bn_exp.c revision 312826
1/* crypto/bn/bn_exp.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) 1998-2005 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#include "cryptlib.h" 113#include "constant_time_locl.h" 114#include "bn_lcl.h" 115 116#include <stdlib.h> 117#ifdef _WIN32 118# include <malloc.h> 119# ifndef alloca 120# define alloca _alloca 121# endif 122#elif defined(__GNUC__) 123# ifndef alloca 124# define alloca(s) __builtin_alloca((s)) 125# endif 126#elif defined(__sun) 127# include <alloca.h> 128#endif 129 130#include "rsaz_exp.h" 131 132#undef SPARC_T4_MONT 133#if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc)) 134# include "sparc_arch.h" 135extern unsigned int OPENSSL_sparcv9cap_P[]; 136# define SPARC_T4_MONT 137#endif 138 139/* maximum precomputation table size for *variable* sliding windows */ 140#define TABLE_SIZE 32 141 142/* this one works - simple but works */ 143int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) 144{ 145 int i, bits, ret = 0; 146 BIGNUM *v, *rr; 147 148 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 149 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 150 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 151 return -1; 152 } 153 154 BN_CTX_start(ctx); 155 if ((r == a) || (r == p)) 156 rr = BN_CTX_get(ctx); 157 else 158 rr = r; 159 v = BN_CTX_get(ctx); 160 if (rr == NULL || v == NULL) 161 goto err; 162 163 if (BN_copy(v, a) == NULL) 164 goto err; 165 bits = BN_num_bits(p); 166 167 if (BN_is_odd(p)) { 168 if (BN_copy(rr, a) == NULL) 169 goto err; 170 } else { 171 if (!BN_one(rr)) 172 goto err; 173 } 174 175 for (i = 1; i < bits; i++) { 176 if (!BN_sqr(v, v, ctx)) 177 goto err; 178 if (BN_is_bit_set(p, i)) { 179 if (!BN_mul(rr, rr, v, ctx)) 180 goto err; 181 } 182 } 183 if (r != rr && BN_copy(r, rr) == NULL) 184 goto err; 185 186 ret = 1; 187 err: 188 BN_CTX_end(ctx); 189 bn_check_top(r); 190 return (ret); 191} 192 193int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 194 BN_CTX *ctx) 195{ 196 int ret; 197 198 bn_check_top(a); 199 bn_check_top(p); 200 bn_check_top(m); 201 202 /*- 203 * For even modulus m = 2^k*m_odd, it might make sense to compute 204 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 205 * exponentiation for the odd part), using appropriate exponent 206 * reductions, and combine the results using the CRT. 207 * 208 * For now, we use Montgomery only if the modulus is odd; otherwise, 209 * exponentiation using the reciprocal-based quick remaindering 210 * algorithm is used. 211 * 212 * (Timing obtained with expspeed.c [computations a^p mod m 213 * where a, p, m are of the same length: 256, 512, 1024, 2048, 214 * 4096, 8192 bits], compared to the running time of the 215 * standard algorithm: 216 * 217 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 218 * 55 .. 77 % [UltraSparc processor, but 219 * debug-solaris-sparcv8-gcc conf.] 220 * 221 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 222 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 223 * 224 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 225 * at 2048 and more bits, but at 512 and 1024 bits, it was 226 * slower even than the standard algorithm! 227 * 228 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 229 * should be obtained when the new Montgomery reduction code 230 * has been integrated into OpenSSL.) 231 */ 232 233#define MONT_MUL_MOD 234#define MONT_EXP_WORD 235#define RECP_MUL_MOD 236 237#ifdef MONT_MUL_MOD 238 /* 239 * I have finally been able to take out this pre-condition of the top bit 240 * being set. It was caused by an error in BN_div with negatives. There 241 * was also another problem when for a^b%m a >= m. eay 07-May-97 242 */ 243 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ 244 245 if (BN_is_odd(m)) { 246# ifdef MONT_EXP_WORD 247 if (a->top == 1 && !a->neg 248 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) { 249 BN_ULONG A = a->d[0]; 250 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); 251 } else 252# endif 253 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); 254 } else 255#endif 256#ifdef RECP_MUL_MOD 257 { 258 ret = BN_mod_exp_recp(r, a, p, m, ctx); 259 } 260#else 261 { 262 ret = BN_mod_exp_simple(r, a, p, m, ctx); 263 } 264#endif 265 266 bn_check_top(r); 267 return (ret); 268} 269 270int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 271 const BIGNUM *m, BN_CTX *ctx) 272{ 273 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 274 int start = 1; 275 BIGNUM *aa; 276 /* Table of variables obtained from 'ctx' */ 277 BIGNUM *val[TABLE_SIZE]; 278 BN_RECP_CTX recp; 279 280 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 281 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 282 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 283 return -1; 284 } 285 286 bits = BN_num_bits(p); 287 if (bits == 0) { 288 /* x**0 mod 1 is still zero. */ 289 if (BN_is_one(m)) { 290 ret = 1; 291 BN_zero(r); 292 } else { 293 ret = BN_one(r); 294 } 295 return ret; 296 } 297 298 BN_CTX_start(ctx); 299 aa = BN_CTX_get(ctx); 300 val[0] = BN_CTX_get(ctx); 301 if (!aa || !val[0]) 302 goto err; 303 304 BN_RECP_CTX_init(&recp); 305 if (m->neg) { 306 /* ignore sign of 'm' */ 307 if (!BN_copy(aa, m)) 308 goto err; 309 aa->neg = 0; 310 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) 311 goto err; 312 } else { 313 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) 314 goto err; 315 } 316 317 if (!BN_nnmod(val[0], a, m, ctx)) 318 goto err; /* 1 */ 319 if (BN_is_zero(val[0])) { 320 BN_zero(r); 321 ret = 1; 322 goto err; 323 } 324 325 window = BN_window_bits_for_exponent_size(bits); 326 if (window > 1) { 327 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) 328 goto err; /* 2 */ 329 j = 1 << (window - 1); 330 for (i = 1; i < j; i++) { 331 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 332 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) 333 goto err; 334 } 335 } 336 337 start = 1; /* This is used to avoid multiplication etc 338 * when there is only the value '1' in the 339 * buffer. */ 340 wvalue = 0; /* The 'value' of the window */ 341 wstart = bits - 1; /* The top bit of the window */ 342 wend = 0; /* The bottom bit of the window */ 343 344 if (!BN_one(r)) 345 goto err; 346 347 for (;;) { 348 if (BN_is_bit_set(p, wstart) == 0) { 349 if (!start) 350 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 351 goto err; 352 if (wstart == 0) 353 break; 354 wstart--; 355 continue; 356 } 357 /* 358 * We now have wstart on a 'set' bit, we now need to work out how bit 359 * a window to do. To do this we need to scan forward until the last 360 * set bit before the end of the window 361 */ 362 j = wstart; 363 wvalue = 1; 364 wend = 0; 365 for (i = 1; i < window; i++) { 366 if (wstart - i < 0) 367 break; 368 if (BN_is_bit_set(p, wstart - i)) { 369 wvalue <<= (i - wend); 370 wvalue |= 1; 371 wend = i; 372 } 373 } 374 375 /* wend is the size of the current window */ 376 j = wend + 1; 377 /* add the 'bytes above' */ 378 if (!start) 379 for (i = 0; i < j; i++) { 380 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 381 goto err; 382 } 383 384 /* wvalue will be an odd number < 2^window */ 385 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) 386 goto err; 387 388 /* move the 'window' down further */ 389 wstart -= wend + 1; 390 wvalue = 0; 391 start = 0; 392 if (wstart < 0) 393 break; 394 } 395 ret = 1; 396 err: 397 BN_CTX_end(ctx); 398 BN_RECP_CTX_free(&recp); 399 bn_check_top(r); 400 return (ret); 401} 402 403int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 404 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 405{ 406 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 407 int start = 1; 408 BIGNUM *d, *r; 409 const BIGNUM *aa; 410 /* Table of variables obtained from 'ctx' */ 411 BIGNUM *val[TABLE_SIZE]; 412 BN_MONT_CTX *mont = NULL; 413 414 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 415 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 416 } 417 418 bn_check_top(a); 419 bn_check_top(p); 420 bn_check_top(m); 421 422 if (!BN_is_odd(m)) { 423 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); 424 return (0); 425 } 426 bits = BN_num_bits(p); 427 if (bits == 0) { 428 /* x**0 mod 1 is still zero. */ 429 if (BN_is_one(m)) { 430 ret = 1; 431 BN_zero(rr); 432 } else { 433 ret = BN_one(rr); 434 } 435 return ret; 436 } 437 438 BN_CTX_start(ctx); 439 d = BN_CTX_get(ctx); 440 r = BN_CTX_get(ctx); 441 val[0] = BN_CTX_get(ctx); 442 if (!d || !r || !val[0]) 443 goto err; 444 445 /* 446 * If this is not done, things will break in the montgomery part 447 */ 448 449 if (in_mont != NULL) 450 mont = in_mont; 451 else { 452 if ((mont = BN_MONT_CTX_new()) == NULL) 453 goto err; 454 if (!BN_MONT_CTX_set(mont, m, ctx)) 455 goto err; 456 } 457 458 if (a->neg || BN_ucmp(a, m) >= 0) { 459 if (!BN_nnmod(val[0], a, m, ctx)) 460 goto err; 461 aa = val[0]; 462 } else 463 aa = a; 464 if (BN_is_zero(aa)) { 465 BN_zero(rr); 466 ret = 1; 467 goto err; 468 } 469 if (!BN_to_montgomery(val[0], aa, mont, ctx)) 470 goto err; /* 1 */ 471 472 window = BN_window_bits_for_exponent_size(bits); 473 if (window > 1) { 474 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) 475 goto err; /* 2 */ 476 j = 1 << (window - 1); 477 for (i = 1; i < j; i++) { 478 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 479 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) 480 goto err; 481 } 482 } 483 484 start = 1; /* This is used to avoid multiplication etc 485 * when there is only the value '1' in the 486 * buffer. */ 487 wvalue = 0; /* The 'value' of the window */ 488 wstart = bits - 1; /* The top bit of the window */ 489 wend = 0; /* The bottom bit of the window */ 490 491#if 1 /* by Shay Gueron's suggestion */ 492 j = m->top; /* borrow j */ 493 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 494 if (bn_wexpand(r, j) == NULL) 495 goto err; 496 /* 2^(top*BN_BITS2) - m */ 497 r->d[0] = (0 - m->d[0]) & BN_MASK2; 498 for (i = 1; i < j; i++) 499 r->d[i] = (~m->d[i]) & BN_MASK2; 500 r->top = j; 501 /* 502 * Upper words will be zero if the corresponding words of 'm' were 503 * 0xfff[...], so decrement r->top accordingly. 504 */ 505 bn_correct_top(r); 506 } else 507#endif 508 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) 509 goto err; 510 for (;;) { 511 if (BN_is_bit_set(p, wstart) == 0) { 512 if (!start) { 513 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 514 goto err; 515 } 516 if (wstart == 0) 517 break; 518 wstart--; 519 continue; 520 } 521 /* 522 * We now have wstart on a 'set' bit, we now need to work out how bit 523 * a window to do. To do this we need to scan forward until the last 524 * set bit before the end of the window 525 */ 526 j = wstart; 527 wvalue = 1; 528 wend = 0; 529 for (i = 1; i < window; i++) { 530 if (wstart - i < 0) 531 break; 532 if (BN_is_bit_set(p, wstart - i)) { 533 wvalue <<= (i - wend); 534 wvalue |= 1; 535 wend = i; 536 } 537 } 538 539 /* wend is the size of the current window */ 540 j = wend + 1; 541 /* add the 'bytes above' */ 542 if (!start) 543 for (i = 0; i < j; i++) { 544 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 545 goto err; 546 } 547 548 /* wvalue will be an odd number < 2^window */ 549 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) 550 goto err; 551 552 /* move the 'window' down further */ 553 wstart -= wend + 1; 554 wvalue = 0; 555 start = 0; 556 if (wstart < 0) 557 break; 558 } 559#if defined(SPARC_T4_MONT) 560 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 561 j = mont->N.top; /* borrow j */ 562 val[0]->d[0] = 1; /* borrow val[0] */ 563 for (i = 1; i < j; i++) 564 val[0]->d[i] = 0; 565 val[0]->top = j; 566 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) 567 goto err; 568 } else 569#endif 570 if (!BN_from_montgomery(rr, r, mont, ctx)) 571 goto err; 572 ret = 1; 573 err: 574 if ((in_mont == NULL) && (mont != NULL)) 575 BN_MONT_CTX_free(mont); 576 BN_CTX_end(ctx); 577 bn_check_top(rr); 578 return (ret); 579} 580 581#if defined(SPARC_T4_MONT) 582static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) 583{ 584 BN_ULONG ret = 0; 585 int wordpos; 586 587 wordpos = bitpos / BN_BITS2; 588 bitpos %= BN_BITS2; 589 if (wordpos >= 0 && wordpos < a->top) { 590 ret = a->d[wordpos] & BN_MASK2; 591 if (bitpos) { 592 ret >>= bitpos; 593 if (++wordpos < a->top) 594 ret |= a->d[wordpos] << (BN_BITS2 - bitpos); 595 } 596 } 597 598 return ret & BN_MASK2; 599} 600#endif 601 602/* 603 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific 604 * layout so that accessing any of these table values shows the same access 605 * pattern as far as cache lines are concerned. The following functions are 606 * used to transfer a BIGNUM from/to that table. 607 */ 608 609static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, 610 unsigned char *buf, int idx, 611 int window) 612{ 613 int i, j; 614 int width = 1 << window; 615 BN_ULONG *table = (BN_ULONG *)buf; 616 617 if (top > b->top) 618 top = b->top; /* this works because 'buf' is explicitly 619 * zeroed */ 620 for (i = 0, j = idx; i < top; i++, j += width) { 621 table[j] = b->d[i]; 622 } 623 624 return 1; 625} 626 627static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, 628 unsigned char *buf, int idx, 629 int window) 630{ 631 int i, j; 632 int width = 1 << window; 633 volatile BN_ULONG *table = (volatile BN_ULONG *)buf; 634 635 if (bn_wexpand(b, top) == NULL) 636 return 0; 637 638 if (window <= 3) { 639 for (i = 0; i < top; i++, table += width) { 640 BN_ULONG acc = 0; 641 642 for (j = 0; j < width; j++) { 643 acc |= table[j] & 644 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 645 } 646 647 b->d[i] = acc; 648 } 649 } else { 650 int xstride = 1 << (window - 2); 651 BN_ULONG y0, y1, y2, y3; 652 653 i = idx >> (window - 2); /* equivalent of idx / xstride */ 654 idx &= xstride - 1; /* equivalent of idx % xstride */ 655 656 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); 657 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); 658 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); 659 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); 660 661 for (i = 0; i < top; i++, table += width) { 662 BN_ULONG acc = 0; 663 664 for (j = 0; j < xstride; j++) { 665 acc |= ( (table[j + 0 * xstride] & y0) | 666 (table[j + 1 * xstride] & y1) | 667 (table[j + 2 * xstride] & y2) | 668 (table[j + 3 * xstride] & y3) ) 669 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 670 } 671 672 b->d[i] = acc; 673 } 674 } 675 676 b->top = top; 677 bn_correct_top(b); 678 return 1; 679} 680 681/* 682 * Given a pointer value, compute the next address that is a cache line 683 * multiple. 684 */ 685#define MOD_EXP_CTIME_ALIGN(x_) \ 686 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 687 688/* 689 * This variant of BN_mod_exp_mont() uses fixed windows and the special 690 * precomputation memory layout to limit data-dependency to a minimum to 691 * protect secret exponents (cf. the hyper-threading timing attacks pointed 692 * out by Colin Percival, 693 * http://www.daemonology.net/hyperthreading-considered-harmful/) 694 */ 695int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 696 const BIGNUM *m, BN_CTX *ctx, 697 BN_MONT_CTX *in_mont) 698{ 699 int i, bits, ret = 0, window, wvalue; 700 int top; 701 BN_MONT_CTX *mont = NULL; 702 703 int numPowers; 704 unsigned char *powerbufFree = NULL; 705 int powerbufLen = 0; 706 unsigned char *powerbuf = NULL; 707 BIGNUM tmp, am; 708#if defined(SPARC_T4_MONT) 709 unsigned int t4 = 0; 710#endif 711 712 bn_check_top(a); 713 bn_check_top(p); 714 bn_check_top(m); 715 716 if (!BN_is_odd(m)) { 717 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); 718 return (0); 719 } 720 721 top = m->top; 722 723 bits = BN_num_bits(p); 724 if (bits == 0) { 725 /* x**0 mod 1 is still zero. */ 726 if (BN_is_one(m)) { 727 ret = 1; 728 BN_zero(rr); 729 } else { 730 ret = BN_one(rr); 731 } 732 return ret; 733 } 734 735 BN_CTX_start(ctx); 736 737 /* 738 * Allocate a montgomery context if it was not supplied by the caller. If 739 * this is not done, things will break in the montgomery part. 740 */ 741 if (in_mont != NULL) 742 mont = in_mont; 743 else { 744 if ((mont = BN_MONT_CTX_new()) == NULL) 745 goto err; 746 if (!BN_MONT_CTX_set(mont, m, ctx)) 747 goto err; 748 } 749 750#ifdef RSAZ_ENABLED 751 /* 752 * If the size of the operands allow it, perform the optimized 753 * RSAZ exponentiation. For further information see 754 * crypto/bn/rsaz_exp.c and accompanying assembly modules. 755 */ 756 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) 757 && rsaz_avx2_eligible()) { 758 if (NULL == bn_wexpand(rr, 16)) 759 goto err; 760 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, 761 mont->n0[0]); 762 rr->top = 16; 763 rr->neg = 0; 764 bn_correct_top(rr); 765 ret = 1; 766 goto err; 767 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { 768 if (NULL == bn_wexpand(rr, 8)) 769 goto err; 770 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); 771 rr->top = 8; 772 rr->neg = 0; 773 bn_correct_top(rr); 774 ret = 1; 775 goto err; 776 } 777#endif 778 779 /* Get the window size to use with size of p. */ 780 window = BN_window_bits_for_ctime_exponent_size(bits); 781#if defined(SPARC_T4_MONT) 782 if (window >= 5 && (top & 15) == 0 && top <= 64 && 783 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == 784 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) 785 window = 5; 786 else 787#endif 788#if defined(OPENSSL_BN_ASM_MONT5) 789 if (window >= 5) { 790 window = 5; /* ~5% improvement for RSA2048 sign, and even 791 * for RSA4096 */ 792 /* reserve space for mont->N.d[] copy */ 793 powerbufLen += top * sizeof(mont->N.d[0]); 794 } 795#endif 796 (void)0; 797 798 /* 799 * Allocate a buffer large enough to hold all of the pre-computed powers 800 * of am, am itself and tmp. 801 */ 802 numPowers = 1 << window; 803 powerbufLen += sizeof(m->d[0]) * (top * numPowers + 804 ((2 * top) > 805 numPowers ? (2 * top) : numPowers)); 806#ifdef alloca 807 if (powerbufLen < 3072) 808 powerbufFree = 809 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); 810 else 811#endif 812 if ((powerbufFree = 813 (unsigned char *)OPENSSL_malloc(powerbufLen + 814 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) 815 == NULL) 816 goto err; 817 818 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 819 memset(powerbuf, 0, powerbufLen); 820 821#ifdef alloca 822 if (powerbufLen < 3072) 823 powerbufFree = NULL; 824#endif 825 826 /* lay down tmp and am right after powers table */ 827 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); 828 am.d = tmp.d + top; 829 tmp.top = am.top = 0; 830 tmp.dmax = am.dmax = top; 831 tmp.neg = am.neg = 0; 832 tmp.flags = am.flags = BN_FLG_STATIC_DATA; 833 834 /* prepare a^0 in Montgomery domain */ 835#if 1 /* by Shay Gueron's suggestion */ 836 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 837 /* 2^(top*BN_BITS2) - m */ 838 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; 839 for (i = 1; i < top; i++) 840 tmp.d[i] = (~m->d[i]) & BN_MASK2; 841 tmp.top = top; 842 } else 843#endif 844 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx)) 845 goto err; 846 847 /* prepare a^1 in Montgomery domain */ 848 if (a->neg || BN_ucmp(a, m) >= 0) { 849 if (!BN_mod(&am, a, m, ctx)) 850 goto err; 851 if (!BN_to_montgomery(&am, &am, mont, ctx)) 852 goto err; 853 } else if (!BN_to_montgomery(&am, a, mont, ctx)) 854 goto err; 855 856#if defined(SPARC_T4_MONT) 857 if (t4) { 858 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, 859 const BN_ULONG *n0, const void *table, 860 int power, int bits); 861 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, 862 const BN_ULONG *n0, const void *table, 863 int power, int bits); 864 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, 865 const BN_ULONG *n0, const void *table, 866 int power, int bits); 867 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, 868 const BN_ULONG *n0, const void *table, 869 int power, int bits); 870 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, 871 const BN_ULONG *n0, const void *table, 872 int power, int bits); 873 static const bn_pwr5_mont_f pwr5_funcs[4] = { 874 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, 875 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 876 }; 877 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; 878 879 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, 880 const void *bp, const BN_ULONG *np, 881 const BN_ULONG *n0); 882 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, 883 const BN_ULONG *np, const BN_ULONG *n0); 884 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, 885 const void *bp, const BN_ULONG *np, 886 const BN_ULONG *n0); 887 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, 888 const void *bp, const BN_ULONG *np, 889 const BN_ULONG *n0); 890 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, 891 const void *bp, const BN_ULONG *np, 892 const BN_ULONG *n0); 893 static const bn_mul_mont_f mul_funcs[4] = { 894 bn_mul_mont_t4_8, bn_mul_mont_t4_16, 895 bn_mul_mont_t4_24, bn_mul_mont_t4_32 896 }; 897 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; 898 899 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, 900 const void *bp, const BN_ULONG *np, 901 const BN_ULONG *n0, int num); 902 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, 903 const void *bp, const BN_ULONG *np, 904 const BN_ULONG *n0, int num); 905 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, 906 const void *table, const BN_ULONG *np, 907 const BN_ULONG *n0, int num, int power); 908 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, 909 void *table, size_t power); 910 void bn_gather5_t4(BN_ULONG *out, size_t num, 911 void *table, size_t power); 912 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); 913 914 BN_ULONG *np = mont->N.d, *n0 = mont->n0; 915 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less 916 * than 32 */ 917 918 /* 919 * BN_to_montgomery can contaminate words above .top [in 920 * BN_DEBUG[_DEBUG] build]... 921 */ 922 for (i = am.top; i < top; i++) 923 am.d[i] = 0; 924 for (i = tmp.top; i < top; i++) 925 tmp.d[i] = 0; 926 927 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); 928 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); 929 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && 930 !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) 931 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); 932 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); 933 934 for (i = 3; i < 32; i++) { 935 /* Calculate a^i = a^(i-1) * a */ 936 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && 937 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) 938 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); 939 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); 940 } 941 942 /* switch to 64-bit domain */ 943 np = alloca(top * sizeof(BN_ULONG)); 944 top /= 2; 945 bn_flip_t4(np, mont->N.d, top); 946 947 bits--; 948 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) 949 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 950 bn_gather5_t4(tmp.d, top, powerbuf, wvalue); 951 952 /* 953 * Scan the exponent one window at a time starting from the most 954 * significant bits. 955 */ 956 while (bits >= 0) { 957 if (bits < stride) 958 stride = bits + 1; 959 bits -= stride; 960 wvalue = bn_get_bits(p, bits + 1); 961 962 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 963 continue; 964 /* retry once and fall back */ 965 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 966 continue; 967 968 bits += stride - 5; 969 wvalue >>= stride - 5; 970 wvalue &= 31; 971 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 972 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 973 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 974 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 975 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 976 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, 977 wvalue); 978 } 979 980 bn_flip_t4(tmp.d, tmp.d, top); 981 top *= 2; 982 /* back to 32-bit domain */ 983 tmp.top = top; 984 bn_correct_top(&tmp); 985 OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); 986 } else 987#endif 988#if defined(OPENSSL_BN_ASM_MONT5) 989 if (window == 5 && top > 1) { 990 /* 991 * This optimization uses ideas from http://eprint.iacr.org/2011/239, 992 * specifically optimization of cache-timing attack countermeasures 993 * and pre-computation optimization. 994 */ 995 996 /* 997 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as 998 * 512-bit RSA is hardly relevant, we omit it to spare size... 999 */ 1000 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, 1001 const void *table, const BN_ULONG *np, 1002 const BN_ULONG *n0, int num, int power); 1003 void bn_scatter5(const BN_ULONG *inp, size_t num, 1004 void *table, size_t power); 1005 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); 1006 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, 1007 const void *table, const BN_ULONG *np, 1008 const BN_ULONG *n0, int num, int power); 1009 int bn_get_bits5(const BN_ULONG *ap, int off); 1010 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, 1011 const BN_ULONG *not_used, const BN_ULONG *np, 1012 const BN_ULONG *n0, int num); 1013 1014 BN_ULONG *n0 = mont->n0, *np; 1015 1016 /* 1017 * BN_to_montgomery can contaminate words above .top [in 1018 * BN_DEBUG[_DEBUG] build]... 1019 */ 1020 for (i = am.top; i < top; i++) 1021 am.d[i] = 0; 1022 for (i = tmp.top; i < top; i++) 1023 tmp.d[i] = 0; 1024 1025 /* 1026 * copy mont->N.d[] to improve cache locality 1027 */ 1028 for (np = am.d + top, i = 0; i < top; i++) 1029 np[i] = mont->N.d[i]; 1030 1031 bn_scatter5(tmp.d, top, powerbuf, 0); 1032 bn_scatter5(am.d, am.top, powerbuf, 1); 1033 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); 1034 bn_scatter5(tmp.d, top, powerbuf, 2); 1035 1036# if 0 1037 for (i = 3; i < 32; i++) { 1038 /* Calculate a^i = a^(i-1) * a */ 1039 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1040 bn_scatter5(tmp.d, top, powerbuf, i); 1041 } 1042# else 1043 /* same as above, but uses squaring for 1/2 of operations */ 1044 for (i = 4; i < 32; i *= 2) { 1045 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1046 bn_scatter5(tmp.d, top, powerbuf, i); 1047 } 1048 for (i = 3; i < 8; i += 2) { 1049 int j; 1050 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1051 bn_scatter5(tmp.d, top, powerbuf, i); 1052 for (j = 2 * i; j < 32; j *= 2) { 1053 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1054 bn_scatter5(tmp.d, top, powerbuf, j); 1055 } 1056 } 1057 for (; i < 16; i += 2) { 1058 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1059 bn_scatter5(tmp.d, top, powerbuf, i); 1060 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1061 bn_scatter5(tmp.d, top, powerbuf, 2 * i); 1062 } 1063 for (; i < 32; i += 2) { 1064 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1065 bn_scatter5(tmp.d, top, powerbuf, i); 1066 } 1067# endif 1068 bits--; 1069 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) 1070 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1071 bn_gather5(tmp.d, top, powerbuf, wvalue); 1072 1073 /* 1074 * Scan the exponent one window at a time starting from the most 1075 * significant bits. 1076 */ 1077 if (top & 7) 1078 while (bits >= 0) { 1079 for (wvalue = 0, i = 0; i < 5; i++, bits--) 1080 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1081 1082 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1083 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1084 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1085 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1086 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1087 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, 1088 wvalue); 1089 } else { 1090 while (bits >= 0) { 1091 wvalue = bn_get_bits5(p->d, bits - 4); 1092 bits -= 5; 1093 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue); 1094 } 1095 } 1096 1097 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top); 1098 tmp.top = top; 1099 bn_correct_top(&tmp); 1100 if (ret) { 1101 if (!BN_copy(rr, &tmp)) 1102 ret = 0; 1103 goto err; /* non-zero ret means it's not error */ 1104 } 1105 } else 1106#endif 1107 { 1108 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) 1109 goto err; 1110 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) 1111 goto err; 1112 1113 /* 1114 * If the window size is greater than 1, then calculate 1115 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even 1116 * powers could instead be computed as (a^(i/2))^2 to use the slight 1117 * performance advantage of sqr over mul). 1118 */ 1119 if (window > 1) { 1120 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) 1121 goto err; 1122 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, 1123 window)) 1124 goto err; 1125 for (i = 3; i < numPowers; i++) { 1126 /* Calculate a^i = a^(i-1) * a */ 1127 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) 1128 goto err; 1129 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, 1130 window)) 1131 goto err; 1132 } 1133 } 1134 1135 bits--; 1136 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) 1137 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1138 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, 1139 window)) 1140 goto err; 1141 1142 /* 1143 * Scan the exponent one window at a time starting from the most 1144 * significant bits. 1145 */ 1146 while (bits >= 0) { 1147 wvalue = 0; /* The 'value' of the window */ 1148 1149 /* Scan the window, squaring the result as we go */ 1150 for (i = 0; i < window; i++, bits--) { 1151 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx)) 1152 goto err; 1153 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1154 } 1155 1156 /* 1157 * Fetch the appropriate pre-computed value from the pre-buf 1158 */ 1159 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, 1160 window)) 1161 goto err; 1162 1163 /* Multiply the result into the intermediate result */ 1164 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx)) 1165 goto err; 1166 } 1167 } 1168 1169 /* Convert the final result from montgomery to standard format */ 1170#if defined(SPARC_T4_MONT) 1171 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 1172 am.d[0] = 1; /* borrow am */ 1173 for (i = 1; i < top; i++) 1174 am.d[i] = 0; 1175 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) 1176 goto err; 1177 } else 1178#endif 1179 if (!BN_from_montgomery(rr, &tmp, mont, ctx)) 1180 goto err; 1181 ret = 1; 1182 err: 1183 if ((in_mont == NULL) && (mont != NULL)) 1184 BN_MONT_CTX_free(mont); 1185 if (powerbuf != NULL) { 1186 OPENSSL_cleanse(powerbuf, powerbufLen); 1187 if (powerbufFree) 1188 OPENSSL_free(powerbufFree); 1189 } 1190 BN_CTX_end(ctx); 1191 return (ret); 1192} 1193 1194int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 1195 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 1196{ 1197 BN_MONT_CTX *mont = NULL; 1198 int b, bits, ret = 0; 1199 int r_is_one; 1200 BN_ULONG w, next_w; 1201 BIGNUM *d, *r, *t; 1202 BIGNUM *swap_tmp; 1203#define BN_MOD_MUL_WORD(r, w, m) \ 1204 (BN_mul_word(r, (w)) && \ 1205 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 1206 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 1207 /* 1208 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is 1209 * probably more overhead than always using BN_mod (which uses BN_copy if 1210 * a similar test returns true). 1211 */ 1212 /* 1213 * We can use BN_mod and do not need BN_nnmod because our accumulator is 1214 * never negative (the result of BN_mod does not depend on the sign of 1215 * the modulus). 1216 */ 1217#define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 1218 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 1219 1220 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 1221 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1222 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1223 return -1; 1224 } 1225 1226 bn_check_top(p); 1227 bn_check_top(m); 1228 1229 if (!BN_is_odd(m)) { 1230 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); 1231 return (0); 1232 } 1233 if (m->top == 1) 1234 a %= m->d[0]; /* make sure that 'a' is reduced */ 1235 1236 bits = BN_num_bits(p); 1237 if (bits == 0) { 1238 /* x**0 mod 1 is still zero. */ 1239 if (BN_is_one(m)) { 1240 ret = 1; 1241 BN_zero(rr); 1242 } else { 1243 ret = BN_one(rr); 1244 } 1245 return ret; 1246 } 1247 if (a == 0) { 1248 BN_zero(rr); 1249 ret = 1; 1250 return ret; 1251 } 1252 1253 BN_CTX_start(ctx); 1254 d = BN_CTX_get(ctx); 1255 r = BN_CTX_get(ctx); 1256 t = BN_CTX_get(ctx); 1257 if (d == NULL || r == NULL || t == NULL) 1258 goto err; 1259 1260 if (in_mont != NULL) 1261 mont = in_mont; 1262 else { 1263 if ((mont = BN_MONT_CTX_new()) == NULL) 1264 goto err; 1265 if (!BN_MONT_CTX_set(mont, m, ctx)) 1266 goto err; 1267 } 1268 1269 r_is_one = 1; /* except for Montgomery factor */ 1270 1271 /* bits-1 >= 0 */ 1272 1273 /* The result is accumulated in the product r*w. */ 1274 w = a; /* bit 'bits-1' of 'p' is always set */ 1275 for (b = bits - 2; b >= 0; b--) { 1276 /* First, square r*w. */ 1277 next_w = w * w; 1278 if ((next_w / w) != w) { /* overflow */ 1279 if (r_is_one) { 1280 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1281 goto err; 1282 r_is_one = 0; 1283 } else { 1284 if (!BN_MOD_MUL_WORD(r, w, m)) 1285 goto err; 1286 } 1287 next_w = 1; 1288 } 1289 w = next_w; 1290 if (!r_is_one) { 1291 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 1292 goto err; 1293 } 1294 1295 /* Second, multiply r*w by 'a' if exponent bit is set. */ 1296 if (BN_is_bit_set(p, b)) { 1297 next_w = w * a; 1298 if ((next_w / a) != w) { /* overflow */ 1299 if (r_is_one) { 1300 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1301 goto err; 1302 r_is_one = 0; 1303 } else { 1304 if (!BN_MOD_MUL_WORD(r, w, m)) 1305 goto err; 1306 } 1307 next_w = a; 1308 } 1309 w = next_w; 1310 } 1311 } 1312 1313 /* Finally, set r:=r*w. */ 1314 if (w != 1) { 1315 if (r_is_one) { 1316 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1317 goto err; 1318 r_is_one = 0; 1319 } else { 1320 if (!BN_MOD_MUL_WORD(r, w, m)) 1321 goto err; 1322 } 1323 } 1324 1325 if (r_is_one) { /* can happen only if a == 1 */ 1326 if (!BN_one(rr)) 1327 goto err; 1328 } else { 1329 if (!BN_from_montgomery(rr, r, mont, ctx)) 1330 goto err; 1331 } 1332 ret = 1; 1333 err: 1334 if ((in_mont == NULL) && (mont != NULL)) 1335 BN_MONT_CTX_free(mont); 1336 BN_CTX_end(ctx); 1337 bn_check_top(rr); 1338 return (ret); 1339} 1340 1341/* The old fallback, simple version :-) */ 1342int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 1343 const BIGNUM *m, BN_CTX *ctx) 1344{ 1345 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 1346 int start = 1; 1347 BIGNUM *d; 1348 /* Table of variables obtained from 'ctx' */ 1349 BIGNUM *val[TABLE_SIZE]; 1350 1351 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 1352 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1353 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1354 return -1; 1355 } 1356 1357 bits = BN_num_bits(p); 1358 if (bits == 0) { 1359 /* x**0 mod 1 is still zero. */ 1360 if (BN_is_one(m)) { 1361 ret = 1; 1362 BN_zero(r); 1363 } else { 1364 ret = BN_one(r); 1365 } 1366 return ret; 1367 } 1368 1369 BN_CTX_start(ctx); 1370 d = BN_CTX_get(ctx); 1371 val[0] = BN_CTX_get(ctx); 1372 if (!d || !val[0]) 1373 goto err; 1374 1375 if (!BN_nnmod(val[0], a, m, ctx)) 1376 goto err; /* 1 */ 1377 if (BN_is_zero(val[0])) { 1378 BN_zero(r); 1379 ret = 1; 1380 goto err; 1381 } 1382 1383 window = BN_window_bits_for_exponent_size(bits); 1384 if (window > 1) { 1385 if (!BN_mod_mul(d, val[0], val[0], m, ctx)) 1386 goto err; /* 2 */ 1387 j = 1 << (window - 1); 1388 for (i = 1; i < j; i++) { 1389 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 1390 !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) 1391 goto err; 1392 } 1393 } 1394 1395 start = 1; /* This is used to avoid multiplication etc 1396 * when there is only the value '1' in the 1397 * buffer. */ 1398 wvalue = 0; /* The 'value' of the window */ 1399 wstart = bits - 1; /* The top bit of the window */ 1400 wend = 0; /* The bottom bit of the window */ 1401 1402 if (!BN_one(r)) 1403 goto err; 1404 1405 for (;;) { 1406 if (BN_is_bit_set(p, wstart) == 0) { 1407 if (!start) 1408 if (!BN_mod_mul(r, r, r, m, ctx)) 1409 goto err; 1410 if (wstart == 0) 1411 break; 1412 wstart--; 1413 continue; 1414 } 1415 /* 1416 * We now have wstart on a 'set' bit, we now need to work out how bit 1417 * a window to do. To do this we need to scan forward until the last 1418 * set bit before the end of the window 1419 */ 1420 j = wstart; 1421 wvalue = 1; 1422 wend = 0; 1423 for (i = 1; i < window; i++) { 1424 if (wstart - i < 0) 1425 break; 1426 if (BN_is_bit_set(p, wstart - i)) { 1427 wvalue <<= (i - wend); 1428 wvalue |= 1; 1429 wend = i; 1430 } 1431 } 1432 1433 /* wend is the size of the current window */ 1434 j = wend + 1; 1435 /* add the 'bytes above' */ 1436 if (!start) 1437 for (i = 0; i < j; i++) { 1438 if (!BN_mod_mul(r, r, r, m, ctx)) 1439 goto err; 1440 } 1441 1442 /* wvalue will be an odd number < 2^window */ 1443 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) 1444 goto err; 1445 1446 /* move the 'window' down further */ 1447 wstart -= wend + 1; 1448 wvalue = 0; 1449 start = 0; 1450 if (wstart < 0) 1451 break; 1452 } 1453 ret = 1; 1454 err: 1455 BN_CTX_end(ctx); 1456 bn_check_top(r); 1457 return (ret); 1458} 1459