1 /* $OpenBSD: bn_mont.c,v 1.23 2014/07/11 08:44:48 jsing Exp $ */ 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 <stdint.h> 121 122 #include "bn_lcl.h" 123 124 #define MONT_WORD /* use the faster word-based algorithm */ 125 126 #ifdef MONT_WORD 127 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont); 128 #endif 129 130 int 131 BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 132 BN_MONT_CTX *mont, BN_CTX *ctx) 133 { 134 BIGNUM *tmp; 135 int ret = 0; 136 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD) 137 int num = mont->N.top; 138 139 if (num > 1 && a->top == num && b->top == num) { 140 if (bn_wexpand(r, num) == NULL) 141 return (0); 142 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { 143 r->neg = a->neg^b->neg; 144 r->top = num; 145 bn_correct_top(r); 146 return (1); 147 } 148 } 149 #endif 150 151 BN_CTX_start(ctx); 152 if ((tmp = BN_CTX_get(ctx)) == NULL) 153 goto err; 154 155 bn_check_top(tmp); 156 if (a == b) { 157 if (!BN_sqr(tmp, a, ctx)) 158 goto err; 159 } else { 160 if (!BN_mul(tmp, a,b, ctx)) 161 goto err; 162 } 163 /* reduce from aRR to aR */ 164 #ifdef MONT_WORD 165 if (!BN_from_montgomery_word(r, tmp, mont)) 166 goto err; 167 #else 168 if (!BN_from_montgomery(r, tmp, mont, ctx)) 169 goto err; 170 #endif 171 bn_check_top(r); 172 ret = 1; 173 err: 174 BN_CTX_end(ctx); 175 return (ret); 176 } 177 178 #ifdef MONT_WORD 179 static int 180 BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont) 181 { 182 BIGNUM *n; 183 BN_ULONG *ap, *np, *rp, n0, v, carry; 184 int nl, max, i; 185 186 n = &(mont->N); 187 nl = n->top; 188 if (nl == 0) { 189 ret->top = 0; 190 return (1); 191 } 192 193 max = (2 * nl); /* carry is stored separately */ 194 if (bn_wexpand(r, max) == NULL) 195 return (0); 196 197 r->neg ^= n->neg; 198 np = n->d; 199 rp = r->d; 200 201 /* clear the top words of T */ 202 #if 1 203 for (i=r->top; i<max; i++) /* memset? XXX */ 204 rp[i] = 0; 205 #else 206 memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG)); 207 #endif 208 209 r->top = max; 210 n0 = mont->n0[0]; 211 212 #ifdef BN_COUNT 213 fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl); 214 #endif 215 for (carry = 0, i = 0; i < nl; i++, rp++) { 216 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); 217 v = (v + carry + rp[nl]) & BN_MASK2; 218 carry |= (v != rp[nl]); 219 carry &= (v <= rp[nl]); 220 rp[nl] = v; 221 } 222 223 if (bn_wexpand(ret, nl) == NULL) 224 return (0); 225 ret->top = nl; 226 ret->neg = r->neg; 227 228 rp = ret->d; 229 ap = &(r->d[nl]); 230 231 #define BRANCH_FREE 1 232 #if BRANCH_FREE 233 { 234 BN_ULONG *nrp; 235 size_t m; 236 237 v = bn_sub_words(rp, ap, np, nl) - carry; 238 /* if subtraction result is real, then 239 * trick unconditional memcpy below to perform in-place 240 * "refresh" instead of actual copy. */ 241 m = (0 - (size_t)v); 242 nrp = (BN_ULONG *)(((uintptr_t)rp & ~m)|((uintptr_t)ap & m)); 243 244 for (i = 0, nl -= 4; i < nl; i += 4) { 245 BN_ULONG t1, t2, t3, t4; 246 247 t1 = nrp[i + 0]; 248 t2 = nrp[i + 1]; 249 t3 = nrp[i + 2]; 250 ap[i + 0] = 0; 251 t4 = nrp[i + 3]; 252 ap[i + 1] = 0; 253 rp[i + 0] = t1; 254 ap[i + 2] = 0; 255 rp[i + 1] = t2; 256 ap[i + 3] = 0; 257 rp[i + 2] = t3; 258 rp[i + 3] = t4; 259 } 260 for (nl += 4; i < nl; i++) 261 rp[i] = nrp[i], ap[i] = 0; 262 } 263 #else 264 if (bn_sub_words (rp, ap, np, nl) - carry) 265 memcpy(rp, ap, nl*sizeof(BN_ULONG)); 266 #endif 267 bn_correct_top(r); 268 bn_correct_top(ret); 269 bn_check_top(ret); 270 271 return (1); 272 } 273 #endif /* MONT_WORD */ 274 275 int 276 BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx) 277 { 278 int retn = 0; 279 #ifdef MONT_WORD 280 BIGNUM *t; 281 282 BN_CTX_start(ctx); 283 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) 284 retn = BN_from_montgomery_word(ret, t, mont); 285 BN_CTX_end(ctx); 286 #else /* !MONT_WORD */ 287 BIGNUM *t1, *t2; 288 289 BN_CTX_start(ctx); 290 if ((t1 = BN_CTX_get(ctx)) == NULL) 291 goto err; 292 if ((t2 = BN_CTX_get(ctx)) == 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); 316 317 err: 318 BN_CTX_end(ctx); 319 #endif /* MONT_WORD */ 320 return (retn); 321 } 322 323 BN_MONT_CTX * 324 BN_MONT_CTX_new(void) 325 { 326 BN_MONT_CTX *ret; 327 328 if ((ret = malloc(sizeof(BN_MONT_CTX))) == NULL) 329 return (NULL); 330 331 BN_MONT_CTX_init(ret); 332 ret->flags = BN_FLG_MALLOCED; 333 return (ret); 334 } 335 336 void 337 BN_MONT_CTX_init(BN_MONT_CTX *ctx) 338 { 339 ctx->ri = 0; 340 BN_init(&(ctx->RR)); 341 BN_init(&(ctx->N)); 342 BN_init(&(ctx->Ni)); 343 ctx->n0[0] = ctx->n0[1] = 0; 344 ctx->flags = 0; 345 } 346 347 void 348 BN_MONT_CTX_free(BN_MONT_CTX *mont) 349 { 350 if (mont == NULL) 351 return; 352 353 BN_clear_free(&(mont->RR)); 354 BN_clear_free(&(mont->N)); 355 BN_clear_free(&(mont->Ni)); 356 if (mont->flags & BN_FLG_MALLOCED) 357 free(mont); 358 } 359 360 int 361 BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) 362 { 363 int ret = 0; 364 BIGNUM *Ri, *R; 365 366 BN_CTX_start(ctx); 367 if ((Ri = BN_CTX_get(ctx)) == NULL) 368 goto err; 369 R = &(mont->RR); /* grab RR as a temp */ 370 if (!BN_copy(&(mont->N), mod)) 371 goto err; /* Set N */ 372 mont->N.neg = 0; 373 374 #ifdef MONT_WORD 375 { 376 BIGNUM tmod; 377 BN_ULONG buf[2]; 378 379 BN_init(&tmod); 380 tmod.d = buf; 381 tmod.dmax = 2; 382 tmod.neg = 0; 383 384 mont->ri = (BN_num_bits(mod) + 385 (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; 386 387 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32) 388 /* Only certain BN_BITS2<=32 platforms actually make use of 389 * n0[1], and we could use the #else case (with a shorter R 390 * value) for the others. However, currently only the assembler 391 * files do know which is which. */ 392 393 BN_zero(R); 394 if (!(BN_set_bit(R, 2 * BN_BITS2))) 395 goto err; 396 397 tmod.top = 0; 398 if ((buf[0] = mod->d[0])) 399 tmod.top = 1; 400 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) 401 tmod.top = 2; 402 403 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) 404 goto err; 405 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) 406 goto err; /* R*Ri */ 407 if (!BN_is_zero(Ri)) { 408 if (!BN_sub_word(Ri, 1)) 409 goto err; 410 } 411 else /* if N mod word size == 1 */ 412 { 413 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) 414 goto err; 415 /* Ri-- (mod double word size) */ 416 Ri->neg = 0; 417 Ri->d[0] = BN_MASK2; 418 Ri->d[1] = BN_MASK2; 419 Ri->top = 2; 420 } 421 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) 422 goto err; 423 /* Ni = (R*Ri-1)/N, 424 * keep only couple of least significant words: */ 425 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 426 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0; 427 #else 428 BN_zero(R); 429 if (!(BN_set_bit(R, BN_BITS2))) 430 goto err; /* R */ 431 432 buf[0] = mod->d[0]; /* tmod = N mod word size */ 433 buf[1] = 0; 434 tmod.top = buf[0] != 0 ? 1 : 0; 435 /* Ri = R^-1 mod N*/ 436 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) 437 goto err; 438 if (!BN_lshift(Ri, Ri, BN_BITS2)) 439 goto err; /* R*Ri */ 440 if (!BN_is_zero(Ri)) { 441 if (!BN_sub_word(Ri, 1)) 442 goto err; 443 } 444 else /* if N mod word size == 1 */ 445 { 446 if (!BN_set_word(Ri, BN_MASK2)) 447 goto err; /* Ri-- (mod word size) */ 448 } 449 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) 450 goto err; 451 /* Ni = (R*Ri-1)/N, 452 * keep only least significant word: */ 453 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 454 mont->n0[1] = 0; 455 #endif 456 } 457 #else /* !MONT_WORD */ 458 { /* bignum version */ 459 mont->ri = BN_num_bits(&mont->N); 460 BN_zero(R); 461 if (!BN_set_bit(R, mont->ri)) 462 goto err; /* R = 2^ri */ 463 /* Ri = R^-1 mod N*/ 464 if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL) 465 goto err; 466 if (!BN_lshift(Ri, Ri, mont->ri)) 467 goto err; /* R*Ri */ 468 if (!BN_sub_word(Ri, 1)) 469 goto err; 470 /* Ni = (R*Ri-1) / N */ 471 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx)) 472 goto err; 473 } 474 #endif 475 476 /* setup RR for conversions */ 477 BN_zero(&(mont->RR)); 478 if (!BN_set_bit(&(mont->RR), mont->ri*2)) 479 goto err; 480 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) 481 goto err; 482 483 ret = 1; 484 485 err: 486 BN_CTX_end(ctx); 487 return ret; 488 } 489 490 BN_MONT_CTX * 491 BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) 492 { 493 if (to == from) 494 return (to); 495 496 if (!BN_copy(&(to->RR), &(from->RR))) 497 return NULL; 498 if (!BN_copy(&(to->N), &(from->N))) 499 return NULL; 500 if (!BN_copy(&(to->Ni), &(from->Ni))) 501 return NULL; 502 to->ri = from->ri; 503 to->n0[0] = from->n0[0]; 504 to->n0[1] = from->n0[1]; 505 return (to); 506 } 507 508 BN_MONT_CTX * 509 BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, const BIGNUM *mod, 510 BN_CTX *ctx) 511 { 512 int got_write_lock = 0; 513 BN_MONT_CTX *ret; 514 515 CRYPTO_r_lock(lock); 516 if (!*pmont) { 517 CRYPTO_r_unlock(lock); 518 CRYPTO_w_lock(lock); 519 got_write_lock = 1; 520 521 if (!*pmont) { 522 ret = BN_MONT_CTX_new(); 523 if (ret && !BN_MONT_CTX_set(ret, mod, ctx)) 524 BN_MONT_CTX_free(ret); 525 else 526 *pmont = ret; 527 } 528 } 529 530 ret = *pmont; 531 532 if (got_write_lock) 533 CRYPTO_w_unlock(lock); 534 else 535 CRYPTO_r_unlock(lock); 536 537 return ret; 538 } 539