1, t2, t1); |
| 1446 | |
| 1447 | /* Continuing similarly... */ |
| 1448 | |
| 1449 | /* t2 = z ** (2 ** 20 - 1) */ |
| 1450 | fe_sq(t2, t1); |
| 1451 | for (i = 1; i < 10; ++i) { |
| 1452 | fe_sq(t2, t2); |
| 1453 | } |
| 1454 | fe_mul(t2, t2, t1); |
| 1455 | |
| 1456 | /* t2 = z ** (2 ** 40 - 1) */ |
| 1457 | fe_sq(t3, t2); |
| 1458 | for (i = 1; i < 20; ++i) { |
| 1459 | fe_sq(t3, t3); |
| 1460 | } |
| 1461 | fe_mul(t2, t3, t2); |
| 1462 | |
| 1463 | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ |
| 1464 | for (i = 0; i < 10; ++i) { |
| 1465 | fe_sq(t2, t2); |
| 1466 | } |
| 1467 | /* t1 = z ** (2 ** 50 - 1) */ |
| 1468 | fe_mul(t1, t2, t1); |
| 1469 | |
| 1470 | /* t2 = z ** (2 ** 100 - 1) */ |
| 1471 | fe_sq(t2, t1); |
| 1472 | for (i = 1; i < 50; ++i) { |
| 1473 | fe_sq(t2, t2); |
| 1474 | } |
| 1475 | fe_mul(t2, t2, t1); |
| 1476 | |
| 1477 | /* t2 = z ** (2 ** 200 - 1) */ |
| 1478 | fe_sq(t3, t2); |
| 1479 | for (i = 1; i < 100; ++i) { |
| 1480 | fe_sq(t3, t3); |
| 1481 | } |
| 1482 | fe_mul(t2, t3, t2); |
| 1483 | |
| 1484 | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ |
| 1485 | fe_sq(t2, t2); |
| 1486 | for (i = 1; i < 50; ++i) { |
| 1487 | fe_sq(t2, t2); |
| 1488 | } |
| 1489 | |
| 1490 | /* t1 = z ** (2 ** 250 - 1) */ |
| 1491 | fe_mul(t1, t2, t1); |
| 1492 | |
| 1493 | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ |
| 1494 | fe_sq(t1, t1); |
| 1495 | for (i = 1; i < 5; ++i) { |
| 1496 | fe_sq(t1, t1); |
| 1497 | } |
| 1498 | |
| 1499 | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ |
| 1500 | fe_mul(out, t1, t0); |
| 1501 | } |
| 1502 | |
| 1503 | /* |
| 1504 | * h = -f |
| 1505 | * |
| 1506 | * Preconditions: |
| 1507 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 1508 | * |
| 1509 | * Postconditions: |
| 1510 | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 1511 | */ |
| 1512 | static void fe_neg(fe h, const fe f) |
| 1513 | { |
| 1514 | unsigned i; |
| 1515 | |
| 1516 | for (i = 0; i < 10; i++) { |
| 1517 | h[i] = -f[i]; |
| 1518 | } |
| 1519 | } |
| 1520 | |
| 1521 | /* |
| 1522 | * Replace (f,g) with (g,g) if b == 1; |
| 1523 | * replace (f,g) with (f,g) if b == 0. |
| 1524 | * |
| 1525 | * Preconditions: b in {0,1}. |
| 1526 | */ |
| 1527 | static void fe_cmov(fe f, const fe g, unsigned b) |
| 1528 | { |
| 1529 | size_t i; |
| 1530 | |
| 1531 | b = 0-b; |
| 1532 | for (i = 0; i < 10; i++) { |
| 1533 | int32_t x = f[i] ^ g[i]; |
| 1534 | x &= b; |
| 1535 | f[i] ^= x; |
| 1536 | } |
| 1537 | } |
| 1538 | |
| 1539 | /* |
| 1540 | * return 0 if f == 0 |
| 1541 | * return 1 if f != 0 |
| 1542 | * |
| 1543 | * Preconditions: |
| 1544 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
| 1545 | */ |
| 1546 | static int fe_isnonzero(const fe f) |
| 1547 | { |
| 1548 | uint8_t s[32]; |
| 1549 | static const uint8_t zero[32] = {0}; |
| 1550 | |
| 1551 | fe_tobytes(s, f); |
| 1552 | |
| 1553 | return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; |
| 1554 | } |
| 1555 | |
| 1556 | /* |
| 1557 | * return 1 if f is in {1,3,5,...,q-2} |
| 1558 | * return 0 if f is in {0,2,4,...,q-1} |
| 1559 | * |
| 1560 | * Preconditions: |
| 1561 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
| 1562 | */ |
| 1563 | static int fe_isnegative(const fe f) |
| 1564 | { |
| 1565 | uint8_t s[32]; |
| 1566 | |
| 1567 | fe_tobytes(s, f); |
| 1568 | return s[0] & 1; |
| 1569 | } |
| 1570 | |
| 1571 | /* |
| 1572 | * h = 2 * f * f |
| 1573 | * |
| 1574 | * Can overlap h with f. |
| 1575 | * |
| 1576 | * Preconditions: |
| 1577 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
| 1578 | * |
| 1579 | * Postconditions: |
| 1580 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
| 1581 | * |
| 1582 | * See fe_mul.c for discussion of implementation strategy. |
| 1583 | */ |
| 1584 | static void fe_sq2(fe h, const fe f) |
| 1585 | { |
| 1586 | int32_t f0 = f[0]; |
| 1587 | int32_t f1 = f[1]; |
| 1588 | int32_t f2 = f[2]; |
| 1589 | int32_t f3 = f[3]; |
| 1590 | int32_t f4 = f[4]; |
| 1591 | int32_t f5 = f[5]; |
| 1592 | int32_t f6 = f[6]; |
| 1593 | int32_t f7 = f[7]; |
| 1594 | int32_t f8 = f[8]; |
| 1595 | int32_t f9 = f[9]; |
| 1596 | int32_t f0_2 = 2 * f0; |
| 1597 | int32_t f1_2 = 2 * f1; |
| 1598 | int32_t f2_2 = 2 * f2; |
| 1599 | int32_t f3_2 = 2 * f3; |
| 1600 | int32_t f4_2 = 2 * f4; |
| 1601 | int32_t f5_2 = 2 * f5; |
| 1602 | int32_t f6_2 = 2 * f6; |
| 1603 | int32_t f7_2 = 2 * f7; |
| 1604 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ |
| 1605 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ |
| 1606 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ |
| 1607 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ |
| 1608 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ |
| 1609 | int64_t f0f0 = f0 * (int64_t) f0; |
| 1610 | int64_t f0f1_2 = f0_2 * (int64_t) f1; |
| 1611 | int64_t f0f2_2 = f0_2 * (int64_t) f2; |
| 1612 | int64_t f0f3_2 = f0_2 * (int64_t) f3; |
| 1613 | int64_t f0f4_2 = f0_2 * (int64_t) f4; |
| 1614 | int64_t f0f5_2 = f0_2 * (int64_t) f5; |
| 1615 | int64_t f0f6_2 = f0_2 * (int64_t) f6; |
| 1616 | int64_t f0f7_2 = f0_2 * (int64_t) f7; |
| 1617 | int64_t f0f8_2 = f0_2 * (int64_t) f8; |
| 1618 | int64_t f0f9_2 = f0_2 * (int64_t) f9; |
| 1619 | int64_t f1f1_2 = f1_2 * (int64_t) f1; |
| 1620 | int64_t f1f2_2 = f1_2 * (int64_t) f2; |
| 1621 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; |
| 1622 | int64_t f1f4_2 = f1_2 * (int64_t) f4; |
| 1623 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; |
| 1624 | int64_t f1f6_2 = f1_2 * (int64_t) f6; |
| 1625 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; |
| 1626 | int64_t f1f8_2 = f1_2 * (int64_t) f8; |
| 1627 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; |
| 1628 | int64_t f2f2 = f2 * (int64_t) f2; |
| 1629 | int64_t f2f3_2 = f2_2 * (int64_t) f3; |
| 1630 | int64_t f2f4_2 = f2_2 * (int64_t) f4; |
| 1631 | int64_t f2f5_2 = f2_2 * (int64_t) f5; |
| 1632 | int64_t f2f6_2 = f2_2 * (int64_t) f6; |
| 1633 | int64_t f2f7_2 = f2_2 * (int64_t) f7; |
| 1634 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; |
| 1635 | int64_t f2f9_38 = f2 * (int64_t) f9_38; |
| 1636 | int64_t f3f3_2 = f3_2 * (int64_t) f3; |
| 1637 | int64_t f3f4_2 = f3_2 * (int64_t) f4; |
| 1638 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; |
| 1639 | int64_t f3f6_2 = f3_2 * (int64_t) f6; |
| 1640 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; |
| 1641 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; |
| 1642 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; |
| 1643 | int64_t f4f4 = f4 * (int64_t) f4; |
| 1644 | int64_t f4f5_2 = f4_2 * (int64_t) f5; |
| 1645 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; |
| 1646 | int64_t f4f7_38 = f4 * (int64_t) f7_38; |
| 1647 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; |
| 1648 | int64_t f4f9_38 = f4 * (int64_t) f9_38; |
| 1649 | int64_t f5f5_38 = f5 * (int64_t) f5_38; |
| 1650 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; |
| 1651 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; |
| 1652 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; |
| 1653 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; |
| 1654 | int64_t f6f6_19 = f6 * (int64_t) f6_19; |
| 1655 | int64_t f6f7_38 = f6 * (int64_t) f7_38; |
| 1656 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; |
| 1657 | int64_t f6f9_38 = f6 * (int64_t) f9_38; |
| 1658 | int64_t f7f7_38 = f7 * (int64_t) f7_38; |
| 1659 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; |
| 1660 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; |
| 1661 | int64_t f8f8_19 = f8 * (int64_t) f8_19; |
| 1662 | int64_t f8f9_38 = f8 * (int64_t) f9_38; |
| 1663 | int64_t f9f9_38 = f9 * (int64_t) f9_38; |
| 1664 | int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; |
| 1665 | int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; |
| 1666 | int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; |
| 1667 | int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; |
| 1668 | int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; |
| 1669 | int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; |
| 1670 | int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; |
| 1671 | int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; |
| 1672 | int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; |
| 1673 | int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; |
| 1674 | int64_t carry0; |
| 1675 | int64_t carry1; |
| 1676 | int64_t carry2; |
| 1677 | int64_t carry3; |
| 1678 | int64_t carry4; |
| 1679 | int64_t carry5; |
| 1680 | int64_t carry6; |
| 1681 | int64_t carry7; |
| 1682 | int64_t carry8; |
| 1683 | int64_t carry9; |
| 1684 | |
| 1685 | h0 += h0; |
| 1686 | h1 += h1; |
| 1687 | h2 += h2; |
| 1688 | h3 += h3; |
| 1689 | h4 += h4; |
| 1690 | h5 += h5; |
| 1691 | h6 += h6; |
| 1692 | h7 += h7; |
| 1693 | h8 += h8; |
| 1694 | h9 += h9; |
| 1695 | |
| 1696 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 1697 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 1698 | |
| 1699 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 1700 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 1701 | |
| 1702 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 1703 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 1704 | |
| 1705 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 1706 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 1707 | |
| 1708 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 1709 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 1710 | |
| 1711 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 1712 | |
| 1713 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 1714 | |
| 1715 | h[0] = (int32_t)h0; |
| 1716 | h[1] = (int32_t)h1; |
| 1717 | h[2] = (int32_t)h2; |
| 1718 | h[3] = (int32_t)h3; |
| 1719 | h[4] = (int32_t)h4; |
| 1720 | h[5] = (int32_t)h5; |
| 1721 | h[6] = (int32_t)h6; |
| 1722 | h[7] = (int32_t)h7; |
| 1723 | h[8] = (int32_t)h8; |
| 1724 | h[9] = (int32_t)h9; |
| 1725 | } |
| 1726 | |
| 1727 | static void fe_pow22523(fe out, const fe z) |
| 1728 | { |
| 1729 | fe t0; |
| 1730 | fe t1; |
| 1731 | fe t2; |
| 1732 | int i; |
| 1733 | |
| 1734 | fe_sq(t0, z); |
| 1735 | fe_sq(t1, t0); |
| 1736 | for (i = 1; i < 2; ++i) { |
| 1737 | fe_sq(t1, t1); |
| 1738 | } |
| 1739 | fe_mul(t1, z, t1); |
| 1740 | fe_mul(t0, t0, t1); |
| 1741 | fe_sq(t0, t0); |
| 1742 | fe_mul(t0, t1, t0); |
| 1743 | fe_sq(t1, t0); |
| 1744 | for (i = 1; i < 5; ++i) { |
| 1745 | fe_sq(t1, t1); |
| 1746 | } |
| 1747 | fe_mul(t0, t1, t0); |
| 1748 | fe_sq(t1, t0); |
| 1749 | for (i = 1; i < 10; ++i) { |
| 1750 | fe_sq(t1, t1); |
| 1751 | } |
| 1752 | fe_mul(t1, t1, t0); |
| 1753 | fe_sq(t2, t1); |
| 1754 | for (i = 1; i < 20; ++i) { |
| 1755 | fe_sq(t2, t2); |
| 1756 | } |
| 1757 | fe_mul(t1, t2, t1); |
| 1758 | fe_sq(t1, t1); |
| 1759 | for (i = 1; i < 10; ++i) { |
| 1760 | fe_sq(t1, t1); |
| 1761 | } |
| 1762 | fe_mul(t0, t1, t0); |
| 1763 | fe_sq(t1, t0); |
| 1764 | for (i = 1; i < 50; ++i) { |
| 1765 | fe_sq(t1, t1); |
| 1766 | } |
| 1767 | fe_mul(t1, t1, t0); |
| 1768 | fe_sq(t2, t1); |
| 1769 | for (i = 1; i < 100; ++i) { |
| 1770 | fe_sq(t2, t2); |
| 1771 | } |
| 1772 | fe_mul(t1, t2, t1); |
| 1773 | fe_sq(t1, t1); |
| 1774 | for (i = 1; i < 50; ++i) { |
| 1775 | fe_sq(t1, t1); |
| 1776 | } |
| 1777 | fe_mul(t0, t1, t0); |
| 1778 | fe_sq(t0, t0); |
| 1779 | for (i = 1; i < 2; ++i) { |
| 1780 | fe_sq(t0, t0); |
| 1781 | } |
| 1782 | fe_mul(out, t0, z); |
| 1783 | } |
| 1784 | |
| 1785 | /* |
| 1786 | * ge means group element. |
| 1787 | * |
| 1788 | * Here the group is the set of pairs (x,y) of field elements (see fe.h) |
| 1789 | * satisfying -x^2 + y^2 = 1 + d x^2y^2 |
| 1790 | * where d = -121665/121666. |
| 1791 | * |
| 1792 | * Representations: |
| 1793 | * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z |
| 1794 | * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT |
| 1795 | * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T |
| 1796 | * ge_precomp (Duif): (y+x,y-x,2dxy) |
| 1797 | */ |
| 1798 | typedef struct { |
| 1799 | fe X; |
| 1800 | fe Y; |
| 1801 | fe Z; |
| 1802 | } ge_p2; |
| 1803 | |
| 1804 | typedef struct { |
| 1805 | fe X; |
| 1806 | fe Y; |
| 1807 | fe Z; |
| 1808 | fe T; |
| 1809 | } ge_p3; |
| 1810 | |
| 1811 | typedef struct { |
| 1812 | fe X; |
| 1813 | fe Y; |
| 1814 | fe Z; |
| 1815 | fe T; |
| 1816 | } ge_p1p1; |
| 1817 | |
| 1818 | typedef struct { |
| 1819 | fe yplusx; |
| 1820 | fe yminusx; |
| 1821 | fe xy2d; |
| 1822 | } ge_precomp; |
| 1823 | |
| 1824 | typedef struct { |
| 1825 | fe YplusX; |
| 1826 | fe YminusX; |
| 1827 | fe Z; |
| 1828 | fe T2d; |
| 1829 | } ge_cached; |
| 1830 | |
| 1831 | static void ge_tobytes(uint8_t *s, const ge_p2 *h) |
| 1832 | { |
| 1833 | fe recip; |
| 1834 | fe x; |
| 1835 | fe y; |
| 1836 | |
| 1837 | fe_invert(recip, h->Z); |
| 1838 | fe_mul(x, h->X, recip); |
| 1839 | fe_mul(y, h->Y, recip); |
| 1840 | fe_tobytes(s, y); |
| 1841 | s[31] ^= fe_isnegative(x) << 7; |
| 1842 | } |
| 1843 | |
| 1844 | static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) |
| 1845 | { |
| 1846 | fe recip; |
| 1847 | fe x; |
| 1848 | fe y; |
| 1849 | |
| 1850 | fe_invert(recip, h->Z); |
| 1851 | fe_mul(x, h->X, recip); |
| 1852 | fe_mul(y, h->Y, recip); |
| 1853 | fe_tobytes(s, y); |
| 1854 | s[31] ^= fe_isnegative(x) << 7; |
| 1855 | } |
| 1856 | |
| 1857 | static const fe d = { |
| 1858 | -10913610, 13857413, -15372611, 6949391, 114729, |
| 1859 | -8787816, -6275908, -3247719, -18696448, -12055116 |
| 1860 | }; |
| 1861 | |
| 1862 | static const fe sqrtm1 = { |
| 1863 | -32595792, -7943725, 9377950, 3500415, 12389472, |
| 1864 | -272473, -25146209, -2005654, 326686, 11406482 |
| 1865 | }; |
| 1866 | |
| 1867 | static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) |
| 1868 | { |
| 1869 | fe u; |
| 1870 | fe v; |
| 1871 | fe v3; |
| 1872 | fe vxx; |
| 1873 | fe check; |
| 1874 | |
| 1875 | fe_frombytes(h->Y, s); |
| 1876 | fe_1(h->Z); |
| 1877 | fe_sq(u, h->Y); |
| 1878 | fe_mul(v, u, d); |
| 1879 | fe_sub(u, u, h->Z); /* u = y^2-1 */ |
| 1880 | fe_add(v, v, h->Z); /* v = dy^2+1 */ |
| 1881 | |
| 1882 | fe_sq(v3, v); |
| 1883 | fe_mul(v3, v3, v); /* v3 = v^3 */ |
| 1884 | fe_sq(h->X, v3); |
| 1885 | fe_mul(h->X, h->X, v); |
| 1886 | fe_mul(h->X, h->X, u); /* x = uv^7 */ |
| 1887 | |
| 1888 | fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ |
| 1889 | fe_mul(h->X, h->X, v3); |
| 1890 | fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ |
| 1891 | |
| 1892 | fe_sq(vxx, h->X); |
| 1893 | fe_mul(vxx, vxx, v); |
| 1894 | fe_sub(check, vxx, u); /* vx^2-u */ |
| 1895 | if (fe_isnonzero(check)) { |
| 1896 | fe_add(check, vxx, u); /* vx^2+u */ |
| 1897 | if (fe_isnonzero(check)) { |
| 1898 | return -1; |
| 1899 | } |
| 1900 | fe_mul(h->X, h->X, sqrtm1); |
| 1901 | } |
| 1902 | |
| 1903 | if (fe_isnegative(h->X) != (s[31] >> 7)) { |
| 1904 | fe_neg(h->X, h->X); |
| 1905 | } |
| 1906 | |
| 1907 | fe_mul(h->T, h->X, h->Y); |
| 1908 | return 0; |
| 1909 | } |
| 1910 | |
| 1911 | static void ge_p2_0(ge_p2 *h) |
| 1912 | { |
| 1913 | fe_0(h->X); |
| 1914 | fe_1(h->Y); |
| 1915 | fe_1(h->Z); |
| 1916 | } |
| 1917 | |
| 1918 | static void ge_p3_0(ge_p3 *h) |
| 1919 | { |
| 1920 | fe_0(h->X); |
| 1921 | fe_1(h->Y); |
| 1922 | fe_1(h->Z); |
| 1923 | fe_0(h->T); |
| 1924 | } |
| 1925 | |
| 1926 | static void ge_precomp_0(ge_precomp *h) |
| 1927 | { |
| 1928 | fe_1(h->yplusx); |
| 1929 | fe_1(h->yminusx); |
| 1930 | fe_0(h->xy2d); |
| 1931 | } |
| 1932 | |
| 1933 | /* r = p */ |
| 1934 | static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) |
| 1935 | { |
| 1936 | fe_copy(r->X, p->X); |
| 1937 | fe_copy(r->Y, p->Y); |
| 1938 | fe_copy(r->Z, p->Z); |
| 1939 | } |
| 1940 | |
| 1941 | static const fe d2 = { |
| 1942 | -21827239, -5839606, -30745221, 13898782, 229458, |
| 1943 | 15978800, -12551817, -6495438, 29715968, 9444199 |
| 1944 | }; |
| 1945 | |
| 1946 | /* r = p */ |
| 1947 | static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) |
| 1948 | { |
| 1949 | fe_add(r->YplusX, p->Y, p->X); |
| 1950 | fe_sub(r->YminusX, p->Y, p->X); |
| 1951 | fe_copy(r->Z, p->Z); |
| 1952 | fe_mul(r->T2d, p->T, d2); |
| 1953 | } |
| 1954 | |
| 1955 | /* r = p */ |
| 1956 | static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) |
| 1957 | { |
| 1958 | fe_mul(r->X, p->X, p->T); |
| 1959 | fe_mul(r->Y, p->Y, p->Z); |
| 1960 | fe_mul(r->Z, p->Z, p->T); |
| 1961 | } |
| 1962 | |
| 1963 | /* r = p */ |
| 1964 | static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) |
| 1965 | { |
| 1966 | fe_mul(r->X, p->X, p->T); |
| 1967 | fe_mul(r->Y, p->Y, p->Z); |
| 1968 | fe_mul(r->Z, p->Z, p->T); |
| 1969 | fe_mul(r->T, p->X, p->Y); |
| 1970 | } |
| 1971 | |
| 1972 | /* r = 2 * p */ |
| 1973 | static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) |
| 1974 | { |
| 1975 | fe t0; |
| 1976 | |
| 1977 | fe_sq(r->X, p->X); |
| 1978 | fe_sq(r->Z, p->Y); |
| 1979 | fe_sq2(r->T, p->Z); |
| 1980 | fe_add(r->Y, p->X, p->Y); |
| 1981 | fe_sq(t0, r->Y); |
| 1982 | fe_add(r->Y, r->Z, r->X); |
| 1983 | fe_sub(r->Z, r->Z, r->X); |
| 1984 | fe_sub(r->X, t0, r->Y); |
| 1985 | fe_sub(r->T, r->T, r->Z); |
| 1986 | } |
| 1987 | |
| 1988 | /* r = 2 * p */ |
| 1989 | static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) |
| 1990 | { |
| 1991 | ge_p2 q; |
| 1992 | ge_p3_to_p2(&q, p); |
| 1993 | ge_p2_dbl(r, &q); |
| 1994 | } |
| 1995 | |
| 1996 | /* r = p + q */ |
| 1997 | static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) |
| 1998 | { |
| 1999 | fe t0; |
| 2000 | |
| 2001 | fe_add(r->X, p->Y, p->X); |
| 2002 | fe_sub(r->Y, p->Y, p->X); |
| 2003 | fe_mul(r->Z, r->X, q->yplusx); |
| 2004 | fe_mul(r->Y, r->Y, q->yminusx); |
| 2005 | fe_mul(r->T, q->xy2d, p->T); |
| 2006 | fe_add(t0, p->Z, p->Z); |
| 2007 | fe_sub(r->X, r->Z, r->Y); |
| 2008 | fe_add(r->Y, r->Z, r->Y); |
| 2009 | fe_add(r->Z, t0, r->T); |
| 2010 | fe_sub(r->T, t0, r->T); |
| 2011 | } |
| 2012 | |
| 2013 | /* r = p - q */ |
| 2014 | static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) |
| 2015 | { |
| 2016 | fe t0; |
| 2017 | |
| 2018 | fe_add(r->X, p->Y, p->X); |
| 2019 | fe_sub(r->Y, p->Y, p->X); |
| 2020 | fe_mul(r->Z, r->X, q->yminusx); |
| 2021 | fe_mul(r->Y, r->Y, q->yplusx); |
| 2022 | fe_mul(r->T, q->xy2d, p->T); |
| 2023 | fe_add(t0, p->Z, p->Z); |
| 2024 | fe_sub(r->X, r->Z, r->Y); |
| 2025 | fe_add(r->Y, r->Z, r->Y); |
| 2026 | fe_sub(r->Z, t0, r->T); |
| 2027 | fe_add(r->T, t0, r->T); |
| 2028 | } |
| 2029 | |
| 2030 | /* r = p + q */ |
| 2031 | static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) |
| 2032 | { |
| 2033 | fe t0; |
| 2034 | |
| 2035 | fe_add(r->X, p->Y, p->X); |
| 2036 | fe_sub(r->Y, p->Y, p->X); |
| 2037 | fe_mul(r->Z, r->X, q->YplusX); |
| 2038 | fe_mul(r->Y, r->Y, q->YminusX); |
| 2039 | fe_mul(r->T, q->T2d, p->T); |
| 2040 | fe_mul(r->X, p->Z, q->Z); |
| 2041 | fe_add(t0, r->X, r->X); |
| 2042 | fe_sub(r->X, r->Z, r->Y); |
| 2043 | fe_add(r->Y, r->Z, r->Y); |
| 2044 | fe_add(r->Z, t0, r->T); |
| 2045 | fe_sub(r->T, t0, r->T); |
| 2046 | } |
| 2047 | |
| 2048 | /* r = p - q */ |
| 2049 | static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) |
| 2050 | { |
| 2051 | fe t0; |
| 2052 | |
| 2053 | fe_add(r->X, p->Y, p->X); |
| 2054 | fe_sub(r->Y, p->Y, p->X); |
| 2055 | fe_mul(r->Z, r->X, q->YminusX); |
| 2056 | fe_mul(r->Y, r->Y, q->YplusX); |
| 2057 | fe_mul(r->T, q->T2d, p->T); |
| 2058 | fe_mul(r->X, p->Z, q->Z); |
| 2059 | fe_add(t0, r->X, r->X); |
| 2060 | fe_sub(r->X, r->Z, r->Y); |
| 2061 | fe_add(r->Y, r->Z, r->Y); |
| 2062 | fe_sub(r->Z, t0, r->T); |
| 2063 | fe_add(r->T, t0, r->T); |
| 2064 | } |
| 2065 | |
| 2066 | static uint8_t equal(signed char b, signed char c) |
| 2067 | { |
| 2068 | uint8_t ub = b; |
| 2069 | uint8_t uc = c; |
| 2070 | uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ |
| 2071 | uint32_t y = x; /* 0: yes; 1..255: no */ |
| 2072 | y -= 1; /* 4294967295: yes; 0..254: no */ |
| 2073 | y >>= 31; /* 1: yes; 0: no */ |
| 2074 | return y; |
| 2075 | } |
| 2076 | |
| 2077 | static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) |
| 2078 | { |
| 2079 | fe_cmov(t->yplusx, u->yplusx, b); |
| 2080 | fe_cmov(t->yminusx, u->yminusx, b); |
| 2081 | fe_cmov(t->xy2d, u->xy2d, b); |
| 2082 | } |
| 2083 | |
| 2084 | /* k25519Precomp[i][j] = (j+1)*256^i*B */ |
| 2085 | static const ge_precomp k25519Precomp[32][8] = { |
| 2086 | { |
| 2087 | { |
| 2088 | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, |
| 2089 | 27544626, -11754271, -6079156, 2047605}, |
| 2090 | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
| 2091 | 5043384, 19500929, -15469378}, |
| 2092 | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, |
| 2093 | 29287919, 11864899, -24514362, -4438546}, |
| 2094 | }, |
| 2095 | { |
| 2096 | {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, |
| 2097 | -11717903, -3814571, -358445, -10211303}, |
| 2098 | {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, |
| 2099 | -15616551, 11189268, -26829678, -5319081}, |
| 2100 | {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, |
| 2101 | -3128826, -9541118, -15472047, -4166697}, |
| 2102 | }, |
| 2103 | { |
| 2104 | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, |
| 2105 | 27787600, -14772189, 28944400, -1550024}, |
| 2106 | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, |
| 2107 | 16354577, -11775962, 7689662, 11199574}, |
| 2108 | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, |
| 2109 | 7512774, 10017326, -17749093, -9920357}, |
| 2110 | }, |
| 2111 | { |
| 2112 | {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, |
| 2113 | -28926210, 15006023, 3284568, -6276540}, |
| 2114 | {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, |
| 2115 | 7464579, 9656445, 13059162, 10374397}, |
| 2116 | {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, |
| 2117 | -3839045, -641708, -101325}, |
| 2118 | }, |
| 2119 | { |
| 2120 | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, |
| 2121 | 32867885, 14515107, -15438304, 10819380}, |
| 2122 | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
| 2123 | 12483688, -12668491, 5581306}, |
| 2124 | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, |
| 2125 | 28542350, 13850243, -23678021, -15815942}, |
| 2126 | }, |
| 2127 | { |
| 2128 | {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, |
| 2129 | -19188627, -15224819, -9818940, -12085777}, |
| 2130 | {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, |
| 2131 | -15689887, 1762328, 14866737}, |
| 2132 | {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, |
| 2133 | -28236412, 3959421, 27914454, 4383652}, |
| 2134 | }, |
| 2135 | { |
| 2136 | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, |
| 2137 | 5230134, -23952439, -15175766}, |
| 2138 | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, |
| 2139 | 20654025, 16520125, 30598449, 7715701}, |
| 2140 | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, |
| 2141 | -31400660, 1370708, 29794553, -1409300}, |
| 2142 | }, |
| 2143 | { |
| 2144 | {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, |
| 2145 | 30290735, 10876454, -33154098, 2381726}, |
| 2146 | {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, |
| 2147 | -6236617, 3696005, -32300832, 15351955}, |
| 2148 | {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, |
| 2149 | -32961401, -2970515, 29551813, 10109425}, |
| 2150 | }, |
| 2151 | }, |
| 2152 | { |
| 2153 | { |
| 2154 | {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, |
| 2155 | -2378284, -1627556, 10092783, -4764171}, |
| 2156 | {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, |
| 2157 | -32508754, 12005538, -17810127, 12803510}, |
| 2158 | {17228999, -15661624, -1233527, 300140, -1224870, -11714777, |
| 2159 | 30364213, -9038194, 18016357, 4397660}, |
| 2160 | }, |
| 2161 | { |
| 2162 | {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, |
| 2163 | -26619106, 14544525, -17477504, 982639}, |
| 2164 | {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, |
| 2165 | -4120128, -21047696, 9934963}, |
| 2166 | {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, |
| 2167 | -14747930, 4559895, -30123922, -10897950}, |
| 2168 | }, |
| 2169 | { |
| 2170 | {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, |
| 2171 | 24191034, 4541697, -13338309, 5500568}, |
| 2172 | {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, |
| 2173 | -17430592, 12264343, 10874051, 13524335}, |
| 2174 | {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, |
| 2175 | 5080568, -22528059, 5376628}, |
| 2176 | }, |
| 2177 | { |
| 2178 | {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, |
| 2179 | -22321305, -9447443, 4535768, 1569007}, |
| 2180 | {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, |
| 2181 | -30494562, 3044290, 31848280, 12543772}, |
| 2182 | {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, |
| 2183 | -27377195, -2062731, 7718482, 14474653}, |
| 2184 | }, |
| 2185 | { |
| 2186 | {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, |
| 2187 | -7236665, 24316168, -5253567}, |
| 2188 | {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, |
| 2189 | 33040651, -13424532, -20729456, 8321686}, |
| 2190 | {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, |
| 2191 | 23845965, -11874838, -9984458, 608372}, |
| 2192 | }, |
| 2193 | { |
| 2194 | {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, |
| 2195 | 1123968, -6780577, 27229399, 23887}, |
| 2196 | {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, |
| 2197 | 12797024, -6440308, -1633405, 16678954}, |
| 2198 | {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, |
| 2199 | -1508144, -4795045, -17169265, 4904953}, |
| 2200 | }, |
| 2201 | { |
| 2202 | {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, |
| 2203 | 5169211, 16191880, 2128236, -4326833}, |
| 2204 | {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, |
| 2205 | -29806336, 916033, -6882542, -2986532}, |
| 2206 | {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, |
| 2207 | 285431, 2763829, 15736322, 4143876}, |
| 2208 | }, |
| 2209 | { |
| 2210 | {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, |
| 2211 | -14594663, 23527084, -16458268}, |
| 2212 | {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, |
| 2213 | -32625340, 4087881, -15188911, -14416214}, |
| 2214 | {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, |
| 2215 | 4357868, -4774191, -16323038}, |
| 2216 | }, |
| 2217 | }, |
| 2218 | { |
| 2219 | { |
| 2220 | {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, |
| 2221 | 23365147, -3949732, 7390890, 2759800}, |
| 2222 | {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, |
| 2223 | -4264057, 1244380, -12919645}, |
| 2224 | {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, |
| 2225 | 9208236, 15886429, 16489664}, |
| 2226 | }, |
| 2227 | { |
| 2228 | {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, |
| 2229 | -13693198, 398369, -30606455, -712933}, |
| 2230 | {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, |
| 2231 | 13348553, 12076947, -30836462, 5113182}, |
| 2232 | {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, |
| 2233 | -30341101, -7336386, 13847711, 5387222}, |
| 2234 | }, |
| 2235 | { |
| 2236 | {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, |
| 2237 | 8763061, 3617786, -19600662, 10370991}, |
| 2238 | {20246567, -14369378, 22358229, -543712, 18507283, -10413996, |
| 2239 | 14554437, -8746092, 32232924, 16763880}, |
| 2240 | {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, |
| 2241 | 11094161, 15689506, 3140038, -16510092}, |
| 2242 | }, |
| 2243 | { |
| 2244 | {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, |
| 2245 | -27224800, 9448613, -28774454, 366295}, |
| 2246 | {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, |
| 2247 | 28344573, 8041113, 719605, 11671788}, |
| 2248 | {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, |
| 2249 | -15266516, 27000813, -10195553}, |
| 2250 | }, |
| 2251 | { |
| 2252 | {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, |
| 2253 | 5336097, 6750977, -14521026}, |
| 2254 | {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, |
| 2255 | 1695823, -8819122, 8169720, 16220347}, |
| 2256 | {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, |
| 2257 | -11144307, -2627664, -5990708, -14166033}, |
| 2258 | }, |
| 2259 | { |
| 2260 | {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, |
| 2261 | 27884329, 2847284, 2655861, 1738395}, |
| 2262 | {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, |
| 2263 | 21651608, -3239336, -19087449, -11005278}, |
| 2264 | {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, |
| 2265 | 5821408, 10478196, 8544890}, |
| 2266 | }, |
| 2267 | { |
| 2268 | {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, |
| 2269 | 19270449, 12217473, 17789017, -3395995}, |
| 2270 | {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, |
| 2271 | 15479401, -3853233, 30460520, 1052596}, |
| 2272 | {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, |
| 2273 | 27491595, -4612359, 3179268, -9478891}, |
| 2274 | }, |
| 2275 | { |
| 2276 | {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, |
| 2277 | -14756777, -16411740, 19072640, -9511060}, |
| 2278 | {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, |
| 2279 | 5977896, -5215017, 473099, 5040608}, |
| 2280 | {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, |
| 2281 | 28326862, 1721092, -19558642, -3131606}, |
| 2282 | }, |
| 2283 | }, |
| 2284 | { |
| 2285 | { |
| 2286 | {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, |
| 2287 | 8076149, -27868496, 11538389}, |
| 2288 | {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, |
| 2289 | 8754525, 7446702, -5676054, 5797016}, |
| 2290 | {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, |
| 2291 | 2014099, -9050574, -2369172, -5877341}, |
| 2292 | }, |
| 2293 | { |
| 2294 | {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, |
| 2295 | 1192730, -3714199, 15123619, 10811505}, |
| 2296 | {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, |
| 2297 | 15776356, -28886779, -11974553}, |
| 2298 | {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, |
| 2299 | -20654173, -16484855, 4714547, -9600655}, |
| 2300 | }, |
| 2301 | { |
| 2302 | {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, |
| 2303 | 24611599, -4543832, -11745876, 12340220}, |
| 2304 | {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, |
| 2305 | 9613953, 8241152, 15370987, 9608631}, |
| 2306 | {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, |
| 2307 | 15866074, -28210621, -8814099}, |
| 2308 | }, |
| 2309 | { |
| 2310 | {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, |
| 2311 | 858697, 20571223, 8420556}, |
| 2312 | {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, |
| 2313 | 33531827, 12516406, -21574435, -12476749}, |
| 2314 | {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, |
| 2315 | 7256740, 8791136, 15069930}, |
| 2316 | }, |
| 2317 | { |
| 2318 | {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, |
| 2319 | 14711875, 4874229, -30663140, -2331391}, |
| 2320 | {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, |
| 2321 | -7912378, -33069337, 9234253}, |
| 2322 | {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, |
| 2323 | 31559055, -11609587, 18979186, 13396066}, |
| 2324 | }, |
| 2325 | { |
| 2326 | {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, |
| 2327 | -18816887, 13594782, 33514650, 7021958}, |
| 2328 | {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, |
| 2329 | -25948728, -3916677, -21480480, 12868082}, |
| 2330 | {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, |
| 2331 | -21446107, 2244500, -12455797, -8089383}, |
| 2332 | }, |
| 2333 | { |
| 2334 | {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, |
| 2335 | 33086546, 8957937, -15233648, 5540521}, |
| 2336 | {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, |
| 2337 | -23710744, -1568984, -16128528, -14962807}, |
| 2338 | {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, |
| 2339 | 892185, -11513277, -15205948}, |
| 2340 | }, |
| 2341 | { |
| 2342 | {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, |
| 2343 | 4763127, -19179614, 5867134}, |
| 2344 | {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, |
| 2345 | 27846559, 5931263, -29749703, -16108455}, |
| 2346 | {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, |
| 2347 | 7283490, -15148073, -19526700, 7734629}, |
| 2348 | }, |
| 2349 | }, |
| 2350 | { |
| 2351 | { |
| 2352 | {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, |
| 2353 | 7585295, -3176626, 18549497, 15302069}, |
| 2354 | {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, |
| 2355 | 10458790, -6418461, -8872242, 8424746}, |
| 2356 | {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, |
| 2357 | 19206234, 7134917, -11284482, -828919}, |
| 2358 | }, |
| 2359 | { |
| 2360 | {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, |
| 2361 | 10243738, -14685461, -5066034, 16498837}, |
| 2362 | {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, |
| 2363 | -14124238, 6536641, 10543906}, |
| 2364 | {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, |
| 2365 | -2669190, -16625574, -27235709, 8876771}, |
| 2366 | }, |
| 2367 | { |
| 2368 | {-25742899, -12566864, -15649966, -846607, -33026686, -796288, |
| 2369 | -33481822, 15824474, -604426, -9039817}, |
| 2370 | {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, |
| 2371 | -4890037, 1657394, 3084098}, |
| 2372 | {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, |
| 2373 | 31280319, 14396151, -30233575, 15272409}, |
| 2374 | }, |
| 2375 | { |
| 2376 | {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, |
| 2377 | -25173957, -12636138, -25014757, 1950504}, |
| 2378 | {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, |
| 2379 | -8384306, -8767532, 15341279, 8373727}, |
| 2380 | {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, |
| 2381 | 298136, -10232602, -2878207, 15190420}, |
| 2382 | }, |
| 2383 | { |
| 2384 | {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, |
| 2385 | 8669718, 2742393, -26033313, -6875003}, |
| 2386 | {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, |
| 2387 | 9291594, -16247779, -12154742, 6048605}, |
| 2388 | {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, |
| 2389 | 13934231, 5128323, 11213262, 9168384}, |
| 2390 | }, |
| 2391 | { |
| 2392 | {-26280513, 11007847, 19408960, -940758, -18592965, -4328580, |
| 2393 | -5088060, -11105150, 20470157, -16398701}, |
| 2394 | {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, |
| 2395 | -22783952, 14461608, 14042978, 5230683}, |
| 2396 | {29969567, -2741594, -16711867, -8552442, 9175486, -2468974, |
| 2397 | 21556951, 3506042, -5933891, -12449708}, |
| 2398 | }, |
| 2399 | { |
| 2400 | {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, |
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| 4049 | { |
| 4050 | {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, |
| 4051 | -910336, -2782495, -19386633, 11994101}, |
| 4052 | {21691500, -13624626, -641331, -14367021, 3285881, -3483596, |
| 4053 | -25064666, 9718258, -7477437, 13381418}, |
| 4054 | {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, |
| 4055 | 23111648, -6375247, 28535282, 15779576}, |
| 4056 | }, |
| 4057 | { |
| 4058 | {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, |
| 4059 | -14068454, 12021730, 9955285, -16303356}, |
| 4060 | {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, |
| 4061 | -18426029, 9924399, 20194861, 13380996}, |
| 4062 | {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, |
| 4063 | -1984914, 15707771, 26342023, 10146099}, |
| 4064 | }, |
| 4065 | }, |
| 4066 | { |
| 4067 | { |
| 4068 | {-26016874, -219943, 21339191, -41388, 19745256, -2878700, |
| 4069 | -29637280, 2227040, 21612326, -545728}, |
| 4070 | {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, |
| 4071 | 25764461, 12243797, -20856566, 11649658}, |
| 4072 | {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, |
| 4073 | 6114064, 33514190, 2333242}, |
| 4074 | }, |
| 4075 | { |
| 4076 | {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, |
| 4077 | -6679750, -12670638, 24350578, -13450001}, |
| 4078 | {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, |
| 4079 | -31536088, -10406836, 8317860, 12352766}, |
| 4080 | {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, |
| 4081 | -23552096, -2287550, 20712163, 6719373}, |
| 4082 | }, |
| 4083 | { |
| 4084 | {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, |
| 4085 | -3763210, 26224235, -3297458}, |
| 4086 | {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, |
| 4087 | 21728352, 9493610, 18620611, -16428628}, |
| 4088 | {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, |
| 4089 | -5269471, -9725556, -30701573, -16479657}, |
| 4090 | }, |
| 4091 | { |
| 4092 | {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, |
| 4093 | 12248509, -5240639, 13735342, 1934062}, |
| 4094 | {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, |
| 4095 | -15136294, -3765346, -21277997, 5473616}, |
| 4096 | {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, |
| 4097 | -7125085, 12469656, 29111212, -5451014}, |
| 4098 | }, |
| 4099 | { |
| 4100 | {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, |
| 4101 | 24367466, 6388839, -10295587, 452383}, |
| 4102 | {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, |
| 4103 | -24236251, -5915248, 15766062, 8407814}, |
| 4104 | {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, |
| 4105 | -8917023, -4388953, -8067909, 2276718}, |
| 4106 | }, |
| 4107 | { |
| 4108 | {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, |
| 4109 | -23827587, 5096219, 22740376, -7303417}, |
| 4110 | {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, |
| 4111 | 24051124, 13742383, -15637599, 13295222}, |
| 4112 | {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, |
| 4113 | -17720195, -4612972, -4451357, -14669444}, |
| 4114 | }, |
| 4115 | { |
| 4116 | {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, |
| 4117 | -2469266, -4141880, 7770569, 9620597}, |
| 4118 | {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, |
| 4119 | -1694323, -33502340, -14767970}, |
| 4120 | {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, |
| 4121 | 1220118, 30494170, -11440799}, |
| 4122 | }, |
| 4123 | { |
| 4124 | {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, |
| 4125 | -26739026, 926050, -1684339, -13333647}, |
| 4126 | {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, |
| 4127 | 9021034, 9078865, 3353509, 4033511}, |
| 4128 | {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, |
| 4129 | 23161163, 8839127, 27485041, 7356032}, |
| 4130 | }, |
| 4131 | }, |
| 4132 | { |
| 4133 | { |
| 4134 | {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, |
| 4135 | 2625015, 28431036, -16771834}, |
| 4136 | {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, |
| 4137 | -22545972, 14150565, 15970762, 4099461}, |
| 4138 | {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, |
| 4139 | 13617293, -9937143, 11465739, 8317062}, |
| 4140 | }, |
| 4141 | { |
| 4142 | {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, |
| 4143 | 14898637, 3848455, 20969334, -5157516}, |
| 4144 | {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, |
| 4145 | -21610826, -3649888, 11177095, 14989547}, |
| 4146 | {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, |
| 4147 | 13515641, 2581286, -28487508, 9930240}, |
| 4148 | }, |
| 4149 | { |
| 4150 | {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, |
| 4151 | 18345767, -13403753, 16291481, -5314038}, |
| 4152 | {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, |
| 4153 | 6957617, 4368891, 9788741}, |
| 4154 | {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, |
| 4155 | -21722536, -8613148, 16250552, -11111103}, |
| 4156 | }, |
| 4157 | { |
| 4158 | {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, |
| 4159 | 10604807, -30190403, 4782747}, |
| 4160 | {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, |
| 4161 | -9981571, 4383045, 22546403, 437323}, |
| 4162 | {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, |
| 4163 | 27343084, 2786261, -30633590, -14097016}, |
| 4164 | }, |
| 4165 | { |
| 4166 | {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, |
| 4167 | -19690631, 2355319, -19284671, -6114373}, |
| 4168 | {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, |
| 4169 | 18952177, 15496498, -29380133, 11754228}, |
| 4170 | {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, |
| 4171 | 7141596, 11724556, 22761615, -10134141}, |
| 4172 | }, |
| 4173 | { |
| 4174 | {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, |
| 4175 | -28741185, -12227393, 32851222, 11717399}, |
| 4176 | {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, |
| 4177 | 31474879, 3483633, -1193175, -4030831}, |
| 4178 | {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, |
| 4179 | 33142652, 6546660, -19985279, -3948376}, |
| 4180 | }, |
| 4181 | { |
| 4182 | {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, |
| 4183 | -8537131, -12833048, -30772034, -15486313}, |
| 4184 | {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, |
| 4185 | -31135347, -16049879, 10928917, 3011958}, |
| 4186 | {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, |
| 4187 | -30831056, -12805180, 18008031, 10258577}, |
| 4188 | }, |
| 4189 | { |
| 4190 | {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, |
| 4191 | -1853465, 1367120, 25127874, 6671743}, |
| 4192 | {29701166, -14373934, -10878120, 9279288, -17568, 13127210, |
| 4193 | 21382910, 11042292, 25838796, 4642684}, |
| 4194 | {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, |
| 4195 | 30468147, -13900640, 18423289, 4177476}, |
| 4196 | }, |
| 4197 | }, |
| 4198 | }; |
| 4199 | |
| 4200 | static uint8_t negative(signed char b) |
| 4201 | { |
| 4202 | uint32_t x = b; |
| 4203 | |
| 4204 | x >>= 31; /* 1: yes; 0: no */ |
| 4205 | return x; |
| 4206 | } |
| 4207 | |
| 4208 | static void table_select(ge_precomp *t, int pos, signed char b) |
| 4209 | { |
| 4210 | ge_precomp minust; |
| 4211 | uint8_t bnegative = negative(b); |
| 4212 | uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); |
| 4213 | |
| 4214 | ge_precomp_0(t); |
| 4215 | cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); |
| 4216 | cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); |
| 4217 | cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); |
| 4218 | cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); |
| 4219 | cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); |
| 4220 | cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); |
| 4221 | cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); |
| 4222 | cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); |
| 4223 | fe_copy(minust.yplusx, t->yminusx); |
| 4224 | fe_copy(minust.yminusx, t->yplusx); |
| 4225 | fe_neg(minust.xy2d, t->xy2d); |
| 4226 | cmov(t, &minust, bnegative); |
| 4227 | } |
| 4228 | |
| 4229 | /* |
| 4230 | * h = a * B |
| 4231 | * |
| 4232 | * where a = a[0]+256*a[1]+...+256^31 a[31] |
| 4233 | * B is the Ed25519 base point (x,4/5) with x positive. |
| 4234 | * |
| 4235 | * Preconditions: |
| 4236 | * a[31] <= 127 |
| 4237 | */ |
| 4238 | static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) |
| 4239 | { |
| 4240 | signed char e[64]; |
| 4241 | signed char carry; |
| 4242 | ge_p1p1 r; |
| 4243 | ge_p2 s; |
| 4244 | ge_precomp t; |
| 4245 | int i; |
| 4246 | |
| 4247 | for (i = 0; i < 32; ++i) { |
| 4248 | e[2 * i + 0] = (a[i] >> 0) & 15; |
| 4249 | e[2 * i + 1] = (a[i] >> 4) & 15; |
| 4250 | } |
| 4251 | /* each e[i] is between 0 and 15 */ |
| 4252 | /* e[63] is between 0 and 7 */ |
| 4253 | |
| 4254 | carry = 0; |
| 4255 | for (i = 0; i < 63; ++i) { |
| 4256 | e[i] += carry; |
| 4257 | carry = e[i] + 8; |
| 4258 | carry >>= 4; |
| 4259 | e[i] -= carry << 4; |
| 4260 | } |
| 4261 | e[63] += carry; |
| 4262 | /* each e[i] is between -8 and 8 */ |
| 4263 | |
| 4264 | ge_p3_0(h); |
| 4265 | for (i = 1; i < 64; i += 2) { |
| 4266 | table_select(&t, i / 2, e[i]); |
| 4267 | ge_madd(&r, h, &t); |
| 4268 | ge_p1p1_to_p3(h, &r); |
| 4269 | } |
| 4270 | |
| 4271 | ge_p3_dbl(&r, h); |
| 4272 | ge_p1p1_to_p2(&s, &r); |
| 4273 | ge_p2_dbl(&r, &s); |
| 4274 | ge_p1p1_to_p2(&s, &r); |
| 4275 | ge_p2_dbl(&r, &s); |
| 4276 | ge_p1p1_to_p2(&s, &r); |
| 4277 | ge_p2_dbl(&r, &s); |
| 4278 | ge_p1p1_to_p3(h, &r); |
| 4279 | |
| 4280 | for (i = 0; i < 64; i += 2) { |
| 4281 | table_select(&t, i / 2, e[i]); |
| 4282 | ge_madd(&r, h, &t); |
| 4283 | ge_p1p1_to_p3(h, &r); |
| 4284 | } |
| 4285 | |
| 4286 | OPENSSL_cleanse(e, sizeof(e)); |
| 4287 | } |
| 4288 | |
| 4289 | #if !defined(BASE_2_51_IMPLEMENTED) |
| 4290 | /* |
| 4291 | * Replace (f,g) with (g,f) if b == 1; |
| 4292 | * replace (f,g) with (f,g) if b == 0. |
| 4293 | * |
| 4294 | * Preconditions: b in {0,1}. |
| 4295 | */ |
| 4296 | static void fe_cswap(fe f, fe g, unsigned int b) |
| 4297 | { |
| 4298 | size_t i; |
| 4299 | |
| 4300 | b = 0-b; |
| 4301 | for (i = 0; i < 10; i++) { |
| 4302 | int32_t x = f[i] ^ g[i]; |
| 4303 | x &= b; |
| 4304 | f[i] ^= x; |
| 4305 | g[i] ^= x; |
| 4306 | } |
| 4307 | } |
| 4308 | |
| 4309 | /* |
| 4310 | * h = f * 121666 |
| 4311 | * |
| 4312 | * Can overlap h with f. |
| 4313 | * |
| 4314 | * Preconditions: |
| 4315 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
| 4316 | * |
| 4317 | * Postconditions: |
| 4318 | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 4319 | */ |
| 4320 | static void fe_mul121666(fe h, fe f) |
| 4321 | { |
| 4322 | int32_t f0 = f[0]; |
| 4323 | int32_t f1 = f[1]; |
| 4324 | int32_t f2 = f[2]; |
| 4325 | int32_t f3 = f[3]; |
| 4326 | int32_t f4 = f[4]; |
| 4327 | int32_t f5 = f[5]; |
| 4328 | int32_t f6 = f[6]; |
| 4329 | int32_t f7 = f[7]; |
| 4330 | int32_t f8 = f[8]; |
| 4331 | int32_t f9 = f[9]; |
| 4332 | int64_t h0 = f0 * (int64_t) 121666; |
| 4333 | int64_t h1 = f1 * (int64_t) 121666; |
| 4334 | int64_t h2 = f2 * (int64_t) 121666; |
| 4335 | int64_t h3 = f3 * (int64_t) 121666; |
| 4336 | int64_t h4 = f4 * (int64_t) 121666; |
| 4337 | int64_t h5 = f5 * (int64_t) 121666; |
| 4338 | int64_t h6 = f6 * (int64_t) 121666; |
| 4339 | int64_t h7 = f7 * (int64_t) 121666; |
| 4340 | int64_t h8 = f8 * (int64_t) 121666; |
| 4341 | int64_t h9 = f9 * (int64_t) 121666; |
| 4342 | int64_t carry0; |
| 4343 | int64_t carry1; |
| 4344 | int64_t carry2; |
| 4345 | int64_t carry3; |
| 4346 | int64_t carry4; |
| 4347 | int64_t carry5; |
| 4348 | int64_t carry6; |
| 4349 | int64_t carry7; |
| 4350 | int64_t carry8; |
| 4351 | int64_t carry9; |
| 4352 | |
| 4353 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 4354 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 4355 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 4356 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 4357 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 4358 | |
| 4359 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 4360 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 4361 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 4362 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 4363 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 4364 | |
| 4365 | h[0] = (int32_t)h0; |
| 4366 | h[1] = (int32_t)h1; |
| 4367 | h[2] = (int32_t)h2; |
| 4368 | h[3] = (int32_t)h3; |
| 4369 | h[4] = (int32_t)h4; |
| 4370 | h[5] = (int32_t)h5; |
| 4371 | h[6] = (int32_t)h6; |
| 4372 | h[7] = (int32_t)h7; |
| 4373 | h[8] = (int32_t)h8; |
| 4374 | h[9] = (int32_t)h9; |
| 4375 | } |
| 4376 | |
| 4377 | static void x25519_scalar_mult_generic(uint8_t out[32], |
| 4378 | const uint8_t scalar[32], |
| 4379 | const uint8_t point[32]) { |
| 4380 | fe x1, x2, z2, x3, z3, tmp0, tmp1; |
| 4381 | uint8_t e[32]; |
| 4382 | unsigned swap = 0; |
| 4383 | int pos; |
| 4384 | |
| 4385 | memcpy(e, scalar, 32); |
| 4386 | e[0] &= 248; |
| 4387 | e[31] &= 127; |
| 4388 | e[31] |= 64; |
| 4389 | fe_frombytes(x1, point); |
| 4390 | fe_1(x2); |
| 4391 | fe_0(z2); |
| 4392 | fe_copy(x3, x1); |
| 4393 | fe_1(z3); |
| 4394 | |
| 4395 | for (pos = 254; pos >= 0; --pos) { |
| 4396 | unsigned b = 1 & (e[pos / 8] >> (pos & 7)); |
| 4397 | swap ^= b; |
| 4398 | fe_cswap(x2, x3, swap); |
| 4399 | fe_cswap(z2, z3, swap); |
| 4400 | swap = b; |
| 4401 | fe_sub(tmp0, x3, z3); |
| 4402 | fe_sub(tmp1, x2, z2); |
| 4403 | fe_add(x2, x2, z2); |
| 4404 | fe_add(z2, x3, z3); |
| 4405 | fe_mul(z3, tmp0, x2); |
| 4406 | fe_mul(z2, z2, tmp1); |
| 4407 | fe_sq(tmp0, tmp1); |
| 4408 | fe_sq(tmp1, x2); |
| 4409 | fe_add(x3, z3, z2); |
| 4410 | fe_sub(z2, z3, z2); |
| 4411 | fe_mul(x2, tmp1, tmp0); |
| 4412 | fe_sub(tmp1, tmp1, tmp0); |
| 4413 | fe_sq(z2, z2); |
| 4414 | fe_mul121666(z3, tmp1); |
| 4415 | fe_sq(x3, x3); |
| 4416 | fe_add(tmp0, tmp0, z3); |
| 4417 | fe_mul(z3, x1, z2); |
| 4418 | fe_mul(z2, tmp1, tmp0); |
| 4419 | } |
| 4420 | |
| 4421 | fe_invert(z2, z2); |
| 4422 | fe_mul(x2, x2, z2); |
| 4423 | fe_tobytes(out, x2); |
| 4424 | |
| 4425 | OPENSSL_cleanse(e, sizeof(e)); |
| 4426 | } |
| 4427 | |
| 4428 | static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], |
| 4429 | const uint8_t point[32]) { |
| 4430 | x25519_scalar_mult_generic(out, scalar, point); |
| 4431 | } |
| 4432 | #endif |
| 4433 | |
| 4434 | static void slide(signed char *r, const uint8_t *a) |
| 4435 | { |
| 4436 | int i; |
| 4437 | int b; |
| 4438 | int k; |
| 4439 | |
| 4440 | for (i = 0; i < 256; ++i) { |
| 4441 | r[i] = 1 & (a[i >> 3] >> (i & 7)); |
| 4442 | } |
| 4443 | |
| 4444 | for (i = 0; i < 256; ++i) { |
| 4445 | if (r[i]) { |
| 4446 | for (b = 1; b <= 6 && i + b < 256; ++b) { |
| 4447 | if (r[i + b]) { |
| 4448 | if (r[i] + (r[i + b] << b) <= 15) { |
| 4449 | r[i] += r[i + b] << b; |
| 4450 | r[i + b] = 0; |
| 4451 | } else if (r[i] - (r[i + b] << b) >= -15) { |
| 4452 | r[i] -= r[i + b] << b; |
| 4453 | for (k = i + b; k < 256; ++k) { |
| 4454 | if (!r[k]) { |
| 4455 | r[k] = 1; |
| 4456 | break; |
| 4457 | } |
| 4458 | r[k] = 0; |
| 4459 | } |
| 4460 | } else { |
| 4461 | break; |
| 4462 | } |
| 4463 | } |
| 4464 | } |
| 4465 | } |
| 4466 | } |
| 4467 | } |
| 4468 | |
| 4469 | static const ge_precomp Bi[8] = { |
| 4470 | { |
| 4471 | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, |
| 4472 | -11754271, -6079156, 2047605}, |
| 4473 | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
| 4474 | 5043384, 19500929, -15469378}, |
| 4475 | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, |
| 4476 | 11864899, -24514362, -4438546}, |
| 4477 | }, |
| 4478 | { |
| 4479 | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, |
| 4480 | -14772189, 28944400, -1550024}, |
| 4481 | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, |
| 4482 | -11775962, 7689662, 11199574}, |
| 4483 | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, |
| 4484 | 10017326, -17749093, -9920357}, |
| 4485 | }, |
| 4486 | { |
| 4487 | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, |
| 4488 | 14515107, -15438304, 10819380}, |
| 4489 | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
| 4490 | 12483688, -12668491, 5581306}, |
| 4491 | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, |
| 4492 | 13850243, -23678021, -15815942}, |
| 4493 | }, |
| 4494 | { |
| 4495 | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, |
| 4496 | 5230134, -23952439, -15175766}, |
| 4497 | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, |
| 4498 | 16520125, 30598449, 7715701}, |
| 4499 | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, |
| 4500 | 1370708, 29794553, -1409300}, |
| 4501 | }, |
| 4502 | { |
| 4503 | {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, |
| 4504 | -1361450, -13062696, 13821877}, |
| 4505 | {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, |
| 4506 | -7212327, 18853322, -14220951}, |
| 4507 | {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, |
| 4508 | -10431137, 2207753, -3209784}, |
| 4509 | }, |
| 4510 | { |
| 4511 | {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, |
| 4512 | -663000, -31111463, -16132436}, |
| 4513 | {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, |
| 4514 | 15725684, 171356, 6466918}, |
| 4515 | {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, |
| 4516 | -14088058, -30714912, 16193877}, |
| 4517 | }, |
| 4518 | { |
| 4519 | {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, |
| 4520 | 4729455, -18074513, 9256800}, |
| 4521 | {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, |
| 4522 | 9761698, -19827198, 630305}, |
| 4523 | {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, |
| 4524 | -15960994, -2449256, -14291300}, |
| 4525 | }, |
| 4526 | { |
| 4527 | {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, |
| 4528 | 15033784, 25105118, -7894876}, |
| 4529 | {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, |
| 4530 | 1573892, -2625887, 2198790, -15804619}, |
| 4531 | {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, |
| 4532 | -16236442, -32461234, -12290683}, |
| 4533 | }, |
| 4534 | }; |
| 4535 | |
| 4536 | /* |
| 4537 | * r = a * A + b * B |
| 4538 | * |
| 4539 | * where a = a[0]+256*a[1]+...+256^31 a[31]. |
| 4540 | * and b = b[0]+256*b[1]+...+256^31 b[31]. |
| 4541 | * B is the Ed25519 base point (x,4/5) with x positive. |
| 4542 | */ |
| 4543 | static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, |
| 4544 | const ge_p3 *A, const uint8_t *b) |
| 4545 | { |
| 4546 | signed char aslide[256]; |
| 4547 | signed char bslide[256]; |
| 4548 | ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ |
| 4549 | ge_p1p1 t; |
| 4550 | ge_p3 u; |
| 4551 | ge_p3 A2; |
| 4552 | int i; |
| 4553 | |
| 4554 | slide(aslide, a); |
| 4555 | slide(bslide, b); |
| 4556 | |
| 4557 | ge_p3_to_cached(&Ai[0], A); |
| 4558 | ge_p3_dbl(&t, A); |
| 4559 | ge_p1p1_to_p3(&A2, &t); |
| 4560 | ge_add(&t, &A2, &Ai[0]); |
| 4561 | ge_p1p1_to_p3(&u, &t); |
| 4562 | ge_p3_to_cached(&Ai[1], &u); |
| 4563 | ge_add(&t, &A2, &Ai[1]); |
| 4564 | ge_p1p1_to_p3(&u, &t); |
| 4565 | ge_p3_to_cached(&Ai[2], &u); |
| 4566 | ge_add(&t, &A2, &Ai[2]); |
| 4567 | ge_p1p1_to_p3(&u, &t); |
| 4568 | ge_p3_to_cached(&Ai[3], &u); |
| 4569 | ge_add(&t, &A2, &Ai[3]); |
| 4570 | ge_p1p1_to_p3(&u, &t); |
| 4571 | ge_p3_to_cached(&Ai[4], &u); |
| 4572 | ge_add(&t, &A2, &Ai[4]); |
| 4573 | ge_p1p1_to_p3(&u, &t); |
| 4574 | ge_p3_to_cached(&Ai[5], &u); |
| 4575 | ge_add(&t, &A2, &Ai[5]); |
| 4576 | ge_p1p1_to_p3(&u, &t); |
| 4577 | ge_p3_to_cached(&Ai[6], &u); |
| 4578 | ge_add(&t, &A2, &Ai[6]); |
| 4579 | ge_p1p1_to_p3(&u, &t); |
| 4580 | ge_p3_to_cached(&Ai[7], &u); |
| 4581 | |
| 4582 | ge_p2_0(r); |
| 4583 | |
| 4584 | for (i = 255; i >= 0; --i) { |
| 4585 | if (aslide[i] || bslide[i]) { |
| 4586 | break; |
| 4587 | } |
| 4588 | } |
| 4589 | |
| 4590 | for (; i >= 0; --i) { |
| 4591 | ge_p2_dbl(&t, r); |
| 4592 | |
| 4593 | if (aslide[i] > 0) { |
| 4594 | ge_p1p1_to_p3(&u, &t); |
| 4595 | ge_add(&t, &u, &Ai[aslide[i] / 2]); |
| 4596 | } else if (aslide[i] < 0) { |
| 4597 | ge_p1p1_to_p3(&u, &t); |
| 4598 | ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); |
| 4599 | } |
| 4600 | |
| 4601 | if (bslide[i] > 0) { |
| 4602 | ge_p1p1_to_p3(&u, &t); |
| 4603 | ge_madd(&t, &u, &Bi[bslide[i] / 2]); |
| 4604 | } else if (bslide[i] < 0) { |
| 4605 | ge_p1p1_to_p3(&u, &t); |
| 4606 | ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); |
| 4607 | } |
| 4608 | |
| 4609 | ge_p1p1_to_p2(r, &t); |
| 4610 | } |
| 4611 | } |
| 4612 | |
| 4613 | /* |
| 4614 | * The set of scalars is \Z/l |
| 4615 | * where l = 2^252 + 27742317777372353535851937790883648493. |
| 4616 | * |
| 4617 | * Input: |
| 4618 | * s[0]+256*s[1]+...+256^63*s[63] = s |
| 4619 | * |
| 4620 | * Output: |
| 4621 | * s[0]+256*s[1]+...+256^31*s[31] = s mod l |
| 4622 | * where l = 2^252 + 27742317777372353535851937790883648493. |
| 4623 | * Overwrites s in place. |
| 4624 | */ |
| 4625 | static void x25519_sc_reduce(uint8_t *s) |
| 4626 | { |
| 4627 | int64_t s0 = kBottom21Bits & load_3(s); |
| 4628 | int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5); |
| 4629 | int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2); |
| 4630 | int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7); |
| 4631 | int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4); |
| 4632 | int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1); |
| 4633 | int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6); |
| 4634 | int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3); |
| 4635 | int64_t s8 = kBottom21Bits & load_3(s + 21); |
| 4636 | int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5); |
| 4637 | int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2); |
| 4638 | int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7); |
| 4639 | int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4); |
| 4640 | int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1); |
| 4641 | int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6); |
| 4642 | int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3); |
| 4643 | int64_t s16 = kBottom21Bits & load_3(s + 42); |
| 4644 | int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5); |
| 4645 | int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2); |
| 4646 | int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7); |
| 4647 | int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4); |
| 4648 | int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1); |
| 4649 | int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6); |
| 4650 | int64_t s23 = (load_4(s + 60) >> 3); |
| 4651 | int64_t carry0; |
| 4652 | int64_t carry1; |
| 4653 | int64_t carry2; |
| 4654 | int64_t carry3; |
| 4655 | int64_t carry4; |
| 4656 | int64_t carry5; |
| 4657 | int64_t carry6; |
| 4658 | int64_t carry7; |
| 4659 | int64_t carry8; |
| 4660 | int64_t carry9; |
| 4661 | int64_t carry10; |
| 4662 | int64_t carry11; |
| 4663 | int64_t carry12; |
| 4664 | int64_t carry13; |
| 4665 | int64_t carry14; |
| 4666 | int64_t carry15; |
| 4667 | int64_t carry16; |
| 4668 | |
| 4669 | s11 += s23 * 666643; |
| 4670 | s12 += s23 * 470296; |
| 4671 | s13 += s23 * 654183; |
| 4672 | s14 -= s23 * 997805; |
| 4673 | s15 += s23 * 136657; |
| 4674 | s16 -= s23 * 683901; |
| 4675 | s23 = 0; |
| 4676 | |
| 4677 | s10 += s22 * 666643; |
| 4678 | s11 += s22 * 470296; |
| 4679 | s12 += s22 * 654183; |
| 4680 | s13 -= s22 * 997805; |
| 4681 | s14 += s22 * 136657; |
| 4682 | s15 -= s22 * 683901; |
| 4683 | s22 = 0; |
| 4684 | |
| 4685 | s9 += s21 * 666643; |
| 4686 | s10 += s21 * 470296; |
| 4687 | s11 += s21 * 654183; |
| 4688 | s12 -= s21 * 997805; |
| 4689 | s13 += s21 * 136657; |
| 4690 | s14 -= s21 * 683901; |
| 4691 | s21 = 0; |
| 4692 | |
| 4693 | s8 += s20 * 666643; |
| 4694 | s9 += s20 * 470296; |
| 4695 | s10 += s20 * 654183; |
| 4696 | s11 -= s20 * 997805; |
| 4697 | s12 += s20 * 136657; |
| 4698 | s13 -= s20 * 683901; |
| 4699 | s20 = 0; |
| 4700 | |
| 4701 | s7 += s19 * 666643; |
| 4702 | s8 += s19 * 470296; |
| 4703 | s9 += s19 * 654183; |
| 4704 | s10 -= s19 * 997805; |
| 4705 | s11 += s19 * 136657; |
| 4706 | s12 -= s19 * 683901; |
| 4707 | s19 = 0; |
| 4708 | |
| 4709 | s6 += s18 * 666643; |
| 4710 | s7 += s18 * 470296; |
| 4711 | s8 += s18 * 654183; |
| 4712 | s9 -= s18 * 997805; |
| 4713 | s10 += s18 * 136657; |
| 4714 | s11 -= s18 * 683901; |
| 4715 | s18 = 0; |
| 4716 | |
| 4717 | carry6 = (s6 + (1 << 20)) >> 21; |
| 4718 | s7 += carry6; |
| 4719 | s6 -= carry6 * (1 << 21); |
| 4720 | carry8 = (s8 + (1 << 20)) >> 21; |
| 4721 | s9 += carry8; |
| 4722 | s8 -= carry8 * (1 << 21); |
| 4723 | carry10 = (s10 + (1 << 20)) >> 21; |
| 4724 | s11 += carry10; |
| 4725 | s10 -= carry10 * (1 << 21); |
| 4726 | carry12 = (s12 + (1 << 20)) >> 21; |
| 4727 | s13 += carry12; |
| 4728 | s12 -= carry12 * (1 << 21); |
| 4729 | carry14 = (s14 + (1 << 20)) >> 21; |
| 4730 | s15 += carry14; |
| 4731 | s14 -= carry14 * (1 << 21); |
| 4732 | carry16 = (s16 + (1 << 20)) >> 21; |
| 4733 | s17 += carry16; |
| 4734 | s16 -= carry16 * (1 << 21); |
| 4735 | |
| 4736 | carry7 = (s7 + (1 << 20)) >> 21; |
| 4737 | s8 += carry7; |
| 4738 | s7 -= carry7 * (1 << 21); |
| 4739 | carry9 = (s9 + (1 << 20)) >> 21; |
| 4740 | s10 += carry9; |
| 4741 | s9 -= carry9 * (1 << 21); |
| 4742 | carry11 = (s11 + (1 << 20)) >> 21; |
| 4743 | s12 += carry11; |
| 4744 | s11 -= carry11 * (1 << 21); |
| 4745 | carry13 = (s13 + (1 << 20)) >> 21; |
| 4746 | s14 += carry13; |
| 4747 | s13 -= carry13 * (1 << 21); |
| 4748 | carry15 = (s15 + (1 << 20)) >> 21; |
| 4749 | s16 += carry15; |
| 4750 | s15 -= carry15 * (1 << 21); |
| 4751 | |
| 4752 | s5 += s17 * 666643; |
| 4753 | s6 += s17 * 470296; |
| 4754 | s7 += s17 * 654183; |
| 4755 | s8 -= s17 * 997805; |
| 4756 | s9 += s17 * 136657; |
| 4757 | s10 -= s17 * 683901; |
| 4758 | s17 = 0; |
| 4759 | |
| 4760 | s4 += s16 * 666643; |
| 4761 | s5 += s16 * 470296; |
| 4762 | s6 += s16 * 654183; |
| 4763 | s7 -= s16 * 997805; |
| 4764 | s8 += s16 * 136657; |
| 4765 | s9 -= s16 * 683901; |
| 4766 | s16 = 0; |
| 4767 | |
| 4768 | s3 += s15 * 666643; |
| 4769 | s4 += s15 * 470296; |
| 4770 | s5 += s15 * 654183; |
| 4771 | s6 -= s15 * 997805; |
| 4772 | s7 += s15 * 136657; |
| 4773 | s8 -= s15 * 683901; |
| 4774 | s15 = 0; |
| 4775 | |
| 4776 | s2 += s14 * 666643; |
| 4777 | s3 += s14 * 470296; |
| 4778 | s4 += s14 * 654183; |
| 4779 | s5 -= s14 * 997805; |
| 4780 | s6 += s14 * 136657; |
| 4781 | s7 -= s14 * 683901; |
| 4782 | s14 = 0; |
| 4783 | |
| 4784 | s1 += s13 * 666643; |
| 4785 | s2 += s13 * 470296; |
| 4786 | s3 += s13 * 654183; |
| 4787 | s4 -= s13 * 997805; |
| 4788 | s5 += s13 * 136657; |
| 4789 | s6 -= s13 * 683901; |
| 4790 | s13 = 0; |
| 4791 | |
| 4792 | s0 += s12 * 666643; |
| 4793 | s1 += s12 * 470296; |
| 4794 | s2 += s12 * 654183; |
| 4795 | s3 -= s12 * 997805; |
| 4796 | s4 += s12 * 136657; |
| 4797 | s5 -= s12 * 683901; |
| 4798 | s12 = 0; |
| 4799 | |
| 4800 | carry0 = (s0 + (1 << 20)) >> 21; |
| 4801 | s1 += carry0; |
| 4802 | s0 -= carry0 * (1 << 21); |
| 4803 | carry2 = (s2 + (1 << 20)) >> 21; |
| 4804 | s3 += carry2; |
| 4805 | s2 -= carry2 * (1 << 21); |
| 4806 | carry4 = (s4 + (1 << 20)) >> 21; |
| 4807 | s5 += carry4; |
| 4808 | s4 -= carry4 * (1 << 21); |
| 4809 | carry6 = (s6 + (1 << 20)) >> 21; |
| 4810 | s7 += carry6; |
| 4811 | s6 -= carry6 * (1 << 21); |
| 4812 | carry8 = (s8 + (1 << 20)) >> 21; |
| 4813 | s9 += carry8; |
| 4814 | s8 -= carry8 * (1 << 21); |
| 4815 | carry10 = (s10 + (1 << 20)) >> 21; |
| 4816 | s11 += carry10; |
| 4817 | s10 -= carry10 * (1 << 21); |
| 4818 | |
| 4819 | carry1 = (s1 + (1 << 20)) >> 21; |
| 4820 | s2 += carry1; |
| 4821 | s1 -= carry1 * (1 << 21); |
| 4822 | carry3 = (s3 + (1 << 20)) >> 21; |
| 4823 | s4 += carry3; |
| 4824 | s3 -= carry3 * (1 << 21); |
| 4825 | carry5 = (s5 + (1 << 20)) >> 21; |
| 4826 | s6 += carry5; |
| 4827 | s5 -= carry5 * (1 << 21); |
| 4828 | carry7 = (s7 + (1 << 20)) >> 21; |
| 4829 | s8 += carry7; |
| 4830 | s7 -= carry7 * (1 << 21); |
| 4831 | carry9 = (s9 + (1 << 20)) >> 21; |
| 4832 | s10 += carry9; |
| 4833 | s9 -= carry9 * (1 << 21); |
| 4834 | carry11 = (s11 + (1 << 20)) >> 21; |
| 4835 | s12 += carry11; |
| 4836 | s11 -= carry11 * (1 << 21); |
| 4837 | |
| 4838 | s0 += s12 * 666643; |
| 4839 | s1 += s12 * 470296; |
| 4840 | s2 += s12 * 654183; |
| 4841 | s3 -= s12 * 997805; |
| 4842 | s4 += s12 * 136657; |
| 4843 | s5 -= s12 * 683901; |
| 4844 | s12 = 0; |
| 4845 | |
| 4846 | carry0 = s0 >> 21; |
| 4847 | s1 += carry0; |
| 4848 | s0 -= carry0 * (1 << 21); |
| 4849 | carry1 = s1 >> 21; |
| 4850 | s2 += carry1; |
| 4851 | s1 -= carry1 * (1 << 21); |
| 4852 | carry2 = s2 >> 21; |
| 4853 | s3 += carry2; |
| 4854 | s2 -= carry2 * (1 << 21); |
| 4855 | carry3 = s3 >> 21; |
| 4856 | s4 += carry3; |
| 4857 | s3 -= carry3 * (1 << 21); |
| 4858 | carry4 = s4 >> 21; |
| 4859 | s5 += carry4; |
| 4860 | s4 -= carry4 * (1 << 21); |
| 4861 | carry5 = s5 >> 21; |
| 4862 | s6 += carry5; |
| 4863 | s5 -= carry5 * (1 << 21); |
| 4864 | carry6 = s6 >> 21; |
| 4865 | s7 += carry6; |
| 4866 | s6 -= carry6 * (1 << 21); |
| 4867 | carry7 = s7 >> 21; |
| 4868 | s8 += carry7; |
| 4869 | s7 -= carry7 * (1 << 21); |
| 4870 | carry8 = s8 >> 21; |
| 4871 | s9 += carry8; |
| 4872 | s8 -= carry8 * (1 << 21); |
| 4873 | carry9 = s9 >> 21; |
| 4874 | s10 += carry9; |
| 4875 | s9 -= carry9 * (1 << 21); |
| 4876 | carry10 = s10 >> 21; |
| 4877 | s11 += carry10; |
| 4878 | s10 -= carry10 * (1 << 21); |
| 4879 | carry11 = s11 >> 21; |
| 4880 | s12 += carry11; |
| 4881 | s11 -= carry11 * (1 << 21); |
| 4882 | |
| 4883 | s0 += s12 * 666643; |
| 4884 | s1 += s12 * 470296; |
| 4885 | s2 += s12 * 654183; |
| 4886 | s3 -= s12 * 997805; |
| 4887 | s4 += s12 * 136657; |
| 4888 | s5 -= s12 * 683901; |
| 4889 | s12 = 0; |
| 4890 | |
| 4891 | carry0 = s0 >> 21; |
| 4892 | s1 += carry0; |
| 4893 | s0 -= carry0 * (1 << 21); |
| 4894 | carry1 = s1 >> 21; |
| 4895 | s2 += carry1; |
| 4896 | s1 -= carry1 * (1 << 21); |
| 4897 | carry2 = s2 >> 21; |
| 4898 | s3 += carry2; |
| 4899 | s2 -= carry2 * (1 << 21); |
| 4900 | carry3 = s3 >> 21; |
| 4901 | s4 += carry3; |
| 4902 | s3 -= carry3 * (1 << 21); |
| 4903 | carry4 = s4 >> 21; |
| 4904 | s5 += carry4; |
| 4905 | s4 -= carry4 * (1 << 21); |
| 4906 | carry5 = s5 >> 21; |
| 4907 | s6 += carry5; |
| 4908 | s5 -= carry5 * (1 << 21); |
| 4909 | carry6 = s6 >> 21; |
| 4910 | s7 += carry6; |
| 4911 | s6 -= carry6 * (1 << 21); |
| 4912 | carry7 = s7 >> 21; |
| 4913 | s8 += carry7; |
| 4914 | s7 -= carry7 * (1 << 21); |
| 4915 | carry8 = s8 >> 21; |
| 4916 | s9 += carry8; |
| 4917 | s8 -= carry8 * (1 << 21); |
| 4918 | carry9 = s9 >> 21; |
| 4919 | s10 += carry9; |
| 4920 | s9 -= carry9 * (1 << 21); |
| 4921 | carry10 = s10 >> 21; |
| 4922 | s11 += carry10; |
| 4923 | s10 -= carry10 * (1 << 21); |
| 4924 | |
| 4925 | s[ 0] = (uint8_t) (s0 >> 0); |
| 4926 | s[ 1] = (uint8_t) (s0 >> 8); |
| 4927 | s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5)); |
| 4928 | s[ 3] = (uint8_t) (s1 >> 3); |
| 4929 | s[ 4] = (uint8_t) (s1 >> 11); |
| 4930 | s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2)); |
| 4931 | s[ 6] = (uint8_t) (s2 >> 6); |
| 4932 | s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7)); |
| 4933 | s[ 8] = (uint8_t) (s3 >> 1); |
| 4934 | s[ 9] = (uint8_t) (s3 >> 9); |
| 4935 | s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); |
| 4936 | s[11] = (uint8_t) (s4 >> 4); |
| 4937 | s[12] = (uint8_t) (s4 >> 12); |
| 4938 | s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); |
| 4939 | s[14] = (uint8_t) (s5 >> 7); |
| 4940 | s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); |
| 4941 | s[16] = (uint8_t) (s6 >> 2); |
| 4942 | s[17] = (uint8_t) (s6 >> 10); |
| 4943 | s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); |
| 4944 | s[19] = (uint8_t) (s7 >> 5); |
| 4945 | s[20] = (uint8_t) (s7 >> 13); |
| 4946 | s[21] = (uint8_t) (s8 >> 0); |
| 4947 | s[22] = (uint8_t) (s8 >> 8); |
| 4948 | s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); |
| 4949 | s[24] = (uint8_t) (s9 >> 3); |
| 4950 | s[25] = (uint8_t) (s9 >> 11); |
| 4951 | s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); |
| 4952 | s[27] = (uint8_t) (s10 >> 6); |
| 4953 | s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); |
| 4954 | s[29] = (uint8_t) (s11 >> 1); |
| 4955 | s[30] = (uint8_t) (s11 >> 9); |
| 4956 | s[31] = (uint8_t) (s11 >> 17); |
| 4957 | } |
| 4958 | |
| 4959 | /* |
| 4960 | * Input: |
| 4961 | * a[0]+256*a[1]+...+256^31*a[31] = a |
| 4962 | * b[0]+256*b[1]+...+256^31*b[31] = b |
| 4963 | * c[0]+256*c[1]+...+256^31*c[31] = c |
| 4964 | * |
| 4965 | * Output: |
| 4966 | * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l |
| 4967 | * where l = 2^252 + 27742317777372353535851937790883648493. |
| 4968 | */ |
| 4969 | static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, |
| 4970 | const uint8_t *c) |
| 4971 | { |
| 4972 | int64_t a0 = kBottom21Bits & load_3(a); |
| 4973 | int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5); |
| 4974 | int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2); |
| 4975 | int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7); |
| 4976 | int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4); |
| 4977 | int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1); |
| 4978 | int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6); |
| 4979 | int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3); |
| 4980 | int64_t a8 = kBottom21Bits & load_3(a + 21); |
| 4981 | int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5); |
| 4982 | int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2); |
| 4983 | int64_t a11 = (load_4(a + 28) >> 7); |
| 4984 | int64_t b0 = kBottom21Bits & load_3(b); |
| 4985 | int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5); |
| 4986 | int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2); |
| 4987 | int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7); |
| 4988 | int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4); |
| 4989 | int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1); |
| 4990 | int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6); |
| 4991 | int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3); |
| 4992 | int64_t b8 = kBottom21Bits & load_3(b + 21); |
| 4993 | int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5); |
| 4994 | int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2); |
| 4995 | int64_t b11 = (load_4(b + 28) >> 7); |
| 4996 | int64_t c0 = kBottom21Bits & load_3(c); |
| 4997 | int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5); |
| 4998 | int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2); |
| 4999 | int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7); |
| 5000 | int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4); |
| 5001 | int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1); |
| 5002 | int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6); |
| 5003 | int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3); |
| 5004 | int64_t c8 = kBottom21Bits & load_3(c + 21); |
| 5005 | int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5); |
| 5006 | int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2); |
| 5007 | int64_t c11 = (load_4(c + 28) >> 7); |
| 5008 | int64_t s0; |
| 5009 | int64_t s1; |
| 5010 | int64_t s2; |
| 5011 | int64_t s3; |
| 5012 | int64_t s4; |
| 5013 | int64_t s5; |
| 5014 | int64_t s6; |
| 5015 | int64_t s7; |
| 5016 | int64_t s8; |
| 5017 | int64_t s9; |
| 5018 | int64_t s10; |
| 5019 | int64_t s11; |
| 5020 | int64_t s12; |
| 5021 | int64_t s13; |
| 5022 | int64_t s14; |
| 5023 | int64_t s15; |
| 5024 | int64_t s16; |
| 5025 | int64_t s17; |
| 5026 | int64_t s18; |
| 5027 | int64_t s19; |
| 5028 | int64_t s20; |
| 5029 | int64_t s21; |
| 5030 | int64_t s22; |
| 5031 | int64_t s23; |
| 5032 | int64_t carry0; |
| 5033 | int64_t carry1; |
| 5034 | int64_t carry2; |
| 5035 | int64_t carry3; |
| 5036 | int64_t carry4; |
| 5037 | int64_t carry5; |
| 5038 | int64_t carry6; |
| 5039 | int64_t carry7; |
| 5040 | int64_t carry8; |
| 5041 | int64_t carry9; |
| 5042 | int64_t carry10; |
| 5043 | int64_t carry11; |
| 5044 | int64_t carry12; |
| 5045 | int64_t carry13; |
| 5046 | int64_t carry14; |
| 5047 | int64_t carry15; |
| 5048 | int64_t carry16; |
| 5049 | int64_t carry17; |
| 5050 | int64_t carry18; |
| 5051 | int64_t carry19; |
| 5052 | int64_t carry20; |
| 5053 | int64_t carry21; |
| 5054 | int64_t carry22; |
| 5055 | |
| 5056 | s0 = c0 + a0 * b0; |
| 5057 | s1 = c1 + a0 * b1 + a1 * b0; |
| 5058 | s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; |
| 5059 | s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; |
| 5060 | s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; |
| 5061 | s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; |
| 5062 | s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; |
| 5063 | s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; |
| 5064 | s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0; |
| 5065 | s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; |
| 5066 | s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; |
| 5067 | s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; |
| 5068 | s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; |
| 5069 | s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; |
| 5070 | s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; |
| 5071 | s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; |
| 5072 | s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; |
| 5073 | s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; |
| 5074 | s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; |
| 5075 | s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; |
| 5076 | s20 = a9 * b11 + a10 * b10 + a11 * b9; |
| 5077 | s21 = a10 * b11 + a11 * b10; |
| 5078 | s22 = a11 * b11; |
| 5079 | s23 = 0; |
| 5080 | |
| 5081 | carry0 = (s0 + (1 << 20)) >> 21; |
| 5082 | s1 += carry0; |
| 5083 | s0 -= carry0 * (1 << 21); |
| 5084 | carry2 = (s2 + (1 << 20)) >> 21; |
| 5085 | s3 += carry2; |
| 5086 | s2 -= carry2 * (1 << 21); |
| 5087 | carry4 = (s4 + (1 << 20)) >> 21; |
| 5088 | s5 += carry4; |
| 5089 | s4 -= carry4 * (1 << 21); |
| 5090 | carry6 = (s6 + (1 << 20)) >> 21; |
| 5091 | s7 += carry6; |
| 5092 | s6 -= carry6 * (1 << 21); |
| 5093 | carry8 = (s8 + (1 << 20)) >> 21; |
| 5094 | s9 += carry8; |
| 5095 | s8 -= carry8 * (1 << 21); |
| 5096 | carry10 = (s10 + (1 << 20)) >> 21; |
| 5097 | s11 += carry10; |
| 5098 | s10 -= carry10 * (1 << 21); |
| 5099 | carry12 = (s12 + (1 << 20)) >> 21; |
| 5100 | s13 += carry12; |
| 5101 | s12 -= carry12 * (1 << 21); |
| 5102 | carry14 = (s14 + (1 << 20)) >> 21; |
| 5103 | s15 += carry14; |
| 5104 | s14 -= carry14 * (1 << 21); |
| 5105 | carry16 = (s16 + (1 << 20)) >> 21; |
| 5106 | s17 += carry16; |
| 5107 | s16 -= carry16 * (1 << 21); |
| 5108 | carry18 = (s18 + (1 << 20)) >> 21; |
| 5109 | s19 += carry18; |
| 5110 | s18 -= carry18 * (1 << 21); |
| 5111 | carry20 = (s20 + (1 << 20)) >> 21; |
| 5112 | s21 += carry20; |
| 5113 | s20 -= carry20 * (1 << 21); |
| 5114 | carry22 = (s22 + (1 << 20)) >> 21; |
| 5115 | s23 += carry22; |
| 5116 | s22 -= carry22 * (1 << 21); |
| 5117 | |
| 5118 | carry1 = (s1 + (1 << 20)) >> 21; |
| 5119 | s2 += carry1; |
| 5120 | s1 -= carry1 * (1 << 21); |
| 5121 | carry3 = (s3 + (1 << 20)) >> 21; |
| 5122 | s4 += carry3; |
| 5123 | s3 -= carry3 * (1 << 21); |
| 5124 | carry5 = (s5 + (1 << 20)) >> 21; |
| 5125 | s6 += carry5; |
| 5126 | s5 -= carry5 * (1 << 21); |
| 5127 | carry7 = (s7 + (1 << 20)) >> 21; |
| 5128 | s8 += carry7; |
| 5129 | s7 -= carry7 * (1 << 21); |
| 5130 | carry9 = (s9 + (1 << 20)) >> 21; |
| 5131 | s10 += carry9; |
| 5132 | s9 -= carry9 * (1 << 21); |
| 5133 | carry11 = (s11 + (1 << 20)) >> 21; |
| 5134 | s12 += carry11; |
| 5135 | s11 -= carry11 * (1 << 21); |
| 5136 | carry13 = (s13 + (1 << 20)) >> 21; |
| 5137 | s14 += carry13; |
| 5138 | s13 -= carry13 * (1 << 21); |
| 5139 | carry15 = (s15 + (1 << 20)) >> 21; |
| 5140 | s16 += carry15; |
| 5141 | s15 -= carry15 * (1 << 21); |
| 5142 | carry17 = (s17 + (1 << 20)) >> 21; |
| 5143 | s18 += carry17; |
| 5144 | s17 -= carry17 * (1 << 21); |
| 5145 | carry19 = (s19 + (1 << 20)) >> 21; |
| 5146 | s20 += carry19; |
| 5147 | s19 -= carry19 * (1 << 21); |
| 5148 | carry21 = (s21 + (1 << 20)) >> 21; |
| 5149 | s22 += carry21; |
| 5150 | s21 -= carry21 * (1 << 21); |
| 5151 | |
| 5152 | s11 += s23 * 666643; |
| 5153 | s12 += s23 * 470296; |
| 5154 | s13 += s23 * 654183; |
| 5155 | s14 -= s23 * 997805; |
| 5156 | s15 += s23 * 136657; |
| 5157 | s16 -= s23 * 683901; |
| 5158 | s23 = 0; |
| 5159 | |
| 5160 | s10 += s22 * 666643; |
| 5161 | s11 += s22 * 470296; |
| 5162 | s12 += s22 * 654183; |
| 5163 | s13 -= s22 * 997805; |
| 5164 | s14 += s22 * 136657; |
| 5165 | s15 -= s22 * 683901; |
| 5166 | s22 = 0; |
| 5167 | |
| 5168 | s9 += s21 * 666643; |
| 5169 | s10 += s21 * 470296; |
| 5170 | s11 += s21 * 654183; |
| 5171 | s12 -= s21 * 997805; |
| 5172 | s13 += s21 * 136657; |
| 5173 | s14 -= s21 * 683901; |
| 5174 | s21 = 0; |
| 5175 | |
| 5176 | s8 += s20 * 666643; |
| 5177 | s9 += s20 * 470296; |
| 5178 | s10 += s20 * 654183; |
| 5179 | s11 -= s20 * 997805; |
| 5180 | s12 += s20 * 136657; |
| 5181 | s13 -= s20 * 683901; |
| 5182 | s20 = 0; |
| 5183 | |
| 5184 | s7 += s19 * 666643; |
| 5185 | s8 += s19 * 470296; |
| 5186 | s9 += s19 * 654183; |
| 5187 | s10 -= s19 * 997805; |
| 5188 | s11 += s19 * 136657; |
| 5189 | s12 -= s19 * 683901; |
| 5190 | s19 = 0; |
| 5191 | |
| 5192 | s6 += s18 * 666643; |
| 5193 | s7 += s18 * 470296; |
| 5194 | s8 += s18 * 654183; |
| 5195 | s9 -= s18 * 997805; |
| 5196 | s10 += s18 * 136657; |
| 5197 | s11 -= s18 * 683901; |
| 5198 | s18 = 0; |
| 5199 | |
| 5200 | carry6 = (s6 + (1 << 20)) >> 21; |
| 5201 | s7 += carry6; |
| 5202 | s6 -= carry6 * (1 << 21); |
| 5203 | carry8 = (s8 + (1 << 20)) >> 21; |
| 5204 | s9 += carry8; |
| 5205 | s8 -= carry8 * (1 << 21); |
| 5206 | carry10 = (s10 + (1 << 20)) >> 21; |
| 5207 | s11 += carry10; |
| 5208 | s10 -= carry10 * (1 << 21); |
| 5209 | carry12 = (s12 + (1 << 20)) >> 21; |
| 5210 | s13 += carry12; |
| 5211 | s12 -= carry12 * (1 << 21); |
| 5212 | carry14 = (s14 + (1 << 20)) >> 21; |
| 5213 | s15 += carry14; |
| 5214 | s14 -= carry14 * (1 << 21); |
| 5215 | carry16 = (s16 + (1 << 20)) >> 21; |
| 5216 | s17 += carry16; |
| 5217 | s16 -= carry16 * (1 << 21); |
| 5218 | |
| 5219 | carry7 = (s7 + (1 << 20)) >> 21; |
| 5220 | s8 += carry7; |
| 5221 | s7 -= carry7 * (1 << 21); |
| 5222 | carry9 = (s9 + (1 << 20)) >> 21; |
| 5223 | s10 += carry9; |
| 5224 | s9 -= carry9 * (1 << 21); |
| 5225 | carry11 = (s11 + (1 << 20)) >> 21; |
| 5226 | s12 += carry11; |
| 5227 | s11 -= carry11 * (1 << 21); |
| 5228 | carry13 = (s13 + (1 << 20)) >> 21; |
| 5229 | s14 += carry13; |
| 5230 | s13 -= carry13 * (1 << 21); |
| 5231 | carry15 = (s15 + (1 << 20)) >> 21; |
| 5232 | s16 += carry15; |
| 5233 | s15 -= carry15 * (1 << 21); |
| 5234 | |
| 5235 | s5 += s17 * 666643; |
| 5236 | s6 += s17 * 470296; |
| 5237 | s7 += s17 * 654183; |
| 5238 | s8 -= s17 * 997805; |
| 5239 | s9 += s17 * 136657; |
| 5240 | s10 -= s17 * 683901; |
| 5241 | s17 = 0; |
| 5242 | |
| 5243 | s4 += s16 * 666643; |
| 5244 | s5 += s16 * 470296; |
| 5245 | s6 += s16 * 654183; |
| 5246 | s7 -= s16 * 997805; |
| 5247 | s8 += s16 * 136657; |
| 5248 | s9 -= s16 * 683901; |
| 5249 | s16 = 0; |
| 5250 | |
| 5251 | s3 += s15 * 666643; |
| 5252 | s4 += s15 * 470296; |
| 5253 | s5 += s15 * 654183; |
| 5254 | s6 -= s15 * 997805; |
| 5255 | s7 += s15 * 136657; |
| 5256 | s8 -= s15 * 683901; |
| 5257 | s15 = 0; |
| 5258 | |
| 5259 | s2 += s14 * 666643; |
| 5260 | s3 += s14 * 470296; |
| 5261 | s4 += s14 * 654183; |
| 5262 | s5 -= s14 * 997805; |
| 5263 | s6 += s14 * 136657; |
| 5264 | s7 -= s14 * 683901; |
| 5265 | s14 = 0; |
| 5266 | |
| 5267 | s1 += s13 * 666643; |
| 5268 | s2 += s13 * 470296; |
| 5269 | s3 += s13 * 654183; |
| 5270 | s4 -= s13 * 997805; |
| 5271 | s5 += s13 * 136657; |
| 5272 | s6 -= s13 * 683901; |
| 5273 | s13 = 0; |
| 5274 | |
| 5275 | s0 += s12 * 666643; |
| 5276 | s1 += s12 * 470296; |
| 5277 | s2 += s12 * 654183; |
| 5278 | s3 -= s12 * 997805; |
| 5279 | s4 += s12 * 136657; |
| 5280 | s5 -= s12 * 683901; |
| 5281 | s12 = 0; |
| 5282 | |
| 5283 | carry0 = (s0 + (1 << 20)) >> 21; |
| 5284 | s1 += carry0; |
| 5285 | s0 -= carry0 * (1 << 21); |
| 5286 | carry2 = (s2 + (1 << 20)) >> 21; |
| 5287 | s3 += carry2; |
| 5288 | s2 -= carry2 * (1 << 21); |
| 5289 | carry4 = (s4 + (1 << 20)) >> 21; |
| 5290 | s5 += carry4; |
| 5291 | s4 -= carry4 * (1 << 21); |
| 5292 | carry6 = (s6 + (1 << 20)) >> 21; |
| 5293 | s7 += carry6; |
| 5294 | s6 -= carry6 * (1 << 21); |
| 5295 | carry8 = (s8 + (1 << 20)) >> 21; |
| 5296 | s9 += carry8; |
| 5297 | s8 -= carry8 * (1 << 21); |
| 5298 | carry10 = (s10 + (1 << 20)) >> 21; |
| 5299 | s11 += carry10; |
| 5300 | s10 -= carry10 * (1 << 21); |
| 5301 | |
| 5302 | carry1 = (s1 + (1 << 20)) >> 21; |
| 5303 | s2 += carry1; |
| 5304 | s1 -= carry1 * (1 << 21); |
| 5305 | carry3 = (s3 + (1 << 20)) >> 21; |
| 5306 | s4 += carry3; |
| 5307 | s3 -= carry3 * (1 << 21); |
| 5308 | carry5 = (s5 + (1 << 20)) >> 21; |
| 5309 | s6 += carry5; |
| 5310 | s5 -= carry5 * (1 << 21); |
| 5311 | carry7 = (s7 + (1 << 20)) >> 21; |
| 5312 | s8 += carry7; |
| 5313 | s7 -= carry7 * (1 << 21); |
| 5314 | carry9 = (s9 + (1 << 20)) >> 21; |
| 5315 | s10 += carry9; |
| 5316 | s9 -= carry9 * (1 << 21); |
| 5317 | carry11 = (s11 + (1 << 20)) >> 21; |
| 5318 | s12 += carry11; |
| 5319 | s11 -= carry11 * (1 << 21); |
| 5320 | |
| 5321 | s0 += s12 * 666643; |
| 5322 | s1 += s12 * 470296; |
| 5323 | s2 += s12 * 654183; |
| 5324 | s3 -= s12 * 997805; |
| 5325 | s4 += s12 * 136657; |
| 5326 | s5 -= s12 * 683901; |
| 5327 | s12 = 0; |
| 5328 | |
| 5329 | carry0 = s0 >> 21; |
| 5330 | s1 += carry0; |
| 5331 | s0 -= carry0 * (1 << 21); |
| 5332 | carry1 = s1 >> 21; |
| 5333 | s2 += carry1; |
| 5334 | s1 -= carry1 * (1 << 21); |
| 5335 | carry2 = s2 >> 21; |
| 5336 | s3 += carry2; |
| 5337 | s2 -= carry2 * (1 << 21); |
| 5338 | carry3 = s3 >> 21; |
| 5339 | s4 += carry3; |
| 5340 | s3 -= carry3 * (1 << 21); |
| 5341 | carry4 = s4 >> 21; |
| 5342 | s5 += carry4; |
| 5343 | s4 -= carry4 * (1 << 21); |
| 5344 | carry5 = s5 >> 21; |
| 5345 | s6 += carry5; |
| 5346 | s5 -= carry5 * (1 << 21); |
| 5347 | carry6 = s6 >> 21; |
| 5348 | s7 += carry6; |
| 5349 | s6 -= carry6 * (1 << 21); |
| 5350 | carry7 = s7 >> 21; |
| 5351 | s8 += carry7; |
| 5352 | s7 -= carry7 * (1 << 21); |
| 5353 | carry8 = s8 >> 21; |
| 5354 | s9 += carry8; |
| 5355 | s8 -= carry8 * (1 << 21); |
| 5356 | carry9 = s9 >> 21; |
| 5357 | s10 += carry9; |
| 5358 | s9 -= carry9 * (1 << 21); |
| 5359 | carry10 = s10 >> 21; |
| 5360 | s11 += carry10; |
| 5361 | s10 -= carry10 * (1 << 21); |
| 5362 | carry11 = s11 >> 21; |
| 5363 | s12 += carry11; |
| 5364 | s11 -= carry11 * (1 << 21); |
| 5365 | |
| 5366 | s0 += s12 * 666643; |
| 5367 | s1 += s12 * 470296; |
| 5368 | s2 += s12 * 654183; |
| 5369 | s3 -= s12 * 997805; |
| 5370 | s4 += s12 * 136657; |
| 5371 | s5 -= s12 * 683901; |
| 5372 | s12 = 0; |
Value stored to 's12' is never read | |
| 5373 | |
| 5374 | carry0 = s0 >> 21; |
| 5375 | s1 += carry0; |
| 5376 | s0 -= carry0 * (1 << 21); |
| 5377 | carry1 = s1 >> 21; |
| 5378 | s2 += carry1; |
| 5379 | s1 -= carry1 * (1 << 21); |
| 5380 | carry2 = s2 >> 21; |
| 5381 | s3 += carry2; |
| 5382 | s2 -= carry2 * (1 << 21); |
| 5383 | carry3 = s3 >> 21; |
| 5384 | s4 += carry3; |
| 5385 | s3 -= carry3 * (1 << 21); |
| 5386 | carry4 = s4 >> 21; |
| 5387 | s5 += carry4; |
| 5388 | s4 -= carry4 * (1 << 21); |
| 5389 | carry5 = s5 >> 21; |
| 5390 | s6 += carry5; |
| 5391 | s5 -= carry5 * (1 << 21); |
| 5392 | carry6 = s6 >> 21; |
| 5393 | s7 += carry6; |
| 5394 | s6 -= carry6 * (1 << 21); |
| 5395 | carry7 = s7 >> 21; |
| 5396 | s8 += carry7; |
| 5397 | s7 -= carry7 * (1 << 21); |
| 5398 | carry8 = s8 >> 21; |
| 5399 | s9 += carry8; |
| 5400 | s8 -= carry8 * (1 << 21); |
| 5401 | carry9 = s9 >> 21; |
| 5402 | s10 += carry9; |
| 5403 | s9 -= carry9 * (1 << 21); |
| 5404 | carry10 = s10 >> 21; |
| 5405 | s11 += carry10; |
| 5406 | s10 -= carry10 * (1 << 21); |
| 5407 | |
| 5408 | s[ 0] = (uint8_t) (s0 >> 0); |
| 5409 | s[ 1] = (uint8_t) (s0 >> 8); |
| 5410 | s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5)); |
| 5411 | s[ 3] = (uint8_t) (s1 >> 3); |
| 5412 | s[ 4] = (uint8_t) (s1 >> 11); |
| 5413 | s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2)); |
| 5414 | s[ 6] = (uint8_t) (s2 >> 6); |
| 5415 | s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7)); |
| 5416 | s[ 8] = (uint8_t) (s3 >> 1); |
| 5417 | s[ 9] = (uint8_t) (s3 >> 9); |
| 5418 | s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); |
| 5419 | s[11] = (uint8_t) (s4 >> 4); |
| 5420 | s[12] = (uint8_t) (s4 >> 12); |
| 5421 | s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); |
| 5422 | s[14] = (uint8_t) (s5 >> 7); |
| 5423 | s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); |
| 5424 | s[16] = (uint8_t) (s6 >> 2); |
| 5425 | s[17] = (uint8_t) (s6 >> 10); |
| 5426 | s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); |
| 5427 | s[19] = (uint8_t) (s7 >> 5); |
| 5428 | s[20] = (uint8_t) (s7 >> 13); |
| 5429 | s[21] = (uint8_t) (s8 >> 0); |
| 5430 | s[22] = (uint8_t) (s8 >> 8); |
| 5431 | s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); |
| 5432 | s[24] = (uint8_t) (s9 >> 3); |
| 5433 | s[25] = (uint8_t) (s9 >> 11); |
| 5434 | s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); |
| 5435 | s[27] = (uint8_t) (s10 >> 6); |
| 5436 | s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); |
| 5437 | s[29] = (uint8_t) (s11 >> 1); |
| 5438 | s[30] = (uint8_t) (s11 >> 9); |
| 5439 | s[31] = (uint8_t) (s11 >> 17); |
| 5440 | } |
| 5441 | |
| 5442 | int |
| 5443 | ossl_ed25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, |
| 5444 | const uint8_t public_key[32], const uint8_t private_key[32], |
| 5445 | OSSL_LIB_CTX *libctx, const char *propq) |
| 5446 | { |
| 5447 | uint8_t az[SHA512_DIGEST_LENGTH64]; |
| 5448 | uint8_t nonce[SHA512_DIGEST_LENGTH64]; |
| 5449 | ge_p3 R; |
| 5450 | uint8_t hram[SHA512_DIGEST_LENGTH64]; |
| 5451 | EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512"SHA512", propq); |
| 5452 | EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new(); |
| 5453 | unsigned int sz; |
| 5454 | int res = 0; |
| 5455 | |
| 5456 | if (sha512 == NULL((void*)0) || hash_ctx == NULL((void*)0)) |
| 5457 | goto err; |
| 5458 | |
| 5459 | if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL((void*)0)) |
| 5460 | || !EVP_DigestUpdate(hash_ctx, private_key, 32) |
| 5461 | || !EVP_DigestFinal_ex(hash_ctx, az, &sz)) |
| 5462 | goto err; |
| 5463 | |
| 5464 | az[0] &= 248; |
| 5465 | az[31] &= 63; |
| 5466 | az[31] |= 64; |
| 5467 | |
| 5468 | if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL((void*)0)) |
| 5469 | || !EVP_DigestUpdate(hash_ctx, az + 32, 32) |
| 5470 | || !EVP_DigestUpdate(hash_ctx, message, message_len) |
| 5471 | || !EVP_DigestFinal_ex(hash_ctx, nonce, &sz)) |
| 5472 | goto err; |
| 5473 | |
| 5474 | x25519_sc_reduce(nonce); |
| 5475 | ge_scalarmult_base(&R, nonce); |
| 5476 | ge_p3_tobytes(out_sig, &R); |
| 5477 | |
| 5478 | if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL((void*)0)) |
| 5479 | || !EVP_DigestUpdate(hash_ctx, out_sig, 32) |
| 5480 | || !EVP_DigestUpdate(hash_ctx, public_key, 32) |
| 5481 | || !EVP_DigestUpdate(hash_ctx, message, message_len) |
| 5482 | || !EVP_DigestFinal_ex(hash_ctx, hram, &sz)) |
| 5483 | goto err; |
| 5484 | |
| 5485 | x25519_sc_reduce(hram); |
| 5486 | sc_muladd(out_sig + 32, hram, az, nonce); |
| 5487 | |
| 5488 | res = 1; |
| 5489 | err: |
| 5490 | OPENSSL_cleanse(nonce, sizeof(nonce)); |
| 5491 | OPENSSL_cleanse(az, sizeof(az)); |
| 5492 | EVP_MD_free(sha512); |
| 5493 | EVP_MD_CTX_free(hash_ctx); |
| 5494 | return res; |
| 5495 | } |
| 5496 | |
| 5497 | static const char allzeroes[15]; |
| 5498 | |
| 5499 | int |
| 5500 | ossl_ed25519_verify(const uint8_t *message, size_t message_len, |
| 5501 | const uint8_t signature[64], const uint8_t public_key[32], |
| 5502 | OSSL_LIB_CTX *libctx, const char *propq) |
| 5503 | { |
| 5504 | int i; |
| 5505 | ge_p3 A; |
| 5506 | const uint8_t *r, *s; |
| 5507 | EVP_MD *sha512; |
| 5508 | EVP_MD_CTX *hash_ctx = NULL((void*)0); |
| 5509 | unsigned int sz; |
| 5510 | int res = 0; |
| 5511 | ge_p2 R; |
| 5512 | uint8_t rcheck[32]; |
| 5513 | uint8_t h[SHA512_DIGEST_LENGTH64]; |
| 5514 | /* 27742317777372353535851937790883648493 in little endian format */ |
| 5515 | const uint8_t l_low[16] = { |
| 5516 | 0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, |
| 5517 | 0xDE, 0xF9, 0xDE, 0x14 |
| 5518 | }; |
| 5519 | |
| 5520 | r = signature; |
| 5521 | s = signature + 32; |
| 5522 | |
| 5523 | /* |
| 5524 | * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493 |
| 5525 | * |
| 5526 | * If not the signature is publicly invalid. Since it's public we can do the |
| 5527 | * check in variable time. |
| 5528 | * |
| 5529 | * First check the most significant byte |
| 5530 | */ |
| 5531 | if (s[31] > 0x10) |
| 5532 | return 0; |
| 5533 | if (s[31] == 0x10) { |
| 5534 | /* |
| 5535 | * Most significant byte indicates a value close to 2^252 so check the |
| 5536 | * rest |
| 5537 | */ |
| 5538 | if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0) |
| 5539 | return 0; |
| 5540 | for (i = 15; i >= 0; i--) { |
| 5541 | if (s[i] < l_low[i]) |
| 5542 | break; |
| 5543 | if (s[i] > l_low[i]) |
| 5544 | return 0; |
| 5545 | } |
| 5546 | if (i < 0) |
| 5547 | return 0; |
| 5548 | } |
| 5549 | |
| 5550 | if (ge_frombytes_vartime(&A, public_key) != 0) { |
| 5551 | return 0; |
| 5552 | } |
| 5553 | |
| 5554 | fe_neg(A.X, A.X); |
| 5555 | fe_neg(A.T, A.T); |
| 5556 | |
| 5557 | sha512 = EVP_MD_fetch(libctx, SN_sha512"SHA512", propq); |
| 5558 | if (sha512 == NULL((void*)0)) |
| 5559 | return 0; |
| 5560 | hash_ctx = EVP_MD_CTX_new(); |
| 5561 | if (hash_ctx == NULL((void*)0)) |
| 5562 | goto err; |
| 5563 | |
| 5564 | if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL((void*)0)) |
| 5565 | || !EVP_DigestUpdate(hash_ctx, r, 32) |
| 5566 | || !EVP_DigestUpdate(hash_ctx, public_key, 32) |
| 5567 | || !EVP_DigestUpdate(hash_ctx, message, message_len) |
| 5568 | || !EVP_DigestFinal_ex(hash_ctx, h, &sz)) |
| 5569 | goto err; |
| 5570 | |
| 5571 | x25519_sc_reduce(h); |
| 5572 | |
| 5573 | ge_double_scalarmult_vartime(&R, h, &A, s); |
| 5574 | |
| 5575 | ge_tobytes(rcheck, &R); |
| 5576 | |
| 5577 | res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0; |
| 5578 | err: |
| 5579 | EVP_MD_free(sha512); |
| 5580 | EVP_MD_CTX_free(hash_ctx); |
| 5581 | return res; |
| 5582 | } |
| 5583 | |
| 5584 | int |
| 5585 | ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32], |
| 5586 | const uint8_t private_key[32], |
| 5587 | const char *propq) |
| 5588 | { |
| 5589 | uint8_t az[SHA512_DIGEST_LENGTH64]; |
| 5590 | ge_p3 A; |
| 5591 | int r; |
| 5592 | EVP_MD *sha512 = NULL((void*)0); |
| 5593 | |
| 5594 | sha512 = EVP_MD_fetch(ctx, SN_sha512"SHA512", propq); |
| 5595 | if (sha512 == NULL((void*)0)) |
| 5596 | return 0; |
| 5597 | r = EVP_Digest(private_key, 32, az, NULL((void*)0), sha512, NULL((void*)0)); |
| 5598 | EVP_MD_free(sha512); |
| 5599 | if (!r) { |
| 5600 | OPENSSL_cleanse(az, sizeof(az)); |
| 5601 | return 0; |
| 5602 | } |
| 5603 | |
| 5604 | az[0] &= 248; |
| 5605 | az[31] &= 63; |
| 5606 | az[31] |= 64; |
| 5607 | |
| 5608 | ge_scalarmult_base(&A, az); |
| 5609 | ge_p3_tobytes(out_public_key, &A); |
| 5610 | |
| 5611 | OPENSSL_cleanse(az, sizeof(az)); |
| 5612 | return 1; |
| 5613 | } |
| 5614 | |
| 5615 | int |
| 5616 | ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32], |
| 5617 | const uint8_t peer_public_value[32]) |
| 5618 | { |
| 5619 | static const uint8_t kZeros[32] = {0}; |
| 5620 | x25519_scalar_mult(out_shared_key, private_key, peer_public_value); |
| 5621 | /* The all-zero output results when the input is a point of small order. */ |
| 5622 | return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; |
| 5623 | } |
| 5624 | |
| 5625 | void |
| 5626 | ossl_x25519_public_from_private(uint8_t out_public_value[32], |
| 5627 | const uint8_t private_key[32]) |
| 5628 | { |
| 5629 | uint8_t e[32]; |
| 5630 | ge_p3 A; |
| 5631 | fe zplusy, zminusy, zminusy_inv; |
| 5632 | |
| 5633 | memcpy(e, private_key, 32); |
| 5634 | e[0] &= 248; |
| 5635 | e[31] &= 127; |
| 5636 | e[31] |= 64; |
| 5637 | |
| 5638 | ge_scalarmult_base(&A, e); |
| 5639 | |
| 5640 | /* |
| 5641 | * We only need the u-coordinate of the curve25519 point. |
| 5642 | * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives |
| 5643 | * u=(Z+Y)/(Z-Y). |
| 5644 | */ |
| 5645 | fe_add(zplusy, A.Z, A.Y); |
| 5646 | fe_sub(zminusy, A.Z, A.Y); |
| 5647 | fe_invert(zminusy_inv, zminusy); |
| 5648 | fe_mul(zplusy, zplusy, zminusy_inv); |
| 5649 | fe_tobytes(out_public_value, zplusy); |
| 5650 | |
| 5651 | OPENSSL_cleanse(e, sizeof(e)); |
| 5652 | } |