bn_exp.c revision 273399
1/* crypto/bn/bn_exp.c */ 2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 3 * All rights reserved. 4 * 5 * This package is an SSL implementation written 6 * by Eric Young (eay@cryptsoft.com). 7 * The implementation was written so as to conform with Netscapes SSL. 8 * 9 * This library is free for commercial and non-commercial use as long as 10 * the following conditions are aheared to. The following conditions 11 * apply to all code found in this distribution, be it the RC4, RSA, 12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation 13 * included with this distribution is covered by the same copyright terms 14 * except that the holder is Tim Hudson (tjh@cryptsoft.com). 15 * 16 * Copyright remains Eric Young's, and as such any Copyright notices in 17 * the code are not to be removed. 18 * If this package is used in a product, Eric Young should be given attribution 19 * as the author of the parts of the library used. 20 * This can be in the form of a textual message at program startup or 21 * in documentation (online or textual) provided with the package. 22 * 23 * Redistribution and use in source and binary forms, with or without 24 * modification, are permitted provided that the following conditions 25 * are met: 26 * 1. Redistributions of source code must retain the copyright 27 * notice, this list of conditions and the following disclaimer. 28 * 2. Redistributions in binary form must reproduce the above copyright 29 * notice, this list of conditions and the following disclaimer in the 30 * documentation and/or other materials provided with the distribution. 31 * 3. All advertising materials mentioning features or use of this software 32 * must display the following acknowledgement: 33 * "This product includes cryptographic software written by 34 * Eric Young (eay@cryptsoft.com)" 35 * The word 'cryptographic' can be left out if the rouines from the library 36 * being used are not cryptographic related :-). 37 * 4. If you include any Windows specific code (or a derivative thereof) from 38 * the apps directory (application code) you must include an acknowledgement: 39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" 40 * 41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 51 * SUCH DAMAGE. 52 * 53 * The licence and distribution terms for any publically available version or 54 * derivative of this code cannot be changed. i.e. this code cannot simply be 55 * copied and put under another distribution licence 56 * [including the GNU Public Licence.] 57 */ 58/* ==================================================================== 59 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. 60 * 61 * Redistribution and use in source and binary forms, with or without 62 * modification, are permitted provided that the following conditions 63 * are met: 64 * 65 * 1. Redistributions of source code must retain the above copyright 66 * notice, this list of conditions and the following disclaimer. 67 * 68 * 2. Redistributions in binary form must reproduce the above copyright 69 * notice, this list of conditions and the following disclaimer in 70 * the documentation and/or other materials provided with the 71 * distribution. 72 * 73 * 3. All advertising materials mentioning features or use of this 74 * software must display the following acknowledgment: 75 * "This product includes software developed by the OpenSSL Project 76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 77 * 78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 79 * endorse or promote products derived from this software without 80 * prior written permission. For written permission, please contact 81 * openssl-core@openssl.org. 82 * 83 * 5. Products derived from this software may not be called "OpenSSL" 84 * nor may "OpenSSL" appear in their names without prior written 85 * permission of the OpenSSL Project. 86 * 87 * 6. Redistributions of any form whatsoever must retain the following 88 * acknowledgment: 89 * "This product includes software developed by the OpenSSL Project 90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 91 * 92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 103 * OF THE POSSIBILITY OF SUCH DAMAGE. 104 * ==================================================================== 105 * 106 * This product includes cryptographic software written by Eric Young 107 * (eay@cryptsoft.com). This product includes software written by Tim 108 * Hudson (tjh@cryptsoft.com). 109 * 110 */ 111 112 113#include "cryptlib.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#endif 127 128/* maximum precomputation table size for *variable* sliding windows */ 129#define TABLE_SIZE 32 130 131/* this one works - simple but works */ 132int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) 133 { 134 int i,bits,ret=0; 135 BIGNUM *v,*rr; 136 137 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 138 { 139 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 140 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 141 return -1; 142 } 143 144 BN_CTX_start(ctx); 145 if ((r == a) || (r == p)) 146 rr = BN_CTX_get(ctx); 147 else 148 rr = r; 149 v = BN_CTX_get(ctx); 150 if (rr == NULL || v == NULL) goto err; 151 152 if (BN_copy(v,a) == NULL) goto err; 153 bits=BN_num_bits(p); 154 155 if (BN_is_odd(p)) 156 { if (BN_copy(rr,a) == NULL) goto err; } 157 else { if (!BN_one(rr)) goto err; } 158 159 for (i=1; i<bits; i++) 160 { 161 if (!BN_sqr(v,v,ctx)) goto err; 162 if (BN_is_bit_set(p,i)) 163 { 164 if (!BN_mul(rr,rr,v,ctx)) goto err; 165 } 166 } 167 ret=1; 168err: 169 if (r != rr) BN_copy(r,rr); 170 BN_CTX_end(ctx); 171 bn_check_top(r); 172 return(ret); 173 } 174 175 176int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 177 BN_CTX *ctx) 178 { 179 int ret; 180 181 bn_check_top(a); 182 bn_check_top(p); 183 bn_check_top(m); 184 185 /* For even modulus m = 2^k*m_odd, it might make sense to compute 186 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 187 * exponentiation for the odd part), using appropriate exponent 188 * reductions, and combine the results using the CRT. 189 * 190 * For now, we use Montgomery only if the modulus is odd; otherwise, 191 * exponentiation using the reciprocal-based quick remaindering 192 * algorithm is used. 193 * 194 * (Timing obtained with expspeed.c [computations a^p mod m 195 * where a, p, m are of the same length: 256, 512, 1024, 2048, 196 * 4096, 8192 bits], compared to the running time of the 197 * standard algorithm: 198 * 199 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 200 * 55 .. 77 % [UltraSparc processor, but 201 * debug-solaris-sparcv8-gcc conf.] 202 * 203 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 204 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 205 * 206 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 207 * at 2048 and more bits, but at 512 and 1024 bits, it was 208 * slower even than the standard algorithm! 209 * 210 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 211 * should be obtained when the new Montgomery reduction code 212 * has been integrated into OpenSSL.) 213 */ 214 215#define MONT_MUL_MOD 216#define MONT_EXP_WORD 217#define RECP_MUL_MOD 218 219#ifdef MONT_MUL_MOD 220 /* I have finally been able to take out this pre-condition of 221 * the top bit being set. It was caused by an error in BN_div 222 * with negatives. There was also another problem when for a^b%m 223 * a >= m. eay 07-May-97 */ 224/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ 225 226 if (BN_is_odd(m)) 227 { 228# ifdef MONT_EXP_WORD 229 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) 230 { 231 BN_ULONG A = a->d[0]; 232 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL); 233 } 234 else 235# endif 236 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); 237 } 238 else 239#endif 240#ifdef RECP_MUL_MOD 241 { ret=BN_mod_exp_recp(r,a,p,m,ctx); } 242#else 243 { ret=BN_mod_exp_simple(r,a,p,m,ctx); } 244#endif 245 246 bn_check_top(r); 247 return(ret); 248 } 249 250 251int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 252 const BIGNUM *m, BN_CTX *ctx) 253 { 254 int i,j,bits,ret=0,wstart,wend,window,wvalue; 255 int start=1; 256 BIGNUM *aa; 257 /* Table of variables obtained from 'ctx' */ 258 BIGNUM *val[TABLE_SIZE]; 259 BN_RECP_CTX recp; 260 261 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 262 { 263 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 264 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 265 return -1; 266 } 267 268 bits=BN_num_bits(p); 269 270 if (bits == 0) 271 { 272 ret = BN_one(r); 273 return ret; 274 } 275 276 BN_CTX_start(ctx); 277 aa = BN_CTX_get(ctx); 278 val[0] = BN_CTX_get(ctx); 279 if(!aa || !val[0]) goto err; 280 281 BN_RECP_CTX_init(&recp); 282 if (m->neg) 283 { 284 /* ignore sign of 'm' */ 285 if (!BN_copy(aa, m)) goto err; 286 aa->neg = 0; 287 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err; 288 } 289 else 290 { 291 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err; 292 } 293 294 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ 295 if (BN_is_zero(val[0])) 296 { 297 BN_zero(r); 298 ret = 1; 299 goto err; 300 } 301 302 window = BN_window_bits_for_exponent_size(bits); 303 if (window > 1) 304 { 305 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx)) 306 goto err; /* 2 */ 307 j=1<<(window-1); 308 for (i=1; i<j; i++) 309 { 310 if(((val[i] = BN_CTX_get(ctx)) == NULL) || 311 !BN_mod_mul_reciprocal(val[i],val[i-1], 312 aa,&recp,ctx)) 313 goto err; 314 } 315 } 316 317 start=1; /* This is used to avoid multiplication etc 318 * when there is only the value '1' in the 319 * buffer. */ 320 wvalue=0; /* The 'value' of the window */ 321 wstart=bits-1; /* The top bit of the window */ 322 wend=0; /* The bottom bit of the window */ 323 324 if (!BN_one(r)) goto err; 325 326 for (;;) 327 { 328 if (BN_is_bit_set(p,wstart) == 0) 329 { 330 if (!start) 331 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) 332 goto err; 333 if (wstart == 0) break; 334 wstart--; 335 continue; 336 } 337 /* We now have wstart on a 'set' bit, we now need to work out 338 * how bit a window to do. To do this we need to scan 339 * forward until the last set bit before the end of the 340 * window */ 341 j=wstart; 342 wvalue=1; 343 wend=0; 344 for (i=1; i<window; i++) 345 { 346 if (wstart-i < 0) break; 347 if (BN_is_bit_set(p,wstart-i)) 348 { 349 wvalue<<=(i-wend); 350 wvalue|=1; 351 wend=i; 352 } 353 } 354 355 /* wend is the size of the current window */ 356 j=wend+1; 357 /* add the 'bytes above' */ 358 if (!start) 359 for (i=0; i<j; i++) 360 { 361 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) 362 goto err; 363 } 364 365 /* wvalue will be an odd number < 2^window */ 366 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx)) 367 goto err; 368 369 /* move the 'window' down further */ 370 wstart-=wend+1; 371 wvalue=0; 372 start=0; 373 if (wstart < 0) break; 374 } 375 ret=1; 376err: 377 BN_CTX_end(ctx); 378 BN_RECP_CTX_free(&recp); 379 bn_check_top(r); 380 return(ret); 381 } 382 383 384int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 385 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 386 { 387 int i,j,bits,ret=0,wstart,wend,window,wvalue; 388 int start=1; 389 BIGNUM *d,*r; 390 const BIGNUM *aa; 391 /* Table of variables obtained from 'ctx' */ 392 BIGNUM *val[TABLE_SIZE]; 393 BN_MONT_CTX *mont=NULL; 394 395 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 396 { 397 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 398 } 399 400 bn_check_top(a); 401 bn_check_top(p); 402 bn_check_top(m); 403 404 if (!BN_is_odd(m)) 405 { 406 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS); 407 return(0); 408 } 409 bits=BN_num_bits(p); 410 if (bits == 0) 411 { 412 ret = BN_one(rr); 413 return ret; 414 } 415 416 BN_CTX_start(ctx); 417 d = BN_CTX_get(ctx); 418 r = BN_CTX_get(ctx); 419 val[0] = BN_CTX_get(ctx); 420 if (!d || !r || !val[0]) goto err; 421 422 /* If this is not done, things will break in the montgomery 423 * part */ 424 425 if (in_mont != NULL) 426 mont=in_mont; 427 else 428 { 429 if ((mont=BN_MONT_CTX_new()) == NULL) goto err; 430 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; 431 } 432 433 if (a->neg || BN_ucmp(a,m) >= 0) 434 { 435 if (!BN_nnmod(val[0],a,m,ctx)) 436 goto err; 437 aa= val[0]; 438 } 439 else 440 aa=a; 441 if (BN_is_zero(aa)) 442 { 443 BN_zero(rr); 444 ret = 1; 445 goto err; 446 } 447 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */ 448 449 window = BN_window_bits_for_exponent_size(bits); 450 if (window > 1) 451 { 452 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */ 453 j=1<<(window-1); 454 for (i=1; i<j; i++) 455 { 456 if(((val[i] = BN_CTX_get(ctx)) == NULL) || 457 !BN_mod_mul_montgomery(val[i],val[i-1], 458 d,mont,ctx)) 459 goto err; 460 } 461 } 462 463 start=1; /* This is used to avoid multiplication etc 464 * when there is only the value '1' in the 465 * buffer. */ 466 wvalue=0; /* The 'value' of the window */ 467 wstart=bits-1; /* The top bit of the window */ 468 wend=0; /* The bottom bit of the window */ 469 470 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err; 471 for (;;) 472 { 473 if (BN_is_bit_set(p,wstart) == 0) 474 { 475 if (!start) 476 { 477 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) 478 goto err; 479 } 480 if (wstart == 0) break; 481 wstart--; 482 continue; 483 } 484 /* We now have wstart on a 'set' bit, we now need to work out 485 * how bit a window to do. To do this we need to scan 486 * forward until the last set bit before the end of the 487 * window */ 488 j=wstart; 489 wvalue=1; 490 wend=0; 491 for (i=1; i<window; i++) 492 { 493 if (wstart-i < 0) break; 494 if (BN_is_bit_set(p,wstart-i)) 495 { 496 wvalue<<=(i-wend); 497 wvalue|=1; 498 wend=i; 499 } 500 } 501 502 /* wend is the size of the current window */ 503 j=wend+1; 504 /* add the 'bytes above' */ 505 if (!start) 506 for (i=0; i<j; i++) 507 { 508 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) 509 goto err; 510 } 511 512 /* wvalue will be an odd number < 2^window */ 513 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx)) 514 goto err; 515 516 /* move the 'window' down further */ 517 wstart-=wend+1; 518 wvalue=0; 519 start=0; 520 if (wstart < 0) break; 521 } 522 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err; 523 ret=1; 524err: 525 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); 526 BN_CTX_end(ctx); 527 bn_check_top(rr); 528 return(ret); 529 } 530 531 532/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout 533 * so that accessing any of these table values shows the same access pattern as far 534 * as cache lines are concerned. The following functions are used to transfer a BIGNUM 535 * from/to that table. */ 536 537static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width) 538 { 539 size_t i, j; 540 541 if (top > b->top) 542 top = b->top; /* this works because 'buf' is explicitly zeroed */ 543 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width) 544 { 545 buf[j] = ((unsigned char*)b->d)[i]; 546 } 547 548 return 1; 549 } 550 551static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width) 552 { 553 size_t i, j; 554 555 if (bn_wexpand(b, top) == NULL) 556 return 0; 557 558 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width) 559 { 560 ((unsigned char*)b->d)[i] = buf[j]; 561 } 562 563 b->top = top; 564 bn_correct_top(b); 565 return 1; 566 } 567 568/* Given a pointer value, compute the next address that is a cache line multiple. */ 569#define MOD_EXP_CTIME_ALIGN(x_) \ 570 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 571 572/* This variant of BN_mod_exp_mont() uses fixed windows and the special 573 * precomputation memory layout to limit data-dependency to a minimum 574 * to protect secret exponents (cf. the hyper-threading timing attacks 575 * pointed out by Colin Percival, 576 * http://www.daemonology.net/hyperthreading-considered-harmful/) 577 */ 578int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 579 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 580 { 581 int i,bits,ret=0,window,wvalue; 582 int top; 583 BN_MONT_CTX *mont=NULL; 584 585 int numPowers; 586 unsigned char *powerbufFree=NULL; 587 int powerbufLen = 0; 588 unsigned char *powerbuf=NULL; 589 BIGNUM tmp, am; 590 591 bn_check_top(a); 592 bn_check_top(p); 593 bn_check_top(m); 594 595 top = m->top; 596 597 if (!(m->d[0] & 1)) 598 { 599 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS); 600 return(0); 601 } 602 bits=BN_num_bits(p); 603 if (bits == 0) 604 { 605 ret = BN_one(rr); 606 return ret; 607 } 608 609 BN_CTX_start(ctx); 610 611 /* Allocate a montgomery context if it was not supplied by the caller. 612 * If this is not done, things will break in the montgomery part. 613 */ 614 if (in_mont != NULL) 615 mont=in_mont; 616 else 617 { 618 if ((mont=BN_MONT_CTX_new()) == NULL) goto err; 619 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; 620 } 621 622 /* Get the window size to use with size of p. */ 623 window = BN_window_bits_for_ctime_exponent_size(bits); 624#if defined(OPENSSL_BN_ASM_MONT5) 625 if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */ 626#endif 627 628 /* Allocate a buffer large enough to hold all of the pre-computed 629 * powers of am, am itself and tmp. 630 */ 631 numPowers = 1 << window; 632 powerbufLen = sizeof(m->d[0])*(top*numPowers + 633 ((2*top)>numPowers?(2*top):numPowers)); 634#ifdef alloca 635 if (powerbufLen < 3072) 636 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); 637 else 638#endif 639 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL) 640 goto err; 641 642 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 643 memset(powerbuf, 0, powerbufLen); 644 645#ifdef alloca 646 if (powerbufLen < 3072) 647 powerbufFree = NULL; 648#endif 649 650 /* lay down tmp and am right after powers table */ 651 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers); 652 am.d = tmp.d + top; 653 tmp.top = am.top = 0; 654 tmp.dmax = am.dmax = top; 655 tmp.neg = am.neg = 0; 656 tmp.flags = am.flags = BN_FLG_STATIC_DATA; 657 658 /* prepare a^0 in Montgomery domain */ 659#if 1 660 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err; 661#else 662 tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */ 663 for (i=1;i<top;i++) 664 tmp.d[i] = (~m->d[i])&BN_MASK2; 665 tmp.top = top; 666#endif 667 668 /* prepare a^1 in Montgomery domain */ 669 if (a->neg || BN_ucmp(a,m) >= 0) 670 { 671 if (!BN_mod(&am,a,m,ctx)) goto err; 672 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err; 673 } 674 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err; 675 676#if defined(OPENSSL_BN_ASM_MONT5) 677 /* This optimization uses ideas from http://eprint.iacr.org/2011/239, 678 * specifically optimization of cache-timing attack countermeasures 679 * and pre-computation optimization. */ 680 681 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as 682 * 512-bit RSA is hardly relevant, we omit it to spare size... */ 683 if (window==5 && top>1) 684 { 685 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap, 686 const void *table,const BN_ULONG *np, 687 const BN_ULONG *n0,int num,int power); 688 void bn_scatter5(const BN_ULONG *inp,size_t num, 689 void *table,size_t power); 690 void bn_gather5(BN_ULONG *out,size_t num, 691 void *table,size_t power); 692 693 BN_ULONG *np=mont->N.d, *n0=mont->n0; 694 695 /* BN_to_montgomery can contaminate words above .top 696 * [in BN_DEBUG[_DEBUG] build]... */ 697 for (i=am.top; i<top; i++) am.d[i]=0; 698 for (i=tmp.top; i<top; i++) tmp.d[i]=0; 699 700 bn_scatter5(tmp.d,top,powerbuf,0); 701 bn_scatter5(am.d,am.top,powerbuf,1); 702 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top); 703 bn_scatter5(tmp.d,top,powerbuf,2); 704 705#if 0 706 for (i=3; i<32; i++) 707 { 708 /* Calculate a^i = a^(i-1) * a */ 709 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1); 710 bn_scatter5(tmp.d,top,powerbuf,i); 711 } 712#else 713 /* same as above, but uses squaring for 1/2 of operations */ 714 for (i=4; i<32; i*=2) 715 { 716 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); 717 bn_scatter5(tmp.d,top,powerbuf,i); 718 } 719 for (i=3; i<8; i+=2) 720 { 721 int j; 722 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1); 723 bn_scatter5(tmp.d,top,powerbuf,i); 724 for (j=2*i; j<32; j*=2) 725 { 726 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); 727 bn_scatter5(tmp.d,top,powerbuf,j); 728 } 729 } 730 for (; i<16; i+=2) 731 { 732 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1); 733 bn_scatter5(tmp.d,top,powerbuf,i); 734 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); 735 bn_scatter5(tmp.d,top,powerbuf,2*i); 736 } 737 for (; i<32; i+=2) 738 { 739 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1); 740 bn_scatter5(tmp.d,top,powerbuf,i); 741 } 742#endif 743 bits--; 744 for (wvalue=0, i=bits%5; i>=0; i--,bits--) 745 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits); 746 bn_gather5(tmp.d,top,powerbuf,wvalue); 747 748 /* Scan the exponent one window at a time starting from the most 749 * significant bits. 750 */ 751 while (bits >= 0) 752 { 753 for (wvalue=0, i=0; i<5; i++,bits--) 754 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits); 755 756 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); 757 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); 758 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); 759 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); 760 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); 761 bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue); 762 } 763 764 tmp.top=top; 765 bn_correct_top(&tmp); 766 } 767 else 768#endif 769 { 770 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err; 771 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err; 772 773 /* If the window size is greater than 1, then calculate 774 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) 775 * (even powers could instead be computed as (a^(i/2))^2 776 * to use the slight performance advantage of sqr over mul). 777 */ 778 if (window > 1) 779 { 780 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err; 781 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err; 782 for (i=3; i<numPowers; i++) 783 { 784 /* Calculate a^i = a^(i-1) * a */ 785 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx)) 786 goto err; 787 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err; 788 } 789 } 790 791 bits--; 792 for (wvalue=0, i=bits%window; i>=0; i--,bits--) 793 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits); 794 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err; 795 796 /* Scan the exponent one window at a time starting from the most 797 * significant bits. 798 */ 799 while (bits >= 0) 800 { 801 wvalue=0; /* The 'value' of the window */ 802 803 /* Scan the window, squaring the result as we go */ 804 for (i=0; i<window; i++,bits--) 805 { 806 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err; 807 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits); 808 } 809 810 /* Fetch the appropriate pre-computed value from the pre-buf */ 811 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err; 812 813 /* Multiply the result into the intermediate result */ 814 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err; 815 } 816 } 817 818 /* Convert the final result from montgomery to standard format */ 819 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err; 820 ret=1; 821err: 822 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); 823 if (powerbuf!=NULL) 824 { 825 OPENSSL_cleanse(powerbuf,powerbufLen); 826 if (powerbufFree) OPENSSL_free(powerbufFree); 827 } 828 BN_CTX_end(ctx); 829 return(ret); 830 } 831 832int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 833 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 834 { 835 BN_MONT_CTX *mont = NULL; 836 int b, bits, ret=0; 837 int r_is_one; 838 BN_ULONG w, next_w; 839 BIGNUM *d, *r, *t; 840 BIGNUM *swap_tmp; 841#define BN_MOD_MUL_WORD(r, w, m) \ 842 (BN_mul_word(r, (w)) && \ 843 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 844 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 845 /* BN_MOD_MUL_WORD is only used with 'w' large, 846 * so the BN_ucmp test is probably more overhead 847 * than always using BN_mod (which uses BN_copy if 848 * a similar test returns true). */ 849 /* We can use BN_mod and do not need BN_nnmod because our 850 * accumulator is never negative (the result of BN_mod does 851 * not depend on the sign of the modulus). 852 */ 853#define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 854 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 855 856 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 857 { 858 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 859 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 860 return -1; 861 } 862 863 bn_check_top(p); 864 bn_check_top(m); 865 866 if (!BN_is_odd(m)) 867 { 868 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS); 869 return(0); 870 } 871 if (m->top == 1) 872 a %= m->d[0]; /* make sure that 'a' is reduced */ 873 874 bits = BN_num_bits(p); 875 if (bits == 0) 876 { 877 /* x**0 mod 1 is still zero. */ 878 if (BN_is_one(m)) 879 { 880 ret = 1; 881 BN_zero(rr); 882 } 883 else 884 ret = BN_one(rr); 885 return ret; 886 } 887 if (a == 0) 888 { 889 BN_zero(rr); 890 ret = 1; 891 return ret; 892 } 893 894 BN_CTX_start(ctx); 895 d = BN_CTX_get(ctx); 896 r = BN_CTX_get(ctx); 897 t = BN_CTX_get(ctx); 898 if (d == NULL || r == NULL || t == NULL) goto err; 899 900 if (in_mont != NULL) 901 mont=in_mont; 902 else 903 { 904 if ((mont = BN_MONT_CTX_new()) == NULL) goto err; 905 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; 906 } 907 908 r_is_one = 1; /* except for Montgomery factor */ 909 910 /* bits-1 >= 0 */ 911 912 /* The result is accumulated in the product r*w. */ 913 w = a; /* bit 'bits-1' of 'p' is always set */ 914 for (b = bits-2; b >= 0; b--) 915 { 916 /* First, square r*w. */ 917 next_w = w*w; 918 if ((next_w/w) != w) /* overflow */ 919 { 920 if (r_is_one) 921 { 922 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 923 r_is_one = 0; 924 } 925 else 926 { 927 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 928 } 929 next_w = 1; 930 } 931 w = next_w; 932 if (!r_is_one) 933 { 934 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err; 935 } 936 937 /* Second, multiply r*w by 'a' if exponent bit is set. */ 938 if (BN_is_bit_set(p, b)) 939 { 940 next_w = w*a; 941 if ((next_w/a) != w) /* overflow */ 942 { 943 if (r_is_one) 944 { 945 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 946 r_is_one = 0; 947 } 948 else 949 { 950 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 951 } 952 next_w = a; 953 } 954 w = next_w; 955 } 956 } 957 958 /* Finally, set r:=r*w. */ 959 if (w != 1) 960 { 961 if (r_is_one) 962 { 963 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 964 r_is_one = 0; 965 } 966 else 967 { 968 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 969 } 970 } 971 972 if (r_is_one) /* can happen only if a == 1*/ 973 { 974 if (!BN_one(rr)) goto err; 975 } 976 else 977 { 978 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err; 979 } 980 ret = 1; 981err: 982 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); 983 BN_CTX_end(ctx); 984 bn_check_top(rr); 985 return(ret); 986 } 987 988 989/* The old fallback, simple version :-) */ 990int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 991 const BIGNUM *m, BN_CTX *ctx) 992 { 993 int i,j,bits,ret=0,wstart,wend,window,wvalue; 994 int start=1; 995 BIGNUM *d; 996 /* Table of variables obtained from 'ctx' */ 997 BIGNUM *val[TABLE_SIZE]; 998 999 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 1000 { 1001 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1002 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1003 return -1; 1004 } 1005 1006 bits=BN_num_bits(p); 1007 1008 if (bits == 0) 1009 { 1010 ret = BN_one(r); 1011 return ret; 1012 } 1013 1014 BN_CTX_start(ctx); 1015 d = BN_CTX_get(ctx); 1016 val[0] = BN_CTX_get(ctx); 1017 if(!d || !val[0]) goto err; 1018 1019 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ 1020 if (BN_is_zero(val[0])) 1021 { 1022 BN_zero(r); 1023 ret = 1; 1024 goto err; 1025 } 1026 1027 window = BN_window_bits_for_exponent_size(bits); 1028 if (window > 1) 1029 { 1030 if (!BN_mod_mul(d,val[0],val[0],m,ctx)) 1031 goto err; /* 2 */ 1032 j=1<<(window-1); 1033 for (i=1; i<j; i++) 1034 { 1035 if(((val[i] = BN_CTX_get(ctx)) == NULL) || 1036 !BN_mod_mul(val[i],val[i-1],d,m,ctx)) 1037 goto err; 1038 } 1039 } 1040 1041 start=1; /* This is used to avoid multiplication etc 1042 * when there is only the value '1' in the 1043 * buffer. */ 1044 wvalue=0; /* The 'value' of the window */ 1045 wstart=bits-1; /* The top bit of the window */ 1046 wend=0; /* The bottom bit of the window */ 1047 1048 if (!BN_one(r)) goto err; 1049 1050 for (;;) 1051 { 1052 if (BN_is_bit_set(p,wstart) == 0) 1053 { 1054 if (!start) 1055 if (!BN_mod_mul(r,r,r,m,ctx)) 1056 goto err; 1057 if (wstart == 0) break; 1058 wstart--; 1059 continue; 1060 } 1061 /* We now have wstart on a 'set' bit, we now need to work out 1062 * how bit a window to do. To do this we need to scan 1063 * forward until the last set bit before the end of the 1064 * window */ 1065 j=wstart; 1066 wvalue=1; 1067 wend=0; 1068 for (i=1; i<window; i++) 1069 { 1070 if (wstart-i < 0) break; 1071 if (BN_is_bit_set(p,wstart-i)) 1072 { 1073 wvalue<<=(i-wend); 1074 wvalue|=1; 1075 wend=i; 1076 } 1077 } 1078 1079 /* wend is the size of the current window */ 1080 j=wend+1; 1081 /* add the 'bytes above' */ 1082 if (!start) 1083 for (i=0; i<j; i++) 1084 { 1085 if (!BN_mod_mul(r,r,r,m,ctx)) 1086 goto err; 1087 } 1088 1089 /* wvalue will be an odd number < 2^window */ 1090 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx)) 1091 goto err; 1092 1093 /* move the 'window' down further */ 1094 wstart-=wend+1; 1095 wvalue=0; 1096 start=0; 1097 if (wstart < 0) break; 1098 } 1099 ret=1; 1100err: 1101 BN_CTX_end(ctx); 1102 bn_check_top(r); 1103 return(ret); 1104 } 1105