crypto/bn/bn_mul.c

   1 /* crypto/bn/bn_mul.c */
   2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
   3  * All rights reserved.
   4  *
   5  * This package is an SSL implementation written
   6  * by Eric Young (eay@cryptsoft.com).
   7  * The implementation was written so as to conform with Netscapes SSL.
   8  *
   9  * This library is free for commercial and non-commercial use as long as
  10  * the following conditions are aheared to.  The following conditions
  11  * apply to all code found in this distribution, be it the RC4, RSA,
  12  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
  13  * included with this distribution is covered by the same copyright terms
  14  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
  15  *
  16  * Copyright remains Eric Young's, and as such any Copyright notices in
  17  * the code are not to be removed.
  18  * If this package is used in a product, Eric Young should be given attribution
  19  * as the author of the parts of the library used.
  20  * This can be in the form of a textual message at program startup or
  21  * in documentation (online or textual) provided with the package.
  22  *
  23  * Redistribution and use in source and binary forms, with or without
  24  * modification, are permitted provided that the following conditions
  25  * are met:
  26  * 1. Redistributions of source code must retain the copyright
  27  *    notice, this list of conditions and the following disclaimer.
  28  * 2. Redistributions in binary form must reproduce the above copyright
  29  *    notice, this list of conditions and the following disclaimer in the
  30  *    documentation and/or other materials provided with the distribution.
  31  * 3. All advertising materials mentioning features or use of this software
  32  *    must display the following acknowledgement:
  33  *    "This product includes cryptographic software written by
  34  *     Eric Young (eay@cryptsoft.com)"
  35  *    The word 'cryptographic' can be left out if the rouines from the library
  36  *    being used are not cryptographic related :-).
  37  * 4. If you include any Windows specific code (or a derivative thereof) from
  38  *    the apps directory (application code) you must include an acknowledgement:
  39  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
  40  *
  41  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
  42  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  43  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  44  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  45  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  46  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  47  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  48  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  49  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  50  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  51  * SUCH DAMAGE.
  52  *
  53  * The licence and distribution terms for any publically available version or
  54  * derivative of this code cannot be changed.  i.e. this code cannot simply be
  55  * copied and put under another distribution licence
  56  * [including the GNU Public Licence.]
  57  */
  58
  59 #include <stdio.h>
  60 #include "cryptlib.h"
  61 #include "bn_lcl.h"
  62
  63 #ifdef BN_RECURSION
  64 /* Karatsuba-Ofman recursive multiplication algorithm */
  65
  66 /* r is 2*n2 words in size,
  67  * a and b are both n2 words in size.
  68  * n2 must be a power of 2.
  69  * We multiply and return the result.
  70  * t must be 2*n2 words in size
  71  * We calculate
  72  * a[0]*b[0]
  73  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
  74  * a[1]*b[1]
  75  */
  76 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
  77              BN_ULONG *t)
  78         {
  79         int n=n2/2,c1,c2;
  80         unsigned int neg,zero;
  81         BN_ULONG ln,lo,*p;
  82
  83 # ifdef BN_COUNT
  84         printf(" bn_mul_recursive %d * %d\n",n2,n2);
  85 # endif
  86 # ifdef BN_MUL_COMBA
  87 #  if 0
  88         if (n2 == 4)
  89                 {
  90                 bn_mul_comba4(r,a,b);
  91                 return;
  92                 }
  93 #  endif
  94         if (n2 == 8)
  95                 {
  96                 bn_mul_comba8(r,a,b);
  97                 return;
  98                 }
  99 # endif /* BN_MUL_COMBA */
 100         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
 101                 {
 102                 /* This should not happen */
 103                 bn_mul_normal(r,a,n2,b,n2);
 104                 return;
 105                 }
 106         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 107         c1=bn_cmp_words(a,&(a[n]),n);
 108         c2=bn_cmp_words(&(b[n]),b,n);
 109         zero=neg=0;
 110         switch (c1*3+c2)
 111                 {
 112         case -4:
 113                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 114                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 115                 break;
 116         case -3:
 117                 zero=1;
 118                 break;
 119         case -2:
 120                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 121                 bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
 122                 neg=1;
 123                 break;
 124         case -1:
 125         case 0:
 126         case 1:
 127                 zero=1;
 128                 break;
 129         case 2:
 130                 bn_sub_words(t,      a,      &(a[n]),n); /* + */
 131                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 132                 neg=1;
 133                 break;
 134         case 3:
 135                 zero=1;
 136                 break;
 137         case 4:
 138                 bn_sub_words(t,      a,      &(a[n]),n);
 139                 bn_sub_words(&(t[n]),&(b[n]),b,      n);
 140                 break;
 141                 }
 142
 143 # ifdef BN_MUL_COMBA
 144         if (n == 4)
 145                 {
 146                 if (!zero)
 147                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 148                 else
 149                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 150
 151                 bn_mul_comba4(r,a,b);
 152                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 153                 }
 154         else if (n == 8)
 155                 {
 156                 if (!zero)
 157                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 158                 else
 159                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 160
 161                 bn_mul_comba8(r,a,b);
 162                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 163                 }
 164         else
 165 # endif /* BN_MUL_COMBA */
 166                 {
 167                 p= &(t[n2*2]);
 168                 if (!zero)
 169                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 170                 else
 171                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 172                 bn_mul_recursive(r,a,b,n,p);
 173                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
 174                 }
 175
 176         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 177          * r[10] holds (a[0]*b[0])
 178          * r[32] holds (b[1]*b[1])
 179          */
 180
 181         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 182
 183         if (neg) /* if t[32] is negative */
 184                 {
 185                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 186                 }
 187         else
 188                 {
 189                 /* Might have a carry */
 190                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 191                 }
 192
 193         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 194          * r[10] holds (a[0]*b[0])
 195          * r[32] holds (b[1]*b[1])
 196          * c1 holds the carry bits
 197          */
 198         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 199         if (c1)
 200                 {
 201                 p= &(r[n+n2]);
 202                 lo= *p;
 203                 ln=(lo+c1)&BN_MASK2;
 204                 *p=ln;
 205
 206                 /* The overflow will stop before we over write
 207                  * words we should not overwrite */
 208                 if (ln < (BN_ULONG)c1)
 209                         {
 210                         do      {
 211                                 p++;
 212                                 lo= *p;
 213                                 ln=(lo+1)&BN_MASK2;
 214                                 *p=ln;
 215                                 } while (ln == 0);
 216                         }
 217                 }
 218         }
 219
 220 /* n+tn is the word length
 221  * t needs to be n*4 is size, as does r */
 222 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
 223              int n, BN_ULONG *t)
 224         {
 225         int i,j,n2=n*2;
 226         unsigned int c1,c2,neg,zero;
 227         BN_ULONG ln,lo,*p;
 228
 229 # ifdef BN_COUNT
 230         printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
 231 # endif
 232         if (n < 8)
 233                 {
 234                 i=tn+n;
 235                 bn_mul_normal(r,a,i,b,i);
 236                 return;
 237                 }
 238
 239         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 240         c1=bn_cmp_words(a,&(a[n]),n);
 241         c2=bn_cmp_words(&(b[n]),b,n);
 242         zero=neg=0;
 243         switch (c1*3+c2)
 244                 {
 245         case -4:
 246                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 247                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 248                 break;
 249         case -3:
 250                 zero=1;
 251                 /* break; */
 252         case -2:
 253                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 254                 bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
 255                 neg=1;
 256                 break;
 257         case -1:
 258         case 0:
 259         case 1:
 260                 zero=1;
 261                 /* break; */
 262         case 2:
 263                 bn_sub_words(t,      a,      &(a[n]),n); /* + */
 264                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 265                 neg=1;
 266                 break;
 267         case 3:
 268                 zero=1;
 269                 /* break; */
 270         case 4:
 271                 bn_sub_words(t,      a,      &(a[n]),n);
 272                 bn_sub_words(&(t[n]),&(b[n]),b,      n);
 273                 break;
 274                 }
 275                 /* The zero case isn't yet implemented here. The speedup
 276                    would probably be negligible. */
 277 # if 0
 278         if (n == 4)
 279                 {
 280                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 281                 bn_mul_comba4(r,a,b);
 282                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 283                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 284                 }
 285         else
 286 # endif
 287         if (n == 8)
 288                 {
 289                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 290                 bn_mul_comba8(r,a,b);
 291                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 292                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 293                 }
 294         else
 295                 {
 296                 p= &(t[n2*2]);
 297                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 298                 bn_mul_recursive(r,a,b,n,p);
 299                 i=n/2;
 300                 /* If there is only a bottom half to the number,
 301                  * just do it */
 302                 j=tn-i;
 303                 if (j == 0)
 304                         {
 305                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
 306                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 307                         }
 308                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 309                                 {
 310                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 311                                         j,i,p);
 312                                 memset(&(r[n2+tn*2]),0,
 313                                         sizeof(BN_ULONG)*(n2-tn*2));
 314                                 }
 315                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 316                         {
 317                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 318                         if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
 319                                 {
 320                                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 321                                 }
 322                         else
 323                                 {
 324                                 for (;;)
 325                                         {
 326                                         i/=2;
 327                                         if (i < tn)
 328                                                 {
 329                                                 bn_mul_part_recursive(&(r[n2]),
 330                                                         &(a[n]),&(b[n]),
 331                                                         tn-i,i,p);
 332                                                 break;
 333                                                 }
 334                                         else if (i == tn)
 335                                                 {
 336                                                 bn_mul_recursive(&(r[n2]),
 337                                                         &(a[n]),&(b[n]),
 338                                                         i,p);
 339                                                 break;
 340                                                 }
 341                                         }
 342                                 }
 343                         }
 344                 }
 345
 346         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 347          * r[10] holds (a[0]*b[0])
 348          * r[32] holds (b[1]*b[1])
 349          */
 350
 351         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 352
 353         if (neg) /* if t[32] is negative */
 354                 {
 355                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 356                 }
 357         else
 358                 {
 359                 /* Might have a carry */
 360                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 361                 }
 362
 363         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 364          * r[10] holds (a[0]*b[0])
 365          * r[32] holds (b[1]*b[1])
 366          * c1 holds the carry bits
 367          */
 368         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 369         if (c1)
 370                 {
 371                 p= &(r[n+n2]);
 372                 lo= *p;
 373                 ln=(lo+c1)&BN_MASK2;
 374                 *p=ln;
 375
 376                 /* The overflow will stop before we over write
 377                  * words we should not overwrite */
 378                 if (ln < c1)
 379                         {
 380                         do      {
 381                                 p++;
 382                                 lo= *p;
 383                                 ln=(lo+1)&BN_MASK2;
 384                                 *p=ln;
 385                                 } while (ln == 0);
 386                         }
 387                 }
 388         }
 389
 390 /* a and b must be the same size, which is n2.
 391  * r needs to be n2 words and t needs to be n2*2
 392  */
 393 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 394              BN_ULONG *t)
 395         {
 396         int n=n2/2;
 397
 398 # ifdef BN_COUNT
 399         printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
 400 # endif
 401
 402         bn_mul_recursive(r,a,b,n,&(t[0]));
 403         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 404                 {
 405                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 406                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 407                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 408                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 409                 }
 410         else
 411                 {
 412                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 413                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 414                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 415                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 416                 }
 417         }
 418
 419 /* a and b must be the same size, which is n2.
 420  * r needs to be n2 words and t needs to be n2*2
 421  * l is the low words of the output.
 422  * t needs to be n2*3
 423  */
 424 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 425              BN_ULONG *t)
 426         {
 427         int i,n;
 428         int c1,c2;
 429         int neg,oneg,zero;
 430         BN_ULONG ll,lc,*lp,*mp;
 431
 432 # ifdef BN_COUNT
 433         printf(" bn_mul_high %d * %d\n",n2,n2);
 434 # endif
 435         n=n2/2;
 436
 437         /* Calculate (al-ah)*(bh-bl) */
 438         neg=zero=0;
 439         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 440         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 441         switch (c1*3+c2)
 442                 {
 443         case -4:
 444                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 445                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 446                 break;
 447         case -3:
 448                 zero=1;
 449                 break;
 450         case -2:
 451                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 452                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 453                 neg=1;
 454                 break;
 455         case -1:
 456         case 0:
 457         case 1:
 458                 zero=1;
 459                 break;
 460         case 2:
 461                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 462                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 463                 neg=1;
 464                 break;
 465         case 3:
 466                 zero=1;
 467                 break;
 468         case 4:
 469                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 470                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 471                 break;
 472                 }
 473
 474         oneg=neg;
 475         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 476         /* r[10] = (a[1]*b[1]) */
 477 # ifdef BN_MUL_COMBA
 478         if (n == 8)
 479                 {
 480                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 481                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 482                 }
 483         else
 484 # endif
 485                 {
 486                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
 487                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
 488                 }
 489
 490         /* s0 == low(al*bl)
 491          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 492          * We know s0 and s1 so the only unknown is high(al*bl)
 493          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 494          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 495          */
 496         if (l != NULL)
 497                 {
 498                 lp= &(t[n2+n]);
 499                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 500                 }
 501         else
 502                 {
 503                 c1=0;
 504                 lp= &(r[0]);
 505                 }
 506
 507         if (neg)
 508                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 509         else
 510                 {
 511                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 512                 neg=0;
 513                 }
 514
 515         if (l != NULL)
 516                 {
 517                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 518                 }
 519         else
 520                 {
 521                 lp= &(t[n2+n]);
 522                 mp= &(t[n2]);
 523                 for (i=0; i<n; i++)
 524                         lp[i]=((~mp[i])+1)&BN_MASK2;
 525                 }
 526
 527         /* s[0] = low(al*bl)
 528          * t[3] = high(al*bl)
 529          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 530          * r[10] = (a[1]*b[1])
 531          */
 532         /* R[10] = al*bl
 533          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 534          * R[32] = ah*bh
 535          */
 536         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 537          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 538          * R[3]=r[1]+(carry/borrow)
 539          */
 540         if (l != NULL)
 541                 {
 542                 lp= &(t[n2]);
 543                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 544                 }
 545         else
 546                 {
 547                 lp= &(t[n2+n]);
 548                 c1=0;
 549                 }
 550         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 551         if (oneg)
 552                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 553         else
 554                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 555
 556         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 557         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 558         if (oneg)
 559                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 560         else
 561                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 562
 563         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 564                 {
 565                 i=0;
 566                 if (c1 > 0)
 567                         {
 568                         lc=c1;
 569                         do      {
 570                                 ll=(r[i]+lc)&BN_MASK2;
 571                                 r[i++]=ll;
 572                                 lc=(lc > ll);
 573                                 } while (lc);
 574                         }
 575                 else
 576                         {
 577                         lc= -c1;
 578                         do      {
 579                                 ll=r[i];
 580                                 r[i++]=(ll-lc)&BN_MASK2;
 581                                 lc=(lc > ll);
 582                                 } while (lc);
 583                         }
 584                 }
 585         if (c2 != 0) /* Add starting at r[1] */
 586                 {
 587                 i=n;
 588                 if (c2 > 0)
 589                         {
 590                         lc=c2;
 591                         do      {
 592                                 ll=(r[i]+lc)&BN_MASK2;
 593                                 r[i++]=ll;
 594                                 lc=(lc > ll);
 595                                 } while (lc);
 596                         }
 597                 else
 598                         {
 599                         lc= -c2;
 600                         do      {
 601                                 ll=r[i];
 602                                 r[i++]=(ll-lc)&BN_MASK2;
 603                                 lc=(lc > ll);
 604                                 } while (lc);
 605                         }
 606                 }
 607         }
 608 #endif /* BN_RECURSION */
 609
 610 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
 611         {
 612         int top,al,bl;
 613         BIGNUM *rr;
 614         int ret = 0;
 615 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 616         int i;
 617 #endif
 618 #ifdef BN_RECURSION
 619         BIGNUM *t;
 620         int j,k;
 621 #endif
 622
 623 #ifdef BN_COUNT
 624         printf("BN_mul %d * %d\n",a->top,b->top);
 625 #endif
 626
 627         bn_check_top(a);
 628         bn_check_top(b);
 629         bn_check_top(r);
 630
 631         al=a->top;
 632         bl=b->top;
 633         r->neg=a->neg^b->neg;
 634
 635         if ((al == 0) || (bl == 0))
 636                 {
 637                 BN_zero(r);
 638                 return(1);
 639                 }
 640         top=al+bl;
 641
 642         BN_CTX_start(ctx);
 643         if ((r == a) || (r == b))
 644                 {
 645                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
 646                 }
 647         else
 648                 rr = r;
 649
 650 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 651         i = al-bl;
 652 #endif
 653 #ifdef BN_MUL_COMBA
 654         if (i == 0)
 655                 {
 656 # if 0
 657                 if (al == 4)
 658                         {
 659                         if (bn_wexpand(rr,8) == NULL) goto err;
 660                         rr->top=8;
 661                         bn_mul_comba4(rr->d,a->d,b->d);
 662                         goto end;
 663                         }
 664 # endif
 665                 if (al == 8)
 666                         {
 667                         if (bn_wexpand(rr,16) == NULL) goto err;
 668                         rr->top=16;
 669                         bn_mul_comba8(rr->d,a->d,b->d);
 670                         goto end;
 671                         }
 672                 }
 673 #endif /* BN_MUL_COMBA */
 674 #ifdef BN_RECURSION
 675         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
 676                 {
 677                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
 678                         {
 679                         bn_wexpand(b,al);
 680                         b->d[bl]=0;
 681                         bl++;
 682                         i--;
 683                         }
 684                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
 685                         {
 686                         bn_wexpand(a,bl);
 687                         a->d[al]=0;
 688                         al++;
 689                         i++;
 690                         }
 691                 if (i == 0)
 692                         {
 693                         /* symmetric and > 4 */
 694                         /* 16 or larger */
 695                         j=BN_num_bits_word((BN_ULONG)al);
 696                         j=1<<(j-1);
 697                         k=j+j;
 698                         t = BN_CTX_get(ctx);
 699                         if (al == j) /* exact multiple */
 700                                 {
 701                                 bn_wexpand(t,k*2);
 702                                 bn_wexpand(rr,k*2);
 703                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
 704                                 }
 705                         else
 706                                 {
 707                                 bn_wexpand(a,k);
 708                                 bn_wexpand(b,k);
 709                                 bn_wexpand(t,k*4);
 710                                 bn_wexpand(rr,k*4);
 711                                 for (i=a->top; i<k; i++)
 712                                         a->d[i]=0;
 713                                 for (i=b->top; i<k; i++)
 714                                         b->d[i]=0;
 715                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
 716                                 }
 717                         rr->top=top;
 718                         goto end;
 719                         }
 720                 }
 721 #endif /* BN_RECURSION */
 722         if (bn_wexpand(rr,top) == NULL) goto err;
 723         rr->top=top;
 724         bn_mul_normal(rr->d,a->d,al,b->d,bl);
 725
 726 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 727 end:
 728 #endif
 729         bn_fix_top(rr);
 730         if (r != rr) BN_copy(r,rr);
 731         ret=1;
 732 err:
 733         BN_CTX_end(ctx);
 734         return(ret);
 735         }
 736
 737 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
 738         {
 739         BN_ULONG *rr;
 740
 741 #ifdef BN_COUNT
 742         printf(" bn_mul_normal %d * %d\n",na,nb);
 743 #endif
 744
 745         if (na < nb)
 746                 {
 747                 int itmp;
 748                 BN_ULONG *ltmp;
 749
 750                 itmp=na; na=nb; nb=itmp;
 751                 ltmp=a;   a=b;   b=ltmp;
 752
 753                 }
 754         rr= &(r[na]);
 755         rr[0]=bn_mul_words(r,a,na,b[0]);
 756
 757         for (;;)
 758                 {
 759                 if (--nb <= 0) return;
 760                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
 761                 if (--nb <= 0) return;
 762                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
 763                 if (--nb <= 0) return;
 764                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
 765                 if (--nb <= 0) return;
 766                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
 767                 rr+=4;
 768                 r+=4;
 769                 b+=4;
 770                 }
 771         }
 772
 773 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
 774         {
 775 #ifdef BN_COUNT
 776         printf(" bn_mul_low_normal %d * %d\n",n,n);
 777 #endif
 778         bn_mul_words(r,a,n,b[0]);
 779
 780         for (;;)
 781                 {
 782                 if (--n <= 0) return;
 783                 bn_mul_add_words(&(r[1]),a,n,b[1]);
 784                 if (--n <= 0) return;
 785                 bn_mul_add_words(&(r[2]),a,n,b[2]);
 786                 if (--n <= 0) return;
 787                 bn_mul_add_words(&(r[3]),a,n,b[3]);
 788                 if (--n <= 0) return;
 789                 bn_mul_add_words(&(r[4]),a,n,b[4]);
 790                 r+=4;
 791                 b+=4;
 792                 }
 793         }