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         int dna, int dnb, BN_ULONG *t)
 387         {
 388         int n=n2/2,c1,c2;
 389         int tna=n+dna, tnb=n+dnb;
 390         unsigned int neg,zero;
 391         BN_ULONG ln,lo,*p;
 392
 393 # ifdef BN_COUNT
 394         fprintf(stderr," bn_mul_recursive %d * %d\n",n2,n2);
 395 # endif
 396 # ifdef BN_MUL_COMBA
 397 #  if 0
 398         if (n2 == 4)
 399                 {
 400                 bn_mul_comba4(r,a,b);
 401                 return;
 402                 }
 403 #  endif
 404         if (n2 == 8)
 405                 {
 406                 bn_mul_comba8(r,a,b);
 407                 return;
 408                 }
 409 # endif /* BN_MUL_COMBA */
 410         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
 411                 {
 412                 /* This should not happen */
 413                 bn_mul_normal(r,a,n2,b,n2);
 414                 return;
 415                 }
 416         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 417         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 418         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 419         zero=neg=0;
 420         switch (c1*3+c2)
 421                 {
 422         case -4:
 423                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 424                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 425                 break;
 426         case -3:
 427                 zero=1;
 428                 break;
 429         case -2:
 430                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 431                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 432                 neg=1;
 433                 break;
 434         case -1:
 435         case 0:
 436         case 1:
 437                 zero=1;
 438                 break;
 439         case 2:
 440                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 441                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 442                 neg=1;
 443                 break;
 444         case 3:
 445                 zero=1;
 446                 break;
 447         case 4:
 448                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 449                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 450                 break;
 451                 }
 452
 453 # ifdef BN_MUL_COMBA
 454         if (n == 4)
 455                 {
 456                 if (!zero)
 457                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 458                 else
 459                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 460
 461                 bn_mul_comba4(r,a,b);
 462                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 463                 }
 464         else if (n == 8)
 465                 {
 466                 if (!zero)
 467                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 468                 else
 469                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 470
 471                 bn_mul_comba8(r,a,b);
 472                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 473                 }
 474         else
 475 # endif /* BN_MUL_COMBA */
 476                 {
 477                 p= &(t[n2*2]);
 478                 if (!zero)
 479                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 480                 else
 481                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 482                 bn_mul_recursive(r,a,b,n,0,0,p);
 483                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
 484                 }
 485
 486         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 487          * r[10] holds (a[0]*b[0])
 488          * r[32] holds (b[1]*b[1])
 489          */
 490
 491         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 492
 493         if (neg) /* if t[32] is negative */
 494                 {
 495                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 496                 }
 497         else
 498                 {
 499                 /* Might have a carry */
 500                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 501                 }
 502
 503         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 504          * r[10] holds (a[0]*b[0])
 505          * r[32] holds (b[1]*b[1])
 506          * c1 holds the carry bits
 507          */
 508         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 509         if (c1)
 510                 {
 511                 p= &(r[n+n2]);
 512                 lo= *p;
 513                 ln=(lo+c1)&BN_MASK2;
 514                 *p=ln;
 515
 516                 /* The overflow will stop before we over write
 517                  * words we should not overwrite */
 518                 if (ln < (BN_ULONG)c1)
 519                         {
 520                         do      {
 521                                 p++;
 522                                 lo= *p;
 523                                 ln=(lo+1)&BN_MASK2;
 524                                 *p=ln;
 525                                 } while (ln == 0);
 526                         }
 527                 }
 528         }
 529
 530 /* n+tn is the word length
 531  * t needs to be n*4 is size, as does r */
 532 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
 533              int tna, int tnb, BN_ULONG *t)
 534         {
 535         int i,j,n2=n*2;
 536         unsigned int c1,c2,neg,zero;
 537         BN_ULONG ln,lo,*p;
 538
 539 # ifdef BN_COUNT
 540         fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
 541                 tna, n, tnb, n);
 542 # endif
 543         if (n < 8)
 544                 {
 545                 bn_mul_normal(r,a,n+tna,b,n+tnb);
 546                 return;
 547                 }
 548
 549         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 550         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 551         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 552         zero=neg=0;
 553         switch (c1*3+c2)
 554                 {
 555         case -4:
 556                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 557                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 558                 break;
 559         case -3:
 560                 zero=1;
 561                 /* break; */
 562         case -2:
 563                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 564                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-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]),tna,n-tna); /* + */
 574                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 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]),tna,n-tna);
 582                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-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]),tna,&(b[n]),tnb);
 602                 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
 603                 }
 604         else
 605                 {
 606                 p= &(t[n2*2]);
 607                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 608                 bn_mul_recursive(r,a,b,n,0,0,p);
 609                 i=n/2;
 610                 /* If there is only a bottom half to the number,
 611                  * just do it */
 612                 if (tna > tnb)
 613                         j = tna - i;
 614                 else
 615                         j = tnb - i;
 616                 if (j == 0)
 617                         {
 618                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
 619                                 i,tna-i,tnb-i,p);
 620                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 621                         }
 622                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 623                                 {
 624                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 625                                         i,tna-i,tnb-i,p);
 626                                 memset(&(r[n2+tna+tnb]),0,
 627                                         sizeof(BN_ULONG)*(n2-tna-tnb));
 628                                 }
 629                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 630                         {
 631                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 632                         if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
 633                                 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
 634                                 {
 635                                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 636                                 }
 637                         else
 638                                 {
 639                                 for (;;)
 640                                         {
 641                                         i/=2;
 642                                         if (i < tna && i < tnb)
 643                                                 {
 644                                                 bn_mul_part_recursive(&(r[n2]),
 645                                                         &(a[n]),&(b[n]),
 646                                                         i,tna-i,tnb-i,p);
 647                                                 break;
 648                                                 }
 649                                         else if (i <= tna && i <= tnb)
 650                                                 {
 651                                                 bn_mul_recursive(&(r[n2]),
 652                                                         &(a[n]),&(b[n]),
 653                                                         i,tna-i,tnb-i,p);
 654                                                 break;
 655                                                 }
 656                                         }
 657                                 }
 658                         }
 659                 }
 660
 661         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 662          * r[10] holds (a[0]*b[0])
 663          * r[32] holds (b[1]*b[1])
 664          */
 665
 666         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 667
 668         if (neg) /* if t[32] is negative */
 669                 {
 670                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 671                 }
 672         else
 673                 {
 674                 /* Might have a carry */
 675                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 676                 }
 677
 678         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 679          * r[10] holds (a[0]*b[0])
 680          * r[32] holds (b[1]*b[1])
 681          * c1 holds the carry bits
 682          */
 683         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 684         if (c1)
 685                 {
 686                 p= &(r[n+n2]);
 687                 lo= *p;
 688                 ln=(lo+c1)&BN_MASK2;
 689                 *p=ln;
 690
 691                 /* The overflow will stop before we over write
 692                  * words we should not overwrite */
 693                 if (ln < c1)
 694                         {
 695                         do      {
 696                                 p++;
 697                                 lo= *p;
 698                                 ln=(lo+1)&BN_MASK2;
 699                                 *p=ln;
 700                                 } while (ln == 0);
 701                         }
 702                 }
 703         }
 704
 705 /* a and b must be the same size, which is n2.
 706  * r needs to be n2 words and t needs to be n2*2
 707  */
 708 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 709              BN_ULONG *t)
 710         {
 711         int n=n2/2;
 712
 713 # ifdef BN_COUNT
 714         fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
 715 # endif
 716
 717         bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
 718         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 719                 {
 720                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 721                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 722                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 723                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 724                 }
 725         else
 726                 {
 727                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 728                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 729                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 730                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 731                 }
 732         }
 733
 734 /* a and b must be the same size, which is n2.
 735  * r needs to be n2 words and t needs to be n2*2
 736  * l is the low words of the output.
 737  * t needs to be n2*3
 738  */
 739 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 740              BN_ULONG *t)
 741         {
 742         int i,n;
 743         int c1,c2;
 744         int neg,oneg,zero;
 745         BN_ULONG ll,lc,*lp,*mp;
 746
 747 # ifdef BN_COUNT
 748         fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
 749 # endif
 750         n=n2/2;
 751
 752         /* Calculate (al-ah)*(bh-bl) */
 753         neg=zero=0;
 754         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 755         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 756         switch (c1*3+c2)
 757                 {
 758         case -4:
 759                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 760                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 761                 break;
 762         case -3:
 763                 zero=1;
 764                 break;
 765         case -2:
 766                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 767                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 768                 neg=1;
 769                 break;
 770         case -1:
 771         case 0:
 772         case 1:
 773                 zero=1;
 774                 break;
 775         case 2:
 776                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 777                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 778                 neg=1;
 779                 break;
 780         case 3:
 781                 zero=1;
 782                 break;
 783         case 4:
 784                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 785                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 786                 break;
 787                 }
 788
 789         oneg=neg;
 790         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 791         /* r[10] = (a[1]*b[1]) */
 792 # ifdef BN_MUL_COMBA
 793         if (n == 8)
 794                 {
 795                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 796                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 797                 }
 798         else
 799 # endif
 800                 {
 801                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
 802                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
 803                 }
 804
 805         /* s0 == low(al*bl)
 806          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 807          * We know s0 and s1 so the only unknown is high(al*bl)
 808          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 809          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 810          */
 811         if (l != NULL)
 812                 {
 813                 lp= &(t[n2+n]);
 814                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 815                 }
 816         else
 817                 {
 818                 c1=0;
 819                 lp= &(r[0]);
 820                 }
 821
 822         if (neg)
 823                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 824         else
 825                 {
 826                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 827                 neg=0;
 828                 }
 829
 830         if (l != NULL)
 831                 {
 832                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 833                 }
 834         else
 835                 {
 836                 lp= &(t[n2+n]);
 837                 mp= &(t[n2]);
 838                 for (i=0; i<n; i++)
 839                         lp[i]=((~mp[i])+1)&BN_MASK2;
 840                 }
 841
 842         /* s[0] = low(al*bl)
 843          * t[3] = high(al*bl)
 844          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 845          * r[10] = (a[1]*b[1])
 846          */
 847         /* R[10] = al*bl
 848          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 849          * R[32] = ah*bh
 850          */
 851         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 852          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 853          * R[3]=r[1]+(carry/borrow)
 854          */
 855         if (l != NULL)
 856                 {
 857                 lp= &(t[n2]);
 858                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 859                 }
 860         else
 861                 {
 862                 lp= &(t[n2+n]);
 863                 c1=0;
 864                 }
 865         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 866         if (oneg)
 867                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 868         else
 869                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 870
 871         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 872         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 873         if (oneg)
 874                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 875         else
 876                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 877
 878         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 879                 {
 880                 i=0;
 881                 if (c1 > 0)
 882                         {
 883                         lc=c1;
 884                         do      {
 885                                 ll=(r[i]+lc)&BN_MASK2;
 886                                 r[i++]=ll;
 887                                 lc=(lc > ll);
 888                                 } while (lc);
 889                         }
 890                 else
 891                         {
 892                         lc= -c1;
 893                         do      {
 894                                 ll=r[i];
 895                                 r[i++]=(ll-lc)&BN_MASK2;
 896                                 lc=(lc > ll);
 897                                 } while (lc);
 898                         }
 899                 }
 900         if (c2 != 0) /* Add starting at r[1] */
 901                 {
 902                 i=n;
 903                 if (c2 > 0)
 904                         {
 905                         lc=c2;
 906                         do      {
 907                                 ll=(r[i]+lc)&BN_MASK2;
 908                                 r[i++]=ll;
 909                                 lc=(lc > ll);
 910                                 } while (lc);
 911                         }
 912                 else
 913                         {
 914                         lc= -c2;
 915                         do      {
 916                                 ll=r[i];
 917                                 r[i++]=(ll-lc)&BN_MASK2;
 918                                 lc=(lc > ll);
 919                                 } while (lc);
 920                         }
 921                 }
 922         }
 923 #endif /* BN_RECURSION */
 924
 925 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 926         {
 927         int ret=0;
 928         int top,al,bl;
 929         BIGNUM *rr;
 930 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 931         int i;
 932 #endif
 933 #ifdef BN_RECURSION
 934         BIGNUM *t;
 935         int j,k;
 936 #endif
 937
 938 #ifdef BN_COUNT
 939         fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
 940 #endif
 941
 942         bn_check_top(a);
 943         bn_check_top(b);
 944         bn_check_top(r);
 945
 946         al=a->top;
 947         bl=b->top;
 948
 949         if ((al == 0) || (bl == 0))
 950                 {
 951                 BN_zero(r);
 952                 return(1);
 953                 }
 954         top=al+bl;
 955
 956         BN_CTX_start(ctx);
 957         if ((r == a) || (r == b))
 958                 {
 959                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
 960                 }
 961         else
 962                 rr = r;
 963         rr->neg=a->neg^b->neg;
 964
 965 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 966         i = al-bl;
 967 #endif
 968 #ifdef BN_MUL_COMBA
 969         if (i == 0)
 970                 {
 971 # if 0
 972                 if (al == 4)
 973                         {
 974                         if (bn_wexpand(rr,8) == NULL) goto err;
 975                         rr->top=8;
 976                         bn_mul_comba4(rr->d,a->d,b->d);
 977                         goto end;
 978                         }
 979 # endif
 980                 if (al == 8)
 981                         {
 982                         if (bn_wexpand(rr,16) == NULL) goto err;
 983                         rr->top=16;
 984                         bn_mul_comba8(rr->d,a->d,b->d);
 985                         goto end;
 986                         }
 987                 }
 988 #endif /* BN_MUL_COMBA */
 989 #ifdef BN_RECURSION
 990         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
 991                 {
 992                 if (i >= -1 && i <= 1)
 993                         {
 994                         int sav_j =0;
 995                         /* Find out the power of two lower or equal
 996                            to the longest of the two numbers */
 997                         if (i >= 0)
 998                                 {
 999                                 j = BN_num_bits_word((BN_ULONG)al);
1000                                 }
1001                         if (i == -1)
1002                                 {
1003                                 j = BN_num_bits_word((BN_ULONG)bl);
1004                                 }
1005                         sav_j = j;
1006                         j = 1<<(j-1);
1007                         assert(j <= al || j <= bl);
1008                         k = j+j;
1009                         t = BN_CTX_get(ctx);
1010                         if (al > j || bl > j)
1011                                 {
1012                                 bn_wexpand(t,k*4);
1013                                 bn_wexpand(rr,k*4);
1014                                 bn_mul_part_recursive(rr->d,a->d,b->d,
1015                                         j,al-j,bl-j,t->d);
1016                                 }
1017                         else    /* al <= j || bl <= j */
1018                                 {
1019                                 bn_wexpand(t,k*2);
1020                                 bn_wexpand(rr,k*2);
1021                                 bn_mul_recursive(rr->d,a->d,b->d,
1022                                         j,al-j,bl-j,t->d);
1023                                 }
1024                         rr->top=top;
1025                         goto end;
1026                         }
1027 #if 0
1028                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1029                         {
1030                         BIGNUM *tmp_bn = (BIGNUM *)b;
1031                         bn_wexpand(tmp_bn,al);
1032                         tmp_bn->d[bl]=0;
1033                         bl++;
1034                         i--;
1035                         }
1036                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1037                         {
1038                         BIGNUM *tmp_bn = (BIGNUM *)a;
1039                         bn_wexpand(tmp_bn,bl);
1040                         tmp_bn->d[al]=0;
1041                         al++;
1042                         i++;
1043                         }
1044                 if (i == 0)
1045                         {
1046                         /* symmetric and > 4 */
1047                         /* 16 or larger */
1048                         j=BN_num_bits_word((BN_ULONG)al);
1049                         j=1<<(j-1);
1050                         k=j+j;
1051                         t = BN_CTX_get(ctx);
1052                         if (al == j) /* exact multiple */
1053                                 {
1054                                 bn_wexpand(t,k*2);
1055                                 bn_wexpand(rr,k*2);
1056                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1057                                 }
1058                         else
1059                                 {
1060                                 bn_wexpand(t,k*4);
1061                                 bn_wexpand(rr,k*4);
1062                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1063                                 }
1064                         rr->top=top;
1065                         goto end;
1066                         }
1067 #endif
1068                 }
1069 #endif /* BN_RECURSION */
1070         if (bn_wexpand(rr,top) == NULL) goto err;
1071         rr->top=top;
1072         bn_mul_normal(rr->d,a->d,al,b->d,bl);
1073
1074 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1075 end:
1076 #endif
1077         bn_fix_top(rr);
1078         if (r != rr) BN_copy(r,rr);
1079         ret=1;
1080 err:
1081         BN_CTX_end(ctx);
1082         return(ret);
1083         }
1084
1085 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1086         {
1087         BN_ULONG *rr;
1088
1089 #ifdef BN_COUNT
1090         fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1091 #endif
1092
1093         if (na < nb)
1094                 {
1095                 int itmp;
1096                 BN_ULONG *ltmp;
1097
1098                 itmp=na; na=nb; nb=itmp;
1099                 ltmp=a;   a=b;   b=ltmp;
1100
1101                 }
1102         rr= &(r[na]);
1103         rr[0]=bn_mul_words(r,a,na,b[0]);
1104
1105         for (;;)
1106                 {
1107                 if (--nb <= 0) return;
1108                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1109                 if (--nb <= 0) return;
1110                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1111                 if (--nb <= 0) return;
1112                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1113                 if (--nb <= 0) return;
1114                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1115                 rr+=4;
1116                 r+=4;
1117                 b+=4;
1118                 }
1119         }
1120
1121 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1122         {
1123 #ifdef BN_COUNT
1124         fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1125 #endif
1126         bn_mul_words(r,a,n,b[0]);
1127
1128         for (;;)
1129                 {
1130                 if (--n <= 0) return;
1131                 bn_mul_add_words(&(r[1]),a,n,b[1]);
1132                 if (--n <= 0) return;
1133                 bn_mul_add_words(&(r[2]),a,n,b[2]);
1134                 if (--n <= 0) return;
1135                 bn_mul_add_words(&(r[3]),a,n,b[3]);
1136                 if (--n <= 0) return;
1137                 bn_mul_add_words(&(r[4]),a,n,b[4]);
1138                 r+=4;
1139                 b+=4;
1140                 }
1141         }