1 /* Copyright (C) 1995-1998 Eric Young (eay (at) cryptsoft.com) 2 * All rights reserved. 3 * 4 * This package is an SSL implementation written 5 * by Eric Young (eay (at) 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 (at) 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 (at) 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 (at) 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) 1998-2006 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 (at) 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 (at) cryptsoft.com). This product includes software written by Tim 107 * Hudson (tjh (at) cryptsoft.com). */ 108 109 #include <openssl/bn.h> 110 111 #include <assert.h> 112 #include <stdio.h> 113 #include <stdlib.h> 114 #include <string.h> 115 116 #include <openssl/err.h> 117 #include <openssl/mem.h> 118 #include <openssl/thread.h> 119 #include <openssl/type_check.h> 120 121 #include "internal.h" 122 #include "../../internal.h" 123 124 125 BN_MONT_CTX *BN_MONT_CTX_new(void) { 126 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX)); 127 128 if (ret == NULL) { 129 return NULL; 130 } 131 132 OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX)); 133 BN_init(&ret->RR); 134 BN_init(&ret->N); 135 136 return ret; 137 } 138 139 void BN_MONT_CTX_free(BN_MONT_CTX *mont) { 140 if (mont == NULL) { 141 return; 142 } 143 144 BN_free(&mont->RR); 145 BN_free(&mont->N); 146 OPENSSL_free(mont); 147 } 148 149 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) { 150 if (to == from) { 151 return to; 152 } 153 154 if (!BN_copy(&to->RR, &from->RR) || 155 !BN_copy(&to->N, &from->N)) { 156 return NULL; 157 } 158 to->n0[0] = from->n0[0]; 159 to->n0[1] = from->n0[1]; 160 return to; 161 } 162 163 static int bn_mont_ctx_set_N_and_n0(BN_MONT_CTX *mont, const BIGNUM *mod) { 164 if (BN_is_zero(mod)) { 165 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO); 166 return 0; 167 } 168 if (!BN_is_odd(mod)) { 169 OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS); 170 return 0; 171 } 172 if (BN_is_negative(mod)) { 173 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); 174 return 0; 175 } 176 177 // Save the modulus. 178 if (!BN_copy(&mont->N, mod)) { 179 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); 180 return 0; 181 } 182 // |mont->N| is always stored minimally. Computing RR efficiently leaks the 183 // size of the modulus. While the modulus may be private in RSA (one of the 184 // primes), their sizes are public, so this is fine. 185 bn_set_minimal_width(&mont->N); 186 187 // Find n0 such that n0 * N == -1 (mod r). 188 // 189 // Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the 190 // others, we could use a shorter R value and use faster |BN_ULONG|-based 191 // math instead of |uint64_t|-based math, which would be double-precision. 192 // However, currently only the assembler files know which is which. 193 OPENSSL_STATIC_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2, 194 "BN_MONT_CTX_N0_LIMBS value is invalid"); 195 OPENSSL_STATIC_ASSERT( 196 sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS == sizeof(uint64_t), 197 "uint64_t is insufficient precision for n0"); 198 uint64_t n0 = bn_mont_n0(&mont->N); 199 mont->n0[0] = (BN_ULONG)n0; 200 #if BN_MONT_CTX_N0_LIMBS == 2 201 mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2); 202 #else 203 mont->n0[1] = 0; 204 #endif 205 return 1; 206 } 207 208 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) { 209 if (!bn_mont_ctx_set_N_and_n0(mont, mod)) { 210 return 0; 211 } 212 213 BN_CTX *new_ctx = NULL; 214 if (ctx == NULL) { 215 new_ctx = BN_CTX_new(); 216 if (new_ctx == NULL) { 217 return 0; 218 } 219 ctx = new_ctx; 220 } 221 222 // Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS2 such that R 223 // > mod. Even though the assembly on some 32-bit platforms works with 64-bit 224 // values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS * 225 // BN_BITS2|, is correct because R**2 will still be a multiple of the latter 226 // as |BN_MONT_CTX_N0_LIMBS| is either one or two. 227 unsigned lgBigR = mont->N.width * BN_BITS2; 228 BN_zero(&mont->RR); 229 int ok = BN_set_bit(&mont->RR, lgBigR * 2) && 230 BN_mod(&mont->RR, &mont->RR, &mont->N, ctx) && 231 bn_resize_words(&mont->RR, mont->N.width); 232 BN_CTX_free(new_ctx); 233 return ok; 234 } 235 236 BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod, BN_CTX *ctx) { 237 BN_MONT_CTX *mont = BN_MONT_CTX_new(); 238 if (mont == NULL || 239 !BN_MONT_CTX_set(mont, mod, ctx)) { 240 BN_MONT_CTX_free(mont); 241 return NULL; 242 } 243 return mont; 244 } 245 246 BN_MONT_CTX *BN_MONT_CTX_new_consttime(const BIGNUM *mod, BN_CTX *ctx) { 247 BN_MONT_CTX *mont = BN_MONT_CTX_new(); 248 if (mont == NULL || 249 !bn_mont_ctx_set_N_and_n0(mont, mod)) { 250 goto err; 251 } 252 unsigned lgBigR = mont->N.width * BN_BITS2; 253 if (!bn_mod_exp_base_2_consttime(&mont->RR, lgBigR * 2, &mont->N, ctx) || 254 !bn_resize_words(&mont->RR, mont->N.width)) { 255 goto err; 256 } 257 return mont; 258 259 err: 260 BN_MONT_CTX_free(mont); 261 return NULL; 262 } 263 264 int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, 265 const BIGNUM *mod, BN_CTX *bn_ctx) { 266 CRYPTO_MUTEX_lock_read(lock); 267 BN_MONT_CTX *ctx = *pmont; 268 CRYPTO_MUTEX_unlock_read(lock); 269 270 if (ctx) { 271 return 1; 272 } 273 274 CRYPTO_MUTEX_lock_write(lock); 275 if (*pmont == NULL) { 276 *pmont = BN_MONT_CTX_new_for_modulus(mod, bn_ctx); 277 } 278 const int ok = *pmont != NULL; 279 CRYPTO_MUTEX_unlock_write(lock); 280 return ok; 281 } 282 283 int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, 284 BN_CTX *ctx) { 285 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx); 286 } 287 288 static int bn_from_montgomery_in_place(BN_ULONG *r, size_t num_r, BN_ULONG *a, 289 size_t num_a, const BN_MONT_CTX *mont) { 290 const BN_ULONG *n = mont->N.d; 291 size_t num_n = mont->N.width; 292 if (num_r != num_n || num_a != 2 * num_n) { 293 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 294 return 0; 295 } 296 297 // Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On 298 // input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r| 299 // includes |carry| which is stored separately. 300 BN_ULONG n0 = mont->n0[0]; 301 BN_ULONG carry = 0; 302 for (size_t i = 0; i < num_n; i++) { 303 BN_ULONG v = bn_mul_add_words(a + i, n, num_n, a[i] * n0); 304 v += carry + a[i + num_n]; 305 carry |= (v != a[i + num_n]); 306 carry &= (v <= a[i + num_n]); 307 a[i + num_n] = v; 308 } 309 310 // Shift |num_n| words to divide by R. We have |a| < 2 * |n|. Note that |a| 311 // includes |carry| which is stored separately. 312 a += num_n; 313 314 // |a| thus requires at most one additional subtraction |n| to be reduced. 315 bn_reduce_once(r, a, carry, n, num_n); 316 return 1; 317 } 318 319 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, 320 const BN_MONT_CTX *mont) { 321 if (r->neg) { 322 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); 323 return 0; 324 } 325 326 const BIGNUM *n = &mont->N; 327 if (n->width == 0) { 328 ret->width = 0; 329 return 1; 330 } 331 332 int max = 2 * n->width; // carry is stored separately 333 if (!bn_resize_words(r, max) || 334 !bn_wexpand(ret, n->width)) { 335 return 0; 336 } 337 338 ret->width = n->width; 339 ret->neg = 0; 340 return bn_from_montgomery_in_place(ret->d, ret->width, r->d, r->width, mont); 341 } 342 343 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont, 344 BN_CTX *ctx) { 345 int ret = 0; 346 BIGNUM *t; 347 348 BN_CTX_start(ctx); 349 t = BN_CTX_get(ctx); 350 if (t == NULL || 351 !BN_copy(t, a)) { 352 goto err; 353 } 354 355 ret = BN_from_montgomery_word(r, t, mont); 356 357 err: 358 BN_CTX_end(ctx); 359 360 return ret; 361 } 362 363 int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx) { 364 // If the high bit of |n| is set, R = 2^(width*BN_BITS2) < 2 * |n|, so we 365 // compute R - |n| rather than perform Montgomery reduction. 366 const BIGNUM *n = &mont->N; 367 if (n->width > 0 && (n->d[n->width - 1] >> (BN_BITS2 - 1)) != 0) { 368 if (!bn_wexpand(r, n->width)) { 369 return 0; 370 } 371 r->d[0] = 0 - n->d[0]; 372 for (int i = 1; i < n->width; i++) { 373 r->d[i] = ~n->d[i]; 374 } 375 r->width = n->width; 376 r->neg = 0; 377 return 1; 378 } 379 380 return BN_from_montgomery(r, &mont->RR, mont, ctx); 381 } 382 383 static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a, 384 const BIGNUM *b, 385 const BN_MONT_CTX *mont, 386 BN_CTX *ctx) { 387 int ret = 0; 388 389 BN_CTX_start(ctx); 390 BIGNUM *tmp = BN_CTX_get(ctx); 391 if (tmp == NULL) { 392 goto err; 393 } 394 395 if (a == b) { 396 if (!bn_sqr_consttime(tmp, a, ctx)) { 397 goto err; 398 } 399 } else { 400 if (!bn_mul_consttime(tmp, a, b, ctx)) { 401 goto err; 402 } 403 } 404 405 // reduce from aRR to aR 406 if (!BN_from_montgomery_word(r, tmp, mont)) { 407 goto err; 408 } 409 410 ret = 1; 411 412 err: 413 BN_CTX_end(ctx); 414 return ret; 415 } 416 417 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 418 const BN_MONT_CTX *mont, BN_CTX *ctx) { 419 if (a->neg || b->neg) { 420 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); 421 return 0; 422 } 423 424 #if defined(OPENSSL_BN_ASM_MONT) 425 // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86. 426 int num = mont->N.width; 427 if (num >= (128 / BN_BITS2) && 428 a->width == num && 429 b->width == num) { 430 if (!bn_wexpand(r, num)) { 431 return 0; 432 } 433 if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { 434 // The check above ensures this won't happen. 435 assert(0); 436 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); 437 return 0; 438 } 439 r->neg = 0; 440 r->width = num; 441 return 1; 442 } 443 #endif 444 445 return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx); 446 } 447 448 int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont) { 449 return !BN_is_negative(bn) && 450 bn_fits_in_words(bn, mont->N.width); 451 } 452 453 void bn_to_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num, 454 const BN_MONT_CTX *mont) { 455 bn_mod_mul_montgomery_small(r, a, mont->RR.d, num, mont); 456 } 457 458 void bn_from_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num, 459 const BN_MONT_CTX *mont) { 460 if (num != (size_t)mont->N.width || num > BN_SMALL_MAX_WORDS) { 461 abort(); 462 } 463 BN_ULONG tmp[BN_SMALL_MAX_WORDS * 2]; 464 OPENSSL_memcpy(tmp, a, num * sizeof(BN_ULONG)); 465 OPENSSL_memset(tmp + num, 0, num * sizeof(BN_ULONG)); 466 if (!bn_from_montgomery_in_place(r, num, tmp, 2 * num, mont)) { 467 abort(); 468 } 469 OPENSSL_cleanse(tmp, 2 * num * sizeof(BN_ULONG)); 470 } 471 472 void bn_mod_mul_montgomery_small(BN_ULONG *r, const BN_ULONG *a, 473 const BN_ULONG *b, size_t num, 474 const BN_MONT_CTX *mont) { 475 if (num != (size_t)mont->N.width || num > BN_SMALL_MAX_WORDS) { 476 abort(); 477 } 478 479 #if defined(OPENSSL_BN_ASM_MONT) 480 // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86. 481 if (num >= (128 / BN_BITS2)) { 482 if (!bn_mul_mont(r, a, b, mont->N.d, mont->n0, num)) { 483 abort(); // The check above ensures this won't happen. 484 } 485 return; 486 } 487 #endif 488 489 // Compute the product. 490 BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS]; 491 if (a == b) { 492 bn_sqr_small(tmp, 2 * num, a, num); 493 } else { 494 bn_mul_small(tmp, 2 * num, a, num, b, num); 495 } 496 497 // Reduce. 498 if (!bn_from_montgomery_in_place(r, num, tmp, 2 * num, mont)) { 499 abort(); 500 } 501 OPENSSL_cleanse(tmp, 2 * num * sizeof(BN_ULONG)); 502 } 503