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

   1 /* -*-c-*-
   2  *
   3  * Montgomery reduction
   4  *
   5  * (c) 1999 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  12  * Catacomb is free software; you can redistribute it and/or modify
  13  * it under the terms of the GNU Library General Public License as
  14  * published by the Free Software Foundation; either version 2 of the
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  22  * You should have received a copy of the GNU Library General Public
  23  * License along with Catacomb; if not, write to the Free
  24  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Header files ------------------------------------------------------*/
  29
  30 #include "mp.h"
  31 #include "mpmont.h"
  32
  33 /*----- Tweakables --------------------------------------------------------*/
  34
  35 /* --- @MPMONT_DISABLE@ --- *
  36  *
  37  * Replace all the clever Montgomery reduction with good old-fashioned long
  38  * division.
  39  */
  40
  41 /* #define MPMONT_DISABLE */
  42
  43 /*----- Reduction and multiplication --------------------------------------*/
  44
  45 /* --- @mpmont_create@ --- *
  46  *
  47  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
  48  *              @mp *m@ = modulus to use
  49  *
  50  * Returns:     Zero on success, nonzero on error.
  51  *
  52  * Use:         Initializes a Montgomery reduction context ready for use.
  53  *              The argument @m@ must be a positive odd integer.
  54  */
  55
  56 #ifdef MPMONT_DISABLE
  57
  58 int mpmont_create(mpmont *mm, mp *m)
  59 {
  60   mp_shrink(m);
  61   mm->m = MP_COPY(m);
  62   mm->r = MP_ONE;
  63   mm->r2 = MP_ONE;
  64   mm->mi = MP_ONE;
  65   return (0);
  66 }
  67
  68 #else
  69
  70 int mpmont_create(mpmont *mm, mp *m)
  71 {
  72   size_t n = MP_LEN(m);
  73   mp *r2 = mp_new(2 * n + 1, 0);
  74   mp r;
  75
  76   /* --- Take a copy of the modulus --- */
  77
  78  if (!MP_POSP(m) || !MP_ODDP(m))
  79    return (-1);
  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   return (0);
 101 }
 102
 103 #endif
 104
 105 /* --- @mpmont_destroy@ --- *
 106  *
 107  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 108  *
 109  * Returns:     ---
 110  *
 111  * Use:         Disposes of a context when it's no longer of any use to
 112  *              anyone.
 113  */
 114
 115 void mpmont_destroy(mpmont *mm)
 116 {
 117   MP_DROP(mm->m);
 118   MP_DROP(mm->r);
 119   MP_DROP(mm->r2);
 120   MP_DROP(mm->mi);
 121 }
 122
 123 /* --- @mpmont_reduce@ --- *
 124  *
 125  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 126  *              @mp *d@ = destination
 127  *              @mp *a@ = source, assumed positive
 128  *
 129  * Returns:     Result, %$a R^{-1} \bmod m$%.
 130  */
 131
 132 #ifdef MPMONT_DISABLE
 133
 134 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 135 {
 136   mp_div(0, &d, a, mm->m);
 137   return (d);
 138 }
 139
 140 #else
 141
 142 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 143 {
 144   size_t n = mm->n;
 145
 146   /* --- Check for serious Karatsuba reduction --- */
 147
 148   if (n > MPK_THRESH * 3) {
 149     mp al;
 150     mpw *vl;
 151     mp *u;
 152
 153     if (MP_LEN(a) >= n)
 154       vl = a->v + n;
 155     else
 156       vl = a->vl;
 157     mp_build(&al, a->v, vl);
 158     u = mp_mul(MP_NEW, &al, mm->mi);
 159     if (MP_LEN(u) > n)
 160       u->vl = u->v + n;
 161     u = mp_mul(u, u, mm->m);
 162     d = mp_add(d, a, u);
 163     MP_ENSURE(d, n);
 164     mp_drop(u);
 165   }
 166
 167   /* --- Otherwise do it the hard way --- */
 168
 169   else {
 170     mpw *dv, *dvl;
 171     mpw *mv, *mvl;
 172     mpw mi;
 173     size_t k = n;
 174
 175     /* --- Initial conditioning of the arguments --- */
 176
 177     a = MP_COPY(a);
 178     if (d)
 179       MP_DROP(d);
 180     d = a;
 181     MP_DEST(d, 2 * n + 1, a->f);
 182
 183     dv = d->v; dvl = d->vl;
 184     mv = mm->m->v; mvl = mm->m->vl;
 185
 186     /* --- Let's go to work --- */
 187
 188     mi = mm->mi->v[0];
 189     while (k--) {
 190       mpw u = MPW(*dv * mi);
 191       MPX_UMLAN(dv, dvl, mv, mvl, u);
 192       dv++;
 193     }
 194   }
 195
 196   /* --- Wrap everything up --- */
 197
 198   memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
 199   d->vl -= n;
 200   if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
 201     mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
 202   if (d->f & MP_NEG) {
 203     mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
 204     d->f &= ~MP_NEG;
 205   }
 206   MP_SHRINK(d);
 207   return (d);
 208 }
 209
 210 #endif
 211
 212 /* --- @mpmont_mul@ --- *
 213  *
 214  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 215  *              @mp *d@ = destination
 216  *              @mp *a, *b@ = sources, assumed positive
 217  *
 218  * Returns:     Result, %$a b R^{-1} \bmod m$%.
 219  */
 220
 221 #ifdef MPMONT_DISABLE
 222
 223 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 224 {
 225   d = mp_mul(d, a, b);
 226   mp_div(0, &d, d, mm->m);
 227   return (d);
 228 }
 229
 230 #else
 231
 232 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 233 {
 234   if (mm->n > MPK_THRESH * 3) {
 235     d = mp_mul(d, a, b);
 236     d = mpmont_reduce(mm, d, d);
 237   } else {
 238     mpw *dv, *dvl;
 239     mpw *av, *avl;
 240     mpw *bv, *bvl;
 241     mpw *mv, *mvl;
 242     mpw y;
 243     size_t n, i;
 244     mpw mi;
 245
 246     /* --- Initial conditioning of the arguments --- */
 247
 248     if (MP_LEN(a) > MP_LEN(b)) {
 249       mp *t = a; a = b; b = t;
 250     }
 251     n = MP_LEN(mm->m);
 252
 253     a = MP_COPY(a);
 254     b = MP_COPY(b);
 255     MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
 256     dv = d->v; dvl = d->vl;
 257     MPX_ZERO(dv, dvl);
 258     av = a->v; avl = a->vl;
 259     bv = b->v; bvl = b->vl;
 260     mv = mm->m->v; mvl = mm->m->vl;
 261     y = *bv;
 262
 263     /* --- Montgomery multiplication phase --- */
 264
 265     i = 0;
 266     mi = mm->mi->v[0];
 267     while (i < n && av < avl) {
 268       mpw x = *av++;
 269       mpw u = MPW((*dv + x * y) * mi);
 270       MPX_UMLAN(dv, dvl, bv, bvl, x);
 271       MPX_UMLAN(dv, dvl, mv, mvl, u);
 272       dv++;
 273       i++;
 274     }
 275
 276     /* --- Simpler Montgomery reduction phase --- */
 277
 278     while (i < n) {
 279       mpw u = MPW(*dv * mi);
 280       MPX_UMLAN(dv, dvl, mv, mvl, u);
 281       dv++;
 282       i++;
 283     }
 284
 285     /* --- Done --- */
 286
 287     memmove(d->v, dv, MPWS(dvl - dv));
 288     d->vl -= dv - d->v;
 289     if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
 290       mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
 291     if ((a->f ^ b->f) & MP_NEG)
 292       mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
 293     MP_SHRINK(d);
 294     d->f = (a->f | b->f) & MP_BURN;
 295     MP_DROP(a);
 296     MP_DROP(b);
 297   }
 298
 299   return (d);
 300 }
 301
 302 #endif
 303
 304 /*----- Test rig ----------------------------------------------------------*/
 305
 306 #ifdef TEST_RIG
 307
 308 static int tcreate(dstr *v)
 309 {
 310   mp *m = *(mp **)v[0].buf;
 311   mp *mi = *(mp **)v[1].buf;
 312   mp *r = *(mp **)v[2].buf;
 313   mp *r2 = *(mp **)v[3].buf;
 314
 315   mpmont mm;
 316   int ok = 1;
 317
 318   mpmont_create(&mm, m);
 319
 320   if (mm.mi->v[0] != mi->v[0]) {
 321     fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
 322             (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
 323     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 324     fputc('\n', stderr);
 325     ok = 0;
 326   }
 327
 328   if (!MP_EQ(mm.r, r)) {
 329     fputs("\n*** bad r", stderr);
 330     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 331     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
 332     fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
 333     fputc('\n', stderr);
 334     ok = 0;
 335   }
 336
 337   if (!MP_EQ(mm.r2, r2)) {
 338     fputs("\n*** bad r2", stderr);
 339     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 340     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
 341     fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
 342     fputc('\n', stderr);
 343     ok = 0;
 344   }
 345
 346   MP_DROP(m);
 347   MP_DROP(mi);
 348   MP_DROP(r);
 349   MP_DROP(r2);
 350   mpmont_destroy(&mm);
 351   assert(mparena_count(MPARENA_GLOBAL) == 0);
 352   return (ok);
 353 }
 354
 355 static int tmul(dstr *v)
 356 {
 357   mp *m = *(mp **)v[0].buf;
 358   mp *a = *(mp **)v[1].buf;
 359   mp *b = *(mp **)v[2].buf;
 360   mp *r = *(mp **)v[3].buf;
 361   int ok = 1;
 362
 363   mpmont mm;
 364   mpmont_create(&mm, m);
 365
 366   {
 367     mp *qr = mp_mul(MP_NEW, a, b);
 368     mp_div(0, &qr, qr, m);
 369
 370     if (!MP_EQ(qr, r)) {
 371       fputs("\n*** classical modmul failed", stderr);
 372       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 373       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 374       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 375       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 376       fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
 377       fputc('\n', stderr);
 378       ok = 0;
 379     }
 380
 381     mp_drop(qr);
 382   }
 383
 384   {
 385     mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
 386     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
 387     mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
 388     mr = mpmont_reduce(&mm, mr, mr);
 389     if (!MP_EQ(mr, r)) {
 390       fputs("\n*** montgomery modmul failed", stderr);
 391       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 392       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 393       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 394       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 395       fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 396       fputc('\n', stderr);
 397       ok = 0;
 398     }
 399     MP_DROP(ar); MP_DROP(br);
 400     mp_drop(mr);
 401   }
 402
 403
 404   MP_DROP(m);
 405   MP_DROP(a);
 406   MP_DROP(b);
 407   MP_DROP(r);
 408   mpmont_destroy(&mm);
 409   assert(mparena_count(MPARENA_GLOBAL) == 0);
 410   return ok;
 411 }
 412
 413 static test_chunk tests[] = {
 414   { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 415   { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 416   { 0, 0, { 0 } },
 417 };
 418
 419 int main(int argc, char *argv[])
 420 {
 421   sub_init();
 422   test_run(argc, argv, tests, SRCDIR "/t/mpmont");
 423   return (0);
 424 }
 425
 426 #endif
 427
 428 /*----- That's all, folks -------------------------------------------------*/