1/* crypto/bn/bn_mont.c */ 2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 3 * All rights reserved. 4 * 5 * This package is an SSL implementation written 6 * by Eric Young (eay@cryptsoft.com). 7 * The implementation was written so as to conform with Netscapes SSL. 8 * 9 * This library is free for commercial and non-commercial use as long as 10 * the following conditions are aheared to. The following conditions 11 * apply to all code found in this distribution, be it the RC4, RSA, 12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation 13 * included with this distribution is covered by the same copyright terms 14 * except that the holder is Tim Hudson (tjh@cryptsoft.com). 15 * 16 * Copyright remains Eric Young's, and as such any Copyright notices in 17 * the code are not to be removed. 18 * If this package is used in a product, Eric Young should be given attribution 19 * as the author of the parts of the library used. 20 * This can be in the form of a textual message at program startup or 21 * in documentation (online or textual) provided with the package. 22 * 23 * Redistribution and use in source and binary forms, with or without 24 * modification, are permitted provided that the following conditions 25 * are met: 26 * 1. Redistributions of source code must retain the copyright 27 * notice, this list of conditions and the following disclaimer. 28 * 2. Redistributions in binary form must reproduce the above copyright 29 * notice, this list of conditions and the following disclaimer in the 30 * documentation and/or other materials provided with the distribution. 31 * 3. All advertising materials mentioning features or use of this software 32 * must display the following acknowledgement: 33 * "This product includes cryptographic software written by 34 * Eric Young (eay@cryptsoft.com)" 35 * The word 'cryptographic' can be left out if the rouines from the library 36 * being used are not cryptographic related :-). 37 * 4. If you include any Windows specific code (or a derivative thereof) from 38 * the apps directory (application code) you must include an acknowledgement: 39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" 40 * 41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 51 * SUCH DAMAGE. 52 * 53 * The licence and distribution terms for any publically available version or 54 * derivative of this code cannot be changed. i.e. this code cannot simply be 55 * copied and put under another distribution licence 56 * [including the GNU Public Licence.] 57 */ 58/* ==================================================================== 59 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved. 60 * 61 * Redistribution and use in source and binary forms, with or without 62 * modification, are permitted provided that the following conditions 63 * are met: 64 * 65 * 1. Redistributions of source code must retain the above copyright 66 * notice, this list of conditions and the following disclaimer. 67 * 68 * 2. Redistributions in binary form must reproduce the above copyright 69 * notice, this list of conditions and the following disclaimer in 70 * the documentation and/or other materials provided with the 71 * distribution. 72 * 73 * 3. All advertising materials mentioning features or use of this 74 * software must display the following acknowledgment: 75 * "This product includes software developed by the OpenSSL Project 76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 77 * 78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 79 * endorse or promote products derived from this software without 80 * prior written permission. For written permission, please contact 81 * openssl-core@openssl.org. 82 * 83 * 5. Products derived from this software may not be called "OpenSSL" 84 * nor may "OpenSSL" appear in their names without prior written 85 * permission of the OpenSSL Project. 86 * 87 * 6. Redistributions of any form whatsoever must retain the following 88 * acknowledgment: 89 * "This product includes software developed by the OpenSSL Project 90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 91 * 92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 103 * OF THE POSSIBILITY OF SUCH DAMAGE. 104 * ==================================================================== 105 * 106 * This product includes cryptographic software written by Eric Young 107 * (eay@cryptsoft.com). This product includes software written by Tim 108 * Hudson (tjh@cryptsoft.com). 109 * 110 */ 111 112/* 113 * Details about Montgomery multiplication algorithms can be found at 114 * http://security.ece.orst.edu/publications.html, e.g. 115 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and 116 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf 117 */ 118 119#include <stdio.h> 120#include "cryptlib.h" 121#include "bn_lcl.h" 122 123#define MONT_WORD /* use the faster word-based algorithm */ 124 125#ifdef MONT_WORD 126static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont); 127#endif 128 129int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 130 BN_MONT_CTX *mont, BN_CTX *ctx) 131{ 132 BIGNUM *tmp; 133 int ret = 0; 134#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD) 135 int num = mont->N.top; 136 137 if (num > 1 && a->top == num && b->top == num) { 138 if (bn_wexpand(r, num) == NULL) 139 return (0); 140 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { 141 r->neg = a->neg ^ b->neg; 142 r->top = num; 143 bn_correct_top(r); 144 return (1); 145 } 146 } 147#endif 148 149 BN_CTX_start(ctx); 150 tmp = BN_CTX_get(ctx); 151 if (tmp == NULL) 152 goto err; 153 154 bn_check_top(tmp); 155 if (a == b) { 156 if (!BN_sqr(tmp, a, ctx)) 157 goto err; 158 } else { 159 if (!BN_mul(tmp, a, b, ctx)) 160 goto err; 161 } 162 /* reduce from aRR to aR */ 163#ifdef MONT_WORD 164 if (!BN_from_montgomery_word(r, tmp, mont)) 165 goto err; 166#else 167 if (!BN_from_montgomery(r, tmp, mont, ctx)) 168 goto err; 169#endif 170 bn_check_top(r); 171 ret = 1; 172 err: 173 BN_CTX_end(ctx); 174 return (ret); 175} 176 177#ifdef MONT_WORD 178static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont) 179{ 180 BIGNUM *n; 181 BN_ULONG *ap, *np, *rp, n0, v, carry; 182 int nl, max, i; 183 184 n = &(mont->N); 185 nl = n->top; 186 if (nl == 0) { 187 ret->top = 0; 188 return (1); 189 } 190 191 max = (2 * nl); /* carry is stored separately */ 192 if (bn_wexpand(r, max) == NULL) 193 return (0); 194 195 r->neg ^= n->neg; 196 np = n->d; 197 rp = r->d; 198 199 /* clear the top words of T */ 200# if 1 201 for (i = r->top; i < max; i++) /* memset? XXX */ 202 rp[i] = 0; 203# else 204 memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG)); 205# endif 206 207 r->top = max; 208 n0 = mont->n0[0]; 209 210# ifdef BN_COUNT 211 fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl); 212# endif 213 for (carry = 0, i = 0; i < nl; i++, rp++) { 214# ifdef __TANDEM 215 { 216 long long t1; 217 long long t2; 218 long long t3; 219 t1 = rp[0] * (n0 & 0177777); 220 t2 = 037777600000l; 221 t2 = n0 & t2; 222 t3 = rp[0] & 0177777; 223 t2 = (t3 * t2) & BN_MASK2; 224 t1 = t1 + t2; 225 v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1); 226 } 227# else 228 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); 229# endif 230 v = (v + carry + rp[nl]) & BN_MASK2; 231 carry |= (v != rp[nl]); 232 carry &= (v <= rp[nl]); 233 rp[nl] = v; 234 } 235 236 if (bn_wexpand(ret, nl) == NULL) 237 return (0); 238 ret->top = nl; 239 ret->neg = r->neg; 240 241 rp = ret->d; 242 ap = &(r->d[nl]); 243 244# define BRANCH_FREE 1 245# if BRANCH_FREE 246 { 247 BN_ULONG *nrp; 248 size_t m; 249 250 v = bn_sub_words(rp, ap, np, nl) - carry; 251 /* 252 * if subtraction result is real, then trick unconditional memcpy 253 * below to perform in-place "refresh" instead of actual copy. 254 */ 255 m = (0 - (size_t)v); 256 nrp = 257 (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m)); 258 259 for (i = 0, nl -= 4; i < nl; i += 4) { 260 BN_ULONG t1, t2, t3, t4; 261 262 t1 = nrp[i + 0]; 263 t2 = nrp[i + 1]; 264 t3 = nrp[i + 2]; 265 ap[i + 0] = 0; 266 t4 = nrp[i + 3]; 267 ap[i + 1] = 0; 268 rp[i + 0] = t1; 269 ap[i + 2] = 0; 270 rp[i + 1] = t2; 271 ap[i + 3] = 0; 272 rp[i + 2] = t3; 273 rp[i + 3] = t4; 274 } 275 for (nl += 4; i < nl; i++) 276 rp[i] = nrp[i], ap[i] = 0; 277 } 278# else 279 if (bn_sub_words(rp, ap, np, nl) - carry) 280 memcpy(rp, ap, nl * sizeof(BN_ULONG)); 281# endif 282 bn_correct_top(r); 283 bn_correct_top(ret); 284 bn_check_top(ret); 285 286 return (1); 287} 288#endif /* MONT_WORD */ 289 290int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, 291 BN_CTX *ctx) 292{ 293 int retn = 0; 294#ifdef MONT_WORD 295 BIGNUM *t; 296 297 BN_CTX_start(ctx); 298 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) 299 retn = BN_from_montgomery_word(ret, t, mont); 300 BN_CTX_end(ctx); 301#else /* !MONT_WORD */ 302 BIGNUM *t1, *t2; 303 304 BN_CTX_start(ctx); 305 t1 = BN_CTX_get(ctx); 306 t2 = BN_CTX_get(ctx); 307 if (t1 == NULL || t2 == NULL) 308 goto err; 309 310 if (!BN_copy(t1, a)) 311 goto err; 312 BN_mask_bits(t1, mont->ri); 313 314 if (!BN_mul(t2, t1, &mont->Ni, ctx)) 315 goto err; 316 BN_mask_bits(t2, mont->ri); 317 318 if (!BN_mul(t1, t2, &mont->N, ctx)) 319 goto err; 320 if (!BN_add(t2, a, t1)) 321 goto err; 322 if (!BN_rshift(ret, t2, mont->ri)) 323 goto err; 324 325 if (BN_ucmp(ret, &(mont->N)) >= 0) { 326 if (!BN_usub(ret, ret, &(mont->N))) 327 goto err; 328 } 329 retn = 1; 330 bn_check_top(ret); 331 err: 332 BN_CTX_end(ctx); 333#endif /* MONT_WORD */ 334 return (retn); 335} 336 337BN_MONT_CTX *BN_MONT_CTX_new(void) 338{ 339 BN_MONT_CTX *ret; 340 341 if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL) 342 return (NULL); 343 344 BN_MONT_CTX_init(ret); 345 ret->flags = BN_FLG_MALLOCED; 346 return (ret); 347} 348 349void BN_MONT_CTX_init(BN_MONT_CTX *ctx) 350{ 351 ctx->ri = 0; 352 BN_init(&(ctx->RR)); 353 BN_init(&(ctx->N)); 354 BN_init(&(ctx->Ni)); 355 ctx->n0[0] = ctx->n0[1] = 0; 356 ctx->flags = 0; 357} 358 359void BN_MONT_CTX_free(BN_MONT_CTX *mont) 360{ 361 if (mont == NULL) 362 return; 363 364 BN_clear_free(&(mont->RR)); 365 BN_clear_free(&(mont->N)); 366 BN_clear_free(&(mont->Ni)); 367 if (mont->flags & BN_FLG_MALLOCED) 368 OPENSSL_free(mont); 369} 370 371int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) 372{ 373 int ret = 0; 374 BIGNUM *Ri, *R; 375 376 if (BN_is_zero(mod)) 377 return 0; 378 379 BN_CTX_start(ctx); 380 if ((Ri = BN_CTX_get(ctx)) == NULL) 381 goto err; 382 R = &(mont->RR); /* grab RR as a temp */ 383 if (!BN_copy(&(mont->N), mod)) 384 goto err; /* Set N */ 385 mont->N.neg = 0; 386 387#ifdef MONT_WORD 388 { 389 BIGNUM tmod; 390 BN_ULONG buf[2]; 391 392 BN_init(&tmod); 393 tmod.d = buf; 394 tmod.dmax = 2; 395 tmod.neg = 0; 396 397 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; 398 399# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32) 400 /* 401 * Only certain BN_BITS2<=32 platforms actually make use of n0[1], 402 * and we could use the #else case (with a shorter R value) for the 403 * others. However, currently only the assembler files do know which 404 * is which. 405 */ 406 407 BN_zero(R); 408 if (!(BN_set_bit(R, 2 * BN_BITS2))) 409 goto err; 410 411 tmod.top = 0; 412 if ((buf[0] = mod->d[0])) 413 tmod.top = 1; 414 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) 415 tmod.top = 2; 416 417 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) 418 goto err; 419 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) 420 goto err; /* R*Ri */ 421 if (!BN_is_zero(Ri)) { 422 if (!BN_sub_word(Ri, 1)) 423 goto err; 424 } else { /* if N mod word size == 1 */ 425 426 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) 427 goto err; 428 /* Ri-- (mod double word size) */ 429 Ri->neg = 0; 430 Ri->d[0] = BN_MASK2; 431 Ri->d[1] = BN_MASK2; 432 Ri->top = 2; 433 } 434 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) 435 goto err; 436 /* 437 * Ni = (R*Ri-1)/N, keep only couple of least significant words: 438 */ 439 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 440 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0; 441# else 442 BN_zero(R); 443 if (!(BN_set_bit(R, BN_BITS2))) 444 goto err; /* R */ 445 446 buf[0] = mod->d[0]; /* tmod = N mod word size */ 447 buf[1] = 0; 448 tmod.top = buf[0] != 0 ? 1 : 0; 449 /* Ri = R^-1 mod N */ 450 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) 451 goto err; 452 if (!BN_lshift(Ri, Ri, BN_BITS2)) 453 goto err; /* R*Ri */ 454 if (!BN_is_zero(Ri)) { 455 if (!BN_sub_word(Ri, 1)) 456 goto err; 457 } else { /* if N mod word size == 1 */ 458 459 if (!BN_set_word(Ri, BN_MASK2)) 460 goto err; /* Ri-- (mod word size) */ 461 } 462 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) 463 goto err; 464 /* 465 * Ni = (R*Ri-1)/N, keep only least significant word: 466 */ 467 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 468 mont->n0[1] = 0; 469# endif 470 } 471#else /* !MONT_WORD */ 472 { /* bignum version */ 473 mont->ri = BN_num_bits(&mont->N); 474 BN_zero(R); 475 if (!BN_set_bit(R, mont->ri)) 476 goto err; /* R = 2^ri */ 477 /* Ri = R^-1 mod N */ 478 if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL) 479 goto err; 480 if (!BN_lshift(Ri, Ri, mont->ri)) 481 goto err; /* R*Ri */ 482 if (!BN_sub_word(Ri, 1)) 483 goto err; 484 /* 485 * Ni = (R*Ri-1) / N 486 */ 487 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx)) 488 goto err; 489 } 490#endif 491 492 /* setup RR for conversions */ 493 BN_zero(&(mont->RR)); 494 if (!BN_set_bit(&(mont->RR), mont->ri * 2)) 495 goto err; 496 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) 497 goto err; 498 499 ret = 1; 500 err: 501 BN_CTX_end(ctx); 502 return ret; 503} 504 505BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) 506{ 507 if (to == from) 508 return (to); 509 510 if (!BN_copy(&(to->RR), &(from->RR))) 511 return NULL; 512 if (!BN_copy(&(to->N), &(from->N))) 513 return NULL; 514 if (!BN_copy(&(to->Ni), &(from->Ni))) 515 return NULL; 516 to->ri = from->ri; 517 to->n0[0] = from->n0[0]; 518 to->n0[1] = from->n0[1]; 519 return (to); 520} 521 522BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, 523 const BIGNUM *mod, BN_CTX *ctx) 524{ 525 BN_MONT_CTX *ret; 526 527 CRYPTO_r_lock(lock); 528 ret = *pmont; 529 CRYPTO_r_unlock(lock); 530 if (ret) 531 return ret; 532 533 /* 534 * We don't want to serialise globally while doing our lazy-init math in 535 * BN_MONT_CTX_set. That punishes threads that are doing independent 536 * things. Instead, punish the case where more than one thread tries to 537 * lazy-init the same 'pmont', by having each do the lazy-init math work 538 * independently and only use the one from the thread that wins the race 539 * (the losers throw away the work they've done). 540 */ 541 ret = BN_MONT_CTX_new(); 542 if (!ret) 543 return NULL; 544 if (!BN_MONT_CTX_set(ret, mod, ctx)) { 545 BN_MONT_CTX_free(ret); 546 return NULL; 547 } 548 549 /* The locked compare-and-set, after the local work is done. */ 550 CRYPTO_w_lock(lock); 551 if (*pmont) { 552 BN_MONT_CTX_free(ret); 553 ret = *pmont; 554 } else 555 *pmont = ret; 556 CRYPTO_w_unlock(lock); 557 return ret; 558} 559