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) 184 BN_copy(r, rr); 185 ret = 1; 186 err: 187 BN_CTX_end(ctx); 188 bn_check_top(r); 189 return (ret); 190} 191 192int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 193 BN_CTX *ctx) 194{ 195 int ret; 196 197 bn_check_top(a); 198 bn_check_top(p); 199 bn_check_top(m); 200 201 /*- 202 * For even modulus m = 2^k*m_odd, it might make sense to compute 203 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 204 * exponentiation for the odd part), using appropriate exponent 205 * reductions, and combine the results using the CRT. 206 * 207 * For now, we use Montgomery only if the modulus is odd; otherwise, 208 * exponentiation using the reciprocal-based quick remaindering 209 * algorithm is used. 210 * 211 * (Timing obtained with expspeed.c [computations a^p mod m 212 * where a, p, m are of the same length: 256, 512, 1024, 2048, 213 * 4096, 8192 bits], compared to the running time of the 214 * standard algorithm: 215 * 216 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 217 * 55 .. 77 % [UltraSparc processor, but 218 * debug-solaris-sparcv8-gcc conf.] 219 * 220 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 221 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 222 * 223 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 224 * at 2048 and more bits, but at 512 and 1024 bits, it was 225 * slower even than the standard algorithm! 226 * 227 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 228 * should be obtained when the new Montgomery reduction code 229 * has been integrated into OpenSSL.) 230 */ 231 232#define MONT_MUL_MOD 233#define MONT_EXP_WORD 234#define RECP_MUL_MOD 235 236#ifdef MONT_MUL_MOD 237 /* 238 * I have finally been able to take out this pre-condition of the top bit 239 * being set. It was caused by an error in BN_div with negatives. There 240 * was also another problem when for a^b%m a >= m. eay 07-May-97 241 */ 242 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ 243 244 if (BN_is_odd(m)) { 245# ifdef MONT_EXP_WORD 246 if (a->top == 1 && !a->neg 247 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) { 248 BN_ULONG A = a->d[0]; 249 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); 250 } else 251# endif 252 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); 253 } else 254#endif 255#ifdef RECP_MUL_MOD 256 { 257 ret = BN_mod_exp_recp(r, a, p, m, ctx); 258 } 259#else 260 { 261 ret = BN_mod_exp_simple(r, a, p, m, ctx); 262 } 263#endif 264 265 bn_check_top(r); 266 return (ret); 267} 268 269int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 270 const BIGNUM *m, BN_CTX *ctx) 271{ 272 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 273 int start = 1; 274 BIGNUM *aa; 275 /* Table of variables obtained from 'ctx' */ 276 BIGNUM *val[TABLE_SIZE]; 277 BN_RECP_CTX recp; 278 279 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 280 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 281 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 282 return -1; 283 } 284 285 bits = BN_num_bits(p); 286 if (bits == 0) { 287 /* x**0 mod 1 is still zero. */ 288 if (BN_is_one(m)) { 289 ret = 1; 290 BN_zero(r); 291 } else { 292 ret = BN_one(r); 293 } 294 return ret; 295 } 296 297 BN_CTX_start(ctx); 298 aa = BN_CTX_get(ctx); 299 val[0] = BN_CTX_get(ctx); 300 if (!aa || !val[0]) 301 goto err; 302 303 BN_RECP_CTX_init(&recp); 304 if (m->neg) { 305 /* ignore sign of 'm' */ 306 if (!BN_copy(aa, m)) 307 goto err; 308 aa->neg = 0; 309 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) 310 goto err; 311 } else { 312 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) 313 goto err; 314 } 315 316 if (!BN_nnmod(val[0], a, m, ctx)) 317 goto err; /* 1 */ 318 if (BN_is_zero(val[0])) { 319 BN_zero(r); 320 ret = 1; 321 goto err; 322 } 323 324 window = BN_window_bits_for_exponent_size(bits); 325 if (window > 1) { 326 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) 327 goto err; /* 2 */ 328 j = 1 << (window - 1); 329 for (i = 1; i < j; i++) { 330 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 331 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) 332 goto err; 333 } 334 } 335 336 start = 1; /* This is used to avoid multiplication etc 337 * when there is only the value '1' in the 338 * buffer. */ 339 wvalue = 0; /* The 'value' of the window */ 340 wstart = bits - 1; /* The top bit of the window */ 341 wend = 0; /* The bottom bit of the window */ 342 343 if (!BN_one(r)) 344 goto err; 345 346 for (;;) { 347 if (BN_is_bit_set(p, wstart) == 0) { 348 if (!start) 349 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 350 goto err; 351 if (wstart == 0) 352 break; 353 wstart--; 354 continue; 355 } 356 /* 357 * We now have wstart on a 'set' bit, we now need to work out how bit 358 * a window to do. To do this we need to scan forward until the last 359 * set bit before the end of the window 360 */ 361 j = wstart; 362 wvalue = 1; 363 wend = 0; 364 for (i = 1; i < window; i++) { 365 if (wstart - i < 0) 366 break; 367 if (BN_is_bit_set(p, wstart - i)) { 368 wvalue <<= (i - wend); 369 wvalue |= 1; 370 wend = i; 371 } 372 } 373 374 /* wend is the size of the current window */ 375 j = wend + 1; 376 /* add the 'bytes above' */ 377 if (!start) 378 for (i = 0; i < j; i++) { 379 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 380 goto err; 381 } 382 383 /* wvalue will be an odd number < 2^window */ 384 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) 385 goto err; 386 387 /* move the 'window' down further */ 388 wstart -= wend + 1; 389 wvalue = 0; 390 start = 0; 391 if (wstart < 0) 392 break; 393 } 394 ret = 1; 395 err: 396 BN_CTX_end(ctx); 397 BN_RECP_CTX_free(&recp); 398 bn_check_top(r); 399 return (ret); 400} 401 402int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 403 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 404{ 405 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 406 int start = 1; 407 BIGNUM *d, *r; 408 const BIGNUM *aa; 409 /* Table of variables obtained from 'ctx' */ 410 BIGNUM *val[TABLE_SIZE]; 411 BN_MONT_CTX *mont = NULL; 412 413 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 414 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 415 } 416 417 bn_check_top(a); 418 bn_check_top(p); 419 bn_check_top(m); 420 421 if (!BN_is_odd(m)) { 422 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); 423 return (0); 424 } 425 bits = BN_num_bits(p); 426 if (bits == 0) { 427 /* x**0 mod 1 is still zero. */ 428 if (BN_is_one(m)) { 429 ret = 1; 430 BN_zero(rr); 431 } else { 432 ret = BN_one(rr); 433 } 434 return ret; 435 } 436 437 BN_CTX_start(ctx); 438 d = BN_CTX_get(ctx); 439 r = BN_CTX_get(ctx); 440 val[0] = BN_CTX_get(ctx); 441 if (!d || !r || !val[0]) 442 goto err; 443 444 /* 445 * If this is not done, things will break in the montgomery part 446 */ 447 448 if (in_mont != NULL) 449 mont = in_mont; 450 else { 451 if ((mont = BN_MONT_CTX_new()) == NULL) 452 goto err; 453 if (!BN_MONT_CTX_set(mont, m, ctx)) 454 goto err; 455 } 456 457 if (a->neg || BN_ucmp(a, m) >= 0) { 458 if (!BN_nnmod(val[0], a, m, ctx)) 459 goto err; 460 aa = val[0]; 461 } else 462 aa = a; 463 if (BN_is_zero(aa)) { 464 BN_zero(rr); 465 ret = 1; 466 goto err; 467 } 468 if (!BN_to_montgomery(val[0], aa, mont, ctx)) 469 goto err; /* 1 */ 470 471 window = BN_window_bits_for_exponent_size(bits); 472 if (window > 1) { 473 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) 474 goto err; /* 2 */ 475 j = 1 << (window - 1); 476 for (i = 1; i < j; i++) { 477 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 478 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) 479 goto err; 480 } 481 } 482 483 start = 1; /* This is used to avoid multiplication etc 484 * when there is only the value '1' in the 485 * buffer. */ 486 wvalue = 0; /* The 'value' of the window */ 487 wstart = bits - 1; /* The top bit of the window */ 488 wend = 0; /* The bottom bit of the window */ 489 490#if 1 /* by Shay Gueron's suggestion */ 491 j = m->top; /* borrow j */ 492 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 493 if (bn_wexpand(r, j) == NULL) 494 goto err; 495 /* 2^(top*BN_BITS2) - m */ 496 r->d[0] = (0 - m->d[0]) & BN_MASK2; 497 for (i = 1; i < j; i++) 498 r->d[i] = (~m->d[i]) & BN_MASK2; 499 r->top = j; 500 /* 501 * Upper words will be zero if the corresponding words of 'm' were 502 * 0xfff[...], so decrement r->top accordingly. 503 */ 504 bn_correct_top(r); 505 } else 506#endif 507 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) 508 goto err; 509 for (;;) { 510 if (BN_is_bit_set(p, wstart) == 0) { 511 if (!start) { 512 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 513 goto err; 514 } 515 if (wstart == 0) 516 break; 517 wstart--; 518 continue; 519 } 520 /* 521 * We now have wstart on a 'set' bit, we now need to work out how bit 522 * a window to do. To do this we need to scan forward until the last 523 * set bit before the end of the window 524 */ 525 j = wstart; 526 wvalue = 1; 527 wend = 0; 528 for (i = 1; i < window; i++) { 529 if (wstart - i < 0) 530 break; 531 if (BN_is_bit_set(p, wstart - i)) { 532 wvalue <<= (i - wend); 533 wvalue |= 1; 534 wend = i; 535 } 536 } 537 538 /* wend is the size of the current window */ 539 j = wend + 1; 540 /* add the 'bytes above' */ 541 if (!start) 542 for (i = 0; i < j; i++) { 543 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 544 goto err; 545 } 546 547 /* wvalue will be an odd number < 2^window */ 548 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) 549 goto err; 550 551 /* move the 'window' down further */ 552 wstart -= wend + 1; 553 wvalue = 0; 554 start = 0; 555 if (wstart < 0) 556 break; 557 } 558#if defined(SPARC_T4_MONT) 559 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 560 j = mont->N.top; /* borrow j */ 561 val[0]->d[0] = 1; /* borrow val[0] */ 562 for (i = 1; i < j; i++) 563 val[0]->d[i] = 0; 564 val[0]->top = j; 565 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) 566 goto err; 567 } else 568#endif 569 if (!BN_from_montgomery(rr, r, mont, ctx)) 570 goto err; 571 ret = 1; 572 err: 573 if ((in_mont == NULL) && (mont != NULL)) 574 BN_MONT_CTX_free(mont); 575 BN_CTX_end(ctx); 576 bn_check_top(rr); 577 return (ret); 578} 579 580#if defined(SPARC_T4_MONT) 581static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) 582{ 583 BN_ULONG ret = 0; 584 int wordpos; 585 586 wordpos = bitpos / BN_BITS2; 587 bitpos %= BN_BITS2; 588 if (wordpos >= 0 && wordpos < a->top) { 589 ret = a->d[wordpos] & BN_MASK2; 590 if (bitpos) { 591 ret >>= bitpos; 592 if (++wordpos < a->top) 593 ret |= a->d[wordpos] << (BN_BITS2 - bitpos); 594 } 595 } 596 597 return ret & BN_MASK2; 598} 599#endif 600 601/* 602 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific 603 * layout so that accessing any of these table values shows the same access 604 * pattern as far as cache lines are concerned. The following functions are 605 * used to transfer a BIGNUM from/to that table. 606 */ 607 608static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, 609 unsigned char *buf, int idx, 610 int window) 611{ 612 int i, j; 613 int width = 1 << window; 614 BN_ULONG *table = (BN_ULONG *)buf; 615 616 if (top > b->top) 617 top = b->top; /* this works because 'buf' is explicitly 618 * zeroed */ 619 for (i = 0, j = idx; i < top; i++, j += width) { 620 table[j] = b->d[i]; 621 } 622 623 return 1; 624} 625 626static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, 627 unsigned char *buf, int idx, 628 int window) 629{ 630 int i, j; 631 int width = 1 << window; 632 volatile BN_ULONG *table = (volatile BN_ULONG *)buf; 633 634 if (bn_wexpand(b, top) == NULL) 635 return 0; 636 637 if (window <= 3) { 638 for (i = 0; i < top; i++, table += width) { 639 BN_ULONG acc = 0; 640 641 for (j = 0; j < width; j++) { 642 acc |= table[j] & 643 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 644 } 645 646 b->d[i] = acc; 647 } 648 } else { 649 int xstride = 1 << (window - 2); 650 BN_ULONG y0, y1, y2, y3; 651 652 i = idx >> (window - 2); /* equivalent of idx / xstride */ 653 idx &= xstride - 1; /* equivalent of idx % xstride */ 654 655 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); 656 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); 657 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); 658 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); 659 660 for (i = 0; i < top; i++, table += width) { 661 BN_ULONG acc = 0; 662 663 for (j = 0; j < xstride; j++) { 664 acc |= ( (table[j + 0 * xstride] & y0) | 665 (table[j + 1 * xstride] & y1) | 666 (table[j + 2 * xstride] & y2) | 667 (table[j + 3 * xstride] & y3) ) 668 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 669 } 670 671 b->d[i] = acc; 672 } 673 } 674 675 b->top = top; 676 bn_correct_top(b); 677 return 1; 678} 679 680/* 681 * Given a pointer value, compute the next address that is a cache line 682 * multiple. 683 */ 684#define MOD_EXP_CTIME_ALIGN(x_) \ 685 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 686 687/* 688 * This variant of BN_mod_exp_mont() uses fixed windows and the special 689 * precomputation memory layout to limit data-dependency to a minimum to 690 * protect secret exponents (cf. the hyper-threading timing attacks pointed 691 * out by Colin Percival, 692 * http://www.daemonology.net/hyperthreading-considered-harmful/) 693 */ 694int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 695 const BIGNUM *m, BN_CTX *ctx, 696 BN_MONT_CTX *in_mont) 697{ 698 int i, bits, ret = 0, window, wvalue; 699 int top; 700 BN_MONT_CTX *mont = NULL; 701 702 int numPowers; 703 unsigned char *powerbufFree = NULL; 704 int powerbufLen = 0; 705 unsigned char *powerbuf = NULL; 706 BIGNUM tmp, am; 707#if defined(SPARC_T4_MONT) 708 unsigned int t4 = 0; 709#endif 710 711 bn_check_top(a); 712 bn_check_top(p); 713 bn_check_top(m); 714 715 if (!BN_is_odd(m)) { 716 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); 717 return (0); 718 } 719 720 top = m->top; 721 722 bits = BN_num_bits(p); 723 if (bits == 0) { 724 /* x**0 mod 1 is still zero. */ 725 if (BN_is_one(m)) { 726 ret = 1; 727 BN_zero(rr); 728 } else { 729 ret = BN_one(rr); 730 } 731 return ret; 732 } 733 734 BN_CTX_start(ctx); 735 736 /* 737 * Allocate a montgomery context if it was not supplied by the caller. If 738 * this is not done, things will break in the montgomery part. 739 */ 740 if (in_mont != NULL) 741 mont = in_mont; 742 else { 743 if ((mont = BN_MONT_CTX_new()) == NULL) 744 goto err; 745 if (!BN_MONT_CTX_set(mont, m, ctx)) 746 goto err; 747 } 748 749#ifdef RSAZ_ENABLED 750 /* 751 * If the size of the operands allow it, perform the optimized 752 * RSAZ exponentiation. For further information see 753 * crypto/bn/rsaz_exp.c and accompanying assembly modules. 754 */ 755 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) 756 && rsaz_avx2_eligible()) { 757 if (NULL == bn_wexpand(rr, 16)) 758 goto err; 759 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, 760 mont->n0[0]); 761 rr->top = 16; 762 rr->neg = 0; 763 bn_correct_top(rr); 764 ret = 1; 765 goto err; 766 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { 767 if (NULL == bn_wexpand(rr, 8)) 768 goto err; 769 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); 770 rr->top = 8; 771 rr->neg = 0; 772 bn_correct_top(rr); 773 ret = 1; 774 goto err; 775 } 776#endif 777 778 /* Get the window size to use with size of p. */ 779 window = BN_window_bits_for_ctime_exponent_size(bits); 780#if defined(SPARC_T4_MONT) 781 if (window >= 5 && (top & 15) == 0 && top <= 64 && 782 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == 783 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) 784 window = 5; 785 else 786#endif 787#if defined(OPENSSL_BN_ASM_MONT5) 788 if (window >= 5) { 789 window = 5; /* ~5% improvement for RSA2048 sign, and even 790 * for RSA4096 */ 791 /* reserve space for mont->N.d[] copy */ 792 powerbufLen += top * sizeof(mont->N.d[0]); 793 } 794#endif 795 (void)0; 796 797 /* 798 * Allocate a buffer large enough to hold all of the pre-computed powers 799 * of am, am itself and tmp. 800 */ 801 numPowers = 1 << window; 802 powerbufLen += sizeof(m->d[0]) * (top * numPowers + 803 ((2 * top) > 804 numPowers ? (2 * top) : numPowers)); 805#ifdef alloca 806 if (powerbufLen < 3072) 807 powerbufFree = 808 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); 809 else 810#endif 811 if ((powerbufFree = 812 (unsigned char *)OPENSSL_malloc(powerbufLen + 813 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) 814 == NULL) 815 goto err; 816 817 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 818 memset(powerbuf, 0, powerbufLen); 819 820#ifdef alloca 821 if (powerbufLen < 3072) 822 powerbufFree = NULL; 823#endif 824 825 /* lay down tmp and am right after powers table */ 826 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); 827 am.d = tmp.d + top; 828 tmp.top = am.top = 0; 829 tmp.dmax = am.dmax = top; 830 tmp.neg = am.neg = 0; 831 tmp.flags = am.flags = BN_FLG_STATIC_DATA; 832 833 /* prepare a^0 in Montgomery domain */ 834#if 1 /* by Shay Gueron's suggestion */ 835 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 836 /* 2^(top*BN_BITS2) - m */ 837 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; 838 for (i = 1; i < top; i++) 839 tmp.d[i] = (~m->d[i]) & BN_MASK2; 840 tmp.top = top; 841 } else 842#endif 843 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx)) 844 goto err; 845 846 /* prepare a^1 in Montgomery domain */ 847 if (a->neg || BN_ucmp(a, m) >= 0) { 848 if (!BN_mod(&am, a, m, ctx)) 849 goto err; 850 if (!BN_to_montgomery(&am, &am, mont, ctx)) 851 goto err; 852 } else if (!BN_to_montgomery(&am, a, mont, ctx)) 853 goto err; 854 855#if defined(SPARC_T4_MONT) 856 if (t4) { 857 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, 858 const BN_ULONG *n0, const void *table, 859 int power, int bits); 860 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, 861 const BN_ULONG *n0, const void *table, 862 int power, int bits); 863 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, 864 const BN_ULONG *n0, const void *table, 865 int power, int bits); 866 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, 867 const BN_ULONG *n0, const void *table, 868 int power, int bits); 869 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, 870 const BN_ULONG *n0, const void *table, 871 int power, int bits); 872 static const bn_pwr5_mont_f pwr5_funcs[4] = { 873 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, 874 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 875 }; 876 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; 877 878 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, 879 const void *bp, const BN_ULONG *np, 880 const BN_ULONG *n0); 881 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, 882 const BN_ULONG *np, const BN_ULONG *n0); 883 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, 884 const void *bp, const BN_ULONG *np, 885 const BN_ULONG *n0); 886 int bn_mul_mont_t4_24(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_32(BN_ULONG *rp, const BN_ULONG *ap, 890 const void *bp, const BN_ULONG *np, 891 const BN_ULONG *n0); 892 static const bn_mul_mont_f mul_funcs[4] = { 893 bn_mul_mont_t4_8, bn_mul_mont_t4_16, 894 bn_mul_mont_t4_24, bn_mul_mont_t4_32 895 }; 896 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; 897 898 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, 899 const void *bp, const BN_ULONG *np, 900 const BN_ULONG *n0, int num); 901 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, 902 const void *bp, const BN_ULONG *np, 903 const BN_ULONG *n0, int num); 904 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, 905 const void *table, const BN_ULONG *np, 906 const BN_ULONG *n0, int num, int power); 907 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, 908 void *table, size_t power); 909 void bn_gather5_t4(BN_ULONG *out, size_t num, 910 void *table, size_t power); 911 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); 912 913 BN_ULONG *np = mont->N.d, *n0 = mont->n0; 914 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less 915 * than 32 */ 916 917 /* 918 * BN_to_montgomery can contaminate words above .top [in 919 * BN_DEBUG[_DEBUG] build]... 920 */ 921 for (i = am.top; i < top; i++) 922 am.d[i] = 0; 923 for (i = tmp.top; i < top; i++) 924 tmp.d[i] = 0; 925 926 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); 927 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); 928 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && 929 !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) 930 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); 931 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); 932 933 for (i = 3; i < 32; i++) { 934 /* Calculate a^i = a^(i-1) * a */ 935 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && 936 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) 937 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); 938 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); 939 } 940 941 /* switch to 64-bit domain */ 942 np = alloca(top * sizeof(BN_ULONG)); 943 top /= 2; 944 bn_flip_t4(np, mont->N.d, top); 945 946 bits--; 947 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) 948 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 949 bn_gather5_t4(tmp.d, top, powerbuf, wvalue); 950 951 /* 952 * Scan the exponent one window at a time starting from the most 953 * significant bits. 954 */ 955 while (bits >= 0) { 956 if (bits < stride) 957 stride = bits + 1; 958 bits -= stride; 959 wvalue = bn_get_bits(p, bits + 1); 960 961 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 962 continue; 963 /* retry once and fall back */ 964 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 965 continue; 966 967 bits += stride - 5; 968 wvalue >>= stride - 5; 969 wvalue &= 31; 970 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 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_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, 976 wvalue); 977 } 978 979 bn_flip_t4(tmp.d, tmp.d, top); 980 top *= 2; 981 /* back to 32-bit domain */ 982 tmp.top = top; 983 bn_correct_top(&tmp); 984 OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); 985 } else 986#endif 987#if defined(OPENSSL_BN_ASM_MONT5) 988 if (window == 5 && top > 1) { 989 /* 990 * This optimization uses ideas from http://eprint.iacr.org/2011/239, 991 * specifically optimization of cache-timing attack countermeasures 992 * and pre-computation optimization. 993 */ 994 995 /* 996 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as 997 * 512-bit RSA is hardly relevant, we omit it to spare size... 998 */ 999 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, 1000 const void *table, const BN_ULONG *np, 1001 const BN_ULONG *n0, int num, int power); 1002 void bn_scatter5(const BN_ULONG *inp, size_t num, 1003 void *table, size_t power); 1004 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); 1005 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, 1006 const void *table, const BN_ULONG *np, 1007 const BN_ULONG *n0, int num, int power); 1008 int bn_get_bits5(const BN_ULONG *ap, int off); 1009 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, 1010 const BN_ULONG *not_used, const BN_ULONG *np, 1011 const BN_ULONG *n0, int num); 1012 1013 BN_ULONG *n0 = mont->n0, *np; 1014 1015 /* 1016 * BN_to_montgomery can contaminate words above .top [in 1017 * BN_DEBUG[_DEBUG] build]... 1018 */ 1019 for (i = am.top; i < top; i++) 1020 am.d[i] = 0; 1021 for (i = tmp.top; i < top; i++) 1022 tmp.d[i] = 0; 1023 1024 /* 1025 * copy mont->N.d[] to improve cache locality 1026 */ 1027 for (np = am.d + top, i = 0; i < top; i++) 1028 np[i] = mont->N.d[i]; 1029 1030 bn_scatter5(tmp.d, top, powerbuf, 0); 1031 bn_scatter5(am.d, am.top, powerbuf, 1); 1032 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); 1033 bn_scatter5(tmp.d, top, powerbuf, 2); 1034 1035# if 0 1036 for (i = 3; i < 32; i++) { 1037 /* Calculate a^i = a^(i-1) * a */ 1038 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1039 bn_scatter5(tmp.d, top, powerbuf, i); 1040 } 1041# else 1042 /* same as above, but uses squaring for 1/2 of operations */ 1043 for (i = 4; i < 32; i *= 2) { 1044 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1045 bn_scatter5(tmp.d, top, powerbuf, i); 1046 } 1047 for (i = 3; i < 8; i += 2) { 1048 int j; 1049 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1050 bn_scatter5(tmp.d, top, powerbuf, i); 1051 for (j = 2 * i; j < 32; j *= 2) { 1052 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1053 bn_scatter5(tmp.d, top, powerbuf, j); 1054 } 1055 } 1056 for (; i < 16; i += 2) { 1057 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1058 bn_scatter5(tmp.d, top, powerbuf, i); 1059 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1060 bn_scatter5(tmp.d, top, powerbuf, 2 * i); 1061 } 1062 for (; i < 32; i += 2) { 1063 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1064 bn_scatter5(tmp.d, top, powerbuf, i); 1065 } 1066# endif 1067 bits--; 1068 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) 1069 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1070 bn_gather5(tmp.d, top, powerbuf, wvalue); 1071 1072 /* 1073 * Scan the exponent one window at a time starting from the most 1074 * significant bits. 1075 */ 1076 if (top & 7) 1077 while (bits >= 0) { 1078 for (wvalue = 0, i = 0; i < 5; i++, bits--) 1079 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1080 1081 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 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_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, 1087 wvalue); 1088 } else { 1089 while (bits >= 0) { 1090 wvalue = bn_get_bits5(p->d, bits - 4); 1091 bits -= 5; 1092 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue); 1093 } 1094 } 1095 1096 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top); 1097 tmp.top = top; 1098 bn_correct_top(&tmp); 1099 if (ret) { 1100 if (!BN_copy(rr, &tmp)) 1101 ret = 0; 1102 goto err; /* non-zero ret means it's not error */ 1103 } 1104 } else 1105#endif 1106 { 1107 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) 1108 goto err; 1109 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) 1110 goto err; 1111 1112 /* 1113 * If the window size is greater than 1, then calculate 1114 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even 1115 * powers could instead be computed as (a^(i/2))^2 to use the slight 1116 * performance advantage of sqr over mul). 1117 */ 1118 if (window > 1) { 1119 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) 1120 goto err; 1121 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, 1122 window)) 1123 goto err; 1124 for (i = 3; i < numPowers; i++) { 1125 /* Calculate a^i = a^(i-1) * a */ 1126 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) 1127 goto err; 1128 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, 1129 window)) 1130 goto err; 1131 } 1132 } 1133 1134 bits--; 1135 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) 1136 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1137 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, 1138 window)) 1139 goto err; 1140 1141 /* 1142 * Scan the exponent one window at a time starting from the most 1143 * significant bits. 1144 */ 1145 while (bits >= 0) { 1146 wvalue = 0; /* The 'value' of the window */ 1147 1148 /* Scan the window, squaring the result as we go */ 1149 for (i = 0; i < window; i++, bits--) { 1150 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx)) 1151 goto err; 1152 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1153 } 1154 1155 /* 1156 * Fetch the appropriate pre-computed value from the pre-buf 1157 */ 1158 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, 1159 window)) 1160 goto err; 1161 1162 /* Multiply the result into the intermediate result */ 1163 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx)) 1164 goto err; 1165 } 1166 } 1167 1168 /* Convert the final result from montgomery to standard format */ 1169#if defined(SPARC_T4_MONT) 1170 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 1171 am.d[0] = 1; /* borrow am */ 1172 for (i = 1; i < top; i++) 1173 am.d[i] = 0; 1174 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) 1175 goto err; 1176 } else 1177#endif 1178 if (!BN_from_montgomery(rr, &tmp, mont, ctx)) 1179 goto err; 1180 ret = 1; 1181 err: 1182 if ((in_mont == NULL) && (mont != NULL)) 1183 BN_MONT_CTX_free(mont); 1184 if (powerbuf != NULL) { 1185 OPENSSL_cleanse(powerbuf, powerbufLen); 1186 if (powerbufFree) 1187 OPENSSL_free(powerbufFree); 1188 } 1189 BN_CTX_end(ctx); 1190 return (ret); 1191} 1192 1193int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 1194 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 1195{ 1196 BN_MONT_CTX *mont = NULL; 1197 int b, bits, ret = 0; 1198 int r_is_one; 1199 BN_ULONG w, next_w; 1200 BIGNUM *d, *r, *t; 1201 BIGNUM *swap_tmp; 1202#define BN_MOD_MUL_WORD(r, w, m) \ 1203 (BN_mul_word(r, (w)) && \ 1204 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 1205 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 1206 /* 1207 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is 1208 * probably more overhead than always using BN_mod (which uses BN_copy if 1209 * a similar test returns true). 1210 */ 1211 /* 1212 * We can use BN_mod and do not need BN_nnmod because our accumulator is 1213 * never negative (the result of BN_mod does not depend on the sign of 1214 * the modulus). 1215 */ 1216#define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 1217 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 1218 1219 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 1220 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1221 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1222 return -1; 1223 } 1224 1225 bn_check_top(p); 1226 bn_check_top(m); 1227 1228 if (!BN_is_odd(m)) { 1229 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); 1230 return (0); 1231 } 1232 if (m->top == 1) 1233 a %= m->d[0]; /* make sure that 'a' is reduced */ 1234 1235 bits = BN_num_bits(p); 1236 if (bits == 0) { 1237 /* x**0 mod 1 is still zero. */ 1238 if (BN_is_one(m)) { 1239 ret = 1; 1240 BN_zero(rr); 1241 } else { 1242 ret = BN_one(rr); 1243 } 1244 return ret; 1245 } 1246 if (a == 0) { 1247 BN_zero(rr); 1248 ret = 1; 1249 return ret; 1250 } 1251 1252 BN_CTX_start(ctx); 1253 d = BN_CTX_get(ctx); 1254 r = BN_CTX_get(ctx); 1255 t = BN_CTX_get(ctx); 1256 if (d == NULL || r == NULL || t == NULL) 1257 goto err; 1258 1259 if (in_mont != NULL) 1260 mont = in_mont; 1261 else { 1262 if ((mont = BN_MONT_CTX_new()) == NULL) 1263 goto err; 1264 if (!BN_MONT_CTX_set(mont, m, ctx)) 1265 goto err; 1266 } 1267 1268 r_is_one = 1; /* except for Montgomery factor */ 1269 1270 /* bits-1 >= 0 */ 1271 1272 /* The result is accumulated in the product r*w. */ 1273 w = a; /* bit 'bits-1' of 'p' is always set */ 1274 for (b = bits - 2; b >= 0; b--) { 1275 /* First, square r*w. */ 1276 next_w = w * w; 1277 if ((next_w / w) != w) { /* overflow */ 1278 if (r_is_one) { 1279 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1280 goto err; 1281 r_is_one = 0; 1282 } else { 1283 if (!BN_MOD_MUL_WORD(r, w, m)) 1284 goto err; 1285 } 1286 next_w = 1; 1287 } 1288 w = next_w; 1289 if (!r_is_one) { 1290 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 1291 goto err; 1292 } 1293 1294 /* Second, multiply r*w by 'a' if exponent bit is set. */ 1295 if (BN_is_bit_set(p, b)) { 1296 next_w = w * a; 1297 if ((next_w / a) != w) { /* overflow */ 1298 if (r_is_one) { 1299 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1300 goto err; 1301 r_is_one = 0; 1302 } else { 1303 if (!BN_MOD_MUL_WORD(r, w, m)) 1304 goto err; 1305 } 1306 next_w = a; 1307 } 1308 w = next_w; 1309 } 1310 } 1311 1312 /* Finally, set r:=r*w. */ 1313 if (w != 1) { 1314 if (r_is_one) { 1315 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1316 goto err; 1317 r_is_one = 0; 1318 } else { 1319 if (!BN_MOD_MUL_WORD(r, w, m)) 1320 goto err; 1321 } 1322 } 1323 1324 if (r_is_one) { /* can happen only if a == 1 */ 1325 if (!BN_one(rr)) 1326 goto err; 1327 } else { 1328 if (!BN_from_montgomery(rr, r, mont, ctx)) 1329 goto err; 1330 } 1331 ret = 1; 1332 err: 1333 if ((in_mont == NULL) && (mont != NULL)) 1334 BN_MONT_CTX_free(mont); 1335 BN_CTX_end(ctx); 1336 bn_check_top(rr); 1337 return (ret); 1338} 1339 1340/* The old fallback, simple version :-) */ 1341int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 1342 const BIGNUM *m, BN_CTX *ctx) 1343{ 1344 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 1345 int start = 1; 1346 BIGNUM *d; 1347 /* Table of variables obtained from 'ctx' */ 1348 BIGNUM *val[TABLE_SIZE]; 1349 1350 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 1351 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1352 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1353 return -1; 1354 } 1355 1356 bits = BN_num_bits(p); 1357 if (bits == 0) { 1358 /* x**0 mod 1 is still zero. */ 1359 if (BN_is_one(m)) { 1360 ret = 1; 1361 BN_zero(r); 1362 } else { 1363 ret = BN_one(r); 1364 } 1365 return ret; 1366 } 1367 1368 BN_CTX_start(ctx); 1369 d = BN_CTX_get(ctx); 1370 val[0] = BN_CTX_get(ctx); 1371 if (!d || !val[0]) 1372 goto err; 1373 1374 if (!BN_nnmod(val[0], a, m, ctx)) 1375 goto err; /* 1 */ 1376 if (BN_is_zero(val[0])) { 1377 BN_zero(r); 1378 ret = 1; 1379 goto err; 1380 } 1381 1382 window = BN_window_bits_for_exponent_size(bits); 1383 if (window > 1) { 1384 if (!BN_mod_mul(d, val[0], val[0], m, ctx)) 1385 goto err; /* 2 */ 1386 j = 1 << (window - 1); 1387 for (i = 1; i < j; i++) { 1388 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 1389 !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) 1390 goto err; 1391 } 1392 } 1393 1394 start = 1; /* This is used to avoid multiplication etc 1395 * when there is only the value '1' in the 1396 * buffer. */ 1397 wvalue = 0; /* The 'value' of the window */ 1398 wstart = bits - 1; /* The top bit of the window */ 1399 wend = 0; /* The bottom bit of the window */ 1400 1401 if (!BN_one(r)) 1402 goto err; 1403 1404 for (;;) { 1405 if (BN_is_bit_set(p, wstart) == 0) { 1406 if (!start) 1407 if (!BN_mod_mul(r, r, r, m, ctx)) 1408 goto err; 1409 if (wstart == 0) 1410 break; 1411 wstart--; 1412 continue; 1413 } 1414 /* 1415 * We now have wstart on a 'set' bit, we now need to work out how bit 1416 * a window to do. To do this we need to scan forward until the last 1417 * set bit before the end of the window 1418 */ 1419 j = wstart; 1420 wvalue = 1; 1421 wend = 0; 1422 for (i = 1; i < window; i++) { 1423 if (wstart - i < 0) 1424 break; 1425 if (BN_is_bit_set(p, wstart - i)) { 1426 wvalue <<= (i - wend); 1427 wvalue |= 1; 1428 wend = i; 1429 } 1430 } 1431 1432 /* wend is the size of the current window */ 1433 j = wend + 1; 1434 /* add the 'bytes above' */ 1435 if (!start) 1436 for (i = 0; i < j; i++) { 1437 if (!BN_mod_mul(r, r, r, m, ctx)) 1438 goto err; 1439 } 1440 1441 /* wvalue will be an odd number < 2^window */ 1442 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) 1443 goto err; 1444 1445 /* move the 'window' down further */ 1446 wstart -= wend + 1; 1447 wvalue = 0; 1448 start = 0; 1449 if (wstart < 0) 1450 break; 1451 } 1452 ret = 1; 1453 err: 1454 BN_CTX_end(ctx); 1455 bn_check_top(r); 1456 return (ret); 1457} 1458