1 /* crypto/bn/bn_mul.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 #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 /* dnX may not be positive, but n2/2+dnX has to be */ 393 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 394 int dna, int dnb, BN_ULONG *t) 395 { 396 int n=n2/2,c1,c2; 397 int tna=n+dna, tnb=n+dnb; 398 unsigned int neg,zero; 399 BN_ULONG ln,lo,*p; 400 401 # ifdef BN_COUNT 402 fprintf(stderr," bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb); 403 # endif 404 # ifdef BN_MUL_COMBA 405 # if 0 406 if (n2 == 4) 407 { 408 bn_mul_comba4(r,a,b); 409 return; 410 } 411 # endif 412 /* Only call bn_mul_comba 8 if n2 == 8 and the 413 * two arrays are complete [steve] 414 */ 415 if (n2 == 8 && dna == 0 && dnb == 0) 416 { 417 bn_mul_comba8(r,a,b); 418 return; 419 } 420 # endif /* BN_MUL_COMBA */ 421 /* Else do normal multiply */ 422 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) 423 { 424 bn_mul_normal(r,a,n2+dna,b,n2+dnb); 425 if ((dna + dnb) < 0) 426 memset(&r[2*n2 + dna + dnb], 0, 427 sizeof(BN_ULONG) * -(dna + dnb)); 428 return; 429 } 430 /* r=(a[0]-a[1])*(b[1]-b[0]) */ 431 c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna); 432 c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n); 433 zero=neg=0; 434 switch (c1*3+c2) 435 { 436 case -4: 437 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */ 438 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */ 439 break; 440 case -3: 441 zero=1; 442 break; 443 case -2: 444 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */ 445 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */ 446 neg=1; 447 break; 448 case -1: 449 case 0: 450 case 1: 451 zero=1; 452 break; 453 case 2: 454 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */ 455 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */ 456 neg=1; 457 break; 458 case 3: 459 zero=1; 460 break; 461 case 4: 462 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); 463 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); 464 break; 465 } 466 467 # ifdef BN_MUL_COMBA 468 if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take 469 extra args to do this well */ 470 { 471 if (!zero) 472 bn_mul_comba4(&(t[n2]),t,&(t[n])); 473 else 474 memset(&(t[n2]),0,8*sizeof(BN_ULONG)); 475 476 bn_mul_comba4(r,a,b); 477 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n])); 478 } 479 else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could 480 take extra args to do this 481 well */ 482 { 483 if (!zero) 484 bn_mul_comba8(&(t[n2]),t,&(t[n])); 485 else 486 memset(&(t[n2]),0,16*sizeof(BN_ULONG)); 487 488 bn_mul_comba8(r,a,b); 489 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n])); 490 } 491 else 492 # endif /* BN_MUL_COMBA */ 493 { 494 p= &(t[n2*2]); 495 if (!zero) 496 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p); 497 else 498 memset(&(t[n2]),0,n2*sizeof(BN_ULONG)); 499 bn_mul_recursive(r,a,b,n,0,0,p); 500 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p); 501 } 502 503 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign 504 * r[10] holds (a[0]*b[0]) 505 * r[32] holds (b[1]*b[1]) 506 */ 507 508 c1=(int)(bn_add_words(t,r,&(r[n2]),n2)); 509 510 if (neg) /* if t[32] is negative */ 511 { 512 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2)); 513 } 514 else 515 { 516 /* Might have a carry */ 517 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2)); 518 } 519 520 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) 521 * r[10] holds (a[0]*b[0]) 522 * r[32] holds (b[1]*b[1]) 523 * c1 holds the carry bits 524 */ 525 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2)); 526 if (c1) 527 { 528 p= &(r[n+n2]); 529 lo= *p; 530 ln=(lo+c1)&BN_MASK2; 531 *p=ln; 532 533 /* The overflow will stop before we over write 534 * words we should not overwrite */ 535 if (ln < (BN_ULONG)c1) 536 { 537 do { 538 p++; 539 lo= *p; 540 ln=(lo+1)&BN_MASK2; 541 *p=ln; 542 } while (ln == 0); 543 } 544 } 545 } 546 547 /* n+tn is the word length 548 * t needs to be n*4 is size, as does r */ 549 /* tnX may not be negative but less than n */ 550 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, 551 int tna, int tnb, BN_ULONG *t) 552 { 553 int i,j,n2=n*2; 554 int c1,c2,neg; 555 BN_ULONG ln,lo,*p; 556 557 # ifdef BN_COUNT 558 fprintf(stderr," bn_mul_part_recursive (%d%+d) * (%d%+d)\n", 559 n, tna, n, tnb); 560 # endif 561 if (n < 8) 562 { 563 bn_mul_normal(r,a,n+tna,b,n+tnb); 564 return; 565 } 566 567 /* r=(a[0]-a[1])*(b[1]-b[0]) */ 568 c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna); 569 c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n); 570 neg=0; 571 switch (c1*3+c2) 572 { 573 case -4: 574 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */ 575 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */ 576 break; 577 case -3: 578 /* break; */ 579 case -2: 580 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */ 581 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */ 582 neg=1; 583 break; 584 case -1: 585 case 0: 586 case 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 /* break; */ 595 case 4: 596 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); 597 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); 598 break; 599 } 600 /* The zero case isn't yet implemented here. The speedup 601 would probably be negligible. */ 602 # if 0 603 if (n == 4) 604 { 605 bn_mul_comba4(&(t[n2]),t,&(t[n])); 606 bn_mul_comba4(r,a,b); 607 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn); 608 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2)); 609 } 610 else 611 # endif 612 if (n == 8) 613 { 614 bn_mul_comba8(&(t[n2]),t,&(t[n])); 615 bn_mul_comba8(r,a,b); 616 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb); 617 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb)); 618 } 619 else 620 { 621 p= &(t[n2*2]); 622 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p); 623 bn_mul_recursive(r,a,b,n,0,0,p); 624 i=n/2; 625 /* If there is only a bottom half to the number, 626 * just do it */ 627 if (tna > tnb) 628 j = tna - i; 629 else 630 j = tnb - i; 631 if (j == 0) 632 { 633 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]), 634 i,tna-i,tnb-i,p); 635 memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2)); 636 } 637 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */ 638 { 639 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]), 640 i,tna-i,tnb-i,p); 641 memset(&(r[n2+tna+tnb]),0, 642 sizeof(BN_ULONG)*(n2-tna-tnb)); 643 } 644 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */ 645 { 646 memset(&(r[n2]),0,sizeof(BN_ULONG)*n2); 647 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL 648 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) 649 { 650 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb); 651 } 652 else 653 { 654 for (;;) 655 { 656 i/=2; 657 /* these simplified conditions work 658 * exclusively because difference 659 * between tna and tnb is 1 or 0 */ 660 if (i < tna || i < tnb) 661 { 662 bn_mul_part_recursive(&(r[n2]), 663 &(a[n]),&(b[n]), 664 i,tna-i,tnb-i,p); 665 break; 666 } 667 else if (i == tna || i == tnb) 668 { 669 bn_mul_recursive(&(r[n2]), 670 &(a[n]),&(b[n]), 671 i,tna-i,tnb-i,p); 672 break; 673 } 674 } 675 } 676 } 677 } 678 679 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign 680 * r[10] holds (a[0]*b[0]) 681 * r[32] holds (b[1]*b[1]) 682 */ 683 684 c1=(int)(bn_add_words(t,r,&(r[n2]),n2)); 685 686 if (neg) /* if t[32] is negative */ 687 { 688 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2)); 689 } 690 else 691 { 692 /* Might have a carry */ 693 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2)); 694 } 695 696 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) 697 * r[10] holds (a[0]*b[0]) 698 * r[32] holds (b[1]*b[1]) 699 * c1 holds the carry bits 700 */ 701 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2)); 702 if (c1) 703 { 704 p= &(r[n+n2]); 705 lo= *p; 706 ln=(lo+c1)&BN_MASK2; 707 *p=ln; 708 709 /* The overflow will stop before we over write 710 * words we should not overwrite */ 711 if (ln < (BN_ULONG)c1) 712 { 713 do { 714 p++; 715 lo= *p; 716 ln=(lo+1)&BN_MASK2; 717 *p=ln; 718 } while (ln == 0); 719 } 720 } 721 } 722 723 /* a and b must be the same size, which is n2. 724 * r needs to be n2 words and t needs to be n2*2 725 */ 726 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 727 BN_ULONG *t) 728 { 729 int n=n2/2; 730 731 # ifdef BN_COUNT 732 fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2); 733 # endif 734 735 bn_mul_recursive(r,a,b,n,0,0,&(t[0])); 736 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) 737 { 738 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2])); 739 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); 740 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2])); 741 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); 742 } 743 else 744 { 745 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n); 746 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n); 747 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); 748 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n); 749 } 750 } 751 752 /* a and b must be the same size, which is n2. 753 * r needs to be n2 words and t needs to be n2*2 754 * l is the low words of the output. 755 * t needs to be n2*3 756 */ 757 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2, 758 BN_ULONG *t) 759 { 760 int i,n; 761 int c1,c2; 762 int neg,oneg,zero; 763 BN_ULONG ll,lc,*lp,*mp; 764 765 # ifdef BN_COUNT 766 fprintf(stderr," bn_mul_high %d * %d\n",n2,n2); 767 # endif 768 n=n2/2; 769 770 /* Calculate (al-ah)*(bh-bl) */ 771 neg=zero=0; 772 c1=bn_cmp_words(&(a[0]),&(a[n]),n); 773 c2=bn_cmp_words(&(b[n]),&(b[0]),n); 774 switch (c1*3+c2) 775 { 776 case -4: 777 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n); 778 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n); 779 break; 780 case -3: 781 zero=1; 782 break; 783 case -2: 784 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n); 785 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n); 786 neg=1; 787 break; 788 case -1: 789 case 0: 790 case 1: 791 zero=1; 792 break; 793 case 2: 794 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n); 795 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n); 796 neg=1; 797 break; 798 case 3: 799 zero=1; 800 break; 801 case 4: 802 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n); 803 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n); 804 break; 805 } 806 807 oneg=neg; 808 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */ 809 /* r[10] = (a[1]*b[1]) */ 810 # ifdef BN_MUL_COMBA 811 if (n == 8) 812 { 813 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n])); 814 bn_mul_comba8(r,&(a[n]),&(b[n])); 815 } 816 else 817 # endif 818 { 819 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2])); 820 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2])); 821 } 822 823 /* s0 == low(al*bl) 824 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl) 825 * We know s0 and s1 so the only unknown is high(al*bl) 826 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl)) 827 * high(al*bl) == s1 - (r[0]+l[0]+t[0]) 828 */ 829 if (l != NULL) 830 { 831 lp= &(t[n2+n]); 832 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n)); 833 } 834 else 835 { 836 c1=0; 837 lp= &(r[0]); 838 } 839 840 if (neg) 841 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n)); 842 else 843 { 844 bn_add_words(&(t[n2]),lp,&(t[0]),n); 845 neg=0; 846 } 847 848 if (l != NULL) 849 { 850 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n); 851 } 852 else 853 { 854 lp= &(t[n2+n]); 855 mp= &(t[n2]); 856 for (i=0; i<n; i++) 857 lp[i]=((~mp[i])+1)&BN_MASK2; 858 } 859 860 /* s[0] = low(al*bl) 861 * t[3] = high(al*bl) 862 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign 863 * r[10] = (a[1]*b[1]) 864 */ 865 /* R[10] = al*bl 866 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0]) 867 * R[32] = ah*bh 868 */ 869 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow) 870 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow) 871 * R[3]=r[1]+(carry/borrow) 872 */ 873 if (l != NULL) 874 { 875 lp= &(t[n2]); 876 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n)); 877 } 878 else 879 { 880 lp= &(t[n2+n]); 881 c1=0; 882 } 883 c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n)); 884 if (oneg) 885 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n)); 886 else 887 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n)); 888 889 c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n)); 890 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n)); 891 if (oneg) 892 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n)); 893 else 894 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n)); 895 896 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */ 897 { 898 i=0; 899 if (c1 > 0) 900 { 901 lc=c1; 902 do { 903 ll=(r[i]+lc)&BN_MASK2; 904 r[i++]=ll; 905 lc=(lc > ll); 906 } while (lc); 907 } 908 else 909 { 910 lc= -c1; 911 do { 912 ll=r[i]; 913 r[i++]=(ll-lc)&BN_MASK2; 914 lc=(lc > ll); 915 } while (lc); 916 } 917 } 918 if (c2 != 0) /* Add starting at r[1] */ 919 { 920 i=n; 921 if (c2 > 0) 922 { 923 lc=c2; 924 do { 925 ll=(r[i]+lc)&BN_MASK2; 926 r[i++]=ll; 927 lc=(lc > ll); 928 } while (lc); 929 } 930 else 931 { 932 lc= -c2; 933 do { 934 ll=r[i]; 935 r[i++]=(ll-lc)&BN_MASK2; 936 lc=(lc > ll); 937 } while (lc); 938 } 939 } 940 } 941 #endif /* BN_RECURSION */ 942 943 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 944 { 945 int ret=0; 946 int top,al,bl; 947 BIGNUM *rr; 948 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION) 949 int i; 950 #endif 951 #ifdef BN_RECURSION 952 BIGNUM *t=NULL; 953 int j=0,k; 954 #endif 955 956 #ifdef BN_COUNT 957 fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top); 958 #endif 959 960 bn_check_top(a); 961 bn_check_top(b); 962 bn_check_top(r); 963 964 al=a->top; 965 bl=b->top; 966 967 if ((al == 0) || (bl == 0)) 968 { 969 BN_zero(r); 970 return(1); 971 } 972 top=al+bl; 973 974 BN_CTX_start(ctx); 975 if ((r == a) || (r == b)) 976 { 977 if ((rr = BN_CTX_get(ctx)) == NULL) goto err; 978 } 979 else 980 rr = r; 981 rr->neg=a->neg^b->neg; 982 983 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION) 984 i = al-bl; 985 #endif 986 #ifdef BN_MUL_COMBA 987 if (i == 0) 988 { 989 # if 0 990 if (al == 4) 991 { 992 if (bn_wexpand(rr,8) == NULL) goto err; 993 rr->top=8; 994 bn_mul_comba4(rr->d,a->d,b->d); 995 goto end; 996 } 997 # endif 998 if (al == 8) 999 { 1000 if (bn_wexpand(rr,16) == NULL) goto err; 1001 rr->top=16; 1002 bn_mul_comba8(rr->d,a->d,b->d); 1003 goto end; 1004 } 1005 } 1006 #endif /* BN_MUL_COMBA */ 1007 #ifdef BN_RECURSION 1008 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) 1009 { 1010 if (i >= -1 && i <= 1) 1011 { 1012 /* Find out the power of two lower or equal 1013 to the longest of the two numbers */ 1014 if (i >= 0) 1015 { 1016 j = BN_num_bits_word((BN_ULONG)al); 1017 } 1018 if (i == -1) 1019 { 1020 j = BN_num_bits_word((BN_ULONG)bl); 1021 } 1022 j = 1<<(j-1); 1023 assert(j <= al || j <= bl); 1024 k = j+j; 1025 t = BN_CTX_get(ctx); 1026 if (t == NULL) 1027 goto err; 1028 if (al > j || bl > j) 1029 { 1030 if (bn_wexpand(t,k*4) == NULL) goto err; 1031 if (bn_wexpand(rr,k*4) == NULL) goto err; 1032 bn_mul_part_recursive(rr->d,a->d,b->d, 1033 j,al-j,bl-j,t->d); 1034 } 1035 else /* al <= j || bl <= j */ 1036 { 1037 if (bn_wexpand(t,k*2) == NULL) goto err; 1038 if (bn_wexpand(rr,k*2) == NULL) goto err; 1039 bn_mul_recursive(rr->d,a->d,b->d, 1040 j,al-j,bl-j,t->d); 1041 } 1042 rr->top=top; 1043 goto end; 1044 } 1045 #if 0 1046 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA)) 1047 { 1048 BIGNUM *tmp_bn = (BIGNUM *)b; 1049 if (bn_wexpand(tmp_bn,al) == NULL) goto err; 1050 tmp_bn->d[bl]=0; 1051 bl++; 1052 i--; 1053 } 1054 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA)) 1055 { 1056 BIGNUM *tmp_bn = (BIGNUM *)a; 1057 if (bn_wexpand(tmp_bn,bl) == NULL) goto err; 1058 tmp_bn->d[al]=0; 1059 al++; 1060 i++; 1061 } 1062 if (i == 0) 1063 { 1064 /* symmetric and > 4 */ 1065 /* 16 or larger */ 1066 j=BN_num_bits_word((BN_ULONG)al); 1067 j=1<<(j-1); 1068 k=j+j; 1069 t = BN_CTX_get(ctx); 1070 if (al == j) /* exact multiple */ 1071 { 1072 if (bn_wexpand(t,k*2) == NULL) goto err; 1073 if (bn_wexpand(rr,k*2) == NULL) goto err; 1074 bn_mul_recursive(rr->d,a->d,b->d,al,t->d); 1075 } 1076 else 1077 { 1078 if (bn_wexpand(t,k*4) == NULL) goto err; 1079 if (bn_wexpand(rr,k*4) == NULL) goto err; 1080 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d); 1081 } 1082 rr->top=top; 1083 goto end; 1084 } 1085 #endif 1086 } 1087 #endif /* BN_RECURSION */ 1088 if (bn_wexpand(rr,top) == NULL) goto err; 1089 rr->top=top; 1090 bn_mul_normal(rr->d,a->d,al,b->d,bl); 1091 1092 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION) 1093 end: 1094 #endif 1095 bn_correct_top(rr); 1096 if (r != rr) BN_copy(r,rr); 1097 ret=1; 1098 err: 1099 bn_check_top(r); 1100 BN_CTX_end(ctx); 1101 return(ret); 1102 } 1103 1104 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) 1105 { 1106 BN_ULONG *rr; 1107 1108 #ifdef BN_COUNT 1109 fprintf(stderr," bn_mul_normal %d * %d\n",na,nb); 1110 #endif 1111 1112 if (na < nb) 1113 { 1114 int itmp; 1115 BN_ULONG *ltmp; 1116 1117 itmp=na; na=nb; nb=itmp; 1118 ltmp=a; a=b; b=ltmp; 1119 1120 } 1121 rr= &(r[na]); 1122 if (nb <= 0) 1123 { 1124 (void)bn_mul_words(r,a,na,0); 1125 return; 1126 } 1127 else 1128 rr[0]=bn_mul_words(r,a,na,b[0]); 1129 1130 for (;;) 1131 { 1132 if (--nb <= 0) return; 1133 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]); 1134 if (--nb <= 0) return; 1135 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]); 1136 if (--nb <= 0) return; 1137 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]); 1138 if (--nb <= 0) return; 1139 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]); 1140 rr+=4; 1141 r+=4; 1142 b+=4; 1143 } 1144 } 1145 1146 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n) 1147 { 1148 #ifdef BN_COUNT 1149 fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n); 1150 #endif 1151 bn_mul_words(r,a,n,b[0]); 1152 1153 for (;;) 1154 { 1155 if (--n <= 0) return; 1156 bn_mul_add_words(&(r[1]),a,n,b[1]); 1157 if (--n <= 0) return; 1158 bn_mul_add_words(&(r[2]),a,n,b[2]); 1159 if (--n <= 0) return; 1160 bn_mul_add_words(&(r[3]),a,n,b[3]); 1161 if (--n <= 0) return; 1162 bn_mul_add_words(&(r[4]),a,n,b[4]); 1163 r+=4; 1164 b+=4; 1165 } 1166 } 1167
