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 <string.h> 112 113 #include <openssl/err.h> 114 #include <openssl/mem.h> 115 #include <openssl/thread.h> 116 117 #include "internal.h" 118 #include "../internal.h" 119 120 121 #if !defined(OPENSSL_NO_ASM) && \ 122 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \ 123 defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64)) 124 #define OPENSSL_BN_ASM_MONT 125 #endif 126 127 BN_MONT_CTX *BN_MONT_CTX_new(void) { 128 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX)); 129 130 if (ret == NULL) { 131 return NULL; 132 } 133 134 memset(ret, 0, sizeof(BN_MONT_CTX)); 135 BN_init(&ret->RR); 136 BN_init(&ret->N); 137 138 return ret; 139 } 140 141 void BN_MONT_CTX_free(BN_MONT_CTX *mont) { 142 if (mont == NULL) { 143 return; 144 } 145 146 BN_free(&mont->RR); 147 BN_free(&mont->N); 148 OPENSSL_free(mont); 149 } 150 151 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) { 152 if (to == from) { 153 return to; 154 } 155 156 if (!BN_copy(&to->RR, &from->RR) || 157 !BN_copy(&to->N, &from->N)) { 158 return NULL; 159 } 160 to->n0[0] = from->n0[0]; 161 to->n0[1] = from->n0[1]; 162 return to; 163 } 164 165 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) { 166 int ret = 0; 167 BIGNUM *Ri, *R; 168 BIGNUM tmod; 169 BN_ULONG buf[2]; 170 171 if (BN_is_zero(mod)) { 172 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO); 173 return 0; 174 } 175 176 BN_CTX_start(ctx); 177 Ri = BN_CTX_get(ctx); 178 if (Ri == NULL) { 179 goto err; 180 } 181 R = &mont->RR; /* grab RR as a temp */ 182 if (!BN_copy(&mont->N, mod)) { 183 goto err; /* Set N */ 184 } 185 mont->N.neg = 0; 186 187 BN_init(&tmod); 188 tmod.d = buf; 189 tmod.dmax = 2; 190 tmod.neg = 0; 191 192 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2 <= 32) 193 /* Only certain BN_BITS2<=32 platforms actually make use of 194 * n0[1], and we could use the #else case (with a shorter R 195 * value) for the others. However, currently only the assembler 196 * files do know which is which. */ 197 198 BN_zero(R); 199 if (!BN_set_bit(R, 2 * BN_BITS2)) { 200 goto err; 201 } 202 203 tmod.top = 0; 204 if ((buf[0] = mod->d[0])) { 205 tmod.top = 1; 206 } 207 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) { 208 tmod.top = 2; 209 } 210 211 if (BN_mod_inverse(Ri, R, &tmod, ctx) == NULL) { 212 goto err; 213 } 214 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) { 215 goto err; /* R*Ri */ 216 } 217 if (!BN_is_zero(Ri)) { 218 if (!BN_sub_word(Ri, 1)) { 219 goto err; 220 } 221 } else { 222 /* if N mod word size == 1 */ 223 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) { 224 goto err; 225 } 226 /* Ri-- (mod double word size) */ 227 Ri->neg = 0; 228 Ri->d[0] = BN_MASK2; 229 Ri->d[1] = BN_MASK2; 230 Ri->top = 2; 231 } 232 233 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) { 234 goto err; 235 } 236 /* Ni = (R*Ri-1)/N, 237 * keep only couple of least significant words: */ 238 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 239 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0; 240 #else 241 BN_zero(R); 242 if (!BN_set_bit(R, BN_BITS2)) { 243 goto err; /* R */ 244 } 245 246 buf[0] = mod->d[0]; /* tmod = N mod word size */ 247 buf[1] = 0; 248 tmod.top = buf[0] != 0 ? 1 : 0; 249 /* Ri = R^-1 mod N*/ 250 if (BN_mod_inverse(Ri, R, &tmod, ctx) == NULL) { 251 goto err; 252 } 253 if (!BN_lshift(Ri, Ri, BN_BITS2)) { 254 goto err; /* R*Ri */ 255 } 256 if (!BN_is_zero(Ri)) { 257 if (!BN_sub_word(Ri, 1)) { 258 goto err; 259 } 260 } else { 261 /* if N mod word size == 1 */ 262 if (!BN_set_word(Ri, BN_MASK2)) { 263 goto err; /* Ri-- (mod word size) */ 264 } 265 } 266 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) { 267 goto err; 268 } 269 /* Ni = (R*Ri-1)/N, 270 * keep only least significant word: */ 271 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 272 mont->n0[1] = 0; 273 #endif 274 275 /* RR = (2^ri)^2 == 2^(ri*2) == 1 << (ri*2), which has its (ri*2)th bit set. */ 276 int ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; 277 BN_zero(&(mont->RR)); 278 if (!BN_set_bit(&(mont->RR), ri * 2)) { 279 goto err; 280 } 281 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) { 282 goto err; 283 } 284 285 ret = 1; 286 287 err: 288 BN_CTX_end(ctx); 289 return ret; 290 } 291 292 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, 293 const BIGNUM *mod, BN_CTX *bn_ctx) { 294 CRYPTO_MUTEX_lock_read(lock); 295 BN_MONT_CTX *ctx = *pmont; 296 CRYPTO_MUTEX_unlock(lock); 297 298 if (ctx) { 299 return ctx; 300 } 301 302 CRYPTO_MUTEX_lock_write(lock); 303 ctx = *pmont; 304 if (ctx) { 305 goto out; 306 } 307 308 ctx = BN_MONT_CTX_new(); 309 if (ctx == NULL) { 310 goto out; 311 } 312 if (!BN_MONT_CTX_set(ctx, mod, bn_ctx)) { 313 BN_MONT_CTX_free(ctx); 314 ctx = NULL; 315 goto out; 316 } 317 *pmont = ctx; 318 319 out: 320 CRYPTO_MUTEX_unlock(lock); 321 return ctx; 322 } 323 324 int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, 325 BN_CTX *ctx) { 326 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx); 327 } 328 329 #if 0 330 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, 331 const BN_MONT_CTX *mont) { 332 const BIGNUM *n; 333 BN_ULONG *ap, *np, *rp, n0, v, carry; 334 int nl, max, i; 335 336 n = &mont->N; 337 nl = n->top; 338 if (nl == 0) { 339 ret->top = 0; 340 return 1; 341 } 342 343 max = (2 * nl); /* carry is stored separately */ 344 if (bn_wexpand(r, max) == NULL) { 345 return 0; 346 } 347 348 r->neg ^= n->neg; 349 np = n->d; 350 rp = r->d; 351 352 /* clear the top words of T */ 353 if (max > r->top) { 354 memset(&rp[r->top], 0, (max - r->top) * sizeof(BN_ULONG)); 355 } 356 357 r->top = max; 358 n0 = mont->n0[0]; 359 360 for (carry = 0, i = 0; i < nl; i++, rp++) { 361 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); 362 v = (v + carry + rp[nl]) & BN_MASK2; 363 carry |= (v != rp[nl]); 364 carry &= (v <= rp[nl]); 365 rp[nl] = v; 366 } 367 368 if (bn_wexpand(ret, nl) == NULL) { 369 return 0; 370 } 371 ret->top = nl; 372 ret->neg = r->neg; 373 374 rp = ret->d; 375 ap = &(r->d[nl]); 376 377 { 378 BN_ULONG *nrp; 379 size_t m; 380 381 v = bn_sub_words(rp, ap, np, nl) - carry; 382 /* if subtraction result is real, then trick unconditional memcpy below to 383 * perform in-place "refresh" instead of actual copy. */ 384 m = (0 - (size_t)v); 385 nrp = (BN_ULONG *)(((intptr_t)rp & ~m) | ((intptr_t)ap & m)); 386 387 for (i = 0, nl -= 4; i < nl; i += 4) { 388 BN_ULONG t1, t2, t3, t4; 389 390 t1 = nrp[i + 0]; 391 t2 = nrp[i + 1]; 392 t3 = nrp[i + 2]; 393 ap[i + 0] = 0; 394 t4 = nrp[i + 3]; 395 ap[i + 1] = 0; 396 rp[i + 0] = t1; 397 ap[i + 2] = 0; 398 rp[i + 1] = t2; 399 ap[i + 3] = 0; 400 rp[i + 2] = t3; 401 rp[i + 3] = t4; 402 } 403 404 for (nl += 4; i < nl; i++) { 405 rp[i] = nrp[i], ap[i] = 0; 406 } 407 } 408 409 bn_correct_top(r); 410 bn_correct_top(ret); 411 412 return 1; 413 } 414 #endif 415 416 #define PTR_SIZE_INT size_t 417 418 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, const BN_MONT_CTX *mont) 419 { 420 BIGNUM *n; 421 BN_ULONG *ap,*np,*rp,n0,v,carry; 422 int nl,max,i; 423 424 n= (BIGNUM*) &(mont->N); 425 nl=n->top; 426 if (nl == 0) { ret->top=0; return(1); } 427 428 max=(2*nl); /* carry is stored separately */ 429 if (bn_wexpand(r,max) == NULL) return(0); 430 431 r->neg^=n->neg; 432 np=n->d; 433 rp=r->d; 434 435 /* clear the top words of T */ 436 #if 1 437 for (i=r->top; i<max; i++) /* memset? XXX */ 438 rp[i]=0; 439 #else 440 memset(&(rp[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); 441 #endif 442 443 r->top=max; 444 n0=mont->n0[0]; 445 446 for (carry=0, i=0; i<nl; i++, rp++) 447 { 448 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2); 449 v = (v+carry+rp[nl])&BN_MASK2; 450 carry |= (v != rp[nl]); 451 carry &= (v <= rp[nl]); 452 rp[nl]=v; 453 } 454 455 if (bn_wexpand(ret,nl) == NULL) return(0); 456 ret->top=nl; 457 ret->neg=r->neg; 458 459 rp=ret->d; 460 ap=&(r->d[nl]); 461 462 { 463 BN_ULONG *nrp; 464 size_t m; 465 466 v=bn_sub_words(rp,ap,np,nl)-carry; 467 /* if subtraction result is real, then 468 * trick unconditional memcpy below to perform in-place 469 * "refresh" instead of actual copy. */ 470 m=(0-(size_t)v); 471 nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)|((PTR_SIZE_INT)ap&m)); 472 473 for (i=0,nl-=4; i<nl; i+=4) 474 { 475 BN_ULONG t1,t2,t3,t4; 476 477 t1=nrp[i+0]; 478 t2=nrp[i+1]; 479 t3=nrp[i+2]; ap[i+0]=0; 480 t4=nrp[i+3]; ap[i+1]=0; 481 rp[i+0]=t1; ap[i+2]=0; 482 rp[i+1]=t2; ap[i+3]=0; 483 rp[i+2]=t3; 484 rp[i+3]=t4; 485 } 486 for (nl+=4; i<nl; i++) 487 rp[i]=nrp[i], ap[i]=0; 488 } 489 bn_correct_top(r); 490 bn_correct_top(ret); 491 492 return(1); 493 } 494 495 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, 496 BN_CTX *ctx) { 497 int retn = 0; 498 BIGNUM *t; 499 500 BN_CTX_start(ctx); 501 t = BN_CTX_get(ctx); 502 if (t == NULL) { 503 return 0; 504 } 505 506 if (BN_copy(t, a)) { 507 retn = BN_from_montgomery_word(ret, t, mont); 508 } 509 BN_CTX_end(ctx); 510 511 return retn; 512 } 513 514 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 515 const BN_MONT_CTX *mont, BN_CTX *ctx) { 516 BIGNUM *tmp; 517 int ret = 0; 518 519 #if defined(OPENSSL_BN_ASM_MONT) 520 int num = mont->N.top; 521 522 if (num > 1 && a->top == num && b->top == num) { 523 if (bn_wexpand(r, num) == NULL) { 524 return 0; 525 } 526 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { 527 r->neg = a->neg ^ b->neg; 528 r->top = num; 529 bn_correct_top(r); 530 return 1; 531 } 532 } 533 #endif 534 535 BN_CTX_start(ctx); 536 tmp = BN_CTX_get(ctx); 537 if (tmp == NULL) { 538 goto err; 539 } 540 541 if (a == b) { 542 if (!BN_sqr(tmp, a, ctx)) { 543 goto err; 544 } 545 } else { 546 if (!BN_mul(tmp, a, b, ctx)) { 547 goto err; 548 } 549 } 550 551 /* reduce from aRR to aR */ 552 if (!BN_from_montgomery_word(r, tmp, mont)) { 553 goto err; 554 } 555 556 ret = 1; 557 558 err: 559 BN_CTX_end(ctx); 560 return ret; 561 } 562
