crypto/bn/bn_mul.c

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