bn_exp.c revision 296611
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/* maximum precomputation table size for *variable* sliding windows */ 117#define TABLE_SIZE 32 118 119/* this one works - simple but works */ 120int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) 121{ 122 int i, bits, ret = 0; 123 BIGNUM *v, *rr; 124 125 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 126 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 127 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 128 return -1; 129 } 130 131 BN_CTX_start(ctx); 132 if ((r == a) || (r == p)) 133 rr = BN_CTX_get(ctx); 134 else 135 rr = r; 136 v = BN_CTX_get(ctx); 137 if (rr == NULL || v == NULL) 138 goto err; 139 140 if (BN_copy(v, a) == NULL) 141 goto err; 142 bits = BN_num_bits(p); 143 144 if (BN_is_odd(p)) { 145 if (BN_copy(rr, a) == NULL) 146 goto err; 147 } else { 148 if (!BN_one(rr)) 149 goto err; 150 } 151 152 for (i = 1; i < bits; i++) { 153 if (!BN_sqr(v, v, ctx)) 154 goto err; 155 if (BN_is_bit_set(p, i)) { 156 if (!BN_mul(rr, rr, v, ctx)) 157 goto err; 158 } 159 } 160 ret = 1; 161 err: 162 if (r != rr) 163 BN_copy(r, rr); 164 BN_CTX_end(ctx); 165 bn_check_top(r); 166 return (ret); 167} 168 169int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 170 BN_CTX *ctx) 171{ 172 int ret; 173 174 bn_check_top(a); 175 bn_check_top(p); 176 bn_check_top(m); 177 178 /*- 179 * For even modulus m = 2^k*m_odd, it might make sense to compute 180 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 181 * exponentiation for the odd part), using appropriate exponent 182 * reductions, and combine the results using the CRT. 183 * 184 * For now, we use Montgomery only if the modulus is odd; otherwise, 185 * exponentiation using the reciprocal-based quick remaindering 186 * algorithm is used. 187 * 188 * (Timing obtained with expspeed.c [computations a^p mod m 189 * where a, p, m are of the same length: 256, 512, 1024, 2048, 190 * 4096, 8192 bits], compared to the running time of the 191 * standard algorithm: 192 * 193 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 194 * 55 .. 77 % [UltraSparc processor, but 195 * debug-solaris-sparcv8-gcc conf.] 196 * 197 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 198 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 199 * 200 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 201 * at 2048 and more bits, but at 512 and 1024 bits, it was 202 * slower even than the standard algorithm! 203 * 204 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 205 * should be obtained when the new Montgomery reduction code 206 * has been integrated into OpenSSL.) 207 */ 208 209#define MONT_MUL_MOD 210#define MONT_EXP_WORD 211#define RECP_MUL_MOD 212 213#ifdef MONT_MUL_MOD 214 /* 215 * I have finally been able to take out this pre-condition of the top bit 216 * being set. It was caused by an error in BN_div with negatives. There 217 * was also another problem when for a^b%m a >= m. eay 07-May-97 218 */ 219 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ 220 221 if (BN_is_odd(m)) { 222# ifdef MONT_EXP_WORD 223 if (a->top == 1 && !a->neg 224 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) { 225 BN_ULONG A = a->d[0]; 226 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); 227 } else 228# endif 229 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); 230 } else 231#endif 232#ifdef RECP_MUL_MOD 233 { 234 ret = BN_mod_exp_recp(r, a, p, m, ctx); 235 } 236#else 237 { 238 ret = BN_mod_exp_simple(r, a, p, m, ctx); 239 } 240#endif 241 242 bn_check_top(r); 243 return (ret); 244} 245 246int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 247 const BIGNUM *m, BN_CTX *ctx) 248{ 249 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 250 int start = 1; 251 BIGNUM *aa; 252 /* Table of variables obtained from 'ctx' */ 253 BIGNUM *val[TABLE_SIZE]; 254 BN_RECP_CTX recp; 255 256 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 257 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 258 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 259 return -1; 260 } 261 262 bits = BN_num_bits(p); 263 264 if (bits == 0) { 265 ret = BN_one(r); 266 return ret; 267 } 268 269 BN_CTX_start(ctx); 270 aa = BN_CTX_get(ctx); 271 val[0] = BN_CTX_get(ctx); 272 if (!aa || !val[0]) 273 goto err; 274 275 BN_RECP_CTX_init(&recp); 276 if (m->neg) { 277 /* ignore sign of 'm' */ 278 if (!BN_copy(aa, m)) 279 goto err; 280 aa->neg = 0; 281 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) 282 goto err; 283 } else { 284 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) 285 goto err; 286 } 287 288 if (!BN_nnmod(val[0], a, m, ctx)) 289 goto err; /* 1 */ 290 if (BN_is_zero(val[0])) { 291 BN_zero(r); 292 ret = 1; 293 goto err; 294 } 295 296 window = BN_window_bits_for_exponent_size(bits); 297 if (window > 1) { 298 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) 299 goto err; /* 2 */ 300 j = 1 << (window - 1); 301 for (i = 1; i < j; i++) { 302 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 303 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) 304 goto err; 305 } 306 } 307 308 start = 1; /* This is used to avoid multiplication etc 309 * when there is only the value '1' in the 310 * buffer. */ 311 wvalue = 0; /* The 'value' of the window */ 312 wstart = bits - 1; /* The top bit of the window */ 313 wend = 0; /* The bottom bit of the window */ 314 315 if (!BN_one(r)) 316 goto err; 317 318 for (;;) { 319 if (BN_is_bit_set(p, wstart) == 0) { 320 if (!start) 321 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 322 goto err; 323 if (wstart == 0) 324 break; 325 wstart--; 326 continue; 327 } 328 /* 329 * We now have wstart on a 'set' bit, we now need to work out how bit 330 * a window to do. To do this we need to scan forward until the last 331 * set bit before the end of the window 332 */ 333 j = wstart; 334 wvalue = 1; 335 wend = 0; 336 for (i = 1; i < window; i++) { 337 if (wstart - i < 0) 338 break; 339 if (BN_is_bit_set(p, wstart - i)) { 340 wvalue <<= (i - wend); 341 wvalue |= 1; 342 wend = i; 343 } 344 } 345 346 /* wend is the size of the current window */ 347 j = wend + 1; 348 /* add the 'bytes above' */ 349 if (!start) 350 for (i = 0; i < j; i++) { 351 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 352 goto err; 353 } 354 355 /* wvalue will be an odd number < 2^window */ 356 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) 357 goto err; 358 359 /* move the 'window' down further */ 360 wstart -= wend + 1; 361 wvalue = 0; 362 start = 0; 363 if (wstart < 0) 364 break; 365 } 366 ret = 1; 367 err: 368 BN_CTX_end(ctx); 369 BN_RECP_CTX_free(&recp); 370 bn_check_top(r); 371 return (ret); 372} 373 374int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 375 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 376{ 377 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 378 int start = 1; 379 BIGNUM *d, *r; 380 const BIGNUM *aa; 381 /* Table of variables obtained from 'ctx' */ 382 BIGNUM *val[TABLE_SIZE]; 383 BN_MONT_CTX *mont = NULL; 384 385 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 386 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 387 } 388 389 bn_check_top(a); 390 bn_check_top(p); 391 bn_check_top(m); 392 393 if (!BN_is_odd(m)) { 394 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); 395 return (0); 396 } 397 bits = BN_num_bits(p); 398 if (bits == 0) { 399 ret = BN_one(rr); 400 return ret; 401 } 402 403 BN_CTX_start(ctx); 404 d = BN_CTX_get(ctx); 405 r = BN_CTX_get(ctx); 406 val[0] = BN_CTX_get(ctx); 407 if (!d || !r || !val[0]) 408 goto err; 409 410 /* 411 * If this is not done, things will break in the montgomery part 412 */ 413 414 if (in_mont != NULL) 415 mont = in_mont; 416 else { 417 if ((mont = BN_MONT_CTX_new()) == NULL) 418 goto err; 419 if (!BN_MONT_CTX_set(mont, m, ctx)) 420 goto err; 421 } 422 423 if (a->neg || BN_ucmp(a, m) >= 0) { 424 if (!BN_nnmod(val[0], a, m, ctx)) 425 goto err; 426 aa = val[0]; 427 } else 428 aa = a; 429 if (BN_is_zero(aa)) { 430 BN_zero(rr); 431 ret = 1; 432 goto err; 433 } 434 if (!BN_to_montgomery(val[0], aa, mont, ctx)) 435 goto err; /* 1 */ 436 437 window = BN_window_bits_for_exponent_size(bits); 438 if (window > 1) { 439 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) 440 goto err; /* 2 */ 441 j = 1 << (window - 1); 442 for (i = 1; i < j; i++) { 443 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 444 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) 445 goto err; 446 } 447 } 448 449 start = 1; /* This is used to avoid multiplication etc 450 * when there is only the value '1' in the 451 * buffer. */ 452 wvalue = 0; /* The 'value' of the window */ 453 wstart = bits - 1; /* The top bit of the window */ 454 wend = 0; /* The bottom bit of the window */ 455 456 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) 457 goto err; 458 for (;;) { 459 if (BN_is_bit_set(p, wstart) == 0) { 460 if (!start) { 461 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 462 goto err; 463 } 464 if (wstart == 0) 465 break; 466 wstart--; 467 continue; 468 } 469 /* 470 * We now have wstart on a 'set' bit, we now need to work out how bit 471 * a window to do. To do this we need to scan forward until the last 472 * set bit before the end of the window 473 */ 474 j = wstart; 475 wvalue = 1; 476 wend = 0; 477 for (i = 1; i < window; i++) { 478 if (wstart - i < 0) 479 break; 480 if (BN_is_bit_set(p, wstart - i)) { 481 wvalue <<= (i - wend); 482 wvalue |= 1; 483 wend = i; 484 } 485 } 486 487 /* wend is the size of the current window */ 488 j = wend + 1; 489 /* add the 'bytes above' */ 490 if (!start) 491 for (i = 0; i < j; i++) { 492 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 493 goto err; 494 } 495 496 /* wvalue will be an odd number < 2^window */ 497 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) 498 goto err; 499 500 /* move the 'window' down further */ 501 wstart -= wend + 1; 502 wvalue = 0; 503 start = 0; 504 if (wstart < 0) 505 break; 506 } 507 if (!BN_from_montgomery(rr, r, mont, ctx)) 508 goto err; 509 ret = 1; 510 err: 511 if ((in_mont == NULL) && (mont != NULL)) 512 BN_MONT_CTX_free(mont); 513 BN_CTX_end(ctx); 514 bn_check_top(rr); 515 return (ret); 516} 517 518/* 519 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific 520 * layout so that accessing any of these table values shows the same access 521 * pattern as far as cache lines are concerned. The following functions are 522 * used to transfer a BIGNUM from/to that table. 523 */ 524 525static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, 526 unsigned char *buf, int idx, 527 int window) 528{ 529 int i, j; 530 int width = 1 << window; 531 BN_ULONG *table = (BN_ULONG *)buf; 532 533 if (bn_wexpand(b, top) == NULL) 534 return 0; 535 while (b->top < top) { 536 b->d[b->top++] = 0; 537 } 538 539 for (i = 0, j = idx; i < top; i++, j += width) { 540 table[j] = b->d[i]; 541 } 542 543 bn_correct_top(b); 544 return 1; 545} 546 547static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, 548 unsigned char *buf, int idx, 549 int window) 550{ 551 int i, j; 552 int width = 1 << window; 553 volatile BN_ULONG *table = (volatile BN_ULONG *)buf; 554 555 if (bn_wexpand(b, top) == NULL) 556 return 0; 557 558 if (window <= 3) { 559 for (i = 0; i < top; i++, table += width) { 560 BN_ULONG acc = 0; 561 562 for (j = 0; j < width; j++) { 563 acc |= table[j] & 564 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 565 } 566 567 b->d[i] = acc; 568 } 569 } else { 570 int xstride = 1 << (window - 2); 571 BN_ULONG y0, y1, y2, y3; 572 573 i = idx >> (window - 2); /* equivalent of idx / xstride */ 574 idx &= xstride - 1; /* equivalent of idx % xstride */ 575 576 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); 577 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); 578 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); 579 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); 580 581 for (i = 0; i < top; i++, table += width) { 582 BN_ULONG acc = 0; 583 584 for (j = 0; j < xstride; j++) { 585 acc |= ( (table[j + 0 * xstride] & y0) | 586 (table[j + 1 * xstride] & y1) | 587 (table[j + 2 * xstride] & y2) | 588 (table[j + 3 * xstride] & y3) ) 589 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 590 } 591 592 b->d[i] = acc; 593 } 594 } 595 596 b->top = top; 597 bn_correct_top(b); 598 return 1; 599} 600 601/* 602 * Given a pointer value, compute the next address that is a cache line 603 * multiple. 604 */ 605#define MOD_EXP_CTIME_ALIGN(x_) \ 606 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 607 608/* 609 * This variant of BN_mod_exp_mont() uses fixed windows and the special 610 * precomputation memory layout to limit data-dependency to a minimum to 611 * protect secret exponents (cf. the hyper-threading timing attacks pointed 612 * out by Colin Percival, 613 * http://www.daemong-consideredperthreading-considered-harmful/) 614 */ 615int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 616 const BIGNUM *m, BN_CTX *ctx, 617 BN_MONT_CTX *in_mont) 618{ 619 int i, bits, ret = 0, idx, window, wvalue; 620 int top; 621 BIGNUM *r; 622 const BIGNUM *aa; 623 BN_MONT_CTX *mont = NULL; 624 625 int numPowers; 626 unsigned char *powerbufFree = NULL; 627 int powerbufLen = 0; 628 unsigned char *powerbuf = NULL; 629 BIGNUM *computeTemp = NULL, *am = NULL; 630 631 bn_check_top(a); 632 bn_check_top(p); 633 bn_check_top(m); 634 635 top = m->top; 636 637 if (!(m->d[0] & 1)) { 638 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); 639 return (0); 640 } 641 bits = BN_num_bits(p); 642 if (bits == 0) { 643 ret = BN_one(rr); 644 return ret; 645 } 646 647 /* Initialize BIGNUM context and allocate intermediate result */ 648 BN_CTX_start(ctx); 649 r = BN_CTX_get(ctx); 650 if (r == NULL) 651 goto err; 652 653 /* 654 * Allocate a montgomery context if it was not supplied by the caller. If 655 * this is not done, things will break in the montgomery part. 656 */ 657 if (in_mont != NULL) 658 mont = in_mont; 659 else { 660 if ((mont = BN_MONT_CTX_new()) == NULL) 661 goto err; 662 if (!BN_MONT_CTX_set(mont, m, ctx)) 663 goto err; 664 } 665 666 /* Get the window size to use with size of p. */ 667 window = BN_window_bits_for_ctime_exponent_size(bits); 668 669 /* 670 * Allocate a buffer large enough to hold all of the pre-computed powers 671 * of a. 672 */ 673 numPowers = 1 << window; 674 powerbufLen = sizeof(m->d[0]) * top * numPowers; 675 if ((powerbufFree = 676 (unsigned char *)OPENSSL_malloc(powerbufLen + 677 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) 678 == NULL) 679 goto err; 680 681 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 682 memset(powerbuf, 0, powerbufLen); 683 684 /* 685 * Initialize the intermediate result. Do this early to save double 686 * conversion, once each for a^0 and intermediate result. 687 */ 688 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) 689 goto err; 690 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, window)) 691 goto err; 692 693 /* Initialize computeTemp as a^1 with montgomery precalcs */ 694 computeTemp = BN_CTX_get(ctx); 695 am = BN_CTX_get(ctx); 696 if (computeTemp == NULL || am == NULL) 697 goto err; 698 699 if (a->neg || BN_ucmp(a, m) >= 0) { 700 if (!BN_mod(am, a, m, ctx)) 701 goto err; 702 aa = am; 703 } else 704 aa = a; 705 if (!BN_to_montgomery(am, aa, mont, ctx)) 706 goto err; 707 if (!BN_copy(computeTemp, am)) 708 goto err; 709 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, window)) 710 goto err; 711 712 /* 713 * If the window size is greater than 1, then calculate 714 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even powers 715 * could instead be computed as (a^(i/2))^2 to use the slight performance 716 * advantage of sqr over mul). 717 */ 718 if (window > 1) { 719 for (i = 2; i < numPowers; i++) { 720 /* Calculate a^i = a^(i-1) * a */ 721 if (!BN_mod_mul_montgomery 722 (computeTemp, am, computeTemp, mont, ctx)) 723 goto err; 724 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, 725 window)) 726 goto err; 727 } 728 } 729 730 /* 731 * Adjust the number of bits up to a multiple of the window size. If the 732 * exponent length is not a multiple of the window size, then this pads 733 * the most significant bits with zeros to normalize the scanning loop to 734 * there's no special cases. * NOTE: Making the window size a power of 735 * two less than the native * word size ensures that the padded bits 736 * won't go past the last * word in the internal BIGNUM structure. Going 737 * past the end will * still produce the correct result, but causes a 738 * different branch * to be taken in the BN_is_bit_set function. 739 */ 740 bits = ((bits + window - 1) / window) * window; 741 idx = bits - 1; /* The top bit of the window */ 742 743 /* 744 * Scan the exponent one window at a time starting from the most 745 * significant bits. 746 */ 747 while (idx >= 0) { 748 wvalue = 0; /* The 'value' of the window */ 749 750 /* Scan the window, squaring the result as we go */ 751 for (i = 0; i < window; i++, idx--) { 752 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 753 goto err; 754 wvalue = (wvalue << 1) + BN_is_bit_set(p, idx); 755 } 756 757 /* 758 * Fetch the appropriate pre-computed value from the pre-buf 759 */ 760 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF 761 (computeTemp, top, powerbuf, wvalue, window)) 762 goto err; 763 764 /* Multiply the result into the intermediate result */ 765 if (!BN_mod_mul_montgomery(r, r, computeTemp, mont, ctx)) 766 goto err; 767 } 768 769 /* Convert the final result from montgomery to standard format */ 770 if (!BN_from_montgomery(rr, r, mont, ctx)) 771 goto err; 772 ret = 1; 773 err: 774 if ((in_mont == NULL) && (mont != NULL)) 775 BN_MONT_CTX_free(mont); 776 if (powerbuf != NULL) { 777 OPENSSL_cleanse(powerbuf, powerbufLen); 778 OPENSSL_free(powerbufFree); 779 } 780 if (am != NULL) 781 BN_clear(am); 782 if (computeTemp != NULL) 783 BN_clear(computeTemp); 784 BN_CTX_end(ctx); 785 return (ret); 786} 787 788int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 789 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 790{ 791 BN_MONT_CTX *mont = NULL; 792 int b, bits, ret = 0; 793 int r_is_one; 794 BN_ULONG w, next_w; 795 BIGNUM *d, *r, *t; 796 BIGNUM *swap_tmp; 797#define BN_MOD_MUL_WORD(r, w, m) \ 798 (BN_mul_word(r, (w)) && \ 799 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 800 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 801 /* 802 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is 803 * probably more overhead than always using BN_mod (which uses BN_copy if 804 * a similar test returns true). 805 */ 806 /* 807 * We can use BN_mod and do not need BN_nnmod because our accumulator is 808 * never negative (the result of BN_mod does not depend on the sign of 809 * the modulus). 810 */ 811#define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 812 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 813 814 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 815 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 816 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 817 return -1; 818 } 819 820 bn_check_top(p); 821 bn_check_top(m); 822 823 if (!BN_is_odd(m)) { 824 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); 825 return (0); 826 } 827 if (m->top == 1) 828 a %= m->d[0]; /* make sure that 'a' is reduced */ 829 830 bits = BN_num_bits(p); 831 if (bits == 0) { 832 /* x**0 mod 1 is still zero. */ 833 if (BN_is_one(m)) { 834 ret = 1; 835 BN_zero(rr); 836 } else 837 ret = BN_one(rr); 838 return ret; 839 } 840 if (a == 0) { 841 BN_zero(rr); 842 ret = 1; 843 return ret; 844 } 845 846 BN_CTX_start(ctx); 847 d = BN_CTX_get(ctx); 848 r = BN_CTX_get(ctx); 849 t = BN_CTX_get(ctx); 850 if (d == NULL || r == NULL || t == NULL) 851 goto err; 852 853 if (in_mont != NULL) 854 mont = in_mont; 855 else { 856 if ((mont = BN_MONT_CTX_new()) == NULL) 857 goto err; 858 if (!BN_MONT_CTX_set(mont, m, ctx)) 859 goto err; 860 } 861 862 r_is_one = 1; /* except for Montgomery factor */ 863 864 /* bits-1 >= 0 */ 865 866 /* The result is accumulated in the product r*w. */ 867 w = a; /* bit 'bits-1' of 'p' is always set */ 868 for (b = bits - 2; b >= 0; b--) { 869 /* First, square r*w. */ 870 next_w = w * w; 871 if ((next_w / w) != w) { /* overflow */ 872 if (r_is_one) { 873 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 874 goto err; 875 r_is_one = 0; 876 } else { 877 if (!BN_MOD_MUL_WORD(r, w, m)) 878 goto err; 879 } 880 next_w = 1; 881 } 882 w = next_w; 883 if (!r_is_one) { 884 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 885 goto err; 886 } 887 888 /* Second, multiply r*w by 'a' if exponent bit is set. */ 889 if (BN_is_bit_set(p, b)) { 890 next_w = w * a; 891 if ((next_w / a) != w) { /* overflow */ 892 if (r_is_one) { 893 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 894 goto err; 895 r_is_one = 0; 896 } else { 897 if (!BN_MOD_MUL_WORD(r, w, m)) 898 goto err; 899 } 900 next_w = a; 901 } 902 w = next_w; 903 } 904 } 905 906 /* Finally, set r:=r*w. */ 907 if (w != 1) { 908 if (r_is_one) { 909 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 910 goto err; 911 r_is_one = 0; 912 } else { 913 if (!BN_MOD_MUL_WORD(r, w, m)) 914 goto err; 915 } 916 } 917 918 if (r_is_one) { /* can happen only if a == 1 */ 919 if (!BN_one(rr)) 920 goto err; 921 } else { 922 if (!BN_from_montgomery(rr, r, mont, ctx)) 923 goto err; 924 } 925 ret = 1; 926 err: 927 if ((in_mont == NULL) && (mont != NULL)) 928 BN_MONT_CTX_free(mont); 929 BN_CTX_end(ctx); 930 bn_check_top(rr); 931 return (ret); 932} 933 934/* The old fallback, simple version :-) */ 935int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 936 const BIGNUM *m, BN_CTX *ctx) 937{ 938 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 939 int start = 1; 940 BIGNUM *d; 941 /* Table of variables obtained from 'ctx' */ 942 BIGNUM *val[TABLE_SIZE]; 943 944 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { 945 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 946 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 947 return -1; 948 } 949 950 bits = BN_num_bits(p); 951 952 if (bits == 0) { 953 ret = BN_one(r); 954 return ret; 955 } 956 957 BN_CTX_start(ctx); 958 d = BN_CTX_get(ctx); 959 val[0] = BN_CTX_get(ctx); 960 if (!d || !val[0]) 961 goto err; 962 963 if (!BN_nnmod(val[0], a, m, ctx)) 964 goto err; /* 1 */ 965 if (BN_is_zero(val[0])) { 966 BN_zero(r); 967 ret = 1; 968 goto err; 969 } 970 971 window = BN_window_bits_for_exponent_size(bits); 972 if (window > 1) { 973 if (!BN_mod_mul(d, val[0], val[0], m, ctx)) 974 goto err; /* 2 */ 975 j = 1 << (window - 1); 976 for (i = 1; i < j; i++) { 977 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 978 !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) 979 goto err; 980 } 981 } 982 983 start = 1; /* This is used to avoid multiplication etc 984 * when there is only the value '1' in the 985 * buffer. */ 986 wvalue = 0; /* The 'value' of the window */ 987 wstart = bits - 1; /* The top bit of the window */ 988 wend = 0; /* The bottom bit of the window */ 989 990 if (!BN_one(r)) 991 goto err; 992 993 for (;;) { 994 if (BN_is_bit_set(p, wstart) == 0) { 995 if (!start) 996 if (!BN_mod_mul(r, r, r, m, ctx)) 997 goto err; 998 if (wstart == 0) 999 break; 1000 wstart--; 1001 continue; 1002 } 1003 /* 1004 * We now have wstart on a 'set' bit, we now need to work out how bit 1005 * a window to do. To do this we need to scan forward until the last 1006 * set bit before the end of the window 1007 */ 1008 j = wstart; 1009 wvalue = 1; 1010 wend = 0; 1011 for (i = 1; i < window; i++) { 1012 if (wstart - i < 0) 1013 break; 1014 if (BN_is_bit_set(p, wstart - i)) { 1015 wvalue <<= (i - wend); 1016 wvalue |= 1; 1017 wend = i; 1018 } 1019 } 1020 1021 /* wend is the size of the current window */ 1022 j = wend + 1; 1023 /* add the 'bytes above' */ 1024 if (!start) 1025 for (i = 0; i < j; i++) { 1026 if (!BN_mod_mul(r, r, r, m, ctx)) 1027 goto err; 1028 } 1029 1030 /* wvalue will be an odd number < 2^window */ 1031 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) 1032 goto err; 1033 1034 /* move the 'window' down further */ 1035 wstart -= wend + 1; 1036 wvalue = 0; 1037 start = 0; 1038 if (wstart < 0) 1039 break; 1040 } 1041 ret = 1; 1042 err: 1043 BN_CTX_end(ctx); 1044 bn_check_top(r); 1045 return (ret); 1046} 1047