bn_exp.c revision 325337
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_get_flags(a, BN_FLG_CONSTTIME) != 0) { 150 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 151 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 152 return -1; 153 } 154 155 BN_CTX_start(ctx); 156 if ((r == a) || (r == p)) 157 rr = BN_CTX_get(ctx); 158 else 159 rr = r; 160 v = BN_CTX_get(ctx); 161 if (rr == NULL || v == NULL) 162 goto err; 163 164 if (BN_copy(v, a) == NULL) 165 goto err; 166 bits = BN_num_bits(p); 167 168 if (BN_is_odd(p)) { 169 if (BN_copy(rr, a) == NULL) 170 goto err; 171 } else { 172 if (!BN_one(rr)) 173 goto err; 174 } 175 176 for (i = 1; i < bits; i++) { 177 if (!BN_sqr(v, v, ctx)) 178 goto err; 179 if (BN_is_bit_set(p, i)) { 180 if (!BN_mul(rr, rr, v, ctx)) 181 goto err; 182 } 183 } 184 if (r != rr && BN_copy(r, rr) == NULL) 185 goto err; 186 187 ret = 1; 188 err: 189 BN_CTX_end(ctx); 190 bn_check_top(r); 191 return (ret); 192} 193 194int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 195 BN_CTX *ctx) 196{ 197 int ret; 198 199 bn_check_top(a); 200 bn_check_top(p); 201 bn_check_top(m); 202 203 /*- 204 * For even modulus m = 2^k*m_odd, it might make sense to compute 205 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 206 * exponentiation for the odd part), using appropriate exponent 207 * reductions, and combine the results using the CRT. 208 * 209 * For now, we use Montgomery only if the modulus is odd; otherwise, 210 * exponentiation using the reciprocal-based quick remaindering 211 * algorithm is used. 212 * 213 * (Timing obtained with expspeed.c [computations a^p mod m 214 * where a, p, m are of the same length: 256, 512, 1024, 2048, 215 * 4096, 8192 bits], compared to the running time of the 216 * standard algorithm: 217 * 218 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 219 * 55 .. 77 % [UltraSparc processor, but 220 * debug-solaris-sparcv8-gcc conf.] 221 * 222 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 223 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 224 * 225 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 226 * at 2048 and more bits, but at 512 and 1024 bits, it was 227 * slower even than the standard algorithm! 228 * 229 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 230 * should be obtained when the new Montgomery reduction code 231 * has been integrated into OpenSSL.) 232 */ 233 234#define MONT_MUL_MOD 235#define MONT_EXP_WORD 236#define RECP_MUL_MOD 237 238#ifdef MONT_MUL_MOD 239 /* 240 * I have finally been able to take out this pre-condition of the top bit 241 * being set. It was caused by an error in BN_div with negatives. There 242 * was also another problem when for a^b%m a >= m. eay 07-May-97 243 */ 244 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ 245 246 if (BN_is_odd(m)) { 247# ifdef MONT_EXP_WORD 248 if (a->top == 1 && !a->neg 249 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0) 250 && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0) 251 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) { 252 BN_ULONG A = a->d[0]; 253 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); 254 } else 255# endif 256 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); 257 } else 258#endif 259#ifdef RECP_MUL_MOD 260 { 261 ret = BN_mod_exp_recp(r, a, p, m, ctx); 262 } 263#else 264 { 265 ret = BN_mod_exp_simple(r, a, p, m, ctx); 266 } 267#endif 268 269 bn_check_top(r); 270 return (ret); 271} 272 273int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 274 const BIGNUM *m, BN_CTX *ctx) 275{ 276 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 277 int start = 1; 278 BIGNUM *aa; 279 /* Table of variables obtained from 'ctx' */ 280 BIGNUM *val[TABLE_SIZE]; 281 BN_RECP_CTX recp; 282 283 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 284 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 285 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 286 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 287 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 288 return -1; 289 } 290 291 bits = BN_num_bits(p); 292 if (bits == 0) { 293 /* x**0 mod 1 is still zero. */ 294 if (BN_is_one(m)) { 295 ret = 1; 296 BN_zero(r); 297 } else { 298 ret = BN_one(r); 299 } 300 return ret; 301 } 302 303 BN_CTX_start(ctx); 304 aa = BN_CTX_get(ctx); 305 val[0] = BN_CTX_get(ctx); 306 if (!aa || !val[0]) 307 goto err; 308 309 BN_RECP_CTX_init(&recp); 310 if (m->neg) { 311 /* ignore sign of 'm' */ 312 if (!BN_copy(aa, m)) 313 goto err; 314 aa->neg = 0; 315 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) 316 goto err; 317 } else { 318 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) 319 goto err; 320 } 321 322 if (!BN_nnmod(val[0], a, m, ctx)) 323 goto err; /* 1 */ 324 if (BN_is_zero(val[0])) { 325 BN_zero(r); 326 ret = 1; 327 goto err; 328 } 329 330 window = BN_window_bits_for_exponent_size(bits); 331 if (window > 1) { 332 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) 333 goto err; /* 2 */ 334 j = 1 << (window - 1); 335 for (i = 1; i < j; i++) { 336 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 337 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) 338 goto err; 339 } 340 } 341 342 start = 1; /* This is used to avoid multiplication etc 343 * when there is only the value '1' in the 344 * buffer. */ 345 wvalue = 0; /* The 'value' of the window */ 346 wstart = bits - 1; /* The top bit of the window */ 347 wend = 0; /* The bottom bit of the window */ 348 349 if (!BN_one(r)) 350 goto err; 351 352 for (;;) { 353 if (BN_is_bit_set(p, wstart) == 0) { 354 if (!start) 355 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 356 goto err; 357 if (wstart == 0) 358 break; 359 wstart--; 360 continue; 361 } 362 /* 363 * We now have wstart on a 'set' bit, we now need to work out how bit 364 * a window to do. To do this we need to scan forward until the last 365 * set bit before the end of the window 366 */ 367 j = wstart; 368 wvalue = 1; 369 wend = 0; 370 for (i = 1; i < window; i++) { 371 if (wstart - i < 0) 372 break; 373 if (BN_is_bit_set(p, wstart - i)) { 374 wvalue <<= (i - wend); 375 wvalue |= 1; 376 wend = i; 377 } 378 } 379 380 /* wend is the size of the current window */ 381 j = wend + 1; 382 /* add the 'bytes above' */ 383 if (!start) 384 for (i = 0; i < j; i++) { 385 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 386 goto err; 387 } 388 389 /* wvalue will be an odd number < 2^window */ 390 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) 391 goto err; 392 393 /* move the 'window' down further */ 394 wstart -= wend + 1; 395 wvalue = 0; 396 start = 0; 397 if (wstart < 0) 398 break; 399 } 400 ret = 1; 401 err: 402 BN_CTX_end(ctx); 403 BN_RECP_CTX_free(&recp); 404 bn_check_top(r); 405 return (ret); 406} 407 408int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 409 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 410{ 411 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 412 int start = 1; 413 BIGNUM *d, *r; 414 const BIGNUM *aa; 415 /* Table of variables obtained from 'ctx' */ 416 BIGNUM *val[TABLE_SIZE]; 417 BN_MONT_CTX *mont = NULL; 418 419 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 420 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 421 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 422 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 423 } 424 425 bn_check_top(a); 426 bn_check_top(p); 427 bn_check_top(m); 428 429 if (!BN_is_odd(m)) { 430 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); 431 return (0); 432 } 433 bits = BN_num_bits(p); 434 if (bits == 0) { 435 /* x**0 mod 1 is still zero. */ 436 if (BN_is_one(m)) { 437 ret = 1; 438 BN_zero(rr); 439 } else { 440 ret = BN_one(rr); 441 } 442 return ret; 443 } 444 445 BN_CTX_start(ctx); 446 d = BN_CTX_get(ctx); 447 r = BN_CTX_get(ctx); 448 val[0] = BN_CTX_get(ctx); 449 if (!d || !r || !val[0]) 450 goto err; 451 452 /* 453 * If this is not done, things will break in the montgomery part 454 */ 455 456 if (in_mont != NULL) 457 mont = in_mont; 458 else { 459 if ((mont = BN_MONT_CTX_new()) == NULL) 460 goto err; 461 if (!BN_MONT_CTX_set(mont, m, ctx)) 462 goto err; 463 } 464 465 if (a->neg || BN_ucmp(a, m) >= 0) { 466 if (!BN_nnmod(val[0], a, m, ctx)) 467 goto err; 468 aa = val[0]; 469 } else 470 aa = a; 471 if (BN_is_zero(aa)) { 472 BN_zero(rr); 473 ret = 1; 474 goto err; 475 } 476 if (!BN_to_montgomery(val[0], aa, mont, ctx)) 477 goto err; /* 1 */ 478 479 window = BN_window_bits_for_exponent_size(bits); 480 if (window > 1) { 481 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) 482 goto err; /* 2 */ 483 j = 1 << (window - 1); 484 for (i = 1; i < j; i++) { 485 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 486 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) 487 goto err; 488 } 489 } 490 491 start = 1; /* This is used to avoid multiplication etc 492 * when there is only the value '1' in the 493 * buffer. */ 494 wvalue = 0; /* The 'value' of the window */ 495 wstart = bits - 1; /* The top bit of the window */ 496 wend = 0; /* The bottom bit of the window */ 497 498#if 1 /* by Shay Gueron's suggestion */ 499 j = m->top; /* borrow j */ 500 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 501 if (bn_wexpand(r, j) == NULL) 502 goto err; 503 /* 2^(top*BN_BITS2) - m */ 504 r->d[0] = (0 - m->d[0]) & BN_MASK2; 505 for (i = 1; i < j; i++) 506 r->d[i] = (~m->d[i]) & BN_MASK2; 507 r->top = j; 508 /* 509 * Upper words will be zero if the corresponding words of 'm' were 510 * 0xfff[...], so decrement r->top accordingly. 511 */ 512 bn_correct_top(r); 513 } else 514#endif 515 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) 516 goto err; 517 for (;;) { 518 if (BN_is_bit_set(p, wstart) == 0) { 519 if (!start) { 520 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 521 goto err; 522 } 523 if (wstart == 0) 524 break; 525 wstart--; 526 continue; 527 } 528 /* 529 * We now have wstart on a 'set' bit, we now need to work out how bit 530 * a window to do. To do this we need to scan forward until the last 531 * set bit before the end of the window 532 */ 533 j = wstart; 534 wvalue = 1; 535 wend = 0; 536 for (i = 1; i < window; i++) { 537 if (wstart - i < 0) 538 break; 539 if (BN_is_bit_set(p, wstart - i)) { 540 wvalue <<= (i - wend); 541 wvalue |= 1; 542 wend = i; 543 } 544 } 545 546 /* wend is the size of the current window */ 547 j = wend + 1; 548 /* add the 'bytes above' */ 549 if (!start) 550 for (i = 0; i < j; i++) { 551 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 552 goto err; 553 } 554 555 /* wvalue will be an odd number < 2^window */ 556 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) 557 goto err; 558 559 /* move the 'window' down further */ 560 wstart -= wend + 1; 561 wvalue = 0; 562 start = 0; 563 if (wstart < 0) 564 break; 565 } 566#if defined(SPARC_T4_MONT) 567 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 568 j = mont->N.top; /* borrow j */ 569 val[0]->d[0] = 1; /* borrow val[0] */ 570 for (i = 1; i < j; i++) 571 val[0]->d[i] = 0; 572 val[0]->top = j; 573 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) 574 goto err; 575 } else 576#endif 577 if (!BN_from_montgomery(rr, r, mont, ctx)) 578 goto err; 579 ret = 1; 580 err: 581 if ((in_mont == NULL) && (mont != NULL)) 582 BN_MONT_CTX_free(mont); 583 BN_CTX_end(ctx); 584 bn_check_top(rr); 585 return (ret); 586} 587 588#if defined(SPARC_T4_MONT) 589static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) 590{ 591 BN_ULONG ret = 0; 592 int wordpos; 593 594 wordpos = bitpos / BN_BITS2; 595 bitpos %= BN_BITS2; 596 if (wordpos >= 0 && wordpos < a->top) { 597 ret = a->d[wordpos] & BN_MASK2; 598 if (bitpos) { 599 ret >>= bitpos; 600 if (++wordpos < a->top) 601 ret |= a->d[wordpos] << (BN_BITS2 - bitpos); 602 } 603 } 604 605 return ret & BN_MASK2; 606} 607#endif 608 609/* 610 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific 611 * layout so that accessing any of these table values shows the same access 612 * pattern as far as cache lines are concerned. The following functions are 613 * used to transfer a BIGNUM from/to that table. 614 */ 615 616static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, 617 unsigned char *buf, int idx, 618 int window) 619{ 620 int i, j; 621 int width = 1 << window; 622 BN_ULONG *table = (BN_ULONG *)buf; 623 624 if (top > b->top) 625 top = b->top; /* this works because 'buf' is explicitly 626 * zeroed */ 627 for (i = 0, j = idx; i < top; i++, j += width) { 628 table[j] = b->d[i]; 629 } 630 631 return 1; 632} 633 634static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, 635 unsigned char *buf, int idx, 636 int window) 637{ 638 int i, j; 639 int width = 1 << window; 640 volatile BN_ULONG *table = (volatile BN_ULONG *)buf; 641 642 if (bn_wexpand(b, top) == NULL) 643 return 0; 644 645 if (window <= 3) { 646 for (i = 0; i < top; i++, table += width) { 647 BN_ULONG acc = 0; 648 649 for (j = 0; j < width; j++) { 650 acc |= table[j] & 651 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 652 } 653 654 b->d[i] = acc; 655 } 656 } else { 657 int xstride = 1 << (window - 2); 658 BN_ULONG y0, y1, y2, y3; 659 660 i = idx >> (window - 2); /* equivalent of idx / xstride */ 661 idx &= xstride - 1; /* equivalent of idx % xstride */ 662 663 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); 664 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); 665 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); 666 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); 667 668 for (i = 0; i < top; i++, table += width) { 669 BN_ULONG acc = 0; 670 671 for (j = 0; j < xstride; j++) { 672 acc |= ( (table[j + 0 * xstride] & y0) | 673 (table[j + 1 * xstride] & y1) | 674 (table[j + 2 * xstride] & y2) | 675 (table[j + 3 * xstride] & y3) ) 676 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 677 } 678 679 b->d[i] = acc; 680 } 681 } 682 683 b->top = top; 684 bn_correct_top(b); 685 return 1; 686} 687 688/* 689 * Given a pointer value, compute the next address that is a cache line 690 * multiple. 691 */ 692#define MOD_EXP_CTIME_ALIGN(x_) \ 693 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 694 695/* 696 * This variant of BN_mod_exp_mont() uses fixed windows and the special 697 * precomputation memory layout to limit data-dependency to a minimum to 698 * protect secret exponents (cf. the hyper-threading timing attacks pointed 699 * out by Colin Percival, 700 * http://www.daemonology.net/hyperthreading-considered-harmful/) 701 */ 702int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 703 const BIGNUM *m, BN_CTX *ctx, 704 BN_MONT_CTX *in_mont) 705{ 706 int i, bits, ret = 0, window, wvalue; 707 int top; 708 BN_MONT_CTX *mont = NULL; 709 710 int numPowers; 711 unsigned char *powerbufFree = NULL; 712 int powerbufLen = 0; 713 unsigned char *powerbuf = NULL; 714 BIGNUM tmp, am; 715#if defined(SPARC_T4_MONT) 716 unsigned int t4 = 0; 717#endif 718 719 bn_check_top(a); 720 bn_check_top(p); 721 bn_check_top(m); 722 723 if (!BN_is_odd(m)) { 724 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); 725 return (0); 726 } 727 728 top = m->top; 729 730 bits = BN_num_bits(p); 731 if (bits == 0) { 732 /* x**0 mod 1 is still zero. */ 733 if (BN_is_one(m)) { 734 ret = 1; 735 BN_zero(rr); 736 } else { 737 ret = BN_one(rr); 738 } 739 return ret; 740 } 741 742 BN_CTX_start(ctx); 743 744 /* 745 * Allocate a montgomery context if it was not supplied by the caller. If 746 * this is not done, things will break in the montgomery part. 747 */ 748 if (in_mont != NULL) 749 mont = in_mont; 750 else { 751 if ((mont = BN_MONT_CTX_new()) == NULL) 752 goto err; 753 if (!BN_MONT_CTX_set(mont, m, ctx)) 754 goto err; 755 } 756 757#ifdef RSAZ_ENABLED 758 /* 759 * If the size of the operands allow it, perform the optimized 760 * RSAZ exponentiation. For further information see 761 * crypto/bn/rsaz_exp.c and accompanying assembly modules. 762 */ 763 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) 764 && rsaz_avx2_eligible()) { 765 if (NULL == bn_wexpand(rr, 16)) 766 goto err; 767 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, 768 mont->n0[0]); 769 rr->top = 16; 770 rr->neg = 0; 771 bn_correct_top(rr); 772 ret = 1; 773 goto err; 774 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { 775 if (NULL == bn_wexpand(rr, 8)) 776 goto err; 777 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); 778 rr->top = 8; 779 rr->neg = 0; 780 bn_correct_top(rr); 781 ret = 1; 782 goto err; 783 } 784#endif 785 786 /* Get the window size to use with size of p. */ 787 window = BN_window_bits_for_ctime_exponent_size(bits); 788#if defined(SPARC_T4_MONT) 789 if (window >= 5 && (top & 15) == 0 && top <= 64 && 790 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == 791 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) 792 window = 5; 793 else 794#endif 795#if defined(OPENSSL_BN_ASM_MONT5) 796 if (window >= 5) { 797 window = 5; /* ~5% improvement for RSA2048 sign, and even 798 * for RSA4096 */ 799 /* reserve space for mont->N.d[] copy */ 800 powerbufLen += top * sizeof(mont->N.d[0]); 801 } 802#endif 803 (void)0; 804 805 /* 806 * Allocate a buffer large enough to hold all of the pre-computed powers 807 * of am, am itself and tmp. 808 */ 809 numPowers = 1 << window; 810 powerbufLen += sizeof(m->d[0]) * (top * numPowers + 811 ((2 * top) > 812 numPowers ? (2 * top) : numPowers)); 813#ifdef alloca 814 if (powerbufLen < 3072) 815 powerbufFree = 816 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); 817 else 818#endif 819 if ((powerbufFree = 820 (unsigned char *)OPENSSL_malloc(powerbufLen + 821 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) 822 == NULL) 823 goto err; 824 825 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 826 memset(powerbuf, 0, powerbufLen); 827 828#ifdef alloca 829 if (powerbufLen < 3072) 830 powerbufFree = NULL; 831#endif 832 833 /* lay down tmp and am right after powers table */ 834 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); 835 am.d = tmp.d + top; 836 tmp.top = am.top = 0; 837 tmp.dmax = am.dmax = top; 838 tmp.neg = am.neg = 0; 839 tmp.flags = am.flags = BN_FLG_STATIC_DATA; 840 841 /* prepare a^0 in Montgomery domain */ 842#if 1 /* by Shay Gueron's suggestion */ 843 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 844 /* 2^(top*BN_BITS2) - m */ 845 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; 846 for (i = 1; i < top; i++) 847 tmp.d[i] = (~m->d[i]) & BN_MASK2; 848 tmp.top = top; 849 } else 850#endif 851 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx)) 852 goto err; 853 854 /* prepare a^1 in Montgomery domain */ 855 if (a->neg || BN_ucmp(a, m) >= 0) { 856 if (!BN_mod(&am, a, m, ctx)) 857 goto err; 858 if (!BN_to_montgomery(&am, &am, mont, ctx)) 859 goto err; 860 } else if (!BN_to_montgomery(&am, a, mont, ctx)) 861 goto err; 862 863#if defined(SPARC_T4_MONT) 864 if (t4) { 865 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, 866 const BN_ULONG *n0, const void *table, 867 int power, int bits); 868 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, 869 const BN_ULONG *n0, const void *table, 870 int power, int bits); 871 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, 872 const BN_ULONG *n0, const void *table, 873 int power, int bits); 874 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, 875 const BN_ULONG *n0, const void *table, 876 int power, int bits); 877 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, 878 const BN_ULONG *n0, const void *table, 879 int power, int bits); 880 static const bn_pwr5_mont_f pwr5_funcs[4] = { 881 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, 882 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 883 }; 884 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; 885 886 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, 887 const void *bp, const BN_ULONG *np, 888 const BN_ULONG *n0); 889 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, 890 const BN_ULONG *np, const BN_ULONG *n0); 891 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, 892 const void *bp, const BN_ULONG *np, 893 const BN_ULONG *n0); 894 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, 895 const void *bp, const BN_ULONG *np, 896 const BN_ULONG *n0); 897 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, 898 const void *bp, const BN_ULONG *np, 899 const BN_ULONG *n0); 900 static const bn_mul_mont_f mul_funcs[4] = { 901 bn_mul_mont_t4_8, bn_mul_mont_t4_16, 902 bn_mul_mont_t4_24, bn_mul_mont_t4_32 903 }; 904 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; 905 906 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, 907 const void *bp, const BN_ULONG *np, 908 const BN_ULONG *n0, int num); 909 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, 910 const void *bp, const BN_ULONG *np, 911 const BN_ULONG *n0, int num); 912 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, 913 const void *table, const BN_ULONG *np, 914 const BN_ULONG *n0, int num, int power); 915 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, 916 void *table, size_t power); 917 void bn_gather5_t4(BN_ULONG *out, size_t num, 918 void *table, size_t power); 919 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); 920 921 BN_ULONG *np = mont->N.d, *n0 = mont->n0; 922 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less 923 * than 32 */ 924 925 /* 926 * BN_to_montgomery can contaminate words above .top [in 927 * BN_DEBUG[_DEBUG] build]... 928 */ 929 for (i = am.top; i < top; i++) 930 am.d[i] = 0; 931 for (i = tmp.top; i < top; i++) 932 tmp.d[i] = 0; 933 934 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); 935 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); 936 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && 937 !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) 938 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); 939 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); 940 941 for (i = 3; i < 32; i++) { 942 /* Calculate a^i = a^(i-1) * a */ 943 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && 944 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) 945 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); 946 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); 947 } 948 949 /* switch to 64-bit domain */ 950 np = alloca(top * sizeof(BN_ULONG)); 951 top /= 2; 952 bn_flip_t4(np, mont->N.d, top); 953 954 bits--; 955 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) 956 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 957 bn_gather5_t4(tmp.d, top, powerbuf, wvalue); 958 959 /* 960 * Scan the exponent one window at a time starting from the most 961 * significant bits. 962 */ 963 while (bits >= 0) { 964 if (bits < stride) 965 stride = bits + 1; 966 bits -= stride; 967 wvalue = bn_get_bits(p, bits + 1); 968 969 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 970 continue; 971 /* retry once and fall back */ 972 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 973 continue; 974 975 bits += stride - 5; 976 wvalue >>= stride - 5; 977 wvalue &= 31; 978 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 979 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 980 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 981 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 982 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 983 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, 984 wvalue); 985 } 986 987 bn_flip_t4(tmp.d, tmp.d, top); 988 top *= 2; 989 /* back to 32-bit domain */ 990 tmp.top = top; 991 bn_correct_top(&tmp); 992 OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); 993 } else 994#endif 995#if defined(OPENSSL_BN_ASM_MONT5) 996 if (window == 5 && top > 1) { 997 /* 998 * This optimization uses ideas from http://eprint.iacr.org/2011/239, 999 * specifically optimization of cache-timing attack countermeasures 1000 * and pre-computation optimization. 1001 */ 1002 1003 /* 1004 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as 1005 * 512-bit RSA is hardly relevant, we omit it to spare size... 1006 */ 1007 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, 1008 const void *table, const BN_ULONG *np, 1009 const BN_ULONG *n0, int num, int power); 1010 void bn_scatter5(const BN_ULONG *inp, size_t num, 1011 void *table, size_t power); 1012 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); 1013 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, 1014 const void *table, const BN_ULONG *np, 1015 const BN_ULONG *n0, int num, int power); 1016 int bn_get_bits5(const BN_ULONG *ap, int off); 1017 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, 1018 const BN_ULONG *not_used, const BN_ULONG *np, 1019 const BN_ULONG *n0, int num); 1020 1021 BN_ULONG *n0 = mont->n0, *np; 1022 1023 /* 1024 * BN_to_montgomery can contaminate words above .top [in 1025 * BN_DEBUG[_DEBUG] build]... 1026 */ 1027 for (i = am.top; i < top; i++) 1028 am.d[i] = 0; 1029 for (i = tmp.top; i < top; i++) 1030 tmp.d[i] = 0; 1031 1032 /* 1033 * copy mont->N.d[] to improve cache locality 1034 */ 1035 for (np = am.d + top, i = 0; i < top; i++) 1036 np[i] = mont->N.d[i]; 1037 1038 bn_scatter5(tmp.d, top, powerbuf, 0); 1039 bn_scatter5(am.d, am.top, powerbuf, 1); 1040 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); 1041 bn_scatter5(tmp.d, top, powerbuf, 2); 1042 1043# if 0 1044 for (i = 3; i < 32; i++) { 1045 /* Calculate a^i = a^(i-1) * a */ 1046 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1047 bn_scatter5(tmp.d, top, powerbuf, i); 1048 } 1049# else 1050 /* same as above, but uses squaring for 1/2 of operations */ 1051 for (i = 4; i < 32; i *= 2) { 1052 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1053 bn_scatter5(tmp.d, top, powerbuf, i); 1054 } 1055 for (i = 3; i < 8; i += 2) { 1056 int j; 1057 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1058 bn_scatter5(tmp.d, top, powerbuf, i); 1059 for (j = 2 * i; j < 32; j *= 2) { 1060 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1061 bn_scatter5(tmp.d, top, powerbuf, j); 1062 } 1063 } 1064 for (; i < 16; i += 2) { 1065 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1066 bn_scatter5(tmp.d, top, powerbuf, i); 1067 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1068 bn_scatter5(tmp.d, top, powerbuf, 2 * i); 1069 } 1070 for (; i < 32; i += 2) { 1071 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1072 bn_scatter5(tmp.d, top, powerbuf, i); 1073 } 1074# endif 1075 bits--; 1076 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) 1077 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1078 bn_gather5(tmp.d, top, powerbuf, wvalue); 1079 1080 /* 1081 * Scan the exponent one window at a time starting from the most 1082 * significant bits. 1083 */ 1084 if (top & 7) 1085 while (bits >= 0) { 1086 for (wvalue = 0, i = 0; i < 5; i++, bits--) 1087 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1088 1089 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1090 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1091 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1092 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1093 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1094 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, 1095 wvalue); 1096 } else { 1097 while (bits >= 0) { 1098 wvalue = bn_get_bits5(p->d, bits - 4); 1099 bits -= 5; 1100 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue); 1101 } 1102 } 1103 1104 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top); 1105 tmp.top = top; 1106 bn_correct_top(&tmp); 1107 if (ret) { 1108 if (!BN_copy(rr, &tmp)) 1109 ret = 0; 1110 goto err; /* non-zero ret means it's not error */ 1111 } 1112 } else 1113#endif 1114 { 1115 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) 1116 goto err; 1117 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) 1118 goto err; 1119 1120 /* 1121 * If the window size is greater than 1, then calculate 1122 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even 1123 * powers could instead be computed as (a^(i/2))^2 to use the slight 1124 * performance advantage of sqr over mul). 1125 */ 1126 if (window > 1) { 1127 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) 1128 goto err; 1129 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, 1130 window)) 1131 goto err; 1132 for (i = 3; i < numPowers; i++) { 1133 /* Calculate a^i = a^(i-1) * a */ 1134 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) 1135 goto err; 1136 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, 1137 window)) 1138 goto err; 1139 } 1140 } 1141 1142 bits--; 1143 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) 1144 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1145 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, 1146 window)) 1147 goto err; 1148 1149 /* 1150 * Scan the exponent one window at a time starting from the most 1151 * significant bits. 1152 */ 1153 while (bits >= 0) { 1154 wvalue = 0; /* The 'value' of the window */ 1155 1156 /* Scan the window, squaring the result as we go */ 1157 for (i = 0; i < window; i++, bits--) { 1158 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx)) 1159 goto err; 1160 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1161 } 1162 1163 /* 1164 * Fetch the appropriate pre-computed value from the pre-buf 1165 */ 1166 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, 1167 window)) 1168 goto err; 1169 1170 /* Multiply the result into the intermediate result */ 1171 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx)) 1172 goto err; 1173 } 1174 } 1175 1176 /* Convert the final result from montgomery to standard format */ 1177#if defined(SPARC_T4_MONT) 1178 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 1179 am.d[0] = 1; /* borrow am */ 1180 for (i = 1; i < top; i++) 1181 am.d[i] = 0; 1182 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) 1183 goto err; 1184 } else 1185#endif 1186 if (!BN_from_montgomery(rr, &tmp, mont, ctx)) 1187 goto err; 1188 ret = 1; 1189 err: 1190 if ((in_mont == NULL) && (mont != NULL)) 1191 BN_MONT_CTX_free(mont); 1192 if (powerbuf != NULL) { 1193 OPENSSL_cleanse(powerbuf, powerbufLen); 1194 if (powerbufFree) 1195 OPENSSL_free(powerbufFree); 1196 } 1197 BN_CTX_end(ctx); 1198 return (ret); 1199} 1200 1201int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 1202 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 1203{ 1204 BN_MONT_CTX *mont = NULL; 1205 int b, bits, ret = 0; 1206 int r_is_one; 1207 BN_ULONG w, next_w; 1208 BIGNUM *d, *r, *t; 1209 BIGNUM *swap_tmp; 1210#define BN_MOD_MUL_WORD(r, w, m) \ 1211 (BN_mul_word(r, (w)) && \ 1212 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 1213 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 1214 /* 1215 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is 1216 * probably more overhead than always using BN_mod (which uses BN_copy if 1217 * a similar test returns true). 1218 */ 1219 /* 1220 * We can use BN_mod and do not need BN_nnmod because our accumulator is 1221 * never negative (the result of BN_mod does not depend on the sign of 1222 * the modulus). 1223 */ 1224#define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 1225 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 1226 1227 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1228 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1229 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1230 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1231 return -1; 1232 } 1233 1234 bn_check_top(p); 1235 bn_check_top(m); 1236 1237 if (!BN_is_odd(m)) { 1238 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); 1239 return (0); 1240 } 1241 if (m->top == 1) 1242 a %= m->d[0]; /* make sure that 'a' is reduced */ 1243 1244 bits = BN_num_bits(p); 1245 if (bits == 0) { 1246 /* x**0 mod 1 is still zero. */ 1247 if (BN_is_one(m)) { 1248 ret = 1; 1249 BN_zero(rr); 1250 } else { 1251 ret = BN_one(rr); 1252 } 1253 return ret; 1254 } 1255 if (a == 0) { 1256 BN_zero(rr); 1257 ret = 1; 1258 return ret; 1259 } 1260 1261 BN_CTX_start(ctx); 1262 d = BN_CTX_get(ctx); 1263 r = BN_CTX_get(ctx); 1264 t = BN_CTX_get(ctx); 1265 if (d == NULL || r == NULL || t == NULL) 1266 goto err; 1267 1268 if (in_mont != NULL) 1269 mont = in_mont; 1270 else { 1271 if ((mont = BN_MONT_CTX_new()) == NULL) 1272 goto err; 1273 if (!BN_MONT_CTX_set(mont, m, ctx)) 1274 goto err; 1275 } 1276 1277 r_is_one = 1; /* except for Montgomery factor */ 1278 1279 /* bits-1 >= 0 */ 1280 1281 /* The result is accumulated in the product r*w. */ 1282 w = a; /* bit 'bits-1' of 'p' is always set */ 1283 for (b = bits - 2; b >= 0; b--) { 1284 /* First, square r*w. */ 1285 next_w = w * w; 1286 if ((next_w / w) != w) { /* overflow */ 1287 if (r_is_one) { 1288 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1289 goto err; 1290 r_is_one = 0; 1291 } else { 1292 if (!BN_MOD_MUL_WORD(r, w, m)) 1293 goto err; 1294 } 1295 next_w = 1; 1296 } 1297 w = next_w; 1298 if (!r_is_one) { 1299 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 1300 goto err; 1301 } 1302 1303 /* Second, multiply r*w by 'a' if exponent bit is set. */ 1304 if (BN_is_bit_set(p, b)) { 1305 next_w = w * a; 1306 if ((next_w / a) != w) { /* overflow */ 1307 if (r_is_one) { 1308 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1309 goto err; 1310 r_is_one = 0; 1311 } else { 1312 if (!BN_MOD_MUL_WORD(r, w, m)) 1313 goto err; 1314 } 1315 next_w = a; 1316 } 1317 w = next_w; 1318 } 1319 } 1320 1321 /* Finally, set r:=r*w. */ 1322 if (w != 1) { 1323 if (r_is_one) { 1324 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1325 goto err; 1326 r_is_one = 0; 1327 } else { 1328 if (!BN_MOD_MUL_WORD(r, w, m)) 1329 goto err; 1330 } 1331 } 1332 1333 if (r_is_one) { /* can happen only if a == 1 */ 1334 if (!BN_one(rr)) 1335 goto err; 1336 } else { 1337 if (!BN_from_montgomery(rr, r, mont, ctx)) 1338 goto err; 1339 } 1340 ret = 1; 1341 err: 1342 if ((in_mont == NULL) && (mont != NULL)) 1343 BN_MONT_CTX_free(mont); 1344 BN_CTX_end(ctx); 1345 bn_check_top(rr); 1346 return (ret); 1347} 1348 1349/* The old fallback, simple version :-) */ 1350int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 1351 const BIGNUM *m, BN_CTX *ctx) 1352{ 1353 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 1354 int start = 1; 1355 BIGNUM *d; 1356 /* Table of variables obtained from 'ctx' */ 1357 BIGNUM *val[TABLE_SIZE]; 1358 1359 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1360 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 1361 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1362 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1363 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1364 return -1; 1365 } 1366 1367 bits = BN_num_bits(p); 1368 if (bits == 0) { 1369 /* x**0 mod 1 is still zero. */ 1370 if (BN_is_one(m)) { 1371 ret = 1; 1372 BN_zero(r); 1373 } else { 1374 ret = BN_one(r); 1375 } 1376 return ret; 1377 } 1378 1379 BN_CTX_start(ctx); 1380 d = BN_CTX_get(ctx); 1381 val[0] = BN_CTX_get(ctx); 1382 if (!d || !val[0]) 1383 goto err; 1384 1385 if (!BN_nnmod(val[0], a, m, ctx)) 1386 goto err; /* 1 */ 1387 if (BN_is_zero(val[0])) { 1388 BN_zero(r); 1389 ret = 1; 1390 goto err; 1391 } 1392 1393 window = BN_window_bits_for_exponent_size(bits); 1394 if (window > 1) { 1395 if (!BN_mod_mul(d, val[0], val[0], m, ctx)) 1396 goto err; /* 2 */ 1397 j = 1 << (window - 1); 1398 for (i = 1; i < j; i++) { 1399 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 1400 !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) 1401 goto err; 1402 } 1403 } 1404 1405 start = 1; /* This is used to avoid multiplication etc 1406 * when there is only the value '1' in the 1407 * buffer. */ 1408 wvalue = 0; /* The 'value' of the window */ 1409 wstart = bits - 1; /* The top bit of the window */ 1410 wend = 0; /* The bottom bit of the window */ 1411 1412 if (!BN_one(r)) 1413 goto err; 1414 1415 for (;;) { 1416 if (BN_is_bit_set(p, wstart) == 0) { 1417 if (!start) 1418 if (!BN_mod_mul(r, r, r, m, ctx)) 1419 goto err; 1420 if (wstart == 0) 1421 break; 1422 wstart--; 1423 continue; 1424 } 1425 /* 1426 * We now have wstart on a 'set' bit, we now need to work out how bit 1427 * a window to do. To do this we need to scan forward until the last 1428 * set bit before the end of the window 1429 */ 1430 j = wstart; 1431 wvalue = 1; 1432 wend = 0; 1433 for (i = 1; i < window; i++) { 1434 if (wstart - i < 0) 1435 break; 1436 if (BN_is_bit_set(p, wstart - i)) { 1437 wvalue <<= (i - wend); 1438 wvalue |= 1; 1439 wend = i; 1440 } 1441 } 1442 1443 /* wend is the size of the current window */ 1444 j = wend + 1; 1445 /* add the 'bytes above' */ 1446 if (!start) 1447 for (i = 0; i < j; i++) { 1448 if (!BN_mod_mul(r, r, r, m, ctx)) 1449 goto err; 1450 } 1451 1452 /* wvalue will be an odd number < 2^window */ 1453 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) 1454 goto err; 1455 1456 /* move the 'window' down further */ 1457 wstart -= wend + 1; 1458 wvalue = 0; 1459 start = 0; 1460 if (wstart < 0) 1461 break; 1462 } 1463 ret = 1; 1464 err: 1465 BN_CTX_end(ctx); 1466 bn_check_top(r); 1467 return (ret); 1468} 1469