1 /* 2 * Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved. 3 * 4 * Licensed under the OpenSSL license (the "License"). You may not use 5 * this file except in compliance with the License. You can obtain a copy 6 * in the file LICENSE in the source distribution or at 7 * https://www.openssl.org/source/license.html 8 */ 9 10 #include "internal/cryptlib.h" 11 #include "internal/constant_time_locl.h" 12 #include "bn_lcl.h" 13 14 #include <stdlib.h> 15 #ifdef _WIN32 16 # include <malloc.h> 17 # ifndef alloca 18 # define alloca _alloca 19 # endif 20 #elif defined(__GNUC__) 21 # ifndef alloca 22 # define alloca(s) __builtin_alloca((s)) 23 # endif 24 #elif defined(__sun) 25 # include <alloca.h> 26 #endif 27 28 #include "rsaz_exp.h" 29 30 #undef SPARC_T4_MONT 31 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc)) 32 # include "sparc_arch.h" 33 extern unsigned int OPENSSL_sparcv9cap_P[]; 34 # define SPARC_T4_MONT 35 #endif 36 37 /* maximum precomputation table size for *variable* sliding windows */ 38 #define TABLE_SIZE 32 39 40 /* this one works - simple but works */ 41 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) 42 { 43 int i, bits, ret = 0; 44 BIGNUM *v, *rr; 45 46 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 47 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) { 48 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 49 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 50 return 0; 51 } 52 53 BN_CTX_start(ctx); 54 rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r; 55 v = BN_CTX_get(ctx); 56 if (rr == NULL || v == NULL) 57 goto err; 58 59 if (BN_copy(v, a) == NULL) 60 goto err; 61 bits = BN_num_bits(p); 62 63 if (BN_is_odd(p)) { 64 if (BN_copy(rr, a) == NULL) 65 goto err; 66 } else { 67 if (!BN_one(rr)) 68 goto err; 69 } 70 71 for (i = 1; i < bits; i++) { 72 if (!BN_sqr(v, v, ctx)) 73 goto err; 74 if (BN_is_bit_set(p, i)) { 75 if (!BN_mul(rr, rr, v, ctx)) 76 goto err; 77 } 78 } 79 if (r != rr && BN_copy(r, rr) == NULL) 80 goto err; 81 82 ret = 1; 83 err: 84 BN_CTX_end(ctx); 85 bn_check_top(r); 86 return ret; 87 } 88 89 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 90 BN_CTX *ctx) 91 { 92 int ret; 93 94 bn_check_top(a); 95 bn_check_top(p); 96 bn_check_top(m); 97 98 /*- 99 * For even modulus m = 2^k*m_odd, it might make sense to compute 100 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 101 * exponentiation for the odd part), using appropriate exponent 102 * reductions, and combine the results using the CRT. 103 * 104 * For now, we use Montgomery only if the modulus is odd; otherwise, 105 * exponentiation using the reciprocal-based quick remaindering 106 * algorithm is used. 107 * 108 * (Timing obtained with expspeed.c [computations a^p mod m 109 * where a, p, m are of the same length: 256, 512, 1024, 2048, 110 * 4096, 8192 bits], compared to the running time of the 111 * standard algorithm: 112 * 113 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 114 * 55 .. 77 % [UltraSparc processor, but 115 * debug-solaris-sparcv8-gcc conf.] 116 * 117 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 118 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 119 * 120 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 121 * at 2048 and more bits, but at 512 and 1024 bits, it was 122 * slower even than the standard algorithm! 123 * 124 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 125 * should be obtained when the new Montgomery reduction code 126 * has been integrated into OpenSSL.) 127 */ 128 129 #define MONT_MUL_MOD 130 #define MONT_EXP_WORD 131 #define RECP_MUL_MOD 132 133 #ifdef MONT_MUL_MOD 134 if (BN_is_odd(m)) { 135 # ifdef MONT_EXP_WORD 136 if (a->top == 1 && !a->neg 137 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0) 138 && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0) 139 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) { 140 BN_ULONG A = a->d[0]; 141 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); 142 } else 143 # endif 144 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); 145 } else 146 #endif 147 #ifdef RECP_MUL_MOD 148 { 149 ret = BN_mod_exp_recp(r, a, p, m, ctx); 150 } 151 #else 152 { 153 ret = BN_mod_exp_simple(r, a, p, m, ctx); 154 } 155 #endif 156 157 bn_check_top(r); 158 return ret; 159 } 160 161 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 162 const BIGNUM *m, BN_CTX *ctx) 163 { 164 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 165 int start = 1; 166 BIGNUM *aa; 167 /* Table of variables obtained from 'ctx' */ 168 BIGNUM *val[TABLE_SIZE]; 169 BN_RECP_CTX recp; 170 171 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 172 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 173 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 174 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 175 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 176 return 0; 177 } 178 179 bits = BN_num_bits(p); 180 if (bits == 0) { 181 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 182 if (BN_abs_is_word(m, 1)) { 183 ret = 1; 184 BN_zero(r); 185 } else { 186 ret = BN_one(r); 187 } 188 return ret; 189 } 190 191 BN_CTX_start(ctx); 192 aa = BN_CTX_get(ctx); 193 val[0] = BN_CTX_get(ctx); 194 if (val[0] == NULL) 195 goto err; 196 197 BN_RECP_CTX_init(&recp); 198 if (m->neg) { 199 /* ignore sign of 'm' */ 200 if (!BN_copy(aa, m)) 201 goto err; 202 aa->neg = 0; 203 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) 204 goto err; 205 } else { 206 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) 207 goto err; 208 } 209 210 if (!BN_nnmod(val[0], a, m, ctx)) 211 goto err; /* 1 */ 212 if (BN_is_zero(val[0])) { 213 BN_zero(r); 214 ret = 1; 215 goto err; 216 } 217 218 window = BN_window_bits_for_exponent_size(bits); 219 if (window > 1) { 220 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) 221 goto err; /* 2 */ 222 j = 1 << (window - 1); 223 for (i = 1; i < j; i++) { 224 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 225 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) 226 goto err; 227 } 228 } 229 230 start = 1; /* This is used to avoid multiplication etc 231 * when there is only the value '1' in the 232 * buffer. */ 233 wvalue = 0; /* The 'value' of the window */ 234 wstart = bits - 1; /* The top bit of the window */ 235 wend = 0; /* The bottom bit of the window */ 236 237 if (!BN_one(r)) 238 goto err; 239 240 for (;;) { 241 if (BN_is_bit_set(p, wstart) == 0) { 242 if (!start) 243 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 244 goto err; 245 if (wstart == 0) 246 break; 247 wstart--; 248 continue; 249 } 250 /* 251 * We now have wstart on a 'set' bit, we now need to work out how bit 252 * a window to do. To do this we need to scan forward until the last 253 * set bit before the end of the window 254 */ 255 j = wstart; 256 wvalue = 1; 257 wend = 0; 258 for (i = 1; i < window; i++) { 259 if (wstart - i < 0) 260 break; 261 if (BN_is_bit_set(p, wstart - i)) { 262 wvalue <<= (i - wend); 263 wvalue |= 1; 264 wend = i; 265 } 266 } 267 268 /* wend is the size of the current window */ 269 j = wend + 1; 270 /* add the 'bytes above' */ 271 if (!start) 272 for (i = 0; i < j; i++) { 273 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 274 goto err; 275 } 276 277 /* wvalue will be an odd number < 2^window */ 278 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) 279 goto err; 280 281 /* move the 'window' down further */ 282 wstart -= wend + 1; 283 wvalue = 0; 284 start = 0; 285 if (wstart < 0) 286 break; 287 } 288 ret = 1; 289 err: 290 BN_CTX_end(ctx); 291 BN_RECP_CTX_free(&recp); 292 bn_check_top(r); 293 return ret; 294 } 295 296 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 297 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 298 { 299 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 300 int start = 1; 301 BIGNUM *d, *r; 302 const BIGNUM *aa; 303 /* Table of variables obtained from 'ctx' */ 304 BIGNUM *val[TABLE_SIZE]; 305 BN_MONT_CTX *mont = NULL; 306 307 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 308 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 309 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 310 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 311 } 312 313 bn_check_top(a); 314 bn_check_top(p); 315 bn_check_top(m); 316 317 if (!BN_is_odd(m)) { 318 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); 319 return 0; 320 } 321 bits = BN_num_bits(p); 322 if (bits == 0) { 323 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 324 if (BN_abs_is_word(m, 1)) { 325 ret = 1; 326 BN_zero(rr); 327 } else { 328 ret = BN_one(rr); 329 } 330 return ret; 331 } 332 333 BN_CTX_start(ctx); 334 d = BN_CTX_get(ctx); 335 r = BN_CTX_get(ctx); 336 val[0] = BN_CTX_get(ctx); 337 if (val[0] == NULL) 338 goto err; 339 340 /* 341 * If this is not done, things will break in the montgomery part 342 */ 343 344 if (in_mont != NULL) 345 mont = in_mont; 346 else { 347 if ((mont = BN_MONT_CTX_new()) == NULL) 348 goto err; 349 if (!BN_MONT_CTX_set(mont, m, ctx)) 350 goto err; 351 } 352 353 if (a->neg || BN_ucmp(a, m) >= 0) { 354 if (!BN_nnmod(val[0], a, m, ctx)) 355 goto err; 356 aa = val[0]; 357 } else 358 aa = a; 359 if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx)) 360 goto err; /* 1 */ 361 362 window = BN_window_bits_for_exponent_size(bits); 363 if (window > 1) { 364 if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx)) 365 goto err; /* 2 */ 366 j = 1 << (window - 1); 367 for (i = 1; i < j; i++) { 368 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 369 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx)) 370 goto err; 371 } 372 } 373 374 start = 1; /* This is used to avoid multiplication etc 375 * when there is only the value '1' in the 376 * buffer. */ 377 wvalue = 0; /* The 'value' of the window */ 378 wstart = bits - 1; /* The top bit of the window */ 379 wend = 0; /* The bottom bit of the window */ 380 381 #if 1 /* by Shay Gueron's suggestion */ 382 j = m->top; /* borrow j */ 383 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 384 if (bn_wexpand(r, j) == NULL) 385 goto err; 386 /* 2^(top*BN_BITS2) - m */ 387 r->d[0] = (0 - m->d[0]) & BN_MASK2; 388 for (i = 1; i < j; i++) 389 r->d[i] = (~m->d[i]) & BN_MASK2; 390 r->top = j; 391 r->flags |= BN_FLG_FIXED_TOP; 392 } else 393 #endif 394 if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx)) 395 goto err; 396 for (;;) { 397 if (BN_is_bit_set(p, wstart) == 0) { 398 if (!start) { 399 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) 400 goto err; 401 } 402 if (wstart == 0) 403 break; 404 wstart--; 405 continue; 406 } 407 /* 408 * We now have wstart on a 'set' bit, we now need to work out how bit 409 * a window to do. To do this we need to scan forward until the last 410 * set bit before the end of the window 411 */ 412 j = wstart; 413 wvalue = 1; 414 wend = 0; 415 for (i = 1; i < window; i++) { 416 if (wstart - i < 0) 417 break; 418 if (BN_is_bit_set(p, wstart - i)) { 419 wvalue <<= (i - wend); 420 wvalue |= 1; 421 wend = i; 422 } 423 } 424 425 /* wend is the size of the current window */ 426 j = wend + 1; 427 /* add the 'bytes above' */ 428 if (!start) 429 for (i = 0; i < j; i++) { 430 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) 431 goto err; 432 } 433 434 /* wvalue will be an odd number < 2^window */ 435 if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx)) 436 goto err; 437 438 /* move the 'window' down further */ 439 wstart -= wend + 1; 440 wvalue = 0; 441 start = 0; 442 if (wstart < 0) 443 break; 444 } 445 /* 446 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery 447 * removes padding [if any] and makes return value suitable for public 448 * API consumer. 449 */ 450 #if defined(SPARC_T4_MONT) 451 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 452 j = mont->N.top; /* borrow j */ 453 val[0]->d[0] = 1; /* borrow val[0] */ 454 for (i = 1; i < j; i++) 455 val[0]->d[i] = 0; 456 val[0]->top = j; 457 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) 458 goto err; 459 } else 460 #endif 461 if (!BN_from_montgomery(rr, r, mont, ctx)) 462 goto err; 463 ret = 1; 464 err: 465 if (in_mont == NULL) 466 BN_MONT_CTX_free(mont); 467 BN_CTX_end(ctx); 468 bn_check_top(rr); 469 return ret; 470 } 471 472 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) 473 { 474 BN_ULONG ret = 0; 475 int wordpos; 476 477 wordpos = bitpos / BN_BITS2; 478 bitpos %= BN_BITS2; 479 if (wordpos >= 0 && wordpos < a->top) { 480 ret = a->d[wordpos] & BN_MASK2; 481 if (bitpos) { 482 ret >>= bitpos; 483 if (++wordpos < a->top) 484 ret |= a->d[wordpos] << (BN_BITS2 - bitpos); 485 } 486 } 487 488 return ret & BN_MASK2; 489 } 490 491 /* 492 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific 493 * layout so that accessing any of these table values shows the same access 494 * pattern as far as cache lines are concerned. The following functions are 495 * used to transfer a BIGNUM from/to that table. 496 */ 497 498 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, 499 unsigned char *buf, int idx, 500 int window) 501 { 502 int i, j; 503 int width = 1 << window; 504 BN_ULONG *table = (BN_ULONG *)buf; 505 506 if (top > b->top) 507 top = b->top; /* this works because 'buf' is explicitly 508 * zeroed */ 509 for (i = 0, j = idx; i < top; i++, j += width) { 510 table[j] = b->d[i]; 511 } 512 513 return 1; 514 } 515 516 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, 517 unsigned char *buf, int idx, 518 int window) 519 { 520 int i, j; 521 int width = 1 << window; 522 /* 523 * We declare table 'volatile' in order to discourage compiler 524 * from reordering loads from the table. Concern is that if 525 * reordered in specific manner loads might give away the 526 * information we are trying to conceal. Some would argue that 527 * compiler can reorder them anyway, but it can as well be 528 * argued that doing so would be violation of standard... 529 */ 530 volatile BN_ULONG *table = (volatile BN_ULONG *)buf; 531 532 if (bn_wexpand(b, top) == NULL) 533 return 0; 534 535 if (window <= 3) { 536 for (i = 0; i < top; i++, table += width) { 537 BN_ULONG acc = 0; 538 539 for (j = 0; j < width; j++) { 540 acc |= table[j] & 541 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 542 } 543 544 b->d[i] = acc; 545 } 546 } else { 547 int xstride = 1 << (window - 2); 548 BN_ULONG y0, y1, y2, y3; 549 550 i = idx >> (window - 2); /* equivalent of idx / xstride */ 551 idx &= xstride - 1; /* equivalent of idx % xstride */ 552 553 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); 554 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); 555 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); 556 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); 557 558 for (i = 0; i < top; i++, table += width) { 559 BN_ULONG acc = 0; 560 561 for (j = 0; j < xstride; j++) { 562 acc |= ( (table[j + 0 * xstride] & y0) | 563 (table[j + 1 * xstride] & y1) | 564 (table[j + 2 * xstride] & y2) | 565 (table[j + 3 * xstride] & y3) ) 566 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 567 } 568 569 b->d[i] = acc; 570 } 571 } 572 573 b->top = top; 574 b->flags |= BN_FLG_FIXED_TOP; 575 return 1; 576 } 577 578 /* 579 * Given a pointer value, compute the next address that is a cache line 580 * multiple. 581 */ 582 #define MOD_EXP_CTIME_ALIGN(x_) \ 583 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 584 585 /* 586 * This variant of BN_mod_exp_mont() uses fixed windows and the special 587 * precomputation memory layout to limit data-dependency to a minimum to 588 * protect secret exponents (cf. the hyper-threading timing attacks pointed 589 * out by Colin Percival, 590 * http://www.daemonology.net/hyperthreading-considered-harmful/) 591 */ 592 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 593 const BIGNUM *m, BN_CTX *ctx, 594 BN_MONT_CTX *in_mont) 595 { 596 int i, bits, ret = 0, window, wvalue, wmask, window0; 597 int top; 598 BN_MONT_CTX *mont = NULL; 599 600 int numPowers; 601 unsigned char *powerbufFree = NULL; 602 int powerbufLen = 0; 603 unsigned char *powerbuf = NULL; 604 BIGNUM tmp, am; 605 #if defined(SPARC_T4_MONT) 606 unsigned int t4 = 0; 607 #endif 608 609 bn_check_top(a); 610 bn_check_top(p); 611 bn_check_top(m); 612 613 if (!BN_is_odd(m)) { 614 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); 615 return 0; 616 } 617 618 top = m->top; 619 620 /* 621 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak 622 * whether the top bits are zero. 623 */ 624 bits = p->top * BN_BITS2; 625 if (bits == 0) { 626 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 627 if (BN_abs_is_word(m, 1)) { 628 ret = 1; 629 BN_zero(rr); 630 } else { 631 ret = BN_one(rr); 632 } 633 return ret; 634 } 635 636 BN_CTX_start(ctx); 637 638 /* 639 * Allocate a montgomery context if it was not supplied by the caller. If 640 * this is not done, things will break in the montgomery part. 641 */ 642 if (in_mont != NULL) 643 mont = in_mont; 644 else { 645 if ((mont = BN_MONT_CTX_new()) == NULL) 646 goto err; 647 if (!BN_MONT_CTX_set(mont, m, ctx)) 648 goto err; 649 } 650 651 if (a->neg || BN_ucmp(a, m) >= 0) { 652 BIGNUM *reduced = BN_CTX_get(ctx); 653 if (reduced == NULL 654 || !BN_nnmod(reduced, a, m, ctx)) { 655 goto err; 656 } 657 a = reduced; 658 } 659 660 #ifdef RSAZ_ENABLED 661 /* 662 * If the size of the operands allow it, perform the optimized 663 * RSAZ exponentiation. For further information see 664 * crypto/bn/rsaz_exp.c and accompanying assembly modules. 665 */ 666 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) 667 && rsaz_avx2_eligible()) { 668 if (NULL == bn_wexpand(rr, 16)) 669 goto err; 670 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, 671 mont->n0[0]); 672 rr->top = 16; 673 rr->neg = 0; 674 bn_correct_top(rr); 675 ret = 1; 676 goto err; 677 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { 678 if (NULL == bn_wexpand(rr, 8)) 679 goto err; 680 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); 681 rr->top = 8; 682 rr->neg = 0; 683 bn_correct_top(rr); 684 ret = 1; 685 goto err; 686 } 687 #endif 688 689 /* Get the window size to use with size of p. */ 690 window = BN_window_bits_for_ctime_exponent_size(bits); 691 #if defined(SPARC_T4_MONT) 692 if (window >= 5 && (top & 15) == 0 && top <= 64 && 693 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == 694 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) 695 window = 5; 696 else 697 #endif 698 #if defined(OPENSSL_BN_ASM_MONT5) 699 if (window >= 5) { 700 window = 5; /* ~5% improvement for RSA2048 sign, and even 701 * for RSA4096 */ 702 /* reserve space for mont->N.d[] copy */ 703 powerbufLen += top * sizeof(mont->N.d[0]); 704 } 705 #endif 706 (void)0; 707 708 /* 709 * Allocate a buffer large enough to hold all of the pre-computed powers 710 * of am, am itself and tmp. 711 */ 712 numPowers = 1 << window; 713 powerbufLen += sizeof(m->d[0]) * (top * numPowers + 714 ((2 * top) > 715 numPowers ? (2 * top) : numPowers)); 716 #ifdef alloca 717 if (powerbufLen < 3072) 718 powerbufFree = 719 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); 720 else 721 #endif 722 if ((powerbufFree = 723 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) 724 == NULL) 725 goto err; 726 727 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 728 memset(powerbuf, 0, powerbufLen); 729 730 #ifdef alloca 731 if (powerbufLen < 3072) 732 powerbufFree = NULL; 733 #endif 734 735 /* lay down tmp and am right after powers table */ 736 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); 737 am.d = tmp.d + top; 738 tmp.top = am.top = 0; 739 tmp.dmax = am.dmax = top; 740 tmp.neg = am.neg = 0; 741 tmp.flags = am.flags = BN_FLG_STATIC_DATA; 742 743 /* prepare a^0 in Montgomery domain */ 744 #if 1 /* by Shay Gueron's suggestion */ 745 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 746 /* 2^(top*BN_BITS2) - m */ 747 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; 748 for (i = 1; i < top; i++) 749 tmp.d[i] = (~m->d[i]) & BN_MASK2; 750 tmp.top = top; 751 } else 752 #endif 753 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx)) 754 goto err; 755 756 /* prepare a^1 in Montgomery domain */ 757 if (!bn_to_mont_fixed_top(&am, a, mont, ctx)) 758 goto err; 759 760 #if defined(SPARC_T4_MONT) 761 if (t4) { 762 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, 763 const BN_ULONG *n0, const void *table, 764 int power, int bits); 765 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, 766 const BN_ULONG *n0, const void *table, 767 int power, int bits); 768 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, 769 const BN_ULONG *n0, const void *table, 770 int power, int bits); 771 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, 772 const BN_ULONG *n0, const void *table, 773 int power, int bits); 774 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, 775 const BN_ULONG *n0, const void *table, 776 int power, int bits); 777 static const bn_pwr5_mont_f pwr5_funcs[4] = { 778 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, 779 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 780 }; 781 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; 782 783 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, 784 const void *bp, const BN_ULONG *np, 785 const BN_ULONG *n0); 786 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, 787 const BN_ULONG *np, const BN_ULONG *n0); 788 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, 789 const void *bp, const BN_ULONG *np, 790 const BN_ULONG *n0); 791 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, 792 const void *bp, const BN_ULONG *np, 793 const BN_ULONG *n0); 794 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, 795 const void *bp, const BN_ULONG *np, 796 const BN_ULONG *n0); 797 static const bn_mul_mont_f mul_funcs[4] = { 798 bn_mul_mont_t4_8, bn_mul_mont_t4_16, 799 bn_mul_mont_t4_24, bn_mul_mont_t4_32 800 }; 801 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; 802 803 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, 804 const void *bp, const BN_ULONG *np, 805 const BN_ULONG *n0, int num); 806 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, 807 const void *bp, const BN_ULONG *np, 808 const BN_ULONG *n0, int num); 809 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, 810 const void *table, const BN_ULONG *np, 811 const BN_ULONG *n0, int num, int power); 812 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, 813 void *table, size_t power); 814 void bn_gather5_t4(BN_ULONG *out, size_t num, 815 void *table, size_t power); 816 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); 817 818 BN_ULONG *np = mont->N.d, *n0 = mont->n0; 819 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less 820 * than 32 */ 821 822 /* 823 * BN_to_montgomery can contaminate words above .top [in 824 * BN_DEBUG[_DEBUG] build]... 825 */ 826 for (i = am.top; i < top; i++) 827 am.d[i] = 0; 828 for (i = tmp.top; i < top; i++) 829 tmp.d[i] = 0; 830 831 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); 832 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); 833 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && 834 !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) 835 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); 836 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); 837 838 for (i = 3; i < 32; i++) { 839 /* Calculate a^i = a^(i-1) * a */ 840 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && 841 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) 842 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); 843 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); 844 } 845 846 /* switch to 64-bit domain */ 847 np = alloca(top * sizeof(BN_ULONG)); 848 top /= 2; 849 bn_flip_t4(np, mont->N.d, top); 850 851 /* 852 * The exponent may not have a whole number of fixed-size windows. 853 * To simplify the main loop, the initial window has between 1 and 854 * full-window-size bits such that what remains is always a whole 855 * number of windows 856 */ 857 window0 = (bits - 1) % 5 + 1; 858 wmask = (1 << window0) - 1; 859 bits -= window0; 860 wvalue = bn_get_bits(p, bits) & wmask; 861 bn_gather5_t4(tmp.d, top, powerbuf, wvalue); 862 863 /* 864 * Scan the exponent one window at a time starting from the most 865 * significant bits. 866 */ 867 while (bits > 0) { 868 if (bits < stride) 869 stride = bits; 870 bits -= stride; 871 wvalue = bn_get_bits(p, bits); 872 873 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 874 continue; 875 /* retry once and fall back */ 876 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 877 continue; 878 879 bits += stride - 5; 880 wvalue >>= stride - 5; 881 wvalue &= 31; 882 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 883 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 884 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 885 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 886 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 887 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, 888 wvalue); 889 } 890 891 bn_flip_t4(tmp.d, tmp.d, top); 892 top *= 2; 893 /* back to 32-bit domain */ 894 tmp.top = top; 895 bn_correct_top(&tmp); 896 OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); 897 } else 898 #endif 899 #if defined(OPENSSL_BN_ASM_MONT5) 900 if (window == 5 && top > 1) { 901 /* 902 * This optimization uses ideas from http://eprint.iacr.org/2011/239, 903 * specifically optimization of cache-timing attack countermeasures 904 * and pre-computation optimization. 905 */ 906 907 /* 908 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as 909 * 512-bit RSA is hardly relevant, we omit it to spare size... 910 */ 911 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, 912 const void *table, const BN_ULONG *np, 913 const BN_ULONG *n0, int num, int power); 914 void bn_scatter5(const BN_ULONG *inp, size_t num, 915 void *table, size_t power); 916 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); 917 void bn_power5(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 int bn_get_bits5(const BN_ULONG *ap, int off); 921 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, 922 const BN_ULONG *not_used, const BN_ULONG *np, 923 const BN_ULONG *n0, int num); 924 925 BN_ULONG *n0 = mont->n0, *np; 926 927 /* 928 * BN_to_montgomery can contaminate words above .top [in 929 * BN_DEBUG[_DEBUG] build]... 930 */ 931 for (i = am.top; i < top; i++) 932 am.d[i] = 0; 933 for (i = tmp.top; i < top; i++) 934 tmp.d[i] = 0; 935 936 /* 937 * copy mont->N.d[] to improve cache locality 938 */ 939 for (np = am.d + top, i = 0; i < top; i++) 940 np[i] = mont->N.d[i]; 941 942 bn_scatter5(tmp.d, top, powerbuf, 0); 943 bn_scatter5(am.d, am.top, powerbuf, 1); 944 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); 945 bn_scatter5(tmp.d, top, powerbuf, 2); 946 947 # if 0 948 for (i = 3; i < 32; i++) { 949 /* Calculate a^i = a^(i-1) * a */ 950 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 951 bn_scatter5(tmp.d, top, powerbuf, i); 952 } 953 # else 954 /* same as above, but uses squaring for 1/2 of operations */ 955 for (i = 4; i < 32; i *= 2) { 956 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 957 bn_scatter5(tmp.d, top, powerbuf, i); 958 } 959 for (i = 3; i < 8; i += 2) { 960 int j; 961 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 962 bn_scatter5(tmp.d, top, powerbuf, i); 963 for (j = 2 * i; j < 32; j *= 2) { 964 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 965 bn_scatter5(tmp.d, top, powerbuf, j); 966 } 967 } 968 for (; i < 16; i += 2) { 969 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 970 bn_scatter5(tmp.d, top, powerbuf, i); 971 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 972 bn_scatter5(tmp.d, top, powerbuf, 2 * i); 973 } 974 for (; i < 32; i += 2) { 975 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 976 bn_scatter5(tmp.d, top, powerbuf, i); 977 } 978 # endif 979 /* 980 * The exponent may not have a whole number of fixed-size windows. 981 * To simplify the main loop, the initial window has between 1 and 982 * full-window-size bits such that what remains is always a whole 983 * number of windows 984 */ 985 window0 = (bits - 1) % 5 + 1; 986 wmask = (1 << window0) - 1; 987 bits -= window0; 988 wvalue = bn_get_bits(p, bits) & wmask; 989 bn_gather5(tmp.d, top, powerbuf, wvalue); 990 991 /* 992 * Scan the exponent one window at a time starting from the most 993 * significant bits. 994 */ 995 if (top & 7) { 996 while (bits > 0) { 997 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 998 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 999 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1000 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1001 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1002 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, 1003 bn_get_bits5(p->d, bits -= 5)); 1004 } 1005 } else { 1006 while (bits > 0) { 1007 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, 1008 bn_get_bits5(p->d, bits -= 5)); 1009 } 1010 } 1011 1012 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top); 1013 tmp.top = top; 1014 bn_correct_top(&tmp); 1015 if (ret) { 1016 if (!BN_copy(rr, &tmp)) 1017 ret = 0; 1018 goto err; /* non-zero ret means it's not error */ 1019 } 1020 } else 1021 #endif 1022 { 1023 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) 1024 goto err; 1025 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) 1026 goto err; 1027 1028 /* 1029 * If the window size is greater than 1, then calculate 1030 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even 1031 * powers could instead be computed as (a^(i/2))^2 to use the slight 1032 * performance advantage of sqr over mul). 1033 */ 1034 if (window > 1) { 1035 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx)) 1036 goto err; 1037 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, 1038 window)) 1039 goto err; 1040 for (i = 3; i < numPowers; i++) { 1041 /* Calculate a^i = a^(i-1) * a */ 1042 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx)) 1043 goto err; 1044 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, 1045 window)) 1046 goto err; 1047 } 1048 } 1049 1050 /* 1051 * The exponent may not have a whole number of fixed-size windows. 1052 * To simplify the main loop, the initial window has between 1 and 1053 * full-window-size bits such that what remains is always a whole 1054 * number of windows 1055 */ 1056 window0 = (bits - 1) % window + 1; 1057 wmask = (1 << window0) - 1; 1058 bits -= window0; 1059 wvalue = bn_get_bits(p, bits) & wmask; 1060 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, 1061 window)) 1062 goto err; 1063 1064 wmask = (1 << window) - 1; 1065 /* 1066 * Scan the exponent one window at a time starting from the most 1067 * significant bits. 1068 */ 1069 while (bits > 0) { 1070 1071 /* Square the result window-size times */ 1072 for (i = 0; i < window; i++) 1073 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx)) 1074 goto err; 1075 1076 /* 1077 * Get a window's worth of bits from the exponent 1078 * This avoids calling BN_is_bit_set for each bit, which 1079 * is not only slower but also makes each bit vulnerable to 1080 * EM (and likely other) side-channel attacks like One&Done 1081 * (for details see "One&Done: A Single-Decryption EM-Based 1082 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam, 1083 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and 1084 * M. Prvulovic, in USENIX Security'18) 1085 */ 1086 bits -= window; 1087 wvalue = bn_get_bits(p, bits) & wmask; 1088 /* 1089 * Fetch the appropriate pre-computed value from the pre-buf 1090 */ 1091 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, 1092 window)) 1093 goto err; 1094 1095 /* Multiply the result into the intermediate result */ 1096 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx)) 1097 goto err; 1098 } 1099 } 1100 1101 /* 1102 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery 1103 * removes padding [if any] and makes return value suitable for public 1104 * API consumer. 1105 */ 1106 #if defined(SPARC_T4_MONT) 1107 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 1108 am.d[0] = 1; /* borrow am */ 1109 for (i = 1; i < top; i++) 1110 am.d[i] = 0; 1111 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) 1112 goto err; 1113 } else 1114 #endif 1115 if (!BN_from_montgomery(rr, &tmp, mont, ctx)) 1116 goto err; 1117 ret = 1; 1118 err: 1119 if (in_mont == NULL) 1120 BN_MONT_CTX_free(mont); 1121 if (powerbuf != NULL) { 1122 OPENSSL_cleanse(powerbuf, powerbufLen); 1123 OPENSSL_free(powerbufFree); 1124 } 1125 BN_CTX_end(ctx); 1126 return ret; 1127 } 1128 1129 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 1130 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 1131 { 1132 BN_MONT_CTX *mont = NULL; 1133 int b, bits, ret = 0; 1134 int r_is_one; 1135 BN_ULONG w, next_w; 1136 BIGNUM *r, *t; 1137 BIGNUM *swap_tmp; 1138 #define BN_MOD_MUL_WORD(r, w, m) \ 1139 (BN_mul_word(r, (w)) && \ 1140 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 1141 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 1142 /* 1143 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is 1144 * probably more overhead than always using BN_mod (which uses BN_copy if 1145 * a similar test returns true). 1146 */ 1147 /* 1148 * We can use BN_mod and do not need BN_nnmod because our accumulator is 1149 * never negative (the result of BN_mod does not depend on the sign of 1150 * the modulus). 1151 */ 1152 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 1153 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 1154 1155 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1156 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1157 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1158 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1159 return 0; 1160 } 1161 1162 bn_check_top(p); 1163 bn_check_top(m); 1164 1165 if (!BN_is_odd(m)) { 1166 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); 1167 return 0; 1168 } 1169 if (m->top == 1) 1170 a %= m->d[0]; /* make sure that 'a' is reduced */ 1171 1172 bits = BN_num_bits(p); 1173 if (bits == 0) { 1174 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 1175 if (BN_abs_is_word(m, 1)) { 1176 ret = 1; 1177 BN_zero(rr); 1178 } else { 1179 ret = BN_one(rr); 1180 } 1181 return ret; 1182 } 1183 if (a == 0) { 1184 BN_zero(rr); 1185 ret = 1; 1186 return ret; 1187 } 1188 1189 BN_CTX_start(ctx); 1190 r = BN_CTX_get(ctx); 1191 t = BN_CTX_get(ctx); 1192 if (t == NULL) 1193 goto err; 1194 1195 if (in_mont != NULL) 1196 mont = in_mont; 1197 else { 1198 if ((mont = BN_MONT_CTX_new()) == NULL) 1199 goto err; 1200 if (!BN_MONT_CTX_set(mont, m, ctx)) 1201 goto err; 1202 } 1203 1204 r_is_one = 1; /* except for Montgomery factor */ 1205 1206 /* bits-1 >= 0 */ 1207 1208 /* The result is accumulated in the product r*w. */ 1209 w = a; /* bit 'bits-1' of 'p' is always set */ 1210 for (b = bits - 2; b >= 0; b--) { 1211 /* First, square r*w. */ 1212 next_w = w * w; 1213 if ((next_w / w) != w) { /* overflow */ 1214 if (r_is_one) { 1215 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1216 goto err; 1217 r_is_one = 0; 1218 } else { 1219 if (!BN_MOD_MUL_WORD(r, w, m)) 1220 goto err; 1221 } 1222 next_w = 1; 1223 } 1224 w = next_w; 1225 if (!r_is_one) { 1226 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 1227 goto err; 1228 } 1229 1230 /* Second, multiply r*w by 'a' if exponent bit is set. */ 1231 if (BN_is_bit_set(p, b)) { 1232 next_w = w * a; 1233 if ((next_w / a) != w) { /* overflow */ 1234 if (r_is_one) { 1235 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1236 goto err; 1237 r_is_one = 0; 1238 } else { 1239 if (!BN_MOD_MUL_WORD(r, w, m)) 1240 goto err; 1241 } 1242 next_w = a; 1243 } 1244 w = next_w; 1245 } 1246 } 1247 1248 /* Finally, set r:=r*w. */ 1249 if (w != 1) { 1250 if (r_is_one) { 1251 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1252 goto err; 1253 r_is_one = 0; 1254 } else { 1255 if (!BN_MOD_MUL_WORD(r, w, m)) 1256 goto err; 1257 } 1258 } 1259 1260 if (r_is_one) { /* can happen only if a == 1 */ 1261 if (!BN_one(rr)) 1262 goto err; 1263 } else { 1264 if (!BN_from_montgomery(rr, r, mont, ctx)) 1265 goto err; 1266 } 1267 ret = 1; 1268 err: 1269 if (in_mont == NULL) 1270 BN_MONT_CTX_free(mont); 1271 BN_CTX_end(ctx); 1272 bn_check_top(rr); 1273 return ret; 1274 } 1275 1276 /* The old fallback, simple version :-) */ 1277 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 1278 const BIGNUM *m, BN_CTX *ctx) 1279 { 1280 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 1281 int start = 1; 1282 BIGNUM *d; 1283 /* Table of variables obtained from 'ctx' */ 1284 BIGNUM *val[TABLE_SIZE]; 1285 1286 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1287 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 1288 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1289 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1290 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1291 return 0; 1292 } 1293 1294 bits = BN_num_bits(p); 1295 if (bits == 0) { 1296 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 1297 if (BN_abs_is_word(m, 1)) { 1298 ret = 1; 1299 BN_zero(r); 1300 } else { 1301 ret = BN_one(r); 1302 } 1303 return ret; 1304 } 1305 1306 BN_CTX_start(ctx); 1307 d = BN_CTX_get(ctx); 1308 val[0] = BN_CTX_get(ctx); 1309 if (val[0] == NULL) 1310 goto err; 1311 1312 if (!BN_nnmod(val[0], a, m, ctx)) 1313 goto err; /* 1 */ 1314 if (BN_is_zero(val[0])) { 1315 BN_zero(r); 1316 ret = 1; 1317 goto err; 1318 } 1319 1320 window = BN_window_bits_for_exponent_size(bits); 1321 if (window > 1) { 1322 if (!BN_mod_mul(d, val[0], val[0], m, ctx)) 1323 goto err; /* 2 */ 1324 j = 1 << (window - 1); 1325 for (i = 1; i < j; i++) { 1326 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 1327 !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) 1328 goto err; 1329 } 1330 } 1331 1332 start = 1; /* This is used to avoid multiplication etc 1333 * when there is only the value '1' in the 1334 * buffer. */ 1335 wvalue = 0; /* The 'value' of the window */ 1336 wstart = bits - 1; /* The top bit of the window */ 1337 wend = 0; /* The bottom bit of the window */ 1338 1339 if (!BN_one(r)) 1340 goto err; 1341 1342 for (;;) { 1343 if (BN_is_bit_set(p, wstart) == 0) { 1344 if (!start) 1345 if (!BN_mod_mul(r, r, r, m, ctx)) 1346 goto err; 1347 if (wstart == 0) 1348 break; 1349 wstart--; 1350 continue; 1351 } 1352 /* 1353 * We now have wstart on a 'set' bit, we now need to work out how bit 1354 * a window to do. To do this we need to scan forward until the last 1355 * set bit before the end of the window 1356 */ 1357 j = wstart; 1358 wvalue = 1; 1359 wend = 0; 1360 for (i = 1; i < window; i++) { 1361 if (wstart - i < 0) 1362 break; 1363 if (BN_is_bit_set(p, wstart - i)) { 1364 wvalue <<= (i - wend); 1365 wvalue |= 1; 1366 wend = i; 1367 } 1368 } 1369 1370 /* wend is the size of the current window */ 1371 j = wend + 1; 1372 /* add the 'bytes above' */ 1373 if (!start) 1374 for (i = 0; i < j; i++) { 1375 if (!BN_mod_mul(r, r, r, m, ctx)) 1376 goto err; 1377 } 1378 1379 /* wvalue will be an odd number < 2^window */ 1380 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) 1381 goto err; 1382 1383 /* move the 'window' down further */ 1384 wstart -= wend + 1; 1385 wvalue = 0; 1386 start = 0; 1387 if (wstart < 0) 1388 break; 1389 } 1390 ret = 1; 1391 err: 1392 BN_CTX_end(ctx); 1393 bn_check_top(r); 1394 return ret; 1395 } 1396