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 <string.h> 113 114 #include <openssl/err.h> 115 #include <openssl/mem.h> 116 #include <openssl/thread.h> 117 #include <openssl/type_check.h> 118 119 #include "internal.h" 120 #include "../../internal.h" 121 122 123 #if !defined(OPENSSL_NO_ASM) && \ 124 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \ 125 defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64)) 126 #define OPENSSL_BN_ASM_MONT 127 #endif 128 129 130 BN_MONT_CTX *BN_MONT_CTX_new(void) { 131 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX)); 132 133 if (ret == NULL) { 134 return NULL; 135 } 136 137 OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX)); 138 BN_init(&ret->RR); 139 BN_init(&ret->N); 140 141 return ret; 142 } 143 144 void BN_MONT_CTX_free(BN_MONT_CTX *mont) { 145 if (mont == NULL) { 146 return; 147 } 148 149 BN_free(&mont->RR); 150 BN_free(&mont->N); 151 OPENSSL_free(mont); 152 } 153 154 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) { 155 if (to == from) { 156 return to; 157 } 158 159 if (!BN_copy(&to->RR, &from->RR) || 160 !BN_copy(&to->N, &from->N)) { 161 return NULL; 162 } 163 to->n0[0] = from->n0[0]; 164 to->n0[1] = from->n0[1]; 165 return to; 166 } 167 168 OPENSSL_COMPILE_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2, 169 BN_MONT_CTX_N0_LIMBS_VALUE_INVALID); 170 OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS == 171 sizeof(uint64_t), BN_MONT_CTX_set_64_bit_mismatch); 172 173 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) { 174 if (BN_is_zero(mod)) { 175 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO); 176 return 0; 177 } 178 if (!BN_is_odd(mod)) { 179 OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS); 180 return 0; 181 } 182 if (BN_is_negative(mod)) { 183 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); 184 return 0; 185 } 186 187 // Save the modulus. 188 if (!BN_copy(&mont->N, mod)) { 189 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); 190 return 0; 191 } 192 // |mont->N| is always stored minimally. Computing RR efficiently leaks the 193 // size of the modulus. While the modulus may be private in RSA (one of the 194 // primes), their sizes are public, so this is fine. 195 bn_correct_top(&mont->N); 196 197 // Find n0 such that n0 * N == -1 (mod r). 198 // 199 // Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the 200 // others, we could use a shorter R value and use faster |BN_ULONG|-based 201 // math instead of |uint64_t|-based math, which would be double-precision. 202 // However, currently only the assembler files know which is which. 203 uint64_t n0 = bn_mont_n0(&mont->N); 204 mont->n0[0] = (BN_ULONG)n0; 205 #if BN_MONT_CTX_N0_LIMBS == 2 206 mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2); 207 #else 208 mont->n0[1] = 0; 209 #endif 210 211 // Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS2 such that R 212 // > mod. Even though the assembly on some 32-bit platforms works with 64-bit 213 // values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS * 214 // BN_BITS2|, is correct because R**2 will still be a multiple of the latter 215 // as |BN_MONT_CTX_N0_LIMBS| is either one or two. 216 // 217 // XXX: This is not constant time with respect to |mont->N|, but it should be. 218 unsigned lgBigR = mont->N.top * BN_BITS2; 219 if (!bn_mod_exp_base_2_vartime(&mont->RR, lgBigR * 2, &mont->N)) { 220 return 0; 221 } 222 223 return 1; 224 } 225 226 BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod, BN_CTX *ctx) { 227 BN_MONT_CTX *mont = BN_MONT_CTX_new(); 228 if (mont == NULL || 229 !BN_MONT_CTX_set(mont, mod, ctx)) { 230 BN_MONT_CTX_free(mont); 231 return NULL; 232 } 233 return mont; 234 } 235 236 int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, 237 const BIGNUM *mod, BN_CTX *bn_ctx) { 238 CRYPTO_MUTEX_lock_read(lock); 239 BN_MONT_CTX *ctx = *pmont; 240 CRYPTO_MUTEX_unlock_read(lock); 241 242 if (ctx) { 243 return 1; 244 } 245 246 CRYPTO_MUTEX_lock_write(lock); 247 if (*pmont == NULL) { 248 *pmont = BN_MONT_CTX_new_for_modulus(mod, bn_ctx); 249 } 250 const int ok = *pmont != NULL; 251 CRYPTO_MUTEX_unlock_write(lock); 252 return ok; 253 } 254 255 int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, 256 BN_CTX *ctx) { 257 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx); 258 } 259 260 static int bn_from_montgomery_in_place(BN_ULONG *r, size_t num_r, BN_ULONG *a, 261 size_t num_a, const BN_MONT_CTX *mont) { 262 const BN_ULONG *n = mont->N.d; 263 size_t num_n = mont->N.top; 264 if (num_r != num_n || num_a != 2 * num_n) { 265 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 266 return 0; 267 } 268 269 // Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On 270 // input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r| 271 // includes |carry| which is stored separately. 272 BN_ULONG n0 = mont->n0[0]; 273 BN_ULONG carry = 0; 274 for (size_t i = 0; i < num_n; i++) { 275 BN_ULONG v = bn_mul_add_words(a + i, n, num_n, a[i] * n0); 276 v += carry + a[i + num_n]; 277 carry |= (v != a[i + num_n]); 278 carry &= (v <= a[i + num_n]); 279 a[i + num_n] = v; 280 } 281 282 // Shift |num_n| words to divide by R. We have |a| < 2 * |n|. Note that |a| 283 // includes |carry| which is stored separately. 284 a += num_n; 285 286 // |a| thus requires at most one additional subtraction |n| to be reduced. 287 // Subtract |n| and select the answer in constant time. 288 OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t), 289 crypto_word_t_too_small); 290 BN_ULONG v = bn_sub_words(r, a, n, num_n) - carry; 291 // |v| is one if |a| - |n| underflowed or zero if it did not. Note |v| cannot 292 // be -1. That would imply the subtraction did not fit in |num_n| words, and 293 // we know at most one subtraction is needed. 294 v = 0u - v; 295 for (size_t i = 0; i < num_n; i++) { 296 r[i] = constant_time_select_w(v, a[i], r[i]); 297 a[i] = 0; 298 } 299 return 1; 300 } 301 302 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, 303 const BN_MONT_CTX *mont) { 304 if (r->neg) { 305 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); 306 return 0; 307 } 308 309 const BIGNUM *n = &mont->N; 310 if (n->top == 0) { 311 ret->top = 0; 312 return 1; 313 } 314 315 int max = (2 * n->top); // carry is stored separately 316 if (!bn_resize_words(r, max) || 317 !bn_wexpand(ret, n->top)) { 318 return 0; 319 } 320 ret->top = n->top; 321 322 if (!bn_from_montgomery_in_place(ret->d, ret->top, r->d, r->top, mont)) { 323 return 0; 324 } 325 ret->neg = 0; 326 327 bn_correct_top(r); 328 bn_correct_top(ret); 329 return 1; 330 } 331 332 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont, 333 BN_CTX *ctx) { 334 int ret = 0; 335 BIGNUM *t; 336 337 BN_CTX_start(ctx); 338 t = BN_CTX_get(ctx); 339 if (t == NULL || 340 !BN_copy(t, a)) { 341 goto err; 342 } 343 344 ret = BN_from_montgomery_word(r, t, mont); 345 346 err: 347 BN_CTX_end(ctx); 348 349 return ret; 350 } 351 352 int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx) { 353 // If the high bit of |n| is set, R = 2^(top*BN_BITS2) < 2 * |n|, so we 354 // compute R - |n| rather than perform Montgomery reduction. 355 const BIGNUM *n = &mont->N; 356 if (n->top > 0 && (n->d[n->top - 1] >> (BN_BITS2 - 1)) != 0) { 357 if (!bn_wexpand(r, n->top)) { 358 return 0; 359 } 360 r->d[0] = 0 - n->d[0]; 361 for (int i = 1; i < n->top; i++) { 362 r->d[i] = ~n->d[i]; 363 } 364 r->top = n->top; 365 r->neg = 0; 366 // The upper words will be zero if the corresponding words of |n| were 367 // 0xfff[...], so call |bn_correct_top|. 368 bn_correct_top(r); 369 return 1; 370 } 371 372 return BN_from_montgomery(r, &mont->RR, mont, ctx); 373 } 374 375 static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a, 376 const BIGNUM *b, 377 const BN_MONT_CTX *mont, 378 BN_CTX *ctx) { 379 int ret = 0; 380 381 BN_CTX_start(ctx); 382 BIGNUM *tmp = BN_CTX_get(ctx); 383 if (tmp == NULL) { 384 goto err; 385 } 386 387 if (a == b) { 388 if (!BN_sqr(tmp, a, ctx)) { 389 goto err; 390 } 391 } else { 392 if (!BN_mul(tmp, a, b, ctx)) { 393 goto err; 394 } 395 } 396 397 // reduce from aRR to aR 398 if (!BN_from_montgomery_word(r, tmp, mont)) { 399 goto err; 400 } 401 402 ret = 1; 403 404 err: 405 BN_CTX_end(ctx); 406 return ret; 407 } 408 409 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 410 const BN_MONT_CTX *mont, BN_CTX *ctx) { 411 if (a->neg || b->neg) { 412 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); 413 return 0; 414 } 415 416 #if defined(OPENSSL_BN_ASM_MONT) 417 // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86. 418 int num = mont->N.top; 419 if (num >= (128 / BN_BITS2) && 420 a->top == num && 421 b->top == num) { 422 if (!bn_wexpand(r, num)) { 423 return 0; 424 } 425 if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { 426 // The check above ensures this won't happen. 427 assert(0); 428 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); 429 return 0; 430 } 431 r->neg = 0; 432 r->top = num; 433 bn_correct_top(r); 434 435 return 1; 436 } 437 #endif 438 439 return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx); 440 } 441 442 int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont) { 443 return !BN_is_negative(bn) && 444 bn_fits_in_words(bn, mont->N.top); 445 } 446 447 int bn_to_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, 448 size_t num_a, const BN_MONT_CTX *mont) { 449 return bn_mod_mul_montgomery_small(r, num_r, a, num_a, mont->RR.d, 450 mont->RR.top, mont); 451 } 452 453 int bn_from_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, 454 size_t num_a, const BN_MONT_CTX *mont) { 455 size_t num_n = mont->N.top; 456 if (num_a > 2 * num_n || num_r != num_n || num_n > BN_SMALL_MAX_WORDS) { 457 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 458 return 0; 459 } 460 BN_ULONG tmp[BN_SMALL_MAX_WORDS * 2]; 461 size_t num_tmp = 2 * num_n; 462 OPENSSL_memcpy(tmp, a, num_a * sizeof(BN_ULONG)); 463 OPENSSL_memset(tmp + num_a, 0, (num_tmp - num_a) * sizeof(BN_ULONG)); 464 int ret = bn_from_montgomery_in_place(r, num_r, tmp, num_tmp, mont); 465 OPENSSL_cleanse(tmp, num_tmp * sizeof(BN_ULONG)); 466 return ret; 467 } 468 469 int bn_one_to_montgomery_small(BN_ULONG *r, size_t num_r, 470 const BN_MONT_CTX *mont) { 471 const BN_ULONG *n = mont->N.d; 472 size_t num_n = mont->N.top; 473 if (num_n == 0 || num_r != num_n) { 474 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 475 return 0; 476 } 477 478 // If the high bit of |n| is set, R = 2^(num_n*BN_BITS2) < 2 * |n|, so we 479 // compute R - |n| rather than perform Montgomery reduction. 480 if (num_n > 0 && (n[num_n - 1] >> (BN_BITS2 - 1)) != 0) { 481 r[0] = 0 - n[0]; 482 for (size_t i = 1; i < num_n; i++) { 483 r[i] = ~n[i]; 484 } 485 return 1; 486 } 487 488 return bn_from_montgomery_small(r, num_r, mont->RR.d, mont->RR.top, mont); 489 } 490 491 int bn_mod_mul_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, 492 size_t num_a, const BN_ULONG *b, size_t num_b, 493 const BN_MONT_CTX *mont) { 494 size_t num_n = mont->N.top; 495 if (num_r != num_n || num_a + num_b > 2 * num_n || 496 num_n > BN_SMALL_MAX_WORDS) { 497 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 498 return 0; 499 } 500 501 #if defined(OPENSSL_BN_ASM_MONT) 502 // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86. 503 if (num_n >= (128 / BN_BITS2) && 504 num_a == num_n && 505 num_b == num_n) { 506 if (!bn_mul_mont(r, a, b, mont->N.d, mont->n0, num_n)) { 507 assert(0); // The check above ensures this won't happen. 508 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); 509 return 0; 510 } 511 return 1; 512 } 513 #endif 514 515 // Compute the product. 516 BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS]; 517 size_t num_tmp = 2 * num_n; 518 size_t num_ab = num_a + num_b; 519 if (a == b && num_a == num_b) { 520 if (!bn_sqr_small(tmp, num_ab, a, num_a)) { 521 return 0; 522 } 523 } else if (!bn_mul_small(tmp, num_ab, a, num_a, b, num_b)) { 524 return 0; 525 } 526 527 // Zero-extend to full width and reduce. 528 OPENSSL_memset(tmp + num_ab, 0, (num_tmp - num_ab) * sizeof(BN_ULONG)); 529 int ret = bn_from_montgomery_in_place(r, num_r, tmp, num_tmp, mont); 530 OPENSSL_cleanse(tmp, num_tmp * sizeof(BN_ULONG)); 531 return ret; 532 } 533
