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   1 /* -*-c-*-
   2  *
   3  * $Id: mpbarrett.c,v 1.6 2000/10/08 12:03:44 mdw Exp $
   4  *
   5  * Barrett modular 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 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: mpbarrett.c,v $
  33  * Revision 1.6  2000/10/08 12:03:44  mdw
  34  * (mpbarrett_reduce): Cope with negative numbers.
  35  *
  36  * Revision 1.5  2000/07/29 17:04:33  mdw
  37  * Change to use left-to-right bitwise exponentiation.  This will improve
  38  * performance when the base is small.
  39  *
  40  * Revision 1.4  2000/06/17 11:45:09  mdw
  41  * Major memory management overhaul.  Added arena support.  Use the secure
  42  * arena for secret integers.  Replace and improve the MP management macros
  43  * (e.g., replace MP_MODIFY by MP_DEST).
  44  *
  45  * Revision 1.3  1999/12/12 15:08:52  mdw
  46  * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
  47  * significant digits.
  48  *
  49  * Revision 1.2  1999/12/11 01:50:56  mdw
  50  * Improve initialization slightly.
  51  *
  52  * Revision 1.1  1999/12/10 23:21:59  mdw
  53  * Barrett reduction support: works with even moduli.
  54  *
  55  */
  56
  57 /*----- Header files ------------------------------------------------------*/
  58
  59 #include "mp.h"
  60 #include "mpbarrett.h"
  61
  62 /*----- Main code ---------------------------------------------------------*/
  63
  64 /* --- @mpbarrett_create@ --- *
  65  *
  66  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  67  *              @mp *m@ = modulus to work to
  68  *
  69  *
  70  * Returns:     ---
  71  *
  72  * Use:         Initializes a Barrett reduction context ready for use.
  73  */
  74
  75 void mpbarrett_create(mpbarrett *mb, mp *m)
  76 {
  77   mp *b;
  78
  79   /* --- Validate the arguments --- */
  80
  81   assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0));
  82
  83   /* --- Compute %$\mu$% --- */
  84
  85   mp_shrink(m);
  86   mb->k = MP_LEN(m);
  87   mb->m = MP_COPY(m);
  88   b = mp_new(2 * mb->k + 1, 0);
  89   MPX_ZERO(b->v, b->vl - 1);
  90   b->vl[-1] = 1;
  91   mp_div(&b, 0, b, m);
  92   mb->mu = b;
  93 }
  94
  95 /* --- @mpbarrett_destroy@ --- *
  96  *
  97  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  98  *
  99  * Returns:     ---
 100  *
 101  * Use:         Destroys a Barrett reduction context releasing any resources
 102  *              claimed.
 103  */
 104
 105 void mpbarrett_destroy(mpbarrett *mb)
 106 {
 107   mp_drop(mb->m);
 108   mp_drop(mb->mu);
 109 }
 110
 111 /* --- @mpbarrett_reduce@ --- *
 112  *
 113  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 114  *              @mp *d@ = destination for result
 115  *              @mp *m@ = number to reduce
 116  *
 117  * Returns:     The residue of @m@ modulo the number in the reduction
 118  *              context.
 119  *
 120  * Use:         Performs an efficient modular reduction.
 121  */
 122
 123 mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
 124 {
 125   mp *q;
 126   size_t k = mb->k;
 127
 128   /* --- Special case if @m@ is too small --- */
 129
 130   if (MP_LEN(m) < k) {
 131     m = MP_COPY(m);
 132     if (d)
 133       MP_DROP(d);
 134     return (m);
 135   }
 136
 137   /* --- First stage --- */
 138
 139   {
 140     mp qq;
 141     mp_build(&qq, m->v + (k - 1), m->vl);
 142     q = mp_mul(MP_NEW, &qq, mb->mu);
 143     if (MP_LEN(q) <= k) {
 144       m = MP_COPY(m);
 145       if (d)
 146         MP_DROP(d);
 147       return (m);
 148     }
 149   }
 150
 151   /* --- Second stage --- */
 152
 153   {
 154     mp *r;
 155     mpw *mvl;
 156
 157     MP_COPY(m);
 158     if (MP_LEN(m) <= k + 1)
 159       mvl = m->vl;
 160     else
 161       mvl = m->v + k + 1;
 162     r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN);
 163     mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
 164     MP_DEST(d, k + 1, r->f);
 165     mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
 166     d->f = (m->f | r->f) & (MP_BURN | MP_NEG);
 167     MP_DROP(r);
 168     MP_DROP(q);
 169     MP_DROP(m);
 170   }
 171
 172   /* --- Final stage --- */
 173
 174   MP_SHRINK(d);
 175   while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
 176     mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
 177
 178   /* --- Fix up the sign --- */
 179
 180   if (d->f & MP_NEG) {
 181     mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl);
 182     d->f &= ~MP_NEG;
 183   }
 184
 185   MP_SHRINK(d);
 186   return (d);
 187 }
 188
 189 /* --- @mpbarrett_exp@ --- *
 190  *
 191  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 192  *              @mp *d@ = fake destination
 193  *              @mp *a@ = base
 194  *              @mp *e@ = exponent
 195  *
 196  * Returns:     Result, %$a^e \bmod m$%.
 197  */
 198
 199 mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
 200 {
 201   mpscan sc;
 202   mp *x = MP_ONE;
 203   mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
 204   unsigned sq = 0;
 205
 206   a = MP_COPY(a);
 207   mp_rscan(&sc, e);
 208   if (!MP_RSTEP(&sc))
 209     goto exit;
 210   while (!MP_RBIT(&sc))
 211     MP_RSTEP(&sc);
 212
 213   /* --- Do the main body of the work --- */
 214
 215   for (;;) {
 216     sq++;
 217     while (sq) {
 218       mp *y;
 219       y = mp_sqr(spare, x);
 220       y = mpbarrett_reduce(mb, y, y);
 221       spare = x; x = y;
 222       sq--;
 223     }
 224     {
 225       mp *y = mp_mul(spare, x, a);
 226       y = mpbarrett_reduce(mb, y, y);
 227       spare = x; x = y;
 228     }
 229     for (;;) {
 230       if (!MP_RSTEP(&sc))
 231         goto done;
 232       if (MP_RBIT(&sc))
 233         break;
 234       sq++;
 235     }
 236   }
 237
 238   /* --- Do a final round of squaring --- */
 239
 240 done:
 241   while (sq) {
 242     mp *y;
 243     y = mp_sqr(spare, x);
 244     y = mpbarrett_reduce(mb, y, y);
 245     spare = x; x = y;
 246     sq--;
 247   }
 248
 249 exit:
 250   MP_DROP(a);
 251   if (spare != MP_NEW)
 252     MP_DROP(spare);
 253   if (d != MP_NEW)
 254     MP_DROP(d);
 255   return (x);
 256 }
 257
 258 /*----- Test rig ----------------------------------------------------------*/
 259
 260 #ifdef TEST_RIG
 261
 262 static int vmod(dstr *v)
 263 {
 264   mp *x = *(mp **)v[0].buf;
 265   mp *n = *(mp **)v[1].buf;
 266   mp *r = *(mp **)v[2].buf;
 267   mp *s;
 268   mpbarrett mb;
 269   int ok = 1;
 270
 271   mpbarrett_create(&mb, n);
 272   s = mpbarrett_reduce(&mb, MP_NEW, x);
 273
 274   if (!MP_EQ(s, r)) {
 275     fputs("\n*** barrett reduction failure\n", stderr);
 276     fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
 277     fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
 278     fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr);
 279     fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr);
 280     ok = 0;
 281   }
 282
 283   mpbarrett_destroy(&mb);
 284   mp_drop(x);
 285   mp_drop(n);
 286   mp_drop(r);
 287   mp_drop(s);
 288   assert(mparena_count(MPARENA_GLOBAL) == 0);
 289   return (ok);
 290 }
 291
 292 static int vexp(dstr *v)
 293 {
 294   mp *m = *(mp **)v[0].buf;
 295   mp *a = *(mp **)v[1].buf;
 296   mp *b = *(mp **)v[2].buf;
 297   mp *r = *(mp **)v[3].buf;
 298   mp *mr;
 299   int ok = 1;
 300
 301   mpbarrett mb;
 302   mpbarrett_create(&mb, m);
 303
 304   mr = mpbarrett_exp(&mb, MP_NEW, a, b);
 305
 306   if (!MP_EQ(mr, r)) {
 307     fputs("\n*** barrett modexp failed", stderr);
 308     fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 309     fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 310     fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
 311     fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 312     fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 313     fputc('\n', stderr);
 314     ok = 0;
 315   }
 316
 317   mp_drop(m);
 318   mp_drop(a);
 319   mp_drop(b);
 320   mp_drop(r);
 321   mp_drop(mr);
 322   mpbarrett_destroy(&mb);
 323   assert(mparena_count(MPARENA_GLOBAL) == 0);
 324   return ok;
 325 }
 326
 327 static test_chunk tests[] = {
 328   { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
 329   { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 330   { 0, 0, { 0 } }
 331 };
 332
 333 int main(int argc, char *argv[])
 334 {
 335   sub_init();
 336   test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett");
 337   return (0);
 338 }
 339
 340 #endif
 341
 342 /*----- That's all, folks -------------------------------------------------*/