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 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
  70 /* Here follows specialised variants of bn_add_words() and
  71    bn_sub_words().  They have the property performing operations on
  72    arrays of different sizes.  The sizes of those arrays is expressed through
  73    cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
  74    which is the delta between the two lengths, calculated as len(a)-len(b).
  75    All lengths are the number of BN_ULONGs...  For the operations that require
  76    a result array as parameter, it must have the length cl+abs(dl).
  77    These functions should probably end up in bn_asm.c as soon as there are
  78    assembler counterparts for the systems that use assembler files.  */
  79
  80 BN_ULONG bn_sub_part_words(BN_ULONG *r,
  81         const BN_ULONG *a, const BN_ULONG *b,
  82         int cl, int dl)
  83         {
  84         BN_ULONG c, t;
  85
  86         assert(cl >= 0);
  87         c = bn_sub_words(r, a, b, cl);
  88
  89         if (dl == 0)
  90                 return c;
  91
  92         r += cl;
  93         a += cl;
  94         b += cl;
  95
  96         if (dl < 0)
  97                 {
  98 #ifdef BN_COUNT
  99                 fprintf(stderr, "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
 100 #endif
 101                 for (;;)
 102                         {
 103                         t = b[0];
 104                         r[0] = (0-t-c)&BN_MASK2;
 105                         if (t != 0) c=1;
 106                         if (++dl >= 0) break;
 107
 108                         t = b[1];
 109                         r[1] = (0-t-c)&BN_MASK2;
 110                         if (t != 0) c=1;
 111                         if (++dl >= 0) break;
 112
 113                         t = b[2];
 114                         r[2] = (0-t-c)&BN_MASK2;
 115                         if (t != 0) c=1;
 116                         if (++dl >= 0) break;
 117
 118                         t = b[3];
 119                         r[3] = (0-t-c)&BN_MASK2;
 120                         if (t != 0) c=1;
 121                         if (++dl >= 0) break;
 122
 123                         b += 4;
 124                         r += 4;
 125                         }
 126                 }
 127         else
 128                 {
 129                 int save_dl = dl;
 130 #ifdef BN_COUNT
 131                 fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
 132 #endif
 133                 while(c)
 134                         {
 135                         t = a[0];
 136                         r[0] = (t-c)&BN_MASK2;
 137                         if (t != 0) c=0;
 138                         if (--dl <= 0) break;
 139
 140                         t = a[1];
 141                         r[1] = (t-c)&BN_MASK2;
 142                         if (t != 0) c=0;
 143                         if (--dl <= 0) break;
 144
 145                         t = a[2];
 146                         r[2] = (t-c)&BN_MASK2;
 147                         if (t != 0) c=0;
 148                         if (--dl <= 0) break;
 149
 150                         t = a[3];
 151                         r[3] = (t-c)&BN_MASK2;
 152                         if (t != 0) c=0;
 153                         if (--dl <= 0) break;
 154
 155                         save_dl = dl;
 156                         a += 4;
 157                         r += 4;
 158                         }
 159                 if (dl > 0)
 160                         {
 161 #ifdef BN_COUNT
 162                         fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
 163 #endif
 164                         if (save_dl > dl)
 165                                 {
 166                                 switch (save_dl - dl)
 167                                         {
 168                                 case 1:
 169                                         r[1] = a[1];
 170                                         if (--dl <= 0) break;
 171                                 case 2:
 172                                         r[2] = a[2];
 173                                         if (--dl <= 0) break;
 174                                 case 3:
 175                                         r[3] = a[3];
 176                                         if (--dl <= 0) break;
 177                                         }
 178                                 a += 4;
 179                                 r += 4;
 180                                 }
 181                         }
 182                 if (dl > 0)
 183                         {
 184 #ifdef BN_COUNT
 185                         fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
 186 #endif
 187                         for(;;)
 188                                 {
 189                                 r[0] = a[0];
 190                                 if (--dl <= 0) break;
 191                                 r[1] = a[1];
 192                                 if (--dl <= 0) break;
 193                                 r[2] = a[2];
 194                                 if (--dl <= 0) break;
 195                                 r[3] = a[3];
 196                                 if (--dl <= 0) break;
 197
 198                                 a += 4;
 199                                 r += 4;
 200                                 }
 201                         }
 202                 }
 203         return c;
 204         }
 205 #endif
 206
 207 BN_ULONG bn_add_part_words(BN_ULONG *r,
 208         const BN_ULONG *a, const BN_ULONG *b,
 209         int cl, int dl)
 210         {
 211         BN_ULONG c, l, t;
 212
 213         assert(cl >= 0);
 214         c = bn_add_words(r, a, b, cl);
 215
 216         if (dl == 0)
 217                 return c;
 218
 219         r += cl;
 220         a += cl;
 221         b += cl;
 222
 223         if (dl < 0)
 224                 {
 225                 int save_dl = dl;
 226 #ifdef BN_COUNT
 227                 fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
 228 #endif
 229                 while (c)
 230                         {
 231                         l=(c+b[0])&BN_MASK2;
 232                         c=(l < c);
 233                         r[0]=l;
 234                         if (++dl >= 0) break;
 235
 236                         l=(c+b[1])&BN_MASK2;
 237                         c=(l < c);
 238                         r[1]=l;
 239                         if (++dl >= 0) break;
 240
 241                         l=(c+b[2])&BN_MASK2;
 242                         c=(l < c);
 243                         r[2]=l;
 244                         if (++dl >= 0) break;
 245
 246                         l=(c+b[3])&BN_MASK2;
 247                         c=(l < c);
 248                         r[3]=l;
 249                         if (++dl >= 0) break;
 250
 251                         save_dl = dl;
 252                         b+=4;
 253                         r+=4;
 254                         }
 255                 if (dl < 0)
 256                         {
 257 #ifdef BN_COUNT
 258                         fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
 259 #endif
 260                         if (save_dl < dl)
 261                                 {
 262                                 switch (dl - save_dl)
 263                                         {
 264                                 case 1:
 265                                         r[1] = b[1];
 266                                         if (++dl >= 0) break;
 267                                 case 2:
 268                                         r[2] = b[2];
 269                                         if (++dl >= 0) break;
 270                                 case 3:
 271                                         r[3] = b[3];
 272                                         if (++dl >= 0) break;
 273                                         }
 274                                 b += 4;
 275                                 r += 4;
 276                                 }
 277                         }
 278                 if (dl < 0)
 279                         {
 280 #ifdef BN_COUNT
 281                         fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
 282 #endif
 283                         for(;;)
 284                                 {
 285                                 r[0] = b[0];
 286                                 if (++dl >= 0) break;
 287                                 r[1] = b[1];
 288                                 if (++dl >= 0) break;
 289                                 r[2] = b[2];
 290                                 if (++dl >= 0) break;
 291                                 r[3] = b[3];
 292                                 if (++dl >= 0) break;
 293
 294                                 b += 4;
 295                                 r += 4;
 296                                 }
 297                         }
 298                 }
 299         else
 300                 {
 301                 int save_dl = dl;
 302 #ifdef BN_COUNT
 303                 fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
 304 #endif
 305                 while (c)
 306                         {
 307                         t=(a[0]+c)&BN_MASK2;
 308                         c=(t < c);
 309                         r[0]=t;
 310                         if (--dl <= 0) break;
 311
 312                         t=(a[1]+c)&BN_MASK2;
 313                         c=(t < c);
 314                         r[1]=t;
 315                         if (--dl <= 0) break;
 316
 317                         t=(a[2]+c)&BN_MASK2;
 318                         c=(t < c);
 319                         r[2]=t;
 320                         if (--dl <= 0) break;
 321
 322                         t=(a[3]+c)&BN_MASK2;
 323                         c=(t < c);
 324                         r[3]=t;
 325                         if (--dl <= 0) break;
 326
 327                         save_dl = dl;
 328                         a+=4;
 329                         r+=4;
 330                         }
 331 #ifdef BN_COUNT
 332                 fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
 333 #endif
 334                 if (dl > 0)
 335                         {
 336                         if (save_dl > dl)
 337                                 {
 338                                 switch (save_dl - dl)
 339                                         {
 340                                 case 1:
 341                                         r[1] = a[1];
 342                                         if (--dl <= 0) break;
 343                                 case 2:
 344                                         r[2] = a[2];
 345                                         if (--dl <= 0) break;
 346                                 case 3:
 347                                         r[3] = a[3];
 348                                         if (--dl <= 0) break;
 349                                         }
 350                                 a += 4;
 351                                 r += 4;
 352                                 }
 353                         }
 354                 if (dl > 0)
 355                         {
 356 #ifdef BN_COUNT
 357                         fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
 358 #endif
 359                         for(;;)
 360                                 {
 361                                 r[0] = a[0];
 362                                 if (--dl <= 0) break;
 363                                 r[1] = a[1];
 364                                 if (--dl <= 0) break;
 365                                 r[2] = a[2];
 366                                 if (--dl <= 0) break;
 367                                 r[3] = a[3];
 368                                 if (--dl <= 0) break;
 369
 370                                 a += 4;
 371                                 r += 4;
 372                                 }
 373                         }
 374                 }
 375         return c;
 376         }
 377
 378 #ifdef BN_RECURSION
 379 /* Karatsuba recursive multiplication algorithm
 380  * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
 381
 382 /*-
 383  * r is 2*n2 words in size,
 384  * a and b are both n2 words in size.
 385  * n2 must be a power of 2.
 386  * We multiply and return the result.
 387  * t must be 2*n2 words in size
 388  * We calculate
 389  * a[0]*b[0]
 390  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
 391  * a[1]*b[1]
 392  */
 393 /* dnX may not be positive, but n2/2+dnX has to be */
 394 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 395         int dna, int dnb, BN_ULONG *t)
 396         {
 397         int n=n2/2,c1,c2;
 398         int tna=n+dna, tnb=n+dnb;
 399         unsigned int neg,zero;
 400         BN_ULONG ln,lo,*p;
 401
 402 # ifdef BN_COUNT
 403         fprintf(stderr," bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
 404 # endif
 405 # ifdef BN_MUL_COMBA
 406 #  if 0
 407         if (n2 == 4)
 408                 {
 409                 bn_mul_comba4(r,a,b);
 410                 return;
 411                 }
 412 #  endif
 413         /* Only call bn_mul_comba 8 if n2 == 8 and the
 414          * two arrays are complete [steve]
 415          */
 416         if (n2 == 8 && dna == 0 && dnb == 0)
 417                 {
 418                 bn_mul_comba8(r,a,b);
 419                 return;
 420                 }
 421 # endif /* BN_MUL_COMBA */
 422         /* Else do normal multiply */
 423         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
 424                 {
 425                 bn_mul_normal(r,a,n2+dna,b,n2+dnb);
 426                 if ((dna + dnb) < 0)
 427                         memset(&r[2*n2 + dna + dnb], 0,
 428                                 sizeof(BN_ULONG) * -(dna + dnb));
 429                 return;
 430                 }
 431         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 432         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 433         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 434         zero=neg=0;
 435         switch (c1*3+c2)
 436                 {
 437         case -4:
 438                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 439                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 440                 break;
 441         case -3:
 442                 zero=1;
 443                 break;
 444         case -2:
 445                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 446                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 447                 neg=1;
 448                 break;
 449         case -1:
 450         case 0:
 451         case 1:
 452                 zero=1;
 453                 break;
 454         case 2:
 455                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 456                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 457                 neg=1;
 458                 break;
 459         case 3:
 460                 zero=1;
 461                 break;
 462         case 4:
 463                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 464                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 465                 break;
 466                 }
 467
 468 # ifdef BN_MUL_COMBA
 469         if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
 470                                                extra args to do this well */
 471                 {
 472                 if (!zero)
 473                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 474                 else
 475                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 476
 477                 bn_mul_comba4(r,a,b);
 478                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 479                 }
 480         else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
 481                                                     take extra args to do this
 482                                                     well */
 483                 {
 484                 if (!zero)
 485                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 486                 else
 487                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 488
 489                 bn_mul_comba8(r,a,b);
 490                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 491                 }
 492         else
 493 # endif /* BN_MUL_COMBA */
 494                 {
 495                 p= &(t[n2*2]);
 496                 if (!zero)
 497                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 498                 else
 499                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 500                 bn_mul_recursive(r,a,b,n,0,0,p);
 501                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
 502                 }
 503
 504         /*-
 505          * t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 506          * r[10] holds (a[0]*b[0])
 507          * r[32] holds (b[1]*b[1])
 508          */
 509
 510         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 511
 512         if (neg) /* if t[32] is negative */
 513                 {
 514                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 515                 }
 516         else
 517                 {
 518                 /* Might have a carry */
 519                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 520                 }
 521
 522         /*-
 523          * t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 524          * r[10] holds (a[0]*b[0])
 525          * r[32] holds (b[1]*b[1])
 526          * c1 holds the carry bits
 527          */
 528         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 529         if (c1)
 530                 {
 531                 p= &(r[n+n2]);
 532                 lo= *p;
 533                 ln=(lo+c1)&BN_MASK2;
 534                 *p=ln;
 535
 536                 /* The overflow will stop before we over write
 537                  * words we should not overwrite */
 538                 if (ln < (BN_ULONG)c1)
 539                         {
 540                         do      {
 541                                 p++;
 542                                 lo= *p;
 543                                 ln=(lo+1)&BN_MASK2;
 544                                 *p=ln;
 545                                 } while (ln == 0);
 546                         }
 547                 }
 548         }
 549
 550 /* n+tn is the word length
 551  * t needs to be n*4 is size, as does r */
 552 /* tnX may not be negative but less than n */
 553 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
 554              int tna, int tnb, BN_ULONG *t)
 555         {
 556         int i,j,n2=n*2;
 557         int c1,c2,neg;
 558         BN_ULONG ln,lo,*p;
 559
 560 # ifdef BN_COUNT
 561         fprintf(stderr," bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
 562                 n, tna, n, tnb);
 563 # endif
 564         if (n < 8)
 565                 {
 566                 bn_mul_normal(r,a,n+tna,b,n+tnb);
 567                 return;
 568                 }
 569
 570         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 571         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 572         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 573         neg=0;
 574         switch (c1*3+c2)
 575                 {
 576         case -4:
 577                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 578                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 579                 break;
 580         case -3:
 581                 /* break; */
 582         case -2:
 583                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 584                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 585                 neg=1;
 586                 break;
 587         case -1:
 588         case 0:
 589         case 1:
 590                 /* break; */
 591         case 2:
 592                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 593                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 594                 neg=1;
 595                 break;
 596         case 3:
 597                 /* break; */
 598         case 4:
 599                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 600                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 601                 break;
 602                 }
 603                 /* The zero case isn't yet implemented here. The speedup
 604                    would probably be negligible. */
 605 # if 0
 606         if (n == 4)
 607                 {
 608                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 609                 bn_mul_comba4(r,a,b);
 610                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 611                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 612                 }
 613         else
 614 # endif
 615         if (n == 8)
 616                 {
 617                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 618                 bn_mul_comba8(r,a,b);
 619                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 620                 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
 621                 }
 622         else
 623                 {
 624                 p= &(t[n2*2]);
 625                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 626                 bn_mul_recursive(r,a,b,n,0,0,p);
 627                 i=n/2;
 628                 /* If there is only a bottom half to the number,
 629                  * just do it */
 630                 if (tna > tnb)
 631                         j = tna - i;
 632                 else
 633                         j = tnb - i;
 634                 if (j == 0)
 635                         {
 636                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
 637                                 i,tna-i,tnb-i,p);
 638                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 639                         }
 640                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 641                                 {
 642                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 643                                         i,tna-i,tnb-i,p);
 644                                 memset(&(r[n2+tna+tnb]),0,
 645                                         sizeof(BN_ULONG)*(n2-tna-tnb));
 646                                 }
 647                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 648                         {
 649                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 650                         if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
 651                                 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
 652                                 {
 653                                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 654                                 }
 655                         else
 656                                 {
 657                                 for (;;)
 658                                         {
 659                                         i/=2;
 660                                         /* these simplified conditions work
 661                                          * exclusively because difference
 662                                          * between tna and tnb is 1 or 0 */
 663                                         if (i < tna || i < tnb)
 664                                                 {
 665                                                 bn_mul_part_recursive(&(r[n2]),
 666                                                         &(a[n]),&(b[n]),
 667                                                         i,tna-i,tnb-i,p);
 668                                                 break;
 669                                                 }
 670                                         else if (i == tna || i == tnb)
 671                                                 {
 672                                                 bn_mul_recursive(&(r[n2]),
 673                                                         &(a[n]),&(b[n]),
 674                                                         i,tna-i,tnb-i,p);
 675                                                 break;
 676                                                 }
 677                                         }
 678                                 }
 679                         }
 680                 }
 681
 682         /*-
 683          * t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 684          * r[10] holds (a[0]*b[0])
 685          * r[32] holds (b[1]*b[1])
 686          */
 687
 688         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 689
 690         if (neg) /* if t[32] is negative */
 691                 {
 692                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 693                 }
 694         else
 695                 {
 696                 /* Might have a carry */
 697                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 698                 }
 699
 700         /*-
 701          * t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 702          * r[10] holds (a[0]*b[0])
 703          * r[32] holds (b[1]*b[1])
 704          * c1 holds the carry bits
 705          */
 706         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 707         if (c1)
 708                 {
 709                 p= &(r[n+n2]);
 710                 lo= *p;
 711                 ln=(lo+c1)&BN_MASK2;
 712                 *p=ln;
 713
 714                 /* The overflow will stop before we over write
 715                  * words we should not overwrite */
 716                 if (ln < (BN_ULONG)c1)
 717                         {
 718                         do      {
 719                                 p++;
 720                                 lo= *p;
 721                                 ln=(lo+1)&BN_MASK2;
 722                                 *p=ln;
 723                                 } while (ln == 0);
 724                         }
 725                 }
 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  */
 732 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 733              BN_ULONG *t)
 734         {
 735         int n=n2/2;
 736
 737 # ifdef BN_COUNT
 738         fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
 739 # endif
 740
 741         bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
 742         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 743                 {
 744                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 745                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 746                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 747                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 748                 }
 749         else
 750                 {
 751                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 752                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 753                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 754                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 755                 }
 756         }
 757
 758 /*-
 759  * a and b must be the same size, which is n2.
 760  * r needs to be n2 words and t needs to be n2*2
 761  * l is the low words of the output.
 762  * t needs to be n2*3
 763  */
 764 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 765              BN_ULONG *t)
 766         {
 767         int i,n;
 768         int c1,c2;
 769         int neg,oneg,zero;
 770         BN_ULONG ll,lc,*lp,*mp;
 771
 772 # ifdef BN_COUNT
 773         fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
 774 # endif
 775         n=n2/2;
 776
 777         /* Calculate (al-ah)*(bh-bl) */
 778         neg=zero=0;
 779         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 780         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 781         switch (c1*3+c2)
 782                 {
 783         case -4:
 784                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 785                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 786                 break;
 787         case -3:
 788                 zero=1;
 789                 break;
 790         case -2:
 791                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 792                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 793                 neg=1;
 794                 break;
 795         case -1:
 796         case 0:
 797         case 1:
 798                 zero=1;
 799                 break;
 800         case 2:
 801                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 802                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 803                 neg=1;
 804                 break;
 805         case 3:
 806                 zero=1;
 807                 break;
 808         case 4:
 809                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 810                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 811                 break;
 812                 }
 813
 814         oneg=neg;
 815         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 816         /* r[10] = (a[1]*b[1]) */
 817 # ifdef BN_MUL_COMBA
 818         if (n == 8)
 819                 {
 820                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 821                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 822                 }
 823         else
 824 # endif
 825                 {
 826                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
 827                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
 828                 }
 829
 830         /*-
 831          * s0 == low(al*bl)
 832          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 833          * We know s0 and s1 so the only unknown is high(al*bl)
 834          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 835          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 836          */
 837         if (l != NULL)
 838                 {
 839                 lp= &(t[n2+n]);
 840                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 841                 }
 842         else
 843                 {
 844                 c1=0;
 845                 lp= &(r[0]);
 846                 }
 847
 848         if (neg)
 849                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 850         else
 851                 {
 852                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 853                 neg=0;
 854                 }
 855
 856         if (l != NULL)
 857                 {
 858                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 859                 }
 860         else
 861                 {
 862                 lp= &(t[n2+n]);
 863                 mp= &(t[n2]);
 864                 for (i=0; i<n; i++)
 865                         lp[i]=((~mp[i])+1)&BN_MASK2;
 866                 }
 867
 868         /*-
 869          * s[0] = low(al*bl)
 870          * t[3] = high(al*bl)
 871          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 872          * r[10] = (a[1]*b[1])
 873          */
 874         /*-
 875          * R[10] = al*bl
 876          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 877          * R[32] = ah*bh
 878          */
 879         /*-
 880          * R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 881          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 882          * R[3]=r[1]+(carry/borrow)
 883          */
 884         if (l != NULL)
 885                 {
 886                 lp= &(t[n2]);
 887                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 888                 }
 889         else
 890                 {
 891                 lp= &(t[n2+n]);
 892                 c1=0;
 893                 }
 894         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 895         if (oneg)
 896                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 897         else
 898                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 899
 900         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 901         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 902         if (oneg)
 903                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 904         else
 905                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 906
 907         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 908                 {
 909                 i=0;
 910                 if (c1 > 0)
 911                         {
 912                         lc=c1;
 913                         do      {
 914                                 ll=(r[i]+lc)&BN_MASK2;
 915                                 r[i++]=ll;
 916                                 lc=(lc > ll);
 917                                 } while (lc);
 918                         }
 919                 else
 920                         {
 921                         lc= -c1;
 922                         do      {
 923                                 ll=r[i];
 924                                 r[i++]=(ll-lc)&BN_MASK2;
 925                                 lc=(lc > ll);
 926                                 } while (lc);
 927                         }
 928                 }
 929         if (c2 != 0) /* Add starting at r[1] */
 930                 {
 931                 i=n;
 932                 if (c2 > 0)
 933                         {
 934                         lc=c2;
 935                         do      {
 936                                 ll=(r[i]+lc)&BN_MASK2;
 937                                 r[i++]=ll;
 938                                 lc=(lc > ll);
 939                                 } while (lc);
 940                         }
 941                 else
 942                         {
 943                         lc= -c2;
 944                         do      {
 945                                 ll=r[i];
 946                                 r[i++]=(ll-lc)&BN_MASK2;
 947                                 lc=(lc > ll);
 948                                 } while (lc);
 949                         }
 950                 }
 951         }
 952 #endif /* BN_RECURSION */
 953
 954 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 955         {
 956         int ret=0;
 957         int top,al,bl;
 958         BIGNUM *rr;
 959 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 960         int i;
 961 #endif
 962 #ifdef BN_RECURSION
 963         BIGNUM *t=NULL;
 964         int j=0,k;
 965 #endif
 966
 967 #ifdef BN_COUNT
 968         fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
 969 #endif
 970
 971         bn_check_top(a);
 972         bn_check_top(b);
 973         bn_check_top(r);
 974
 975         al=a->top;
 976         bl=b->top;
 977
 978         if ((al == 0) || (bl == 0))
 979                 {
 980                 BN_zero(r);
 981                 return(1);
 982                 }
 983         top=al+bl;
 984
 985         BN_CTX_start(ctx);
 986         if ((r == a) || (r == b))
 987                 {
 988                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
 989                 }
 990         else
 991                 rr = r;
 992         rr->neg=a->neg^b->neg;
 993
 994 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 995         i = al-bl;
 996 #endif
 997 #ifdef BN_MUL_COMBA
 998         if (i == 0)
 999                 {
1000 # if 0
1001                 if (al == 4)
1002                         {
1003                         if (bn_wexpand(rr,8) == NULL) goto err;
1004                         rr->top=8;
1005                         bn_mul_comba4(rr->d,a->d,b->d);
1006                         goto end;
1007                         }
1008 # endif
1009                 if (al == 8)
1010                         {
1011                         if (bn_wexpand(rr,16) == NULL) goto err;
1012                         rr->top=16;
1013                         bn_mul_comba8(rr->d,a->d,b->d);
1014                         goto end;
1015                         }
1016                 }
1017 #endif /* BN_MUL_COMBA */
1018 #ifdef BN_RECURSION
1019         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
1020                 {
1021                 if (i >= -1 && i <= 1)
1022                         {
1023                         /* Find out the power of two lower or equal
1024                            to the longest of the two numbers */
1025                         if (i >= 0)
1026                                 {
1027                                 j = BN_num_bits_word((BN_ULONG)al);
1028                                 }
1029                         if (i == -1)
1030                                 {
1031                                 j = BN_num_bits_word((BN_ULONG)bl);
1032                                 }
1033                         j = 1<<(j-1);
1034                         assert(j <= al || j <= bl);
1035                         k = j+j;
1036                         t = BN_CTX_get(ctx);
1037                         if (t == NULL)
1038                                 goto err;
1039                         if (al > j || bl > j)
1040                                 {
1041                                 if (bn_wexpand(t,k*4) == NULL) goto err;
1042                                 if (bn_wexpand(rr,k*4) == NULL) goto err;
1043                                 bn_mul_part_recursive(rr->d,a->d,b->d,
1044                                         j,al-j,bl-j,t->d);
1045                                 }
1046                         else    /* al <= j || bl <= j */
1047                                 {
1048                                 if (bn_wexpand(t,k*2) == NULL) goto err;
1049                                 if (bn_wexpand(rr,k*2) == NULL) goto err;
1050                                 bn_mul_recursive(rr->d,a->d,b->d,
1051                                         j,al-j,bl-j,t->d);
1052                                 }
1053                         rr->top=top;
1054                         goto end;
1055                         }
1056 #if 0
1057                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1058                         {
1059                         BIGNUM *tmp_bn = (BIGNUM *)b;
1060                         if (bn_wexpand(tmp_bn,al) == NULL) goto err;
1061                         tmp_bn->d[bl]=0;
1062                         bl++;
1063                         i--;
1064                         }
1065                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1066                         {
1067                         BIGNUM *tmp_bn = (BIGNUM *)a;
1068                         if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
1069                         tmp_bn->d[al]=0;
1070                         al++;
1071                         i++;
1072                         }
1073                 if (i == 0)
1074                         {
1075                         /* symmetric and > 4 */
1076                         /* 16 or larger */
1077                         j=BN_num_bits_word((BN_ULONG)al);
1078                         j=1<<(j-1);
1079                         k=j+j;
1080                         t = BN_CTX_get(ctx);
1081                         if (al == j) /* exact multiple */
1082                                 {
1083                                 if (bn_wexpand(t,k*2) == NULL) goto err;
1084                                 if (bn_wexpand(rr,k*2) == NULL) goto err;
1085                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1086                                 }
1087                         else
1088                                 {
1089                                 if (bn_wexpand(t,k*4) == NULL) goto err;
1090                                 if (bn_wexpand(rr,k*4) == NULL) goto err;
1091                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1092                                 }
1093                         rr->top=top;
1094                         goto end;
1095                         }
1096 #endif
1097                 }
1098 #endif /* BN_RECURSION */
1099         if (bn_wexpand(rr,top) == NULL) goto err;
1100         rr->top=top;
1101         bn_mul_normal(rr->d,a->d,al,b->d,bl);
1102
1103 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1104 end:
1105 #endif
1106         bn_correct_top(rr);
1107         if (r != rr) BN_copy(r,rr);
1108         ret=1;
1109 err:
1110         bn_check_top(r);
1111         BN_CTX_end(ctx);
1112         return(ret);
1113         }
1114
1115 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1116         {
1117         BN_ULONG *rr;
1118
1119 #ifdef BN_COUNT
1120         fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1121 #endif
1122
1123         if (na < nb)
1124                 {
1125                 int itmp;
1126                 BN_ULONG *ltmp;
1127
1128                 itmp=na; na=nb; nb=itmp;
1129                 ltmp=a;   a=b;   b=ltmp;
1130
1131                 }
1132         rr= &(r[na]);
1133         if (nb <= 0)
1134                 {
1135                 (void)bn_mul_words(r,a,na,0);
1136                 return;
1137                 }
1138         else
1139                 rr[0]=bn_mul_words(r,a,na,b[0]);
1140
1141         for (;;)
1142                 {
1143                 if (--nb <= 0) return;
1144                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1145                 if (--nb <= 0) return;
1146                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1147                 if (--nb <= 0) return;
1148                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1149                 if (--nb <= 0) return;
1150                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1151                 rr+=4;
1152                 r+=4;
1153                 b+=4;
1154                 }
1155         }
1156
1157 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1158         {
1159 #ifdef BN_COUNT
1160         fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1161 #endif
1162         bn_mul_words(r,a,n,b[0]);
1163
1164         for (;;)
1165                 {
1166                 if (--n <= 0) return;
1167                 bn_mul_add_words(&(r[1]),a,n,b[1]);
1168                 if (--n <= 0) return;
1169                 bn_mul_add_words(&(r[2]),a,n,b[2]);
1170                 if (--n <= 0) return;
1171                 bn_mul_add_words(&(r[3]),a,n,b[3]);
1172                 if (--n <= 0) return;
1173                 bn_mul_add_words(&(r[4]),a,n,b[4]);
1174                 r+=4;
1175                 b+=4;
1176                 }
1177         }