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