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   1 /* -*-c-*-
   2  *
   3  * $Id: mpbarrett.c,v 1.8 2001/06/16 13:00:20 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 1.8  2001/06/16 13:00:20  mdw
  34  * Use the generic exponentiation functions.
  35  *
  36  * Revision 1.7  2001/04/19 18:25:26  mdw
  37  * Use sliding-window exponentiation.
  38  *
  39  * Revision 1.6  2000/10/08 12:03:44  mdw
  40  * (mpbarrett_reduce): Cope with negative numbers.
  41  *
  42  * Revision 1.5  2000/07/29 17:04:33  mdw
  43  * Change to use left-to-right bitwise exponentiation.  This will improve
  44  * performance when the base is small.
  45  *
  46  * Revision 1.4  2000/06/17 11:45:09  mdw
  47  * Major memory management overhaul.  Added arena support.  Use the secure
  48  * arena for secret integers.  Replace and improve the MP management macros
  49  * (e.g., replace MP_MODIFY by MP_DEST).
  50  *
  51  * Revision 1.3  1999/12/12 15:08:52  mdw
  52  * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
  53  * significant digits.
  54  *
  55  * Revision 1.2  1999/12/11 01:50:56  mdw
  56  * Improve initialization slightly.
  57  *
  58  * Revision 1.1  1999/12/10 23:21:59  mdw
  59  * Barrett reduction support: works with even moduli.
  60  *
  61  */
  62
  63 /*----- Header files ------------------------------------------------------*/
  64
  65 #include "mp.h"
  66 #include "mpbarrett.h"
  67 #include "mpbarrett-exp.h"
  68
  69 /*----- Main code ---------------------------------------------------------*/
  70
  71 /* --- @mpbarrett_create@ --- *
  72  *
  73  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  74  *              @mp *m@ = modulus to work to
  75  *
  76  *
  77  * Returns:     ---
  78  *
  79  * Use:         Initializes a Barrett reduction context ready for use.
  80  */
  81
  82 void mpbarrett_create(mpbarrett *mb, mp *m)
  83 {
  84   mp *b;
  85
  86   /* --- Validate the arguments --- */
  87
  88   assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0));
  89
  90   /* --- Compute %$\mu$% --- */
  91
  92   mp_shrink(m);
  93   mb->k = MP_LEN(m);
  94   mb->m = MP_COPY(m);
  95   b = mp_new(2 * mb->k + 1, 0);
  96   MPX_ZERO(b->v, b->vl - 1);
  97   b->vl[-1] = 1;
  98   mp_div(&b, 0, b, m);
  99   mb->mu = b;
 100 }
 101
 102 /* --- @mpbarrett_destroy@ --- *
 103  *
 104  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 105  *
 106  * Returns:     ---
 107  *
 108  * Use:         Destroys a Barrett reduction context releasing any resources
 109  *              claimed.
 110  */
 111
 112 void mpbarrett_destroy(mpbarrett *mb)
 113 {
 114   mp_drop(mb->m);
 115   mp_drop(mb->mu);
 116 }
 117
 118 /* --- @mpbarrett_reduce@ --- *
 119  *
 120  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 121  *              @mp *d@ = destination for result
 122  *              @mp *m@ = number to reduce
 123  *
 124  * Returns:     The residue of @m@ modulo the number in the reduction
 125  *              context.
 126  *
 127  * Use:         Performs an efficient modular reduction.
 128  */
 129
 130 mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
 131 {
 132   mp *q;
 133   size_t k = mb->k;
 134
 135   /* --- Special case if @m@ is too small --- */
 136
 137   if (MP_LEN(m) < k) {
 138     m = MP_COPY(m);
 139     if (d)
 140       MP_DROP(d);
 141     return (m);
 142   }
 143
 144   /* --- First stage --- */
 145
 146   {
 147     mp qq;
 148     mp_build(&qq, m->v + (k - 1), m->vl);
 149     q = mp_mul(MP_NEW, &qq, mb->mu);
 150     if (MP_LEN(q) <= k) {
 151       m = MP_COPY(m);
 152       if (d)
 153         MP_DROP(d);
 154       return (m);
 155     }
 156   }
 157
 158   /* --- Second stage --- */
 159
 160   {
 161     mp *r;
 162     mpw *mvl;
 163
 164     MP_COPY(m);
 165     if (MP_LEN(m) <= k + 1)
 166       mvl = m->vl;
 167     else
 168       mvl = m->v + k + 1;
 169     r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN);
 170     mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
 171     MP_DEST(d, k + 1, r->f);
 172     mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
 173     d->f = (m->f | r->f) & (MP_BURN | MP_NEG);
 174     MP_DROP(r);
 175     MP_DROP(q);
 176     MP_DROP(m);
 177   }
 178
 179   /* --- Final stage --- */
 180
 181   MP_SHRINK(d);
 182   while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
 183     mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
 184
 185   /* --- Fix up the sign --- */
 186
 187   if (d->f & MP_NEG) {
 188     mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl);
 189     d->f &= ~MP_NEG;
 190   }
 191
 192   MP_SHRINK(d);
 193   return (d);
 194 }
 195
 196 /* --- @mpbarrett_exp@ --- *
 197  *
 198  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 199  *              @mp *d@ = fake destination
 200  *              @mp *a@ = base
 201  *              @mp *e@ = exponent
 202  *
 203  * Returns:     Result, %$a^e \bmod m$%.
 204  */
 205
 206 mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
 207 {
 208   mp *x = MP_ONE;
 209   mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
 210
 211   MP_SHRINK(e);
 212   if (!MP_LEN(e))
 213     ;
 214   else if (MP_LEN(e) < EXP_THRESH)
 215     EXP_SIMPLE(x, a, e);
 216   else
 217     EXP_WINDOW(x, a, e);
 218   mp_drop(d);
 219   mp_drop(spare);
 220   return (x);
 221 }
 222
 223 /*----- Test rig ----------------------------------------------------------*/
 224
 225 #ifdef TEST_RIG
 226
 227 static int vmod(dstr *v)
 228 {
 229   mp *x = *(mp **)v[0].buf;
 230   mp *n = *(mp **)v[1].buf;
 231   mp *r = *(mp **)v[2].buf;
 232   mp *s;
 233   mpbarrett mb;
 234   int ok = 1;
 235
 236   mpbarrett_create(&mb, n);
 237   s = mpbarrett_reduce(&mb, MP_NEW, x);
 238
 239   if (!MP_EQ(s, r)) {
 240     fputs("\n*** barrett reduction failure\n", stderr);
 241     fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
 242     fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
 243     fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr);
 244     fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr);
 245     ok = 0;
 246   }
 247
 248   mpbarrett_destroy(&mb);
 249   mp_drop(x);
 250   mp_drop(n);
 251   mp_drop(r);
 252   mp_drop(s);
 253   assert(mparena_count(MPARENA_GLOBAL) == 0);
 254   return (ok);
 255 }
 256
 257 static int vexp(dstr *v)
 258 {
 259   mp *m = *(mp **)v[0].buf;
 260   mp *a = *(mp **)v[1].buf;
 261   mp *b = *(mp **)v[2].buf;
 262   mp *r = *(mp **)v[3].buf;
 263   mp *mr;
 264   int ok = 1;
 265
 266   mpbarrett mb;
 267   mpbarrett_create(&mb, m);
 268
 269   mr = mpbarrett_exp(&mb, MP_NEW, a, b);
 270
 271   if (!MP_EQ(mr, r)) {
 272     fputs("\n*** barrett modexp failed", stderr);
 273     fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 274     fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 275     fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
 276     fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 277     fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 278     fputc('\n', stderr);
 279     ok = 0;
 280   }
 281
 282   mp_drop(m);
 283   mp_drop(a);
 284   mp_drop(b);
 285   mp_drop(r);
 286   mp_drop(mr);
 287   mpbarrett_destroy(&mb);
 288   assert(mparena_count(MPARENA_GLOBAL) == 0);
 289   return ok;
 290 }
 291
 292 static test_chunk tests[] = {
 293   { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
 294   { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 295   { 0, 0, { 0 } }
 296 };
 297
 298 int main(int argc, char *argv[])
 299 {
 300   sub_init();
 301   test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett");
 302   return (0);
 303 }
 304
 305 #endif
 306
 307 /*----- That's all, folks -------------------------------------------------*/