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 /* 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 /* dnX may not be positive, but n2/2+dnX has to be */
 393 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 394         int dna, int dnb, BN_ULONG *t)
 395         {
 396         int n=n2/2,c1,c2;
 397         int tna=n+dna, tnb=n+dnb;
 398         unsigned int neg,zero;
 399         BN_ULONG ln,lo,*p;
 400
 401 # ifdef BN_COUNT
 402         fprintf(stderr," bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
 403 # endif
 404 # ifdef BN_MUL_COMBA
 405 #  if 0
 406         if (n2 == 4)
 407                 {
 408                 bn_mul_comba4(r,a,b);
 409                 return;
 410                 }
 411 #  endif
 412         /* Only call bn_mul_comba 8 if n2 == 8 and the
 413          * two arrays are complete [steve]
 414          */
 415         if (n2 == 8 && dna == 0 && dnb == 0)
 416                 {
 417                 bn_mul_comba8(r,a,b);
 418                 return;
 419                 }
 420 # endif /* BN_MUL_COMBA */
 421         /* Else do normal multiply */
 422         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
 423                 {
 424                 bn_mul_normal(r,a,n2+dna,b,n2+dnb);
 425                 if ((dna + dnb) < 0)
 426                         memset(&r[2*n2 + dna + dnb], 0,
 427                                 sizeof(BN_ULONG) * -(dna + dnb));
 428                 return;
 429                 }
 430         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 431         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 432         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 433         zero=neg=0;
 434         switch (c1*3+c2)
 435                 {
 436         case -4:
 437                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 438                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 439                 break;
 440         case -3:
 441                 zero=1;
 442                 break;
 443         case -2:
 444                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 445                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 446                 neg=1;
 447                 break;
 448         case -1:
 449         case 0:
 450         case 1:
 451                 zero=1;
 452                 break;
 453         case 2:
 454                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 455                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 456                 neg=1;
 457                 break;
 458         case 3:
 459                 zero=1;
 460                 break;
 461         case 4:
 462                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 463                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 464                 break;
 465                 }
 466
 467 # ifdef BN_MUL_COMBA
 468         if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
 469                                                extra args to do this well */
 470                 {
 471                 if (!zero)
 472                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 473                 else
 474                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 475
 476                 bn_mul_comba4(r,a,b);
 477                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 478                 }
 479         else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
 480                                                     take extra args to do this
 481                                                     well */
 482                 {
 483                 if (!zero)
 484                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 485                 else
 486                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 487
 488                 bn_mul_comba8(r,a,b);
 489                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 490                 }
 491         else
 492 # endif /* BN_MUL_COMBA */
 493                 {
 494                 p= &(t[n2*2]);
 495                 if (!zero)
 496                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 497                 else
 498                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 499                 bn_mul_recursive(r,a,b,n,0,0,p);
 500                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
 501                 }
 502
 503         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 504          * r[10] holds (a[0]*b[0])
 505          * r[32] holds (b[1]*b[1])
 506          */
 507
 508         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 509
 510         if (neg) /* if t[32] is negative */
 511                 {
 512                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 513                 }
 514         else
 515                 {
 516                 /* Might have a carry */
 517                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 518                 }
 519
 520         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 521          * r[10] holds (a[0]*b[0])
 522          * r[32] holds (b[1]*b[1])
 523          * c1 holds the carry bits
 524          */
 525         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 526         if (c1)
 527                 {
 528                 p= &(r[n+n2]);
 529                 lo= *p;
 530                 ln=(lo+c1)&BN_MASK2;
 531                 *p=ln;
 532
 533                 /* The overflow will stop before we over write
 534                  * words we should not overwrite */
 535                 if (ln < (BN_ULONG)c1)
 536                         {
 537                         do      {
 538                                 p++;
 539                                 lo= *p;
 540                                 ln=(lo+1)&BN_MASK2;
 541                                 *p=ln;
 542                                 } while (ln == 0);
 543                         }
 544                 }
 545         }
 546
 547 /* n+tn is the word length
 548  * t needs to be n*4 is size, as does r */
 549 /* tnX may not be negative but less than n */
 550 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
 551              int tna, int tnb, BN_ULONG *t)
 552         {
 553         int i,j,n2=n*2;
 554         int c1,c2,neg;
 555         BN_ULONG ln,lo,*p;
 556
 557 # ifdef BN_COUNT
 558         fprintf(stderr," bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
 559                 n, tna, n, tnb);
 560 # endif
 561         if (n < 8)
 562                 {
 563                 bn_mul_normal(r,a,n+tna,b,n+tnb);
 564                 return;
 565                 }
 566
 567         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 568         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 569         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 570         neg=0;
 571         switch (c1*3+c2)
 572                 {
 573         case -4:
 574                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 575                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 576                 break;
 577         case -3:
 578                 /* break; */
 579         case -2:
 580                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 581                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 582                 neg=1;
 583                 break;
 584         case -1:
 585         case 0:
 586         case 1:
 587                 /* break; */
 588         case 2:
 589                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 590                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 591                 neg=1;
 592                 break;
 593         case 3:
 594                 /* break; */
 595         case 4:
 596                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 597                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 598                 break;
 599                 }
 600                 /* The zero case isn't yet implemented here. The speedup
 601                    would probably be negligible. */
 602 # if 0
 603         if (n == 4)
 604                 {
 605                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 606                 bn_mul_comba4(r,a,b);
 607                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 608                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 609                 }
 610         else
 611 # endif
 612         if (n == 8)
 613                 {
 614                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 615                 bn_mul_comba8(r,a,b);
 616                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 617                 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
 618                 }
 619         else
 620                 {
 621                 p= &(t[n2*2]);
 622                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 623                 bn_mul_recursive(r,a,b,n,0,0,p);
 624                 i=n/2;
 625                 /* If there is only a bottom half to the number,
 626                  * just do it */
 627                 if (tna > tnb)
 628                         j = tna - i;
 629                 else
 630                         j = tnb - i;
 631                 if (j == 0)
 632                         {
 633                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
 634                                 i,tna-i,tnb-i,p);
 635                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 636                         }
 637                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 638                                 {
 639                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 640                                         i,tna-i,tnb-i,p);
 641                                 memset(&(r[n2+tna+tnb]),0,
 642                                         sizeof(BN_ULONG)*(n2-tna-tnb));
 643                                 }
 644                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 645                         {
 646                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 647                         if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
 648                                 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
 649                                 {
 650                                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 651                                 }
 652                         else
 653                                 {
 654                                 for (;;)
 655                                         {
 656                                         i/=2;
 657                                         /* these simplified conditions work
 658                                          * exclusively because difference
 659                                          * between tna and tnb is 1 or 0 */
 660                                         if (i < tna || i < tnb)
 661                                                 {
 662                                                 bn_mul_part_recursive(&(r[n2]),
 663                                                         &(a[n]),&(b[n]),
 664                                                         i,tna-i,tnb-i,p);
 665                                                 break;
 666                                                 }
 667                                         else if (i == tna || i == tnb)
 668                                                 {
 669                                                 bn_mul_recursive(&(r[n2]),
 670                                                         &(a[n]),&(b[n]),
 671                                                         i,tna-i,tnb-i,p);
 672                                                 break;
 673                                                 }
 674                                         }
 675                                 }
 676                         }
 677                 }
 678
 679         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 680          * r[10] holds (a[0]*b[0])
 681          * r[32] holds (b[1]*b[1])
 682          */
 683
 684         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 685
 686         if (neg) /* if t[32] is negative */
 687                 {
 688                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 689                 }
 690         else
 691                 {
 692                 /* Might have a carry */
 693                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 694                 }
 695
 696         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 697          * r[10] holds (a[0]*b[0])
 698          * r[32] holds (b[1]*b[1])
 699          * c1 holds the carry bits
 700          */
 701         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 702         if (c1)
 703                 {
 704                 p= &(r[n+n2]);
 705                 lo= *p;
 706                 ln=(lo+c1)&BN_MASK2;
 707                 *p=ln;
 708
 709                 /* The overflow will stop before we over write
 710                  * words we should not overwrite */
 711                 if (ln < (BN_ULONG)c1)
 712                         {
 713                         do      {
 714                                 p++;
 715                                 lo= *p;
 716                                 ln=(lo+1)&BN_MASK2;
 717                                 *p=ln;
 718                                 } while (ln == 0);
 719                         }
 720                 }
 721         }
 722
 723 /* a and b must be the same size, which is n2.
 724  * r needs to be n2 words and t needs to be n2*2
 725  */
 726 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 727              BN_ULONG *t)
 728         {
 729         int n=n2/2;
 730
 731 # ifdef BN_COUNT
 732         fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
 733 # endif
 734
 735         bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
 736         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 737                 {
 738                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 739                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 740                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 741                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 742                 }
 743         else
 744                 {
 745                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 746                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 747                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 748                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 749                 }
 750         }
 751
 752 /* a and b must be the same size, which is n2.
 753  * r needs to be n2 words and t needs to be n2*2
 754  * l is the low words of the output.
 755  * t needs to be n2*3
 756  */
 757 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 758              BN_ULONG *t)
 759         {
 760         int i,n;
 761         int c1,c2;
 762         int neg,oneg,zero;
 763         BN_ULONG ll,lc,*lp,*mp;
 764
 765 # ifdef BN_COUNT
 766         fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
 767 # endif
 768         n=n2/2;
 769
 770         /* Calculate (al-ah)*(bh-bl) */
 771         neg=zero=0;
 772         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 773         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 774         switch (c1*3+c2)
 775                 {
 776         case -4:
 777                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 778                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 779                 break;
 780         case -3:
 781                 zero=1;
 782                 break;
 783         case -2:
 784                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 785                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 786                 neg=1;
 787                 break;
 788         case -1:
 789         case 0:
 790         case 1:
 791                 zero=1;
 792                 break;
 793         case 2:
 794                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 795                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 796                 neg=1;
 797                 break;
 798         case 3:
 799                 zero=1;
 800                 break;
 801         case 4:
 802                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 803                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 804                 break;
 805                 }
 806
 807         oneg=neg;
 808         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 809         /* r[10] = (a[1]*b[1]) */
 810 # ifdef BN_MUL_COMBA
 811         if (n == 8)
 812                 {
 813                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 814                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 815                 }
 816         else
 817 # endif
 818                 {
 819                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
 820                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
 821                 }
 822
 823         /* s0 == low(al*bl)
 824          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 825          * We know s0 and s1 so the only unknown is high(al*bl)
 826          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 827          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 828          */
 829         if (l != NULL)
 830                 {
 831                 lp= &(t[n2+n]);
 832                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 833                 }
 834         else
 835                 {
 836                 c1=0;
 837                 lp= &(r[0]);
 838                 }
 839
 840         if (neg)
 841                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 842         else
 843                 {
 844                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 845                 neg=0;
 846                 }
 847
 848         if (l != NULL)
 849                 {
 850                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 851                 }
 852         else
 853                 {
 854                 lp= &(t[n2+n]);
 855                 mp= &(t[n2]);
 856                 for (i=0; i<n; i++)
 857                         lp[i]=((~mp[i])+1)&BN_MASK2;
 858                 }
 859
 860         /* s[0] = low(al*bl)
 861          * t[3] = high(al*bl)
 862          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 863          * r[10] = (a[1]*b[1])
 864          */
 865         /* R[10] = al*bl
 866          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 867          * R[32] = ah*bh
 868          */
 869         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 870          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 871          * R[3]=r[1]+(carry/borrow)
 872          */
 873         if (l != NULL)
 874                 {
 875                 lp= &(t[n2]);
 876                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 877                 }
 878         else
 879                 {
 880                 lp= &(t[n2+n]);
 881                 c1=0;
 882                 }
 883         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 884         if (oneg)
 885                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 886         else
 887                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 888
 889         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 890         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 891         if (oneg)
 892                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 893         else
 894                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 895
 896         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 897                 {
 898                 i=0;
 899                 if (c1 > 0)
 900                         {
 901                         lc=c1;
 902                         do      {
 903                                 ll=(r[i]+lc)&BN_MASK2;
 904                                 r[i++]=ll;
 905                                 lc=(lc > ll);
 906                                 } while (lc);
 907                         }
 908                 else
 909                         {
 910                         lc= -c1;
 911                         do      {
 912                                 ll=r[i];
 913                                 r[i++]=(ll-lc)&BN_MASK2;
 914                                 lc=(lc > ll);
 915                                 } while (lc);
 916                         }
 917                 }
 918         if (c2 != 0) /* Add starting at r[1] */
 919                 {
 920                 i=n;
 921                 if (c2 > 0)
 922                         {
 923                         lc=c2;
 924                         do      {
 925                                 ll=(r[i]+lc)&BN_MASK2;
 926                                 r[i++]=ll;
 927                                 lc=(lc > ll);
 928                                 } while (lc);
 929                         }
 930                 else
 931                         {
 932                         lc= -c2;
 933                         do      {
 934                                 ll=r[i];
 935                                 r[i++]=(ll-lc)&BN_MASK2;
 936                                 lc=(lc > ll);
 937                                 } while (lc);
 938                         }
 939                 }
 940         }
 941 #endif /* BN_RECURSION */
 942
 943 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 944         {
 945         int ret=0;
 946         int top,al,bl;
 947         BIGNUM *rr;
 948 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 949         int i;
 950 #endif
 951 #ifdef BN_RECURSION
 952         BIGNUM *t=NULL;
 953         int j=0,k;
 954 #endif
 955
 956 #ifdef BN_COUNT
 957         fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
 958 #endif
 959
 960         bn_check_top(a);
 961         bn_check_top(b);
 962         bn_check_top(r);
 963
 964         al=a->top;
 965         bl=b->top;
 966
 967         if ((al == 0) || (bl == 0))
 968                 {
 969                 BN_zero(r);
 970                 return(1);
 971                 }
 972         top=al+bl;
 973
 974         BN_CTX_start(ctx);
 975         if ((r == a) || (r == b))
 976                 {
 977                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
 978                 }
 979         else
 980                 rr = r;
 981         rr->neg=a->neg^b->neg;
 982
 983 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 984         i = al-bl;
 985 #endif
 986 #ifdef BN_MUL_COMBA
 987         if (i == 0)
 988                 {
 989 # if 0
 990                 if (al == 4)
 991                         {
 992                         if (bn_wexpand(rr,8) == NULL) goto err;
 993                         rr->top=8;
 994                         bn_mul_comba4(rr->d,a->d,b->d);
 995                         goto end;
 996                         }
 997 # endif
 998                 if (al == 8)
 999                         {
1000                         if (bn_wexpand(rr,16) == NULL) goto err;
1001                         rr->top=16;
1002                         bn_mul_comba8(rr->d,a->d,b->d);
1003                         goto end;
1004                         }
1005                 }
1006 #endif /* BN_MUL_COMBA */
1007 #ifdef BN_RECURSION
1008         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
1009                 {
1010                 if (i >= -1 && i <= 1)
1011                         {
1012                         /* Find out the power of two lower or equal
1013                            to the longest of the two numbers */
1014                         if (i >= 0)
1015                                 {
1016                                 j = BN_num_bits_word((BN_ULONG)al);
1017                                 }
1018                         if (i == -1)
1019                                 {
1020                                 j = BN_num_bits_word((BN_ULONG)bl);
1021                                 }
1022                         j = 1<<(j-1);
1023                         assert(j <= al || j <= bl);
1024                         k = j+j;
1025                         t = BN_CTX_get(ctx);
1026                         if (t == NULL)
1027                                 goto err;
1028                         if (al > j || bl > j)
1029                                 {
1030                                 if (bn_wexpand(t,k*4) == NULL) goto err;
1031                                 if (bn_wexpand(rr,k*4) == NULL) goto err;
1032                                 bn_mul_part_recursive(rr->d,a->d,b->d,
1033                                         j,al-j,bl-j,t->d);
1034                                 }
1035                         else    /* al <= j || bl <= j */
1036                                 {
1037                                 if (bn_wexpand(t,k*2) == NULL) goto err;
1038                                 if (bn_wexpand(rr,k*2) == NULL) goto err;
1039                                 bn_mul_recursive(rr->d,a->d,b->d,
1040                                         j,al-j,bl-j,t->d);
1041                                 }
1042                         rr->top=top;
1043                         goto end;
1044                         }
1045 #if 0
1046                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1047                         {
1048                         BIGNUM *tmp_bn = (BIGNUM *)b;
1049                         if (bn_wexpand(tmp_bn,al) == NULL) goto err;
1050                         tmp_bn->d[bl]=0;
1051                         bl++;
1052                         i--;
1053                         }
1054                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1055                         {
1056                         BIGNUM *tmp_bn = (BIGNUM *)a;
1057                         if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
1058                         tmp_bn->d[al]=0;
1059                         al++;
1060                         i++;
1061                         }
1062                 if (i == 0)
1063                         {
1064                         /* symmetric and > 4 */
1065                         /* 16 or larger */
1066                         j=BN_num_bits_word((BN_ULONG)al);
1067                         j=1<<(j-1);
1068                         k=j+j;
1069                         t = BN_CTX_get(ctx);
1070                         if (al == j) /* exact multiple */
1071                                 {
1072                                 if (bn_wexpand(t,k*2) == NULL) goto err;
1073                                 if (bn_wexpand(rr,k*2) == NULL) goto err;
1074                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1075                                 }
1076                         else
1077                                 {
1078                                 if (bn_wexpand(t,k*4) == NULL) goto err;
1079                                 if (bn_wexpand(rr,k*4) == NULL) goto err;
1080                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1081                                 }
1082                         rr->top=top;
1083                         goto end;
1084                         }
1085 #endif
1086                 }
1087 #endif /* BN_RECURSION */
1088         if (bn_wexpand(rr,top) == NULL) goto err;
1089         rr->top=top;
1090         bn_mul_normal(rr->d,a->d,al,b->d,bl);
1091
1092 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1093 end:
1094 #endif
1095         bn_correct_top(rr);
1096         if (r != rr) BN_copy(r,rr);
1097         ret=1;
1098 err:
1099         bn_check_top(r);
1100         BN_CTX_end(ctx);
1101         return(ret);
1102         }
1103
1104 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1105         {
1106         BN_ULONG *rr;
1107
1108 #ifdef BN_COUNT
1109         fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1110 #endif
1111
1112         if (na < nb)
1113                 {
1114                 int itmp;
1115                 BN_ULONG *ltmp;
1116
1117                 itmp=na; na=nb; nb=itmp;
1118                 ltmp=a;   a=b;   b=ltmp;
1119
1120                 }
1121         rr= &(r[na]);
1122         if (nb <= 0)
1123                 {
1124                 (void)bn_mul_words(r,a,na,0);
1125                 return;
1126                 }
1127         else
1128                 rr[0]=bn_mul_words(r,a,na,b[0]);
1129
1130         for (;;)
1131                 {
1132                 if (--nb <= 0) return;
1133                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1134                 if (--nb <= 0) return;
1135                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1136                 if (--nb <= 0) return;
1137                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1138                 if (--nb <= 0) return;
1139                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1140                 rr+=4;
1141                 r+=4;
1142                 b+=4;
1143                 }
1144         }
1145
1146 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1147         {
1148 #ifdef BN_COUNT
1149         fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1150 #endif
1151         bn_mul_words(r,a,n,b[0]);
1152
1153         for (;;)
1154                 {
1155                 if (--n <= 0) return;
1156                 bn_mul_add_words(&(r[1]),a,n,b[1]);
1157                 if (--n <= 0) return;
1158                 bn_mul_add_words(&(r[2]),a,n,b[2]);
1159                 if (--n <= 0) return;
1160                 bn_mul_add_words(&(r[3]),a,n,b[3]);
1161                 if (--n <= 0) return;
1162                 bn_mul_add_words(&(r[4]),a,n,b[4]);
1163                 r+=4;
1164                 b+=4;
1165                 }
1166         }