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:     Zero on success, nonzero on error.
  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 int 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   return (0);
  68 }
  69
  70 #else
  71
  72 int mpmont_create(mpmont *mm, mp *m)
  73 {
  74   size_t n = MP_LEN(m);
  75   mp *r2 = mp_new(2 * n + 1, 0);
  76   mp r;
  77
  78   /* --- Take a copy of the modulus --- */
  79
  80  if (!MP_POSP(m) || !MP_ODDP(m))
  81    return (-1);
  82   mm->m = MP_COPY(m);
  83
  84   /* --- Determine %$R^2$% --- */
  85
  86   mm->n = n;
  87   MPX_ZERO(r2->v, r2->vl - 1);
  88   r2->vl[-1] = 1;
  89
  90   /* --- Find the magic value @mi@ --- */
  91
  92   mp_build(&r, r2->v + n, r2->vl);
  93   mm->mi = mp_modinv(MP_NEW, m, &r);
  94   mm->mi = mp_sub(mm->mi, &r, mm->mi);
  95
  96   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
  97
  98   mm->r2 = MP_NEW;
  99   mp_div(0, &mm->r2, r2, m);
 100   mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
 101   MP_DROP(r2);
 102   return (0);
 103 }
 104
 105 #endif
 106
 107 /* --- @mpmont_destroy@ --- *
 108  *
 109  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 110  *
 111  * Returns:     ---
 112  *
 113  * Use:         Disposes of a context when it's no longer of any use to
 114  *              anyone.
 115  */
 116
 117 void mpmont_destroy(mpmont *mm)
 118 {
 119   MP_DROP(mm->m);
 120   MP_DROP(mm->r);
 121   MP_DROP(mm->r2);
 122   MP_DROP(mm->mi);
 123 }
 124
 125 /* --- @mpmont_reduce@ --- *
 126  *
 127  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 128  *              @mp *d@ = destination
 129  *              @mp *a@ = source, assumed positive
 130  *
 131  * Returns:     Result, %$a R^{-1} \bmod m$%.
 132  */
 133
 134 #ifdef MPMONT_DISABLE
 135
 136 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 137 {
 138   mp_div(0, &d, a, mm->m);
 139   return (d);
 140 }
 141
 142 #else
 143
 144 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 145 {
 146   size_t n = mm->n;
 147
 148   /* --- Check for serious Karatsuba reduction --- */
 149
 150   if (n > MPK_THRESH * 3) {
 151     mp al;
 152     mpw *vl;
 153     mp *u;
 154
 155     if (MP_LEN(a) >= n)
 156       vl = a->v + n;
 157     else
 158       vl = a->vl;
 159     mp_build(&al, a->v, vl);
 160     u = mp_mul(MP_NEW, &al, mm->mi);
 161     if (MP_LEN(u) > n)
 162       u->vl = u->v + n;
 163     u = mp_mul(u, u, mm->m);
 164     d = mp_add(d, a, u);
 165     mp_drop(u);
 166   }
 167
 168   /* --- Otherwise do it the hard way --- */
 169
 170   else {
 171     mpw *dv, *dvl;
 172     mpw *mv, *mvl;
 173     mpw mi;
 174     size_t k = n;
 175
 176     /* --- Initial conditioning of the arguments --- */
 177
 178     a = MP_COPY(a);
 179     if (d)
 180       MP_DROP(d);
 181     d = a;
 182     MP_DEST(d, 2 * n + 1, a->f);
 183
 184     dv = d->v; dvl = d->vl;
 185     mv = mm->m->v; mvl = mm->m->vl;
 186
 187     /* --- Let's go to work --- */
 188
 189     mi = mm->mi->v[0];
 190     while (k--) {
 191       mpw u = MPW(*dv * mi);
 192       MPX_UMLAN(dv, dvl, mv, mvl, u);
 193       dv++;
 194     }
 195   }
 196
 197   /* --- Wrap everything up --- */
 198
 199   memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
 200   d->vl -= n;
 201   if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
 202     mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
 203   if (d->f & MP_NEG) {
 204     mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
 205     d->f &= ~MP_NEG;
 206   }
 207   MP_SHRINK(d);
 208   return (d);
 209 }
 210
 211 #endif
 212
 213 /* --- @mpmont_mul@ --- *
 214  *
 215  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 216  *              @mp *d@ = destination
 217  *              @mp *a, *b@ = sources, assumed positive
 218  *
 219  * Returns:     Result, %$a b R^{-1} \bmod m$%.
 220  */
 221
 222 #ifdef MPMONT_DISABLE
 223
 224 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 225 {
 226   d = mp_mul(d, a, b);
 227   mp_div(0, &d, d, mm->m);
 228   return (d);
 229 }
 230
 231 #else
 232
 233 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 234 {
 235   if (mm->n > MPK_THRESH * 3) {
 236     d = mp_mul(d, a, b);
 237     d = mpmont_reduce(mm, d, d);
 238   } else {
 239     mpw *dv, *dvl;
 240     mpw *av, *avl;
 241     mpw *bv, *bvl;
 242     mpw *mv, *mvl;
 243     mpw y;
 244     size_t n, i;
 245     mpw mi;
 246
 247     /* --- Initial conditioning of the arguments --- */
 248
 249     if (MP_LEN(a) > MP_LEN(b)) {
 250       mp *t = a; a = b; b = t;
 251     }
 252     n = MP_LEN(mm->m);
 253
 254     a = MP_COPY(a);
 255     b = MP_COPY(b);
 256     MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
 257     dv = d->v; dvl = d->vl;
 258     MPX_ZERO(dv, dvl);
 259     av = a->v; avl = a->vl;
 260     bv = b->v; bvl = b->vl;
 261     mv = mm->m->v; mvl = mm->m->vl;
 262     y = *bv;
 263
 264     /* --- Montgomery multiplication phase --- */
 265
 266     i = 0;
 267     mi = mm->mi->v[0];
 268     while (i < n && av < avl) {
 269       mpw x = *av++;
 270       mpw u = MPW((*dv + x * y) * mi);
 271       MPX_UMLAN(dv, dvl, bv, bvl, x);
 272       MPX_UMLAN(dv, dvl, mv, mvl, u);
 273       dv++;
 274       i++;
 275     }
 276
 277     /* --- Simpler Montgomery reduction phase --- */
 278
 279     while (i < n) {
 280       mpw u = MPW(*dv * mi);
 281       MPX_UMLAN(dv, dvl, mv, mvl, u);
 282       dv++;
 283       i++;
 284     }
 285
 286     /* --- Done --- */
 287
 288     memmove(d->v, dv, MPWS(dvl - dv));
 289     d->vl -= dv - d->v;
 290     if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
 291       mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
 292     if ((a->f ^ b->f) & MP_NEG)
 293       mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
 294     MP_SHRINK(d);
 295     d->f = (a->f | b->f) & MP_BURN;
 296     MP_DROP(a);
 297     MP_DROP(b);
 298   }
 299
 300   return (d);
 301 }
 302
 303 #endif
 304
 305 /*----- Test rig ----------------------------------------------------------*/
 306
 307 #ifdef TEST_RIG
 308
 309 static int tcreate(dstr *v)
 310 {
 311   mp *m = *(mp **)v[0].buf;
 312   mp *mi = *(mp **)v[1].buf;
 313   mp *r = *(mp **)v[2].buf;
 314   mp *r2 = *(mp **)v[3].buf;
 315
 316   mpmont mm;
 317   int ok = 1;
 318
 319   mpmont_create(&mm, m);
 320
 321   if (mm.mi->v[0] != mi->v[0]) {
 322     fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
 323             (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
 324     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 325     fputc('\n', stderr);
 326     ok = 0;
 327   }
 328
 329   if (!MP_EQ(mm.r, r)) {
 330     fputs("\n*** bad r", stderr);
 331     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 332     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
 333     fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
 334     fputc('\n', stderr);
 335     ok = 0;
 336   }
 337
 338   if (!MP_EQ(mm.r2, r2)) {
 339     fputs("\n*** bad r2", stderr);
 340     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 341     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
 342     fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
 343     fputc('\n', stderr);
 344     ok = 0;
 345   }
 346
 347   MP_DROP(m);
 348   MP_DROP(mi);
 349   MP_DROP(r);
 350   MP_DROP(r2);
 351   mpmont_destroy(&mm);
 352   assert(mparena_count(MPARENA_GLOBAL) == 0);
 353   return (ok);
 354 }
 355
 356 static int tmul(dstr *v)
 357 {
 358   mp *m = *(mp **)v[0].buf;
 359   mp *a = *(mp **)v[1].buf;
 360   mp *b = *(mp **)v[2].buf;
 361   mp *r = *(mp **)v[3].buf;
 362   int ok = 1;
 363
 364   mpmont mm;
 365   mpmont_create(&mm, m);
 366
 367   {
 368     mp *qr = mp_mul(MP_NEW, a, b);
 369     mp_div(0, &qr, qr, m);
 370
 371     if (!MP_EQ(qr, r)) {
 372       fputs("\n*** classical modmul failed", stderr);
 373       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 374       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 375       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 376       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 377       fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
 378       fputc('\n', stderr);
 379       ok = 0;
 380     }
 381
 382     mp_drop(qr);
 383   }
 384
 385   {
 386     mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
 387     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
 388     mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
 389     mr = mpmont_reduce(&mm, mr, mr);
 390     if (!MP_EQ(mr, r)) {
 391       fputs("\n*** montgomery modmul failed", stderr);
 392       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 393       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 394       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 395       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 396       fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 397       fputc('\n', stderr);
 398       ok = 0;
 399     }
 400     MP_DROP(ar); MP_DROP(br);
 401     mp_drop(mr);
 402   }
 403
 404
 405   MP_DROP(m);
 406   MP_DROP(a);
 407   MP_DROP(b);
 408   MP_DROP(r);
 409   mpmont_destroy(&mm);
 410   assert(mparena_count(MPARENA_GLOBAL) == 0);
 411   return ok;
 412 }
 413
 414 static test_chunk tests[] = {
 415   { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 416   { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 417   { 0, 0, { 0 } },
 418 };
 419
 420 int main(int argc, char *argv[])
 421 {
 422   sub_init();
 423   test_run(argc, argv, tests, SRCDIR "/tests/mpmont");
 424   return (0);
 425 }
 426
 427 #endif
 428
 429 /*----- That's all, folks -------------------------------------------------*/