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) 1998-2000 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#define TABLE_SIZE 32 117 118/* this one works - simple but works */ 119int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) 120 { 121 int i,bits,ret=0; 122 BIGNUM *v,*rr; 123 124 BN_CTX_start(ctx); 125 if ((r == a) || (r == p)) 126 rr = BN_CTX_get(ctx); 127 else 128 rr = r; 129 if ((v = BN_CTX_get(ctx)) == NULL) goto err; 130 131 if (BN_copy(v,a) == NULL) goto err; 132 bits=BN_num_bits(p); 133 134 if (BN_is_odd(p)) 135 { if (BN_copy(rr,a) == NULL) goto err; } 136 else { if (!BN_one(rr)) goto err; } 137 138 for (i=1; i<bits; i++) 139 { 140 if (!BN_sqr(v,v,ctx)) goto err; 141 if (BN_is_bit_set(p,i)) 142 { 143 if (!BN_mul(rr,rr,v,ctx)) goto err; 144 } 145 } 146 ret=1; 147err: 148 if (r != rr) BN_copy(r,rr); 149 BN_CTX_end(ctx); 150 return(ret); 151 } 152 153 154int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 155 BN_CTX *ctx) 156 { 157 int ret; 158 159 bn_check_top(a); 160 bn_check_top(p); 161 bn_check_top(m); 162 163 /* For even modulus m = 2^k*m_odd, it might make sense to compute 164 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 165 * exponentiation for the odd part), using appropriate exponent 166 * reductions, and combine the results using the CRT. 167 * 168 * For now, we use Montgomery only if the modulus is odd; otherwise, 169 * exponentiation using the reciprocal-based quick remaindering 170 * algorithm is used. 171 * 172 * (Timing obtained with expspeed.c [computations a^p mod m 173 * where a, p, m are of the same length: 256, 512, 1024, 2048, 174 * 4096, 8192 bits], compared to the running time of the 175 * standard algorithm: 176 * 177 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 178 * 55 .. 77 % [UltraSparc processor, but 179 * debug-solaris-sparcv8-gcc conf.] 180 * 181 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 182 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 183 * 184 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 185 * at 2048 and more bits, but at 512 and 1024 bits, it was 186 * slower even than the standard algorithm! 187 * 188 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 189 * should be obtained when the new Montgomery reduction code 190 * has been integrated into OpenSSL.) 191 */ 192 193#define MONT_MUL_MOD 194#define MONT_EXP_WORD 195#define RECP_MUL_MOD 196 197#ifdef MONT_MUL_MOD 198 /* I have finally been able to take out this pre-condition of 199 * the top bit being set. It was caused by an error in BN_div 200 * with negatives. There was also another problem when for a^b%m 201 * a >= m. eay 07-May-97 */ 202/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ 203 204 if (BN_is_odd(m)) 205 { 206# ifdef MONT_EXP_WORD 207 if (a->top == 1 && !a->neg) 208 { 209 BN_ULONG A = a->d[0]; 210 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL); 211 } 212 else 213# endif 214 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); 215 } 216 else 217#endif 218#ifdef RECP_MUL_MOD 219 { ret=BN_mod_exp_recp(r,a,p,m,ctx); } 220#else 221 { ret=BN_mod_exp_simple(r,a,p,m,ctx); } 222#endif 223 224 return(ret); 225 } 226 227 228int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 229 const BIGNUM *m, BN_CTX *ctx) 230 { 231 int i,j,bits,ret=0,wstart,wend,window,wvalue; 232 int start=1,ts=0; 233 BIGNUM *aa; 234 BIGNUM val[TABLE_SIZE]; 235 BN_RECP_CTX recp; 236 237 bits=BN_num_bits(p); 238 239 if (bits == 0) 240 { 241 ret = BN_one(r); 242 return ret; 243 } 244 245 BN_CTX_start(ctx); 246 if ((aa = BN_CTX_get(ctx)) == NULL) goto err; 247 248 BN_RECP_CTX_init(&recp); 249 if (m->neg) 250 { 251 /* ignore sign of 'm' */ 252 if (!BN_copy(aa, m)) goto err; 253 aa->neg = 0; 254 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err; 255 } 256 else 257 { 258 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err; 259 } 260 261 BN_init(&(val[0])); 262 ts=1; 263 264 if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */ 265 if (BN_is_zero(&(val[0]))) 266 { 267 ret = BN_zero(r); 268 goto err; 269 } 270 271 window = BN_window_bits_for_exponent_size(bits); 272 if (window > 1) 273 { 274 if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx)) 275 goto err; /* 2 */ 276 j=1<<(window-1); 277 for (i=1; i<j; i++) 278 { 279 BN_init(&val[i]); 280 if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx)) 281 goto err; 282 } 283 ts=i; 284 } 285 286 start=1; /* This is used to avoid multiplication etc 287 * when there is only the value '1' in the 288 * buffer. */ 289 wvalue=0; /* The 'value' of the window */ 290 wstart=bits-1; /* The top bit of the window */ 291 wend=0; /* The bottom bit of the window */ 292 293 if (!BN_one(r)) goto err; 294 295 for (;;) 296 { 297 if (BN_is_bit_set(p,wstart) == 0) 298 { 299 if (!start) 300 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) 301 goto err; 302 if (wstart == 0) break; 303 wstart--; 304 continue; 305 } 306 /* We now have wstart on a 'set' bit, we now need to work out 307 * how bit a window to do. To do this we need to scan 308 * forward until the last set bit before the end of the 309 * window */ 310 j=wstart; 311 wvalue=1; 312 wend=0; 313 for (i=1; i<window; i++) 314 { 315 if (wstart-i < 0) break; 316 if (BN_is_bit_set(p,wstart-i)) 317 { 318 wvalue<<=(i-wend); 319 wvalue|=1; 320 wend=i; 321 } 322 } 323 324 /* wend is the size of the current window */ 325 j=wend+1; 326 /* add the 'bytes above' */ 327 if (!start) 328 for (i=0; i<j; i++) 329 { 330 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) 331 goto err; 332 } 333 334 /* wvalue will be an odd number < 2^window */ 335 if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx)) 336 goto err; 337 338 /* move the 'window' down further */ 339 wstart-=wend+1; 340 wvalue=0; 341 start=0; 342 if (wstart < 0) break; 343 } 344 ret=1; 345err: 346 BN_CTX_end(ctx); 347 for (i=0; i<ts; i++) 348 BN_clear_free(&(val[i])); 349 BN_RECP_CTX_free(&recp); 350 return(ret); 351 } 352 353 354int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 355 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 356 { 357 int i,j,bits,ret=0,wstart,wend,window,wvalue; 358 int start=1,ts=0; 359 BIGNUM *d,*r; 360 const BIGNUM *aa; 361 BIGNUM val[TABLE_SIZE]; 362 BN_MONT_CTX *mont=NULL; 363 364 bn_check_top(a); 365 bn_check_top(p); 366 bn_check_top(m); 367 368 if (!(m->d[0] & 1)) 369 { 370 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS); 371 return(0); 372 } 373 bits=BN_num_bits(p); 374 if (bits == 0) 375 { 376 ret = BN_one(rr); 377 return ret; 378 } 379 380 BN_CTX_start(ctx); 381 d = BN_CTX_get(ctx); 382 r = BN_CTX_get(ctx); 383 if (d == NULL || r == NULL) goto err; 384 385 /* If this is not done, things will break in the montgomery 386 * part */ 387 388 if (in_mont != NULL) 389 mont=in_mont; 390 else 391 { 392 if ((mont=BN_MONT_CTX_new()) == NULL) goto err; 393 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; 394 } 395 396 BN_init(&val[0]); 397 ts=1; 398 if (a->neg || BN_ucmp(a,m) >= 0) 399 { 400 if (!BN_nnmod(&(val[0]),a,m,ctx)) 401 goto err; 402 aa= &(val[0]); 403 } 404 else 405 aa=a; 406 if (BN_is_zero(aa)) 407 { 408 ret = BN_zero(rr); 409 goto err; 410 } 411 if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */ 412 413 window = BN_window_bits_for_exponent_size(bits); 414 if (window > 1) 415 { 416 if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */ 417 j=1<<(window-1); 418 for (i=1; i<j; i++) 419 { 420 BN_init(&(val[i])); 421 if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx)) 422 goto err; 423 } 424 ts=i; 425 } 426 427 start=1; /* This is used to avoid multiplication etc 428 * when there is only the value '1' in the 429 * buffer. */ 430 wvalue=0; /* The 'value' of the window */ 431 wstart=bits-1; /* The top bit of the window */ 432 wend=0; /* The bottom bit of the window */ 433 434 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err; 435 for (;;) 436 { 437 if (BN_is_bit_set(p,wstart) == 0) 438 { 439 if (!start) 440 { 441 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) 442 goto err; 443 } 444 if (wstart == 0) break; 445 wstart--; 446 continue; 447 } 448 /* We now have wstart on a 'set' bit, we now need to work out 449 * how bit a window to do. To do this we need to scan 450 * forward until the last set bit before the end of the 451 * window */ 452 j=wstart; 453 wvalue=1; 454 wend=0; 455 for (i=1; i<window; i++) 456 { 457 if (wstart-i < 0) break; 458 if (BN_is_bit_set(p,wstart-i)) 459 { 460 wvalue<<=(i-wend); 461 wvalue|=1; 462 wend=i; 463 } 464 } 465 466 /* wend is the size of the current window */ 467 j=wend+1; 468 /* add the 'bytes above' */ 469 if (!start) 470 for (i=0; i<j; i++) 471 { 472 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) 473 goto err; 474 } 475 476 /* wvalue will be an odd number < 2^window */ 477 if (!BN_mod_mul_montgomery(r,r,&(val[wvalue>>1]),mont,ctx)) 478 goto err; 479 480 /* move the 'window' down further */ 481 wstart-=wend+1; 482 wvalue=0; 483 start=0; 484 if (wstart < 0) break; 485 } 486 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err; 487 ret=1; 488err: 489 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); 490 BN_CTX_end(ctx); 491 for (i=0; i<ts; i++) 492 BN_clear_free(&(val[i])); 493 return(ret); 494 } 495 496int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 497 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 498 { 499 BN_MONT_CTX *mont = NULL; 500 int b, bits, ret=0; 501 int r_is_one; 502 BN_ULONG w, next_w; 503 BIGNUM *d, *r, *t; 504 BIGNUM *swap_tmp; 505#define BN_MOD_MUL_WORD(r, w, m) \ 506 (BN_mul_word(r, (w)) && \ 507 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 508 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 509 /* BN_MOD_MUL_WORD is only used with 'w' large, 510 * so the BN_ucmp test is probably more overhead 511 * than always using BN_mod (which uses BN_copy if 512 * a similar test returns true). */ 513 /* We can use BN_mod and do not need BN_nnmod because our 514 * accumulator is never negative (the result of BN_mod does 515 * not depend on the sign of the modulus). 516 */ 517#define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 518 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 519 520 bn_check_top(p); 521 bn_check_top(m); 522 523 if (m->top == 0 || !(m->d[0] & 1)) 524 { 525 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS); 526 return(0); 527 } 528 if (m->top == 1) 529 a %= m->d[0]; /* make sure that 'a' is reduced */ 530 531 bits = BN_num_bits(p); 532 if (bits == 0) 533 { 534 ret = BN_one(rr); 535 return ret; 536 } 537 if (a == 0) 538 { 539 ret = BN_zero(rr); 540 return ret; 541 } 542 543 BN_CTX_start(ctx); 544 d = BN_CTX_get(ctx); 545 r = BN_CTX_get(ctx); 546 t = BN_CTX_get(ctx); 547 if (d == NULL || r == NULL || t == NULL) goto err; 548 549 if (in_mont != NULL) 550 mont=in_mont; 551 else 552 { 553 if ((mont = BN_MONT_CTX_new()) == NULL) goto err; 554 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; 555 } 556 557 r_is_one = 1; /* except for Montgomery factor */ 558 559 /* bits-1 >= 0 */ 560 561 /* The result is accumulated in the product r*w. */ 562 w = a; /* bit 'bits-1' of 'p' is always set */ 563 for (b = bits-2; b >= 0; b--) 564 { 565 /* First, square r*w. */ 566 next_w = w*w; 567 if ((next_w/w) != w) /* overflow */ 568 { 569 if (r_is_one) 570 { 571 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 572 r_is_one = 0; 573 } 574 else 575 { 576 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 577 } 578 next_w = 1; 579 } 580 w = next_w; 581 if (!r_is_one) 582 { 583 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err; 584 } 585 586 /* Second, multiply r*w by 'a' if exponent bit is set. */ 587 if (BN_is_bit_set(p, b)) 588 { 589 next_w = w*a; 590 if ((next_w/a) != w) /* overflow */ 591 { 592 if (r_is_one) 593 { 594 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 595 r_is_one = 0; 596 } 597 else 598 { 599 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 600 } 601 next_w = a; 602 } 603 w = next_w; 604 } 605 } 606 607 /* Finally, set r:=r*w. */ 608 if (w != 1) 609 { 610 if (r_is_one) 611 { 612 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; 613 r_is_one = 0; 614 } 615 else 616 { 617 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; 618 } 619 } 620 621 if (r_is_one) /* can happen only if a == 1*/ 622 { 623 if (!BN_one(rr)) goto err; 624 } 625 else 626 { 627 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err; 628 } 629 ret = 1; 630err: 631 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); 632 BN_CTX_end(ctx); 633 return(ret); 634 } 635 636 637/* The old fallback, simple version :-) */ 638int BN_mod_exp_simple(BIGNUM *r, 639 const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 640 BN_CTX *ctx) 641 { 642 int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0; 643 int start=1; 644 BIGNUM *d; 645 BIGNUM val[TABLE_SIZE]; 646 647 bits=BN_num_bits(p); 648 649 if (bits == 0) 650 { 651 ret = BN_one(r); 652 return ret; 653 } 654 655 BN_CTX_start(ctx); 656 if ((d = BN_CTX_get(ctx)) == NULL) goto err; 657 658 BN_init(&(val[0])); 659 ts=1; 660 if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */ 661 if (BN_is_zero(&(val[0]))) 662 { 663 ret = BN_zero(r); 664 goto err; 665 } 666 667 window = BN_window_bits_for_exponent_size(bits); 668 if (window > 1) 669 { 670 if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx)) 671 goto err; /* 2 */ 672 j=1<<(window-1); 673 for (i=1; i<j; i++) 674 { 675 BN_init(&(val[i])); 676 if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx)) 677 goto err; 678 } 679 ts=i; 680 } 681 682 start=1; /* This is used to avoid multiplication etc 683 * when there is only the value '1' in the 684 * buffer. */ 685 wvalue=0; /* The 'value' of the window */ 686 wstart=bits-1; /* The top bit of the window */ 687 wend=0; /* The bottom bit of the window */ 688 689 if (!BN_one(r)) goto err; 690 691 for (;;) 692 { 693 if (BN_is_bit_set(p,wstart) == 0) 694 { 695 if (!start) 696 if (!BN_mod_mul(r,r,r,m,ctx)) 697 goto err; 698 if (wstart == 0) break; 699 wstart--; 700 continue; 701 } 702 /* We now have wstart on a 'set' bit, we now need to work out 703 * how bit a window to do. To do this we need to scan 704 * forward until the last set bit before the end of the 705 * window */ 706 j=wstart; 707 wvalue=1; 708 wend=0; 709 for (i=1; i<window; i++) 710 { 711 if (wstart-i < 0) break; 712 if (BN_is_bit_set(p,wstart-i)) 713 { 714 wvalue<<=(i-wend); 715 wvalue|=1; 716 wend=i; 717 } 718 } 719 720 /* wend is the size of the current window */ 721 j=wend+1; 722 /* add the 'bytes above' */ 723 if (!start) 724 for (i=0; i<j; i++) 725 { 726 if (!BN_mod_mul(r,r,r,m,ctx)) 727 goto err; 728 } 729 730 /* wvalue will be an odd number < 2^window */ 731 if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx)) 732 goto err; 733 734 /* move the 'window' down further */ 735 wstart-=wend+1; 736 wvalue=0; 737 start=0; 738 if (wstart < 0) break; 739 } 740 ret=1; 741err: 742 BN_CTX_end(ctx); 743 for (i=0; i<ts; i++) 744 BN_clear_free(&(val[i])); 745 return(ret); 746 } 747 748