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 /*----- Low-level implementation ------------------------------------------*/
  44
  45 #ifndef MPMONT_DISABLE
  46
  47 /* --- @redccore@ --- *
  48  *
  49  * Arguments:   @mpw *dv, *dvl@ = base and limit of source/destination
  50  *              @const mpw *mv@ = base of modulus %$m$%
  51  *              @size_t n@ = length of modulus
  52  *              @const mpw *mi@ = base of REDC coefficient %$m'$%
  53  *
  54  * Returns:     ---
  55  *
  56  * Use:         Let %$a$% be the input operand.  Store in %$d$% the value
  57  *              %$a + (m' a \bmod R) m$%.  The destination has space for at
  58  *              least %$2 n + 1$% words of result.
  59  */
  60
  61 static void redccore(mpw *dv, mpw *dvl, const mpw *mv,
  62                      size_t n, const mpw *mi)
  63 {
  64   mpw mi0 = *mi;
  65   size_t i;
  66
  67   for (i = 0; i < n; i++) {
  68     MPX_UMLAN(dv, dvl, mv, mv + n, MPW(*dv*mi0));
  69     dv++;
  70   }
  71 }
  72
  73 /* --- @redccore@ --- *
  74  *
  75  * Arguments:   @mpw *dv, *dvl@ = base and limit of source/destination
  76  *              @const mpw *av, *avl@ = base and limit of first multiplicand
  77  *              @const mpw *bv, *bvl@ = base and limit of second multiplicand
  78  *              @const mpw *mv@ = base of modulus %$m$%
  79  *              @size_t n@ = length of modulus
  80  *              @const mpw *mi@ = base of REDC coefficient %$m'$%
  81  *
  82  * Returns:     ---
  83  *
  84  * Use:         Let %$a$% and %$b$% be the multiplicands.  Let %$w = a b$%.
  85  *              Store in %$d$% the value %$a b + (m' a b \bmod R) m$%.
  86  */
  87
  88 static void mulcore(mpw *dv, mpw *dvl,
  89                     const mpw *av, const mpw *avl,
  90                     const mpw *bv, const mpw *bvl,
  91                     const mpw *mv, size_t n, const mpw *mi)
  92 {
  93   mpw ai, b0, y, mi0 = *mi;
  94   const mpw *tv, *tvl;
  95   const mpw *mvl = mv + n;
  96   size_t i = 0;
  97
  98   /* --- Initial setup --- */
  99
 100   MPX_ZERO(dv, dvl);
 101   if (avl - av > bvl - bv) {
 102     tv = av; av = bv; bv = tv;
 103     tvl = avl; avl = bvl; bvl = tvl;
 104   }
 105   b0 = *bv;
 106
 107   /* --- Multiply, until we run out of multiplicand --- */
 108
 109   while (i < n && av < avl) {
 110     ai = *av++;
 111     y = MPW((*dv + ai*b0)*mi0);
 112     MPX_UMLAN(dv, dvl, bv, bvl, ai);
 113     MPX_UMLAN(dv, dvl, mv, mvl, y);
 114     dv++; i++;
 115   }
 116
 117   /* --- Continue reducing until we run out of modulus --- */
 118
 119   while (i < n) {
 120     y = MPW(*dv*mi0);
 121     MPX_UMLAN(dv, dvl, mv, mvl, y);
 122     dv++; i++;
 123   }
 124 }
 125
 126 /* --- @finish@ --- *
 127  *
 128  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 129  *              *mp *d@ = pointer to mostly-reduced operand
 130  *
 131  * Returns:     ---
 132  *
 133  * Use:         Applies the finishing touches to Montgomery reduction.  The
 134  *              operand @d@ is a multiple of %$R%$ at this point, so it needs
 135  *              to be shifted down; the result might need a further
 136  *              subtraction to get it into the right interval; and we may
 137  *              need to do an additional subtraction if %$d$% is negative.
 138  */
 139
 140 static void finish(mpmont *mm, mp *d)
 141 {
 142   mpw *dv = d->v, *dvl = d->vl;
 143   size_t n = mm->n;
 144
 145   memmove(dv, dv + n, MPWS(dvl - (dv + n)));
 146   dvl -= n;
 147
 148   if (MPX_UCMP(dv, dvl, >=, mm->m->v, mm->m->vl))
 149     mpx_usub(dv, dvl, dv, dvl, mm->m->v, mm->m->vl);
 150
 151   if (d->f & MP_NEG) {
 152     mpx_usub(dv, dvl, mm->m->v, mm->m->vl, dv, dvl);
 153     d->f &= ~MP_NEG;
 154   }
 155
 156   d->vl = dvl;
 157   MP_SHRINK(d);
 158 }
 159
 160 #endif
 161
 162 /*----- Reduction and multiplication --------------------------------------*/
 163
 164 /* --- @mpmont_create@ --- *
 165  *
 166  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 167  *              @mp *m@ = modulus to use
 168  *
 169  * Returns:     Zero on success, nonzero on error.
 170  *
 171  * Use:         Initializes a Montgomery reduction context ready for use.
 172  *              The argument @m@ must be a positive odd integer.
 173  */
 174
 175 #ifdef MPMONT_DISABLE
 176
 177 int mpmont_create(mpmont *mm, mp *m)
 178 {
 179   mp_shrink(m);
 180   mm->m = MP_COPY(m);
 181   mm->r = MP_ONE;
 182   mm->r2 = MP_ONE;
 183   mm->mi = MP_ONE;
 184   return (0);
 185 }
 186
 187 #else
 188
 189 int mpmont_create(mpmont *mm, mp *m)
 190 {
 191   size_t n = MP_LEN(m);
 192   mp *r2 = mp_new(2 * n + 1, 0);
 193   mp r;
 194
 195   /* --- Take a copy of the modulus --- */
 196
 197  if (!MP_POSP(m) || !MP_ODDP(m))
 198    return (-1);
 199   mm->m = MP_COPY(m);
 200
 201   /* --- Determine %$R^2$% --- */
 202
 203   mm->n = n;
 204   MPX_ZERO(r2->v, r2->vl - 1);
 205   r2->vl[-1] = 1;
 206
 207   /* --- Find the magic value @mi@ --- */
 208
 209   mp_build(&r, r2->v + n, r2->vl);
 210   mm->mi = mp_modinv(MP_NEW, m, &r);
 211   mm->mi = mp_sub(mm->mi, &r, mm->mi);
 212
 213   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
 214
 215   mm->r2 = MP_NEW;
 216   mp_div(0, &mm->r2, r2, m);
 217   mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
 218   MP_DROP(r2);
 219   return (0);
 220 }
 221
 222 #endif
 223
 224 /* --- @mpmont_destroy@ --- *
 225  *
 226  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 227  *
 228  * Returns:     ---
 229  *
 230  * Use:         Disposes of a context when it's no longer of any use to
 231  *              anyone.
 232  */
 233
 234 void mpmont_destroy(mpmont *mm)
 235 {
 236   MP_DROP(mm->m);
 237   MP_DROP(mm->r);
 238   MP_DROP(mm->r2);
 239   MP_DROP(mm->mi);
 240 }
 241
 242 /* --- @mpmont_reduce@ --- *
 243  *
 244  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 245  *              @mp *d@ = destination
 246  *              @mp *a@ = source, assumed positive
 247  *
 248  * Returns:     Result, %$a R^{-1} \bmod m$%.
 249  */
 250
 251 #ifdef MPMONT_DISABLE
 252
 253 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 254 {
 255   mp_div(0, &d, a, mm->m);
 256   return (d);
 257 }
 258
 259 #else
 260
 261 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 262 {
 263   size_t n = mm->n;
 264
 265   /* --- Check for serious Karatsuba reduction --- */
 266
 267   if (n > MPK_THRESH * 3) {
 268     mp al;
 269     mpw *vl;
 270     mp *u;
 271
 272     if (MP_LEN(a) >= n) vl = a->v + n;
 273     else vl = a->vl;
 274     mp_build(&al, a->v, vl);
 275     u = mp_mul(MP_NEW, &al, mm->mi);
 276     if (MP_LEN(u) > n) u->vl = u->v + n;
 277     u = mp_mul(u, u, mm->m);
 278     d = mp_add(d, a, u);
 279     MP_ENSURE(d, n);
 280     mp_drop(u);
 281   }
 282
 283   /* --- Otherwise do it the hard way --- */
 284
 285   else {
 286     a = MP_COPY(a);
 287     if (d) MP_DROP(d);
 288     d = a;
 289     MP_DEST(d, 2*mm->n + 1, a->f);
 290     redccore(d->v, d->vl, mm->m->v, mm->n, mm->mi->v);
 291   }
 292
 293   /* --- Wrap everything up --- */
 294
 295   finish(mm, d);
 296   return (d);
 297 }
 298
 299 #endif
 300
 301 /* --- @mpmont_mul@ --- *
 302  *
 303  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 304  *              @mp *d@ = destination
 305  *              @mp *a, *b@ = sources, assumed positive
 306  *
 307  * Returns:     Result, %$a b R^{-1} \bmod m$%.
 308  */
 309
 310 #ifdef MPMONT_DISABLE
 311
 312 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 313 {
 314   d = mp_mul(d, a, b);
 315   mp_div(0, &d, d, mm->m);
 316   return (d);
 317 }
 318
 319 #else
 320
 321 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 322 {
 323   if (mm->n > MPK_THRESH * 3) {
 324     d = mp_mul(d, a, b);
 325     d = mpmont_reduce(mm, d, d);
 326   } else {
 327     a = MP_COPY(a);
 328     b = MP_COPY(b);
 329     MP_DEST(d, 2*mm->n + 1, a->f | b->f | MP_UNDEF);
 330     mulcore(d->v, d->vl, a->v, a->vl, b->v, b->vl,
 331             mm->m->v, mm->n, mm->mi->v);
 332     d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
 333     finish(mm, d);
 334     MP_DROP(a); MP_DROP(b);
 335   }
 336
 337   return (d);
 338 }
 339
 340 #endif
 341
 342 /*----- Test rig ----------------------------------------------------------*/
 343
 344 #ifdef TEST_RIG
 345
 346 static int tcreate(dstr *v)
 347 {
 348   mp *m = *(mp **)v[0].buf;
 349   mp *mi = *(mp **)v[1].buf;
 350   mp *r = *(mp **)v[2].buf;
 351   mp *r2 = *(mp **)v[3].buf;
 352
 353   mpmont mm;
 354   int ok = 1;
 355
 356   mpmont_create(&mm, m);
 357
 358   if (mm.mi->v[0] != mi->v[0]) {
 359     fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
 360             (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
 361     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 362     fputc('\n', stderr);
 363     ok = 0;
 364   }
 365
 366   if (!MP_EQ(mm.r, r)) {
 367     fputs("\n*** bad r", stderr);
 368     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 369     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
 370     fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
 371     fputc('\n', stderr);
 372     ok = 0;
 373   }
 374
 375   if (!MP_EQ(mm.r2, r2)) {
 376     fputs("\n*** bad r2", stderr);
 377     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 378     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
 379     fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
 380     fputc('\n', stderr);
 381     ok = 0;
 382   }
 383
 384   MP_DROP(m);
 385   MP_DROP(mi);
 386   MP_DROP(r);
 387   MP_DROP(r2);
 388   mpmont_destroy(&mm);
 389   assert(mparena_count(MPARENA_GLOBAL) == 0);
 390   return (ok);
 391 }
 392
 393 static int tmul(dstr *v)
 394 {
 395   mp *m = *(mp **)v[0].buf;
 396   mp *a = *(mp **)v[1].buf;
 397   mp *b = *(mp **)v[2].buf;
 398   mp *r = *(mp **)v[3].buf;
 399   int ok = 1;
 400
 401   mpmont mm;
 402   mpmont_create(&mm, m);
 403
 404   {
 405     mp *qr = mp_mul(MP_NEW, a, b);
 406     mp_div(0, &qr, qr, m);
 407
 408     if (!MP_EQ(qr, r)) {
 409       fputs("\n*** classical modmul failed", stderr);
 410       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 411       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 412       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 413       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 414       fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
 415       fputc('\n', stderr);
 416       ok = 0;
 417     }
 418
 419     mp_drop(qr);
 420   }
 421
 422   {
 423     mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
 424     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
 425     mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
 426     mr = mpmont_reduce(&mm, mr, mr);
 427     if (!MP_EQ(mr, r)) {
 428       fputs("\n*** montgomery modmul failed", stderr);
 429       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 430       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 431       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 432       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 433       fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 434       fputc('\n', stderr);
 435       ok = 0;
 436     }
 437     MP_DROP(ar); MP_DROP(br);
 438     mp_drop(mr);
 439   }
 440
 441
 442   MP_DROP(m);
 443   MP_DROP(a);
 444   MP_DROP(b);
 445   MP_DROP(r);
 446   mpmont_destroy(&mm);
 447   assert(mparena_count(MPARENA_GLOBAL) == 0);
 448   return ok;
 449 }
 450
 451 static test_chunk tests[] = {
 452   { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 453   { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 454   { 0, 0, { 0 } },
 455 };
 456
 457 int main(int argc, char *argv[])
 458 {
 459   sub_init();
 460   test_run(argc, argv, tests, SRCDIR "/t/mpmont");
 461   return (0);
 462 }
 463
 464 #endif
 465
 466 /*----- That's all, folks -------------------------------------------------*/