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(__i386) /* Assembler implementation exists only for x86 */
  70 /* Here follows specialised variants of bn_add_words() and
  71    bn_sub_words().  They have the property performing operations on
  72    arrays of different sizes.  The sizes of those arrays is expressed through
  73    cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
  74    which is the delta between the two lengths, calculated as len(a)-len(b).
  75    All lengths are the number of BN_ULONGs...  For the operations that require
  76    a result array as parameter, it must have the length cl+abs(dl).
  77    These functions should probably end up in bn_asm.c as soon as there are
  78    assembler counterparts for the systems that use assembler files.  */
  79
  80 BN_ULONG bn_sub_part_words(BN_ULONG *r,
  81         const BN_ULONG *a, const BN_ULONG *b,
  82         int cl, int dl)
  83         {
  84         BN_ULONG c, t;
  85
  86         assert(cl >= 0);
  87         c = bn_sub_words(r, a, b, cl);
  88
  89         if (dl == 0)
  90                 return c;
  91
  92         r += cl;
  93         a += cl;
  94         b += cl;
  95
  96         if (dl < 0)
  97                 {
  98 #ifdef BN_COUNT
  99                 fprintf(stderr, "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
 100 #endif
 101                 for (;;)
 102                         {
 103                         t = b[0];
 104                         r[0] = (0-t-c)&BN_MASK2;
 105                         if (t != 0) c=1;
 106                         if (++dl >= 0) break;
 107
 108                         t = b[1];
 109                         r[1] = (0-t-c)&BN_MASK2;
 110                         if (t != 0) c=1;
 111                         if (++dl >= 0) break;
 112
 113                         t = b[2];
 114                         r[2] = (0-t-c)&BN_MASK2;
 115                         if (t != 0) c=1;
 116                         if (++dl >= 0) break;
 117
 118                         t = b[3];
 119                         r[3] = (0-t-c)&BN_MASK2;
 120                         if (t != 0) c=1;
 121                         if (++dl >= 0) break;
 122
 123                         b += 4;
 124                         r += 4;
 125                         }
 126                 }
 127         else
 128                 {
 129                 int save_dl = dl;
 130 #ifdef BN_COUNT
 131                 fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
 132 #endif
 133                 while(c)
 134                         {
 135                         t = a[0];
 136                         r[0] = (t-c)&BN_MASK2;
 137                         if (t != 0) c=0;
 138                         if (--dl <= 0) break;
 139
 140                         t = a[1];
 141                         r[1] = (t-c)&BN_MASK2;
 142                         if (t != 0) c=0;
 143                         if (--dl <= 0) break;
 144
 145                         t = a[2];
 146                         r[2] = (t-c)&BN_MASK2;
 147                         if (t != 0) c=0;
 148                         if (--dl <= 0) break;
 149
 150                         t = a[3];
 151                         r[3] = (t-c)&BN_MASK2;
 152                         if (t != 0) c=0;
 153                         if (--dl <= 0) break;
 154
 155                         save_dl = dl;
 156                         a += 4;
 157                         r += 4;
 158                         }
 159                 if (dl > 0)
 160                         {
 161 #ifdef BN_COUNT
 162                         fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
 163 #endif
 164                         if (save_dl > dl)
 165                                 {
 166                                 switch (save_dl - dl)
 167                                         {
 168                                 case 1:
 169                                         r[1] = a[1];
 170                                         if (--dl <= 0) break;
 171                                 case 2:
 172                                         r[2] = a[2];
 173                                         if (--dl <= 0) break;
 174                                 case 3:
 175                                         r[3] = a[3];
 176                                         if (--dl <= 0) break;
 177                                         }
 178                                 a += 4;
 179                                 r += 4;
 180                                 }
 181                         }
 182                 if (dl > 0)
 183                         {
 184 #ifdef BN_COUNT
 185                         fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
 186 #endif
 187                         for(;;)
 188                                 {
 189                                 r[0] = a[0];
 190                                 if (--dl <= 0) break;
 191                                 r[1] = a[1];
 192                                 if (--dl <= 0) break;
 193                                 r[2] = a[2];
 194                                 if (--dl <= 0) break;
 195                                 r[3] = a[3];
 196                                 if (--dl <= 0) break;
 197
 198                                 a += 4;
 199                                 r += 4;
 200                                 }
 201                         }
 202                 }
 203         return c;
 204         }
 205 #endif
 206
 207 BN_ULONG bn_add_part_words(BN_ULONG *r,
 208         const BN_ULONG *a, const BN_ULONG *b,
 209         int cl, int dl)
 210         {
 211         BN_ULONG c, l, t;
 212
 213         assert(cl >= 0);
 214         c = bn_add_words(r, a, b, cl);
 215
 216         if (dl == 0)
 217                 return c;
 218
 219         r += cl;
 220         a += cl;
 221         b += cl;
 222
 223         if (dl < 0)
 224                 {
 225                 int save_dl = dl;
 226 #ifdef BN_COUNT
 227                 fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
 228 #endif
 229                 while (c)
 230                         {
 231                         l=(c+b[0])&BN_MASK2;
 232                         c=(l < c);
 233                         r[0]=l;
 234                         if (++dl >= 0) break;
 235
 236                         l=(c+b[1])&BN_MASK2;
 237                         c=(l < c);
 238                         r[1]=l;
 239                         if (++dl >= 0) break;
 240
 241                         l=(c+b[2])&BN_MASK2;
 242                         c=(l < c);
 243                         r[2]=l;
 244                         if (++dl >= 0) break;
 245
 246                         l=(c+b[3])&BN_MASK2;
 247                         c=(l < c);
 248                         r[3]=l;
 249                         if (++dl >= 0) break;
 250
 251                         save_dl = dl;
 252                         b+=4;
 253                         r+=4;
 254                         }
 255                 if (dl < 0)
 256                         {
 257 #ifdef BN_COUNT
 258                         fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
 259 #endif
 260                         if (save_dl < dl)
 261                                 {
 262                                 switch (dl - save_dl)
 263                                         {
 264                                 case 1:
 265                                         r[1] = b[1];
 266                                         if (++dl >= 0) break;
 267                                 case 2:
 268                                         r[2] = b[2];
 269                                         if (++dl >= 0) break;
 270                                 case 3:
 271                                         r[3] = b[3];
 272                                         if (++dl >= 0) break;
 273                                         }
 274                                 b += 4;
 275                                 r += 4;
 276                                 }
 277                         }
 278                 if (dl < 0)
 279                         {
 280 #ifdef BN_COUNT
 281                         fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
 282 #endif
 283                         for(;;)
 284                                 {
 285                                 r[0] = b[0];
 286                                 if (++dl >= 0) break;
 287                                 r[1] = b[1];
 288                                 if (++dl >= 0) break;
 289                                 r[2] = b[2];
 290                                 if (++dl >= 0) break;
 291                                 r[3] = b[3];
 292                                 if (++dl >= 0) break;
 293
 294                                 b += 4;
 295                                 r += 4;
 296                                 }
 297                         }
 298                 }
 299         else
 300                 {
 301                 int save_dl = dl;
 302 #ifdef BN_COUNT
 303                 fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
 304 #endif
 305                 while (c)
 306                         {
 307                         t=(a[0]+c)&BN_MASK2;
 308                         c=(t < c);
 309                         r[0]=t;
 310                         if (--dl <= 0) break;
 311
 312                         t=(a[1]+c)&BN_MASK2;
 313                         c=(t < c);
 314                         r[1]=t;
 315                         if (--dl <= 0) break;
 316
 317                         t=(a[2]+c)&BN_MASK2;
 318                         c=(t < c);
 319                         r[2]=t;
 320                         if (--dl <= 0) break;
 321
 322                         t=(a[3]+c)&BN_MASK2;
 323                         c=(t < c);
 324                         r[3]=t;
 325                         if (--dl <= 0) break;
 326
 327                         save_dl = dl;
 328                         a+=4;
 329                         r+=4;
 330                         }
 331 #ifdef BN_COUNT
 332                 fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
 333 #endif
 334                 if (dl > 0)
 335                         {
 336                         if (save_dl > dl)
 337                                 {
 338                                 switch (save_dl - dl)
 339                                         {
 340                                 case 1:
 341                                         r[1] = a[1];
 342                                         if (--dl <= 0) break;
 343                                 case 2:
 344                                         r[2] = a[2];
 345                                         if (--dl <= 0) break;
 346                                 case 3:
 347                                         r[3] = a[3];
 348                                         if (--dl <= 0) break;
 349                                         }
 350                                 a += 4;
 351                                 r += 4;
 352                                 }
 353                         }
 354                 if (dl > 0)
 355                         {
 356 #ifdef BN_COUNT
 357                         fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
 358 #endif
 359                         for(;;)
 360                                 {
 361                                 r[0] = a[0];
 362                                 if (--dl <= 0) break;
 363                                 r[1] = a[1];
 364                                 if (--dl <= 0) break;
 365                                 r[2] = a[2];
 366                                 if (--dl <= 0) break;
 367                                 r[3] = a[3];
 368                                 if (--dl <= 0) break;
 369
 370                                 a += 4;
 371                                 r += 4;
 372                                 }
 373                         }
 374                 }
 375         return c;
 376         }
 377
 378 #ifdef BN_RECURSION
 379 /* Karatsuba recursive multiplication algorithm
 380  * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
 381
 382 /* r is 2*n2 words in size,
 383  * a and b are both n2 words in size.
 384  * n2 must be a power of 2.
 385  * We multiply and return the result.
 386  * t must be 2*n2 words in size
 387  * We calculate
 388  * a[0]*b[0]
 389  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
 390  * a[1]*b[1]
 391  */
 392 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 393         int dna, int dnb, BN_ULONG *t)
 394         {
 395         int n=n2/2,c1,c2;
 396         int tna=n+dna, tnb=n+dnb;
 397         unsigned int neg,zero;
 398         BN_ULONG ln,lo,*p;
 399
 400 # ifdef BN_COUNT
 401         fprintf(stderr," bn_mul_recursive %d * %d\n",n2,n2);
 402 # endif
 403 # ifdef BN_MUL_COMBA
 404 #  if 0
 405         if (n2 == 4)
 406                 {
 407                 bn_mul_comba4(r,a,b);
 408                 return;
 409                 }
 410 #  endif
 411         if (n2 == 8)
 412                 {
 413                 bn_mul_comba8(r,a,b);
 414                 return;
 415                 }
 416 # endif /* BN_MUL_COMBA */
 417         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
 418                 {
 419                 /* This should not happen */
 420                 bn_mul_normal(r,a,n2,b,n2);
 421                 return;
 422                 }
 423         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 424         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 425         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 426         zero=neg=0;
 427         switch (c1*3+c2)
 428                 {
 429         case -4:
 430                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 431                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 432                 break;
 433         case -3:
 434                 zero=1;
 435                 break;
 436         case -2:
 437                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 438                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 439                 neg=1;
 440                 break;
 441         case -1:
 442         case 0:
 443         case 1:
 444                 zero=1;
 445                 break;
 446         case 2:
 447                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 448                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 449                 neg=1;
 450                 break;
 451         case 3:
 452                 zero=1;
 453                 break;
 454         case 4:
 455                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 456                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 457                 break;
 458                 }
 459
 460 # ifdef BN_MUL_COMBA
 461         if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
 462                                                extra args to do this well */
 463                 {
 464                 if (!zero)
 465                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 466                 else
 467                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 468
 469                 bn_mul_comba4(r,a,b);
 470                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 471                 }
 472         else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
 473                                                     take extra args to do this
 474                                                     well */
 475                 {
 476                 if (!zero)
 477                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 478                 else
 479                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 480
 481                 bn_mul_comba8(r,a,b);
 482                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 483                 }
 484         else
 485 # endif /* BN_MUL_COMBA */
 486                 {
 487                 p= &(t[n2*2]);
 488                 if (!zero)
 489                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 490                 else
 491                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 492                 bn_mul_recursive(r,a,b,n,0,0,p);
 493                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
 494                 }
 495
 496         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 497          * r[10] holds (a[0]*b[0])
 498          * r[32] holds (b[1]*b[1])
 499          */
 500
 501         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 502
 503         if (neg) /* if t[32] is negative */
 504                 {
 505                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 506                 }
 507         else
 508                 {
 509                 /* Might have a carry */
 510                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 511                 }
 512
 513         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 514          * r[10] holds (a[0]*b[0])
 515          * r[32] holds (b[1]*b[1])
 516          * c1 holds the carry bits
 517          */
 518         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 519         if (c1)
 520                 {
 521                 p= &(r[n+n2]);
 522                 lo= *p;
 523                 ln=(lo+c1)&BN_MASK2;
 524                 *p=ln;
 525
 526                 /* The overflow will stop before we over write
 527                  * words we should not overwrite */
 528                 if (ln < (BN_ULONG)c1)
 529                         {
 530                         do      {
 531                                 p++;
 532                                 lo= *p;
 533                                 ln=(lo+1)&BN_MASK2;
 534                                 *p=ln;
 535                                 } while (ln == 0);
 536                         }
 537                 }
 538         }
 539
 540 /* n+tn is the word length
 541  * t needs to be n*4 is size, as does r */
 542 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
 543              int tna, int tnb, BN_ULONG *t)
 544         {
 545         int i,j,n2=n*2;
 546         unsigned int c1,c2,neg,zero;
 547         BN_ULONG ln,lo,*p;
 548
 549 # ifdef BN_COUNT
 550         fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
 551                 tna, n, tnb, n);
 552 # endif
 553         if (n < 8)
 554                 {
 555                 bn_mul_normal(r,a,n+tna,b,n+tnb);
 556                 return;
 557                 }
 558
 559         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 560         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 561         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 562         zero=neg=0;
 563         switch (c1*3+c2)
 564                 {
 565         case -4:
 566                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 567                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 568                 break;
 569         case -3:
 570                 zero=1;
 571                 /* break; */
 572         case -2:
 573                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 574                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 575                 neg=1;
 576                 break;
 577         case -1:
 578         case 0:
 579         case 1:
 580                 zero=1;
 581                 /* break; */
 582         case 2:
 583                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 584                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 585                 neg=1;
 586                 break;
 587         case 3:
 588                 zero=1;
 589                 /* break; */
 590         case 4:
 591                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 592                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 593                 break;
 594                 }
 595                 /* The zero case isn't yet implemented here. The speedup
 596                    would probably be negligible. */
 597 # if 0
 598         if (n == 4)
 599                 {
 600                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 601                 bn_mul_comba4(r,a,b);
 602                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 603                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 604                 }
 605         else
 606 # endif
 607         if (n == 8)
 608                 {
 609                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 610                 bn_mul_comba8(r,a,b);
 611                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 612                 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
 613                 }
 614         else
 615                 {
 616                 p= &(t[n2*2]);
 617                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 618                 bn_mul_recursive(r,a,b,n,0,0,p);
 619                 i=n/2;
 620                 /* If there is only a bottom half to the number,
 621                  * just do it */
 622                 if (tna > tnb)
 623                         j = tna - i;
 624                 else
 625                         j = tnb - i;
 626                 if (j == 0)
 627                         {
 628                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
 629                                 i,tna-i,tnb-i,p);
 630                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 631                         }
 632                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 633                                 {
 634                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 635                                         i,tna-i,tnb-i,p);
 636                                 memset(&(r[n2+tna+tnb]),0,
 637                                         sizeof(BN_ULONG)*(n2-tna-tnb));
 638                                 }
 639                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 640                         {
 641                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 642                         if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
 643                                 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
 644                                 {
 645                                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 646                                 }
 647                         else
 648                                 {
 649                                 for (;;)
 650                                         {
 651                                         i/=2;
 652                                         if (i < tna && i < tnb)
 653                                                 {
 654                                                 bn_mul_part_recursive(&(r[n2]),
 655                                                         &(a[n]),&(b[n]),
 656                                                         i,tna-i,tnb-i,p);
 657                                                 break;
 658                                                 }
 659                                         else if (i <= tna && i <= tnb)
 660                                                 {
 661                                                 bn_mul_recursive(&(r[n2]),
 662                                                         &(a[n]),&(b[n]),
 663                                                         i,tna-i,tnb-i,p);
 664                                                 break;
 665                                                 }
 666                                         }
 667                                 }
 668                         }
 669                 }
 670
 671         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 672          * r[10] holds (a[0]*b[0])
 673          * r[32] holds (b[1]*b[1])
 674          */
 675
 676         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 677
 678         if (neg) /* if t[32] is negative */
 679                 {
 680                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 681                 }
 682         else
 683                 {
 684                 /* Might have a carry */
 685                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 686                 }
 687
 688         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 689          * r[10] holds (a[0]*b[0])
 690          * r[32] holds (b[1]*b[1])
 691          * c1 holds the carry bits
 692          */
 693         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 694         if (c1)
 695                 {
 696                 p= &(r[n+n2]);
 697                 lo= *p;
 698                 ln=(lo+c1)&BN_MASK2;
 699                 *p=ln;
 700
 701                 /* The overflow will stop before we over write
 702                  * words we should not overwrite */
 703                 if (ln < c1)
 704                         {
 705                         do      {
 706                                 p++;
 707                                 lo= *p;
 708                                 ln=(lo+1)&BN_MASK2;
 709                                 *p=ln;
 710                                 } while (ln == 0);
 711                         }
 712                 }
 713         }
 714
 715 /* a and b must be the same size, which is n2.
 716  * r needs to be n2 words and t needs to be n2*2
 717  */
 718 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 719              BN_ULONG *t)
 720         {
 721         int n=n2/2;
 722
 723 # ifdef BN_COUNT
 724         fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
 725 # endif
 726
 727         bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
 728         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 729                 {
 730                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 731                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 732                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 733                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 734                 }
 735         else
 736                 {
 737                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 738                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 739                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 740                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 741                 }
 742         }
 743
 744 /* a and b must be the same size, which is n2.
 745  * r needs to be n2 words and t needs to be n2*2
 746  * l is the low words of the output.
 747  * t needs to be n2*3
 748  */
 749 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 750              BN_ULONG *t)
 751         {
 752         int i,n;
 753         int c1,c2;
 754         int neg,oneg,zero;
 755         BN_ULONG ll,lc,*lp,*mp;
 756
 757 # ifdef BN_COUNT
 758         fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
 759 # endif
 760         n=n2/2;
 761
 762         /* Calculate (al-ah)*(bh-bl) */
 763         neg=zero=0;
 764         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 765         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 766         switch (c1*3+c2)
 767                 {
 768         case -4:
 769                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 770                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 771                 break;
 772         case -3:
 773                 zero=1;
 774                 break;
 775         case -2:
 776                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 777                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 778                 neg=1;
 779                 break;
 780         case -1:
 781         case 0:
 782         case 1:
 783                 zero=1;
 784                 break;
 785         case 2:
 786                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 787                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 788                 neg=1;
 789                 break;
 790         case 3:
 791                 zero=1;
 792                 break;
 793         case 4:
 794                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 795                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 796                 break;
 797                 }
 798
 799         oneg=neg;
 800         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 801         /* r[10] = (a[1]*b[1]) */
 802 # ifdef BN_MUL_COMBA
 803         if (n == 8)
 804                 {
 805                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 806                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 807                 }
 808         else
 809 # endif
 810                 {
 811                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
 812                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
 813                 }
 814
 815         /* s0 == low(al*bl)
 816          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 817          * We know s0 and s1 so the only unknown is high(al*bl)
 818          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 819          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 820          */
 821         if (l != NULL)
 822                 {
 823                 lp= &(t[n2+n]);
 824                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 825                 }
 826         else
 827                 {
 828                 c1=0;
 829                 lp= &(r[0]);
 830                 }
 831
 832         if (neg)
 833                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 834         else
 835                 {
 836                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 837                 neg=0;
 838                 }
 839
 840         if (l != NULL)
 841                 {
 842                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 843                 }
 844         else
 845                 {
 846                 lp= &(t[n2+n]);
 847                 mp= &(t[n2]);
 848                 for (i=0; i<n; i++)
 849                         lp[i]=((~mp[i])+1)&BN_MASK2;
 850                 }
 851
 852         /* s[0] = low(al*bl)
 853          * t[3] = high(al*bl)
 854          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 855          * r[10] = (a[1]*b[1])
 856          */
 857         /* R[10] = al*bl
 858          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 859          * R[32] = ah*bh
 860          */
 861         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 862          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 863          * R[3]=r[1]+(carry/borrow)
 864          */
 865         if (l != NULL)
 866                 {
 867                 lp= &(t[n2]);
 868                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 869                 }
 870         else
 871                 {
 872                 lp= &(t[n2+n]);
 873                 c1=0;
 874                 }
 875         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 876         if (oneg)
 877                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 878         else
 879                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 880
 881         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 882         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 883         if (oneg)
 884                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 885         else
 886                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 887
 888         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 889                 {
 890                 i=0;
 891                 if (c1 > 0)
 892                         {
 893                         lc=c1;
 894                         do      {
 895                                 ll=(r[i]+lc)&BN_MASK2;
 896                                 r[i++]=ll;
 897                                 lc=(lc > ll);
 898                                 } while (lc);
 899                         }
 900                 else
 901                         {
 902                         lc= -c1;
 903                         do      {
 904                                 ll=r[i];
 905                                 r[i++]=(ll-lc)&BN_MASK2;
 906                                 lc=(lc > ll);
 907                                 } while (lc);
 908                         }
 909                 }
 910         if (c2 != 0) /* Add starting at r[1] */
 911                 {
 912                 i=n;
 913                 if (c2 > 0)
 914                         {
 915                         lc=c2;
 916                         do      {
 917                                 ll=(r[i]+lc)&BN_MASK2;
 918                                 r[i++]=ll;
 919                                 lc=(lc > ll);
 920                                 } while (lc);
 921                         }
 922                 else
 923                         {
 924                         lc= -c2;
 925                         do      {
 926                                 ll=r[i];
 927                                 r[i++]=(ll-lc)&BN_MASK2;
 928                                 lc=(lc > ll);
 929                                 } while (lc);
 930                         }
 931                 }
 932         }
 933 #endif /* BN_RECURSION */
 934
 935 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 936         {
 937         int ret=0;
 938         int top,al,bl;
 939         BIGNUM *rr;
 940 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 941         int i;
 942 #endif
 943 #ifdef BN_RECURSION
 944         BIGNUM *t=NULL;
 945         int j=0,k;
 946 #endif
 947
 948 #ifdef BN_COUNT
 949         fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
 950 #endif
 951
 952         bn_check_top(a);
 953         bn_check_top(b);
 954         bn_check_top(r);
 955
 956         al=a->top;
 957         bl=b->top;
 958
 959         if ((al == 0) || (bl == 0))
 960                 {
 961                 BN_zero(r);
 962                 return(1);
 963                 }
 964         top=al+bl;
 965
 966         BN_CTX_start(ctx);
 967         if ((r == a) || (r == b))
 968                 {
 969                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
 970                 }
 971         else
 972                 rr = r;
 973         rr->neg=a->neg^b->neg;
 974
 975 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 976         i = al-bl;
 977 #endif
 978 #ifdef BN_MUL_COMBA
 979         if (i == 0)
 980                 {
 981 # if 0
 982                 if (al == 4)
 983                         {
 984                         if (bn_wexpand(rr,8) == NULL) goto err;
 985                         rr->top=8;
 986                         bn_mul_comba4(rr->d,a->d,b->d);
 987                         goto end;
 988                         }
 989 # endif
 990                 if (al == 8)
 991                         {
 992                         if (bn_wexpand(rr,16) == NULL) goto err;
 993                         rr->top=16;
 994                         bn_mul_comba8(rr->d,a->d,b->d);
 995                         goto end;
 996                         }
 997                 }
 998 #endif /* BN_MUL_COMBA */
 999 #ifdef BN_RECURSION
1000         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
1001                 {
1002                 if (i >= -1 && i <= 1)
1003                         {
1004                         int sav_j =0;
1005                         /* Find out the power of two lower or equal
1006                            to the longest of the two numbers */
1007                         if (i >= 0)
1008                                 {
1009                                 j = BN_num_bits_word((BN_ULONG)al);
1010                                 }
1011                         if (i == -1)
1012                                 {
1013                                 j = BN_num_bits_word((BN_ULONG)bl);
1014                                 }
1015                         sav_j = j;
1016                         j = 1<<(j-1);
1017                         assert(j <= al || j <= bl);
1018                         k = j+j;
1019                         t = BN_CTX_get(ctx);
1020                         if (al > j || bl > j)
1021                                 {
1022                                 bn_wexpand(t,k*4);
1023                                 bn_wexpand(rr,k*4);
1024                                 bn_mul_part_recursive(rr->d,a->d,b->d,
1025                                         j,al-j,bl-j,t->d);
1026                                 }
1027                         else    /* al <= j || bl <= j */
1028                                 {
1029                                 bn_wexpand(t,k*2);
1030                                 bn_wexpand(rr,k*2);
1031                                 bn_mul_recursive(rr->d,a->d,b->d,
1032                                         j,al-j,bl-j,t->d);
1033                                 }
1034                         rr->top=top;
1035                         goto end;
1036                         }
1037 #if 0
1038                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1039                         {
1040                         BIGNUM *tmp_bn = (BIGNUM *)b;
1041                         bn_wexpand(tmp_bn,al);
1042                         tmp_bn->d[bl]=0;
1043                         bl++;
1044                         i--;
1045                         }
1046                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1047                         {
1048                         BIGNUM *tmp_bn = (BIGNUM *)a;
1049                         bn_wexpand(tmp_bn,bl);
1050                         tmp_bn->d[al]=0;
1051                         al++;
1052                         i++;
1053                         }
1054                 if (i == 0)
1055                         {
1056                         /* symmetric and > 4 */
1057                         /* 16 or larger */
1058                         j=BN_num_bits_word((BN_ULONG)al);
1059                         j=1<<(j-1);
1060                         k=j+j;
1061                         t = BN_CTX_get(ctx);
1062                         if (al == j) /* exact multiple */
1063                                 {
1064                                 bn_wexpand(t,k*2);
1065                                 bn_wexpand(rr,k*2);
1066                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1067                                 }
1068                         else
1069                                 {
1070                                 bn_wexpand(t,k*4);
1071                                 bn_wexpand(rr,k*4);
1072                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1073                                 }
1074                         rr->top=top;
1075                         goto end;
1076                         }
1077 #endif
1078                 }
1079 #endif /* BN_RECURSION */
1080         if (bn_wexpand(rr,top) == NULL) goto err;
1081         rr->top=top;
1082         bn_mul_normal(rr->d,a->d,al,b->d,bl);
1083
1084 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1085 end:
1086 #endif
1087         bn_fix_top(rr);
1088         if (r != rr) BN_copy(r,rr);
1089         ret=1;
1090 err:
1091         BN_CTX_end(ctx);
1092         return(ret);
1093         }
1094
1095 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1096         {
1097         BN_ULONG *rr;
1098
1099 #ifdef BN_COUNT
1100         fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1101 #endif
1102
1103         if (na < nb)
1104                 {
1105                 int itmp;
1106                 BN_ULONG *ltmp;
1107
1108                 itmp=na; na=nb; nb=itmp;
1109                 ltmp=a;   a=b;   b=ltmp;
1110
1111                 }
1112         rr= &(r[na]);
1113         if (nb <= 0)
1114                 {
1115                 (void)bn_mul_words(r,a,na,0);
1116                 return;
1117                 }
1118         else
1119                 rr[0]=bn_mul_words(r,a,na,b[0]);
1120
1121         for (;;)
1122                 {
1123                 if (--nb <= 0) return;
1124                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1125                 if (--nb <= 0) return;
1126                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1127                 if (--nb <= 0) return;
1128                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1129                 if (--nb <= 0) return;
1130                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1131                 rr+=4;
1132                 r+=4;
1133                 b+=4;
1134                 }
1135         }
1136
1137 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1138         {
1139 #ifdef BN_COUNT
1140         fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1141 #endif
1142         bn_mul_words(r,a,n,b[0]);
1143
1144         for (;;)
1145                 {
1146                 if (--n <= 0) return;
1147                 bn_mul_add_words(&(r[1]),a,n,b[1]);
1148                 if (--n <= 0) return;
1149                 bn_mul_add_words(&(r[2]),a,n,b[2]);
1150                 if (--n <= 0) return;
1151                 bn_mul_add_words(&(r[3]),a,n,b[3]);
1152                 if (--n <= 0) return;
1153                 bn_mul_add_words(&(r[4]),a,n,b[4]);
1154                 r+=4;
1155                 b+=4;
1156                 }
1157         }