1/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 2 * All rights reserved. 3 * 4 * This package is an SSL implementation written 5 * by Eric Young (eay@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@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@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@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@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@cryptsoft.com). This product includes software written by Tim 107 * Hudson (tjh@cryptsoft.com). */ 108 109#include <openssl/bn.h> 110 111#include <string.h> 112 113#include <openssl/mem.h> 114#include <openssl/thread.h> 115 116#include "internal.h" 117#include "../internal.h" 118 119 120#if !defined(OPENSSL_NO_ASM) && \ 121 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64)) 122#define OPENSSL_BN_ASM_MONT 123#endif 124 125BN_MONT_CTX *BN_MONT_CTX_new(void) { 126 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX)); 127 128 if (ret == NULL) { 129 return NULL; 130 } 131 132 BN_MONT_CTX_init(ret); 133 ret->flags = BN_FLG_MALLOCED; 134 return ret; 135} 136 137void BN_MONT_CTX_init(BN_MONT_CTX *mont) { 138 memset(mont, 0, sizeof(BN_MONT_CTX)); 139 BN_init(&mont->RR); 140 BN_init(&mont->N); 141 BN_init(&mont->Ni); 142} 143 144void 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 BN_free(&mont->Ni); 152 if (mont->flags & BN_FLG_MALLOCED) { 153 OPENSSL_free(mont); 154 } 155} 156 157BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, 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 !BN_copy(&to->Ni, &from->Ni)) { 165 return NULL; 166 } 167 to->ri = from->ri; 168 to->n0[0] = from->n0[0]; 169 to->n0[1] = from->n0[1]; 170 return to; 171} 172 173int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) { 174 int ret = 0; 175 BIGNUM *Ri, *R; 176 BIGNUM tmod; 177 BN_ULONG buf[2]; 178 179 BN_CTX_start(ctx); 180 Ri = BN_CTX_get(ctx); 181 if (Ri == NULL) { 182 goto err; 183 } 184 R = &mont->RR; /* grab RR as a temp */ 185 if (!BN_copy(&mont->N, mod)) { 186 goto err; /* Set N */ 187 } 188 mont->N.neg = 0; 189 190 BN_init(&tmod); 191 tmod.d = buf; 192 tmod.dmax = 2; 193 tmod.neg = 0; 194 195 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; 196 197#if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2 <= 32) 198 /* Only certain BN_BITS2<=32 platforms actually make use of 199 * n0[1], and we could use the #else case (with a shorter R 200 * value) for the others. However, currently only the assembler 201 * files do know which is which. */ 202 203 BN_zero(R); 204 if (!BN_set_bit(R, 2 * BN_BITS2)) { 205 goto err; 206 } 207 208 tmod.top = 0; 209 if ((buf[0] = mod->d[0])) { 210 tmod.top = 1; 211 } 212 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) { 213 tmod.top = 2; 214 } 215 216 if (BN_mod_inverse(Ri, R, &tmod, ctx) == NULL) { 217 goto err; 218 } 219 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) { 220 goto err; /* R*Ri */ 221 } 222 if (!BN_is_zero(Ri)) { 223 if (!BN_sub_word(Ri, 1)) { 224 goto err; 225 } 226 } else { 227 /* if N mod word size == 1 */ 228 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) { 229 goto err; 230 } 231 /* Ri-- (mod double word size) */ 232 Ri->neg = 0; 233 Ri->d[0] = BN_MASK2; 234 Ri->d[1] = BN_MASK2; 235 Ri->top = 2; 236 } 237 238 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) { 239 goto err; 240 } 241 /* Ni = (R*Ri-1)/N, 242 * keep only couple of least significant words: */ 243 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 244 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0; 245#else 246 BN_zero(R); 247 if (!BN_set_bit(R, BN_BITS2)) { 248 goto err; /* R */ 249 } 250 251 buf[0] = mod->d[0]; /* tmod = N mod word size */ 252 buf[1] = 0; 253 tmod.top = buf[0] != 0 ? 1 : 0; 254 /* Ri = R^-1 mod N*/ 255 if (BN_mod_inverse(Ri, R, &tmod, ctx) == NULL) { 256 goto err; 257 } 258 if (!BN_lshift(Ri, Ri, BN_BITS2)) { 259 goto err; /* R*Ri */ 260 } 261 if (!BN_is_zero(Ri)) { 262 if (!BN_sub_word(Ri, 1)) { 263 goto err; 264 } 265 } else { 266 /* if N mod word size == 1 */ 267 if (!BN_set_word(Ri, BN_MASK2)) { 268 goto err; /* Ri-- (mod word size) */ 269 } 270 } 271 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) { 272 goto err; 273 } 274 /* Ni = (R*Ri-1)/N, 275 * keep only least significant word: */ 276 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 277 mont->n0[1] = 0; 278#endif 279 280 /* setup RR for conversions */ 281 BN_zero(&(mont->RR)); 282 if (!BN_set_bit(&(mont->RR), mont->ri * 2)) { 283 goto err; 284 } 285 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) { 286 goto err; 287 } 288 289 ret = 1; 290 291err: 292 BN_CTX_end(ctx); 293 return ret; 294} 295 296BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, 297 const BIGNUM *mod, BN_CTX *bn_ctx) { 298 CRYPTO_MUTEX_lock_read(lock); 299 BN_MONT_CTX *ctx = *pmont; 300 CRYPTO_MUTEX_unlock(lock); 301 302 if (ctx) { 303 return ctx; 304 } 305 306 CRYPTO_MUTEX_lock_write(lock); 307 ctx = *pmont; 308 if (ctx) { 309 goto out; 310 } 311 312 ctx = BN_MONT_CTX_new(); 313 if (ctx == NULL) { 314 goto out; 315 } 316 if (!BN_MONT_CTX_set(ctx, mod, bn_ctx)) { 317 BN_MONT_CTX_free(ctx); 318 ctx = NULL; 319 goto out; 320 } 321 *pmont = ctx; 322 323out: 324 CRYPTO_MUTEX_unlock(lock); 325 return ctx; 326} 327 328int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, 329 BN_CTX *ctx) { 330 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx); 331} 332 333#if 0 334static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, 335 const BN_MONT_CTX *mont) { 336 const BIGNUM *n; 337 BN_ULONG *ap, *np, *rp, n0, v, carry; 338 int nl, max, i; 339 340 n = &mont->N; 341 nl = n->top; 342 if (nl == 0) { 343 ret->top = 0; 344 return 1; 345 } 346 347 max = (2 * nl); /* carry is stored separately */ 348 if (bn_wexpand(r, max) == NULL) { 349 return 0; 350 } 351 352 r->neg ^= n->neg; 353 np = n->d; 354 rp = r->d; 355 356 /* clear the top words of T */ 357 if (max > r->top) { 358 memset(&rp[r->top], 0, (max - r->top) * sizeof(BN_ULONG)); 359 } 360 361 r->top = max; 362 n0 = mont->n0[0]; 363 364 for (carry = 0, i = 0; i < nl; i++, rp++) { 365 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); 366 v = (v + carry + rp[nl]) & BN_MASK2; 367 carry |= (v != rp[nl]); 368 carry &= (v <= rp[nl]); 369 rp[nl] = v; 370 } 371 372 if (bn_wexpand(ret, nl) == NULL) { 373 return 0; 374 } 375 ret->top = nl; 376 ret->neg = r->neg; 377 378 rp = ret->d; 379 ap = &(r->d[nl]); 380 381 { 382 BN_ULONG *nrp; 383 size_t m; 384 385 v = bn_sub_words(rp, ap, np, nl) - carry; 386 /* if subtraction result is real, then trick unconditional memcpy below to 387 * perform in-place "refresh" instead of actual copy. */ 388 m = (0 - (size_t)v); 389 nrp = (BN_ULONG *)(((intptr_t)rp & ~m) | ((intptr_t)ap & m)); 390 391 for (i = 0, nl -= 4; i < nl; i += 4) { 392 BN_ULONG t1, t2, t3, t4; 393 394 t1 = nrp[i + 0]; 395 t2 = nrp[i + 1]; 396 t3 = nrp[i + 2]; 397 ap[i + 0] = 0; 398 t4 = nrp[i + 3]; 399 ap[i + 1] = 0; 400 rp[i + 0] = t1; 401 ap[i + 2] = 0; 402 rp[i + 1] = t2; 403 ap[i + 3] = 0; 404 rp[i + 2] = t3; 405 rp[i + 3] = t4; 406 } 407 408 for (nl += 4; i < nl; i++) { 409 rp[i] = nrp[i], ap[i] = 0; 410 } 411 } 412 413 bn_correct_top(r); 414 bn_correct_top(ret); 415 416 return 1; 417} 418#endif 419 420#define PTR_SIZE_INT size_t 421 422static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, const BN_MONT_CTX *mont) 423 { 424 BIGNUM *n; 425 BN_ULONG *ap,*np,*rp,n0,v,carry; 426 int nl,max,i; 427 428 n= (BIGNUM*) &(mont->N); 429 nl=n->top; 430 if (nl == 0) { ret->top=0; return(1); } 431 432 max=(2*nl); /* carry is stored separately */ 433 if (bn_wexpand(r,max) == NULL) return(0); 434 435 r->neg^=n->neg; 436 np=n->d; 437 rp=r->d; 438 439 /* clear the top words of T */ 440#if 1 441 for (i=r->top; i<max; i++) /* memset? XXX */ 442 rp[i]=0; 443#else 444 memset(&(rp[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); 445#endif 446 447 r->top=max; 448 n0=mont->n0[0]; 449 450 for (carry=0, i=0; i<nl; i++, rp++) 451 { 452 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2); 453 v = (v+carry+rp[nl])&BN_MASK2; 454 carry |= (v != rp[nl]); 455 carry &= (v <= rp[nl]); 456 rp[nl]=v; 457 } 458 459 if (bn_wexpand(ret,nl) == NULL) return(0); 460 ret->top=nl; 461 ret->neg=r->neg; 462 463 rp=ret->d; 464 ap=&(r->d[nl]); 465 466 { 467 BN_ULONG *nrp; 468 size_t m; 469 470 v=bn_sub_words(rp,ap,np,nl)-carry; 471 /* if subtraction result is real, then 472 * trick unconditional memcpy below to perform in-place 473 * "refresh" instead of actual copy. */ 474 m=(0-(size_t)v); 475 nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)|((PTR_SIZE_INT)ap&m)); 476 477 for (i=0,nl-=4; i<nl; i+=4) 478 { 479 BN_ULONG t1,t2,t3,t4; 480 481 t1=nrp[i+0]; 482 t2=nrp[i+1]; 483 t3=nrp[i+2]; ap[i+0]=0; 484 t4=nrp[i+3]; ap[i+1]=0; 485 rp[i+0]=t1; ap[i+2]=0; 486 rp[i+1]=t2; ap[i+3]=0; 487 rp[i+2]=t3; 488 rp[i+3]=t4; 489 } 490 for (nl+=4; i<nl; i++) 491 rp[i]=nrp[i], ap[i]=0; 492 } 493 bn_correct_top(r); 494 bn_correct_top(ret); 495 496 return(1); 497 } 498 499int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, 500 BN_CTX *ctx) { 501 int retn = 0; 502 BIGNUM *t; 503 504 BN_CTX_start(ctx); 505 t = BN_CTX_get(ctx); 506 if (t == NULL) { 507 return 0; 508 } 509 510 if (BN_copy(t, a)) { 511 retn = BN_from_montgomery_word(ret, t, mont); 512 } 513 BN_CTX_end(ctx); 514 515 return retn; 516} 517 518int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 519 const BN_MONT_CTX *mont, BN_CTX *ctx) { 520 BIGNUM *tmp; 521 int ret = 0; 522 523#if defined(OPENSSL_BN_ASM_MONT) 524 int num = mont->N.top; 525 526 if (num > 1 && a->top == num && b->top == num) { 527 if (bn_wexpand(r, num) == NULL) { 528 return 0; 529 } 530 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { 531 r->neg = a->neg ^ b->neg; 532 r->top = num; 533 bn_correct_top(r); 534 return 1; 535 } 536 } 537#endif 538 539 BN_CTX_start(ctx); 540 tmp = BN_CTX_get(ctx); 541 if (tmp == NULL) { 542 goto err; 543 } 544 545 if (a == b) { 546 if (!BN_sqr(tmp, a, ctx)) { 547 goto err; 548 } 549 } else { 550 if (!BN_mul(tmp, a, b, ctx)) { 551 goto err; 552 } 553 } 554 555 /* reduce from aRR to aR */ 556 if (!BN_from_montgomery_word(r, tmp, mont)) { 557 goto err; 558 } 559 560 ret = 1; 561 562err: 563 BN_CTX_end(ctx); 564 return ret; 565} 566