Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1 | /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
| 2 | * All rights reserved. |
| 3 | * |
| 4 | * This package is an SSL implementation written |
| 5 | * by Eric Young (eay@cryptsoft.com). |
| 6 | * The implementation was written so as to conform with Netscapes SSL. |
| 7 | * |
| 8 | * This library is free for commercial and non-commercial use as long as |
| 9 | * the following conditions are aheared to. The following conditions |
| 10 | * apply to all code found in this distribution, be it the RC4, RSA, |
| 11 | * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
| 12 | * included with this distribution is covered by the same copyright terms |
| 13 | * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
| 14 | * |
| 15 | * Copyright remains Eric Young's, and as such any Copyright notices in |
| 16 | * the code are not to be removed. |
| 17 | * If this package is used in a product, Eric Young should be given attribution |
| 18 | * as the author of the parts of the library used. |
| 19 | * This can be in the form of a textual message at program startup or |
| 20 | * in documentation (online or textual) provided with the package. |
| 21 | * |
| 22 | * Redistribution and use in source and binary forms, with or without |
| 23 | * modification, are permitted provided that the following conditions |
| 24 | * are met: |
| 25 | * 1. Redistributions of source code must retain the copyright |
| 26 | * notice, this list of conditions and the following disclaimer. |
| 27 | * 2. Redistributions in binary form must reproduce the above copyright |
| 28 | * notice, this list of conditions and the following disclaimer in the |
| 29 | * documentation and/or other materials provided with the distribution. |
| 30 | * 3. All advertising materials mentioning features or use of this software |
| 31 | * must display the following acknowledgement: |
| 32 | * "This product includes cryptographic software written by |
| 33 | * Eric Young (eay@cryptsoft.com)" |
| 34 | * The word 'cryptographic' can be left out if the rouines from the library |
| 35 | * being used are not cryptographic related :-). |
| 36 | * 4. If you include any Windows specific code (or a derivative thereof) from |
| 37 | * the apps directory (application code) you must include an acknowledgement: |
| 38 | * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
| 39 | * |
| 40 | * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
| 41 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 42 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 43 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| 44 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| 45 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| 46 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 47 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| 48 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| 49 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| 50 | * SUCH DAMAGE. |
| 51 | * |
| 52 | * The licence and distribution terms for any publically available version or |
| 53 | * derivative of this code cannot be changed. i.e. this code cannot simply be |
| 54 | * copied and put under another distribution licence |
| 55 | * [including the GNU Public Licence.] |
| 56 | */ |
| 57 | /* ==================================================================== |
| 58 | * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. |
| 59 | * |
| 60 | * Redistribution and use in source and binary forms, with or without |
| 61 | * modification, are permitted provided that the following conditions |
| 62 | * are met: |
| 63 | * |
| 64 | * 1. Redistributions of source code must retain the above copyright |
| 65 | * notice, this list of conditions and the following disclaimer. |
| 66 | * |
| 67 | * 2. Redistributions in binary form must reproduce the above copyright |
| 68 | * notice, this list of conditions and the following disclaimer in |
| 69 | * the documentation and/or other materials provided with the |
| 70 | * distribution. |
| 71 | * |
| 72 | * 3. All advertising materials mentioning features or use of this |
| 73 | * software must display the following acknowledgment: |
| 74 | * "This product includes software developed by the OpenSSL Project |
| 75 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| 76 | * |
| 77 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| 78 | * endorse or promote products derived from this software without |
| 79 | * prior written permission. For written permission, please contact |
| 80 | * openssl-core@openssl.org. |
| 81 | * |
| 82 | * 5. Products derived from this software may not be called "OpenSSL" |
| 83 | * nor may "OpenSSL" appear in their names without prior written |
| 84 | * permission of the OpenSSL Project. |
| 85 | * |
| 86 | * 6. Redistributions of any form whatsoever must retain the following |
| 87 | * acknowledgment: |
| 88 | * "This product includes software developed by the OpenSSL Project |
| 89 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| 90 | * |
| 91 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| 92 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 93 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| 94 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| 95 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 96 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| 97 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| 98 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 99 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| 100 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 101 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| 102 | * OF THE POSSIBILITY OF SUCH DAMAGE. |
| 103 | * ==================================================================== |
| 104 | * |
| 105 | * This product includes cryptographic software written by Eric Young |
| 106 | * (eay@cryptsoft.com). This product includes software written by Tim |
| 107 | * Hudson (tjh@cryptsoft.com). */ |
| 108 | |
| 109 | #include <openssl/bn.h> |
| 110 | |
| 111 | #include <assert.h> |
| 112 | #include <string.h> |
| 113 | |
| 114 | #include <openssl/cpu.h> |
| 115 | #include <openssl/err.h> |
| 116 | #include <openssl/mem.h> |
| 117 | |
| 118 | #include "internal.h" |
| 119 | |
| 120 | |
| 121 | #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) |
| 122 | #define OPENSSL_BN_ASM_MONT5 |
| 123 | #define RSAZ_ENABLED |
| 124 | |
| 125 | #include "rsaz_exp.h" |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 126 | |
| 127 | void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, const void *table, |
| 128 | const BN_ULONG *np, const BN_ULONG *n0, int num, |
| 129 | int power); |
| 130 | void bn_scatter5(const BN_ULONG *inp, size_t num, void *table, size_t power); |
| 131 | void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); |
| 132 | void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, const void *table, |
| 133 | const BN_ULONG *np, const BN_ULONG *n0, int num, int power); |
| 134 | int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, |
| 135 | const BN_ULONG *not_used, const BN_ULONG *np, |
| 136 | const BN_ULONG *n0, int num); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 137 | #endif |
| 138 | |
| 139 | int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) { |
| 140 | int i, bits, ret = 0; |
| 141 | BIGNUM *v, *rr; |
| 142 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 143 | BN_CTX_start(ctx); |
| 144 | if (r == a || r == p) { |
| 145 | rr = BN_CTX_get(ctx); |
| 146 | } else { |
| 147 | rr = r; |
| 148 | } |
| 149 | |
| 150 | v = BN_CTX_get(ctx); |
| 151 | if (rr == NULL || v == NULL) { |
| 152 | goto err; |
| 153 | } |
| 154 | |
| 155 | if (BN_copy(v, a) == NULL) { |
| 156 | goto err; |
| 157 | } |
| 158 | bits = BN_num_bits(p); |
| 159 | |
| 160 | if (BN_is_odd(p)) { |
| 161 | if (BN_copy(rr, a) == NULL) { |
| 162 | goto err; |
| 163 | } |
| 164 | } else { |
| 165 | if (!BN_one(rr)) { |
| 166 | goto err; |
| 167 | } |
| 168 | } |
| 169 | |
| 170 | for (i = 1; i < bits; i++) { |
| 171 | if (!BN_sqr(v, v, ctx)) { |
| 172 | goto err; |
| 173 | } |
| 174 | if (BN_is_bit_set(p, i)) { |
| 175 | if (!BN_mul(rr, rr, v, ctx)) { |
| 176 | goto err; |
| 177 | } |
| 178 | } |
| 179 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 180 | |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 181 | if (r != rr && !BN_copy(r, rr)) { |
| 182 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 183 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 184 | ret = 1; |
| 185 | |
| 186 | err: |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 187 | BN_CTX_end(ctx); |
| 188 | return ret; |
| 189 | } |
| 190 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 191 | typedef struct bn_recp_ctx_st { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 192 | BIGNUM N; // the divisor |
| 193 | BIGNUM Nr; // the reciprocal |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 194 | int num_bits; |
| 195 | int shift; |
| 196 | int flags; |
| 197 | } BN_RECP_CTX; |
| 198 | |
| 199 | static void BN_RECP_CTX_init(BN_RECP_CTX *recp) { |
| 200 | BN_init(&recp->N); |
| 201 | BN_init(&recp->Nr); |
| 202 | recp->num_bits = 0; |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 203 | recp->shift = 0; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 204 | recp->flags = 0; |
| 205 | } |
| 206 | |
| 207 | static void BN_RECP_CTX_free(BN_RECP_CTX *recp) { |
| 208 | if (recp == NULL) { |
| 209 | return; |
| 210 | } |
| 211 | |
| 212 | BN_free(&recp->N); |
| 213 | BN_free(&recp->Nr); |
| 214 | } |
| 215 | |
| 216 | static int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx) { |
| 217 | if (!BN_copy(&(recp->N), d)) { |
| 218 | return 0; |
| 219 | } |
| 220 | BN_zero(&recp->Nr); |
| 221 | recp->num_bits = BN_num_bits(d); |
| 222 | recp->shift = 0; |
| 223 | |
| 224 | return 1; |
| 225 | } |
| 226 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 227 | // len is the expected size of the result We actually calculate with an extra |
| 228 | // word of precision, so we can do faster division if the remainder is not |
| 229 | // required. |
| 230 | // r := 2^len / m |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 231 | static int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx) { |
| 232 | int ret = -1; |
| 233 | BIGNUM *t; |
| 234 | |
| 235 | BN_CTX_start(ctx); |
| 236 | t = BN_CTX_get(ctx); |
| 237 | if (t == NULL) { |
| 238 | goto err; |
| 239 | } |
| 240 | |
| 241 | if (!BN_set_bit(t, len)) { |
| 242 | goto err; |
| 243 | } |
| 244 | |
| 245 | if (!BN_div(r, NULL, t, m, ctx)) { |
| 246 | goto err; |
| 247 | } |
| 248 | |
| 249 | ret = len; |
| 250 | |
| 251 | err: |
| 252 | BN_CTX_end(ctx); |
| 253 | return ret; |
| 254 | } |
| 255 | |
| 256 | static int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, |
| 257 | BN_RECP_CTX *recp, BN_CTX *ctx) { |
| 258 | int i, j, ret = 0; |
| 259 | BIGNUM *a, *b, *d, *r; |
| 260 | |
| 261 | BN_CTX_start(ctx); |
| 262 | a = BN_CTX_get(ctx); |
| 263 | b = BN_CTX_get(ctx); |
| 264 | if (dv != NULL) { |
| 265 | d = dv; |
| 266 | } else { |
| 267 | d = BN_CTX_get(ctx); |
| 268 | } |
| 269 | |
| 270 | if (rem != NULL) { |
| 271 | r = rem; |
| 272 | } else { |
| 273 | r = BN_CTX_get(ctx); |
| 274 | } |
| 275 | |
| 276 | if (a == NULL || b == NULL || d == NULL || r == NULL) { |
| 277 | goto err; |
| 278 | } |
| 279 | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 280 | if (BN_ucmp(m, &recp->N) < 0) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 281 | BN_zero(d); |
| 282 | if (!BN_copy(r, m)) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 283 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 284 | } |
| 285 | BN_CTX_end(ctx); |
| 286 | return 1; |
| 287 | } |
| 288 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 289 | // We want the remainder |
| 290 | // Given input of ABCDEF / ab |
| 291 | // we need multiply ABCDEF by 3 digests of the reciprocal of ab |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 292 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 293 | // i := max(BN_num_bits(m), 2*BN_num_bits(N)) |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 294 | i = BN_num_bits(m); |
| 295 | j = recp->num_bits << 1; |
| 296 | if (j > i) { |
| 297 | i = j; |
| 298 | } |
| 299 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 300 | // Nr := round(2^i / N) |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 301 | if (i != recp->shift) { |
| 302 | recp->shift = |
| 303 | BN_reciprocal(&(recp->Nr), &(recp->N), i, |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 304 | ctx); // BN_reciprocal returns i, or -1 for an error |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 305 | } |
| 306 | |
| 307 | if (recp->shift == -1) { |
| 308 | goto err; |
| 309 | } |
| 310 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 311 | // d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - |
| 312 | // BN_num_bits(N)))| |
| 313 | // = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - |
| 314 | // BN_num_bits(N)))| |
| 315 | // <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)| |
| 316 | // = |m/N| |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 317 | if (!BN_rshift(a, m, recp->num_bits)) { |
| 318 | goto err; |
| 319 | } |
| 320 | if (!BN_mul(b, a, &(recp->Nr), ctx)) { |
| 321 | goto err; |
| 322 | } |
| 323 | if (!BN_rshift(d, b, i - recp->num_bits)) { |
| 324 | goto err; |
| 325 | } |
| 326 | d->neg = 0; |
| 327 | |
| 328 | if (!BN_mul(b, &(recp->N), d, ctx)) { |
| 329 | goto err; |
| 330 | } |
| 331 | if (!BN_usub(r, m, b)) { |
| 332 | goto err; |
| 333 | } |
| 334 | r->neg = 0; |
| 335 | |
| 336 | j = 0; |
| 337 | while (BN_ucmp(r, &(recp->N)) >= 0) { |
| 338 | if (j++ > 2) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 339 | OPENSSL_PUT_ERROR(BN, BN_R_BAD_RECIPROCAL); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 340 | goto err; |
| 341 | } |
| 342 | if (!BN_usub(r, r, &(recp->N))) { |
| 343 | goto err; |
| 344 | } |
| 345 | if (!BN_add_word(d, 1)) { |
| 346 | goto err; |
| 347 | } |
| 348 | } |
| 349 | |
| 350 | r->neg = BN_is_zero(r) ? 0 : m->neg; |
| 351 | d->neg = m->neg ^ recp->N.neg; |
| 352 | ret = 1; |
| 353 | |
| 354 | err: |
| 355 | BN_CTX_end(ctx); |
| 356 | return ret; |
| 357 | } |
| 358 | |
| 359 | static int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, |
| 360 | BN_RECP_CTX *recp, BN_CTX *ctx) { |
| 361 | int ret = 0; |
| 362 | BIGNUM *a; |
| 363 | const BIGNUM *ca; |
| 364 | |
| 365 | BN_CTX_start(ctx); |
| 366 | a = BN_CTX_get(ctx); |
| 367 | if (a == NULL) { |
| 368 | goto err; |
| 369 | } |
| 370 | |
| 371 | if (y != NULL) { |
| 372 | if (x == y) { |
| 373 | if (!BN_sqr(a, x, ctx)) { |
| 374 | goto err; |
| 375 | } |
| 376 | } else { |
| 377 | if (!BN_mul(a, x, y, ctx)) { |
| 378 | goto err; |
| 379 | } |
| 380 | } |
| 381 | ca = a; |
| 382 | } else { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 383 | ca = x; // Just do the mod |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 384 | } |
| 385 | |
| 386 | ret = BN_div_recp(NULL, r, ca, recp, ctx); |
| 387 | |
| 388 | err: |
| 389 | BN_CTX_end(ctx); |
| 390 | return ret; |
| 391 | } |
| 392 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 393 | // BN_window_bits_for_exponent_size returns sliding window size for mod_exp with |
| 394 | // a |b| bit exponent. |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 395 | // |
| 396 | // For window size 'w' (w >= 2) and a random 'b' bits exponent, the number of |
| 397 | // multiplications is a constant plus on average |
| 398 | // |
| 399 | // 2^(w-1) + (b-w)/(w+1); |
| 400 | // |
| 401 | // here 2^(w-1) is for precomputing the table (we actually need entries only |
| 402 | // for windows that have the lowest bit set), and (b-w)/(w+1) is an |
| 403 | // approximation for the expected number of w-bit windows, not counting the |
| 404 | // first one. |
| 405 | // |
| 406 | // Thus we should use |
| 407 | // |
| 408 | // w >= 6 if b > 671 |
| 409 | // w = 5 if 671 > b > 239 |
| 410 | // w = 4 if 239 > b > 79 |
| 411 | // w = 3 if 79 > b > 23 |
| 412 | // w <= 2 if 23 > b |
| 413 | // |
| 414 | // (with draws in between). Very small exponents are often selected |
| 415 | // with low Hamming weight, so we use w = 1 for b <= 23. |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 416 | static int BN_window_bits_for_exponent_size(int b) { |
| 417 | if (b > 671) { |
| 418 | return 6; |
| 419 | } |
| 420 | if (b > 239) { |
| 421 | return 5; |
| 422 | } |
| 423 | if (b > 79) { |
| 424 | return 4; |
| 425 | } |
| 426 | if (b > 23) { |
| 427 | return 3; |
| 428 | } |
| 429 | return 1; |
| 430 | } |
| 431 | |
| 432 | // TABLE_SIZE is the maximum precomputation table size for *variable* sliding |
| 433 | // windows. This must be 2^(max_window - 1), where max_window is the largest |
| 434 | // value returned from |BN_window_bits_for_exponent_size|. |
| 435 | #define TABLE_SIZE 32 |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 436 | |
Robert Sloan | 99319a1 | 2017-11-27 10:32:46 -0800 | [diff] [blame] | 437 | // TABLE_BITS_SMALL is the smallest value returned from |
| 438 | // |BN_window_bits_for_exponent_size| when |b| is at most |BN_BITS2| * |
| 439 | // |BN_SMALL_MAX_WORDS| words. |
| 440 | #define TABLE_BITS_SMALL 5 |
| 441 | |
| 442 | // TABLE_SIZE_SMALL is the same as |TABLE_SIZE|, but when |b| is at most |
| 443 | // |BN_BITS2| * |BN_SMALL_MAX_WORDS|. |
| 444 | #define TABLE_SIZE_SMALL (1 << (TABLE_BITS_SMALL - 1)) |
| 445 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 446 | static int mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
| 447 | const BIGNUM *m, BN_CTX *ctx) { |
| 448 | int i, j, bits, ret = 0, wstart, window; |
| 449 | int start = 1; |
| 450 | BIGNUM *aa; |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 451 | // Table of variables obtained from 'ctx' |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 452 | BIGNUM *val[TABLE_SIZE]; |
| 453 | BN_RECP_CTX recp; |
| 454 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 455 | bits = BN_num_bits(p); |
| 456 | |
| 457 | if (bits == 0) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 458 | // x**0 mod 1 is still zero. |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 459 | if (BN_is_one(m)) { |
| 460 | BN_zero(r); |
| 461 | return 1; |
| 462 | } |
| 463 | return BN_one(r); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 464 | } |
| 465 | |
| 466 | BN_CTX_start(ctx); |
| 467 | aa = BN_CTX_get(ctx); |
| 468 | val[0] = BN_CTX_get(ctx); |
| 469 | if (!aa || !val[0]) { |
| 470 | goto err; |
| 471 | } |
| 472 | |
| 473 | BN_RECP_CTX_init(&recp); |
| 474 | if (m->neg) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 475 | // ignore sign of 'm' |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 476 | if (!BN_copy(aa, m)) { |
| 477 | goto err; |
| 478 | } |
| 479 | aa->neg = 0; |
| 480 | if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) { |
| 481 | goto err; |
| 482 | } |
| 483 | } else { |
| 484 | if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) { |
| 485 | goto err; |
| 486 | } |
| 487 | } |
| 488 | |
| 489 | if (!BN_nnmod(val[0], a, m, ctx)) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 490 | goto err; // 1 |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 491 | } |
| 492 | if (BN_is_zero(val[0])) { |
| 493 | BN_zero(r); |
| 494 | ret = 1; |
| 495 | goto err; |
| 496 | } |
| 497 | |
| 498 | window = BN_window_bits_for_exponent_size(bits); |
| 499 | if (window > 1) { |
| 500 | if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 501 | goto err; // 2 |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 502 | } |
| 503 | j = 1 << (window - 1); |
| 504 | for (i = 1; i < j; i++) { |
| 505 | if (((val[i] = BN_CTX_get(ctx)) == NULL) || |
| 506 | !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) { |
| 507 | goto err; |
| 508 | } |
| 509 | } |
| 510 | } |
| 511 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 512 | start = 1; // This is used to avoid multiplication etc |
| 513 | // when there is only the value '1' in the |
| 514 | // buffer. |
| 515 | wstart = bits - 1; // The top bit of the window |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 516 | |
| 517 | if (!BN_one(r)) { |
| 518 | goto err; |
| 519 | } |
| 520 | |
| 521 | for (;;) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 522 | int wvalue; // The 'value' of the window |
| 523 | int wend; // The bottom bit of the window |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 524 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 525 | if (!BN_is_bit_set(p, wstart)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 526 | if (!start) { |
| 527 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) { |
| 528 | goto err; |
| 529 | } |
| 530 | } |
| 531 | if (wstart == 0) { |
| 532 | break; |
| 533 | } |
| 534 | wstart--; |
| 535 | continue; |
| 536 | } |
| 537 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 538 | // We now have wstart on a 'set' bit, we now need to work out |
| 539 | // how bit a window to do. To do this we need to scan |
| 540 | // forward until the last set bit before the end of the |
| 541 | // window |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 542 | wvalue = 1; |
| 543 | wend = 0; |
| 544 | for (i = 1; i < window; i++) { |
| 545 | if (wstart - i < 0) { |
| 546 | break; |
| 547 | } |
| 548 | if (BN_is_bit_set(p, wstart - i)) { |
| 549 | wvalue <<= (i - wend); |
| 550 | wvalue |= 1; |
| 551 | wend = i; |
| 552 | } |
| 553 | } |
| 554 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 555 | // wend is the size of the current window |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 556 | j = wend + 1; |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 557 | // add the 'bytes above' |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 558 | if (!start) { |
| 559 | for (i = 0; i < j; i++) { |
| 560 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) { |
| 561 | goto err; |
| 562 | } |
| 563 | } |
| 564 | } |
| 565 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 566 | // wvalue will be an odd number < 2^window |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 567 | if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) { |
| 568 | goto err; |
| 569 | } |
| 570 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 571 | // move the 'window' down further |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 572 | wstart -= wend + 1; |
| 573 | start = 0; |
| 574 | if (wstart < 0) { |
| 575 | break; |
| 576 | } |
| 577 | } |
| 578 | ret = 1; |
| 579 | |
| 580 | err: |
| 581 | BN_CTX_end(ctx); |
| 582 | BN_RECP_CTX_free(&recp); |
| 583 | return ret; |
| 584 | } |
| 585 | |
| 586 | int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, |
| 587 | BN_CTX *ctx) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 588 | if (BN_is_odd(m)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 589 | return BN_mod_exp_mont(r, a, p, m, ctx, NULL); |
| 590 | } |
| 591 | |
| 592 | return mod_exp_recp(r, a, p, m, ctx); |
| 593 | } |
| 594 | |
| 595 | int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 596 | const BIGNUM *m, BN_CTX *ctx, const BN_MONT_CTX *mont) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 597 | if (!BN_is_odd(m)) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 598 | OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 599 | return 0; |
| 600 | } |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 601 | int bits = BN_num_bits(p); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 602 | if (bits == 0) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 603 | // x**0 mod 1 is still zero. |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 604 | if (BN_is_one(m)) { |
| 605 | BN_zero(rr); |
| 606 | return 1; |
| 607 | } |
| 608 | return BN_one(rr); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 609 | } |
| 610 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 611 | int ret = 0; |
| 612 | BIGNUM *val[TABLE_SIZE]; |
| 613 | BN_MONT_CTX *new_mont = NULL; |
| 614 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 615 | BN_CTX_start(ctx); |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 616 | BIGNUM *d = BN_CTX_get(ctx); |
| 617 | BIGNUM *r = BN_CTX_get(ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 618 | val[0] = BN_CTX_get(ctx); |
| 619 | if (!d || !r || !val[0]) { |
| 620 | goto err; |
| 621 | } |
| 622 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 623 | // Allocate a montgomery context if it was not supplied by the caller. |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 624 | if (mont == NULL) { |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 625 | new_mont = BN_MONT_CTX_new_for_modulus(m, ctx); |
| 626 | if (new_mont == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 627 | goto err; |
| 628 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 629 | mont = new_mont; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 630 | } |
| 631 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 632 | const BIGNUM *aa; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 633 | if (a->neg || BN_ucmp(a, m) >= 0) { |
| 634 | if (!BN_nnmod(val[0], a, m, ctx)) { |
| 635 | goto err; |
| 636 | } |
| 637 | aa = val[0]; |
| 638 | } else { |
| 639 | aa = a; |
| 640 | } |
| 641 | |
| 642 | if (BN_is_zero(aa)) { |
| 643 | BN_zero(rr); |
| 644 | ret = 1; |
| 645 | goto err; |
| 646 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 647 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 648 | // We exponentiate by looking at sliding windows of the exponent and |
| 649 | // precomputing powers of |aa|. Windows may be shifted so they always end on a |
| 650 | // set bit, so only precompute odd powers. We compute val[i] = aa^(2*i + 1) |
| 651 | // for i = 0 to 2^(window-1), all in Montgomery form. |
| 652 | int window = BN_window_bits_for_exponent_size(bits); |
| 653 | if (!BN_to_montgomery(val[0], aa, mont, ctx)) { |
| 654 | goto err; |
| 655 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 656 | if (window > 1) { |
| 657 | if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) { |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 658 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 659 | } |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 660 | for (int i = 1; i < 1 << (window - 1); i++) { |
| 661 | val[i] = BN_CTX_get(ctx); |
| 662 | if (val[i] == NULL || |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 663 | !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) { |
| 664 | goto err; |
| 665 | } |
| 666 | } |
| 667 | } |
| 668 | |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 669 | if (!bn_one_to_montgomery(r, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 670 | goto err; |
| 671 | } |
| 672 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 673 | int r_is_one = 1; |
| 674 | int wstart = bits - 1; // The top bit of the window. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 675 | for (;;) { |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 676 | if (!BN_is_bit_set(p, wstart)) { |
| 677 | if (!r_is_one && !BN_mod_mul_montgomery(r, r, r, mont, ctx)) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 678 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 679 | } |
| 680 | if (wstart == 0) { |
| 681 | break; |
| 682 | } |
| 683 | wstart--; |
| 684 | continue; |
| 685 | } |
| 686 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 687 | // We now have wstart on a set bit. Find the largest window we can use. |
| 688 | int wvalue = 1; |
| 689 | int wsize = 0; |
| 690 | for (int i = 1; i < window && i <= wstart; i++) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 691 | if (BN_is_bit_set(p, wstart - i)) { |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 692 | wvalue <<= (i - wsize); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 693 | wvalue |= 1; |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 694 | wsize = i; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 695 | } |
| 696 | } |
| 697 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 698 | // Shift |r| to the end of the window. |
| 699 | if (!r_is_one) { |
| 700 | for (int i = 0; i < wsize + 1; i++) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 701 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) { |
| 702 | goto err; |
| 703 | } |
| 704 | } |
| 705 | } |
| 706 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 707 | assert(wvalue & 1); |
| 708 | assert(wvalue < (1 << window)); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 709 | if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) { |
| 710 | goto err; |
| 711 | } |
| 712 | |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 713 | r_is_one = 0; |
| 714 | if (wstart == wsize) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 715 | break; |
| 716 | } |
Robert Sloan | d5c2215 | 2017-11-13 09:22:12 -0800 | [diff] [blame] | 717 | wstart -= wsize + 1; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 718 | } |
| 719 | |
| 720 | if (!BN_from_montgomery(rr, r, mont, ctx)) { |
| 721 | goto err; |
| 722 | } |
| 723 | ret = 1; |
| 724 | |
| 725 | err: |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 726 | BN_MONT_CTX_free(new_mont); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 727 | BN_CTX_end(ctx); |
| 728 | return ret; |
| 729 | } |
| 730 | |
Robert Sloan | 99319a1 | 2017-11-27 10:32:46 -0800 | [diff] [blame] | 731 | int bn_mod_exp_mont_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, |
| 732 | size_t num_a, const BN_ULONG *p, size_t num_p, |
| 733 | const BN_MONT_CTX *mont) { |
Robert Sloan | 99319a1 | 2017-11-27 10:32:46 -0800 | [diff] [blame] | 734 | size_t num_n = mont->N.top; |
| 735 | if (num_n != num_a || num_n != num_r || num_n > BN_SMALL_MAX_WORDS) { |
| 736 | OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| 737 | return 0; |
| 738 | } |
| 739 | if (!BN_is_odd(&mont->N)) { |
| 740 | OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS); |
| 741 | return 0; |
| 742 | } |
| 743 | unsigned bits = 0; |
| 744 | if (num_p != 0) { |
| 745 | bits = BN_num_bits_word(p[num_p - 1]) + (num_p - 1) * BN_BITS2; |
| 746 | } |
| 747 | if (bits == 0) { |
| 748 | OPENSSL_memset(r, 0, num_r * sizeof(BN_ULONG)); |
| 749 | if (!BN_is_one(&mont->N)) { |
| 750 | r[0] = 1; |
| 751 | } |
| 752 | return 1; |
| 753 | } |
| 754 | |
| 755 | // We exponentiate by looking at sliding windows of the exponent and |
| 756 | // precomputing powers of |a|. Windows may be shifted so they always end on a |
| 757 | // set bit, so only precompute odd powers. We compute val[i] = a^(2*i + 1) for |
| 758 | // i = 0 to 2^(window-1), all in Montgomery form. |
| 759 | unsigned window = BN_window_bits_for_exponent_size(bits); |
| 760 | if (window > TABLE_BITS_SMALL) { |
| 761 | window = TABLE_BITS_SMALL; // Tolerate excessively large |p|. |
| 762 | } |
| 763 | int ret = 0; |
| 764 | BN_ULONG val[TABLE_SIZE_SMALL][BN_SMALL_MAX_WORDS]; |
| 765 | OPENSSL_memcpy(val[0], a, num_n * sizeof(BN_ULONG)); |
| 766 | if (window > 1) { |
| 767 | BN_ULONG d[BN_SMALL_MAX_WORDS]; |
| 768 | if (!bn_mod_mul_montgomery_small(d, num_n, val[0], num_n, val[0], num_n, |
| 769 | mont)) { |
| 770 | goto err; |
| 771 | } |
| 772 | for (unsigned i = 1; i < 1u << (window - 1); i++) { |
| 773 | if (!bn_mod_mul_montgomery_small(val[i], num_n, val[i - 1], num_n, d, |
| 774 | num_n, mont)) { |
| 775 | goto err; |
| 776 | } |
| 777 | } |
| 778 | } |
| 779 | |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 780 | if (!bn_one_to_montgomery_small(r, num_r, mont)) { |
Robert Sloan | 99319a1 | 2017-11-27 10:32:46 -0800 | [diff] [blame] | 781 | goto err; |
| 782 | } |
| 783 | |
| 784 | int r_is_one = 1; |
| 785 | unsigned wstart = bits - 1; // The top bit of the window. |
| 786 | for (;;) { |
| 787 | if (!bn_is_bit_set_words(p, num_p, wstart)) { |
| 788 | if (!r_is_one && |
| 789 | !bn_mod_mul_montgomery_small(r, num_r, r, num_r, r, num_r, mont)) { |
| 790 | goto err; |
| 791 | } |
| 792 | if (wstart == 0) { |
| 793 | break; |
| 794 | } |
| 795 | wstart--; |
| 796 | continue; |
| 797 | } |
| 798 | |
| 799 | // We now have wstart on a set bit. Find the largest window we can use. |
| 800 | unsigned wvalue = 1; |
| 801 | unsigned wsize = 0; |
| 802 | for (unsigned i = 1; i < window && i <= wstart; i++) { |
| 803 | if (bn_is_bit_set_words(p, num_p, wstart - i)) { |
| 804 | wvalue <<= (i - wsize); |
| 805 | wvalue |= 1; |
| 806 | wsize = i; |
| 807 | } |
| 808 | } |
| 809 | |
| 810 | // Shift |r| to the end of the window. |
| 811 | if (!r_is_one) { |
| 812 | for (unsigned i = 0; i < wsize + 1; i++) { |
| 813 | if (!bn_mod_mul_montgomery_small(r, num_r, r, num_r, r, num_r, mont)) { |
| 814 | goto err; |
| 815 | } |
| 816 | } |
| 817 | } |
| 818 | |
| 819 | assert(wvalue & 1); |
| 820 | assert(wvalue < (1u << window)); |
| 821 | if (!bn_mod_mul_montgomery_small(r, num_r, r, num_r, val[wvalue >> 1], |
| 822 | num_n, mont)) { |
| 823 | goto err; |
| 824 | } |
| 825 | |
| 826 | r_is_one = 0; |
| 827 | if (wstart == wsize) { |
| 828 | break; |
| 829 | } |
| 830 | wstart -= wsize + 1; |
| 831 | } |
| 832 | |
| 833 | ret = 1; |
| 834 | |
| 835 | err: |
| 836 | OPENSSL_cleanse(val, sizeof(val)); |
| 837 | return ret; |
| 838 | } |
| 839 | |
| 840 | int bn_mod_inverse_prime_mont_small(BN_ULONG *r, size_t num_r, |
| 841 | const BN_ULONG *a, size_t num_a, |
| 842 | const BN_MONT_CTX *mont) { |
| 843 | const BN_ULONG *p = mont->N.d; |
| 844 | size_t num_p = mont->N.top; |
| 845 | if (num_p > BN_SMALL_MAX_WORDS || num_p == 0) { |
| 846 | OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| 847 | return 0; |
| 848 | } |
| 849 | |
| 850 | // Per Fermat's Little Theorem, a^-1 = a^(p-2) (mod p) for p prime. |
| 851 | BN_ULONG p_minus_two[BN_SMALL_MAX_WORDS]; |
| 852 | OPENSSL_memcpy(p_minus_two, p, num_p * sizeof(BN_ULONG)); |
| 853 | if (p_minus_two[0] >= 2) { |
| 854 | p_minus_two[0] -= 2; |
| 855 | } else { |
| 856 | p_minus_two[0] -= 2; |
| 857 | for (size_t i = 1; i < num_p; i++) { |
| 858 | if (p_minus_two[i]-- != 0) { |
| 859 | break; |
| 860 | } |
| 861 | } |
| 862 | } |
| 863 | |
| 864 | return bn_mod_exp_mont_small(r, num_r, a, num_a, p_minus_two, num_p, mont); |
| 865 | } |
| 866 | |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 867 | |
| 868 | // |BN_mod_exp_mont_consttime| stores the precomputed powers in a specific |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 869 | // layout so that accessing any of these table values shows the same access |
| 870 | // pattern as far as cache lines are concerned. The following functions are |
| 871 | // used to transfer a BIGNUM from/to that table. |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 872 | |
| 873 | static void copy_to_prebuf(const BIGNUM *b, int top, unsigned char *buf, |
| 874 | int idx, int window) { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 875 | int i, j; |
| 876 | const int width = 1 << window; |
| 877 | BN_ULONG *table = (BN_ULONG *) buf; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 878 | |
| 879 | if (top > b->top) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 880 | top = b->top; // this works because 'buf' is explicitly zeroed |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 881 | } |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 882 | |
| 883 | for (i = 0, j = idx; i < top; i++, j += width) { |
| 884 | table[j] = b->d[i]; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 885 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 886 | } |
| 887 | |
| 888 | static int copy_from_prebuf(BIGNUM *b, int top, unsigned char *buf, int idx, |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 889 | int window) { |
| 890 | int i, j; |
| 891 | const int width = 1 << window; |
| 892 | volatile BN_ULONG *table = (volatile BN_ULONG *)buf; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 893 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 894 | if (!bn_wexpand(b, top)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 895 | return 0; |
| 896 | } |
| 897 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 898 | if (window <= 3) { |
| 899 | for (i = 0; i < top; i++, table += width) { |
| 900 | BN_ULONG acc = 0; |
| 901 | |
| 902 | for (j = 0; j < width; j++) { |
| 903 | acc |= table[j] & ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1)); |
| 904 | } |
| 905 | |
| 906 | b->d[i] = acc; |
| 907 | } |
| 908 | } else { |
| 909 | int xstride = 1 << (window - 2); |
| 910 | BN_ULONG y0, y1, y2, y3; |
| 911 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 912 | i = idx >> (window - 2); // equivalent of idx / xstride |
| 913 | idx &= xstride - 1; // equivalent of idx % xstride |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 914 | |
| 915 | y0 = (BN_ULONG)0 - (constant_time_eq_int(i, 0) & 1); |
| 916 | y1 = (BN_ULONG)0 - (constant_time_eq_int(i, 1) & 1); |
| 917 | y2 = (BN_ULONG)0 - (constant_time_eq_int(i, 2) & 1); |
| 918 | y3 = (BN_ULONG)0 - (constant_time_eq_int(i, 3) & 1); |
| 919 | |
| 920 | for (i = 0; i < top; i++, table += width) { |
| 921 | BN_ULONG acc = 0; |
| 922 | |
| 923 | for (j = 0; j < xstride; j++) { |
| 924 | acc |= ((table[j + 0 * xstride] & y0) | (table[j + 1 * xstride] & y1) | |
| 925 | (table[j + 2 * xstride] & y2) | (table[j + 3 * xstride] & y3)) & |
| 926 | ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1)); |
| 927 | } |
| 928 | |
| 929 | b->d[i] = acc; |
| 930 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 931 | } |
| 932 | |
| 933 | b->top = top; |
| 934 | bn_correct_top(b); |
| 935 | return 1; |
| 936 | } |
| 937 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 938 | // BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache |
| 939 | // line width of the target processor is at least the following value. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 940 | #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH (64) |
| 941 | #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK \ |
| 942 | (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1) |
| 943 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 944 | // Window sizes optimized for fixed window size modular exponentiation |
| 945 | // algorithm (BN_mod_exp_mont_consttime). |
| 946 | // |
| 947 | // To achieve the security goals of BN_mode_exp_mont_consttime, the maximum |
| 948 | // size of the window must not exceed |
| 949 | // log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). |
| 950 | // |
| 951 | // Window size thresholds are defined for cache line sizes of 32 and 64, cache |
| 952 | // line sizes where log_2(32)=5 and log_2(64)=6 respectively. A window size of |
| 953 | // 7 should only be used on processors that have a 128 byte or greater cache |
| 954 | // line size. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 955 | #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64 |
| 956 | |
| 957 | #define BN_window_bits_for_ctime_exponent_size(b) \ |
| 958 | ((b) > 937 ? 6 : (b) > 306 ? 5 : (b) > 89 ? 4 : (b) > 22 ? 3 : 1) |
| 959 | #define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6) |
| 960 | |
| 961 | #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32 |
| 962 | |
| 963 | #define BN_window_bits_for_ctime_exponent_size(b) \ |
| 964 | ((b) > 306 ? 5 : (b) > 89 ? 4 : (b) > 22 ? 3 : 1) |
| 965 | #define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5) |
| 966 | |
| 967 | #endif |
| 968 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 969 | // Given a pointer value, compute the next address that is a cache line |
| 970 | // multiple. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 971 | #define MOD_EXP_CTIME_ALIGN(x_) \ |
| 972 | ((unsigned char *)(x_) + \ |
| 973 | (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - \ |
| 974 | (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) |
| 975 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 976 | // This variant of BN_mod_exp_mont() uses fixed windows and the special |
| 977 | // precomputation memory layout to limit data-dependency to a minimum |
| 978 | // to protect secret exponents (cf. the hyper-threading timing attacks |
| 979 | // pointed out by Colin Percival, |
| 980 | // http://www.daemonology.net/hyperthreading-considered-harmful/) |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 981 | int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, |
| 982 | const BIGNUM *m, BN_CTX *ctx, |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 983 | const BN_MONT_CTX *mont) { |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 984 | int i, ret = 0, window, wvalue; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 985 | int top; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 986 | BN_MONT_CTX *new_mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 987 | |
| 988 | int numPowers; |
| 989 | unsigned char *powerbufFree = NULL; |
| 990 | int powerbufLen = 0; |
| 991 | unsigned char *powerbuf = NULL; |
| 992 | BIGNUM tmp, am; |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 993 | BIGNUM *new_a = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 994 | |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 995 | if (!BN_is_odd(m)) { |
| 996 | OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS); |
Kenny Root | a04d78d | 2015-09-25 00:26:37 +0000 | [diff] [blame] | 997 | return 0; |
| 998 | } |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 999 | |
| 1000 | top = m->top; |
| 1001 | |
Robert Sloan | 309a31e | 2018-01-29 10:22:47 -0800 | [diff] [blame] | 1002 | // Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak |
| 1003 | // whether the top bits are zero. |
| 1004 | int max_bits = p->top * BN_BITS2; |
| 1005 | int bits = max_bits; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1006 | if (bits == 0) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1007 | // x**0 mod 1 is still zero. |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 1008 | if (BN_is_one(m)) { |
| 1009 | BN_zero(rr); |
| 1010 | return 1; |
| 1011 | } |
| 1012 | return BN_one(rr); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1013 | } |
| 1014 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1015 | // Allocate a montgomery context if it was not supplied by the caller. |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1016 | if (mont == NULL) { |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 1017 | new_mont = BN_MONT_CTX_new_for_modulus(m, ctx); |
| 1018 | if (new_mont == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1019 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1020 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1021 | mont = new_mont; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1022 | } |
| 1023 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1024 | if (a->neg || BN_ucmp(a, m) >= 0) { |
| 1025 | new_a = BN_new(); |
| 1026 | if (new_a == NULL || |
| 1027 | !BN_nnmod(new_a, a, m, ctx)) { |
| 1028 | goto err; |
| 1029 | } |
| 1030 | a = new_a; |
| 1031 | } |
| 1032 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1033 | #ifdef RSAZ_ENABLED |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1034 | // If the size of the operands allow it, perform the optimized |
| 1035 | // RSAZ exponentiation. For further information see |
| 1036 | // crypto/bn/rsaz_exp.c and accompanying assembly modules. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1037 | if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) && |
| 1038 | rsaz_avx2_eligible()) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 1039 | if (!bn_wexpand(rr, 16)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1040 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1041 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1042 | RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, mont->n0[0]); |
| 1043 | rr->top = 16; |
| 1044 | rr->neg = 0; |
| 1045 | bn_correct_top(rr); |
| 1046 | ret = 1; |
| 1047 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1048 | } |
| 1049 | #endif |
| 1050 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1051 | // Get the window size to use with size of p. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1052 | window = BN_window_bits_for_ctime_exponent_size(bits); |
| 1053 | #if defined(OPENSSL_BN_ASM_MONT5) |
| 1054 | if (window >= 5) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1055 | window = 5; // ~5% improvement for RSA2048 sign, and even for RSA4096 |
| 1056 | // reserve space for mont->N.d[] copy |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1057 | powerbufLen += top * sizeof(mont->N.d[0]); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1058 | } |
| 1059 | #endif |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1060 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1061 | // Allocate a buffer large enough to hold all of the pre-computed |
| 1062 | // powers of am, am itself and tmp. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1063 | numPowers = 1 << window; |
| 1064 | powerbufLen += |
| 1065 | sizeof(m->d[0]) * |
| 1066 | (top * numPowers + ((2 * top) > numPowers ? (2 * top) : numPowers)); |
| 1067 | #ifdef alloca |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1068 | if (powerbufLen < 3072) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1069 | powerbufFree = alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1070 | } else |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1071 | #endif |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1072 | { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1073 | if ((powerbufFree = OPENSSL_malloc( |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1074 | powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL) { |
| 1075 | goto err; |
| 1076 | } |
| 1077 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1078 | |
| 1079 | powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1080 | OPENSSL_memset(powerbuf, 0, powerbufLen); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1081 | |
| 1082 | #ifdef alloca |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1083 | if (powerbufLen < 3072) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1084 | powerbufFree = NULL; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1085 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1086 | #endif |
| 1087 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1088 | // lay down tmp and am right after powers table |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1089 | tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); |
| 1090 | am.d = tmp.d + top; |
| 1091 | tmp.top = am.top = 0; |
| 1092 | tmp.dmax = am.dmax = top; |
| 1093 | tmp.neg = am.neg = 0; |
| 1094 | tmp.flags = am.flags = BN_FLG_STATIC_DATA; |
| 1095 | |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 1096 | if (!bn_one_to_montgomery(&tmp, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1097 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1098 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1099 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1100 | // prepare a^1 in Montgomery domain |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1101 | assert(!a->neg); |
| 1102 | assert(BN_ucmp(a, m) < 0); |
| 1103 | if (!BN_to_montgomery(&am, a, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1104 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1105 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1106 | |
| 1107 | #if defined(OPENSSL_BN_ASM_MONT5) |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1108 | // This optimization uses ideas from http://eprint.iacr.org/2011/239, |
| 1109 | // specifically optimization of cache-timing attack countermeasures |
| 1110 | // and pre-computation optimization. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1111 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1112 | // Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as |
| 1113 | // 512-bit RSA is hardly relevant, we omit it to spare size... |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1114 | if (window == 5 && top > 1) { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1115 | const BN_ULONG *n0 = mont->n0; |
| 1116 | BN_ULONG *np; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1117 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1118 | // BN_to_montgomery can contaminate words above .top |
| 1119 | // [in BN_DEBUG[_DEBUG] build]... |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1120 | for (i = am.top; i < top; i++) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1121 | am.d[i] = 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1122 | } |
| 1123 | for (i = tmp.top; i < top; i++) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1124 | tmp.d[i] = 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1125 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1126 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1127 | // copy mont->N.d[] to improve cache locality |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1128 | for (np = am.d + top, i = 0; i < top; i++) { |
| 1129 | np[i] = mont->N.d[i]; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1130 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1131 | |
| 1132 | bn_scatter5(tmp.d, top, powerbuf, 0); |
| 1133 | bn_scatter5(am.d, am.top, powerbuf, 1); |
| 1134 | bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); |
| 1135 | bn_scatter5(tmp.d, top, powerbuf, 2); |
| 1136 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1137 | // same as above, but uses squaring for 1/2 of operations |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1138 | for (i = 4; i < 32; i *= 2) { |
| 1139 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
| 1140 | bn_scatter5(tmp.d, top, powerbuf, i); |
| 1141 | } |
| 1142 | for (i = 3; i < 8; i += 2) { |
| 1143 | int j; |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1144 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1145 | bn_scatter5(tmp.d, top, powerbuf, i); |
| 1146 | for (j = 2 * i; j < 32; j *= 2) { |
| 1147 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
| 1148 | bn_scatter5(tmp.d, top, powerbuf, j); |
| 1149 | } |
| 1150 | } |
| 1151 | for (; i < 16; i += 2) { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1152 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1153 | bn_scatter5(tmp.d, top, powerbuf, i); |
| 1154 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
| 1155 | bn_scatter5(tmp.d, top, powerbuf, 2 * i); |
| 1156 | } |
| 1157 | for (; i < 32; i += 2) { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1158 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1159 | bn_scatter5(tmp.d, top, powerbuf, i); |
| 1160 | } |
| 1161 | |
| 1162 | bits--; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1163 | for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1164 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1165 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1166 | bn_gather5(tmp.d, top, powerbuf, wvalue); |
| 1167 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1168 | // At this point |bits| is 4 mod 5 and at least -1. (|bits| is the first bit |
| 1169 | // that has not been read yet.) |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1170 | assert(bits >= -1 && (bits == -1 || bits % 5 == 4)); |
| 1171 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1172 | // Scan the exponent one window at a time starting from the most |
| 1173 | // significant bits. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1174 | if (top & 7) { |
| 1175 | while (bits >= 0) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1176 | for (wvalue = 0, i = 0; i < 5; i++, bits--) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1177 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1178 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1179 | |
| 1180 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
| 1181 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
| 1182 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
| 1183 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
| 1184 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
| 1185 | bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue); |
| 1186 | } |
| 1187 | } else { |
| 1188 | const uint8_t *p_bytes = (const uint8_t *)p->d; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1189 | assert(bits < max_bits); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1190 | // |p = 0| has been handled as a special case, so |max_bits| is at least |
| 1191 | // one word. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1192 | assert(max_bits >= 64); |
| 1193 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1194 | // If the first bit to be read lands in the last byte, unroll the first |
| 1195 | // iteration to avoid reading past the bounds of |p->d|. (After the first |
| 1196 | // iteration, we are guaranteed to be past the last byte.) Note |bits| |
| 1197 | // here is the top bit, inclusive. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1198 | if (bits - 4 >= max_bits - 8) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1199 | // Read five bits from |bits-4| through |bits|, inclusive. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1200 | wvalue = p_bytes[p->top * BN_BYTES - 1]; |
| 1201 | wvalue >>= (bits - 4) & 7; |
| 1202 | wvalue &= 0x1f; |
| 1203 | bits -= 5; |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1204 | bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1205 | } |
| 1206 | while (bits >= 0) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1207 | // Read five bits from |bits-4| through |bits|, inclusive. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1208 | int first_bit = bits - 4; |
Robert Sloan | a12bf46 | 2017-07-17 07:08:26 -0700 | [diff] [blame] | 1209 | uint16_t val; |
| 1210 | OPENSSL_memcpy(&val, p_bytes + (first_bit >> 3), sizeof(val)); |
| 1211 | val >>= first_bit & 7; |
| 1212 | val &= 0x1f; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1213 | bits -= 5; |
Robert Sloan | a12bf46 | 2017-07-17 07:08:26 -0700 | [diff] [blame] | 1214 | bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, val); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1215 | } |
| 1216 | } |
| 1217 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1218 | ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1219 | tmp.top = top; |
| 1220 | bn_correct_top(&tmp); |
| 1221 | if (ret) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1222 | if (!BN_copy(rr, &tmp)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1223 | ret = 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1224 | } |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1225 | goto err; // non-zero ret means it's not error |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1226 | } |
| 1227 | } else |
| 1228 | #endif |
| 1229 | { |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1230 | copy_to_prebuf(&tmp, top, powerbuf, 0, window); |
| 1231 | copy_to_prebuf(&am, top, powerbuf, 1, window); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1232 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1233 | // If the window size is greater than 1, then calculate |
| 1234 | // val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) |
| 1235 | // (even powers could instead be computed as (a^(i/2))^2 |
| 1236 | // to use the slight performance advantage of sqr over mul). |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1237 | if (window > 1) { |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1238 | if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1239 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1240 | } |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1241 | |
| 1242 | copy_to_prebuf(&tmp, top, powerbuf, 2, window); |
| 1243 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1244 | for (i = 3; i < numPowers; i++) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1245 | // Calculate a^i = a^(i-1) * a |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1246 | if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1247 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1248 | } |
Robert Sloan | b1b54b8 | 2017-11-06 13:50:02 -0800 | [diff] [blame] | 1249 | |
| 1250 | copy_to_prebuf(&tmp, top, powerbuf, i, window); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1251 | } |
| 1252 | } |
| 1253 | |
| 1254 | bits--; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1255 | for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1256 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1257 | } |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1258 | if (!copy_from_prebuf(&tmp, top, powerbuf, wvalue, window)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1259 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1260 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1261 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1262 | // Scan the exponent one window at a time starting from the most |
| 1263 | // significant bits. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1264 | while (bits >= 0) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1265 | wvalue = 0; // The 'value' of the window |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1266 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1267 | // Scan the window, squaring the result as we go |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1268 | for (i = 0; i < window; i++, bits--) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1269 | if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1270 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1271 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1272 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); |
| 1273 | } |
| 1274 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1275 | // Fetch the appropriate pre-computed value from the pre-buf |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1276 | if (!copy_from_prebuf(&am, top, powerbuf, wvalue, window)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1277 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1278 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1279 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1280 | // Multiply the result into the intermediate result |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1281 | if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1282 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1283 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1284 | } |
| 1285 | } |
| 1286 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1287 | // Convert the final result from montgomery to standard format |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1288 | if (!BN_from_montgomery(rr, &tmp, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1289 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1290 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1291 | ret = 1; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1292 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1293 | err: |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1294 | BN_MONT_CTX_free(new_mont); |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1295 | BN_clear_free(new_a); |
Robert Sloan | 2e9e66a | 2017-09-25 09:08:29 -0700 | [diff] [blame] | 1296 | OPENSSL_free(powerbufFree); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1297 | return (ret); |
| 1298 | } |
| 1299 | |
| 1300 | int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1301 | const BIGNUM *m, BN_CTX *ctx, |
| 1302 | const BN_MONT_CTX *mont) { |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 1303 | BIGNUM a_bignum; |
| 1304 | BN_init(&a_bignum); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1305 | |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 1306 | int ret = 0; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1307 | |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 1308 | if (!BN_set_word(&a_bignum, a)) { |
| 1309 | OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1310 | goto err; |
| 1311 | } |
| 1312 | |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 1313 | ret = BN_mod_exp_mont(rr, &a_bignum, p, m, ctx, mont); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1314 | |
| 1315 | err: |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 1316 | BN_free(&a_bignum); |
| 1317 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1318 | return ret; |
| 1319 | } |
| 1320 | |
| 1321 | #define TABLE_SIZE 32 |
| 1322 | |
| 1323 | int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1, |
| 1324 | const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m, |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1325 | BN_CTX *ctx, const BN_MONT_CTX *mont) { |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 1326 | BIGNUM tmp; |
| 1327 | BN_init(&tmp); |
| 1328 | |
| 1329 | int ret = 0; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1330 | BN_MONT_CTX *new_mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1331 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1332 | // Allocate a montgomery context if it was not supplied by the caller. |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1333 | if (mont == NULL) { |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 1334 | new_mont = BN_MONT_CTX_new_for_modulus(m, ctx); |
| 1335 | if (new_mont == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1336 | goto err; |
| 1337 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1338 | mont = new_mont; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1339 | } |
| 1340 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1341 | // BN_mod_mul_montgomery removes one Montgomery factor, so passing one |
| 1342 | // Montgomery-encoded and one non-Montgomery-encoded value gives a |
| 1343 | // non-Montgomery-encoded result. |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 1344 | if (!BN_mod_exp_mont(rr, a1, p1, m, ctx, mont) || |
| 1345 | !BN_mod_exp_mont(&tmp, a2, p2, m, ctx, mont) || |
| 1346 | !BN_to_montgomery(rr, rr, mont, ctx) || |
| 1347 | !BN_mod_mul_montgomery(rr, rr, &tmp, mont, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1348 | goto err; |
| 1349 | } |
| 1350 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1351 | ret = 1; |
| 1352 | |
| 1353 | err: |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1354 | BN_MONT_CTX_free(new_mont); |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 1355 | BN_free(&tmp); |
| 1356 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1357 | return ret; |
| 1358 | } |