| File: | src/lib/libcrypto/curve25519/curve25519.c |
| Warning: | line 3935, column 3 Value stored to 's16' is never read |
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| 1 | /* $OpenBSD: curve25519.c,v 1.16 2023/07/08 15:12:49 beck Exp $ */ |
| 2 | /* |
| 3 | * Copyright (c) 2015, Google Inc. |
| 4 | * |
| 5 | * Permission to use, copy, modify, and/or distribute this software for any |
| 6 | * purpose with or without fee is hereby granted, provided that the above |
| 7 | * copyright notice and this permission notice appear in all copies. |
| 8 | * |
| 9 | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| 10 | * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| 11 | * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY |
| 12 | * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| 13 | * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION |
| 14 | * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN |
| 15 | * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. |
| 16 | */ |
| 17 | |
| 18 | /* |
| 19 | * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP |
| 20 | * 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as |
| 21 | * public domain but this file has the ISC license just to keep licencing |
| 22 | * simple. |
| 23 | * |
| 24 | * The field functions are shared by Ed25519 and X25519 where possible. |
| 25 | */ |
| 26 | |
| 27 | #include <stdio.h> |
| 28 | #include <stdlib.h> |
| 29 | #include <string.h> |
| 30 | |
| 31 | #include <openssl/curve25519.h> |
| 32 | #include <openssl/sha.h> |
| 33 | |
| 34 | #include "curve25519_internal.h" |
| 35 | |
| 36 | static const int64_t kBottom25Bits = 0x1ffffffLL; |
| 37 | static const int64_t kBottom26Bits = 0x3ffffffLL; |
| 38 | static const int64_t kTop39Bits = 0xfffffffffe000000LL; |
| 39 | static const int64_t kTop38Bits = 0xfffffffffc000000LL; |
| 40 | |
| 41 | static uint64_t load_3(const uint8_t *in) { |
| 42 | uint64_t result; |
| 43 | result = (uint64_t)in[0]; |
| 44 | result |= ((uint64_t)in[1]) << 8; |
| 45 | result |= ((uint64_t)in[2]) << 16; |
| 46 | return result; |
| 47 | } |
| 48 | |
| 49 | static uint64_t load_4(const uint8_t *in) { |
| 50 | uint64_t result; |
| 51 | result = (uint64_t)in[0]; |
| 52 | result |= ((uint64_t)in[1]) << 8; |
| 53 | result |= ((uint64_t)in[2]) << 16; |
| 54 | result |= ((uint64_t)in[3]) << 24; |
| 55 | return result; |
| 56 | } |
| 57 | |
| 58 | static void fe_frombytes(fe h, const uint8_t *s) { |
| 59 | /* Ignores top bit of h. */ |
| 60 | int64_t h0 = load_4(s); |
| 61 | int64_t h1 = load_3(s + 4) << 6; |
| 62 | int64_t h2 = load_3(s + 7) << 5; |
| 63 | int64_t h3 = load_3(s + 10) << 3; |
| 64 | int64_t h4 = load_3(s + 13) << 2; |
| 65 | int64_t h5 = load_4(s + 16); |
| 66 | int64_t h6 = load_3(s + 20) << 7; |
| 67 | int64_t h7 = load_3(s + 23) << 5; |
| 68 | int64_t h8 = load_3(s + 26) << 4; |
| 69 | int64_t h9 = (load_3(s + 29) & 8388607) << 2; |
| 70 | int64_t carry0; |
| 71 | int64_t carry1; |
| 72 | int64_t carry2; |
| 73 | int64_t carry3; |
| 74 | int64_t carry4; |
| 75 | int64_t carry5; |
| 76 | int64_t carry6; |
| 77 | int64_t carry7; |
| 78 | int64_t carry8; |
| 79 | int64_t carry9; |
| 80 | |
| 81 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 82 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 83 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 84 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 85 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 86 | |
| 87 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 88 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 89 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 90 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 91 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 92 | |
| 93 | h[0] = h0; |
| 94 | h[1] = h1; |
| 95 | h[2] = h2; |
| 96 | h[3] = h3; |
| 97 | h[4] = h4; |
| 98 | h[5] = h5; |
| 99 | h[6] = h6; |
| 100 | h[7] = h7; |
| 101 | h[8] = h8; |
| 102 | h[9] = h9; |
| 103 | } |
| 104 | |
| 105 | /* Preconditions: |
| 106 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
| 107 | * |
| 108 | * Write p=2^255-19; q=floor(h/p). |
| 109 | * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). |
| 110 | * |
| 111 | * Proof: |
| 112 | * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. |
| 113 | * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. |
| 114 | * |
| 115 | * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). |
| 116 | * Then 0<y<1. |
| 117 | * |
| 118 | * Write r=h-pq. |
| 119 | * Have 0<=r<=p-1=2^255-20. |
| 120 | * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. |
| 121 | * |
| 122 | * Write x=r+19(2^-255)r+y. |
| 123 | * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. |
| 124 | * |
| 125 | * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) |
| 126 | * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ |
| 127 | static void fe_tobytes(uint8_t *s, const fe h) { |
| 128 | int32_t h0 = h[0]; |
| 129 | int32_t h1 = h[1]; |
| 130 | int32_t h2 = h[2]; |
| 131 | int32_t h3 = h[3]; |
| 132 | int32_t h4 = h[4]; |
| 133 | int32_t h5 = h[5]; |
| 134 | int32_t h6 = h[6]; |
| 135 | int32_t h7 = h[7]; |
| 136 | int32_t h8 = h[8]; |
| 137 | int32_t h9 = h[9]; |
| 138 | int32_t q; |
| 139 | |
| 140 | q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; |
| 141 | q = (h0 + q) >> 26; |
| 142 | q = (h1 + q) >> 25; |
| 143 | q = (h2 + q) >> 26; |
| 144 | q = (h3 + q) >> 25; |
| 145 | q = (h4 + q) >> 26; |
| 146 | q = (h5 + q) >> 25; |
| 147 | q = (h6 + q) >> 26; |
| 148 | q = (h7 + q) >> 25; |
| 149 | q = (h8 + q) >> 26; |
| 150 | q = (h9 + q) >> 25; |
| 151 | |
| 152 | /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ |
| 153 | h0 += 19 * q; |
| 154 | /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ |
| 155 | |
| 156 | h1 += h0 >> 26; h0 &= kBottom26Bits; |
| 157 | h2 += h1 >> 25; h1 &= kBottom25Bits; |
| 158 | h3 += h2 >> 26; h2 &= kBottom26Bits; |
| 159 | h4 += h3 >> 25; h3 &= kBottom25Bits; |
| 160 | h5 += h4 >> 26; h4 &= kBottom26Bits; |
| 161 | h6 += h5 >> 25; h5 &= kBottom25Bits; |
| 162 | h7 += h6 >> 26; h6 &= kBottom26Bits; |
| 163 | h8 += h7 >> 25; h7 &= kBottom25Bits; |
| 164 | h9 += h8 >> 26; h8 &= kBottom26Bits; |
| 165 | h9 &= kBottom25Bits; |
| 166 | /* h10 = carry9 */ |
| 167 | |
| 168 | /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. |
| 169 | * Have h0+...+2^230 h9 between 0 and 2^255-1; |
| 170 | * evidently 2^255 h10-2^255 q = 0. |
| 171 | * Goal: Output h0+...+2^230 h9. */ |
| 172 | |
| 173 | s[0] = h0 >> 0; |
| 174 | s[1] = h0 >> 8; |
| 175 | s[2] = h0 >> 16; |
| 176 | s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2); |
| 177 | s[4] = h1 >> 6; |
| 178 | s[5] = h1 >> 14; |
| 179 | s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3); |
| 180 | s[7] = h2 >> 5; |
| 181 | s[8] = h2 >> 13; |
| 182 | s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5); |
| 183 | s[10] = h3 >> 3; |
| 184 | s[11] = h3 >> 11; |
| 185 | s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6); |
| 186 | s[13] = h4 >> 2; |
| 187 | s[14] = h4 >> 10; |
| 188 | s[15] = h4 >> 18; |
| 189 | s[16] = h5 >> 0; |
| 190 | s[17] = h5 >> 8; |
| 191 | s[18] = h5 >> 16; |
| 192 | s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1); |
| 193 | s[20] = h6 >> 7; |
| 194 | s[21] = h6 >> 15; |
| 195 | s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3); |
| 196 | s[23] = h7 >> 5; |
| 197 | s[24] = h7 >> 13; |
| 198 | s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4); |
| 199 | s[26] = h8 >> 4; |
| 200 | s[27] = h8 >> 12; |
| 201 | s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6); |
| 202 | s[29] = h9 >> 2; |
| 203 | s[30] = h9 >> 10; |
| 204 | s[31] = h9 >> 18; |
| 205 | } |
| 206 | |
| 207 | /* h = f */ |
| 208 | static void fe_copy(fe h, const fe f) { |
| 209 | memmove(h, f, sizeof(int32_t) * 10); |
| 210 | } |
| 211 | |
| 212 | /* h = 0 */ |
| 213 | static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } |
| 214 | |
| 215 | /* h = 1 */ |
| 216 | static void fe_1(fe h) { |
| 217 | memset(h, 0, sizeof(int32_t) * 10); |
| 218 | h[0] = 1; |
| 219 | } |
| 220 | |
| 221 | /* h = f + g |
| 222 | * Can overlap h with f or g. |
| 223 | * |
| 224 | * Preconditions: |
| 225 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 226 | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 227 | * |
| 228 | * Postconditions: |
| 229 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
| 230 | static void fe_add(fe h, const fe f, const fe g) { |
| 231 | unsigned i; |
| 232 | for (i = 0; i < 10; i++) { |
| 233 | h[i] = f[i] + g[i]; |
| 234 | } |
| 235 | } |
| 236 | |
| 237 | /* h = f - g |
| 238 | * Can overlap h with f or g. |
| 239 | * |
| 240 | * Preconditions: |
| 241 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 242 | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 243 | * |
| 244 | * Postconditions: |
| 245 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
| 246 | static void fe_sub(fe h, const fe f, const fe g) { |
| 247 | unsigned i; |
| 248 | for (i = 0; i < 10; i++) { |
| 249 | h[i] = f[i] - g[i]; |
| 250 | } |
| 251 | } |
| 252 | |
| 253 | /* h = f * g |
| 254 | * Can overlap h with f or g. |
| 255 | * |
| 256 | * Preconditions: |
| 257 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
| 258 | * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
| 259 | * |
| 260 | * Postconditions: |
| 261 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
| 262 | * |
| 263 | * Notes on implementation strategy: |
| 264 | * |
| 265 | * Using schoolbook multiplication. |
| 266 | * Karatsuba would save a little in some cost models. |
| 267 | * |
| 268 | * Most multiplications by 2 and 19 are 32-bit precomputations; |
| 269 | * cheaper than 64-bit postcomputations. |
| 270 | * |
| 271 | * There is one remaining multiplication by 19 in the carry chain; |
| 272 | * one *19 precomputation can be merged into this, |
| 273 | * but the resulting data flow is considerably less clean. |
| 274 | * |
| 275 | * There are 12 carries below. |
| 276 | * 10 of them are 2-way parallelizable and vectorizable. |
| 277 | * Can get away with 11 carries, but then data flow is much deeper. |
| 278 | * |
| 279 | * With tighter constraints on inputs can squeeze carries into int32. */ |
| 280 | static void fe_mul(fe h, const fe f, const fe g) { |
| 281 | int32_t f0 = f[0]; |
| 282 | int32_t f1 = f[1]; |
| 283 | int32_t f2 = f[2]; |
| 284 | int32_t f3 = f[3]; |
| 285 | int32_t f4 = f[4]; |
| 286 | int32_t f5 = f[5]; |
| 287 | int32_t f6 = f[6]; |
| 288 | int32_t f7 = f[7]; |
| 289 | int32_t f8 = f[8]; |
| 290 | int32_t f9 = f[9]; |
| 291 | int32_t g0 = g[0]; |
| 292 | int32_t g1 = g[1]; |
| 293 | int32_t g2 = g[2]; |
| 294 | int32_t g3 = g[3]; |
| 295 | int32_t g4 = g[4]; |
| 296 | int32_t g5 = g[5]; |
| 297 | int32_t g6 = g[6]; |
| 298 | int32_t g7 = g[7]; |
| 299 | int32_t g8 = g[8]; |
| 300 | int32_t g9 = g[9]; |
| 301 | int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ |
| 302 | int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ |
| 303 | int32_t g3_19 = 19 * g3; |
| 304 | int32_t g4_19 = 19 * g4; |
| 305 | int32_t g5_19 = 19 * g5; |
| 306 | int32_t g6_19 = 19 * g6; |
| 307 | int32_t g7_19 = 19 * g7; |
| 308 | int32_t g8_19 = 19 * g8; |
| 309 | int32_t g9_19 = 19 * g9; |
| 310 | int32_t f1_2 = 2 * f1; |
| 311 | int32_t f3_2 = 2 * f3; |
| 312 | int32_t f5_2 = 2 * f5; |
| 313 | int32_t f7_2 = 2 * f7; |
| 314 | int32_t f9_2 = 2 * f9; |
| 315 | int64_t f0g0 = f0 * (int64_t) g0; |
| 316 | int64_t f0g1 = f0 * (int64_t) g1; |
| 317 | int64_t f0g2 = f0 * (int64_t) g2; |
| 318 | int64_t f0g3 = f0 * (int64_t) g3; |
| 319 | int64_t f0g4 = f0 * (int64_t) g4; |
| 320 | int64_t f0g5 = f0 * (int64_t) g5; |
| 321 | int64_t f0g6 = f0 * (int64_t) g6; |
| 322 | int64_t f0g7 = f0 * (int64_t) g7; |
| 323 | int64_t f0g8 = f0 * (int64_t) g8; |
| 324 | int64_t f0g9 = f0 * (int64_t) g9; |
| 325 | int64_t f1g0 = f1 * (int64_t) g0; |
| 326 | int64_t f1g1_2 = f1_2 * (int64_t) g1; |
| 327 | int64_t f1g2 = f1 * (int64_t) g2; |
| 328 | int64_t f1g3_2 = f1_2 * (int64_t) g3; |
| 329 | int64_t f1g4 = f1 * (int64_t) g4; |
| 330 | int64_t f1g5_2 = f1_2 * (int64_t) g5; |
| 331 | int64_t f1g6 = f1 * (int64_t) g6; |
| 332 | int64_t f1g7_2 = f1_2 * (int64_t) g7; |
| 333 | int64_t f1g8 = f1 * (int64_t) g8; |
| 334 | int64_t f1g9_38 = f1_2 * (int64_t) g9_19; |
| 335 | int64_t f2g0 = f2 * (int64_t) g0; |
| 336 | int64_t f2g1 = f2 * (int64_t) g1; |
| 337 | int64_t f2g2 = f2 * (int64_t) g2; |
| 338 | int64_t f2g3 = f2 * (int64_t) g3; |
| 339 | int64_t f2g4 = f2 * (int64_t) g4; |
| 340 | int64_t f2g5 = f2 * (int64_t) g5; |
| 341 | int64_t f2g6 = f2 * (int64_t) g6; |
| 342 | int64_t f2g7 = f2 * (int64_t) g7; |
| 343 | int64_t f2g8_19 = f2 * (int64_t) g8_19; |
| 344 | int64_t f2g9_19 = f2 * (int64_t) g9_19; |
| 345 | int64_t f3g0 = f3 * (int64_t) g0; |
| 346 | int64_t f3g1_2 = f3_2 * (int64_t) g1; |
| 347 | int64_t f3g2 = f3 * (int64_t) g2; |
| 348 | int64_t f3g3_2 = f3_2 * (int64_t) g3; |
| 349 | int64_t f3g4 = f3 * (int64_t) g4; |
| 350 | int64_t f3g5_2 = f3_2 * (int64_t) g5; |
| 351 | int64_t f3g6 = f3 * (int64_t) g6; |
| 352 | int64_t f3g7_38 = f3_2 * (int64_t) g7_19; |
| 353 | int64_t f3g8_19 = f3 * (int64_t) g8_19; |
| 354 | int64_t f3g9_38 = f3_2 * (int64_t) g9_19; |
| 355 | int64_t f4g0 = f4 * (int64_t) g0; |
| 356 | int64_t f4g1 = f4 * (int64_t) g1; |
| 357 | int64_t f4g2 = f4 * (int64_t) g2; |
| 358 | int64_t f4g3 = f4 * (int64_t) g3; |
| 359 | int64_t f4g4 = f4 * (int64_t) g4; |
| 360 | int64_t f4g5 = f4 * (int64_t) g5; |
| 361 | int64_t f4g6_19 = f4 * (int64_t) g6_19; |
| 362 | int64_t f4g7_19 = f4 * (int64_t) g7_19; |
| 363 | int64_t f4g8_19 = f4 * (int64_t) g8_19; |
| 364 | int64_t f4g9_19 = f4 * (int64_t) g9_19; |
| 365 | int64_t f5g0 = f5 * (int64_t) g0; |
| 366 | int64_t f5g1_2 = f5_2 * (int64_t) g1; |
| 367 | int64_t f5g2 = f5 * (int64_t) g2; |
| 368 | int64_t f5g3_2 = f5_2 * (int64_t) g3; |
| 369 | int64_t f5g4 = f5 * (int64_t) g4; |
| 370 | int64_t f5g5_38 = f5_2 * (int64_t) g5_19; |
| 371 | int64_t f5g6_19 = f5 * (int64_t) g6_19; |
| 372 | int64_t f5g7_38 = f5_2 * (int64_t) g7_19; |
| 373 | int64_t f5g8_19 = f5 * (int64_t) g8_19; |
| 374 | int64_t f5g9_38 = f5_2 * (int64_t) g9_19; |
| 375 | int64_t f6g0 = f6 * (int64_t) g0; |
| 376 | int64_t f6g1 = f6 * (int64_t) g1; |
| 377 | int64_t f6g2 = f6 * (int64_t) g2; |
| 378 | int64_t f6g3 = f6 * (int64_t) g3; |
| 379 | int64_t f6g4_19 = f6 * (int64_t) g4_19; |
| 380 | int64_t f6g5_19 = f6 * (int64_t) g5_19; |
| 381 | int64_t f6g6_19 = f6 * (int64_t) g6_19; |
| 382 | int64_t f6g7_19 = f6 * (int64_t) g7_19; |
| 383 | int64_t f6g8_19 = f6 * (int64_t) g8_19; |
| 384 | int64_t f6g9_19 = f6 * (int64_t) g9_19; |
| 385 | int64_t f7g0 = f7 * (int64_t) g0; |
| 386 | int64_t f7g1_2 = f7_2 * (int64_t) g1; |
| 387 | int64_t f7g2 = f7 * (int64_t) g2; |
| 388 | int64_t f7g3_38 = f7_2 * (int64_t) g3_19; |
| 389 | int64_t f7g4_19 = f7 * (int64_t) g4_19; |
| 390 | int64_t f7g5_38 = f7_2 * (int64_t) g5_19; |
| 391 | int64_t f7g6_19 = f7 * (int64_t) g6_19; |
| 392 | int64_t f7g7_38 = f7_2 * (int64_t) g7_19; |
| 393 | int64_t f7g8_19 = f7 * (int64_t) g8_19; |
| 394 | int64_t f7g9_38 = f7_2 * (int64_t) g9_19; |
| 395 | int64_t f8g0 = f8 * (int64_t) g0; |
| 396 | int64_t f8g1 = f8 * (int64_t) g1; |
| 397 | int64_t f8g2_19 = f8 * (int64_t) g2_19; |
| 398 | int64_t f8g3_19 = f8 * (int64_t) g3_19; |
| 399 | int64_t f8g4_19 = f8 * (int64_t) g4_19; |
| 400 | int64_t f8g5_19 = f8 * (int64_t) g5_19; |
| 401 | int64_t f8g6_19 = f8 * (int64_t) g6_19; |
| 402 | int64_t f8g7_19 = f8 * (int64_t) g7_19; |
| 403 | int64_t f8g8_19 = f8 * (int64_t) g8_19; |
| 404 | int64_t f8g9_19 = f8 * (int64_t) g9_19; |
| 405 | int64_t f9g0 = f9 * (int64_t) g0; |
| 406 | int64_t f9g1_38 = f9_2 * (int64_t) g1_19; |
| 407 | int64_t f9g2_19 = f9 * (int64_t) g2_19; |
| 408 | int64_t f9g3_38 = f9_2 * (int64_t) g3_19; |
| 409 | int64_t f9g4_19 = f9 * (int64_t) g4_19; |
| 410 | int64_t f9g5_38 = f9_2 * (int64_t) g5_19; |
| 411 | int64_t f9g6_19 = f9 * (int64_t) g6_19; |
| 412 | int64_t f9g7_38 = f9_2 * (int64_t) g7_19; |
| 413 | int64_t f9g8_19 = f9 * (int64_t) g8_19; |
| 414 | int64_t f9g9_38 = f9_2 * (int64_t) g9_19; |
| 415 | int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; |
| 416 | int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; |
| 417 | int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; |
| 418 | int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; |
| 419 | int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; |
| 420 | int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; |
| 421 | int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; |
| 422 | int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; |
| 423 | int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; |
| 424 | int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; |
| 425 | int64_t carry0; |
| 426 | int64_t carry1; |
| 427 | int64_t carry2; |
| 428 | int64_t carry3; |
| 429 | int64_t carry4; |
| 430 | int64_t carry5; |
| 431 | int64_t carry6; |
| 432 | int64_t carry7; |
| 433 | int64_t carry8; |
| 434 | int64_t carry9; |
| 435 | |
| 436 | /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) |
| 437 | * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 |
| 438 | * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) |
| 439 | * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ |
| 440 | |
| 441 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 442 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 443 | /* |h0| <= 2^25 */ |
| 444 | /* |h4| <= 2^25 */ |
| 445 | /* |h1| <= 1.71*2^59 */ |
| 446 | /* |h5| <= 1.71*2^59 */ |
| 447 | |
| 448 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 449 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 450 | /* |h1| <= 2^24; from now on fits into int32 */ |
| 451 | /* |h5| <= 2^24; from now on fits into int32 */ |
| 452 | /* |h2| <= 1.41*2^60 */ |
| 453 | /* |h6| <= 1.41*2^60 */ |
| 454 | |
| 455 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 456 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 457 | /* |h2| <= 2^25; from now on fits into int32 unchanged */ |
| 458 | /* |h6| <= 2^25; from now on fits into int32 unchanged */ |
| 459 | /* |h3| <= 1.71*2^59 */ |
| 460 | /* |h7| <= 1.71*2^59 */ |
| 461 | |
| 462 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 463 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 464 | /* |h3| <= 2^24; from now on fits into int32 unchanged */ |
| 465 | /* |h7| <= 2^24; from now on fits into int32 unchanged */ |
| 466 | /* |h4| <= 1.72*2^34 */ |
| 467 | /* |h8| <= 1.41*2^60 */ |
| 468 | |
| 469 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 470 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 471 | /* |h4| <= 2^25; from now on fits into int32 unchanged */ |
| 472 | /* |h8| <= 2^25; from now on fits into int32 unchanged */ |
| 473 | /* |h5| <= 1.01*2^24 */ |
| 474 | /* |h9| <= 1.71*2^59 */ |
| 475 | |
| 476 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 477 | /* |h9| <= 2^24; from now on fits into int32 unchanged */ |
| 478 | /* |h0| <= 1.1*2^39 */ |
| 479 | |
| 480 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 481 | /* |h0| <= 2^25; from now on fits into int32 unchanged */ |
| 482 | /* |h1| <= 1.01*2^24 */ |
| 483 | |
| 484 | h[0] = h0; |
| 485 | h[1] = h1; |
| 486 | h[2] = h2; |
| 487 | h[3] = h3; |
| 488 | h[4] = h4; |
| 489 | h[5] = h5; |
| 490 | h[6] = h6; |
| 491 | h[7] = h7; |
| 492 | h[8] = h8; |
| 493 | h[9] = h9; |
| 494 | } |
| 495 | |
| 496 | /* h = f * f |
| 497 | * Can overlap h with f. |
| 498 | * |
| 499 | * Preconditions: |
| 500 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
| 501 | * |
| 502 | * Postconditions: |
| 503 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
| 504 | * |
| 505 | * See fe_mul.c for discussion of implementation strategy. */ |
| 506 | static void fe_sq(fe h, const fe f) { |
| 507 | int32_t f0 = f[0]; |
| 508 | int32_t f1 = f[1]; |
| 509 | int32_t f2 = f[2]; |
| 510 | int32_t f3 = f[3]; |
| 511 | int32_t f4 = f[4]; |
| 512 | int32_t f5 = f[5]; |
| 513 | int32_t f6 = f[6]; |
| 514 | int32_t f7 = f[7]; |
| 515 | int32_t f8 = f[8]; |
| 516 | int32_t f9 = f[9]; |
| 517 | int32_t f0_2 = 2 * f0; |
| 518 | int32_t f1_2 = 2 * f1; |
| 519 | int32_t f2_2 = 2 * f2; |
| 520 | int32_t f3_2 = 2 * f3; |
| 521 | int32_t f4_2 = 2 * f4; |
| 522 | int32_t f5_2 = 2 * f5; |
| 523 | int32_t f6_2 = 2 * f6; |
| 524 | int32_t f7_2 = 2 * f7; |
| 525 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ |
| 526 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ |
| 527 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ |
| 528 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ |
| 529 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ |
| 530 | int64_t f0f0 = f0 * (int64_t) f0; |
| 531 | int64_t f0f1_2 = f0_2 * (int64_t) f1; |
| 532 | int64_t f0f2_2 = f0_2 * (int64_t) f2; |
| 533 | int64_t f0f3_2 = f0_2 * (int64_t) f3; |
| 534 | int64_t f0f4_2 = f0_2 * (int64_t) f4; |
| 535 | int64_t f0f5_2 = f0_2 * (int64_t) f5; |
| 536 | int64_t f0f6_2 = f0_2 * (int64_t) f6; |
| 537 | int64_t f0f7_2 = f0_2 * (int64_t) f7; |
| 538 | int64_t f0f8_2 = f0_2 * (int64_t) f8; |
| 539 | int64_t f0f9_2 = f0_2 * (int64_t) f9; |
| 540 | int64_t f1f1_2 = f1_2 * (int64_t) f1; |
| 541 | int64_t f1f2_2 = f1_2 * (int64_t) f2; |
| 542 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; |
| 543 | int64_t f1f4_2 = f1_2 * (int64_t) f4; |
| 544 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; |
| 545 | int64_t f1f6_2 = f1_2 * (int64_t) f6; |
| 546 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; |
| 547 | int64_t f1f8_2 = f1_2 * (int64_t) f8; |
| 548 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; |
| 549 | int64_t f2f2 = f2 * (int64_t) f2; |
| 550 | int64_t f2f3_2 = f2_2 * (int64_t) f3; |
| 551 | int64_t f2f4_2 = f2_2 * (int64_t) f4; |
| 552 | int64_t f2f5_2 = f2_2 * (int64_t) f5; |
| 553 | int64_t f2f6_2 = f2_2 * (int64_t) f6; |
| 554 | int64_t f2f7_2 = f2_2 * (int64_t) f7; |
| 555 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; |
| 556 | int64_t f2f9_38 = f2 * (int64_t) f9_38; |
| 557 | int64_t f3f3_2 = f3_2 * (int64_t) f3; |
| 558 | int64_t f3f4_2 = f3_2 * (int64_t) f4; |
| 559 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; |
| 560 | int64_t f3f6_2 = f3_2 * (int64_t) f6; |
| 561 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; |
| 562 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; |
| 563 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; |
| 564 | int64_t f4f4 = f4 * (int64_t) f4; |
| 565 | int64_t f4f5_2 = f4_2 * (int64_t) f5; |
| 566 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; |
| 567 | int64_t f4f7_38 = f4 * (int64_t) f7_38; |
| 568 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; |
| 569 | int64_t f4f9_38 = f4 * (int64_t) f9_38; |
| 570 | int64_t f5f5_38 = f5 * (int64_t) f5_38; |
| 571 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; |
| 572 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; |
| 573 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; |
| 574 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; |
| 575 | int64_t f6f6_19 = f6 * (int64_t) f6_19; |
| 576 | int64_t f6f7_38 = f6 * (int64_t) f7_38; |
| 577 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; |
| 578 | int64_t f6f9_38 = f6 * (int64_t) f9_38; |
| 579 | int64_t f7f7_38 = f7 * (int64_t) f7_38; |
| 580 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; |
| 581 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; |
| 582 | int64_t f8f8_19 = f8 * (int64_t) f8_19; |
| 583 | int64_t f8f9_38 = f8 * (int64_t) f9_38; |
| 584 | int64_t f9f9_38 = f9 * (int64_t) f9_38; |
| 585 | int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; |
| 586 | int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; |
| 587 | int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; |
| 588 | int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; |
| 589 | int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; |
| 590 | int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; |
| 591 | int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; |
| 592 | int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; |
| 593 | int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; |
| 594 | int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; |
| 595 | int64_t carry0; |
| 596 | int64_t carry1; |
| 597 | int64_t carry2; |
| 598 | int64_t carry3; |
| 599 | int64_t carry4; |
| 600 | int64_t carry5; |
| 601 | int64_t carry6; |
| 602 | int64_t carry7; |
| 603 | int64_t carry8; |
| 604 | int64_t carry9; |
| 605 | |
| 606 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 607 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 608 | |
| 609 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 610 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 611 | |
| 612 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 613 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 614 | |
| 615 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 616 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 617 | |
| 618 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 619 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 620 | |
| 621 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 622 | |
| 623 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 624 | |
| 625 | h[0] = h0; |
| 626 | h[1] = h1; |
| 627 | h[2] = h2; |
| 628 | h[3] = h3; |
| 629 | h[4] = h4; |
| 630 | h[5] = h5; |
| 631 | h[6] = h6; |
| 632 | h[7] = h7; |
| 633 | h[8] = h8; |
| 634 | h[9] = h9; |
| 635 | } |
| 636 | |
| 637 | static void fe_invert(fe out, const fe z) { |
| 638 | fe t0; |
| 639 | fe t1; |
| 640 | fe t2; |
| 641 | fe t3; |
| 642 | int i; |
| 643 | |
| 644 | fe_sq(t0, z); |
| 645 | fe_sq(t1, t0); |
| 646 | for (i = 1; i < 2; ++i) { |
| 647 | fe_sq(t1, t1); |
| 648 | } |
| 649 | fe_mul(t1, z, t1); |
| 650 | fe_mul(t0, t0, t1); |
| 651 | fe_sq(t2, t0); |
| 652 | fe_mul(t1, t1, t2); |
| 653 | fe_sq(t2, t1); |
| 654 | for (i = 1; i < 5; ++i) { |
| 655 | fe_sq(t2, t2); |
| 656 | } |
| 657 | fe_mul(t1, t2, t1); |
| 658 | fe_sq(t2, t1); |
| 659 | for (i = 1; i < 10; ++i) { |
| 660 | fe_sq(t2, t2); |
| 661 | } |
| 662 | fe_mul(t2, t2, t1); |
| 663 | fe_sq(t3, t2); |
| 664 | for (i = 1; i < 20; ++i) { |
| 665 | fe_sq(t3, t3); |
| 666 | } |
| 667 | fe_mul(t2, t3, t2); |
| 668 | fe_sq(t2, t2); |
| 669 | for (i = 1; i < 10; ++i) { |
| 670 | fe_sq(t2, t2); |
| 671 | } |
| 672 | fe_mul(t1, t2, t1); |
| 673 | fe_sq(t2, t1); |
| 674 | for (i = 1; i < 50; ++i) { |
| 675 | fe_sq(t2, t2); |
| 676 | } |
| 677 | fe_mul(t2, t2, t1); |
| 678 | fe_sq(t3, t2); |
| 679 | for (i = 1; i < 100; ++i) { |
| 680 | fe_sq(t3, t3); |
| 681 | } |
| 682 | fe_mul(t2, t3, t2); |
| 683 | fe_sq(t2, t2); |
| 684 | for (i = 1; i < 50; ++i) { |
| 685 | fe_sq(t2, t2); |
| 686 | } |
| 687 | fe_mul(t1, t2, t1); |
| 688 | fe_sq(t1, t1); |
| 689 | for (i = 1; i < 5; ++i) { |
| 690 | fe_sq(t1, t1); |
| 691 | } |
| 692 | fe_mul(out, t1, t0); |
| 693 | } |
| 694 | |
| 695 | /* h = -f |
| 696 | * |
| 697 | * Preconditions: |
| 698 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
| 699 | * |
| 700 | * Postconditions: |
| 701 | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ |
| 702 | static void fe_neg(fe h, const fe f) { |
| 703 | unsigned i; |
| 704 | for (i = 0; i < 10; i++) { |
| 705 | h[i] = -f[i]; |
| 706 | } |
| 707 | } |
| 708 | |
| 709 | /* Replace (f,g) with (g,g) if b == 1; |
| 710 | * replace (f,g) with (f,g) if b == 0. |
| 711 | * |
| 712 | * Preconditions: b in {0,1}. */ |
| 713 | static void fe_cmov(fe f, const fe g, unsigned b) { |
| 714 | b = 0-b; |
| 715 | unsigned i; |
| 716 | for (i = 0; i < 10; i++) { |
| 717 | int32_t x = f[i] ^ g[i]; |
| 718 | x &= b; |
| 719 | f[i] ^= x; |
| 720 | } |
| 721 | } |
| 722 | |
| 723 | /* return 0 if f == 0 |
| 724 | * return 1 if f != 0 |
| 725 | * |
| 726 | * Preconditions: |
| 727 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
| 728 | static int fe_isnonzero(const fe f) { |
| 729 | uint8_t s[32]; |
| 730 | fe_tobytes(s, f); |
| 731 | |
| 732 | static const uint8_t zero[32] = {0}; |
| 733 | return timingsafe_memcmp(s, zero, sizeof(zero)) != 0; |
| 734 | } |
| 735 | |
| 736 | /* return 1 if f is in {1,3,5,...,q-2} |
| 737 | * return 0 if f is in {0,2,4,...,q-1} |
| 738 | * |
| 739 | * Preconditions: |
| 740 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
| 741 | static int fe_isnegative(const fe f) { |
| 742 | uint8_t s[32]; |
| 743 | fe_tobytes(s, f); |
| 744 | return s[0] & 1; |
| 745 | } |
| 746 | |
| 747 | /* h = 2 * f * f |
| 748 | * Can overlap h with f. |
| 749 | * |
| 750 | * Preconditions: |
| 751 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
| 752 | * |
| 753 | * Postconditions: |
| 754 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
| 755 | * |
| 756 | * See fe_mul.c for discussion of implementation strategy. */ |
| 757 | static void fe_sq2(fe h, const fe f) { |
| 758 | int32_t f0 = f[0]; |
| 759 | int32_t f1 = f[1]; |
| 760 | int32_t f2 = f[2]; |
| 761 | int32_t f3 = f[3]; |
| 762 | int32_t f4 = f[4]; |
| 763 | int32_t f5 = f[5]; |
| 764 | int32_t f6 = f[6]; |
| 765 | int32_t f7 = f[7]; |
| 766 | int32_t f8 = f[8]; |
| 767 | int32_t f9 = f[9]; |
| 768 | int32_t f0_2 = 2 * f0; |
| 769 | int32_t f1_2 = 2 * f1; |
| 770 | int32_t f2_2 = 2 * f2; |
| 771 | int32_t f3_2 = 2 * f3; |
| 772 | int32_t f4_2 = 2 * f4; |
| 773 | int32_t f5_2 = 2 * f5; |
| 774 | int32_t f6_2 = 2 * f6; |
| 775 | int32_t f7_2 = 2 * f7; |
| 776 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ |
| 777 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ |
| 778 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ |
| 779 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ |
| 780 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ |
| 781 | int64_t f0f0 = f0 * (int64_t) f0; |
| 782 | int64_t f0f1_2 = f0_2 * (int64_t) f1; |
| 783 | int64_t f0f2_2 = f0_2 * (int64_t) f2; |
| 784 | int64_t f0f3_2 = f0_2 * (int64_t) f3; |
| 785 | int64_t f0f4_2 = f0_2 * (int64_t) f4; |
| 786 | int64_t f0f5_2 = f0_2 * (int64_t) f5; |
| 787 | int64_t f0f6_2 = f0_2 * (int64_t) f6; |
| 788 | int64_t f0f7_2 = f0_2 * (int64_t) f7; |
| 789 | int64_t f0f8_2 = f0_2 * (int64_t) f8; |
| 790 | int64_t f0f9_2 = f0_2 * (int64_t) f9; |
| 791 | int64_t f1f1_2 = f1_2 * (int64_t) f1; |
| 792 | int64_t f1f2_2 = f1_2 * (int64_t) f2; |
| 793 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; |
| 794 | int64_t f1f4_2 = f1_2 * (int64_t) f4; |
| 795 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; |
| 796 | int64_t f1f6_2 = f1_2 * (int64_t) f6; |
| 797 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; |
| 798 | int64_t f1f8_2 = f1_2 * (int64_t) f8; |
| 799 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; |
| 800 | int64_t f2f2 = f2 * (int64_t) f2; |
| 801 | int64_t f2f3_2 = f2_2 * (int64_t) f3; |
| 802 | int64_t f2f4_2 = f2_2 * (int64_t) f4; |
| 803 | int64_t f2f5_2 = f2_2 * (int64_t) f5; |
| 804 | int64_t f2f6_2 = f2_2 * (int64_t) f6; |
| 805 | int64_t f2f7_2 = f2_2 * (int64_t) f7; |
| 806 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; |
| 807 | int64_t f2f9_38 = f2 * (int64_t) f9_38; |
| 808 | int64_t f3f3_2 = f3_2 * (int64_t) f3; |
| 809 | int64_t f3f4_2 = f3_2 * (int64_t) f4; |
| 810 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; |
| 811 | int64_t f3f6_2 = f3_2 * (int64_t) f6; |
| 812 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; |
| 813 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; |
| 814 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; |
| 815 | int64_t f4f4 = f4 * (int64_t) f4; |
| 816 | int64_t f4f5_2 = f4_2 * (int64_t) f5; |
| 817 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; |
| 818 | int64_t f4f7_38 = f4 * (int64_t) f7_38; |
| 819 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; |
| 820 | int64_t f4f9_38 = f4 * (int64_t) f9_38; |
| 821 | int64_t f5f5_38 = f5 * (int64_t) f5_38; |
| 822 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; |
| 823 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; |
| 824 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; |
| 825 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; |
| 826 | int64_t f6f6_19 = f6 * (int64_t) f6_19; |
| 827 | int64_t f6f7_38 = f6 * (int64_t) f7_38; |
| 828 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; |
| 829 | int64_t f6f9_38 = f6 * (int64_t) f9_38; |
| 830 | int64_t f7f7_38 = f7 * (int64_t) f7_38; |
| 831 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; |
| 832 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; |
| 833 | int64_t f8f8_19 = f8 * (int64_t) f8_19; |
| 834 | int64_t f8f9_38 = f8 * (int64_t) f9_38; |
| 835 | int64_t f9f9_38 = f9 * (int64_t) f9_38; |
| 836 | int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; |
| 837 | int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; |
| 838 | int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; |
| 839 | int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; |
| 840 | int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; |
| 841 | int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; |
| 842 | int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; |
| 843 | int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; |
| 844 | int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; |
| 845 | int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; |
| 846 | int64_t carry0; |
| 847 | int64_t carry1; |
| 848 | int64_t carry2; |
| 849 | int64_t carry3; |
| 850 | int64_t carry4; |
| 851 | int64_t carry5; |
| 852 | int64_t carry6; |
| 853 | int64_t carry7; |
| 854 | int64_t carry8; |
| 855 | int64_t carry9; |
| 856 | |
| 857 | h0 += h0; |
| 858 | h1 += h1; |
| 859 | h2 += h2; |
| 860 | h3 += h3; |
| 861 | h4 += h4; |
| 862 | h5 += h5; |
| 863 | h6 += h6; |
| 864 | h7 += h7; |
| 865 | h8 += h8; |
| 866 | h9 += h9; |
| 867 | |
| 868 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 869 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 870 | |
| 871 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 872 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 873 | |
| 874 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 875 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 876 | |
| 877 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 878 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 879 | |
| 880 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 881 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 882 | |
| 883 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 884 | |
| 885 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 886 | |
| 887 | h[0] = h0; |
| 888 | h[1] = h1; |
| 889 | h[2] = h2; |
| 890 | h[3] = h3; |
| 891 | h[4] = h4; |
| 892 | h[5] = h5; |
| 893 | h[6] = h6; |
| 894 | h[7] = h7; |
| 895 | h[8] = h8; |
| 896 | h[9] = h9; |
| 897 | } |
| 898 | |
| 899 | static void fe_pow22523(fe out, const fe z) { |
| 900 | fe t0; |
| 901 | fe t1; |
| 902 | fe t2; |
| 903 | int i; |
| 904 | |
| 905 | fe_sq(t0, z); |
| 906 | fe_sq(t1, t0); |
| 907 | for (i = 1; i < 2; ++i) { |
| 908 | fe_sq(t1, t1); |
| 909 | } |
| 910 | fe_mul(t1, z, t1); |
| 911 | fe_mul(t0, t0, t1); |
| 912 | fe_sq(t0, t0); |
| 913 | fe_mul(t0, t1, t0); |
| 914 | fe_sq(t1, t0); |
| 915 | for (i = 1; i < 5; ++i) { |
| 916 | fe_sq(t1, t1); |
| 917 | } |
| 918 | fe_mul(t0, t1, t0); |
| 919 | fe_sq(t1, t0); |
| 920 | for (i = 1; i < 10; ++i) { |
| 921 | fe_sq(t1, t1); |
| 922 | } |
| 923 | fe_mul(t1, t1, t0); |
| 924 | fe_sq(t2, t1); |
| 925 | for (i = 1; i < 20; ++i) { |
| 926 | fe_sq(t2, t2); |
| 927 | } |
| 928 | fe_mul(t1, t2, t1); |
| 929 | fe_sq(t1, t1); |
| 930 | for (i = 1; i < 10; ++i) { |
| 931 | fe_sq(t1, t1); |
| 932 | } |
| 933 | fe_mul(t0, t1, t0); |
| 934 | fe_sq(t1, t0); |
| 935 | for (i = 1; i < 50; ++i) { |
| 936 | fe_sq(t1, t1); |
| 937 | } |
| 938 | fe_mul(t1, t1, t0); |
| 939 | fe_sq(t2, t1); |
| 940 | for (i = 1; i < 100; ++i) { |
| 941 | fe_sq(t2, t2); |
| 942 | } |
| 943 | fe_mul(t1, t2, t1); |
| 944 | fe_sq(t1, t1); |
| 945 | for (i = 1; i < 50; ++i) { |
| 946 | fe_sq(t1, t1); |
| 947 | } |
| 948 | fe_mul(t0, t1, t0); |
| 949 | fe_sq(t0, t0); |
| 950 | for (i = 1; i < 2; ++i) { |
| 951 | fe_sq(t0, t0); |
| 952 | } |
| 953 | fe_mul(out, t0, z); |
| 954 | } |
| 955 | |
| 956 | void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) { |
| 957 | fe recip; |
| 958 | fe x; |
| 959 | fe y; |
| 960 | |
| 961 | fe_invert(recip, h->Z); |
| 962 | fe_mul(x, h->X, recip); |
| 963 | fe_mul(y, h->Y, recip); |
| 964 | fe_tobytes(s, y); |
| 965 | s[31] ^= fe_isnegative(x) << 7; |
| 966 | } |
| 967 | |
| 968 | static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) { |
| 969 | fe recip; |
| 970 | fe x; |
| 971 | fe y; |
| 972 | |
| 973 | fe_invert(recip, h->Z); |
| 974 | fe_mul(x, h->X, recip); |
| 975 | fe_mul(y, h->Y, recip); |
| 976 | fe_tobytes(s, y); |
| 977 | s[31] ^= fe_isnegative(x) << 7; |
| 978 | } |
| 979 | |
| 980 | static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, |
| 981 | -8787816, -6275908, -3247719, -18696448, -12055116}; |
| 982 | |
| 983 | static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, |
| 984 | -272473, -25146209, -2005654, 326686, 11406482}; |
| 985 | |
| 986 | int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { |
| 987 | fe u; |
| 988 | fe v; |
| 989 | fe v3; |
| 990 | fe vxx; |
| 991 | fe check; |
| 992 | |
| 993 | fe_frombytes(h->Y, s); |
| 994 | fe_1(h->Z); |
| 995 | fe_sq(u, h->Y); |
| 996 | fe_mul(v, u, d); |
| 997 | fe_sub(u, u, h->Z); /* u = y^2-1 */ |
| 998 | fe_add(v, v, h->Z); /* v = dy^2+1 */ |
| 999 | |
| 1000 | fe_sq(v3, v); |
| 1001 | fe_mul(v3, v3, v); /* v3 = v^3 */ |
| 1002 | fe_sq(h->X, v3); |
| 1003 | fe_mul(h->X, h->X, v); |
| 1004 | fe_mul(h->X, h->X, u); /* x = uv^7 */ |
| 1005 | |
| 1006 | fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ |
| 1007 | fe_mul(h->X, h->X, v3); |
| 1008 | fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ |
| 1009 | |
| 1010 | fe_sq(vxx, h->X); |
| 1011 | fe_mul(vxx, vxx, v); |
| 1012 | fe_sub(check, vxx, u); /* vx^2-u */ |
| 1013 | if (fe_isnonzero(check)) { |
| 1014 | fe_add(check, vxx, u); /* vx^2+u */ |
| 1015 | if (fe_isnonzero(check)) { |
| 1016 | return -1; |
| 1017 | } |
| 1018 | fe_mul(h->X, h->X, sqrtm1); |
| 1019 | } |
| 1020 | |
| 1021 | if (fe_isnegative(h->X) != (s[31] >> 7)) { |
| 1022 | fe_neg(h->X, h->X); |
| 1023 | } |
| 1024 | |
| 1025 | fe_mul(h->T, h->X, h->Y); |
| 1026 | return 0; |
| 1027 | } |
| 1028 | |
| 1029 | static void ge_p2_0(ge_p2 *h) { |
| 1030 | fe_0(h->X); |
| 1031 | fe_1(h->Y); |
| 1032 | fe_1(h->Z); |
| 1033 | } |
| 1034 | |
| 1035 | static void ge_p3_0(ge_p3 *h) { |
| 1036 | fe_0(h->X); |
| 1037 | fe_1(h->Y); |
| 1038 | fe_1(h->Z); |
| 1039 | fe_0(h->T); |
| 1040 | } |
| 1041 | |
| 1042 | static void ge_cached_0(ge_cached *h) { |
| 1043 | fe_1(h->YplusX); |
| 1044 | fe_1(h->YminusX); |
| 1045 | fe_1(h->Z); |
| 1046 | fe_0(h->T2d); |
| 1047 | } |
| 1048 | |
| 1049 | static void ge_precomp_0(ge_precomp *h) { |
| 1050 | fe_1(h->yplusx); |
| 1051 | fe_1(h->yminusx); |
| 1052 | fe_0(h->xy2d); |
| 1053 | } |
| 1054 | |
| 1055 | /* r = p */ |
| 1056 | static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { |
| 1057 | fe_copy(r->X, p->X); |
| 1058 | fe_copy(r->Y, p->Y); |
| 1059 | fe_copy(r->Z, p->Z); |
| 1060 | } |
| 1061 | |
| 1062 | static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, |
| 1063 | 15978800, -12551817, -6495438, 29715968, 9444199}; |
| 1064 | |
| 1065 | /* r = p */ |
| 1066 | void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { |
| 1067 | fe_add(r->YplusX, p->Y, p->X); |
| 1068 | fe_sub(r->YminusX, p->Y, p->X); |
| 1069 | fe_copy(r->Z, p->Z); |
| 1070 | fe_mul(r->T2d, p->T, d2); |
| 1071 | } |
| 1072 | |
| 1073 | /* r = p */ |
| 1074 | void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { |
| 1075 | fe_mul(r->X, p->X, p->T); |
| 1076 | fe_mul(r->Y, p->Y, p->Z); |
| 1077 | fe_mul(r->Z, p->Z, p->T); |
| 1078 | } |
| 1079 | |
| 1080 | /* r = p */ |
| 1081 | void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { |
| 1082 | fe_mul(r->X, p->X, p->T); |
| 1083 | fe_mul(r->Y, p->Y, p->Z); |
| 1084 | fe_mul(r->Z, p->Z, p->T); |
| 1085 | fe_mul(r->T, p->X, p->Y); |
| 1086 | } |
| 1087 | |
| 1088 | /* r = p */ |
| 1089 | static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) { |
| 1090 | ge_p3 t; |
| 1091 | x25519_ge_p1p1_to_p3(&t, p); |
| 1092 | x25519_ge_p3_to_cached(r, &t); |
| 1093 | } |
| 1094 | |
| 1095 | /* r = 2 * p */ |
| 1096 | static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { |
| 1097 | fe t0; |
| 1098 | |
| 1099 | fe_sq(r->X, p->X); |
| 1100 | fe_sq(r->Z, p->Y); |
| 1101 | fe_sq2(r->T, p->Z); |
| 1102 | fe_add(r->Y, p->X, p->Y); |
| 1103 | fe_sq(t0, r->Y); |
| 1104 | fe_add(r->Y, r->Z, r->X); |
| 1105 | fe_sub(r->Z, r->Z, r->X); |
| 1106 | fe_sub(r->X, t0, r->Y); |
| 1107 | fe_sub(r->T, r->T, r->Z); |
| 1108 | } |
| 1109 | |
| 1110 | /* r = 2 * p */ |
| 1111 | static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { |
| 1112 | ge_p2 q; |
| 1113 | ge_p3_to_p2(&q, p); |
| 1114 | ge_p2_dbl(r, &q); |
| 1115 | } |
| 1116 | |
| 1117 | /* r = p + q */ |
| 1118 | static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
| 1119 | fe t0; |
| 1120 | |
| 1121 | fe_add(r->X, p->Y, p->X); |
| 1122 | fe_sub(r->Y, p->Y, p->X); |
| 1123 | fe_mul(r->Z, r->X, q->yplusx); |
| 1124 | fe_mul(r->Y, r->Y, q->yminusx); |
| 1125 | fe_mul(r->T, q->xy2d, p->T); |
| 1126 | fe_add(t0, p->Z, p->Z); |
| 1127 | fe_sub(r->X, r->Z, r->Y); |
| 1128 | fe_add(r->Y, r->Z, r->Y); |
| 1129 | fe_add(r->Z, t0, r->T); |
| 1130 | fe_sub(r->T, t0, r->T); |
| 1131 | } |
| 1132 | |
| 1133 | /* r = p - q */ |
| 1134 | static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
| 1135 | fe t0; |
| 1136 | |
| 1137 | fe_add(r->X, p->Y, p->X); |
| 1138 | fe_sub(r->Y, p->Y, p->X); |
| 1139 | fe_mul(r->Z, r->X, q->yminusx); |
| 1140 | fe_mul(r->Y, r->Y, q->yplusx); |
| 1141 | fe_mul(r->T, q->xy2d, p->T); |
| 1142 | fe_add(t0, p->Z, p->Z); |
| 1143 | fe_sub(r->X, r->Z, r->Y); |
| 1144 | fe_add(r->Y, r->Z, r->Y); |
| 1145 | fe_sub(r->Z, t0, r->T); |
| 1146 | fe_add(r->T, t0, r->T); |
| 1147 | } |
| 1148 | |
| 1149 | /* r = p + q */ |
| 1150 | void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
| 1151 | fe t0; |
| 1152 | |
| 1153 | fe_add(r->X, p->Y, p->X); |
| 1154 | fe_sub(r->Y, p->Y, p->X); |
| 1155 | fe_mul(r->Z, r->X, q->YplusX); |
| 1156 | fe_mul(r->Y, r->Y, q->YminusX); |
| 1157 | fe_mul(r->T, q->T2d, p->T); |
| 1158 | fe_mul(r->X, p->Z, q->Z); |
| 1159 | fe_add(t0, r->X, r->X); |
| 1160 | fe_sub(r->X, r->Z, r->Y); |
| 1161 | fe_add(r->Y, r->Z, r->Y); |
| 1162 | fe_add(r->Z, t0, r->T); |
| 1163 | fe_sub(r->T, t0, r->T); |
| 1164 | } |
| 1165 | |
| 1166 | /* r = p - q */ |
| 1167 | void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
| 1168 | fe t0; |
| 1169 | |
| 1170 | fe_add(r->X, p->Y, p->X); |
| 1171 | fe_sub(r->Y, p->Y, p->X); |
| 1172 | fe_mul(r->Z, r->X, q->YminusX); |
| 1173 | fe_mul(r->Y, r->Y, q->YplusX); |
| 1174 | fe_mul(r->T, q->T2d, p->T); |
| 1175 | fe_mul(r->X, p->Z, q->Z); |
| 1176 | fe_add(t0, r->X, r->X); |
| 1177 | fe_sub(r->X, r->Z, r->Y); |
| 1178 | fe_add(r->Y, r->Z, r->Y); |
| 1179 | fe_sub(r->Z, t0, r->T); |
| 1180 | fe_add(r->T, t0, r->T); |
| 1181 | } |
| 1182 | |
| 1183 | static uint8_t equal(signed char b, signed char c) { |
| 1184 | uint8_t ub = b; |
| 1185 | uint8_t uc = c; |
| 1186 | uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ |
| 1187 | uint32_t y = x; /* 0: yes; 1..255: no */ |
| 1188 | y -= 1; /* 4294967295: yes; 0..254: no */ |
| 1189 | y >>= 31; /* 1: yes; 0: no */ |
| 1190 | return y; |
| 1191 | } |
| 1192 | |
| 1193 | static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { |
| 1194 | fe_cmov(t->yplusx, u->yplusx, b); |
| 1195 | fe_cmov(t->yminusx, u->yminusx, b); |
| 1196 | fe_cmov(t->xy2d, u->xy2d, b); |
| 1197 | } |
| 1198 | |
| 1199 | void x25519_ge_scalarmult_small_precomp( |
| 1200 | ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) { |
| 1201 | /* precomp_table is first expanded into matching |ge_precomp| |
| 1202 | * elements. */ |
| 1203 | ge_precomp multiples[15]; |
| 1204 | |
| 1205 | unsigned i; |
| 1206 | for (i = 0; i < 15; i++) { |
| 1207 | const uint8_t *bytes = &precomp_table[i*(2 * 32)]; |
| 1208 | fe x, y; |
| 1209 | fe_frombytes(x, bytes); |
| 1210 | fe_frombytes(y, bytes + 32); |
| 1211 | |
| 1212 | ge_precomp *out = &multiples[i]; |
| 1213 | fe_add(out->yplusx, y, x); |
| 1214 | fe_sub(out->yminusx, y, x); |
| 1215 | fe_mul(out->xy2d, x, y); |
| 1216 | fe_mul(out->xy2d, out->xy2d, d2); |
| 1217 | } |
| 1218 | |
| 1219 | /* See the comment above |k25519SmallPrecomp| about the structure of the |
| 1220 | * precomputed elements. This loop does 64 additions and 64 doublings to |
| 1221 | * calculate the result. */ |
| 1222 | ge_p3_0(h); |
| 1223 | |
| 1224 | for (i = 63; i < 64; i--) { |
| 1225 | unsigned j; |
| 1226 | signed char index = 0; |
| 1227 | |
| 1228 | for (j = 0; j < 4; j++) { |
| 1229 | const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7)); |
| 1230 | index |= (bit << j); |
| 1231 | } |
| 1232 | |
| 1233 | ge_precomp e; |
| 1234 | ge_precomp_0(&e); |
| 1235 | |
| 1236 | for (j = 1; j < 16; j++) { |
| 1237 | cmov(&e, &multiples[j-1], equal(index, j)); |
| 1238 | } |
| 1239 | |
| 1240 | ge_cached cached; |
| 1241 | ge_p1p1 r; |
| 1242 | x25519_ge_p3_to_cached(&cached, h); |
| 1243 | x25519_ge_add(&r, h, &cached); |
| 1244 | x25519_ge_p1p1_to_p3(h, &r); |
| 1245 | |
| 1246 | ge_madd(&r, h, &e); |
| 1247 | x25519_ge_p1p1_to_p3(h, &r); |
| 1248 | } |
| 1249 | } |
| 1250 | |
| 1251 | #if defined(OPENSSL_SMALL) |
| 1252 | |
| 1253 | /* This block of code replaces the standard base-point table with a much smaller |
| 1254 | * one. The standard table is 30,720 bytes while this one is just 960. |
| 1255 | * |
| 1256 | * This table contains 15 pairs of group elements, (x, y), where each field |
| 1257 | * element is serialised with |fe_tobytes|. If |i| is the index of the group |
| 1258 | * element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀ |
| 1259 | * is the most significant bit). The value of the group element is then: |
| 1260 | * (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */ |
| 1261 | static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = { |
| 1262 | 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, |
| 1263 | 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, |
| 1264 | 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66, |
| 1265 | 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, |
| 1266 | 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, |
| 1267 | 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e, |
| 1268 | 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4, |
| 1269 | 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62, |
| 1270 | 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba, |
| 1271 | 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd, |
| 1272 | 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61, |
| 1273 | 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c, |
| 1274 | 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c, |
| 1275 | 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5, |
| 1276 | 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3, |
| 1277 | 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18, |
| 1278 | 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2, |
| 1279 | 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95, |
| 1280 | 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b, |
| 1281 | 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90, |
| 1282 | 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52, |
| 1283 | 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb, |
| 1284 | 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c, |
| 1285 | 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e, |
| 1286 | 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e, |
| 1287 | 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a, |
| 1288 | 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43, |
| 1289 | 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53, |
| 1290 | 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8, |
| 1291 | 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89, |
| 1292 | 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef, |
| 1293 | 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60, |
| 1294 | 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a, |
| 1295 | 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8, |
| 1296 | 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54, |
| 1297 | 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b, |
| 1298 | 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd, |
| 1299 | 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb, |
| 1300 | 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c, |
| 1301 | 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b, |
| 1302 | 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63, |
| 1303 | 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a, |
| 1304 | 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07, |
| 1305 | 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa, |
| 1306 | 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a, |
| 1307 | 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84, |
| 1308 | 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc, |
| 1309 | 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42, |
| 1310 | 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0, |
| 1311 | 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0, |
| 1312 | 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a, |
| 1313 | 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5, |
| 1314 | 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c, |
| 1315 | 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27, |
| 1316 | 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31, |
| 1317 | 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c, |
| 1318 | 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87, |
| 1319 | 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0, |
| 1320 | 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23, |
| 1321 | 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2, |
| 1322 | 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87, |
| 1323 | 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d, |
| 1324 | 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b, |
| 1325 | 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d, |
| 1326 | 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6, |
| 1327 | 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84, |
| 1328 | 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04, |
| 1329 | 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19, |
| 1330 | 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b, |
| 1331 | 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a, |
| 1332 | 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea, |
| 1333 | 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30, |
| 1334 | 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7, |
| 1335 | 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa, |
| 1336 | 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5, |
| 1337 | 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71, |
| 1338 | 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab, |
| 1339 | 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb, |
| 1340 | 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c, |
| 1341 | 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25, |
| 1342 | }; |
| 1343 | |
| 1344 | void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { |
| 1345 | x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp); |
| 1346 | } |
| 1347 | |
| 1348 | #else |
| 1349 | |
| 1350 | /* k25519Precomp[i][j] = (j+1)*256^i*B */ |
| 1351 | static const ge_precomp k25519Precomp[32][8] = { |
| 1352 | { |
| 1353 | { |
| 1354 | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, |
| 1355 | 27544626, -11754271, -6079156, 2047605}, |
| 1356 | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
| 1357 | 5043384, 19500929, -15469378}, |
| 1358 | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, |
| 1359 | 29287919, 11864899, -24514362, -4438546}, |
| 1360 | }, |
| 1361 | { |
| 1362 | {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, |
| 1363 | -11717903, -3814571, -358445, -10211303}, |
| 1364 | {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, |
| 1365 | -15616551, 11189268, -26829678, -5319081}, |
| 1366 | {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, |
| 1367 | -3128826, -9541118, -15472047, -4166697}, |
| 1368 | }, |
| 1369 | { |
| 1370 | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, |
| 1371 | 27787600, -14772189, 28944400, -1550024}, |
| 1372 | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, |
| 1373 | 16354577, -11775962, 7689662, 11199574}, |
| 1374 | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, |
| 1375 | 7512774, 10017326, -17749093, -9920357}, |
| 1376 | }, |
| 1377 | { |
| 1378 | {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, |
| 1379 | -28926210, 15006023, 3284568, -6276540}, |
| 1380 | {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, |
| 1381 | 7464579, 9656445, 13059162, 10374397}, |
| 1382 | {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, |
| 1383 | -3839045, -641708, -101325}, |
| 1384 | }, |
| 1385 | { |
| 1386 | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, |
| 1387 | 32867885, 14515107, -15438304, 10819380}, |
| 1388 | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
| 1389 | 12483688, -12668491, 5581306}, |
| 1390 | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, |
| 1391 | 28542350, 13850243, -23678021, -15815942}, |
| 1392 | }, |
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| 1839 | { |
| 1840 | {15564307, -14311570, 3101243, 5684148, 30446780, -8051356, |
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| 1847 | { |
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| 1850 | {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445, |
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| 1860 | {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117, |
| 1861 | -32719404, -5322751, 24216882, 5944158}, |
| 1862 | }, |
| 1863 | { |
| 1864 | {8894125, 7450974, -2664149, -9765752, -28080517, -12389115, |
| 1865 | 19345746, 14680796, 11632993, 5847885}, |
| 1866 | {26942781, -2315317, 9129564, -4906607, 26024105, 11769399, |
| 1867 | -11518837, 6367194, -9727230, 4782140}, |
| 1868 | {19916461, -4828410, -22910704, -11414391, 25606324, -5972441, |
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| 1870 | }, |
| 1871 | { |
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| 1876 | {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, |
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| 1878 | }, |
| 1879 | }, |
| 1880 | { |
| 1881 | { |
| 1882 | {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, |
| 1883 | -12618185, 12228557, -7003677}, |
| 1884 | {32944382, 14922211, -22844894, 5188528, 21913450, -8719943, |
| 1885 | 4001465, 13238564, -6114803, 8653815}, |
| 1886 | {22865569, -4652735, 27603668, -12545395, 14348958, 8234005, |
| 1887 | 24808405, 5719875, 28483275, 2841751}, |
| 1888 | }, |
| 1889 | { |
| 1890 | {-16420968, -1113305, -327719, -12107856, 21886282, -15552774, |
| 1891 | -1887966, -315658, 19932058, -12739203}, |
| 1892 | {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912, |
| 1893 | 3999228, 13239134, -4777469, -13910208}, |
| 1894 | {1382174, -11694719, 17266790, 9194690, -13324356, 9720081, |
| 1895 | 20403944, 11284705, -14013818, 3093230}, |
| 1896 | }, |
| 1897 | { |
| 1898 | {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, |
| 1899 | 16271225, -24049421, -6691850}, |
| 1900 | {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293, |
| 1901 | 24123614, 15193618, -21652117, -16739389}, |
| 1902 | {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484, |
| 1903 | 31870908, 14690798, 17361620, 11864968}, |
| 1904 | }, |
| 1905 | { |
| 1906 | {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200, |
| 1907 | -12331205, -7486601, -25578460, -16240689}, |
| 1908 | {14668462, -12270235, 26039039, 15305210, 25515617, 4542480, |
| 1909 | 10453892, 6577524, 9145645, -6443880}, |
| 1910 | {5974874, 3053895, -9433049, -10385191, -31865124, 3225009, |
| 1911 | -7972642, 3936128, -5652273, -3050304}, |
| 1912 | }, |
| 1913 | { |
| 1914 | {30625386, -4729400, -25555961, -12792866, -20484575, 7695099, |
| 1915 | 17097188, -16303496, -27999779, 1803632}, |
| 1916 | {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700, |
| 1917 | 14911344, 12196514, -21405489, 7047412}, |
| 1918 | {20093277, 9920966, -11138194, -5343857, 13161587, 12044805, |
| 1919 | -32856851, 4124601, -32343828, -10257566}, |
| 1920 | }, |
| 1921 | { |
| 1922 | {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605, |
| 1923 | 4752377, -8714640, -21679658, 2288038}, |
| 1924 | {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457, |
| 1925 | 29457502, 14625692, -24819617, 12570232}, |
| 1926 | {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109, |
| 1927 | -21159943, -3498680, -11974704, 4724943}, |
| 1928 | }, |
| 1929 | { |
| 1930 | {17960970, -11775534, -4140968, -9702530, -8876562, -1410617, |
| 1931 | -12907383, -8659932, -29576300, 1903856}, |
| 1932 | {23134274, -14279132, -10681997, -1611936, 20684485, 15770816, |
| 1933 | -12989750, 3190296, 26955097, 14109738}, |
| 1934 | {15308788, 5320727, -30113809, -14318877, 22902008, 7767164, |
| 1935 | 29425325, -11277562, 31960942, 11934971}, |
| 1936 | }, |
| 1937 | { |
| 1938 | {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669, |
| 1939 | 20638173, 4875028, 10491392, 1379718}, |
| 1940 | {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801, |
| 1941 | 33518459, 16176658, 21432314, 12180697}, |
| 1942 | {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205, |
| 1943 | 1465425, 12689540, -10301319, -13872883}, |
| 1944 | }, |
| 1945 | }, |
| 1946 | { |
| 1947 | { |
| 1948 | {5414091, -15386041, -21007664, 9643570, 12834970, 1186149, |
| 1949 | -2622916, -1342231, 26128231, 6032912}, |
| 1950 | {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156, |
| 1951 | 3604025, 8316894, -25875034, -10437358}, |
| 1952 | {3296484, 6223048, 24680646, -12246460, -23052020, 5903205, |
| 1953 | -8862297, -4639164, 12376617, 3188849}, |
| 1954 | }, |
| 1955 | { |
| 1956 | {29190488, -14659046, 27549113, -1183516, 3520066, -10697301, |
| 1957 | 32049515, -7309113, -16109234, -9852307}, |
| 1958 | {-14744486, -9309156, 735818, -598978, -20407687, -5057904, |
| 1959 | 25246078, -15795669, 18640741, -960977}, |
| 1960 | {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252, |
| 1961 | -31638386, -494430, 10530747, 1053335}, |
| 1962 | }, |
| 1963 | { |
| 1964 | {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384, |
| 1965 | -31462369, -2948985, 24018831, 15026644}, |
| 1966 | {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631, |
| 1967 | 25310643, 13003497, -2314791, -15145616}, |
| 1968 | {-27419985, -603321, -8043984, -1669117, -26092265, 13987819, |
| 1969 | -27297622, 187899, -23166419, -2531735}, |
| 1970 | }, |
| 1971 | { |
| 1972 | {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473, |
| 1973 | 9716667, 16266922, -5070217, 726099}, |
| 1974 | {29370922, -6053998, 7334071, -15342259, 9385287, 2247707, |
| 1975 | -13661962, -4839461, 30007388, -15823341}, |
| 1976 | {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, |
| 1977 | 730663, 9835848, 4555336}, |
| 1978 | }, |
| 1979 | { |
| 1980 | {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977, |
| 1981 | 17693930, 544696, -11985298, 12422646}, |
| 1982 | {31117226, -12215734, -13502838, 6561947, -9876867, -12757670, |
| 1983 | -5118685, -4096706, 29120153, 13924425}, |
| 1984 | {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820, |
| 1985 | -9383939, -11317700, 7240931, -237388}, |
| 1986 | }, |
| 1987 | { |
| 1988 | {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771, |
| 1989 | 1222336, 4389483, 3293637, -15551743}, |
| 1990 | {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533, |
| 1991 | -24319580, 7733547, 12796905, -6335822}, |
| 1992 | {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811, |
| 1993 | -28253339, 3647836, 3222231, -11160462}, |
| 1994 | }, |
| 1995 | { |
| 1996 | {18606113, 1693100, -25448386, -15170272, 4112353, 10045021, |
| 1997 | 23603893, -2048234, -7550776, 2484985}, |
| 1998 | {9255317, -3131197, -12156162, -1004256, 13098013, -9214866, |
| 1999 | 16377220, -2102812, -19802075, -3034702}, |
| 2000 | {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502, |
| 2001 | -31718148, 9936966, -30097688, -10618797}, |
| 2002 | }, |
| 2003 | { |
| 2004 | {21878590, -5001297, 4338336, 13643897, -3036865, 13160960, |
| 2005 | 19708896, 5415497, -7360503, -4109293}, |
| 2006 | {27736861, 10103576, 12500508, 8502413, -3413016, -9633558, |
| 2007 | 10436918, -1550276, -23659143, -8132100}, |
| 2008 | {19492550, -12104365, -29681976, -852630, -3208171, 12403437, |
| 2009 | 30066266, 8367329, 13243957, 8709688}, |
| 2010 | }, |
| 2011 | }, |
| 2012 | { |
| 2013 | { |
| 2014 | {12015105, 2801261, 28198131, 10151021, 24818120, -4743133, |
| 2015 | -11194191, -5645734, 5150968, 7274186}, |
| 2016 | {2831366, -12492146, 1478975, 6122054, 23825128, -12733586, |
| 2017 | 31097299, 6083058, 31021603, -9793610}, |
| 2018 | {-2529932, -2229646, 445613, 10720828, -13849527, -11505937, |
| 2019 | -23507731, 16354465, 15067285, -14147707}, |
| 2020 | }, |
| 2021 | { |
| 2022 | {7840942, 14037873, -33364863, 15934016, -728213, -3642706, |
| 2023 | 21403988, 1057586, -19379462, -12403220}, |
| 2024 | {915865, -16469274, 15608285, -8789130, -24357026, 6060030, |
| 2025 | -17371319, 8410997, -7220461, 16527025}, |
| 2026 | {32922597, -556987, 20336074, -16184568, 10903705, -5384487, |
| 2027 | 16957574, 52992, 23834301, 6588044}, |
| 2028 | }, |
| 2029 | { |
| 2030 | {32752030, 11232950, 3381995, -8714866, 22652988, -10744103, |
| 2031 | 17159699, 16689107, -20314580, -1305992}, |
| 2032 | {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943, |
| 2033 | 7924251, -2752281, 1976123, -7249027}, |
| 2034 | {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, |
| 2035 | -3371252, 12331345, -8237197}, |
| 2036 | }, |
| 2037 | { |
| 2038 | {8651614, -4477032, -16085636, -4996994, 13002507, 2950805, |
| 2039 | 29054427, -5106970, 10008136, -4667901}, |
| 2040 | {31486080, 15114593, -14261250, 12951354, 14369431, -7387845, |
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| 2042 | {19443825, 11385320, 24468943, -9659068, -23919258, 2187569, |
| 2043 | -26263207, -6086921, 31316348, 14219878}, |
| 2044 | }, |
| 2045 | { |
| 2046 | {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801, |
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| 2049 | -4980517, 10843782, -7957600, -14435730}, |
| 2050 | {2814918, 7836403, 27519878, -7868156, -20894015, -11553689, |
| 2051 | -21494559, 8550130, 28346258, 1994730}, |
| 2052 | }, |
| 2053 | { |
| 2054 | {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307, |
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| 2059 | 24091212, -1388970, -22765376, -10650715}, |
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| 3382 | {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, |
| 3383 | -2469266, -4141880, 7770569, 9620597}, |
| 3384 | {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, |
| 3385 | -1694323, -33502340, -14767970}, |
| 3386 | {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, |
| 3387 | 1220118, 30494170, -11440799}, |
| 3388 | }, |
| 3389 | { |
| 3390 | {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, |
| 3391 | -26739026, 926050, -1684339, -13333647}, |
| 3392 | {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, |
| 3393 | 9021034, 9078865, 3353509, 4033511}, |
| 3394 | {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, |
| 3395 | 23161163, 8839127, 27485041, 7356032}, |
| 3396 | }, |
| 3397 | }, |
| 3398 | { |
| 3399 | { |
| 3400 | {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, |
| 3401 | 2625015, 28431036, -16771834}, |
| 3402 | {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, |
| 3403 | -22545972, 14150565, 15970762, 4099461}, |
| 3404 | {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, |
| 3405 | 13617293, -9937143, 11465739, 8317062}, |
| 3406 | }, |
| 3407 | { |
| 3408 | {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, |
| 3409 | 14898637, 3848455, 20969334, -5157516}, |
| 3410 | {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, |
| 3411 | -21610826, -3649888, 11177095, 14989547}, |
| 3412 | {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, |
| 3413 | 13515641, 2581286, -28487508, 9930240}, |
| 3414 | }, |
| 3415 | { |
| 3416 | {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, |
| 3417 | 18345767, -13403753, 16291481, -5314038}, |
| 3418 | {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, |
| 3419 | 6957617, 4368891, 9788741}, |
| 3420 | {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, |
| 3421 | -21722536, -8613148, 16250552, -11111103}, |
| 3422 | }, |
| 3423 | { |
| 3424 | {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, |
| 3425 | 10604807, -30190403, 4782747}, |
| 3426 | {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, |
| 3427 | -9981571, 4383045, 22546403, 437323}, |
| 3428 | {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, |
| 3429 | 27343084, 2786261, -30633590, -14097016}, |
| 3430 | }, |
| 3431 | { |
| 3432 | {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, |
| 3433 | -19690631, 2355319, -19284671, -6114373}, |
| 3434 | {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, |
| 3435 | 18952177, 15496498, -29380133, 11754228}, |
| 3436 | {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, |
| 3437 | 7141596, 11724556, 22761615, -10134141}, |
| 3438 | }, |
| 3439 | { |
| 3440 | {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, |
| 3441 | -28741185, -12227393, 32851222, 11717399}, |
| 3442 | {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, |
| 3443 | 31474879, 3483633, -1193175, -4030831}, |
| 3444 | {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, |
| 3445 | 33142652, 6546660, -19985279, -3948376}, |
| 3446 | }, |
| 3447 | { |
| 3448 | {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, |
| 3449 | -8537131, -12833048, -30772034, -15486313}, |
| 3450 | {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, |
| 3451 | -31135347, -16049879, 10928917, 3011958}, |
| 3452 | {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, |
| 3453 | -30831056, -12805180, 18008031, 10258577}, |
| 3454 | }, |
| 3455 | { |
| 3456 | {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, |
| 3457 | -1853465, 1367120, 25127874, 6671743}, |
| 3458 | {29701166, -14373934, -10878120, 9279288, -17568, 13127210, |
| 3459 | 21382910, 11042292, 25838796, 4642684}, |
| 3460 | {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, |
| 3461 | 30468147, -13900640, 18423289, 4177476}, |
| 3462 | }, |
| 3463 | }, |
| 3464 | }; |
| 3465 | |
| 3466 | static uint8_t negative(signed char b) { |
| 3467 | uint32_t x = b; |
| 3468 | x >>= 31; /* 1: yes; 0: no */ |
| 3469 | return x; |
| 3470 | } |
| 3471 | |
| 3472 | static void table_select(ge_precomp *t, int pos, signed char b) { |
| 3473 | ge_precomp minust; |
| 3474 | uint8_t bnegative = negative(b); |
| 3475 | uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); |
| 3476 | |
| 3477 | ge_precomp_0(t); |
| 3478 | cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); |
| 3479 | cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); |
| 3480 | cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); |
| 3481 | cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); |
| 3482 | cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); |
| 3483 | cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); |
| 3484 | cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); |
| 3485 | cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); |
| 3486 | fe_copy(minust.yplusx, t->yminusx); |
| 3487 | fe_copy(minust.yminusx, t->yplusx); |
| 3488 | fe_neg(minust.xy2d, t->xy2d); |
| 3489 | cmov(t, &minust, bnegative); |
| 3490 | } |
| 3491 | |
| 3492 | /* h = a * B |
| 3493 | * where a = a[0]+256*a[1]+...+256^31 a[31] |
| 3494 | * B is the Ed25519 base point (x,4/5) with x positive. |
| 3495 | * |
| 3496 | * Preconditions: |
| 3497 | * a[31] <= 127 */ |
| 3498 | void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { |
| 3499 | signed char e[64]; |
| 3500 | signed char carry; |
| 3501 | ge_p1p1 r; |
| 3502 | ge_p2 s; |
| 3503 | ge_precomp t; |
| 3504 | int i; |
| 3505 | |
| 3506 | for (i = 0; i < 32; ++i) { |
| 3507 | e[2 * i + 0] = (a[i] >> 0) & 15; |
| 3508 | e[2 * i + 1] = (a[i] >> 4) & 15; |
| 3509 | } |
| 3510 | /* each e[i] is between 0 and 15 */ |
| 3511 | /* e[63] is between 0 and 7 */ |
| 3512 | |
| 3513 | carry = 0; |
| 3514 | for (i = 0; i < 63; ++i) { |
| 3515 | e[i] += carry; |
| 3516 | carry = e[i] + 8; |
| 3517 | carry >>= 4; |
| 3518 | e[i] -= carry << 4; |
| 3519 | } |
| 3520 | e[63] += carry; |
| 3521 | /* each e[i] is between -8 and 8 */ |
| 3522 | |
| 3523 | ge_p3_0(h); |
| 3524 | for (i = 1; i < 64; i += 2) { |
| 3525 | table_select(&t, i / 2, e[i]); |
| 3526 | ge_madd(&r, h, &t); |
| 3527 | x25519_ge_p1p1_to_p3(h, &r); |
| 3528 | } |
| 3529 | |
| 3530 | ge_p3_dbl(&r, h); |
| 3531 | x25519_ge_p1p1_to_p2(&s, &r); |
| 3532 | ge_p2_dbl(&r, &s); |
| 3533 | x25519_ge_p1p1_to_p2(&s, &r); |
| 3534 | ge_p2_dbl(&r, &s); |
| 3535 | x25519_ge_p1p1_to_p2(&s, &r); |
| 3536 | ge_p2_dbl(&r, &s); |
| 3537 | x25519_ge_p1p1_to_p3(h, &r); |
| 3538 | |
| 3539 | for (i = 0; i < 64; i += 2) { |
| 3540 | table_select(&t, i / 2, e[i]); |
| 3541 | ge_madd(&r, h, &t); |
| 3542 | x25519_ge_p1p1_to_p3(h, &r); |
| 3543 | } |
| 3544 | } |
| 3545 | |
| 3546 | #endif |
| 3547 | |
| 3548 | static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) { |
| 3549 | fe_cmov(t->YplusX, u->YplusX, b); |
| 3550 | fe_cmov(t->YminusX, u->YminusX, b); |
| 3551 | fe_cmov(t->Z, u->Z, b); |
| 3552 | fe_cmov(t->T2d, u->T2d, b); |
| 3553 | } |
| 3554 | |
| 3555 | /* r = scalar * A. |
| 3556 | * where a = a[0]+256*a[1]+...+256^31 a[31]. */ |
| 3557 | void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) { |
| 3558 | ge_p2 Ai_p2[8]; |
| 3559 | ge_cached Ai[16]; |
| 3560 | ge_p1p1 t; |
| 3561 | |
| 3562 | ge_cached_0(&Ai[0]); |
| 3563 | x25519_ge_p3_to_cached(&Ai[1], A); |
| 3564 | ge_p3_to_p2(&Ai_p2[1], A); |
| 3565 | |
| 3566 | unsigned i; |
| 3567 | for (i = 2; i < 16; i += 2) { |
| 3568 | ge_p2_dbl(&t, &Ai_p2[i / 2]); |
| 3569 | ge_p1p1_to_cached(&Ai[i], &t); |
| 3570 | if (i < 8) { |
| 3571 | x25519_ge_p1p1_to_p2(&Ai_p2[i], &t); |
| 3572 | } |
| 3573 | x25519_ge_add(&t, A, &Ai[i]); |
| 3574 | ge_p1p1_to_cached(&Ai[i + 1], &t); |
| 3575 | if (i < 7) { |
| 3576 | x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t); |
| 3577 | } |
| 3578 | } |
| 3579 | |
| 3580 | ge_p2_0(r); |
| 3581 | ge_p3 u; |
| 3582 | |
| 3583 | for (i = 0; i < 256; i += 4) { |
| 3584 | ge_p2_dbl(&t, r); |
| 3585 | x25519_ge_p1p1_to_p2(r, &t); |
| 3586 | ge_p2_dbl(&t, r); |
| 3587 | x25519_ge_p1p1_to_p2(r, &t); |
| 3588 | ge_p2_dbl(&t, r); |
| 3589 | x25519_ge_p1p1_to_p2(r, &t); |
| 3590 | ge_p2_dbl(&t, r); |
| 3591 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3592 | |
| 3593 | uint8_t index = scalar[31 - i/8]; |
| 3594 | index >>= 4 - (i & 4); |
| 3595 | index &= 0xf; |
| 3596 | |
| 3597 | unsigned j; |
| 3598 | ge_cached selected; |
| 3599 | ge_cached_0(&selected); |
| 3600 | for (j = 0; j < 16; j++) { |
| 3601 | cmov_cached(&selected, &Ai[j], equal(j, index)); |
| 3602 | } |
| 3603 | |
| 3604 | x25519_ge_add(&t, &u, &selected); |
| 3605 | x25519_ge_p1p1_to_p2(r, &t); |
| 3606 | } |
| 3607 | } |
| 3608 | |
| 3609 | static void slide(signed char *r, const uint8_t *a) { |
| 3610 | int i; |
| 3611 | int b; |
| 3612 | int k; |
| 3613 | |
| 3614 | for (i = 0; i < 256; ++i) { |
| 3615 | r[i] = 1 & (a[i >> 3] >> (i & 7)); |
| 3616 | } |
| 3617 | |
| 3618 | for (i = 0; i < 256; ++i) { |
| 3619 | if (r[i]) { |
| 3620 | for (b = 1; b <= 6 && i + b < 256; ++b) { |
| 3621 | if (r[i + b]) { |
| 3622 | if (r[i] + (r[i + b] << b) <= 15) { |
| 3623 | r[i] += r[i + b] << b; |
| 3624 | r[i + b] = 0; |
| 3625 | } else if (r[i] - (r[i + b] << b) >= -15) { |
| 3626 | r[i] -= r[i + b] << b; |
| 3627 | for (k = i + b; k < 256; ++k) { |
| 3628 | if (!r[k]) { |
| 3629 | r[k] = 1; |
| 3630 | break; |
| 3631 | } |
| 3632 | r[k] = 0; |
| 3633 | } |
| 3634 | } else { |
| 3635 | break; |
| 3636 | } |
| 3637 | } |
| 3638 | } |
| 3639 | } |
| 3640 | } |
| 3641 | } |
| 3642 | |
| 3643 | static const ge_precomp Bi[8] = { |
| 3644 | { |
| 3645 | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, |
| 3646 | -11754271, -6079156, 2047605}, |
| 3647 | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
| 3648 | 5043384, 19500929, -15469378}, |
| 3649 | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, |
| 3650 | 11864899, -24514362, -4438546}, |
| 3651 | }, |
| 3652 | { |
| 3653 | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, |
| 3654 | -14772189, 28944400, -1550024}, |
| 3655 | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, |
| 3656 | -11775962, 7689662, 11199574}, |
| 3657 | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, |
| 3658 | 10017326, -17749093, -9920357}, |
| 3659 | }, |
| 3660 | { |
| 3661 | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, |
| 3662 | 14515107, -15438304, 10819380}, |
| 3663 | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
| 3664 | 12483688, -12668491, 5581306}, |
| 3665 | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, |
| 3666 | 13850243, -23678021, -15815942}, |
| 3667 | }, |
| 3668 | { |
| 3669 | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, |
| 3670 | 5230134, -23952439, -15175766}, |
| 3671 | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, |
| 3672 | 16520125, 30598449, 7715701}, |
| 3673 | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, |
| 3674 | 1370708, 29794553, -1409300}, |
| 3675 | }, |
| 3676 | { |
| 3677 | {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, |
| 3678 | -1361450, -13062696, 13821877}, |
| 3679 | {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, |
| 3680 | -7212327, 18853322, -14220951}, |
| 3681 | {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, |
| 3682 | -10431137, 2207753, -3209784}, |
| 3683 | }, |
| 3684 | { |
| 3685 | {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, |
| 3686 | -663000, -31111463, -16132436}, |
| 3687 | {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, |
| 3688 | 15725684, 171356, 6466918}, |
| 3689 | {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, |
| 3690 | -14088058, -30714912, 16193877}, |
| 3691 | }, |
| 3692 | { |
| 3693 | {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, |
| 3694 | 4729455, -18074513, 9256800}, |
| 3695 | {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, |
| 3696 | 9761698, -19827198, 630305}, |
| 3697 | {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, |
| 3698 | -15960994, -2449256, -14291300}, |
| 3699 | }, |
| 3700 | { |
| 3701 | {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, |
| 3702 | 15033784, 25105118, -7894876}, |
| 3703 | {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, |
| 3704 | 1573892, -2625887, 2198790, -15804619}, |
| 3705 | {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, |
| 3706 | -16236442, -32461234, -12290683}, |
| 3707 | }, |
| 3708 | }; |
| 3709 | |
| 3710 | /* r = a * A + b * B |
| 3711 | * where a = a[0]+256*a[1]+...+256^31 a[31]. |
| 3712 | * and b = b[0]+256*b[1]+...+256^31 b[31]. |
| 3713 | * B is the Ed25519 base point (x,4/5) with x positive. */ |
| 3714 | static void |
| 3715 | ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, |
| 3716 | const ge_p3 *A, const uint8_t *b) { |
| 3717 | signed char aslide[256]; |
| 3718 | signed char bslide[256]; |
| 3719 | ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ |
| 3720 | ge_p1p1 t; |
| 3721 | ge_p3 u; |
| 3722 | ge_p3 A2; |
| 3723 | int i; |
| 3724 | |
| 3725 | slide(aslide, a); |
| 3726 | slide(bslide, b); |
| 3727 | |
| 3728 | x25519_ge_p3_to_cached(&Ai[0], A); |
| 3729 | ge_p3_dbl(&t, A); |
| 3730 | x25519_ge_p1p1_to_p3(&A2, &t); |
| 3731 | x25519_ge_add(&t, &A2, &Ai[0]); |
| 3732 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3733 | x25519_ge_p3_to_cached(&Ai[1], &u); |
| 3734 | x25519_ge_add(&t, &A2, &Ai[1]); |
| 3735 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3736 | x25519_ge_p3_to_cached(&Ai[2], &u); |
| 3737 | x25519_ge_add(&t, &A2, &Ai[2]); |
| 3738 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3739 | x25519_ge_p3_to_cached(&Ai[3], &u); |
| 3740 | x25519_ge_add(&t, &A2, &Ai[3]); |
| 3741 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3742 | x25519_ge_p3_to_cached(&Ai[4], &u); |
| 3743 | x25519_ge_add(&t, &A2, &Ai[4]); |
| 3744 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3745 | x25519_ge_p3_to_cached(&Ai[5], &u); |
| 3746 | x25519_ge_add(&t, &A2, &Ai[5]); |
| 3747 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3748 | x25519_ge_p3_to_cached(&Ai[6], &u); |
| 3749 | x25519_ge_add(&t, &A2, &Ai[6]); |
| 3750 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3751 | x25519_ge_p3_to_cached(&Ai[7], &u); |
| 3752 | |
| 3753 | ge_p2_0(r); |
| 3754 | |
| 3755 | for (i = 255; i >= 0; --i) { |
| 3756 | if (aslide[i] || bslide[i]) { |
| 3757 | break; |
| 3758 | } |
| 3759 | } |
| 3760 | |
| 3761 | for (; i >= 0; --i) { |
| 3762 | ge_p2_dbl(&t, r); |
| 3763 | |
| 3764 | if (aslide[i] > 0) { |
| 3765 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3766 | x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]); |
| 3767 | } else if (aslide[i] < 0) { |
| 3768 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3769 | x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); |
| 3770 | } |
| 3771 | |
| 3772 | if (bslide[i] > 0) { |
| 3773 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3774 | ge_madd(&t, &u, &Bi[bslide[i] / 2]); |
| 3775 | } else if (bslide[i] < 0) { |
| 3776 | x25519_ge_p1p1_to_p3(&u, &t); |
| 3777 | ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); |
| 3778 | } |
| 3779 | |
| 3780 | x25519_ge_p1p1_to_p2(r, &t); |
| 3781 | } |
| 3782 | } |
| 3783 | |
| 3784 | /* The set of scalars is \Z/l |
| 3785 | * where l = 2^252 + 27742317777372353535851937790883648493. */ |
| 3786 | |
| 3787 | /* Input: |
| 3788 | * s[0]+256*s[1]+...+256^63*s[63] = s |
| 3789 | * |
| 3790 | * Output: |
| 3791 | * s[0]+256*s[1]+...+256^31*s[31] = s mod l |
| 3792 | * where l = 2^252 + 27742317777372353535851937790883648493. |
| 3793 | * Overwrites s in place. */ |
| 3794 | void |
| 3795 | x25519_sc_reduce(uint8_t *s) { |
| 3796 | int64_t s0 = 2097151 & load_3(s); |
| 3797 | int64_t s1 = 2097151 & (load_4(s + 2) >> 5); |
| 3798 | int64_t s2 = 2097151 & (load_3(s + 5) >> 2); |
| 3799 | int64_t s3 = 2097151 & (load_4(s + 7) >> 7); |
| 3800 | int64_t s4 = 2097151 & (load_4(s + 10) >> 4); |
| 3801 | int64_t s5 = 2097151 & (load_3(s + 13) >> 1); |
| 3802 | int64_t s6 = 2097151 & (load_4(s + 15) >> 6); |
| 3803 | int64_t s7 = 2097151 & (load_3(s + 18) >> 3); |
| 3804 | int64_t s8 = 2097151 & load_3(s + 21); |
| 3805 | int64_t s9 = 2097151 & (load_4(s + 23) >> 5); |
| 3806 | int64_t s10 = 2097151 & (load_3(s + 26) >> 2); |
| 3807 | int64_t s11 = 2097151 & (load_4(s + 28) >> 7); |
| 3808 | int64_t s12 = 2097151 & (load_4(s + 31) >> 4); |
| 3809 | int64_t s13 = 2097151 & (load_3(s + 34) >> 1); |
| 3810 | int64_t s14 = 2097151 & (load_4(s + 36) >> 6); |
| 3811 | int64_t s15 = 2097151 & (load_3(s + 39) >> 3); |
| 3812 | int64_t s16 = 2097151 & load_3(s + 42); |
| 3813 | int64_t s17 = 2097151 & (load_4(s + 44) >> 5); |
| 3814 | int64_t s18 = 2097151 & (load_3(s + 47) >> 2); |
| 3815 | int64_t s19 = 2097151 & (load_4(s + 49) >> 7); |
| 3816 | int64_t s20 = 2097151 & (load_4(s + 52) >> 4); |
| 3817 | int64_t s21 = 2097151 & (load_3(s + 55) >> 1); |
| 3818 | int64_t s22 = 2097151 & (load_4(s + 57) >> 6); |
| 3819 | int64_t s23 = (load_4(s + 60) >> 3); |
| 3820 | int64_t carry0; |
| 3821 | int64_t carry1; |
| 3822 | int64_t carry2; |
| 3823 | int64_t carry3; |
| 3824 | int64_t carry4; |
| 3825 | int64_t carry5; |
| 3826 | int64_t carry6; |
| 3827 | int64_t carry7; |
| 3828 | int64_t carry8; |
| 3829 | int64_t carry9; |
| 3830 | int64_t carry10; |
| 3831 | int64_t carry11; |
| 3832 | int64_t carry12; |
| 3833 | int64_t carry13; |
| 3834 | int64_t carry14; |
| 3835 | int64_t carry15; |
| 3836 | int64_t carry16; |
| 3837 | |
| 3838 | s11 += s23 * 666643; |
| 3839 | s12 += s23 * 470296; |
| 3840 | s13 += s23 * 654183; |
| 3841 | s14 -= s23 * 997805; |
| 3842 | s15 += s23 * 136657; |
| 3843 | s16 -= s23 * 683901; |
| 3844 | s23 = 0; |
| 3845 | |
| 3846 | s10 += s22 * 666643; |
| 3847 | s11 += s22 * 470296; |
| 3848 | s12 += s22 * 654183; |
| 3849 | s13 -= s22 * 997805; |
| 3850 | s14 += s22 * 136657; |
| 3851 | s15 -= s22 * 683901; |
| 3852 | s22 = 0; |
| 3853 | |
| 3854 | s9 += s21 * 666643; |
| 3855 | s10 += s21 * 470296; |
| 3856 | s11 += s21 * 654183; |
| 3857 | s12 -= s21 * 997805; |
| 3858 | s13 += s21 * 136657; |
| 3859 | s14 -= s21 * 683901; |
| 3860 | s21 = 0; |
| 3861 | |
| 3862 | s8 += s20 * 666643; |
| 3863 | s9 += s20 * 470296; |
| 3864 | s10 += s20 * 654183; |
| 3865 | s11 -= s20 * 997805; |
| 3866 | s12 += s20 * 136657; |
| 3867 | s13 -= s20 * 683901; |
| 3868 | s20 = 0; |
| 3869 | |
| 3870 | s7 += s19 * 666643; |
| 3871 | s8 += s19 * 470296; |
| 3872 | s9 += s19 * 654183; |
| 3873 | s10 -= s19 * 997805; |
| 3874 | s11 += s19 * 136657; |
| 3875 | s12 -= s19 * 683901; |
| 3876 | s19 = 0; |
| 3877 | |
| 3878 | s6 += s18 * 666643; |
| 3879 | s7 += s18 * 470296; |
| 3880 | s8 += s18 * 654183; |
| 3881 | s9 -= s18 * 997805; |
| 3882 | s10 += s18 * 136657; |
| 3883 | s11 -= s18 * 683901; |
| 3884 | s18 = 0; |
| 3885 | |
| 3886 | carry6 = (s6 + (1 << 20)) >> 21; |
| 3887 | s7 += carry6; |
| 3888 | s6 -= carry6 << 21; |
| 3889 | carry8 = (s8 + (1 << 20)) >> 21; |
| 3890 | s9 += carry8; |
| 3891 | s8 -= carry8 << 21; |
| 3892 | carry10 = (s10 + (1 << 20)) >> 21; |
| 3893 | s11 += carry10; |
| 3894 | s10 -= carry10 << 21; |
| 3895 | carry12 = (s12 + (1 << 20)) >> 21; |
| 3896 | s13 += carry12; |
| 3897 | s12 -= carry12 << 21; |
| 3898 | carry14 = (s14 + (1 << 20)) >> 21; |
| 3899 | s15 += carry14; |
| 3900 | s14 -= carry14 << 21; |
| 3901 | carry16 = (s16 + (1 << 20)) >> 21; |
| 3902 | s17 += carry16; |
| 3903 | s16 -= carry16 << 21; |
| 3904 | |
| 3905 | carry7 = (s7 + (1 << 20)) >> 21; |
| 3906 | s8 += carry7; |
| 3907 | s7 -= carry7 << 21; |
| 3908 | carry9 = (s9 + (1 << 20)) >> 21; |
| 3909 | s10 += carry9; |
| 3910 | s9 -= carry9 << 21; |
| 3911 | carry11 = (s11 + (1 << 20)) >> 21; |
| 3912 | s12 += carry11; |
| 3913 | s11 -= carry11 << 21; |
| 3914 | carry13 = (s13 + (1 << 20)) >> 21; |
| 3915 | s14 += carry13; |
| 3916 | s13 -= carry13 << 21; |
| 3917 | carry15 = (s15 + (1 << 20)) >> 21; |
| 3918 | s16 += carry15; |
| 3919 | s15 -= carry15 << 21; |
| 3920 | |
| 3921 | s5 += s17 * 666643; |
| 3922 | s6 += s17 * 470296; |
| 3923 | s7 += s17 * 654183; |
| 3924 | s8 -= s17 * 997805; |
| 3925 | s9 += s17 * 136657; |
| 3926 | s10 -= s17 * 683901; |
| 3927 | s17 = 0; |
| 3928 | |
| 3929 | s4 += s16 * 666643; |
| 3930 | s5 += s16 * 470296; |
| 3931 | s6 += s16 * 654183; |
| 3932 | s7 -= s16 * 997805; |
| 3933 | s8 += s16 * 136657; |
| 3934 | s9 -= s16 * 683901; |
| 3935 | s16 = 0; |
Value stored to 's16' is never read | |
| 3936 | |
| 3937 | s3 += s15 * 666643; |
| 3938 | s4 += s15 * 470296; |
| 3939 | s5 += s15 * 654183; |
| 3940 | s6 -= s15 * 997805; |
| 3941 | s7 += s15 * 136657; |
| 3942 | s8 -= s15 * 683901; |
| 3943 | s15 = 0; |
| 3944 | |
| 3945 | s2 += s14 * 666643; |
| 3946 | s3 += s14 * 470296; |
| 3947 | s4 += s14 * 654183; |
| 3948 | s5 -= s14 * 997805; |
| 3949 | s6 += s14 * 136657; |
| 3950 | s7 -= s14 * 683901; |
| 3951 | s14 = 0; |
| 3952 | |
| 3953 | s1 += s13 * 666643; |
| 3954 | s2 += s13 * 470296; |
| 3955 | s3 += s13 * 654183; |
| 3956 | s4 -= s13 * 997805; |
| 3957 | s5 += s13 * 136657; |
| 3958 | s6 -= s13 * 683901; |
| 3959 | s13 = 0; |
| 3960 | |
| 3961 | s0 += s12 * 666643; |
| 3962 | s1 += s12 * 470296; |
| 3963 | s2 += s12 * 654183; |
| 3964 | s3 -= s12 * 997805; |
| 3965 | s4 += s12 * 136657; |
| 3966 | s5 -= s12 * 683901; |
| 3967 | s12 = 0; |
| 3968 | |
| 3969 | carry0 = (s0 + (1 << 20)) >> 21; |
| 3970 | s1 += carry0; |
| 3971 | s0 -= carry0 << 21; |
| 3972 | carry2 = (s2 + (1 << 20)) >> 21; |
| 3973 | s3 += carry2; |
| 3974 | s2 -= carry2 << 21; |
| 3975 | carry4 = (s4 + (1 << 20)) >> 21; |
| 3976 | s5 += carry4; |
| 3977 | s4 -= carry4 << 21; |
| 3978 | carry6 = (s6 + (1 << 20)) >> 21; |
| 3979 | s7 += carry6; |
| 3980 | s6 -= carry6 << 21; |
| 3981 | carry8 = (s8 + (1 << 20)) >> 21; |
| 3982 | s9 += carry8; |
| 3983 | s8 -= carry8 << 21; |
| 3984 | carry10 = (s10 + (1 << 20)) >> 21; |
| 3985 | s11 += carry10; |
| 3986 | s10 -= carry10 << 21; |
| 3987 | |
| 3988 | carry1 = (s1 + (1 << 20)) >> 21; |
| 3989 | s2 += carry1; |
| 3990 | s1 -= carry1 << 21; |
| 3991 | carry3 = (s3 + (1 << 20)) >> 21; |
| 3992 | s4 += carry3; |
| 3993 | s3 -= carry3 << 21; |
| 3994 | carry5 = (s5 + (1 << 20)) >> 21; |
| 3995 | s6 += carry5; |
| 3996 | s5 -= carry5 << 21; |
| 3997 | carry7 = (s7 + (1 << 20)) >> 21; |
| 3998 | s8 += carry7; |
| 3999 | s7 -= carry7 << 21; |
| 4000 | carry9 = (s9 + (1 << 20)) >> 21; |
| 4001 | s10 += carry9; |
| 4002 | s9 -= carry9 << 21; |
| 4003 | carry11 = (s11 + (1 << 20)) >> 21; |
| 4004 | s12 += carry11; |
| 4005 | s11 -= carry11 << 21; |
| 4006 | |
| 4007 | s0 += s12 * 666643; |
| 4008 | s1 += s12 * 470296; |
| 4009 | s2 += s12 * 654183; |
| 4010 | s3 -= s12 * 997805; |
| 4011 | s4 += s12 * 136657; |
| 4012 | s5 -= s12 * 683901; |
| 4013 | s12 = 0; |
| 4014 | |
| 4015 | carry0 = s0 >> 21; |
| 4016 | s1 += carry0; |
| 4017 | s0 -= carry0 << 21; |
| 4018 | carry1 = s1 >> 21; |
| 4019 | s2 += carry1; |
| 4020 | s1 -= carry1 << 21; |
| 4021 | carry2 = s2 >> 21; |
| 4022 | s3 += carry2; |
| 4023 | s2 -= carry2 << 21; |
| 4024 | carry3 = s3 >> 21; |
| 4025 | s4 += carry3; |
| 4026 | s3 -= carry3 << 21; |
| 4027 | carry4 = s4 >> 21; |
| 4028 | s5 += carry4; |
| 4029 | s4 -= carry4 << 21; |
| 4030 | carry5 = s5 >> 21; |
| 4031 | s6 += carry5; |
| 4032 | s5 -= carry5 << 21; |
| 4033 | carry6 = s6 >> 21; |
| 4034 | s7 += carry6; |
| 4035 | s6 -= carry6 << 21; |
| 4036 | carry7 = s7 >> 21; |
| 4037 | s8 += carry7; |
| 4038 | s7 -= carry7 << 21; |
| 4039 | carry8 = s8 >> 21; |
| 4040 | s9 += carry8; |
| 4041 | s8 -= carry8 << 21; |
| 4042 | carry9 = s9 >> 21; |
| 4043 | s10 += carry9; |
| 4044 | s9 -= carry9 << 21; |
| 4045 | carry10 = s10 >> 21; |
| 4046 | s11 += carry10; |
| 4047 | s10 -= carry10 << 21; |
| 4048 | carry11 = s11 >> 21; |
| 4049 | s12 += carry11; |
| 4050 | s11 -= carry11 << 21; |
| 4051 | |
| 4052 | s0 += s12 * 666643; |
| 4053 | s1 += s12 * 470296; |
| 4054 | s2 += s12 * 654183; |
| 4055 | s3 -= s12 * 997805; |
| 4056 | s4 += s12 * 136657; |
| 4057 | s5 -= s12 * 683901; |
| 4058 | s12 = 0; |
| 4059 | |
| 4060 | carry0 = s0 >> 21; |
| 4061 | s1 += carry0; |
| 4062 | s0 -= carry0 << 21; |
| 4063 | carry1 = s1 >> 21; |
| 4064 | s2 += carry1; |
| 4065 | s1 -= carry1 << 21; |
| 4066 | carry2 = s2 >> 21; |
| 4067 | s3 += carry2; |
| 4068 | s2 -= carry2 << 21; |
| 4069 | carry3 = s3 >> 21; |
| 4070 | s4 += carry3; |
| 4071 | s3 -= carry3 << 21; |
| 4072 | carry4 = s4 >> 21; |
| 4073 | s5 += carry4; |
| 4074 | s4 -= carry4 << 21; |
| 4075 | carry5 = s5 >> 21; |
| 4076 | s6 += carry5; |
| 4077 | s5 -= carry5 << 21; |
| 4078 | carry6 = s6 >> 21; |
| 4079 | s7 += carry6; |
| 4080 | s6 -= carry6 << 21; |
| 4081 | carry7 = s7 >> 21; |
| 4082 | s8 += carry7; |
| 4083 | s7 -= carry7 << 21; |
| 4084 | carry8 = s8 >> 21; |
| 4085 | s9 += carry8; |
| 4086 | s8 -= carry8 << 21; |
| 4087 | carry9 = s9 >> 21; |
| 4088 | s10 += carry9; |
| 4089 | s9 -= carry9 << 21; |
| 4090 | carry10 = s10 >> 21; |
| 4091 | s11 += carry10; |
| 4092 | s10 -= carry10 << 21; |
| 4093 | |
| 4094 | s[0] = s0 >> 0; |
| 4095 | s[1] = s0 >> 8; |
| 4096 | s[2] = (s0 >> 16) | (s1 << 5); |
| 4097 | s[3] = s1 >> 3; |
| 4098 | s[4] = s1 >> 11; |
| 4099 | s[5] = (s1 >> 19) | (s2 << 2); |
| 4100 | s[6] = s2 >> 6; |
| 4101 | s[7] = (s2 >> 14) | (s3 << 7); |
| 4102 | s[8] = s3 >> 1; |
| 4103 | s[9] = s3 >> 9; |
| 4104 | s[10] = (s3 >> 17) | (s4 << 4); |
| 4105 | s[11] = s4 >> 4; |
| 4106 | s[12] = s4 >> 12; |
| 4107 | s[13] = (s4 >> 20) | (s5 << 1); |
| 4108 | s[14] = s5 >> 7; |
| 4109 | s[15] = (s5 >> 15) | (s6 << 6); |
| 4110 | s[16] = s6 >> 2; |
| 4111 | s[17] = s6 >> 10; |
| 4112 | s[18] = (s6 >> 18) | (s7 << 3); |
| 4113 | s[19] = s7 >> 5; |
| 4114 | s[20] = s7 >> 13; |
| 4115 | s[21] = s8 >> 0; |
| 4116 | s[22] = s8 >> 8; |
| 4117 | s[23] = (s8 >> 16) | (s9 << 5); |
| 4118 | s[24] = s9 >> 3; |
| 4119 | s[25] = s9 >> 11; |
| 4120 | s[26] = (s9 >> 19) | (s10 << 2); |
| 4121 | s[27] = s10 >> 6; |
| 4122 | s[28] = (s10 >> 14) | (s11 << 7); |
| 4123 | s[29] = s11 >> 1; |
| 4124 | s[30] = s11 >> 9; |
| 4125 | s[31] = s11 >> 17; |
| 4126 | } |
| 4127 | |
| 4128 | /* Input: |
| 4129 | * a[0]+256*a[1]+...+256^31*a[31] = a |
| 4130 | * b[0]+256*b[1]+...+256^31*b[31] = b |
| 4131 | * c[0]+256*c[1]+...+256^31*c[31] = c |
| 4132 | * |
| 4133 | * Output: |
| 4134 | * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l |
| 4135 | * where l = 2^252 + 27742317777372353535851937790883648493. */ |
| 4136 | static void |
| 4137 | sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, |
| 4138 | const uint8_t *c) |
| 4139 | { |
| 4140 | int64_t a0 = 2097151 & load_3(a); |
| 4141 | int64_t a1 = 2097151 & (load_4(a + 2) >> 5); |
| 4142 | int64_t a2 = 2097151 & (load_3(a + 5) >> 2); |
| 4143 | int64_t a3 = 2097151 & (load_4(a + 7) >> 7); |
| 4144 | int64_t a4 = 2097151 & (load_4(a + 10) >> 4); |
| 4145 | int64_t a5 = 2097151 & (load_3(a + 13) >> 1); |
| 4146 | int64_t a6 = 2097151 & (load_4(a + 15) >> 6); |
| 4147 | int64_t a7 = 2097151 & (load_3(a + 18) >> 3); |
| 4148 | int64_t a8 = 2097151 & load_3(a + 21); |
| 4149 | int64_t a9 = 2097151 & (load_4(a + 23) >> 5); |
| 4150 | int64_t a10 = 2097151 & (load_3(a + 26) >> 2); |
| 4151 | int64_t a11 = (load_4(a + 28) >> 7); |
| 4152 | int64_t b0 = 2097151 & load_3(b); |
| 4153 | int64_t b1 = 2097151 & (load_4(b + 2) >> 5); |
| 4154 | int64_t b2 = 2097151 & (load_3(b + 5) >> 2); |
| 4155 | int64_t b3 = 2097151 & (load_4(b + 7) >> 7); |
| 4156 | int64_t b4 = 2097151 & (load_4(b + 10) >> 4); |
| 4157 | int64_t b5 = 2097151 & (load_3(b + 13) >> 1); |
| 4158 | int64_t b6 = 2097151 & (load_4(b + 15) >> 6); |
| 4159 | int64_t b7 = 2097151 & (load_3(b + 18) >> 3); |
| 4160 | int64_t b8 = 2097151 & load_3(b + 21); |
| 4161 | int64_t b9 = 2097151 & (load_4(b + 23) >> 5); |
| 4162 | int64_t b10 = 2097151 & (load_3(b + 26) >> 2); |
| 4163 | int64_t b11 = (load_4(b + 28) >> 7); |
| 4164 | int64_t c0 = 2097151 & load_3(c); |
| 4165 | int64_t c1 = 2097151 & (load_4(c + 2) >> 5); |
| 4166 | int64_t c2 = 2097151 & (load_3(c + 5) >> 2); |
| 4167 | int64_t c3 = 2097151 & (load_4(c + 7) >> 7); |
| 4168 | int64_t c4 = 2097151 & (load_4(c + 10) >> 4); |
| 4169 | int64_t c5 = 2097151 & (load_3(c + 13) >> 1); |
| 4170 | int64_t c6 = 2097151 & (load_4(c + 15) >> 6); |
| 4171 | int64_t c7 = 2097151 & (load_3(c + 18) >> 3); |
| 4172 | int64_t c8 = 2097151 & load_3(c + 21); |
| 4173 | int64_t c9 = 2097151 & (load_4(c + 23) >> 5); |
| 4174 | int64_t c10 = 2097151 & (load_3(c + 26) >> 2); |
| 4175 | int64_t c11 = (load_4(c + 28) >> 7); |
| 4176 | int64_t s0; |
| 4177 | int64_t s1; |
| 4178 | int64_t s2; |
| 4179 | int64_t s3; |
| 4180 | int64_t s4; |
| 4181 | int64_t s5; |
| 4182 | int64_t s6; |
| 4183 | int64_t s7; |
| 4184 | int64_t s8; |
| 4185 | int64_t s9; |
| 4186 | int64_t s10; |
| 4187 | int64_t s11; |
| 4188 | int64_t s12; |
| 4189 | int64_t s13; |
| 4190 | int64_t s14; |
| 4191 | int64_t s15; |
| 4192 | int64_t s16; |
| 4193 | int64_t s17; |
| 4194 | int64_t s18; |
| 4195 | int64_t s19; |
| 4196 | int64_t s20; |
| 4197 | int64_t s21; |
| 4198 | int64_t s22; |
| 4199 | int64_t s23; |
| 4200 | int64_t carry0; |
| 4201 | int64_t carry1; |
| 4202 | int64_t carry2; |
| 4203 | int64_t carry3; |
| 4204 | int64_t carry4; |
| 4205 | int64_t carry5; |
| 4206 | int64_t carry6; |
| 4207 | int64_t carry7; |
| 4208 | int64_t carry8; |
| 4209 | int64_t carry9; |
| 4210 | int64_t carry10; |
| 4211 | int64_t carry11; |
| 4212 | int64_t carry12; |
| 4213 | int64_t carry13; |
| 4214 | int64_t carry14; |
| 4215 | int64_t carry15; |
| 4216 | int64_t carry16; |
| 4217 | int64_t carry17; |
| 4218 | int64_t carry18; |
| 4219 | int64_t carry19; |
| 4220 | int64_t carry20; |
| 4221 | int64_t carry21; |
| 4222 | int64_t carry22; |
| 4223 | |
| 4224 | s0 = c0 + a0 * b0; |
| 4225 | s1 = c1 + a0 * b1 + a1 * b0; |
| 4226 | s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; |
| 4227 | s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; |
| 4228 | s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; |
| 4229 | s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; |
| 4230 | s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; |
| 4231 | s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + |
| 4232 | a6 * b1 + a7 * b0; |
| 4233 | s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + |
| 4234 | a6 * b2 + a7 * b1 + a8 * b0; |
| 4235 | s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + |
| 4236 | a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; |
| 4237 | s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + |
| 4238 | a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; |
| 4239 | s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + |
| 4240 | a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; |
| 4241 | s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + |
| 4242 | a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; |
| 4243 | s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + |
| 4244 | a9 * b4 + a10 * b3 + a11 * b2; |
| 4245 | s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + |
| 4246 | a10 * b4 + a11 * b3; |
| 4247 | s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + |
| 4248 | a11 * b4; |
| 4249 | s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; |
| 4250 | s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; |
| 4251 | s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; |
| 4252 | s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; |
| 4253 | s20 = a9 * b11 + a10 * b10 + a11 * b9; |
| 4254 | s21 = a10 * b11 + a11 * b10; |
| 4255 | s22 = a11 * b11; |
| 4256 | s23 = 0; |
| 4257 | |
| 4258 | carry0 = (s0 + (1 << 20)) >> 21; |
| 4259 | s1 += carry0; |
| 4260 | s0 -= carry0 << 21; |
| 4261 | carry2 = (s2 + (1 << 20)) >> 21; |
| 4262 | s3 += carry2; |
| 4263 | s2 -= carry2 << 21; |
| 4264 | carry4 = (s4 + (1 << 20)) >> 21; |
| 4265 | s5 += carry4; |
| 4266 | s4 -= carry4 << 21; |
| 4267 | carry6 = (s6 + (1 << 20)) >> 21; |
| 4268 | s7 += carry6; |
| 4269 | s6 -= carry6 << 21; |
| 4270 | carry8 = (s8 + (1 << 20)) >> 21; |
| 4271 | s9 += carry8; |
| 4272 | s8 -= carry8 << 21; |
| 4273 | carry10 = (s10 + (1 << 20)) >> 21; |
| 4274 | s11 += carry10; |
| 4275 | s10 -= carry10 << 21; |
| 4276 | carry12 = (s12 + (1 << 20)) >> 21; |
| 4277 | s13 += carry12; |
| 4278 | s12 -= carry12 << 21; |
| 4279 | carry14 = (s14 + (1 << 20)) >> 21; |
| 4280 | s15 += carry14; |
| 4281 | s14 -= carry14 << 21; |
| 4282 | carry16 = (s16 + (1 << 20)) >> 21; |
| 4283 | s17 += carry16; |
| 4284 | s16 -= carry16 << 21; |
| 4285 | carry18 = (s18 + (1 << 20)) >> 21; |
| 4286 | s19 += carry18; |
| 4287 | s18 -= carry18 << 21; |
| 4288 | carry20 = (s20 + (1 << 20)) >> 21; |
| 4289 | s21 += carry20; |
| 4290 | s20 -= carry20 << 21; |
| 4291 | carry22 = (s22 + (1 << 20)) >> 21; |
| 4292 | s23 += carry22; |
| 4293 | s22 -= carry22 << 21; |
| 4294 | |
| 4295 | carry1 = (s1 + (1 << 20)) >> 21; |
| 4296 | s2 += carry1; |
| 4297 | s1 -= carry1 << 21; |
| 4298 | carry3 = (s3 + (1 << 20)) >> 21; |
| 4299 | s4 += carry3; |
| 4300 | s3 -= carry3 << 21; |
| 4301 | carry5 = (s5 + (1 << 20)) >> 21; |
| 4302 | s6 += carry5; |
| 4303 | s5 -= carry5 << 21; |
| 4304 | carry7 = (s7 + (1 << 20)) >> 21; |
| 4305 | s8 += carry7; |
| 4306 | s7 -= carry7 << 21; |
| 4307 | carry9 = (s9 + (1 << 20)) >> 21; |
| 4308 | s10 += carry9; |
| 4309 | s9 -= carry9 << 21; |
| 4310 | carry11 = (s11 + (1 << 20)) >> 21; |
| 4311 | s12 += carry11; |
| 4312 | s11 -= carry11 << 21; |
| 4313 | carry13 = (s13 + (1 << 20)) >> 21; |
| 4314 | s14 += carry13; |
| 4315 | s13 -= carry13 << 21; |
| 4316 | carry15 = (s15 + (1 << 20)) >> 21; |
| 4317 | s16 += carry15; |
| 4318 | s15 -= carry15 << 21; |
| 4319 | carry17 = (s17 + (1 << 20)) >> 21; |
| 4320 | s18 += carry17; |
| 4321 | s17 -= carry17 << 21; |
| 4322 | carry19 = (s19 + (1 << 20)) >> 21; |
| 4323 | s20 += carry19; |
| 4324 | s19 -= carry19 << 21; |
| 4325 | carry21 = (s21 + (1 << 20)) >> 21; |
| 4326 | s22 += carry21; |
| 4327 | s21 -= carry21 << 21; |
| 4328 | |
| 4329 | s11 += s23 * 666643; |
| 4330 | s12 += s23 * 470296; |
| 4331 | s13 += s23 * 654183; |
| 4332 | s14 -= s23 * 997805; |
| 4333 | s15 += s23 * 136657; |
| 4334 | s16 -= s23 * 683901; |
| 4335 | s23 = 0; |
| 4336 | |
| 4337 | s10 += s22 * 666643; |
| 4338 | s11 += s22 * 470296; |
| 4339 | s12 += s22 * 654183; |
| 4340 | s13 -= s22 * 997805; |
| 4341 | s14 += s22 * 136657; |
| 4342 | s15 -= s22 * 683901; |
| 4343 | s22 = 0; |
| 4344 | |
| 4345 | s9 += s21 * 666643; |
| 4346 | s10 += s21 * 470296; |
| 4347 | s11 += s21 * 654183; |
| 4348 | s12 -= s21 * 997805; |
| 4349 | s13 += s21 * 136657; |
| 4350 | s14 -= s21 * 683901; |
| 4351 | s21 = 0; |
| 4352 | |
| 4353 | s8 += s20 * 666643; |
| 4354 | s9 += s20 * 470296; |
| 4355 | s10 += s20 * 654183; |
| 4356 | s11 -= s20 * 997805; |
| 4357 | s12 += s20 * 136657; |
| 4358 | s13 -= s20 * 683901; |
| 4359 | s20 = 0; |
| 4360 | |
| 4361 | s7 += s19 * 666643; |
| 4362 | s8 += s19 * 470296; |
| 4363 | s9 += s19 * 654183; |
| 4364 | s10 -= s19 * 997805; |
| 4365 | s11 += s19 * 136657; |
| 4366 | s12 -= s19 * 683901; |
| 4367 | s19 = 0; |
| 4368 | |
| 4369 | s6 += s18 * 666643; |
| 4370 | s7 += s18 * 470296; |
| 4371 | s8 += s18 * 654183; |
| 4372 | s9 -= s18 * 997805; |
| 4373 | s10 += s18 * 136657; |
| 4374 | s11 -= s18 * 683901; |
| 4375 | s18 = 0; |
| 4376 | |
| 4377 | carry6 = (s6 + (1 << 20)) >> 21; |
| 4378 | s7 += carry6; |
| 4379 | s6 -= carry6 << 21; |
| 4380 | carry8 = (s8 + (1 << 20)) >> 21; |
| 4381 | s9 += carry8; |
| 4382 | s8 -= carry8 << 21; |
| 4383 | carry10 = (s10 + (1 << 20)) >> 21; |
| 4384 | s11 += carry10; |
| 4385 | s10 -= carry10 << 21; |
| 4386 | carry12 = (s12 + (1 << 20)) >> 21; |
| 4387 | s13 += carry12; |
| 4388 | s12 -= carry12 << 21; |
| 4389 | carry14 = (s14 + (1 << 20)) >> 21; |
| 4390 | s15 += carry14; |
| 4391 | s14 -= carry14 << 21; |
| 4392 | carry16 = (s16 + (1 << 20)) >> 21; |
| 4393 | s17 += carry16; |
| 4394 | s16 -= carry16 << 21; |
| 4395 | |
| 4396 | carry7 = (s7 + (1 << 20)) >> 21; |
| 4397 | s8 += carry7; |
| 4398 | s7 -= carry7 << 21; |
| 4399 | carry9 = (s9 + (1 << 20)) >> 21; |
| 4400 | s10 += carry9; |
| 4401 | s9 -= carry9 << 21; |
| 4402 | carry11 = (s11 + (1 << 20)) >> 21; |
| 4403 | s12 += carry11; |
| 4404 | s11 -= carry11 << 21; |
| 4405 | carry13 = (s13 + (1 << 20)) >> 21; |
| 4406 | s14 += carry13; |
| 4407 | s13 -= carry13 << 21; |
| 4408 | carry15 = (s15 + (1 << 20)) >> 21; |
| 4409 | s16 += carry15; |
| 4410 | s15 -= carry15 << 21; |
| 4411 | |
| 4412 | s5 += s17 * 666643; |
| 4413 | s6 += s17 * 470296; |
| 4414 | s7 += s17 * 654183; |
| 4415 | s8 -= s17 * 997805; |
| 4416 | s9 += s17 * 136657; |
| 4417 | s10 -= s17 * 683901; |
| 4418 | s17 = 0; |
| 4419 | |
| 4420 | s4 += s16 * 666643; |
| 4421 | s5 += s16 * 470296; |
| 4422 | s6 += s16 * 654183; |
| 4423 | s7 -= s16 * 997805; |
| 4424 | s8 += s16 * 136657; |
| 4425 | s9 -= s16 * 683901; |
| 4426 | s16 = 0; |
| 4427 | |
| 4428 | s3 += s15 * 666643; |
| 4429 | s4 += s15 * 470296; |
| 4430 | s5 += s15 * 654183; |
| 4431 | s6 -= s15 * 997805; |
| 4432 | s7 += s15 * 136657; |
| 4433 | s8 -= s15 * 683901; |
| 4434 | s15 = 0; |
| 4435 | |
| 4436 | s2 += s14 * 666643; |
| 4437 | s3 += s14 * 470296; |
| 4438 | s4 += s14 * 654183; |
| 4439 | s5 -= s14 * 997805; |
| 4440 | s6 += s14 * 136657; |
| 4441 | s7 -= s14 * 683901; |
| 4442 | s14 = 0; |
| 4443 | |
| 4444 | s1 += s13 * 666643; |
| 4445 | s2 += s13 * 470296; |
| 4446 | s3 += s13 * 654183; |
| 4447 | s4 -= s13 * 997805; |
| 4448 | s5 += s13 * 136657; |
| 4449 | s6 -= s13 * 683901; |
| 4450 | s13 = 0; |
| 4451 | |
| 4452 | s0 += s12 * 666643; |
| 4453 | s1 += s12 * 470296; |
| 4454 | s2 += s12 * 654183; |
| 4455 | s3 -= s12 * 997805; |
| 4456 | s4 += s12 * 136657; |
| 4457 | s5 -= s12 * 683901; |
| 4458 | s12 = 0; |
| 4459 | |
| 4460 | carry0 = (s0 + (1 << 20)) >> 21; |
| 4461 | s1 += carry0; |
| 4462 | s0 -= carry0 << 21; |
| 4463 | carry2 = (s2 + (1 << 20)) >> 21; |
| 4464 | s3 += carry2; |
| 4465 | s2 -= carry2 << 21; |
| 4466 | carry4 = (s4 + (1 << 20)) >> 21; |
| 4467 | s5 += carry4; |
| 4468 | s4 -= carry4 << 21; |
| 4469 | carry6 = (s6 + (1 << 20)) >> 21; |
| 4470 | s7 += carry6; |
| 4471 | s6 -= carry6 << 21; |
| 4472 | carry8 = (s8 + (1 << 20)) >> 21; |
| 4473 | s9 += carry8; |
| 4474 | s8 -= carry8 << 21; |
| 4475 | carry10 = (s10 + (1 << 20)) >> 21; |
| 4476 | s11 += carry10; |
| 4477 | s10 -= carry10 << 21; |
| 4478 | |
| 4479 | carry1 = (s1 + (1 << 20)) >> 21; |
| 4480 | s2 += carry1; |
| 4481 | s1 -= carry1 << 21; |
| 4482 | carry3 = (s3 + (1 << 20)) >> 21; |
| 4483 | s4 += carry3; |
| 4484 | s3 -= carry3 << 21; |
| 4485 | carry5 = (s5 + (1 << 20)) >> 21; |
| 4486 | s6 += carry5; |
| 4487 | s5 -= carry5 << 21; |
| 4488 | carry7 = (s7 + (1 << 20)) >> 21; |
| 4489 | s8 += carry7; |
| 4490 | s7 -= carry7 << 21; |
| 4491 | carry9 = (s9 + (1 << 20)) >> 21; |
| 4492 | s10 += carry9; |
| 4493 | s9 -= carry9 << 21; |
| 4494 | carry11 = (s11 + (1 << 20)) >> 21; |
| 4495 | s12 += carry11; |
| 4496 | s11 -= carry11 << 21; |
| 4497 | |
| 4498 | s0 += s12 * 666643; |
| 4499 | s1 += s12 * 470296; |
| 4500 | s2 += s12 * 654183; |
| 4501 | s3 -= s12 * 997805; |
| 4502 | s4 += s12 * 136657; |
| 4503 | s5 -= s12 * 683901; |
| 4504 | s12 = 0; |
| 4505 | |
| 4506 | carry0 = s0 >> 21; |
| 4507 | s1 += carry0; |
| 4508 | s0 -= carry0 << 21; |
| 4509 | carry1 = s1 >> 21; |
| 4510 | s2 += carry1; |
| 4511 | s1 -= carry1 << 21; |
| 4512 | carry2 = s2 >> 21; |
| 4513 | s3 += carry2; |
| 4514 | s2 -= carry2 << 21; |
| 4515 | carry3 = s3 >> 21; |
| 4516 | s4 += carry3; |
| 4517 | s3 -= carry3 << 21; |
| 4518 | carry4 = s4 >> 21; |
| 4519 | s5 += carry4; |
| 4520 | s4 -= carry4 << 21; |
| 4521 | carry5 = s5 >> 21; |
| 4522 | s6 += carry5; |
| 4523 | s5 -= carry5 << 21; |
| 4524 | carry6 = s6 >> 21; |
| 4525 | s7 += carry6; |
| 4526 | s6 -= carry6 << 21; |
| 4527 | carry7 = s7 >> 21; |
| 4528 | s8 += carry7; |
| 4529 | s7 -= carry7 << 21; |
| 4530 | carry8 = s8 >> 21; |
| 4531 | s9 += carry8; |
| 4532 | s8 -= carry8 << 21; |
| 4533 | carry9 = s9 >> 21; |
| 4534 | s10 += carry9; |
| 4535 | s9 -= carry9 << 21; |
| 4536 | carry10 = s10 >> 21; |
| 4537 | s11 += carry10; |
| 4538 | s10 -= carry10 << 21; |
| 4539 | carry11 = s11 >> 21; |
| 4540 | s12 += carry11; |
| 4541 | s11 -= carry11 << 21; |
| 4542 | |
| 4543 | s0 += s12 * 666643; |
| 4544 | s1 += s12 * 470296; |
| 4545 | s2 += s12 * 654183; |
| 4546 | s3 -= s12 * 997805; |
| 4547 | s4 += s12 * 136657; |
| 4548 | s5 -= s12 * 683901; |
| 4549 | s12 = 0; |
| 4550 | |
| 4551 | carry0 = s0 >> 21; |
| 4552 | s1 += carry0; |
| 4553 | s0 -= carry0 << 21; |
| 4554 | carry1 = s1 >> 21; |
| 4555 | s2 += carry1; |
| 4556 | s1 -= carry1 << 21; |
| 4557 | carry2 = s2 >> 21; |
| 4558 | s3 += carry2; |
| 4559 | s2 -= carry2 << 21; |
| 4560 | carry3 = s3 >> 21; |
| 4561 | s4 += carry3; |
| 4562 | s3 -= carry3 << 21; |
| 4563 | carry4 = s4 >> 21; |
| 4564 | s5 += carry4; |
| 4565 | s4 -= carry4 << 21; |
| 4566 | carry5 = s5 >> 21; |
| 4567 | s6 += carry5; |
| 4568 | s5 -= carry5 << 21; |
| 4569 | carry6 = s6 >> 21; |
| 4570 | s7 += carry6; |
| 4571 | s6 -= carry6 << 21; |
| 4572 | carry7 = s7 >> 21; |
| 4573 | s8 += carry7; |
| 4574 | s7 -= carry7 << 21; |
| 4575 | carry8 = s8 >> 21; |
| 4576 | s9 += carry8; |
| 4577 | s8 -= carry8 << 21; |
| 4578 | carry9 = s9 >> 21; |
| 4579 | s10 += carry9; |
| 4580 | s9 -= carry9 << 21; |
| 4581 | carry10 = s10 >> 21; |
| 4582 | s11 += carry10; |
| 4583 | s10 -= carry10 << 21; |
| 4584 | |
| 4585 | s[0] = s0 >> 0; |
| 4586 | s[1] = s0 >> 8; |
| 4587 | s[2] = (s0 >> 16) | (s1 << 5); |
| 4588 | s[3] = s1 >> 3; |
| 4589 | s[4] = s1 >> 11; |
| 4590 | s[5] = (s1 >> 19) | (s2 << 2); |
| 4591 | s[6] = s2 >> 6; |
| 4592 | s[7] = (s2 >> 14) | (s3 << 7); |
| 4593 | s[8] = s3 >> 1; |
| 4594 | s[9] = s3 >> 9; |
| 4595 | s[10] = (s3 >> 17) | (s4 << 4); |
| 4596 | s[11] = s4 >> 4; |
| 4597 | s[12] = s4 >> 12; |
| 4598 | s[13] = (s4 >> 20) | (s5 << 1); |
| 4599 | s[14] = s5 >> 7; |
| 4600 | s[15] = (s5 >> 15) | (s6 << 6); |
| 4601 | s[16] = s6 >> 2; |
| 4602 | s[17] = s6 >> 10; |
| 4603 | s[18] = (s6 >> 18) | (s7 << 3); |
| 4604 | s[19] = s7 >> 5; |
| 4605 | s[20] = s7 >> 13; |
| 4606 | s[21] = s8 >> 0; |
| 4607 | s[22] = s8 >> 8; |
| 4608 | s[23] = (s8 >> 16) | (s9 << 5); |
| 4609 | s[24] = s9 >> 3; |
| 4610 | s[25] = s9 >> 11; |
| 4611 | s[26] = (s9 >> 19) | (s10 << 2); |
| 4612 | s[27] = s10 >> 6; |
| 4613 | s[28] = (s10 >> 14) | (s11 << 7); |
| 4614 | s[29] = s11 >> 1; |
| 4615 | s[30] = s11 >> 9; |
| 4616 | s[31] = s11 >> 17; |
| 4617 | } |
| 4618 | |
| 4619 | void ED25519_public_from_private(uint8_t out_public_key[ED25519_PUBLIC_KEY_LENGTH32], |
| 4620 | const uint8_t private_key[ED25519_PRIVATE_KEY_LENGTH32]) { |
| 4621 | uint8_t az[SHA512_DIGEST_LENGTH64]; |
| 4622 | SHA512(private_key, 32, az); |
| 4623 | |
| 4624 | az[0] &= 248; |
| 4625 | az[31] &= 63; |
| 4626 | az[31] |= 64; |
| 4627 | |
| 4628 | ge_p3 A; |
| 4629 | x25519_ge_scalarmult_base(&A, az); |
| 4630 | ge_p3_tobytes(out_public_key, &A); |
| 4631 | } |
| 4632 | |
| 4633 | void ED25519_keypair(uint8_t out_public_key[ED25519_PUBLIC_KEY_LENGTH32], |
| 4634 | uint8_t out_private_key[ED25519_PRIVATE_KEY_LENGTH32]) { |
| 4635 | arc4random_buf(out_private_key, 32); |
| 4636 | |
| 4637 | ED25519_public_from_private(out_public_key, out_private_key); |
| 4638 | } |
| 4639 | LCRYPTO_ALIAS(ED25519_keypair)asm(""); |
| 4640 | |
| 4641 | int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, |
| 4642 | const uint8_t public_key[ED25519_PUBLIC_KEY_LENGTH32], |
| 4643 | const uint8_t private_key[ED25519_PRIVATE_KEY_LENGTH32]) { |
| 4644 | uint8_t az[SHA512_DIGEST_LENGTH64]; |
| 4645 | SHA512(private_key, 32, az); |
| 4646 | |
| 4647 | az[0] &= 248; |
| 4648 | az[31] &= 63; |
| 4649 | az[31] |= 64; |
| 4650 | |
| 4651 | SHA512_CTX hash_ctx; |
| 4652 | SHA512_Init(&hash_ctx); |
| 4653 | SHA512_Update(&hash_ctx, az + 32, 32); |
| 4654 | SHA512_Update(&hash_ctx, message, message_len); |
| 4655 | uint8_t nonce[SHA512_DIGEST_LENGTH64]; |
| 4656 | SHA512_Final(nonce, &hash_ctx); |
| 4657 | |
| 4658 | x25519_sc_reduce(nonce); |
| 4659 | ge_p3 R; |
| 4660 | x25519_ge_scalarmult_base(&R, nonce); |
| 4661 | ge_p3_tobytes(out_sig, &R); |
| 4662 | |
| 4663 | SHA512_Init(&hash_ctx); |
| 4664 | SHA512_Update(&hash_ctx, out_sig, 32); |
| 4665 | SHA512_Update(&hash_ctx, public_key, 32); |
| 4666 | SHA512_Update(&hash_ctx, message, message_len); |
| 4667 | uint8_t hram[SHA512_DIGEST_LENGTH64]; |
| 4668 | SHA512_Final(hram, &hash_ctx); |
| 4669 | |
| 4670 | x25519_sc_reduce(hram); |
| 4671 | sc_muladd(out_sig + 32, hram, az, nonce); |
| 4672 | |
| 4673 | return 1; |
| 4674 | } |
| 4675 | LCRYPTO_ALIAS(ED25519_sign)asm(""); |
| 4676 | |
| 4677 | /* |
| 4678 | * Little endian representation of the order of edwards25519, |
| 4679 | * see https://www.rfc-editor.org/rfc/rfc7748#section-4.1 |
| 4680 | */ |
| 4681 | static const uint8_t order[] = { |
| 4682 | 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, |
| 4683 | 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, |
| 4684 | 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
| 4685 | 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, |
| 4686 | }; |
| 4687 | |
| 4688 | int ED25519_verify(const uint8_t *message, size_t message_len, |
| 4689 | const uint8_t signature[ED25519_SIGNATURE_LENGTH64], |
| 4690 | const uint8_t public_key[ED25519_PUBLIC_KEY_LENGTH32]) { |
| 4691 | ge_p3 A; |
| 4692 | int i; |
| 4693 | if ((signature[63] & 224) != 0 || |
| 4694 | x25519_ge_frombytes_vartime(&A, public_key) != 0) { |
| 4695 | return 0; |
| 4696 | } |
| 4697 | |
| 4698 | fe_neg(A.X, A.X); |
| 4699 | fe_neg(A.T, A.T); |
| 4700 | |
| 4701 | uint8_t pkcopy[32]; |
| 4702 | memcpy(pkcopy, public_key, 32); |
| 4703 | uint8_t rcopy[32]; |
| 4704 | memcpy(rcopy, signature, 32); |
| 4705 | uint8_t scopy[32]; |
| 4706 | memcpy(scopy, signature + 32, 32); |
| 4707 | |
| 4708 | /* |
| 4709 | * https://tools.ietf.org/html/rfc8032#section-5.1.7 requires that scopy be |
| 4710 | * in the range [0, order) to prevent signature malleability. This value is |
| 4711 | * public, so there is no need to make this constant time. |
| 4712 | */ |
| 4713 | for (i = 31; i >= 0; i--) { |
| 4714 | if (scopy[i] > order[i]) |
| 4715 | return 0; |
| 4716 | if (scopy[i] < order[i]) |
| 4717 | break; |
| 4718 | if (i == 0) |
| 4719 | return 0; |
| 4720 | } |
| 4721 | |
| 4722 | SHA512_CTX hash_ctx; |
| 4723 | SHA512_Init(&hash_ctx); |
| 4724 | SHA512_Update(&hash_ctx, signature, 32); |
| 4725 | SHA512_Update(&hash_ctx, public_key, 32); |
| 4726 | SHA512_Update(&hash_ctx, message, message_len); |
| 4727 | uint8_t h[SHA512_DIGEST_LENGTH64]; |
| 4728 | SHA512_Final(h, &hash_ctx); |
| 4729 | |
| 4730 | x25519_sc_reduce(h); |
| 4731 | |
| 4732 | ge_p2 R; |
| 4733 | ge_double_scalarmult_vartime(&R, h, &A, scopy); |
| 4734 | |
| 4735 | uint8_t rcheck[32]; |
| 4736 | x25519_ge_tobytes(rcheck, &R); |
| 4737 | |
| 4738 | return timingsafe_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0; |
| 4739 | } |
| 4740 | LCRYPTO_ALIAS(ED25519_verify)asm(""); |
| 4741 | |
| 4742 | /* Replace (f,g) with (g,f) if b == 1; |
| 4743 | * replace (f,g) with (f,g) if b == 0. |
| 4744 | * |
| 4745 | * Preconditions: b in {0,1}. */ |
| 4746 | static void fe_cswap(fe f, fe g, unsigned int b) { |
| 4747 | b = 0-b; |
| 4748 | unsigned i; |
| 4749 | for (i = 0; i < 10; i++) { |
| 4750 | int32_t x = f[i] ^ g[i]; |
| 4751 | x &= b; |
| 4752 | f[i] ^= x; |
| 4753 | g[i] ^= x; |
| 4754 | } |
| 4755 | } |
| 4756 | |
| 4757 | /* h = f * 121666 |
| 4758 | * Can overlap h with f. |
| 4759 | * |
| 4760 | * Preconditions: |
| 4761 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
| 4762 | * |
| 4763 | * Postconditions: |
| 4764 | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ |
| 4765 | static void fe_mul121666(fe h, fe f) { |
| 4766 | int32_t f0 = f[0]; |
| 4767 | int32_t f1 = f[1]; |
| 4768 | int32_t f2 = f[2]; |
| 4769 | int32_t f3 = f[3]; |
| 4770 | int32_t f4 = f[4]; |
| 4771 | int32_t f5 = f[5]; |
| 4772 | int32_t f6 = f[6]; |
| 4773 | int32_t f7 = f[7]; |
| 4774 | int32_t f8 = f[8]; |
| 4775 | int32_t f9 = f[9]; |
| 4776 | int64_t h0 = f0 * (int64_t) 121666; |
| 4777 | int64_t h1 = f1 * (int64_t) 121666; |
| 4778 | int64_t h2 = f2 * (int64_t) 121666; |
| 4779 | int64_t h3 = f3 * (int64_t) 121666; |
| 4780 | int64_t h4 = f4 * (int64_t) 121666; |
| 4781 | int64_t h5 = f5 * (int64_t) 121666; |
| 4782 | int64_t h6 = f6 * (int64_t) 121666; |
| 4783 | int64_t h7 = f7 * (int64_t) 121666; |
| 4784 | int64_t h8 = f8 * (int64_t) 121666; |
| 4785 | int64_t h9 = f9 * (int64_t) 121666; |
| 4786 | int64_t carry0; |
| 4787 | int64_t carry1; |
| 4788 | int64_t carry2; |
| 4789 | int64_t carry3; |
| 4790 | int64_t carry4; |
| 4791 | int64_t carry5; |
| 4792 | int64_t carry6; |
| 4793 | int64_t carry7; |
| 4794 | int64_t carry8; |
| 4795 | int64_t carry9; |
| 4796 | |
| 4797 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
| 4798 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
| 4799 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
| 4800 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
| 4801 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
| 4802 | |
| 4803 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
| 4804 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
| 4805 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
| 4806 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
| 4807 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
| 4808 | |
| 4809 | h[0] = h0; |
| 4810 | h[1] = h1; |
| 4811 | h[2] = h2; |
| 4812 | h[3] = h3; |
| 4813 | h[4] = h4; |
| 4814 | h[5] = h5; |
| 4815 | h[6] = h6; |
| 4816 | h[7] = h7; |
| 4817 | h[8] = h8; |
| 4818 | h[9] = h9; |
| 4819 | } |
| 4820 | |
| 4821 | void |
| 4822 | x25519_scalar_mult_generic(uint8_t out[32], const uint8_t scalar[32], |
| 4823 | const uint8_t point[32]) { |
| 4824 | fe x1, x2, z2, x3, z3, tmp0, tmp1; |
| 4825 | |
| 4826 | uint8_t e[32]; |
| 4827 | memcpy(e, scalar, 32); |
| 4828 | e[0] &= 248; |
| 4829 | e[31] &= 127; |
| 4830 | e[31] |= 64; |
| 4831 | fe_frombytes(x1, point); |
| 4832 | fe_1(x2); |
| 4833 | fe_0(z2); |
| 4834 | fe_copy(x3, x1); |
| 4835 | fe_1(z3); |
| 4836 | |
| 4837 | unsigned swap = 0; |
| 4838 | int pos; |
| 4839 | for (pos = 254; pos >= 0; --pos) { |
| 4840 | unsigned b = 1 & (e[pos / 8] >> (pos & 7)); |
| 4841 | swap ^= b; |
| 4842 | fe_cswap(x2, x3, swap); |
| 4843 | fe_cswap(z2, z3, swap); |
| 4844 | swap = b; |
| 4845 | fe_sub(tmp0, x3, z3); |
| 4846 | fe_sub(tmp1, x2, z2); |
| 4847 | fe_add(x2, x2, z2); |
| 4848 | fe_add(z2, x3, z3); |
| 4849 | fe_mul(z3, tmp0, x2); |
| 4850 | fe_mul(z2, z2, tmp1); |
| 4851 | fe_sq(tmp0, tmp1); |
| 4852 | fe_sq(tmp1, x2); |
| 4853 | fe_add(x3, z3, z2); |
| 4854 | fe_sub(z2, z3, z2); |
| 4855 | fe_mul(x2, tmp1, tmp0); |
| 4856 | fe_sub(tmp1, tmp1, tmp0); |
| 4857 | fe_sq(z2, z2); |
| 4858 | fe_mul121666(z3, tmp1); |
| 4859 | fe_sq(x3, x3); |
| 4860 | fe_add(tmp0, tmp0, z3); |
| 4861 | fe_mul(z3, x1, z2); |
| 4862 | fe_mul(z2, tmp1, tmp0); |
| 4863 | } |
| 4864 | fe_cswap(x2, x3, swap); |
| 4865 | fe_cswap(z2, z3, swap); |
| 4866 | |
| 4867 | fe_invert(z2, z2); |
| 4868 | fe_mul(x2, x2, z2); |
| 4869 | fe_tobytes(out, x2); |
| 4870 | } |
| 4871 | |
| 4872 | #ifdef unused |
| 4873 | void |
| 4874 | x25519_public_from_private_generic(uint8_t out_public_key[32], |
| 4875 | const uint8_t private_key[32]) |
| 4876 | { |
| 4877 | uint8_t e[32]; |
| 4878 | |
| 4879 | memcpy(e, private_key, 32); |
| 4880 | e[0] &= 248; |
| 4881 | e[31] &= 127; |
| 4882 | e[31] |= 64; |
| 4883 | |
| 4884 | ge_p3 A; |
| 4885 | x25519_ge_scalarmult_base(&A, e); |
| 4886 | |
| 4887 | /* We only need the u-coordinate of the curve25519 point. The map is |
| 4888 | * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ |
| 4889 | fe zplusy, zminusy, zminusy_inv; |
| 4890 | fe_add(zplusy, A.Z, A.Y); |
| 4891 | fe_sub(zminusy, A.Z, A.Y); |
| 4892 | fe_invert(zminusy_inv, zminusy); |
| 4893 | fe_mul(zplusy, zplusy, zminusy_inv); |
| 4894 | fe_tobytes(out_public_key, zplusy); |
| 4895 | } |
| 4896 | #endif |
| 4897 | |
| 4898 | void |
| 4899 | X25519_public_from_private(uint8_t out_public_key[X25519_KEY_LENGTH32], |
| 4900 | const uint8_t private_key[X25519_KEY_LENGTH32]) |
| 4901 | { |
| 4902 | static const uint8_t kMongomeryBasePoint[32] = {9}; |
| 4903 | |
| 4904 | x25519_scalar_mult(out_public_key, private_key, kMongomeryBasePoint); |
| 4905 | } |
| 4906 | |
| 4907 | void |
| 4908 | X25519_keypair(uint8_t out_public_key[X25519_KEY_LENGTH32], |
| 4909 | uint8_t out_private_key[X25519_KEY_LENGTH32]) |
| 4910 | { |
| 4911 | /* All X25519 implementations should decode scalars correctly (see |
| 4912 | * https://tools.ietf.org/html/rfc7748#section-5). However, if an |
| 4913 | * implementation doesn't then it might interoperate with random keys a |
| 4914 | * fraction of the time because they'll, randomly, happen to be correctly |
| 4915 | * formed. |
| 4916 | * |
| 4917 | * Thus we do the opposite of the masking here to make sure that our private |
| 4918 | * keys are never correctly masked and so, hopefully, any incorrect |
| 4919 | * implementations are deterministically broken. |
| 4920 | * |
| 4921 | * This does not affect security because, although we're throwing away |
| 4922 | * entropy, a valid implementation of scalarmult should throw away the exact |
| 4923 | * same bits anyway. */ |
| 4924 | arc4random_buf(out_private_key, 32); |
| 4925 | |
| 4926 | out_private_key[0] |= 7; |
| 4927 | out_private_key[31] &= 63; |
| 4928 | out_private_key[31] |= 128; |
| 4929 | |
| 4930 | X25519_public_from_private(out_public_key, out_private_key); |
| 4931 | } |
| 4932 | LCRYPTO_ALIAS(X25519_keypair)asm(""); |
| 4933 | |
| 4934 | int |
| 4935 | X25519(uint8_t out_shared_key[X25519_KEY_LENGTH32], |
| 4936 | const uint8_t private_key[X25519_KEY_LENGTH32], |
| 4937 | const uint8_t peer_public_key[X25519_KEY_LENGTH32]) |
| 4938 | { |
| 4939 | static const uint8_t kZeros[32] = {0}; |
| 4940 | |
| 4941 | x25519_scalar_mult(out_shared_key, private_key, peer_public_key); |
| 4942 | |
| 4943 | /* The all-zero output results when the input is a point of small order. */ |
| 4944 | return timingsafe_memcmp(kZeros, out_shared_key, 32) != 0; |
| 4945 | } |
| 4946 | LCRYPTO_ALIAS(X25519)asm(""); |