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) 1998-2018 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 0; 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 0; 289 } 290 291 bits = BN_num_bits(p); 292 if (bits == 0) { 293 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 294 if (BN_abs_is_word(m, 1)) { 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, or x**0 mod -1 is still zero. */ 436 if (BN_abs_is_word(m, 1)) { 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_mont_fixed_top(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_mul_mont_fixed_top(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_mul_mont_fixed_top(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 r->flags |= BN_FLG_FIXED_TOP; 509 } else 510#endif 511 if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx)) 512 goto err; 513 for (;;) { 514 if (BN_is_bit_set(p, wstart) == 0) { 515 if (!start) { 516 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) 517 goto err; 518 } 519 if (wstart == 0) 520 break; 521 wstart--; 522 continue; 523 } 524 /* 525 * We now have wstart on a 'set' bit, we now need to work out how bit 526 * a window to do. To do this we need to scan forward until the last 527 * set bit before the end of the window 528 */ 529 j = wstart; 530 wvalue = 1; 531 wend = 0; 532 for (i = 1; i < window; i++) { 533 if (wstart - i < 0) 534 break; 535 if (BN_is_bit_set(p, wstart - i)) { 536 wvalue <<= (i - wend); 537 wvalue |= 1; 538 wend = i; 539 } 540 } 541 542 /* wend is the size of the current window */ 543 j = wend + 1; 544 /* add the 'bytes above' */ 545 if (!start) 546 for (i = 0; i < j; i++) { 547 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) 548 goto err; 549 } 550 551 /* wvalue will be an odd number < 2^window */ 552 if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx)) 553 goto err; 554 555 /* move the 'window' down further */ 556 wstart -= wend + 1; 557 wvalue = 0; 558 start = 0; 559 if (wstart < 0) 560 break; 561 } 562 /* 563 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery 564 * removes padding [if any] and makes return value suitable for public 565 * API consumer. 566 */ 567#if defined(SPARC_T4_MONT) 568 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 569 j = mont->N.top; /* borrow j */ 570 val[0]->d[0] = 1; /* borrow val[0] */ 571 for (i = 1; i < j; i++) 572 val[0]->d[i] = 0; 573 val[0]->top = j; 574 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) 575 goto err; 576 } else 577#endif 578 if (!BN_from_montgomery(rr, r, mont, ctx)) 579 goto err; 580 ret = 1; 581 err: 582 if ((in_mont == NULL) && (mont != NULL)) 583 BN_MONT_CTX_free(mont); 584 BN_CTX_end(ctx); 585 bn_check_top(rr); 586 return (ret); 587} 588 589#if defined(SPARC_T4_MONT) 590static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) 591{ 592 BN_ULONG ret = 0; 593 int wordpos; 594 595 wordpos = bitpos / BN_BITS2; 596 bitpos %= BN_BITS2; 597 if (wordpos >= 0 && wordpos < a->top) { 598 ret = a->d[wordpos] & BN_MASK2; 599 if (bitpos) { 600 ret >>= bitpos; 601 if (++wordpos < a->top) 602 ret |= a->d[wordpos] << (BN_BITS2 - bitpos); 603 } 604 } 605 606 return ret & BN_MASK2; 607} 608#endif 609 610/* 611 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific 612 * layout so that accessing any of these table values shows the same access 613 * pattern as far as cache lines are concerned. The following functions are 614 * used to transfer a BIGNUM from/to that table. 615 */ 616 617static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, 618 unsigned char *buf, int idx, 619 int window) 620{ 621 int i, j; 622 int width = 1 << window; 623 BN_ULONG *table = (BN_ULONG *)buf; 624 625 if (top > b->top) 626 top = b->top; /* this works because 'buf' is explicitly 627 * zeroed */ 628 for (i = 0, j = idx; i < top; i++, j += width) { 629 table[j] = b->d[i]; 630 } 631 632 return 1; 633} 634 635static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, 636 unsigned char *buf, int idx, 637 int window) 638{ 639 int i, j; 640 int width = 1 << window; 641 volatile BN_ULONG *table = (volatile BN_ULONG *)buf; 642 643 if (bn_wexpand(b, top) == NULL) 644 return 0; 645 646 if (window <= 3) { 647 for (i = 0; i < top; i++, table += width) { 648 BN_ULONG acc = 0; 649 650 for (j = 0; j < width; j++) { 651 acc |= table[j] & 652 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 653 } 654 655 b->d[i] = acc; 656 } 657 } else { 658 int xstride = 1 << (window - 2); 659 BN_ULONG y0, y1, y2, y3; 660 661 i = idx >> (window - 2); /* equivalent of idx / xstride */ 662 idx &= xstride - 1; /* equivalent of idx % xstride */ 663 664 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); 665 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); 666 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); 667 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); 668 669 for (i = 0; i < top; i++, table += width) { 670 BN_ULONG acc = 0; 671 672 for (j = 0; j < xstride; j++) { 673 acc |= ( (table[j + 0 * xstride] & y0) | 674 (table[j + 1 * xstride] & y1) | 675 (table[j + 2 * xstride] & y2) | 676 (table[j + 3 * xstride] & y3) ) 677 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 678 } 679 680 b->d[i] = acc; 681 } 682 } 683 684 b->top = top; 685 b->flags |= BN_FLG_FIXED_TOP; 686 return 1; 687} 688 689/* 690 * Given a pointer value, compute the next address that is a cache line 691 * multiple. 692 */ 693#define MOD_EXP_CTIME_ALIGN(x_) \ 694 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 695 696/* 697 * This variant of BN_mod_exp_mont() uses fixed windows and the special 698 * precomputation memory layout to limit data-dependency to a minimum to 699 * protect secret exponents (cf. the hyper-threading timing attacks pointed 700 * out by Colin Percival, 701 * http://www.daemonology.net/hyperthreading-considered-harmful/) 702 */ 703int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 704 const BIGNUM *m, BN_CTX *ctx, 705 BN_MONT_CTX *in_mont) 706{ 707 int i, bits, ret = 0, window, wvalue; 708 int top; 709 BN_MONT_CTX *mont = NULL; 710 711 int numPowers; 712 unsigned char *powerbufFree = NULL; 713 int powerbufLen = 0; 714 unsigned char *powerbuf = NULL; 715 BIGNUM tmp, am; 716#if defined(SPARC_T4_MONT) 717 unsigned int t4 = 0; 718#endif 719 720 bn_check_top(a); 721 bn_check_top(p); 722 bn_check_top(m); 723 724 if (!BN_is_odd(m)) { 725 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); 726 return (0); 727 } 728 729 top = m->top; 730 731 /* 732 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak 733 * whether the top bits are zero. 734 */ 735 bits = p->top * BN_BITS2; 736 if (bits == 0) { 737 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 738 if (BN_abs_is_word(m, 1)) { 739 ret = 1; 740 BN_zero(rr); 741 } else { 742 ret = BN_one(rr); 743 } 744 return ret; 745 } 746 747 BN_CTX_start(ctx); 748 749 /* 750 * Allocate a montgomery context if it was not supplied by the caller. If 751 * this is not done, things will break in the montgomery part. 752 */ 753 if (in_mont != NULL) 754 mont = in_mont; 755 else { 756 if ((mont = BN_MONT_CTX_new()) == NULL) 757 goto err; 758 if (!BN_MONT_CTX_set(mont, m, ctx)) 759 goto err; 760 } 761 762#ifdef RSAZ_ENABLED 763 /* 764 * If the size of the operands allow it, perform the optimized 765 * RSAZ exponentiation. For further information see 766 * crypto/bn/rsaz_exp.c and accompanying assembly modules. 767 */ 768 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) 769 && rsaz_avx2_eligible()) { 770 if (NULL == bn_wexpand(rr, 16)) 771 goto err; 772 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, 773 mont->n0[0]); 774 rr->top = 16; 775 rr->neg = 0; 776 bn_correct_top(rr); 777 ret = 1; 778 goto err; 779 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { 780 if (NULL == bn_wexpand(rr, 8)) 781 goto err; 782 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); 783 rr->top = 8; 784 rr->neg = 0; 785 bn_correct_top(rr); 786 ret = 1; 787 goto err; 788 } 789#endif 790 791 /* Get the window size to use with size of p. */ 792 window = BN_window_bits_for_ctime_exponent_size(bits); 793#if defined(SPARC_T4_MONT) 794 if (window >= 5 && (top & 15) == 0 && top <= 64 && 795 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == 796 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) 797 window = 5; 798 else 799#endif 800#if defined(OPENSSL_BN_ASM_MONT5) 801 if (window >= 5) { 802 window = 5; /* ~5% improvement for RSA2048 sign, and even 803 * for RSA4096 */ 804 /* reserve space for mont->N.d[] copy */ 805 powerbufLen += top * sizeof(mont->N.d[0]); 806 } 807#endif 808 (void)0; 809 810 /* 811 * Allocate a buffer large enough to hold all of the pre-computed powers 812 * of am, am itself and tmp. 813 */ 814 numPowers = 1 << window; 815 powerbufLen += sizeof(m->d[0]) * (top * numPowers + 816 ((2 * top) > 817 numPowers ? (2 * top) : numPowers)); 818#ifdef alloca 819 if (powerbufLen < 3072) 820 powerbufFree = 821 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); 822 else 823#endif 824 if ((powerbufFree = 825 (unsigned char *)OPENSSL_malloc(powerbufLen + 826 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) 827 == NULL) 828 goto err; 829 830 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 831 memset(powerbuf, 0, powerbufLen); 832 833#ifdef alloca 834 if (powerbufLen < 3072) 835 powerbufFree = NULL; 836#endif 837 838 /* lay down tmp and am right after powers table */ 839 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); 840 am.d = tmp.d + top; 841 tmp.top = am.top = 0; 842 tmp.dmax = am.dmax = top; 843 tmp.neg = am.neg = 0; 844 tmp.flags = am.flags = BN_FLG_STATIC_DATA; 845 846 /* prepare a^0 in Montgomery domain */ 847#if 1 /* by Shay Gueron's suggestion */ 848 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 849 /* 2^(top*BN_BITS2) - m */ 850 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; 851 for (i = 1; i < top; i++) 852 tmp.d[i] = (~m->d[i]) & BN_MASK2; 853 tmp.top = top; 854 } else 855#endif 856 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx)) 857 goto err; 858 859 /* prepare a^1 in Montgomery domain */ 860 if (a->neg || BN_ucmp(a, m) >= 0) { 861 if (!BN_mod(&am, a, m, ctx)) 862 goto err; 863 if (!bn_to_mont_fixed_top(&am, &am, mont, ctx)) 864 goto err; 865 } else if (!bn_to_mont_fixed_top(&am, a, mont, ctx)) 866 goto err; 867 868#if defined(SPARC_T4_MONT) 869 if (t4) { 870 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, 871 const BN_ULONG *n0, const void *table, 872 int power, int bits); 873 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, 874 const BN_ULONG *n0, const void *table, 875 int power, int bits); 876 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, 877 const BN_ULONG *n0, const void *table, 878 int power, int bits); 879 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, 880 const BN_ULONG *n0, const void *table, 881 int power, int bits); 882 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, 883 const BN_ULONG *n0, const void *table, 884 int power, int bits); 885 static const bn_pwr5_mont_f pwr5_funcs[4] = { 886 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, 887 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 888 }; 889 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; 890 891 typedef int (*bn_mul_mont_f) (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_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, 895 const BN_ULONG *np, const BN_ULONG *n0); 896 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, 897 const void *bp, const BN_ULONG *np, 898 const BN_ULONG *n0); 899 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, 900 const void *bp, const BN_ULONG *np, 901 const BN_ULONG *n0); 902 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, 903 const void *bp, const BN_ULONG *np, 904 const BN_ULONG *n0); 905 static const bn_mul_mont_f mul_funcs[4] = { 906 bn_mul_mont_t4_8, bn_mul_mont_t4_16, 907 bn_mul_mont_t4_24, bn_mul_mont_t4_32 908 }; 909 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; 910 911 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, 912 const void *bp, const BN_ULONG *np, 913 const BN_ULONG *n0, int num); 914 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, 915 const void *bp, const BN_ULONG *np, 916 const BN_ULONG *n0, int num); 917 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, 918 const void *table, const BN_ULONG *np, 919 const BN_ULONG *n0, int num, int power); 920 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, 921 void *table, size_t power); 922 void bn_gather5_t4(BN_ULONG *out, size_t num, 923 void *table, size_t power); 924 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); 925 926 BN_ULONG *np = mont->N.d, *n0 = mont->n0; 927 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less 928 * than 32 */ 929 930 /* 931 * BN_to_montgomery can contaminate words above .top [in 932 * BN_DEBUG[_DEBUG] build]... 933 */ 934 for (i = am.top; i < top; i++) 935 am.d[i] = 0; 936 for (i = tmp.top; i < top; i++) 937 tmp.d[i] = 0; 938 939 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); 940 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); 941 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && 942 !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) 943 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); 944 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); 945 946 for (i = 3; i < 32; i++) { 947 /* Calculate a^i = a^(i-1) * a */ 948 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && 949 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) 950 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); 951 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); 952 } 953 954 /* switch to 64-bit domain */ 955 np = alloca(top * sizeof(BN_ULONG)); 956 top /= 2; 957 bn_flip_t4(np, mont->N.d, top); 958 959 bits--; 960 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) 961 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 962 bn_gather5_t4(tmp.d, top, powerbuf, wvalue); 963 964 /* 965 * Scan the exponent one window at a time starting from the most 966 * significant bits. 967 */ 968 while (bits >= 0) { 969 if (bits < stride) 970 stride = bits + 1; 971 bits -= stride; 972 wvalue = bn_get_bits(p, bits + 1); 973 974 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 975 continue; 976 /* retry once and fall back */ 977 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 978 continue; 979 980 bits += stride - 5; 981 wvalue >>= stride - 5; 982 wvalue &= 31; 983 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 984 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 985 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 986 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 987 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 988 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, 989 wvalue); 990 } 991 992 bn_flip_t4(tmp.d, tmp.d, top); 993 top *= 2; 994 /* back to 32-bit domain */ 995 tmp.top = top; 996 bn_correct_top(&tmp); 997 OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); 998 } else 999#endif 1000#if defined(OPENSSL_BN_ASM_MONT5) 1001 if (window == 5 && top > 1) { 1002 /* 1003 * This optimization uses ideas from http://eprint.iacr.org/2011/239, 1004 * specifically optimization of cache-timing attack countermeasures 1005 * and pre-computation optimization. 1006 */ 1007 1008 /* 1009 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as 1010 * 512-bit RSA is hardly relevant, we omit it to spare size... 1011 */ 1012 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, 1013 const void *table, const BN_ULONG *np, 1014 const BN_ULONG *n0, int num, int power); 1015 void bn_scatter5(const BN_ULONG *inp, size_t num, 1016 void *table, size_t power); 1017 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); 1018 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, 1019 const void *table, const BN_ULONG *np, 1020 const BN_ULONG *n0, int num, int power); 1021 int bn_get_bits5(const BN_ULONG *ap, int off); 1022 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, 1023 const BN_ULONG *not_used, const BN_ULONG *np, 1024 const BN_ULONG *n0, int num); 1025 1026 BN_ULONG *n0 = mont->n0, *np; 1027 1028 /* 1029 * BN_to_montgomery can contaminate words above .top [in 1030 * BN_DEBUG[_DEBUG] build]... 1031 */ 1032 for (i = am.top; i < top; i++) 1033 am.d[i] = 0; 1034 for (i = tmp.top; i < top; i++) 1035 tmp.d[i] = 0; 1036 1037 /* 1038 * copy mont->N.d[] to improve cache locality 1039 */ 1040 for (np = am.d + top, i = 0; i < top; i++) 1041 np[i] = mont->N.d[i]; 1042 1043 bn_scatter5(tmp.d, top, powerbuf, 0); 1044 bn_scatter5(am.d, am.top, powerbuf, 1); 1045 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); 1046 bn_scatter5(tmp.d, top, powerbuf, 2); 1047 1048# if 0 1049 for (i = 3; i < 32; i++) { 1050 /* Calculate a^i = a^(i-1) * a */ 1051 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1052 bn_scatter5(tmp.d, top, powerbuf, i); 1053 } 1054# else 1055 /* same as above, but uses squaring for 1/2 of operations */ 1056 for (i = 4; i < 32; i *= 2) { 1057 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1058 bn_scatter5(tmp.d, top, powerbuf, i); 1059 } 1060 for (i = 3; i < 8; i += 2) { 1061 int j; 1062 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1063 bn_scatter5(tmp.d, top, powerbuf, i); 1064 for (j = 2 * i; j < 32; j *= 2) { 1065 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1066 bn_scatter5(tmp.d, top, powerbuf, j); 1067 } 1068 } 1069 for (; i < 16; i += 2) { 1070 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1071 bn_scatter5(tmp.d, top, powerbuf, i); 1072 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1073 bn_scatter5(tmp.d, top, powerbuf, 2 * i); 1074 } 1075 for (; i < 32; i += 2) { 1076 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 1077 bn_scatter5(tmp.d, top, powerbuf, i); 1078 } 1079# endif 1080 bits--; 1081 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) 1082 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1083 bn_gather5(tmp.d, top, powerbuf, wvalue); 1084 1085 /* 1086 * Scan the exponent one window at a time starting from the most 1087 * significant bits. 1088 */ 1089 if (top & 7) 1090 while (bits >= 0) { 1091 for (wvalue = 0, i = 0; i < 5; i++, bits--) 1092 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1093 1094 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1095 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1096 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1097 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1098 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1099 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, 1100 wvalue); 1101 } else { 1102 while (bits >= 0) { 1103 wvalue = bn_get_bits5(p->d, bits - 4); 1104 bits -= 5; 1105 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue); 1106 } 1107 } 1108 1109 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top); 1110 tmp.top = top; 1111 bn_correct_top(&tmp); 1112 if (ret) { 1113 if (!BN_copy(rr, &tmp)) 1114 ret = 0; 1115 goto err; /* non-zero ret means it's not error */ 1116 } 1117 } else 1118#endif 1119 { 1120 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) 1121 goto err; 1122 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) 1123 goto err; 1124 1125 /* 1126 * If the window size is greater than 1, then calculate 1127 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even 1128 * powers could instead be computed as (a^(i/2))^2 to use the slight 1129 * performance advantage of sqr over mul). 1130 */ 1131 if (window > 1) { 1132 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx)) 1133 goto err; 1134 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, 1135 window)) 1136 goto err; 1137 for (i = 3; i < numPowers; i++) { 1138 /* Calculate a^i = a^(i-1) * a */ 1139 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx)) 1140 goto err; 1141 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, 1142 window)) 1143 goto err; 1144 } 1145 } 1146 1147 bits--; 1148 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) 1149 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1150 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, 1151 window)) 1152 goto err; 1153 1154 /* 1155 * Scan the exponent one window at a time starting from the most 1156 * significant bits. 1157 */ 1158 while (bits >= 0) { 1159 wvalue = 0; /* The 'value' of the window */ 1160 1161 /* Scan the window, squaring the result as we go */ 1162 for (i = 0; i < window; i++, bits--) { 1163 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx)) 1164 goto err; 1165 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); 1166 } 1167 1168 /* 1169 * Fetch the appropriate pre-computed value from the pre-buf 1170 */ 1171 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, 1172 window)) 1173 goto err; 1174 1175 /* Multiply the result into the intermediate result */ 1176 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx)) 1177 goto err; 1178 } 1179 } 1180 1181 /* 1182 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery 1183 * removes padding [if any] and makes return value suitable for public 1184 * API consumer. 1185 */ 1186#if defined(SPARC_T4_MONT) 1187 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 1188 am.d[0] = 1; /* borrow am */ 1189 for (i = 1; i < top; i++) 1190 am.d[i] = 0; 1191 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) 1192 goto err; 1193 } else 1194#endif 1195 if (!BN_from_montgomery(rr, &tmp, mont, ctx)) 1196 goto err; 1197 ret = 1; 1198 err: 1199 if ((in_mont == NULL) && (mont != NULL)) 1200 BN_MONT_CTX_free(mont); 1201 if (powerbuf != NULL) { 1202 OPENSSL_cleanse(powerbuf, powerbufLen); 1203 if (powerbufFree) 1204 OPENSSL_free(powerbufFree); 1205 } 1206 BN_CTX_end(ctx); 1207 return (ret); 1208} 1209 1210int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 1211 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 1212{ 1213 BN_MONT_CTX *mont = NULL; 1214 int b, bits, ret = 0; 1215 int r_is_one; 1216 BN_ULONG w, next_w; 1217 BIGNUM *d, *r, *t; 1218 BIGNUM *swap_tmp; 1219#define BN_MOD_MUL_WORD(r, w, m) \ 1220 (BN_mul_word(r, (w)) && \ 1221 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 1222 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 1223 /* 1224 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is 1225 * probably more overhead than always using BN_mod (which uses BN_copy if 1226 * a similar test returns true). 1227 */ 1228 /* 1229 * We can use BN_mod and do not need BN_nnmod because our accumulator is 1230 * never negative (the result of BN_mod does not depend on the sign of 1231 * the modulus). 1232 */ 1233#define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 1234 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 1235 1236 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1237 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1238 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1239 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1240 return 0; 1241 } 1242 1243 bn_check_top(p); 1244 bn_check_top(m); 1245 1246 if (!BN_is_odd(m)) { 1247 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); 1248 return (0); 1249 } 1250 if (m->top == 1) 1251 a %= m->d[0]; /* make sure that 'a' is reduced */ 1252 1253 bits = BN_num_bits(p); 1254 if (bits == 0) { 1255 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 1256 if (BN_abs_is_word(m, 1)) { 1257 ret = 1; 1258 BN_zero(rr); 1259 } else { 1260 ret = BN_one(rr); 1261 } 1262 return ret; 1263 } 1264 if (a == 0) { 1265 BN_zero(rr); 1266 ret = 1; 1267 return ret; 1268 } 1269 1270 BN_CTX_start(ctx); 1271 d = BN_CTX_get(ctx); 1272 r = BN_CTX_get(ctx); 1273 t = BN_CTX_get(ctx); 1274 if (d == NULL || r == NULL || t == NULL) 1275 goto err; 1276 1277 if (in_mont != NULL) 1278 mont = in_mont; 1279 else { 1280 if ((mont = BN_MONT_CTX_new()) == NULL) 1281 goto err; 1282 if (!BN_MONT_CTX_set(mont, m, ctx)) 1283 goto err; 1284 } 1285 1286 r_is_one = 1; /* except for Montgomery factor */ 1287 1288 /* bits-1 >= 0 */ 1289 1290 /* The result is accumulated in the product r*w. */ 1291 w = a; /* bit 'bits-1' of 'p' is always set */ 1292 for (b = bits - 2; b >= 0; b--) { 1293 /* First, square r*w. */ 1294 next_w = w * w; 1295 if ((next_w / w) != w) { /* overflow */ 1296 if (r_is_one) { 1297 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1298 goto err; 1299 r_is_one = 0; 1300 } else { 1301 if (!BN_MOD_MUL_WORD(r, w, m)) 1302 goto err; 1303 } 1304 next_w = 1; 1305 } 1306 w = next_w; 1307 if (!r_is_one) { 1308 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 1309 goto err; 1310 } 1311 1312 /* Second, multiply r*w by 'a' if exponent bit is set. */ 1313 if (BN_is_bit_set(p, b)) { 1314 next_w = w * a; 1315 if ((next_w / a) != w) { /* overflow */ 1316 if (r_is_one) { 1317 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1318 goto err; 1319 r_is_one = 0; 1320 } else { 1321 if (!BN_MOD_MUL_WORD(r, w, m)) 1322 goto err; 1323 } 1324 next_w = a; 1325 } 1326 w = next_w; 1327 } 1328 } 1329 1330 /* Finally, set r:=r*w. */ 1331 if (w != 1) { 1332 if (r_is_one) { 1333 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1334 goto err; 1335 r_is_one = 0; 1336 } else { 1337 if (!BN_MOD_MUL_WORD(r, w, m)) 1338 goto err; 1339 } 1340 } 1341 1342 if (r_is_one) { /* can happen only if a == 1 */ 1343 if (!BN_one(rr)) 1344 goto err; 1345 } else { 1346 if (!BN_from_montgomery(rr, r, mont, ctx)) 1347 goto err; 1348 } 1349 ret = 1; 1350 err: 1351 if ((in_mont == NULL) && (mont != NULL)) 1352 BN_MONT_CTX_free(mont); 1353 BN_CTX_end(ctx); 1354 bn_check_top(rr); 1355 return (ret); 1356} 1357 1358/* The old fallback, simple version :-) */ 1359int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 1360 const BIGNUM *m, BN_CTX *ctx) 1361{ 1362 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 1363 int start = 1; 1364 BIGNUM *d; 1365 /* Table of variables obtained from 'ctx' */ 1366 BIGNUM *val[TABLE_SIZE]; 1367 1368 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1369 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 1370 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1371 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1372 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1373 return 0; 1374 } 1375 1376 bits = BN_num_bits(p); 1377 if (bits == 0) { 1378 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 1379 if (BN_abs_is_word(m, 1)) { 1380 ret = 1; 1381 BN_zero(r); 1382 } else { 1383 ret = BN_one(r); 1384 } 1385 return ret; 1386 } 1387 1388 BN_CTX_start(ctx); 1389 d = BN_CTX_get(ctx); 1390 val[0] = BN_CTX_get(ctx); 1391 if (!d || !val[0]) 1392 goto err; 1393 1394 if (!BN_nnmod(val[0], a, m, ctx)) 1395 goto err; /* 1 */ 1396 if (BN_is_zero(val[0])) { 1397 BN_zero(r); 1398 ret = 1; 1399 goto err; 1400 } 1401 1402 window = BN_window_bits_for_exponent_size(bits); 1403 if (window > 1) { 1404 if (!BN_mod_mul(d, val[0], val[0], m, ctx)) 1405 goto err; /* 2 */ 1406 j = 1 << (window - 1); 1407 for (i = 1; i < j; i++) { 1408 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 1409 !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) 1410 goto err; 1411 } 1412 } 1413 1414 start = 1; /* This is used to avoid multiplication etc 1415 * when there is only the value '1' in the 1416 * buffer. */ 1417 wvalue = 0; /* The 'value' of the window */ 1418 wstart = bits - 1; /* The top bit of the window */ 1419 wend = 0; /* The bottom bit of the window */ 1420 1421 if (!BN_one(r)) 1422 goto err; 1423 1424 for (;;) { 1425 if (BN_is_bit_set(p, wstart) == 0) { 1426 if (!start) 1427 if (!BN_mod_mul(r, r, r, m, ctx)) 1428 goto err; 1429 if (wstart == 0) 1430 break; 1431 wstart--; 1432 continue; 1433 } 1434 /* 1435 * We now have wstart on a 'set' bit, we now need to work out how bit 1436 * a window to do. To do this we need to scan forward until the last 1437 * set bit before the end of the window 1438 */ 1439 j = wstart; 1440 wvalue = 1; 1441 wend = 0; 1442 for (i = 1; i < window; i++) { 1443 if (wstart - i < 0) 1444 break; 1445 if (BN_is_bit_set(p, wstart - i)) { 1446 wvalue <<= (i - wend); 1447 wvalue |= 1; 1448 wend = i; 1449 } 1450 } 1451 1452 /* wend is the size of the current window */ 1453 j = wend + 1; 1454 /* add the 'bytes above' */ 1455 if (!start) 1456 for (i = 0; i < j; i++) { 1457 if (!BN_mod_mul(r, r, r, m, ctx)) 1458 goto err; 1459 } 1460 1461 /* wvalue will be an odd number < 2^window */ 1462 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) 1463 goto err; 1464 1465 /* move the 'window' down further */ 1466 wstart -= wend + 1; 1467 wvalue = 0; 1468 start = 0; 1469 if (wstart < 0) 1470 break; 1471 } 1472 ret = 1; 1473 err: 1474 BN_CTX_end(ctx); 1475 bn_check_top(r); 1476 return (ret); 1477} 1478