git.distorted.org.uk Git - u/mdw/catacomb/blob - mpmont.c

   1 /* -*-c-*-
   2  *
   3  * $Id$
   4  *
   5  * Montgomery reduction
   6  *
   7  * (c) 1999 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Header files ------------------------------------------------------*/
  31
  32 #include "mp.h"
  33 #include "mpmont.h"
  34
  35 /*----- Tweakables --------------------------------------------------------*/
  36
  37 /* --- @MPMONT_DISABLE@ --- *
  38  *
  39  * Replace all the clever Montgomery reduction with good old-fashioned long
  40  * division.
  41  */
  42
  43 /* #define MPMONT_DISABLE */
  44
  45 /*----- Reduction and multiplication --------------------------------------*/
  46
  47 /* --- @mpmont_create@ --- *
  48  *
  49  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
  50  *              @mp *m@ = modulus to use
  51  *
  52  * Returns:     ---
  53  *
  54  * Use:         Initializes a Montgomery reduction context ready for use.
  55  *              The argument @m@ must be a positive odd integer.
  56  */
  57
  58 #ifdef MPMONT_DISABLE
  59
  60 void mpmont_create(mpmont *mm, mp *m)
  61 {
  62   mp_shrink(m);
  63   mm->m = MP_COPY(m);
  64   mm->r = MP_ONE;
  65   mm->r2 = MP_ONE;
  66   mm->mi = MP_ONE;
  67 }
  68
  69 #else
  70
  71 void mpmont_create(mpmont *mm, mp *m)
  72 {
  73   size_t n = MP_LEN(m);
  74   mp *r2 = mp_new(2 * n + 1, 0);
  75   mp r;
  76
  77   /* --- Take a copy of the modulus --- */
  78
  79   assert(MP_POSP(m) && MP_ODDP(m));
  80   mm->m = MP_COPY(m);
  81
  82   /* --- Determine %$R^2$% --- */
  83
  84   mm->n = n;
  85   MPX_ZERO(r2->v, r2->vl - 1);
  86   r2->vl[-1] = 1;
  87
  88   /* --- Find the magic value @mi@ --- */
  89
  90   mp_build(&r, r2->v + n, r2->vl);
  91   mm->mi = mp_modinv(MP_NEW, m, &r);
  92   mm->mi = mp_sub(mm->mi, &r, mm->mi);
  93
  94   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
  95
  96   mm->r2 = MP_NEW;
  97   mp_div(0, &mm->r2, r2, m);
  98   mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
  99   MP_DROP(r2);
 100 }
 101
 102 #endif
 103
 104 /* --- @mpmont_destroy@ --- *
 105  *
 106  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 107  *
 108  * Returns:     ---
 109  *
 110  * Use:         Disposes of a context when it's no longer of any use to
 111  *              anyone.
 112  */
 113
 114 void mpmont_destroy(mpmont *mm)
 115 {
 116   MP_DROP(mm->m);
 117   MP_DROP(mm->r);
 118   MP_DROP(mm->r2);
 119   MP_DROP(mm->mi);
 120 }
 121
 122 /* --- @mpmont_reduce@ --- *
 123  *
 124  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 125  *              @mp *d@ = destination
 126  *              @mp *a@ = source, assumed positive
 127  *
 128  * Returns:     Result, %$a R^{-1} \bmod m$%.
 129  */
 130
 131 #ifdef MPMONT_DISABLE
 132
 133 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 134 {
 135   mp_div(0, &d, a, mm->m);
 136   return (d);
 137 }
 138
 139 #else
 140
 141 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 142 {
 143   size_t n = mm->n;
 144
 145   /* --- Check for serious Karatsuba reduction --- */
 146
 147   if (n > MPK_THRESH * 3) {
 148     mp al;
 149     mpw *vl;
 150     mp *u;
 151
 152     if (MP_LEN(a) >= n)
 153       vl = a->v + n;
 154     else
 155       vl = a->vl;
 156     mp_build(&al, a->v, vl);
 157     u = mp_mul(MP_NEW, &al, mm->mi);
 158     if (MP_LEN(u) > n)
 159       u->vl = u->v + n;
 160     u = mp_mul(u, u, mm->m);
 161     d = mp_add(d, a, u);
 162     mp_drop(u);
 163   }
 164
 165   /* --- Otherwise do it the hard way --- */
 166
 167   else {
 168     mpw *dv, *dvl;
 169     mpw *mv, *mvl;
 170     mpw mi;
 171     size_t k = n;
 172
 173     /* --- Initial conditioning of the arguments --- */
 174
 175     a = MP_COPY(a);
 176     if (d)
 177       MP_DROP(d);
 178     d = a;
 179     MP_DEST(d, 2 * n + 1, a->f);
 180
 181     dv = d->v; dvl = d->vl;
 182     mv = mm->m->v; mvl = mm->m->vl;
 183
 184     /* --- Let's go to work --- */
 185
 186     mi = mm->mi->v[0];
 187     while (k--) {
 188       mpw u = MPW(*dv * mi);
 189       MPX_UMLAN(dv, dvl, mv, mvl, u);
 190       dv++;
 191     }
 192   }
 193
 194   /* --- Wrap everything up --- */
 195
 196   memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
 197   d->vl -= n;
 198   if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
 199     mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
 200   if (d->f & MP_NEG) {
 201     mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
 202     d->f &= ~MP_NEG;
 203   }
 204   MP_SHRINK(d);
 205   return (d);
 206 }
 207
 208 #endif
 209
 210 /* --- @mpmont_mul@ --- *
 211  *
 212  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 213  *              @mp *d@ = destination
 214  *              @mp *a, *b@ = sources, assumed positive
 215  *
 216  * Returns:     Result, %$a b R^{-1} \bmod m$%.
 217  */
 218
 219 #ifdef MPMONT_DISABLE
 220
 221 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 222 {
 223   d = mp_mul(d, a, b);
 224   mp_div(0, &d, d, mm->m);
 225   return (d);
 226 }
 227
 228 #else
 229
 230 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 231 {
 232   if (mm->n > MPK_THRESH * 3) {
 233     d = mp_mul(d, a, b);
 234     d = mpmont_reduce(mm, d, d);
 235   } else {
 236     mpw *dv, *dvl;
 237     mpw *av, *avl;
 238     mpw *bv, *bvl;
 239     mpw *mv, *mvl;
 240     mpw y;
 241     size_t n, i;
 242     mpw mi;
 243
 244     /* --- Initial conditioning of the arguments --- */
 245
 246     if (MP_LEN(a) > MP_LEN(b)) {
 247       mp *t = a; a = b; b = t;
 248     }
 249     n = MP_LEN(mm->m);
 250
 251     a = MP_COPY(a);
 252     b = MP_COPY(b);
 253     MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
 254     dv = d->v; dvl = d->vl;
 255     MPX_ZERO(dv, dvl);
 256     av = a->v; avl = a->vl;
 257     bv = b->v; bvl = b->vl;
 258     mv = mm->m->v; mvl = mm->m->vl;
 259     y = *bv;
 260
 261     /* --- Montgomery multiplication phase --- */
 262
 263     i = 0;
 264     mi = mm->mi->v[0];
 265     while (i < n && av < avl) {
 266       mpw x = *av++;
 267       mpw u = MPW((*dv + x * y) * mi);
 268       MPX_UMLAN(dv, dvl, bv, bvl, x);
 269       MPX_UMLAN(dv, dvl, mv, mvl, u);
 270       dv++;
 271       i++;
 272     }
 273
 274     /* --- Simpler Montgomery reduction phase --- */
 275
 276     while (i < n) {
 277       mpw u = MPW(*dv * mi);
 278       MPX_UMLAN(dv, dvl, mv, mvl, u);
 279       dv++;
 280       i++;
 281     }
 282
 283     /* --- Done --- */
 284
 285     memmove(d->v, dv, MPWS(dvl - dv));
 286     d->vl -= dv - d->v;
 287     if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
 288       mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
 289     if ((a->f ^ b->f) & MP_NEG)
 290       mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
 291     MP_SHRINK(d);
 292     d->f = (a->f | b->f) & MP_BURN;
 293     MP_DROP(a);
 294     MP_DROP(b);
 295   }
 296
 297   return (d);
 298 }
 299
 300 #endif
 301
 302 /*----- Test rig ----------------------------------------------------------*/
 303
 304 #ifdef TEST_RIG
 305
 306 static int tcreate(dstr *v)
 307 {
 308   mp *m = *(mp **)v[0].buf;
 309   mp *mi = *(mp **)v[1].buf;
 310   mp *r = *(mp **)v[2].buf;
 311   mp *r2 = *(mp **)v[3].buf;
 312
 313   mpmont mm;
 314   int ok = 1;
 315
 316   mpmont_create(&mm, m);
 317
 318   if (mm.mi->v[0] != mi->v[0]) {
 319     fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
 320             (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
 321     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 322     fputc('\n', stderr);
 323     ok = 0;
 324   }
 325
 326   if (!MP_EQ(mm.r, r)) {
 327     fputs("\n*** bad r", stderr);
 328     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 329     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
 330     fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
 331     fputc('\n', stderr);
 332     ok = 0;
 333   }
 334
 335   if (!MP_EQ(mm.r2, r2)) {
 336     fputs("\n*** bad r2", stderr);
 337     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 338     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
 339     fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
 340     fputc('\n', stderr);
 341     ok = 0;
 342   }
 343
 344   MP_DROP(m);
 345   MP_DROP(mi);
 346   MP_DROP(r);
 347   MP_DROP(r2);
 348   mpmont_destroy(&mm);
 349   assert(mparena_count(MPARENA_GLOBAL) == 0);
 350   return (ok);
 351 }
 352
 353 static int tmul(dstr *v)
 354 {
 355   mp *m = *(mp **)v[0].buf;
 356   mp *a = *(mp **)v[1].buf;
 357   mp *b = *(mp **)v[2].buf;
 358   mp *r = *(mp **)v[3].buf;
 359   int ok = 1;
 360
 361   mpmont mm;
 362   mpmont_create(&mm, m);
 363
 364   {
 365     mp *qr = mp_mul(MP_NEW, a, b);
 366     mp_div(0, &qr, qr, m);
 367
 368     if (!MP_EQ(qr, r)) {
 369       fputs("\n*** classical modmul failed", stderr);
 370       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 371       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 372       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 373       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 374       fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
 375       fputc('\n', stderr);
 376       ok = 0;
 377     }
 378
 379     mp_drop(qr);
 380   }
 381
 382   {
 383     mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
 384     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
 385     mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
 386     mr = mpmont_reduce(&mm, mr, mr);
 387     if (!MP_EQ(mr, r)) {
 388       fputs("\n*** montgomery modmul failed", stderr);
 389       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 390       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 391       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 392       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 393       fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 394       fputc('\n', stderr);
 395       ok = 0;
 396     }
 397     MP_DROP(ar); MP_DROP(br);
 398     mp_drop(mr);
 399   }
 400
 401
 402   MP_DROP(m);
 403   MP_DROP(a);
 404   MP_DROP(b);
 405   MP_DROP(r);
 406   mpmont_destroy(&mm);
 407   assert(mparena_count(MPARENA_GLOBAL) == 0);
 408   return ok;
 409 }
 410
 411 static test_chunk tests[] = {
 412   { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 413   { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 414   { 0, 0, { 0 } },
 415 };
 416
 417 int main(int argc, char *argv[])
 418 {
 419   sub_init();
 420   test_run(argc, argv, tests, SRCDIR "/tests/mpmont");
 421   return (0);
 422 }
 423
 424 #endif
 425
 426 /*----- That's all, folks -------------------------------------------------*/