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