1 /* 2 * Copyright 1995-2023 The OpenSSL Project Authors. All Rights Reserved. 3 * 4 * Licensed under the Apache License 2.0 (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.h" 12 #include "bn_local.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 "crypto/sparc_arch.h" 33 # define SPARC_T4_MONT 34 #endif 35 36 /* maximum precomputation table size for *variable* sliding windows */ 37 #define TABLE_SIZE 32 38 39 /* 40 * Beyond this limit the constant time code is disabled due to 41 * the possible overflow in the computation of powerbufLen in 42 * BN_mod_exp_mont_consttime. 43 * When this limit is exceeded, the computation will be done using 44 * non-constant time code, but it will take very long. 45 */ 46 #define BN_CONSTTIME_SIZE_LIMIT (INT_MAX / BN_BYTES / 256) 47 48 /* this one works - simple but works */ 49 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) 50 { 51 int i, bits, ret = 0; 52 BIGNUM *v, *rr; 53 54 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 55 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) { 56 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 57 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 58 return 0; 59 } 60 61 BN_CTX_start(ctx); 62 rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r; 63 v = BN_CTX_get(ctx); 64 if (rr == NULL || v == NULL) 65 goto err; 66 67 if (BN_copy(v, a) == NULL) 68 goto err; 69 bits = BN_num_bits(p); 70 71 if (BN_is_odd(p)) { 72 if (BN_copy(rr, a) == NULL) 73 goto err; 74 } else { 75 if (!BN_one(rr)) 76 goto err; 77 } 78 79 for (i = 1; i < bits; i++) { 80 if (!BN_sqr(v, v, ctx)) 81 goto err; 82 if (BN_is_bit_set(p, i)) { 83 if (!BN_mul(rr, rr, v, ctx)) 84 goto err; 85 } 86 } 87 if (r != rr && BN_copy(r, rr) == NULL) 88 goto err; 89 90 ret = 1; 91 err: 92 BN_CTX_end(ctx); 93 bn_check_top(r); 94 return ret; 95 } 96 97 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 98 BN_CTX *ctx) 99 { 100 int ret; 101 102 bn_check_top(a); 103 bn_check_top(p); 104 bn_check_top(m); 105 106 /*- 107 * For even modulus m = 2^k*m_odd, it might make sense to compute 108 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 109 * exponentiation for the odd part), using appropriate exponent 110 * reductions, and combine the results using the CRT. 111 * 112 * For now, we use Montgomery only if the modulus is odd; otherwise, 113 * exponentiation using the reciprocal-based quick remaindering 114 * algorithm is used. 115 * 116 * (Timing obtained with expspeed.c [computations a^p mod m 117 * where a, p, m are of the same length: 256, 512, 1024, 2048, 118 * 4096, 8192 bits], compared to the running time of the 119 * standard algorithm: 120 * 121 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 122 * 55 .. 77 % [UltraSparc processor, but 123 * debug-solaris-sparcv8-gcc conf.] 124 * 125 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 126 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 127 * 128 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 129 * at 2048 and more bits, but at 512 and 1024 bits, it was 130 * slower even than the standard algorithm! 131 * 132 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 133 * should be obtained when the new Montgomery reduction code 134 * has been integrated into OpenSSL.) 135 */ 136 137 #define MONT_MUL_MOD 138 #define MONT_EXP_WORD 139 #define RECP_MUL_MOD 140 141 #ifdef MONT_MUL_MOD 142 if (BN_is_odd(m)) { 143 # ifdef MONT_EXP_WORD 144 if (a->top == 1 && !a->neg 145 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0) 146 && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0) 147 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) { 148 BN_ULONG A = a->d[0]; 149 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); 150 } else 151 # endif 152 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); 153 } else 154 #endif 155 #ifdef RECP_MUL_MOD 156 { 157 ret = BN_mod_exp_recp(r, a, p, m, ctx); 158 } 159 #else 160 { 161 ret = BN_mod_exp_simple(r, a, p, m, ctx); 162 } 163 #endif 164 165 bn_check_top(r); 166 return ret; 167 } 168 169 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 170 const BIGNUM *m, BN_CTX *ctx) 171 { 172 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 173 int start = 1; 174 BIGNUM *aa; 175 /* Table of variables obtained from 'ctx' */ 176 BIGNUM *val[TABLE_SIZE]; 177 BN_RECP_CTX recp; 178 179 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 180 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 181 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 182 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 183 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 184 return 0; 185 } 186 187 bits = BN_num_bits(p); 188 if (bits == 0) { 189 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 190 if (BN_abs_is_word(m, 1)) { 191 ret = 1; 192 BN_zero(r); 193 } else { 194 ret = BN_one(r); 195 } 196 return ret; 197 } 198 199 BN_RECP_CTX_init(&recp); 200 201 BN_CTX_start(ctx); 202 aa = BN_CTX_get(ctx); 203 val[0] = BN_CTX_get(ctx); 204 if (val[0] == NULL) 205 goto err; 206 207 if (m->neg) { 208 /* ignore sign of 'm' */ 209 if (!BN_copy(aa, m)) 210 goto err; 211 aa->neg = 0; 212 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) 213 goto err; 214 } else { 215 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) 216 goto err; 217 } 218 219 if (!BN_nnmod(val[0], a, m, ctx)) 220 goto err; /* 1 */ 221 if (BN_is_zero(val[0])) { 222 BN_zero(r); 223 ret = 1; 224 goto err; 225 } 226 227 window = BN_window_bits_for_exponent_size(bits); 228 if (window > 1) { 229 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) 230 goto err; /* 2 */ 231 j = 1 << (window - 1); 232 for (i = 1; i < j; i++) { 233 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 234 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) 235 goto err; 236 } 237 } 238 239 start = 1; /* This is used to avoid multiplication etc 240 * when there is only the value '1' in the 241 * buffer. */ 242 wvalue = 0; /* The 'value' of the window */ 243 wstart = bits - 1; /* The top bit of the window */ 244 wend = 0; /* The bottom bit of the window */ 245 246 if (!BN_one(r)) 247 goto err; 248 249 for (;;) { 250 if (BN_is_bit_set(p, wstart) == 0) { 251 if (!start) 252 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 253 goto err; 254 if (wstart == 0) 255 break; 256 wstart--; 257 continue; 258 } 259 /* 260 * We now have wstart on a 'set' bit, we now need to work out how bit 261 * a window to do. To do this we need to scan forward until the last 262 * set bit before the end of the window 263 */ 264 wvalue = 1; 265 wend = 0; 266 for (i = 1; i < window; i++) { 267 if (wstart - i < 0) 268 break; 269 if (BN_is_bit_set(p, wstart - i)) { 270 wvalue <<= (i - wend); 271 wvalue |= 1; 272 wend = i; 273 } 274 } 275 276 /* wend is the size of the current window */ 277 j = wend + 1; 278 /* add the 'bytes above' */ 279 if (!start) 280 for (i = 0; i < j; i++) { 281 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 282 goto err; 283 } 284 285 /* wvalue will be an odd number < 2^window */ 286 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) 287 goto err; 288 289 /* move the 'window' down further */ 290 wstart -= wend + 1; 291 wvalue = 0; 292 start = 0; 293 if (wstart < 0) 294 break; 295 } 296 ret = 1; 297 err: 298 BN_CTX_end(ctx); 299 BN_RECP_CTX_free(&recp); 300 bn_check_top(r); 301 return ret; 302 } 303 304 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 305 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 306 { 307 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 308 int start = 1; 309 BIGNUM *d, *r; 310 const BIGNUM *aa; 311 /* Table of variables obtained from 'ctx' */ 312 BIGNUM *val[TABLE_SIZE]; 313 BN_MONT_CTX *mont = NULL; 314 315 bn_check_top(a); 316 bn_check_top(p); 317 bn_check_top(m); 318 319 if (!BN_is_odd(m)) { 320 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS); 321 return 0; 322 } 323 324 if (m->top <= BN_CONSTTIME_SIZE_LIMIT 325 && (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 326 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 327 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0)) { 328 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 329 } 330 331 bits = BN_num_bits(p); 332 if (bits == 0) { 333 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 334 if (BN_abs_is_word(m, 1)) { 335 ret = 1; 336 BN_zero(rr); 337 } else { 338 ret = BN_one(rr); 339 } 340 return ret; 341 } 342 343 BN_CTX_start(ctx); 344 d = BN_CTX_get(ctx); 345 r = BN_CTX_get(ctx); 346 val[0] = BN_CTX_get(ctx); 347 if (val[0] == NULL) 348 goto err; 349 350 /* 351 * If this is not done, things will break in the montgomery part 352 */ 353 354 if (in_mont != NULL) 355 mont = in_mont; 356 else { 357 if ((mont = BN_MONT_CTX_new()) == NULL) 358 goto err; 359 if (!BN_MONT_CTX_set(mont, m, ctx)) 360 goto err; 361 } 362 363 if (a->neg || BN_ucmp(a, m) >= 0) { 364 if (!BN_nnmod(val[0], a, m, ctx)) 365 goto err; 366 aa = val[0]; 367 } else 368 aa = a; 369 if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx)) 370 goto err; /* 1 */ 371 372 window = BN_window_bits_for_exponent_size(bits); 373 if (window > 1) { 374 if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx)) 375 goto err; /* 2 */ 376 j = 1 << (window - 1); 377 for (i = 1; i < j; i++) { 378 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 379 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx)) 380 goto err; 381 } 382 } 383 384 start = 1; /* This is used to avoid multiplication etc 385 * when there is only the value '1' in the 386 * buffer. */ 387 wvalue = 0; /* The 'value' of the window */ 388 wstart = bits - 1; /* The top bit of the window */ 389 wend = 0; /* The bottom bit of the window */ 390 391 #if 1 /* by Shay Gueron's suggestion */ 392 j = m->top; /* borrow j */ 393 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 394 if (bn_wexpand(r, j) == NULL) 395 goto err; 396 /* 2^(top*BN_BITS2) - m */ 397 r->d[0] = (0 - m->d[0]) & BN_MASK2; 398 for (i = 1; i < j; i++) 399 r->d[i] = (~m->d[i]) & BN_MASK2; 400 r->top = j; 401 r->flags |= BN_FLG_FIXED_TOP; 402 } else 403 #endif 404 if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx)) 405 goto err; 406 for (;;) { 407 if (BN_is_bit_set(p, wstart) == 0) { 408 if (!start) { 409 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) 410 goto err; 411 } 412 if (wstart == 0) 413 break; 414 wstart--; 415 continue; 416 } 417 /* 418 * We now have wstart on a 'set' bit, we now need to work out how bit 419 * a window to do. To do this we need to scan forward until the last 420 * set bit before the end of the window 421 */ 422 wvalue = 1; 423 wend = 0; 424 for (i = 1; i < window; i++) { 425 if (wstart - i < 0) 426 break; 427 if (BN_is_bit_set(p, wstart - i)) { 428 wvalue <<= (i - wend); 429 wvalue |= 1; 430 wend = i; 431 } 432 } 433 434 /* wend is the size of the current window */ 435 j = wend + 1; 436 /* add the 'bytes above' */ 437 if (!start) 438 for (i = 0; i < j; i++) { 439 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) 440 goto err; 441 } 442 443 /* wvalue will be an odd number < 2^window */ 444 if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx)) 445 goto err; 446 447 /* move the 'window' down further */ 448 wstart -= wend + 1; 449 wvalue = 0; 450 start = 0; 451 if (wstart < 0) 452 break; 453 } 454 /* 455 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery 456 * removes padding [if any] and makes return value suitable for public 457 * API consumer. 458 */ 459 #if defined(SPARC_T4_MONT) 460 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 461 j = mont->N.top; /* borrow j */ 462 val[0]->d[0] = 1; /* borrow val[0] */ 463 for (i = 1; i < j; i++) 464 val[0]->d[i] = 0; 465 val[0]->top = j; 466 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) 467 goto err; 468 } else 469 #endif 470 if (!BN_from_montgomery(rr, r, mont, ctx)) 471 goto err; 472 ret = 1; 473 err: 474 if (in_mont == NULL) 475 BN_MONT_CTX_free(mont); 476 BN_CTX_end(ctx); 477 bn_check_top(rr); 478 return ret; 479 } 480 481 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) 482 { 483 BN_ULONG ret = 0; 484 int wordpos; 485 486 wordpos = bitpos / BN_BITS2; 487 bitpos %= BN_BITS2; 488 if (wordpos >= 0 && wordpos < a->top) { 489 ret = a->d[wordpos] & BN_MASK2; 490 if (bitpos) { 491 ret >>= bitpos; 492 if (++wordpos < a->top) 493 ret |= a->d[wordpos] << (BN_BITS2 - bitpos); 494 } 495 } 496 497 return ret & BN_MASK2; 498 } 499 500 /* 501 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific 502 * layout so that accessing any of these table values shows the same access 503 * pattern as far as cache lines are concerned. The following functions are 504 * used to transfer a BIGNUM from/to that table. 505 */ 506 507 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, 508 unsigned char *buf, int idx, 509 int window) 510 { 511 int i, j; 512 int width = 1 << window; 513 BN_ULONG *table = (BN_ULONG *)buf; 514 515 if (top > b->top) 516 top = b->top; /* this works because 'buf' is explicitly 517 * zeroed */ 518 for (i = 0, j = idx; i < top; i++, j += width) { 519 table[j] = b->d[i]; 520 } 521 522 return 1; 523 } 524 525 static int MOD_EXP_CTIME_COPY_FROM_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 /* 532 * We declare table 'volatile' in order to discourage compiler 533 * from reordering loads from the table. Concern is that if 534 * reordered in specific manner loads might give away the 535 * information we are trying to conceal. Some would argue that 536 * compiler can reorder them anyway, but it can as well be 537 * argued that doing so would be violation of standard... 538 */ 539 volatile BN_ULONG *table = (volatile BN_ULONG *)buf; 540 541 if (bn_wexpand(b, top) == NULL) 542 return 0; 543 544 if (window <= 3) { 545 for (i = 0; i < top; i++, table += width) { 546 BN_ULONG acc = 0; 547 548 for (j = 0; j < width; j++) { 549 acc |= table[j] & 550 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 551 } 552 553 b->d[i] = acc; 554 } 555 } else { 556 int xstride = 1 << (window - 2); 557 BN_ULONG y0, y1, y2, y3; 558 559 i = idx >> (window - 2); /* equivalent of idx / xstride */ 560 idx &= xstride - 1; /* equivalent of idx % xstride */ 561 562 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); 563 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); 564 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); 565 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); 566 567 for (i = 0; i < top; i++, table += width) { 568 BN_ULONG acc = 0; 569 570 for (j = 0; j < xstride; j++) { 571 acc |= ( (table[j + 0 * xstride] & y0) | 572 (table[j + 1 * xstride] & y1) | 573 (table[j + 2 * xstride] & y2) | 574 (table[j + 3 * xstride] & y3) ) 575 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 576 } 577 578 b->d[i] = acc; 579 } 580 } 581 582 b->top = top; 583 b->flags |= BN_FLG_FIXED_TOP; 584 return 1; 585 } 586 587 /* 588 * Given a pointer value, compute the next address that is a cache line 589 * multiple. 590 */ 591 #define MOD_EXP_CTIME_ALIGN(x_) \ 592 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 593 594 /* 595 * This variant of BN_mod_exp_mont() uses fixed windows and the special 596 * precomputation memory layout to limit data-dependency to a minimum to 597 * protect secret exponents (cf. the hyper-threading timing attacks pointed 598 * out by Colin Percival, 599 * http://www.daemonology.net/hyperthreading-considered-harmful/) 600 */ 601 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 602 const BIGNUM *m, BN_CTX *ctx, 603 BN_MONT_CTX *in_mont) 604 { 605 int i, bits, ret = 0, window, wvalue, wmask, window0; 606 int top; 607 BN_MONT_CTX *mont = NULL; 608 609 int numPowers; 610 unsigned char *powerbufFree = NULL; 611 int powerbufLen = 0; 612 unsigned char *powerbuf = NULL; 613 BIGNUM tmp, am; 614 #if defined(SPARC_T4_MONT) 615 unsigned int t4 = 0; 616 #endif 617 618 bn_check_top(a); 619 bn_check_top(p); 620 bn_check_top(m); 621 622 if (!BN_is_odd(m)) { 623 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS); 624 return 0; 625 } 626 627 top = m->top; 628 629 if (top > BN_CONSTTIME_SIZE_LIMIT) { 630 /* Prevent overflowing the powerbufLen computation below */ 631 return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont); 632 } 633 634 /* 635 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak 636 * whether the top bits are zero. 637 */ 638 bits = p->top * BN_BITS2; 639 if (bits == 0) { 640 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 641 if (BN_abs_is_word(m, 1)) { 642 ret = 1; 643 BN_zero(rr); 644 } else { 645 ret = BN_one(rr); 646 } 647 return ret; 648 } 649 650 BN_CTX_start(ctx); 651 652 /* 653 * Allocate a montgomery context if it was not supplied by the caller. If 654 * this is not done, things will break in the montgomery part. 655 */ 656 if (in_mont != NULL) 657 mont = in_mont; 658 else { 659 if ((mont = BN_MONT_CTX_new()) == NULL) 660 goto err; 661 if (!BN_MONT_CTX_set(mont, m, ctx)) 662 goto err; 663 } 664 665 if (a->neg || BN_ucmp(a, m) >= 0) { 666 BIGNUM *reduced = BN_CTX_get(ctx); 667 if (reduced == NULL 668 || !BN_nnmod(reduced, a, m, ctx)) { 669 goto err; 670 } 671 a = reduced; 672 } 673 674 #ifdef RSAZ_ENABLED 675 /* 676 * If the size of the operands allow it, perform the optimized 677 * RSAZ exponentiation. For further information see 678 * crypto/bn/rsaz_exp.c and accompanying assembly modules. 679 */ 680 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) 681 && rsaz_avx2_eligible()) { 682 if (NULL == bn_wexpand(rr, 16)) 683 goto err; 684 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, 685 mont->n0[0]); 686 rr->top = 16; 687 rr->neg = 0; 688 bn_correct_top(rr); 689 ret = 1; 690 goto err; 691 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { 692 if (NULL == bn_wexpand(rr, 8)) 693 goto err; 694 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); 695 rr->top = 8; 696 rr->neg = 0; 697 bn_correct_top(rr); 698 ret = 1; 699 goto err; 700 } 701 #endif 702 703 /* Get the window size to use with size of p. */ 704 window = BN_window_bits_for_ctime_exponent_size(bits); 705 #if defined(SPARC_T4_MONT) 706 if (window >= 5 && (top & 15) == 0 && top <= 64 && 707 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == 708 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) 709 window = 5; 710 else 711 #endif 712 #if defined(OPENSSL_BN_ASM_MONT5) 713 if (window >= 5 && top <= BN_SOFT_LIMIT) { 714 window = 5; /* ~5% improvement for RSA2048 sign, and even 715 * for RSA4096 */ 716 /* reserve space for mont->N.d[] copy */ 717 powerbufLen += top * sizeof(mont->N.d[0]); 718 } 719 #endif 720 (void)0; 721 722 /* 723 * Allocate a buffer large enough to hold all of the pre-computed powers 724 * of am, am itself and tmp. 725 */ 726 numPowers = 1 << window; 727 powerbufLen += sizeof(m->d[0]) * (top * numPowers + 728 ((2 * top) > 729 numPowers ? (2 * top) : numPowers)); 730 #ifdef alloca 731 if (powerbufLen < 3072) 732 powerbufFree = 733 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); 734 else 735 #endif 736 if ((powerbufFree = 737 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) 738 == NULL) 739 goto err; 740 741 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 742 memset(powerbuf, 0, powerbufLen); 743 744 #ifdef alloca 745 if (powerbufLen < 3072) 746 powerbufFree = NULL; 747 #endif 748 749 /* lay down tmp and am right after powers table */ 750 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); 751 am.d = tmp.d + top; 752 tmp.top = am.top = 0; 753 tmp.dmax = am.dmax = top; 754 tmp.neg = am.neg = 0; 755 tmp.flags = am.flags = BN_FLG_STATIC_DATA; 756 757 /* prepare a^0 in Montgomery domain */ 758 #if 1 /* by Shay Gueron's suggestion */ 759 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 760 /* 2^(top*BN_BITS2) - m */ 761 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; 762 for (i = 1; i < top; i++) 763 tmp.d[i] = (~m->d[i]) & BN_MASK2; 764 tmp.top = top; 765 } else 766 #endif 767 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx)) 768 goto err; 769 770 /* prepare a^1 in Montgomery domain */ 771 if (!bn_to_mont_fixed_top(&am, a, mont, ctx)) 772 goto err; 773 774 if (top > BN_SOFT_LIMIT) 775 goto fallback; 776 777 #if defined(SPARC_T4_MONT) 778 if (t4) { 779 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, 780 const BN_ULONG *n0, const void *table, 781 int power, int bits); 782 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, 783 const BN_ULONG *n0, const void *table, 784 int power, int bits); 785 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, 786 const BN_ULONG *n0, const void *table, 787 int power, int bits); 788 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, 789 const BN_ULONG *n0, const void *table, 790 int power, int bits); 791 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, 792 const BN_ULONG *n0, const void *table, 793 int power, int bits); 794 static const bn_pwr5_mont_f pwr5_funcs[4] = { 795 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, 796 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 797 }; 798 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; 799 800 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, 801 const void *bp, const BN_ULONG *np, 802 const BN_ULONG *n0); 803 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, 804 const BN_ULONG *np, const BN_ULONG *n0); 805 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, 806 const void *bp, const BN_ULONG *np, 807 const BN_ULONG *n0); 808 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, 809 const void *bp, const BN_ULONG *np, 810 const BN_ULONG *n0); 811 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, 812 const void *bp, const BN_ULONG *np, 813 const BN_ULONG *n0); 814 static const bn_mul_mont_f mul_funcs[4] = { 815 bn_mul_mont_t4_8, bn_mul_mont_t4_16, 816 bn_mul_mont_t4_24, bn_mul_mont_t4_32 817 }; 818 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; 819 820 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, 821 const void *bp, const BN_ULONG *np, 822 const BN_ULONG *n0, int num); 823 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, 824 const void *bp, const BN_ULONG *np, 825 const BN_ULONG *n0, int num); 826 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, 827 const void *table, const BN_ULONG *np, 828 const BN_ULONG *n0, int num, int power); 829 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, 830 void *table, size_t power); 831 void bn_gather5_t4(BN_ULONG *out, size_t num, 832 void *table, size_t power); 833 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); 834 835 BN_ULONG *np = mont->N.d, *n0 = mont->n0; 836 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less 837 * than 32 */ 838 839 /* 840 * BN_to_montgomery can contaminate words above .top [in 841 * BN_DEBUG build... 842 */ 843 for (i = am.top; i < top; i++) 844 am.d[i] = 0; 845 for (i = tmp.top; i < top; i++) 846 tmp.d[i] = 0; 847 848 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); 849 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); 850 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && 851 !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) 852 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); 853 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); 854 855 for (i = 3; i < 32; i++) { 856 /* Calculate a^i = a^(i-1) * a */ 857 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && 858 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) 859 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); 860 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); 861 } 862 863 /* switch to 64-bit domain */ 864 np = alloca(top * sizeof(BN_ULONG)); 865 top /= 2; 866 bn_flip_t4(np, mont->N.d, top); 867 868 /* 869 * The exponent may not have a whole number of fixed-size windows. 870 * To simplify the main loop, the initial window has between 1 and 871 * full-window-size bits such that what remains is always a whole 872 * number of windows 873 */ 874 window0 = (bits - 1) % 5 + 1; 875 wmask = (1 << window0) - 1; 876 bits -= window0; 877 wvalue = bn_get_bits(p, bits) & wmask; 878 bn_gather5_t4(tmp.d, top, powerbuf, wvalue); 879 880 /* 881 * Scan the exponent one window at a time starting from the most 882 * significant bits. 883 */ 884 while (bits > 0) { 885 if (bits < stride) 886 stride = bits; 887 bits -= stride; 888 wvalue = bn_get_bits(p, bits); 889 890 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 891 continue; 892 /* retry once and fall back */ 893 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 894 continue; 895 896 bits += stride - 5; 897 wvalue >>= stride - 5; 898 wvalue &= 31; 899 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 900 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 901 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 902 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 903 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 904 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, 905 wvalue); 906 } 907 908 bn_flip_t4(tmp.d, tmp.d, top); 909 top *= 2; 910 /* back to 32-bit domain */ 911 tmp.top = top; 912 bn_correct_top(&tmp); 913 OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); 914 } else 915 #endif 916 #if defined(OPENSSL_BN_ASM_MONT5) 917 if (window == 5 && top > 1) { 918 /* 919 * This optimization uses ideas from https://eprint.iacr.org/2011/239, 920 * specifically optimization of cache-timing attack countermeasures, 921 * pre-computation optimization, and Almost Montgomery Multiplication. 922 * 923 * The paper discusses a 4-bit window to optimize 512-bit modular 924 * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer 925 * important. 926 * 927 * |bn_mul_mont_gather5| and |bn_power5| implement the "almost" 928 * reduction variant, so the values here may not be fully reduced. 929 * They are bounded by R (i.e. they fit in |top| words), not |m|. 930 * Additionally, we pass these "almost" reduced inputs into 931 * |bn_mul_mont|, which implements the normal reduction variant. 932 * Given those inputs, |bn_mul_mont| may not give reduced 933 * output, but it will still produce "almost" reduced output. 934 */ 935 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, 936 const void *table, const BN_ULONG *np, 937 const BN_ULONG *n0, int num, int power); 938 void bn_scatter5(const BN_ULONG *inp, size_t num, 939 void *table, size_t power); 940 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); 941 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, 942 const void *table, const BN_ULONG *np, 943 const BN_ULONG *n0, int num, int power); 944 int bn_get_bits5(const BN_ULONG *ap, int off); 945 946 BN_ULONG *n0 = mont->n0, *np; 947 948 /* 949 * BN_to_montgomery can contaminate words above .top [in 950 * BN_DEBUG build... 951 */ 952 for (i = am.top; i < top; i++) 953 am.d[i] = 0; 954 for (i = tmp.top; i < top; i++) 955 tmp.d[i] = 0; 956 957 /* 958 * copy mont->N.d[] to improve cache locality 959 */ 960 for (np = am.d + top, i = 0; i < top; i++) 961 np[i] = mont->N.d[i]; 962 963 bn_scatter5(tmp.d, top, powerbuf, 0); 964 bn_scatter5(am.d, am.top, powerbuf, 1); 965 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); 966 bn_scatter5(tmp.d, top, powerbuf, 2); 967 968 # if 0 969 for (i = 3; i < 32; i++) { 970 /* Calculate a^i = a^(i-1) * a */ 971 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 972 bn_scatter5(tmp.d, top, powerbuf, i); 973 } 974 # else 975 /* same as above, but uses squaring for 1/2 of operations */ 976 for (i = 4; i < 32; i *= 2) { 977 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 978 bn_scatter5(tmp.d, top, powerbuf, i); 979 } 980 for (i = 3; i < 8; i += 2) { 981 int j; 982 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 983 bn_scatter5(tmp.d, top, powerbuf, i); 984 for (j = 2 * i; j < 32; j *= 2) { 985 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 986 bn_scatter5(tmp.d, top, powerbuf, j); 987 } 988 } 989 for (; i < 16; i += 2) { 990 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 991 bn_scatter5(tmp.d, top, powerbuf, i); 992 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 993 bn_scatter5(tmp.d, top, powerbuf, 2 * i); 994 } 995 for (; i < 32; i += 2) { 996 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 997 bn_scatter5(tmp.d, top, powerbuf, i); 998 } 999 # endif 1000 /* 1001 * The exponent may not have a whole number of fixed-size windows. 1002 * To simplify the main loop, the initial window has between 1 and 1003 * full-window-size bits such that what remains is always a whole 1004 * number of windows 1005 */ 1006 window0 = (bits - 1) % 5 + 1; 1007 wmask = (1 << window0) - 1; 1008 bits -= window0; 1009 wvalue = bn_get_bits(p, bits) & wmask; 1010 bn_gather5(tmp.d, top, powerbuf, wvalue); 1011 1012 /* 1013 * Scan the exponent one window at a time starting from the most 1014 * significant bits. 1015 */ 1016 if (top & 7) { 1017 while (bits > 0) { 1018 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1019 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1020 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1021 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1022 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1023 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, 1024 bn_get_bits5(p->d, bits -= 5)); 1025 } 1026 } else { 1027 while (bits > 0) { 1028 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, 1029 bn_get_bits5(p->d, bits -= 5)); 1030 } 1031 } 1032 1033 tmp.top = top; 1034 /* 1035 * The result is now in |tmp| in Montgomery form, but it may not be 1036 * fully reduced. This is within bounds for |BN_from_montgomery| 1037 * (tmp < R <= m*R) so it will, when converting from Montgomery form, 1038 * produce a fully reduced result. 1039 * 1040 * This differs from Figure 2 of the paper, which uses AMM(h, 1) to 1041 * convert from Montgomery form with unreduced output, followed by an 1042 * extra reduction step. In the paper's terminology, we replace 1043 * steps 9 and 10 with MM(h, 1). 1044 */ 1045 } else 1046 #endif 1047 { 1048 fallback: 1049 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) 1050 goto err; 1051 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) 1052 goto err; 1053 1054 /* 1055 * If the window size is greater than 1, then calculate 1056 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even 1057 * powers could instead be computed as (a^(i/2))^2 to use the slight 1058 * performance advantage of sqr over mul). 1059 */ 1060 if (window > 1) { 1061 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx)) 1062 goto err; 1063 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, 1064 window)) 1065 goto err; 1066 for (i = 3; i < numPowers; i++) { 1067 /* Calculate a^i = a^(i-1) * a */ 1068 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx)) 1069 goto err; 1070 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, 1071 window)) 1072 goto err; 1073 } 1074 } 1075 1076 /* 1077 * The exponent may not have a whole number of fixed-size windows. 1078 * To simplify the main loop, the initial window has between 1 and 1079 * full-window-size bits such that what remains is always a whole 1080 * number of windows 1081 */ 1082 window0 = (bits - 1) % window + 1; 1083 wmask = (1 << window0) - 1; 1084 bits -= window0; 1085 wvalue = bn_get_bits(p, bits) & wmask; 1086 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, 1087 window)) 1088 goto err; 1089 1090 wmask = (1 << window) - 1; 1091 /* 1092 * Scan the exponent one window at a time starting from the most 1093 * significant bits. 1094 */ 1095 while (bits > 0) { 1096 1097 /* Square the result window-size times */ 1098 for (i = 0; i < window; i++) 1099 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx)) 1100 goto err; 1101 1102 /* 1103 * Get a window's worth of bits from the exponent 1104 * This avoids calling BN_is_bit_set for each bit, which 1105 * is not only slower but also makes each bit vulnerable to 1106 * EM (and likely other) side-channel attacks like One&Done 1107 * (for details see "One&Done: A Single-Decryption EM-Based 1108 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam, 1109 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and 1110 * M. Prvulovic, in USENIX Security'18) 1111 */ 1112 bits -= window; 1113 wvalue = bn_get_bits(p, bits) & wmask; 1114 /* 1115 * Fetch the appropriate pre-computed value from the pre-buf 1116 */ 1117 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, 1118 window)) 1119 goto err; 1120 1121 /* Multiply the result into the intermediate result */ 1122 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx)) 1123 goto err; 1124 } 1125 } 1126 1127 /* 1128 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery 1129 * removes padding [if any] and makes return value suitable for public 1130 * API consumer. 1131 */ 1132 #if defined(SPARC_T4_MONT) 1133 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 1134 am.d[0] = 1; /* borrow am */ 1135 for (i = 1; i < top; i++) 1136 am.d[i] = 0; 1137 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) 1138 goto err; 1139 } else 1140 #endif 1141 if (!BN_from_montgomery(rr, &tmp, mont, ctx)) 1142 goto err; 1143 ret = 1; 1144 err: 1145 if (in_mont == NULL) 1146 BN_MONT_CTX_free(mont); 1147 if (powerbuf != NULL) { 1148 OPENSSL_cleanse(powerbuf, powerbufLen); 1149 OPENSSL_free(powerbufFree); 1150 } 1151 BN_CTX_end(ctx); 1152 return ret; 1153 } 1154 1155 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 1156 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 1157 { 1158 BN_MONT_CTX *mont = NULL; 1159 int b, bits, ret = 0; 1160 int r_is_one; 1161 BN_ULONG w, next_w; 1162 BIGNUM *r, *t; 1163 BIGNUM *swap_tmp; 1164 #define BN_MOD_MUL_WORD(r, w, m) \ 1165 (BN_mul_word(r, (w)) && \ 1166 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 1167 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 1168 /* 1169 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is 1170 * probably more overhead than always using BN_mod (which uses BN_copy if 1171 * a similar test returns true). 1172 */ 1173 /* 1174 * We can use BN_mod and do not need BN_nnmod because our accumulator is 1175 * never negative (the result of BN_mod does not depend on the sign of 1176 * the modulus). 1177 */ 1178 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 1179 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 1180 1181 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1182 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1183 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1184 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1185 return 0; 1186 } 1187 1188 bn_check_top(p); 1189 bn_check_top(m); 1190 1191 if (!BN_is_odd(m)) { 1192 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS); 1193 return 0; 1194 } 1195 if (m->top == 1) 1196 a %= m->d[0]; /* make sure that 'a' is reduced */ 1197 1198 bits = BN_num_bits(p); 1199 if (bits == 0) { 1200 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 1201 if (BN_abs_is_word(m, 1)) { 1202 ret = 1; 1203 BN_zero(rr); 1204 } else { 1205 ret = BN_one(rr); 1206 } 1207 return ret; 1208 } 1209 if (a == 0) { 1210 BN_zero(rr); 1211 ret = 1; 1212 return ret; 1213 } 1214 1215 BN_CTX_start(ctx); 1216 r = BN_CTX_get(ctx); 1217 t = BN_CTX_get(ctx); 1218 if (t == NULL) 1219 goto err; 1220 1221 if (in_mont != NULL) 1222 mont = in_mont; 1223 else { 1224 if ((mont = BN_MONT_CTX_new()) == NULL) 1225 goto err; 1226 if (!BN_MONT_CTX_set(mont, m, ctx)) 1227 goto err; 1228 } 1229 1230 r_is_one = 1; /* except for Montgomery factor */ 1231 1232 /* bits-1 >= 0 */ 1233 1234 /* The result is accumulated in the product r*w. */ 1235 w = a; /* bit 'bits-1' of 'p' is always set */ 1236 for (b = bits - 2; b >= 0; b--) { 1237 /* First, square r*w. */ 1238 next_w = w * w; 1239 if ((next_w / w) != w) { /* overflow */ 1240 if (r_is_one) { 1241 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1242 goto err; 1243 r_is_one = 0; 1244 } else { 1245 if (!BN_MOD_MUL_WORD(r, w, m)) 1246 goto err; 1247 } 1248 next_w = 1; 1249 } 1250 w = next_w; 1251 if (!r_is_one) { 1252 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 1253 goto err; 1254 } 1255 1256 /* Second, multiply r*w by 'a' if exponent bit is set. */ 1257 if (BN_is_bit_set(p, b)) { 1258 next_w = w * a; 1259 if ((next_w / a) != w) { /* overflow */ 1260 if (r_is_one) { 1261 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1262 goto err; 1263 r_is_one = 0; 1264 } else { 1265 if (!BN_MOD_MUL_WORD(r, w, m)) 1266 goto err; 1267 } 1268 next_w = a; 1269 } 1270 w = next_w; 1271 } 1272 } 1273 1274 /* Finally, set r:=r*w. */ 1275 if (w != 1) { 1276 if (r_is_one) { 1277 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1278 goto err; 1279 r_is_one = 0; 1280 } else { 1281 if (!BN_MOD_MUL_WORD(r, w, m)) 1282 goto err; 1283 } 1284 } 1285 1286 if (r_is_one) { /* can happen only if a == 1 */ 1287 if (!BN_one(rr)) 1288 goto err; 1289 } else { 1290 if (!BN_from_montgomery(rr, r, mont, ctx)) 1291 goto err; 1292 } 1293 ret = 1; 1294 err: 1295 if (in_mont == NULL) 1296 BN_MONT_CTX_free(mont); 1297 BN_CTX_end(ctx); 1298 bn_check_top(rr); 1299 return ret; 1300 } 1301 1302 /* The old fallback, simple version :-) */ 1303 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 1304 const BIGNUM *m, BN_CTX *ctx) 1305 { 1306 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 1307 int start = 1; 1308 BIGNUM *d; 1309 /* Table of variables obtained from 'ctx' */ 1310 BIGNUM *val[TABLE_SIZE]; 1311 1312 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1313 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 1314 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1315 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1316 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1317 return 0; 1318 } 1319 1320 bits = BN_num_bits(p); 1321 if (bits == 0) { 1322 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 1323 if (BN_abs_is_word(m, 1)) { 1324 ret = 1; 1325 BN_zero(r); 1326 } else { 1327 ret = BN_one(r); 1328 } 1329 return ret; 1330 } 1331 1332 BN_CTX_start(ctx); 1333 d = BN_CTX_get(ctx); 1334 val[0] = BN_CTX_get(ctx); 1335 if (val[0] == NULL) 1336 goto err; 1337 1338 if (!BN_nnmod(val[0], a, m, ctx)) 1339 goto err; /* 1 */ 1340 if (BN_is_zero(val[0])) { 1341 BN_zero(r); 1342 ret = 1; 1343 goto err; 1344 } 1345 1346 window = BN_window_bits_for_exponent_size(bits); 1347 if (window > 1) { 1348 if (!BN_mod_mul(d, val[0], val[0], m, ctx)) 1349 goto err; /* 2 */ 1350 j = 1 << (window - 1); 1351 for (i = 1; i < j; i++) { 1352 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 1353 !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) 1354 goto err; 1355 } 1356 } 1357 1358 start = 1; /* This is used to avoid multiplication etc 1359 * when there is only the value '1' in the 1360 * buffer. */ 1361 wvalue = 0; /* The 'value' of the window */ 1362 wstart = bits - 1; /* The top bit of the window */ 1363 wend = 0; /* The bottom bit of the window */ 1364 1365 if (!BN_one(r)) 1366 goto err; 1367 1368 for (;;) { 1369 if (BN_is_bit_set(p, wstart) == 0) { 1370 if (!start) 1371 if (!BN_mod_mul(r, r, r, m, ctx)) 1372 goto err; 1373 if (wstart == 0) 1374 break; 1375 wstart--; 1376 continue; 1377 } 1378 /* 1379 * We now have wstart on a 'set' bit, we now need to work out how bit 1380 * a window to do. To do this we need to scan forward until the last 1381 * set bit before the end of the window 1382 */ 1383 wvalue = 1; 1384 wend = 0; 1385 for (i = 1; i < window; i++) { 1386 if (wstart - i < 0) 1387 break; 1388 if (BN_is_bit_set(p, wstart - i)) { 1389 wvalue <<= (i - wend); 1390 wvalue |= 1; 1391 wend = i; 1392 } 1393 } 1394 1395 /* wend is the size of the current window */ 1396 j = wend + 1; 1397 /* add the 'bytes above' */ 1398 if (!start) 1399 for (i = 0; i < j; i++) { 1400 if (!BN_mod_mul(r, r, r, m, ctx)) 1401 goto err; 1402 } 1403 1404 /* wvalue will be an odd number < 2^window */ 1405 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) 1406 goto err; 1407 1408 /* move the 'window' down further */ 1409 wstart -= wend + 1; 1410 wvalue = 0; 1411 start = 0; 1412 if (wstart < 0) 1413 break; 1414 } 1415 ret = 1; 1416 err: 1417 BN_CTX_end(ctx); 1418 bn_check_top(r); 1419 return ret; 1420 } 1421 1422 /* 1423 * This is a variant of modular exponentiation optimization that does 1424 * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA 1425 * in 52-bit binary redundant representation. 1426 * If such instructions are not available, or input data size is not supported, 1427 * it falls back to two BN_mod_exp_mont_consttime() calls. 1428 */ 1429 int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1, const BIGNUM *p1, 1430 const BIGNUM *m1, BN_MONT_CTX *in_mont1, 1431 BIGNUM *rr2, const BIGNUM *a2, const BIGNUM *p2, 1432 const BIGNUM *m2, BN_MONT_CTX *in_mont2, 1433 BN_CTX *ctx) 1434 { 1435 int ret = 0; 1436 1437 #ifdef RSAZ_ENABLED 1438 BN_MONT_CTX *mont1 = NULL; 1439 BN_MONT_CTX *mont2 = NULL; 1440 1441 if (ossl_rsaz_avx512ifma_eligible() && 1442 ((a1->top == 16) && (p1->top == 16) && (BN_num_bits(m1) == 1024) && 1443 (a2->top == 16) && (p2->top == 16) && (BN_num_bits(m2) == 1024))) { 1444 1445 if (bn_wexpand(rr1, 16) == NULL) 1446 goto err; 1447 if (bn_wexpand(rr2, 16) == NULL) 1448 goto err; 1449 1450 /* Ensure that montgomery contexts are initialized */ 1451 if (in_mont1 != NULL) { 1452 mont1 = in_mont1; 1453 } else { 1454 if ((mont1 = BN_MONT_CTX_new()) == NULL) 1455 goto err; 1456 if (!BN_MONT_CTX_set(mont1, m1, ctx)) 1457 goto err; 1458 } 1459 if (in_mont2 != NULL) { 1460 mont2 = in_mont2; 1461 } else { 1462 if ((mont2 = BN_MONT_CTX_new()) == NULL) 1463 goto err; 1464 if (!BN_MONT_CTX_set(mont2, m2, ctx)) 1465 goto err; 1466 } 1467 1468 ret = ossl_rsaz_mod_exp_avx512_x2(rr1->d, a1->d, p1->d, m1->d, 1469 mont1->RR.d, mont1->n0[0], 1470 rr2->d, a2->d, p2->d, m2->d, 1471 mont2->RR.d, mont2->n0[0], 1472 1024 /* factor bit size */); 1473 1474 rr1->top = 16; 1475 rr1->neg = 0; 1476 bn_correct_top(rr1); 1477 bn_check_top(rr1); 1478 1479 rr2->top = 16; 1480 rr2->neg = 0; 1481 bn_correct_top(rr2); 1482 bn_check_top(rr2); 1483 1484 goto err; 1485 } 1486 #endif 1487 1488 /* rr1 = a1^p1 mod m1 */ 1489 ret = BN_mod_exp_mont_consttime(rr1, a1, p1, m1, ctx, in_mont1); 1490 /* rr2 = a2^p2 mod m2 */ 1491 ret &= BN_mod_exp_mont_consttime(rr2, a2, p2, m2, ctx, in_mont2); 1492 1493 #ifdef RSAZ_ENABLED 1494 err: 1495 if (in_mont2 == NULL) 1496 BN_MONT_CTX_free(mont2); 1497 if (in_mont1 == NULL) 1498 BN_MONT_CTX_free(mont1); 1499 #endif 1500 1501 return ret; 1502 } 1503