1 /* $OpenBSD: bn_mul.c,v 1.20 2015/02/09 15:49:22 jsing Exp $ */ 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 #ifndef BN_DEBUG 60 # undef NDEBUG /* avoid conflicting definitions */ 61 # define NDEBUG 62 #endif 63 64 #include <assert.h> 65 #include <stdio.h> 66 #include <string.h> 67 68 #include <openssl/opensslconf.h> 69 70 #include "bn_lcl.h" 71 72 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS) 73 /* Here follows specialised variants of bn_add_words() and 74 bn_sub_words(). They have the property performing operations on 75 arrays of different sizes. The sizes of those arrays is expressed through 76 cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl, 77 which is the delta between the two lengths, calculated as len(a)-len(b). 78 All lengths are the number of BN_ULONGs... For the operations that require 79 a result array as parameter, it must have the length cl+abs(dl). 80 These functions should probably end up in bn_asm.c as soon as there are 81 assembler counterparts for the systems that use assembler files. */ 82 83 BN_ULONG 84 bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl, 85 int dl) 86 { 87 BN_ULONG c, t; 88 89 assert(cl >= 0); 90 c = bn_sub_words(r, a, b, cl); 91 92 if (dl == 0) 93 return c; 94 95 r += cl; 96 a += cl; 97 b += cl; 98 99 if (dl < 0) { 100 #ifdef BN_COUNT 101 fprintf(stderr, 102 " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", 103 cl, dl, c); 104 #endif 105 for (;;) { 106 t = b[0]; 107 r[0] = (0 - t - c) & BN_MASK2; 108 if (t != 0) 109 c = 1; 110 if (++dl >= 0) 111 break; 112 113 t = b[1]; 114 r[1] = (0 - t - c) & BN_MASK2; 115 if (t != 0) 116 c = 1; 117 if (++dl >= 0) 118 break; 119 120 t = b[2]; 121 r[2] = (0 - t - c) & BN_MASK2; 122 if (t != 0) 123 c = 1; 124 if (++dl >= 0) 125 break; 126 127 t = b[3]; 128 r[3] = (0 - t - c) & BN_MASK2; 129 if (t != 0) 130 c = 1; 131 if (++dl >= 0) 132 break; 133 134 b += 4; 135 r += 4; 136 } 137 } else { 138 int save_dl = dl; 139 #ifdef BN_COUNT 140 fprintf(stderr, 141 " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", 142 cl, dl, c); 143 #endif 144 while (c) { 145 t = a[0]; 146 r[0] = (t - c) & BN_MASK2; 147 if (t != 0) 148 c = 0; 149 if (--dl <= 0) 150 break; 151 152 t = a[1]; 153 r[1] = (t - c) & BN_MASK2; 154 if (t != 0) 155 c = 0; 156 if (--dl <= 0) 157 break; 158 159 t = a[2]; 160 r[2] = (t - c) & BN_MASK2; 161 if (t != 0) 162 c = 0; 163 if (--dl <= 0) 164 break; 165 166 t = a[3]; 167 r[3] = (t - c) & BN_MASK2; 168 if (t != 0) 169 c = 0; 170 if (--dl <= 0) 171 break; 172 173 save_dl = dl; 174 a += 4; 175 r += 4; 176 } 177 if (dl > 0) { 178 #ifdef BN_COUNT 179 fprintf(stderr, 180 " bn_sub_part_words %d + %d (dl > 0, c == 0)\n", 181 cl, dl); 182 #endif 183 if (save_dl > dl) { 184 switch (save_dl - dl) { 185 case 1: 186 r[1] = a[1]; 187 if (--dl <= 0) 188 break; 189 case 2: 190 r[2] = a[2]; 191 if (--dl <= 0) 192 break; 193 case 3: 194 r[3] = a[3]; 195 if (--dl <= 0) 196 break; 197 } 198 a += 4; 199 r += 4; 200 } 201 } 202 if (dl > 0) { 203 #ifdef BN_COUNT 204 fprintf(stderr, 205 " bn_sub_part_words %d + %d (dl > 0, copy)\n", 206 cl, dl); 207 #endif 208 for (;;) { 209 r[0] = a[0]; 210 if (--dl <= 0) 211 break; 212 r[1] = a[1]; 213 if (--dl <= 0) 214 break; 215 r[2] = a[2]; 216 if (--dl <= 0) 217 break; 218 r[3] = a[3]; 219 if (--dl <= 0) 220 break; 221 222 a += 4; 223 r += 4; 224 } 225 } 226 } 227 return c; 228 } 229 #endif 230 231 BN_ULONG 232 bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl, 233 int dl) 234 { 235 BN_ULONG c, l, t; 236 237 assert(cl >= 0); 238 c = bn_add_words(r, a, b, cl); 239 240 if (dl == 0) 241 return c; 242 243 r += cl; 244 a += cl; 245 b += cl; 246 247 if (dl < 0) { 248 int save_dl = dl; 249 #ifdef BN_COUNT 250 fprintf(stderr, 251 " bn_add_part_words %d + %d (dl < 0, c = %d)\n", 252 cl, dl, c); 253 #endif 254 while (c) { 255 l = (c + b[0]) & BN_MASK2; 256 c = (l < c); 257 r[0] = l; 258 if (++dl >= 0) 259 break; 260 261 l = (c + b[1]) & BN_MASK2; 262 c = (l < c); 263 r[1] = l; 264 if (++dl >= 0) 265 break; 266 267 l = (c + b[2]) & BN_MASK2; 268 c = (l < c); 269 r[2] = l; 270 if (++dl >= 0) 271 break; 272 273 l = (c + b[3]) & BN_MASK2; 274 c = (l < c); 275 r[3] = l; 276 if (++dl >= 0) 277 break; 278 279 save_dl = dl; 280 b += 4; 281 r += 4; 282 } 283 if (dl < 0) { 284 #ifdef BN_COUNT 285 fprintf(stderr, 286 " bn_add_part_words %d + %d (dl < 0, c == 0)\n", 287 cl, dl); 288 #endif 289 if (save_dl < dl) { 290 switch (dl - save_dl) { 291 case 1: 292 r[1] = b[1]; 293 if (++dl >= 0) 294 break; 295 case 2: 296 r[2] = b[2]; 297 if (++dl >= 0) 298 break; 299 case 3: 300 r[3] = b[3]; 301 if (++dl >= 0) 302 break; 303 } 304 b += 4; 305 r += 4; 306 } 307 } 308 if (dl < 0) { 309 #ifdef BN_COUNT 310 fprintf(stderr, 311 " bn_add_part_words %d + %d (dl < 0, copy)\n", 312 cl, dl); 313 #endif 314 for (;;) { 315 r[0] = b[0]; 316 if (++dl >= 0) 317 break; 318 r[1] = b[1]; 319 if (++dl >= 0) 320 break; 321 r[2] = b[2]; 322 if (++dl >= 0) 323 break; 324 r[3] = b[3]; 325 if (++dl >= 0) 326 break; 327 328 b += 4; 329 r += 4; 330 } 331 } 332 } else { 333 int save_dl = dl; 334 #ifdef BN_COUNT 335 fprintf(stderr, 336 " bn_add_part_words %d + %d (dl > 0)\n", cl, dl); 337 #endif 338 while (c) { 339 t = (a[0] + c) & BN_MASK2; 340 c = (t < c); 341 r[0] = t; 342 if (--dl <= 0) 343 break; 344 345 t = (a[1] + c) & BN_MASK2; 346 c = (t < c); 347 r[1] = t; 348 if (--dl <= 0) 349 break; 350 351 t = (a[2] + c) & BN_MASK2; 352 c = (t < c); 353 r[2] = t; 354 if (--dl <= 0) 355 break; 356 357 t = (a[3] + c) & BN_MASK2; 358 c = (t < c); 359 r[3] = t; 360 if (--dl <= 0) 361 break; 362 363 save_dl = dl; 364 a += 4; 365 r += 4; 366 } 367 #ifdef BN_COUNT 368 fprintf(stderr, 369 " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl); 370 #endif 371 if (dl > 0) { 372 if (save_dl > dl) { 373 switch (save_dl - dl) { 374 case 1: 375 r[1] = a[1]; 376 if (--dl <= 0) 377 break; 378 case 2: 379 r[2] = a[2]; 380 if (--dl <= 0) 381 break; 382 case 3: 383 r[3] = a[3]; 384 if (--dl <= 0) 385 break; 386 } 387 a += 4; 388 r += 4; 389 } 390 } 391 if (dl > 0) { 392 #ifdef BN_COUNT 393 fprintf(stderr, 394 " bn_add_part_words %d + %d (dl > 0, copy)\n", 395 cl, dl); 396 #endif 397 for (;;) { 398 r[0] = a[0]; 399 if (--dl <= 0) 400 break; 401 r[1] = a[1]; 402 if (--dl <= 0) 403 break; 404 r[2] = a[2]; 405 if (--dl <= 0) 406 break; 407 r[3] = a[3]; 408 if (--dl <= 0) 409 break; 410 411 a += 4; 412 r += 4; 413 } 414 } 415 } 416 return c; 417 } 418 419 #ifdef BN_RECURSION 420 /* Karatsuba recursive multiplication algorithm 421 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */ 422 423 /* r is 2*n2 words in size, 424 * a and b are both n2 words in size. 425 * n2 must be a power of 2. 426 * We multiply and return the result. 427 * t must be 2*n2 words in size 428 * We calculate 429 * a[0]*b[0] 430 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0]) 431 * a[1]*b[1] 432 */ 433 /* dnX may not be positive, but n2/2+dnX has to be */ 434 void 435 bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, int dna, 436 int dnb, BN_ULONG *t) 437 { 438 int n = n2 / 2, c1, c2; 439 int tna = n + dna, tnb = n + dnb; 440 unsigned int neg, zero; 441 BN_ULONG ln, lo, *p; 442 443 # ifdef BN_COUNT 444 fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb); 445 # endif 446 # ifdef BN_MUL_COMBA 447 # if 0 448 if (n2 == 4) { 449 bn_mul_comba4(r, a, b); 450 return; 451 } 452 # endif 453 /* Only call bn_mul_comba 8 if n2 == 8 and the 454 * two arrays are complete [steve] 455 */ 456 if (n2 == 8 && dna == 0 && dnb == 0) { 457 bn_mul_comba8(r, a, b); 458 return; 459 } 460 # endif /* BN_MUL_COMBA */ 461 /* Else do normal multiply */ 462 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) { 463 bn_mul_normal(r, a, n2 + dna, b, n2 + dnb); 464 if ((dna + dnb) < 0) 465 memset(&r[2*n2 + dna + dnb], 0, 466 sizeof(BN_ULONG) * -(dna + dnb)); 467 return; 468 } 469 /* r=(a[0]-a[1])*(b[1]-b[0]) */ 470 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna); 471 c2 = bn_cmp_part_words(&(b[n]), b,tnb, tnb - n); 472 zero = neg = 0; 473 switch (c1 * 3 + c2) { 474 case -4: 475 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ 476 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ 477 break; 478 case -3: 479 zero = 1; 480 break; 481 case -2: 482 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ 483 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */ 484 neg = 1; 485 break; 486 case -1: 487 case 0: 488 case 1: 489 zero = 1; 490 break; 491 case 2: 492 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */ 493 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ 494 neg = 1; 495 break; 496 case 3: 497 zero = 1; 498 break; 499 case 4: 500 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); 501 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); 502 break; 503 } 504 505 # ifdef BN_MUL_COMBA 506 if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take 507 extra args to do this well */ 508 { 509 if (!zero) 510 bn_mul_comba4(&(t[n2]), t, &(t[n])); 511 else 512 memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG)); 513 514 bn_mul_comba4(r, a, b); 515 bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n])); 516 } else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could 517 take extra args to do this 518 well */ 519 { 520 if (!zero) 521 bn_mul_comba8(&(t[n2]), t, &(t[n])); 522 else 523 memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG)); 524 525 bn_mul_comba8(r, a, b); 526 bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n])); 527 } else 528 # endif /* BN_MUL_COMBA */ 529 { 530 p = &(t[n2 * 2]); 531 if (!zero) 532 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); 533 else 534 memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG)); 535 bn_mul_recursive(r, a, b, n, 0, 0, p); 536 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p); 537 } 538 539 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign 540 * r[10] holds (a[0]*b[0]) 541 * r[32] holds (b[1]*b[1]) 542 */ 543 544 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2)); 545 546 if (neg) /* if t[32] is negative */ 547 { 548 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2)); 549 } else { 550 /* Might have a carry */ 551 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2)); 552 } 553 554 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) 555 * r[10] holds (a[0]*b[0]) 556 * r[32] holds (b[1]*b[1]) 557 * c1 holds the carry bits 558 */ 559 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); 560 if (c1) { 561 p = &(r[n + n2]); 562 lo= *p; 563 ln = (lo + c1) & BN_MASK2; 564 *p = ln; 565 566 /* The overflow will stop before we over write 567 * words we should not overwrite */ 568 if (ln < (BN_ULONG)c1) { 569 do { 570 p++; 571 lo= *p; 572 ln = (lo + 1) & BN_MASK2; 573 *p = ln; 574 } while (ln == 0); 575 } 576 } 577 } 578 579 /* n+tn is the word length 580 * t needs to be n*4 is size, as does r */ 581 /* tnX may not be negative but less than n */ 582 void 583 bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna, 584 int tnb, BN_ULONG *t) 585 { 586 int i, j, n2 = n * 2; 587 int c1, c2, neg; 588 BN_ULONG ln, lo, *p; 589 590 # ifdef BN_COUNT 591 fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n", 592 n, tna, n, tnb); 593 # endif 594 if (n < 8) { 595 bn_mul_normal(r, a, n + tna, b, n + tnb); 596 return; 597 } 598 599 /* r=(a[0]-a[1])*(b[1]-b[0]) */ 600 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna); 601 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n); 602 neg = 0; 603 switch (c1 * 3 + c2) { 604 case -4: 605 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ 606 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ 607 break; 608 case -3: 609 /* break; */ 610 case -2: 611 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ 612 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */ 613 neg = 1; 614 break; 615 case -1: 616 case 0: 617 case 1: 618 /* break; */ 619 case 2: 620 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */ 621 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ 622 neg = 1; 623 break; 624 case 3: 625 /* break; */ 626 case 4: 627 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); 628 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); 629 break; 630 } 631 /* The zero case isn't yet implemented here. The speedup 632 would probably be negligible. */ 633 # if 0 634 if (n == 4) { 635 bn_mul_comba4(&(t[n2]), t, &(t[n])); 636 bn_mul_comba4(r, a, b); 637 bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn); 638 memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2)); 639 } else 640 # endif 641 if (n == 8) { 642 bn_mul_comba8(&(t[n2]), t, &(t[n])); 643 bn_mul_comba8(r, a, b); 644 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb); 645 memset(&(r[n2 + tna + tnb]), 0, 646 sizeof(BN_ULONG) * (n2 - tna - tnb)); 647 } else { 648 p = &(t[n2*2]); 649 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); 650 bn_mul_recursive(r, a, b, n, 0, 0, p); 651 i = n / 2; 652 /* If there is only a bottom half to the number, 653 * just do it */ 654 if (tna > tnb) 655 j = tna - i; 656 else 657 j = tnb - i; 658 if (j == 0) { 659 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), 660 i, tna - i, tnb - i, p); 661 memset(&(r[n2 + i * 2]), 0, 662 sizeof(BN_ULONG) * (n2 - i * 2)); 663 } 664 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */ 665 { 666 bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), 667 i, tna - i, tnb - i, p); 668 memset(&(r[n2 + tna + tnb]), 0, 669 sizeof(BN_ULONG) * (n2 - tna - tnb)); 670 } 671 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */ 672 { 673 memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2); 674 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL && 675 tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) { 676 bn_mul_normal(&(r[n2]), &(a[n]), tna, 677 &(b[n]), tnb); 678 } else { 679 for (;;) { 680 i /= 2; 681 /* these simplified conditions work 682 * exclusively because difference 683 * between tna and tnb is 1 or 0 */ 684 if (i < tna || i < tnb) { 685 bn_mul_part_recursive(&(r[n2]), 686 &(a[n]), &(b[n]), i, 687 tna - i, tnb - i, p); 688 break; 689 } else if (i == tna || i == tnb) { 690 bn_mul_recursive(&(r[n2]), 691 &(a[n]), &(b[n]), i, 692 tna - i, tnb - i, p); 693 break; 694 } 695 } 696 } 697 } 698 } 699 700 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign 701 * r[10] holds (a[0]*b[0]) 702 * r[32] holds (b[1]*b[1]) 703 */ 704 705 c1 = (int)(bn_add_words(t, r,&(r[n2]), n2)); 706 707 if (neg) /* if t[32] is negative */ 708 { 709 c1 -= (int)(bn_sub_words(&(t[n2]), t,&(t[n2]), n2)); 710 } else { 711 /* Might have a carry */ 712 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2)); 713 } 714 715 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) 716 * r[10] holds (a[0]*b[0]) 717 * r[32] holds (b[1]*b[1]) 718 * c1 holds the carry bits 719 */ 720 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); 721 if (c1) { 722 p = &(r[n + n2]); 723 lo= *p; 724 ln = (lo + c1)&BN_MASK2; 725 *p = ln; 726 727 /* The overflow will stop before we over write 728 * words we should not overwrite */ 729 if (ln < (BN_ULONG)c1) { 730 do { 731 p++; 732 lo= *p; 733 ln = (lo + 1) & BN_MASK2; 734 *p = ln; 735 } while (ln == 0); 736 } 737 } 738 } 739 740 /* a and b must be the same size, which is n2. 741 * r needs to be n2 words and t needs to be n2*2 742 */ 743 void 744 bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, BN_ULONG *t) 745 { 746 int n = n2 / 2; 747 748 # ifdef BN_COUNT 749 fprintf(stderr, " bn_mul_low_recursive %d * %d\n",n2,n2); 750 # endif 751 752 bn_mul_recursive(r, a, b, n, 0, 0, &(t[0])); 753 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) { 754 bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2])); 755 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n); 756 bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2])); 757 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n); 758 } else { 759 bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n); 760 bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n); 761 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n); 762 bn_add_words(&(r[n]), &(r[n]), &(t[n]), n); 763 } 764 } 765 766 /* a and b must be the same size, which is n2. 767 * r needs to be n2 words and t needs to be n2*2 768 * l is the low words of the output. 769 * t needs to be n2*3 770 */ 771 void 772 bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2, 773 BN_ULONG *t) 774 { 775 int i, n; 776 int c1, c2; 777 int neg, oneg, zero; 778 BN_ULONG ll, lc, *lp, *mp; 779 780 # ifdef BN_COUNT 781 fprintf(stderr, " bn_mul_high %d * %d\n",n2,n2); 782 # endif 783 n = n2 / 2; 784 785 /* Calculate (al-ah)*(bh-bl) */ 786 neg = zero = 0; 787 c1 = bn_cmp_words(&(a[0]), &(a[n]), n); 788 c2 = bn_cmp_words(&(b[n]), &(b[0]), n); 789 switch (c1 * 3 + c2) { 790 case -4: 791 bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n); 792 bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n); 793 break; 794 case -3: 795 zero = 1; 796 break; 797 case -2: 798 bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n); 799 bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n); 800 neg = 1; 801 break; 802 case -1: 803 case 0: 804 case 1: 805 zero = 1; 806 break; 807 case 2: 808 bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n); 809 bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n); 810 neg = 1; 811 break; 812 case 3: 813 zero = 1; 814 break; 815 case 4: 816 bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n); 817 bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n); 818 break; 819 } 820 821 oneg = neg; 822 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */ 823 /* r[10] = (a[1]*b[1]) */ 824 # ifdef BN_MUL_COMBA 825 if (n == 8) { 826 bn_mul_comba8(&(t[0]), &(r[0]), &(r[n])); 827 bn_mul_comba8(r, &(a[n]), &(b[n])); 828 } else 829 # endif 830 { 831 bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2])); 832 bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2])); 833 } 834 835 /* s0 == low(al*bl) 836 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl) 837 * We know s0 and s1 so the only unknown is high(al*bl) 838 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl)) 839 * high(al*bl) == s1 - (r[0]+l[0]+t[0]) 840 */ 841 if (l != NULL) { 842 lp = &(t[n2 + n]); 843 c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n)); 844 } else { 845 c1 = 0; 846 lp = &(r[0]); 847 } 848 849 if (neg) 850 neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n)); 851 else { 852 bn_add_words(&(t[n2]), lp, &(t[0]), n); 853 neg = 0; 854 } 855 856 if (l != NULL) { 857 bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n); 858 } else { 859 lp = &(t[n2 + n]); 860 mp = &(t[n2]); 861 for (i = 0; i < n; i++) 862 lp[i] = ((~mp[i]) + 1) & BN_MASK2; 863 } 864 865 /* s[0] = low(al*bl) 866 * t[3] = high(al*bl) 867 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign 868 * r[10] = (a[1]*b[1]) 869 */ 870 /* R[10] = al*bl 871 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0]) 872 * R[32] = ah*bh 873 */ 874 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow) 875 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow) 876 * R[3]=r[1]+(carry/borrow) 877 */ 878 if (l != NULL) { 879 lp = &(t[n2]); 880 c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n)); 881 } else { 882 lp = &(t[n2 + n]); 883 c1 = 0; 884 } 885 c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n)); 886 if (oneg) 887 c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n)); 888 else 889 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n)); 890 891 c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n)); 892 c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n)); 893 if (oneg) 894 c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n)); 895 else 896 c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n)); 897 898 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */ 899 { 900 i = 0; 901 if (c1 > 0) { 902 lc = c1; 903 do { 904 ll = (r[i] + lc) & BN_MASK2; 905 r[i++] = ll; 906 lc = (lc > ll); 907 } while (lc); 908 } else { 909 lc = -c1; 910 do { 911 ll = r[i]; 912 r[i++] = (ll - lc) & BN_MASK2; 913 lc = (lc > ll); 914 } while (lc); 915 } 916 } 917 if (c2 != 0) /* Add starting at r[1] */ 918 { 919 i = n; 920 if (c2 > 0) { 921 lc = c2; 922 do { 923 ll = (r[i] + lc) & BN_MASK2; 924 r[i++] = ll; 925 lc = (lc > ll); 926 } while (lc); 927 } else { 928 lc = -c2; 929 do { 930 ll = r[i]; 931 r[i++] = (ll - lc) & BN_MASK2; 932 lc = (lc > ll); 933 } while (lc); 934 } 935 } 936 } 937 #endif /* BN_RECURSION */ 938 939 int 940 BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 941 { 942 int ret = 0; 943 int top, al, bl; 944 BIGNUM *rr; 945 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION) 946 int i; 947 #endif 948 #ifdef BN_RECURSION 949 BIGNUM *t = NULL; 950 int j = 0, k; 951 #endif 952 953 #ifdef BN_COUNT 954 fprintf(stderr, "BN_mul %d * %d\n",a->top,b->top); 955 #endif 956 957 bn_check_top(a); 958 bn_check_top(b); 959 bn_check_top(r); 960 961 al = a->top; 962 bl = b->top; 963 964 if ((al == 0) || (bl == 0)) { 965 BN_zero(r); 966 return (1); 967 } 968 top = al + bl; 969 970 BN_CTX_start(ctx); 971 if ((r == a) || (r == b)) { 972 if ((rr = BN_CTX_get(ctx)) == NULL) 973 goto err; 974 } else 975 rr = r; 976 rr->neg = a->neg ^ b->neg; 977 978 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION) 979 i = al - bl; 980 #endif 981 #ifdef BN_MUL_COMBA 982 if (i == 0) { 983 # if 0 984 if (al == 4) { 985 if (bn_wexpand(rr, 8) == NULL) 986 goto err; 987 rr->top = 8; 988 bn_mul_comba4(rr->d, a->d, b->d); 989 goto end; 990 } 991 # endif 992 if (al == 8) { 993 if (bn_wexpand(rr, 16) == NULL) 994 goto err; 995 rr->top = 16; 996 bn_mul_comba8(rr->d, a->d, b->d); 997 goto end; 998 } 999 } 1000 #endif /* BN_MUL_COMBA */ 1001 #ifdef BN_RECURSION 1002 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) { 1003 if (i >= -1 && i <= 1) { 1004 /* Find out the power of two lower or equal 1005 to the longest of the two numbers */ 1006 if (i >= 0) { 1007 j = BN_num_bits_word((BN_ULONG)al); 1008 } 1009 if (i == -1) { 1010 j = BN_num_bits_word((BN_ULONG)bl); 1011 } 1012 j = 1 << (j - 1); 1013 assert(j <= al || j <= bl); 1014 k = j + j; 1015 if ((t = BN_CTX_get(ctx)) == NULL) 1016 goto err; 1017 if (al > j || bl > j) { 1018 if (bn_wexpand(t, k * 4) == NULL) 1019 goto err; 1020 if (bn_wexpand(rr, k * 4) == NULL) 1021 goto err; 1022 bn_mul_part_recursive(rr->d, a->d, b->d, 1023 j, al - j, bl - j, t->d); 1024 } 1025 else /* al <= j || bl <= j */ 1026 { 1027 if (bn_wexpand(t, k * 2) == NULL) 1028 goto err; 1029 if (bn_wexpand(rr, k * 2) == NULL) 1030 goto err; 1031 bn_mul_recursive(rr->d, a->d, b->d, 1032 j, al - j, bl - j, t->d); 1033 } 1034 rr->top = top; 1035 goto end; 1036 } 1037 #if 0 1038 if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) { 1039 BIGNUM *tmp_bn = (BIGNUM *)b; 1040 if (bn_wexpand(tmp_bn, al) == NULL) 1041 goto err; 1042 tmp_bn->d[bl] = 0; 1043 bl++; 1044 i--; 1045 } else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) { 1046 BIGNUM *tmp_bn = (BIGNUM *)a; 1047 if (bn_wexpand(tmp_bn, bl) == NULL) 1048 goto err; 1049 tmp_bn->d[al] = 0; 1050 al++; 1051 i++; 1052 } 1053 if (i == 0) { 1054 /* symmetric and > 4 */ 1055 /* 16 or larger */ 1056 j = BN_num_bits_word((BN_ULONG)al); 1057 j = 1 << (j - 1); 1058 k = j + j; 1059 if ((t = BN_CTX_get(ctx)) == NULL) 1060 goto err; 1061 if (al == j) /* exact multiple */ 1062 { 1063 if (bn_wexpand(t, k * 2) == NULL) 1064 goto err; 1065 if (bn_wexpand(rr, k * 2) == NULL) 1066 goto err; 1067 bn_mul_recursive(rr->d, a->d, b->d, al, t->d); 1068 } else { 1069 if (bn_wexpand(t, k * 4) == NULL) 1070 goto err; 1071 if (bn_wexpand(rr, k * 4) == NULL) 1072 goto err; 1073 bn_mul_part_recursive(rr->d, a->d, b->d, 1074 al - j, j, t->d); 1075 } 1076 rr->top = top; 1077 goto end; 1078 } 1079 #endif 1080 } 1081 #endif /* BN_RECURSION */ 1082 if (bn_wexpand(rr, top) == NULL) 1083 goto err; 1084 rr->top = top; 1085 bn_mul_normal(rr->d, a->d, al, b->d, bl); 1086 1087 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION) 1088 end: 1089 #endif 1090 bn_correct_top(rr); 1091 if (r != rr) 1092 BN_copy(r, rr); 1093 ret = 1; 1094 err: 1095 bn_check_top(r); 1096 BN_CTX_end(ctx); 1097 return (ret); 1098 } 1099 1100 void 1101 bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) 1102 { 1103 BN_ULONG *rr; 1104 1105 #ifdef BN_COUNT 1106 fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb); 1107 #endif 1108 1109 if (na < nb) { 1110 int itmp; 1111 BN_ULONG *ltmp; 1112 1113 itmp = na; 1114 na = nb; 1115 nb = itmp; 1116 ltmp = a; 1117 a = b; 1118 b = ltmp; 1119 1120 } 1121 rr = &(r[na]); 1122 if (nb <= 0) { 1123 (void)bn_mul_words(r, a, na, 0); 1124 return; 1125 } else 1126 rr[0] = bn_mul_words(r, a, na, b[0]); 1127 1128 for (;;) { 1129 if (--nb <= 0) 1130 return; 1131 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]); 1132 if (--nb <= 0) 1133 return; 1134 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]); 1135 if (--nb <= 0) 1136 return; 1137 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]); 1138 if (--nb <= 0) 1139 return; 1140 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]); 1141 rr += 4; 1142 r += 4; 1143 b += 4; 1144 } 1145 } 1146 1147 void 1148 bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n) 1149 { 1150 #ifdef BN_COUNT 1151 fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n); 1152 #endif 1153 bn_mul_words(r, a, n, b[0]); 1154 1155 for (;;) { 1156 if (--n <= 0) 1157 return; 1158 bn_mul_add_words(&(r[1]), a, n, b[1]); 1159 if (--n <= 0) 1160 return; 1161 bn_mul_add_words(&(r[2]), a, n, b[2]); 1162 if (--n <= 0) 1163 return; 1164 bn_mul_add_words(&(r[3]), a, n, b[3]); 1165 if (--n <= 0) 1166 return; 1167 bn_mul_add_words(&(r[4]), a, n, b[4]); 1168 r += 4; 1169 b += 4; 1170 } 1171 } 1172