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> 117 118 #include "internal.h" 119 #include "../internal.h" 120 121 122 #if !defined(OPENSSL_NO_ASM) && \ 123 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \ 124 defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64)) 125 #define OPENSSL_BN_ASM_MONT 126 #endif 127 128 static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a, 129 const BIGNUM *b, 130 const BN_MONT_CTX *mont, BN_CTX *ctx); 131 132 133 BN_MONT_CTX *BN_MONT_CTX_new(void) { 134 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX)); 135 136 if (ret == NULL) { 137 return NULL; 138 } 139 140 OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX)); 141 BN_init(&ret->RR); 142 BN_init(&ret->N); 143 144 return ret; 145 } 146 147 void BN_MONT_CTX_free(BN_MONT_CTX *mont) { 148 if (mont == NULL) { 149 return; 150 } 151 152 BN_free(&mont->RR); 153 BN_free(&mont->N); 154 OPENSSL_free(mont); 155 } 156 157 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) { 158 if (to == from) { 159 return to; 160 } 161 162 if (!BN_copy(&to->RR, &from->RR) || 163 !BN_copy(&to->N, &from->N)) { 164 return NULL; 165 } 166 to->n0[0] = from->n0[0]; 167 to->n0[1] = from->n0[1]; 168 return to; 169 } 170 171 OPENSSL_COMPILE_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2, 172 BN_MONT_CTX_N0_LIMBS_VALUE_INVALID); 173 OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS == 174 sizeof(uint64_t), BN_MONT_CTX_set_64_bit_mismatch); 175 176 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) { 177 if (BN_is_zero(mod)) { 178 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO); 179 return 0; 180 } 181 if (!BN_is_odd(mod)) { 182 OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS); 183 return 0; 184 } 185 if (BN_is_negative(mod)) { 186 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); 187 return 0; 188 } 189 190 /* Save the modulus. */ 191 if (!BN_copy(&mont->N, mod)) { 192 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); 193 return 0; 194 } 195 196 /* Find n0 such that n0 * N == -1 (mod r). 197 * 198 * Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the 199 * others, we could use a shorter R value and use faster |BN_ULONG|-based 200 * math instead of |uint64_t|-based math, which would be double-precision. 201 * However, currently only the assembler files know which is which. */ 202 uint64_t n0 = bn_mont_n0(mod); 203 mont->n0[0] = (BN_ULONG)n0; 204 #if BN_MONT_CTX_N0_LIMBS == 2 205 mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2); 206 #else 207 mont->n0[1] = 0; 208 #endif 209 210 /* Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS such that R 211 * > mod. Even though the assembly on some 32-bit platforms works with 64-bit 212 * values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS * 213 * BN_BITS2|, is correct because R**2 will still be a multiple of the latter 214 * as |BN_MONT_CTX_N0_LIMBS| is either one or two. 215 * 216 * XXX: This is not constant time with respect to |mont->N|, but it should 217 * be. */ 218 unsigned lgBigR = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * 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 int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, 227 const BIGNUM *mod, BN_CTX *bn_ctx) { 228 CRYPTO_MUTEX_lock_read(lock); 229 BN_MONT_CTX *ctx = *pmont; 230 CRYPTO_MUTEX_unlock_read(lock); 231 232 if (ctx) { 233 return 1; 234 } 235 236 CRYPTO_MUTEX_lock_write(lock); 237 ctx = *pmont; 238 if (ctx) { 239 goto out; 240 } 241 242 ctx = BN_MONT_CTX_new(); 243 if (ctx == NULL) { 244 goto out; 245 } 246 if (!BN_MONT_CTX_set(ctx, mod, bn_ctx)) { 247 BN_MONT_CTX_free(ctx); 248 ctx = NULL; 249 goto out; 250 } 251 *pmont = ctx; 252 253 out: 254 CRYPTO_MUTEX_unlock_write(lock); 255 return ctx != NULL; 256 } 257 258 int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, 259 BN_CTX *ctx) { 260 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx); 261 } 262 263 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, 264 const BN_MONT_CTX *mont) { 265 BN_ULONG *ap, *np, *rp, n0, v, carry; 266 int nl, max, i; 267 268 const BIGNUM *n = &mont->N; 269 nl = n->top; 270 if (nl == 0) { 271 ret->top = 0; 272 return 1; 273 } 274 275 max = (2 * nl); /* carry is stored separately */ 276 if (bn_wexpand(r, max) == NULL) { 277 return 0; 278 } 279 280 r->neg ^= n->neg; 281 np = n->d; 282 rp = r->d; 283 284 /* clear the top words of T */ 285 if (max > r->top) { 286 OPENSSL_memset(&rp[r->top], 0, (max - r->top) * sizeof(BN_ULONG)); 287 } 288 289 r->top = max; 290 n0 = mont->n0[0]; 291 292 for (carry = 0, i = 0; i < nl; i++, rp++) { 293 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); 294 v = (v + carry + rp[nl]) & BN_MASK2; 295 carry |= (v != rp[nl]); 296 carry &= (v <= rp[nl]); 297 rp[nl] = v; 298 } 299 300 if (bn_wexpand(ret, nl) == NULL) { 301 return 0; 302 } 303 ret->top = nl; 304 ret->neg = r->neg; 305 306 rp = ret->d; 307 ap = &(r->d[nl]); 308 309 { 310 BN_ULONG *nrp; 311 uintptr_t m; 312 313 v = bn_sub_words(rp, ap, np, nl) - carry; 314 /* if subtraction result is real, then trick unconditional memcpy below to 315 * perform in-place "refresh" instead of actual copy. */ 316 m = (0u - (uintptr_t)v); 317 nrp = (BN_ULONG *)(((uintptr_t)rp & ~m) | ((uintptr_t)ap & m)); 318 319 for (i = 0, nl -= 4; i < nl; i += 4) { 320 BN_ULONG t1, t2, t3, t4; 321 322 t1 = nrp[i + 0]; 323 t2 = nrp[i + 1]; 324 t3 = nrp[i + 2]; 325 ap[i + 0] = 0; 326 t4 = nrp[i + 3]; 327 ap[i + 1] = 0; 328 rp[i + 0] = t1; 329 ap[i + 2] = 0; 330 rp[i + 1] = t2; 331 ap[i + 3] = 0; 332 rp[i + 2] = t3; 333 rp[i + 3] = t4; 334 } 335 336 for (nl += 4; i < nl; i++) { 337 rp[i] = nrp[i], ap[i] = 0; 338 } 339 } 340 341 bn_correct_top(r); 342 bn_correct_top(ret); 343 344 return 1; 345 } 346 347 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont, 348 BN_CTX *ctx) { 349 int ret = 0; 350 BIGNUM *t; 351 352 BN_CTX_start(ctx); 353 t = BN_CTX_get(ctx); 354 if (t == NULL || 355 !BN_copy(t, a)) { 356 goto err; 357 } 358 359 ret = BN_from_montgomery_word(r, t, mont); 360 361 err: 362 BN_CTX_end(ctx); 363 364 return ret; 365 } 366 367 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 368 const BN_MONT_CTX *mont, BN_CTX *ctx) { 369 #if !defined(OPENSSL_BN_ASM_MONT) 370 return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx); 371 #else 372 int num = mont->N.top; 373 374 /* |bn_mul_mont| requires at least 128 bits of limbs, at least for x86. */ 375 if (num < (128 / BN_BITS2) || 376 a->top != num || 377 b->top != num) { 378 return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx); 379 } 380 381 if (bn_wexpand(r, num) == NULL) { 382 return 0; 383 } 384 if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { 385 /* The check above ensures this won't happen. */ 386 assert(0); 387 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); 388 return 0; 389 } 390 r->neg = a->neg ^ b->neg; 391 r->top = num; 392 bn_correct_top(r); 393 394 return 1; 395 #endif 396 } 397 398 static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a, 399 const BIGNUM *b, 400 const BN_MONT_CTX *mont, 401 BN_CTX *ctx) { 402 int ret = 0; 403 404 BN_CTX_start(ctx); 405 BIGNUM *tmp = BN_CTX_get(ctx); 406 if (tmp == NULL) { 407 goto err; 408 } 409 410 if (a == b) { 411 if (!BN_sqr(tmp, a, ctx)) { 412 goto err; 413 } 414 } else { 415 if (!BN_mul(tmp, a, b, ctx)) { 416 goto err; 417 } 418 } 419 420 /* reduce from aRR to aR */ 421 if (!BN_from_montgomery_word(r, tmp, mont)) { 422 goto err; 423 } 424 425 ret = 1; 426 427 err: 428 BN_CTX_end(ctx); 429 return ret; 430 } 431
