1 /* crypto/bn/bn_exp.c */ 2 /* Copyright (C) 1995-1998 Eric Young (eay (at) cryptsoft.com) 3 * All rights reserved. 4 * 5 * This package is an SSL implementation written 6 * by Eric Young (eay (at) 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 (at) 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 (at) 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 (at) 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 (at) 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 (at) cryptsoft.com). This product includes software written by Tim 108 * Hudson (tjh (at) 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 */ 120 int 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_CONSTTIME) != 0) 126 { 127 /* BN_FLG_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 v = BN_CTX_get(ctx); 138 if (rr == NULL || v == NULL) goto err; 139 140 if (BN_copy(v,a) == NULL) goto err; 141 bits=BN_num_bits(p); 142 143 if (BN_is_odd(p)) 144 { if (BN_copy(rr,a) == NULL) goto err; } 145 else { if (!BN_one(rr)) goto err; } 146 147 for (i=1; i<bits; i++) 148 { 149 if (!BN_sqr(v,v,ctx)) goto err; 150 if (BN_is_bit_set(p,i)) 151 { 152 if (!BN_mul(rr,rr,v,ctx)) goto err; 153 } 154 } 155 ret=1; 156 err: 157 if (r != rr) BN_copy(r,rr); 158 BN_CTX_end(ctx); 159 bn_check_top(r); 160 return(ret); 161 } 162 163 164 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 165 BN_CTX *ctx) 166 { 167 int ret; 168 169 bn_check_top(a); 170 bn_check_top(p); 171 bn_check_top(m); 172 173 /* For even modulus m = 2^k*m_odd, it might make sense to compute 174 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 175 * exponentiation for the odd part), using appropriate exponent 176 * reductions, and combine the results using the CRT. 177 * 178 * For now, we use Montgomery only if the modulus is odd; otherwise, 179 * exponentiation using the reciprocal-based quick remaindering 180 * algorithm is used. 181 * 182 * (Timing obtained with expspeed.c [computations a^p mod m 183 * where a, p, m are of the same length: 256, 512, 1024, 2048, 184 * 4096, 8192 bits], compared to the running time of the 185 * standard algorithm: 186 * 187 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 188 * 55 .. 77 % [UltraSparc processor, but 189 * debug-solaris-sparcv8-gcc conf.] 190 * 191 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 192 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 193 * 194 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 195 * at 2048 and more bits, but at 512 and 1024 bits, it was 196 * slower even than the standard algorithm! 197 * 198 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 199 * should be obtained when the new Montgomery reduction code 200 * has been integrated into OpenSSL.) 201 */ 202 203 #define MONT_MUL_MOD 204 #define MONT_EXP_WORD 205 #define RECP_MUL_MOD 206 207 #ifdef MONT_MUL_MOD 208 /* I have finally been able to take out this pre-condition of 209 * the top bit being set. It was caused by an error in BN_div 210 * with negatives. There was also another problem when for a^b%m 211 * a >= m. eay 07-May-97 */ 212 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ 213 214 if (BN_is_odd(m)) 215 { 216 # ifdef MONT_EXP_WORD 217 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) 218 { 219 BN_ULONG A = a->d[0]; 220 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL); 221 } 222 else 223 # endif 224 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); 225 } 226 else 227 #endif 228 #ifdef RECP_MUL_MOD 229 { ret=BN_mod_exp_recp(r,a,p,m,ctx); } 230 #else 231 { ret=BN_mod_exp_simple(r,a,p,m,ctx); } 232 #endif 233 234 bn_check_top(r); 235 return(ret); 236 } 237 238 239 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 240 const BIGNUM *m, BN_CTX *ctx) 241 { 242 int i,j,bits,ret=0,wstart,wend,window,wvalue; 243 int start=1; 244 BIGNUM *aa; 245 /* Table of variables obtained from 'ctx' */ 246 BIGNUM *val[TABLE_SIZE]; 247 BN_RECP_CTX recp; 248 249 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 250 { 251 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 252 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 253 return -1; 254 } 255 256 bits=BN_num_bits(p); 257 258 if (bits == 0) 259 { 260 ret = BN_one(r); 261 return ret; 262 } 263 264 BN_CTX_start(ctx); 265 aa = BN_CTX_get(ctx); 266 val[0] = BN_CTX_get(ctx); 267 if(!aa || !val[0]) goto err; 268 269 BN_RECP_CTX_init(&recp); 270 if (m->neg) 271 { 272 /* ignore sign of 'm' */ 273 if (!BN_copy(aa, m)) goto err; 274 aa->neg = 0; 275 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err; 276 } 277 else 278 { 279 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err; 280 } 281 282 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ 283 if (BN_is_zero(val[0])) 284 { 285 BN_zero(r); 286 ret = 1; 287 goto err; 288 } 289 290 window = BN_window_bits_for_exponent_size(bits); 291 if (window > 1) 292 { 293 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx)) 294 goto err; /* 2 */ 295 j=1<<(window-1); 296 for (i=1; i<j; i++) 297 { 298 if(((val[i] = BN_CTX_get(ctx)) == NULL) || 299 !BN_mod_mul_reciprocal(val[i],val[i-1], 300 aa,&recp,ctx)) 301 goto err; 302 } 303 } 304 305 start=1; /* This is used to avoid multiplication etc 306 * when there is only the value '1' in the 307 * buffer. */ 308 wvalue=0; /* The 'value' of the window */ 309 wstart=bits-1; /* The top bit of the window */ 310 wend=0; /* The bottom bit of the window */ 311 312 if (!BN_one(r)) goto err; 313 314 for (;;) 315 { 316 if (BN_is_bit_set(p,wstart) == 0) 317 { 318 if (!start) 319 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) 320 goto err; 321 if (wstart == 0) break; 322 wstart--; 323 continue; 324 } 325 /* We now have wstart on a 'set' bit, we now need to work out 326 * how bit a window to do. To do this we need to scan 327 * forward until the last set bit before the end of the 328 * window */ 329 j=wstart; 330 wvalue=1; 331 wend=0; 332 for (i=1; i<window; i++) 333 { 334 if (wstart-i < 0) break; 335 if (BN_is_bit_set(p,wstart-i)) 336 { 337 wvalue<<=(i-wend); 338 wvalue|=1; 339 wend=i; 340 } 341 } 342 343 /* wend is the size of the current window */ 344 j=wend+1; 345 /* add the 'bytes above' */ 346 if (!start) 347 for (i=0; i<j; i++) 348 { 349 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) 350 goto err; 351 } 352 353 /* wvalue will be an odd number < 2^window */ 354 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx)) 355 goto err; 356 357 /* move the 'window' down further */ 358 wstart-=wend+1; 359 wvalue=0; 360 start=0; 361 if (wstart < 0) break; 362 } 363 ret=1; 364 err: 365 BN_CTX_end(ctx); 366 BN_RECP_CTX_free(&recp); 367 bn_check_top(r); 368 return(ret); 369 } 370 371 372 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 373 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 374 { 375 int i,j,bits,ret=0,wstart,wend,window,wvalue; 376 int start=1; 377 BIGNUM *d,*r; 378 const BIGNUM *aa; 379 /* Table of variables obtained from 'ctx' */ 380 BIGNUM *val[TABLE_SIZE]; 381 BN_MONT_CTX *mont=NULL; 382 383 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 384 { 385 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 386 } 387 388 bn_check_top(a); 389 bn_check_top(p); 390 bn_check_top(m); 391 392 if (!BN_is_odd(m)) 393 { 394 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS); 395 return(0); 396 } 397 bits=BN_num_bits(p); 398 if (bits == 0) 399 { 400 ret = BN_one(rr); 401 return ret; 402 } 403 404 BN_CTX_start(ctx); 405 d = BN_CTX_get(ctx); 406 r = BN_CTX_get(ctx); 407 val[0] = BN_CTX_get(ctx); 408 if (!d || !r || !val[0]) goto err; 409 410 /* If this is not done, things will break in the montgomery 411 * part */ 412 413 if (in_mont != NULL) 414 mont=in_mont; 415 else 416 { 417 if ((mont=BN_MONT_CTX_new()) == NULL) goto err; 418 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; 419 } 420 421 if (a->neg || BN_ucmp(a,m) >= 0) 422 { 423 if (!BN_nnmod(val[0],a,m,ctx)) 424 goto err; 425 aa= val[0]; 426 } 427 else 428 aa=a; 429 if (BN_is_zero(aa)) 430 { 431 BN_zero(rr); 432 ret = 1; 433 goto err; 434 } 435 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */ 436 437 window = BN_window_bits_for_exponent_size(bits); 438 if (window > 1) 439 { 440 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */ 441 j=1<<(window-1); 442 for (i=1; i<j; i++) 443 { 444 if(((val[i] = BN_CTX_get(ctx)) == NULL) || 445 !BN_mod_mul_montgomery(val[i],val[i-1], 446 d,mont,ctx)) 447 goto err; 448 } 449 } 450 451 start=1; /* This is used to avoid multiplication etc 452 * when there is only the value '1' in the 453 * buffer. */ 454 wvalue=0; /* The 'value' of the window */ 455 wstart=bits-1; /* The top bit of the window */ 456 wend=0; /* The bottom bit of the window */ 457 458 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err; 459 for (;;) 460 { 461 if (BN_is_bit_set(p,wstart) == 0) 462 { 463 if (!start) 464 { 465 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) 466 goto err; 467 } 468 if (wstart == 0) break; 469 wstart--; 470 continue; 471 } 472 /* We now have wstart on a 'set' bit, we now need to work out 473 * how bit a window to do. To do this we need to scan 474 * forward until the last set bit before the end of the 475 * window */ 476 j=wstart; 477 wvalue=1; 478 wend=0; 479 for (i=1; i<window; i++) 480 { 481 if (wstart-i < 0) break; 482 if (BN_is_bit_set(p,wstart-i)) 483 { 484 wvalue<<=(i-wend); 485 wvalue|=1; 486 wend=i; 487 } 488 } 489 490 /* wend is the size of the current window */ 491 j=wend+1; 492 /* add the 'bytes above' */ 493 if (!start) 494 for (i=0; i<j; i++) 495 { 496 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) 497 goto err; 498 } 499 500 /* wvalue will be an odd number < 2^window */ 501 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx)) 502 goto err; 503 504 /* move the 'window' down further */ 505 wstart-=wend+1; 506 wvalue=0; 507 start=0; 508 if (wstart < 0) break; 509 } 510 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err; 511 ret=1; 512 err: 513 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); 514 BN_CTX_end(ctx); 515 bn_check_top(rr); 516 return(ret); 517 } 518 519 520 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout 521 * so that accessing any of these table values shows the same access pattern as far 522 * as cache lines are concerned. The following functions are used to transfer a BIGNUM 523 * from/to that table. */ 524 525 static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width) 526 { 527 size_t i, j; 528 529 if (bn_wexpand(b, top) == NULL) 530 return 0; 531 while (b->top < top) 532 { 533 b->d[b->top++] = 0; 534 } 535 536 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width) 537 { 538 buf[j] = ((unsigned char*)b->d)[i]; 539 } 540 541 bn_correct_top(b); 542 return 1; 543 } 544 545 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width) 546 { 547 size_t i, j; 548 549 if (bn_wexpand(b, top) == NULL) 550 return 0; 551 552 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width) 553 { 554 ((unsigned char*)b->d)[i] = buf[j]; 555 } 556 557 b->top = top; 558 bn_correct_top(b); 559 return 1; 560 } 561 562 /* Given a pointer value, compute the next address that is a cache line multiple. */ 563 #define MOD_EXP_CTIME_ALIGN(x_) \ 564 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 565 566 /* This variant of BN_mod_exp_mont() uses fixed windows and the special 567 * precomputation memory layout to limit data-dependency to a minimum 568 * to protect secret exponents (cf. the hyper-threading timing attacks 569 * pointed out by Colin Percival, 570 * http://www.daemonology.net/hyperthreading-considered-harmful/) 571 */ 572 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 573 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 574 { 575 int i,bits,ret=0,idx,window,wvalue; 576 int top; 577 BIGNUM *r; 578 const BIGNUM *aa; 579 BN_MONT_CTX *mont=NULL; 580 581 int numPowers; 582 unsigned char *powerbufFree=NULL; 583 int powerbufLen = 0; 584 unsigned char *powerbuf=NULL; 585 BIGNUM *computeTemp=NULL, *am=NULL; 586 587 bn_check_top(a); 588 bn_check_top(p); 589 bn_check_top(m); 590 591 top = m->top; 592 593 if (!(m->d[0] & 1)) 594 { 595 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS); 596 return(0); 597 } 598 bits=BN_num_bits(p); 599 if (bits == 0) 600 { 601 ret = BN_one(rr); 602 return ret; 603 } 604 605 /* Initialize BIGNUM context and allocate intermediate result */ 606 BN_CTX_start(ctx); 607 r = BN_CTX_get(ctx); 608 if (r == NULL) goto err; 609 610 /* Allocate a montgomery context if it was not supplied by the caller. 611 * If this is not done, things will break in the montgomery part. 612 */ 613 if (in_mont != NULL) 614 mont=in_mont; 615 else 616 { 617 if ((mont=BN_MONT_CTX_new()) == NULL) goto err; 618 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; 619 } 620 621 /* Get the window size to use with size of p. */ 622 window = BN_window_bits_for_ctime_exponent_size(bits); 623 624 /* Allocate a buffer large enough to hold all of the pre-computed 625 * powers of a. 626 */ 627 numPowers = 1 << window; 628 powerbufLen = sizeof(m->d[0])*top*numPowers; 629 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL) 630 goto err; 631 632 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 633 memset(powerbuf, 0, powerbufLen); 634 635 /* Initialize the intermediate result. Do this early to save double conversion, 636 * once each for a^0 and intermediate result. 637 */ 638 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err; 639 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err; 640 641 /* Initialize computeTemp as a^1 with montgomery precalcs */ 642 computeTemp = BN_CTX_get(ctx); 643 am = BN_CTX_get(ctx); 644 if (computeTemp==NULL || am==NULL) goto err; 645 646 if (a->neg || BN_ucmp(a,m) >= 0) 647 { 648 if (!BN_mod(am,a,m,ctx)) 649 goto err; 650 aa= am; 651 } 652 else 653 aa=a; 654 if (!BN_to_montgomery(am,aa,mont,ctx)) goto err; 655 if (!BN_copy(computeTemp, am)) goto err; 656 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err; 657 658 /* If the window size is greater than 1, then calculate 659 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) 660 * (even powers could instead be computed as (a^(i/2))^2 661 * to use the slight performance advantage of sqr over mul). 662 */ 663 if (window > 1) 664 { 665 for (i=2; i<numPowers; i++) 666 { 667 /* Calculate a^i = a^(i-1) * a */ 668 if (!BN_mod_mul_montgomery(computeTemp,am,computeTemp,mont,ctx)) 669 goto err; 670 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, numPowers)) goto err; 671 } 672 } 673 674 /* Adjust the number of bits up to a multiple of the window size. 675 * If the exponent length is not a multiple of the window size, then 676 * this pads the most significant bits with zeros to normalize the 677 * scanning loop to there's no special cases. 678 * 679 * * NOTE: Making the window size a power of two less than the native 680 * * word size ensures that the padded bits won't go past the last 681 * * word in the internal BIGNUM structure. Going past the end will 682 * * still produce the correct result, but causes a different branch 683 * * to be taken in the BN_is_bit_set function. 684 */ 685 bits = ((bits+window-1)/window)*window; 686 idx=bits-1; /* The top bit of the window */ 687 688 /* Scan the exponent one window at a time starting from the most 689 * significant bits. 690 */ 691 while (idx >= 0) 692 { 693 wvalue=0; /* The 'value' of the window */ 694 695 /* Scan the window, squaring the result as we go */ 696 for (i=0; i<window; i++,idx--) 697 { 698 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) goto err; 699 wvalue = (wvalue<<1)+BN_is_bit_set(p,idx); 700 } 701 702 /* Fetch the appropriate pre-computed value from the pre-buf */ 703 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(computeTemp, top, powerbuf, wvalue, numPowers)) goto err; 704 705 /* Multiply the result into the intermediate result */ 706 if (!BN_mod_mul_montgomery(r,r,computeTemp,mont,ctx)) goto err; 707 } 708 709 /* Convert the final result from montgomery to standard format */ 710 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err; 711 ret=1; 712 err: 713 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); 714 if (powerbuf!=NULL) 715 { 716 OPENSSL_cleanse(powerbuf,powerbufLen); 717 OPENSSL_free(powerbufFree); 718 } 719 if (am!=NULL) BN_clear(am); 720 if (computeTemp!=NULL) BN_clear(computeTemp); 721 BN_CTX_end(ctx); 722 return(ret); 723 } 724 725 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 726 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 727 { 728 BN_MONT_CTX *mont = NULL; 729 int b, bits, ret=0; 730 int r_is_one; 731 BN_ULONG w, next_w; 732 BIGNUM *d, *r, *t; 733 BIGNUM *swap_tmp; 734 #define BN_MOD_MUL_WORD(r, w, m) \ 735 (BN_mul_word(r, (w)) && \ 736 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 737 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 738 /* BN_MOD_MUL_WORD is only used with 'w' large, 739 * so the BN_ucmp test is probably more overhead 740 * than always using BN_mod (which uses BN_copy if 741 * a similar test returns true). */ 742 /* We can use BN_mod and do not need BN_nnmod because our 743 * accumulator is never negative (the result of BN_mod does 744 * not depend on the sign of the modulus). 745 */ 746 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 747 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 748 749 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 750 { 751 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 752 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 753 return -1; 754 } 755 756 bn_check_top(p); 757 bn_check_top(m); 758 759 if (!BN_is_odd(m)) 760 { 761 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS); 762 return(0); 763 } 764 if (m->top == 1) 765 a %= m->d[0]; /* make sure that 'a' is reduced */ 766 767 bits = BN_num_bits(p); 768 if (bits == 0) 769 { 770 ret = BN_one(rr); 771 return ret; 772 } 773 if (a == 0) 774 { 775 BN_zero(rr); 776 ret = 1; 777 return ret; 778 } 779 780 BN_CTX_start(ctx); 781 d = BN_CTX_get(ctx); 782 r = BN_CTX_get(ctx); 783 t = BN_CTX_get(ctx); 784 if (d == NULL || r == NULL || t == NULL) goto err; 785 786 if (in_mont != NULL) 787 mont=in_mont; 788 else 789 { 790 if ((mont = BN_MONT_CTX_new()) == NULL) goto err; 791 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; 792 } 793 794 r_is_one = 1; /* except for Montgomery factor */ 795 796 /* bits-1 >= 0 */ 797 798 /* The result is accumulated in the product r*w. */ 799 w = a; /* bit 'bits-1' of 'p' is always set */ 800 for (b = bits-2; b >= 0; b--) 801 { 802 /* First, square r*w. */ 803 next_w = w*w; 804 if ((next_w/w) != w) /* overflow */ 805 { 806 if (r_is_one) 807 { 808 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 809 r_is_one = 0; 810 } 811 else 812 { 813 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 814 } 815 next_w = 1; 816 } 817 w = next_w; 818 if (!r_is_one) 819 { 820 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err; 821 } 822 823 /* Second, multiply r*w by 'a' if exponent bit is set. */ 824 if (BN_is_bit_set(p, b)) 825 { 826 next_w = w*a; 827 if ((next_w/a) != w) /* overflow */ 828 { 829 if (r_is_one) 830 { 831 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 832 r_is_one = 0; 833 } 834 else 835 { 836 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 837 } 838 next_w = a; 839 } 840 w = next_w; 841 } 842 } 843 844 /* Finally, set r:=r*w. */ 845 if (w != 1) 846 { 847 if (r_is_one) 848 { 849 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 850 r_is_one = 0; 851 } 852 else 853 { 854 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 855 } 856 } 857 858 if (r_is_one) /* can happen only if a == 1*/ 859 { 860 if (!BN_one(rr)) goto err; 861 } 862 else 863 { 864 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err; 865 } 866 ret = 1; 867 err: 868 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); 869 BN_CTX_end(ctx); 870 bn_check_top(rr); 871 return(ret); 872 } 873 874 875 /* The old fallback, simple version :-) */ 876 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 877 const BIGNUM *m, BN_CTX *ctx) 878 { 879 int i,j,bits,ret=0,wstart,wend,window,wvalue; 880 int start=1; 881 BIGNUM *d; 882 /* Table of variables obtained from 'ctx' */ 883 BIGNUM *val[TABLE_SIZE]; 884 885 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) 886 { 887 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 888 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 889 return -1; 890 } 891 892 bits=BN_num_bits(p); 893 894 if (bits == 0) 895 { 896 ret = BN_one(r); 897 return ret; 898 } 899 900 BN_CTX_start(ctx); 901 d = BN_CTX_get(ctx); 902 val[0] = BN_CTX_get(ctx); 903 if(!d || !val[0]) goto err; 904 905 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ 906 if (BN_is_zero(val[0])) 907 { 908 BN_zero(r); 909 ret = 1; 910 goto err; 911 } 912 913 window = BN_window_bits_for_exponent_size(bits); 914 if (window > 1) 915 { 916 if (!BN_mod_mul(d,val[0],val[0],m,ctx)) 917 goto err; /* 2 */ 918 j=1<<(window-1); 919 for (i=1; i<j; i++) 920 { 921 if(((val[i] = BN_CTX_get(ctx)) == NULL) || 922 !BN_mod_mul(val[i],val[i-1],d,m,ctx)) 923 goto err; 924 } 925 } 926 927 start=1; /* This is used to avoid multiplication etc 928 * when there is only the value '1' in the 929 * buffer. */ 930 wvalue=0; /* The 'value' of the window */ 931 wstart=bits-1; /* The top bit of the window */ 932 wend=0; /* The bottom bit of the window */ 933 934 if (!BN_one(r)) goto err; 935 936 for (;;) 937 { 938 if (BN_is_bit_set(p,wstart) == 0) 939 { 940 if (!start) 941 if (!BN_mod_mul(r,r,r,m,ctx)) 942 goto err; 943 if (wstart == 0) break; 944 wstart--; 945 continue; 946 } 947 /* We now have wstart on a 'set' bit, we now need to work out 948 * how bit a window to do. To do this we need to scan 949 * forward until the last set bit before the end of the 950 * window */ 951 j=wstart; 952 wvalue=1; 953 wend=0; 954 for (i=1; i<window; i++) 955 { 956 if (wstart-i < 0) break; 957 if (BN_is_bit_set(p,wstart-i)) 958 { 959 wvalue<<=(i-wend); 960 wvalue|=1; 961 wend=i; 962 } 963 } 964 965 /* wend is the size of the current window */ 966 j=wend+1; 967 /* add the 'bytes above' */ 968 if (!start) 969 for (i=0; i<j; i++) 970 { 971 if (!BN_mod_mul(r,r,r,m,ctx)) 972 goto err; 973 } 974 975 /* wvalue will be an odd number < 2^window */ 976 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx)) 977 goto err; 978 979 /* move the 'window' down further */ 980 wstart-=wend+1; 981 wvalue=0; 982 start=0; 983 if (wstart < 0) break; 984 } 985 ret=1; 986 err: 987 BN_CTX_end(ctx); 988 bn_check_top(r); 989 return(ret); 990 } 991 992
