bn_mont.c revision 340704
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) 1998-2018 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 int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx); 133 134 bn_correct_top(r); 135 bn_check_top(r); 136 137 return ret; 138} 139 140int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 141 BN_MONT_CTX *mont, BN_CTX *ctx) 142{ 143 BIGNUM *tmp; 144 int ret = 0; 145#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD) 146 int num = mont->N.top; 147 148 if (num > 1 && a->top == num && b->top == num) { 149 if (bn_wexpand(r, num) == NULL) 150 return (0); 151 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { 152 r->neg = a->neg ^ b->neg; 153 r->top = num; 154 r->flags |= BN_FLG_FIXED_TOP; 155 return 1; 156 } 157 } 158#endif 159 160 BN_CTX_start(ctx); 161 tmp = BN_CTX_get(ctx); 162 if (tmp == NULL) 163 goto err; 164 165 bn_check_top(tmp); 166 if (a == b) { 167 if (!bn_sqr_fixed_top(tmp, a, ctx)) 168 goto err; 169 } else { 170 if (!bn_mul_fixed_top(tmp, a, b, ctx)) 171 goto err; 172 } 173 /* reduce from aRR to aR */ 174#ifdef MONT_WORD 175 if (!bn_from_montgomery_word(r, tmp, mont)) 176 goto err; 177#else 178 if (!BN_from_montgomery(r, tmp, mont, ctx)) 179 goto err; 180#endif 181 ret = 1; 182 err: 183 BN_CTX_end(ctx); 184 return (ret); 185} 186 187#ifdef MONT_WORD 188static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont) 189{ 190 BIGNUM *n; 191 BN_ULONG *ap, *np, *rp, n0, v, carry; 192 int nl, max, i; 193 unsigned int rtop; 194 195 n = &(mont->N); 196 nl = n->top; 197 if (nl == 0) { 198 ret->top = 0; 199 return (1); 200 } 201 202 max = (2 * nl); /* carry is stored separately */ 203 if (bn_wexpand(r, max) == NULL) 204 return (0); 205 206 r->neg ^= n->neg; 207 np = n->d; 208 rp = r->d; 209 210 /* clear the top words of T */ 211 for (rtop = r->top, i = 0; i < max; i++) { 212 v = (BN_ULONG)0 - ((i - rtop) >> (8 * sizeof(rtop) - 1)); 213 rp[i] &= v; 214 } 215 216 r->top = max; 217 r->flags |= BN_FLG_FIXED_TOP; 218 n0 = mont->n0[0]; 219 220 /* 221 * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On 222 * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r| 223 * includes |carry| which is stored separately. 224 */ 225 for (carry = 0, i = 0; i < nl; i++, rp++) { 226 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); 227 v = (v + carry + rp[nl]) & BN_MASK2; 228 carry |= (v != rp[nl]); 229 carry &= (v <= rp[nl]); 230 rp[nl] = v; 231 } 232 233 if (bn_wexpand(ret, nl) == NULL) 234 return (0); 235 ret->top = nl; 236 ret->flags |= BN_FLG_FIXED_TOP; 237 ret->neg = r->neg; 238 239 rp = ret->d; 240 241 /* 242 * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap| 243 * includes |carry| which is stored separately. 244 */ 245 ap = &(r->d[nl]); 246 247 carry -= bn_sub_words(rp, ap, np, nl); 248 /* 249 * |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note 250 * |carry| cannot be 1. That would imply the subtraction did not fit in 251 * |nl| words, and we know at most one subtraction is needed. 252 */ 253 for (i = 0; i < nl; i++) { 254 rp[i] = (carry & ap[i]) | (~carry & rp[i]); 255 ap[i] = 0; 256 } 257 258 return (1); 259} 260#endif /* MONT_WORD */ 261 262int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, 263 BN_CTX *ctx) 264{ 265 int retn; 266 267 retn = bn_from_mont_fixed_top(ret, a, mont, ctx); 268 bn_correct_top(ret); 269 bn_check_top(ret); 270 271 return retn; 272} 273 274int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, 275 BN_CTX *ctx) 276{ 277 int retn = 0; 278#ifdef MONT_WORD 279 BIGNUM *t; 280 281 BN_CTX_start(ctx); 282 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) { 283 retn = bn_from_montgomery_word(ret, t, mont); 284 } 285 BN_CTX_end(ctx); 286#else /* !MONT_WORD */ 287 BIGNUM *t1, *t2; 288 289 BN_CTX_start(ctx); 290 t1 = BN_CTX_get(ctx); 291 t2 = BN_CTX_get(ctx); 292 if (t1 == NULL || t2 == NULL) 293 goto err; 294 295 if (!BN_copy(t1, a)) 296 goto err; 297 BN_mask_bits(t1, mont->ri); 298 299 if (!BN_mul(t2, t1, &mont->Ni, ctx)) 300 goto err; 301 BN_mask_bits(t2, mont->ri); 302 303 if (!BN_mul(t1, t2, &mont->N, ctx)) 304 goto err; 305 if (!BN_add(t2, a, t1)) 306 goto err; 307 if (!BN_rshift(ret, t2, mont->ri)) 308 goto err; 309 310 if (BN_ucmp(ret, &(mont->N)) >= 0) { 311 if (!BN_usub(ret, ret, &(mont->N))) 312 goto err; 313 } 314 retn = 1; 315 bn_check_top(ret); 316 err: 317 BN_CTX_end(ctx); 318#endif /* MONT_WORD */ 319 return (retn); 320} 321 322int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont, 323 BN_CTX *ctx) 324{ 325 return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx); 326} 327 328BN_MONT_CTX *BN_MONT_CTX_new(void) 329{ 330 BN_MONT_CTX *ret; 331 332 if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL) 333 return (NULL); 334 335 BN_MONT_CTX_init(ret); 336 ret->flags = BN_FLG_MALLOCED; 337 return (ret); 338} 339 340void BN_MONT_CTX_init(BN_MONT_CTX *ctx) 341{ 342 ctx->ri = 0; 343 BN_init(&(ctx->RR)); 344 BN_init(&(ctx->N)); 345 BN_init(&(ctx->Ni)); 346 ctx->n0[0] = ctx->n0[1] = 0; 347 ctx->flags = 0; 348} 349 350void BN_MONT_CTX_free(BN_MONT_CTX *mont) 351{ 352 if (mont == NULL) 353 return; 354 355 BN_clear_free(&(mont->RR)); 356 BN_clear_free(&(mont->N)); 357 BN_clear_free(&(mont->Ni)); 358 if (mont->flags & BN_FLG_MALLOCED) 359 OPENSSL_free(mont); 360} 361 362int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) 363{ 364 int i, ret = 0; 365 BIGNUM *Ri, *R; 366 367 if (BN_is_zero(mod)) 368 return 0; 369 370 BN_CTX_start(ctx); 371 if ((Ri = BN_CTX_get(ctx)) == NULL) 372 goto err; 373 R = &(mont->RR); /* grab RR as a temp */ 374 if (!BN_copy(&(mont->N), mod)) 375 goto err; /* Set N */ 376 if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0) 377 BN_set_flags(&(mont->N), BN_FLG_CONSTTIME); 378 mont->N.neg = 0; 379 380#ifdef MONT_WORD 381 { 382 BIGNUM tmod; 383 BN_ULONG buf[2]; 384 385 BN_init(&tmod); 386 tmod.d = buf; 387 tmod.dmax = 2; 388 tmod.neg = 0; 389 390 if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0) 391 BN_set_flags(&tmod, BN_FLG_CONSTTIME); 392 393 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; 394 395# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32) 396 /* 397 * Only certain BN_BITS2<=32 platforms actually make use of n0[1], 398 * and we could use the #else case (with a shorter R value) for the 399 * others. However, currently only the assembler files do know which 400 * is which. 401 */ 402 403 BN_zero(R); 404 if (!(BN_set_bit(R, 2 * BN_BITS2))) 405 goto err; 406 407 tmod.top = 0; 408 if ((buf[0] = mod->d[0])) 409 tmod.top = 1; 410 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) 411 tmod.top = 2; 412 413 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) 414 goto err; 415 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) 416 goto err; /* R*Ri */ 417 if (!BN_is_zero(Ri)) { 418 if (!BN_sub_word(Ri, 1)) 419 goto err; 420 } else { /* if N mod word size == 1 */ 421 422 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) 423 goto err; 424 /* Ri-- (mod double word size) */ 425 Ri->neg = 0; 426 Ri->d[0] = BN_MASK2; 427 Ri->d[1] = BN_MASK2; 428 Ri->top = 2; 429 } 430 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) 431 goto err; 432 /* 433 * Ni = (R*Ri-1)/N, keep only couple of least significant words: 434 */ 435 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 436 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0; 437# else 438 BN_zero(R); 439 if (!(BN_set_bit(R, BN_BITS2))) 440 goto err; /* R */ 441 442 buf[0] = mod->d[0]; /* tmod = N mod word size */ 443 buf[1] = 0; 444 tmod.top = buf[0] != 0 ? 1 : 0; 445 /* Ri = R^-1 mod N */ 446 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) 447 goto err; 448 if (!BN_lshift(Ri, Ri, BN_BITS2)) 449 goto err; /* R*Ri */ 450 if (!BN_is_zero(Ri)) { 451 if (!BN_sub_word(Ri, 1)) 452 goto err; 453 } else { /* if N mod word size == 1 */ 454 455 if (!BN_set_word(Ri, BN_MASK2)) 456 goto err; /* Ri-- (mod word size) */ 457 } 458 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) 459 goto err; 460 /* 461 * Ni = (R*Ri-1)/N, keep only least significant word: 462 */ 463 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 464 mont->n0[1] = 0; 465# endif 466 } 467#else /* !MONT_WORD */ 468 { /* bignum version */ 469 mont->ri = BN_num_bits(&mont->N); 470 BN_zero(R); 471 if (!BN_set_bit(R, mont->ri)) 472 goto err; /* R = 2^ri */ 473 /* Ri = R^-1 mod N */ 474 if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL) 475 goto err; 476 if (!BN_lshift(Ri, Ri, mont->ri)) 477 goto err; /* R*Ri */ 478 if (!BN_sub_word(Ri, 1)) 479 goto err; 480 /* 481 * Ni = (R*Ri-1) / N 482 */ 483 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx)) 484 goto err; 485 } 486#endif 487 488 /* setup RR for conversions */ 489 BN_zero(&(mont->RR)); 490 if (!BN_set_bit(&(mont->RR), mont->ri * 2)) 491 goto err; 492 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) 493 goto err; 494 495 for (i = mont->RR.top, ret = mont->N.top; i < ret; i++) 496 mont->RR.d[i] = 0; 497 mont->RR.top = ret; 498 mont->RR.flags |= BN_FLG_FIXED_TOP; 499 500 ret = 1; 501 err: 502 BN_CTX_end(ctx); 503 return ret; 504} 505 506BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) 507{ 508 if (to == from) 509 return (to); 510 511 if (!BN_copy(&(to->RR), &(from->RR))) 512 return NULL; 513 if (!BN_copy(&(to->N), &(from->N))) 514 return NULL; 515 if (!BN_copy(&(to->Ni), &(from->Ni))) 516 return NULL; 517 to->ri = from->ri; 518 to->n0[0] = from->n0[0]; 519 to->n0[1] = from->n0[1]; 520 return (to); 521} 522 523BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, 524 const BIGNUM *mod, BN_CTX *ctx) 525{ 526 BN_MONT_CTX *ret; 527 528 CRYPTO_r_lock(lock); 529 ret = *pmont; 530 CRYPTO_r_unlock(lock); 531 if (ret) 532 return ret; 533 534 /* 535 * We don't want to serialise globally while doing our lazy-init math in 536 * BN_MONT_CTX_set. That punishes threads that are doing independent 537 * things. Instead, punish the case where more than one thread tries to 538 * lazy-init the same 'pmont', by having each do the lazy-init math work 539 * independently and only use the one from the thread that wins the race 540 * (the losers throw away the work they've done). 541 */ 542 ret = BN_MONT_CTX_new(); 543 if (!ret) 544 return NULL; 545 if (!BN_MONT_CTX_set(ret, mod, ctx)) { 546 BN_MONT_CTX_free(ret); 547 return NULL; 548 } 549 550 /* The locked compare-and-set, after the local work is done. */ 551 CRYPTO_w_lock(lock); 552 if (*pmont) { 553 BN_MONT_CTX_free(ret); 554 ret = *pmont; 555 } else 556 *pmont = ret; 557 CRYPTO_w_unlock(lock); 558 return ret; 559} 560