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