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   1 /* -*-c-*-
   2  *
   3  * $Id: rabin.c,v 1.8 2004/04/02 01:03:49 mdw Exp $
   4  *
   5  * Miller-Rabin primality test
   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: rabin.c,v $
  33  * Revision 1.8  2004/04/02 01:03:49  mdw
  34  * Miscellaneous constification.
  35  *
  36  * Revision 1.7  2002/01/13 13:42:53  mdw
  37  * More efficient Rabin-Miller test: with random witnesses, skip redundant
  38  * Montgomerization.  (Being bijective, it can't affect the distribution.)
  39  *
  40  * Revision 1.6  2001/06/16 12:56:38  mdw
  41  * Fixes for interface change to @mpmont_expr@ and @mpmont_mexpr@.
  42  *
  43  * Revision 1.5  2000/10/08 12:11:22  mdw
  44  * Use @MP_EQ@ instead of @MP_CMP@.
  45  *
  46  * Revision 1.4  2000/06/22 19:03:02  mdw
  47  * Use the new @mp_odd@ function.
  48  *
  49  * Revision 1.3  1999/12/22 15:50:29  mdw
  50  * Reworking for new prime-search system.  Add function for working out how
  51  * many iterations to use for a particular number.
  52  *
  53  * Revision 1.2  1999/12/10 23:29:48  mdw
  54  * Change header file guard names.
  55  *
  56  * Revision 1.1  1999/11/19 13:17:57  mdw
  57  * Prime number generator and tester.
  58  *
  59  */
  60
  61 /*----- Header files ------------------------------------------------------*/
  62
  63 #include "mp.h"
  64 #include "mpbarrett.h"
  65 #include "mpmont.h"
  66 #include "pgen.h"
  67 #include "rabin.h"
  68
  69 /*----- Main code ---------------------------------------------------------*/
  70
  71 /* --- @rabin_create@ --- *
  72  *
  73  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  74  *              @mp *m@ = pointer to number to test
  75  *
  76  * Returns:     ---
  77  *
  78  * Use:         Precomputes some useful values for performing the
  79  *              Miller-Rabin probabilistic primality test.
  80  */
  81
  82 void rabin_create(rabin *r, mp *m)
  83 {
  84   mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
  85   mpmont_create(&r->mm, m);
  86   r->r = mp_odd(MP_NEW, m1, &r->s);
  87   r->m1 = mp_sub(MP_NEW, m, r->mm.r);
  88   mp_drop(m1);
  89 }
  90
  91 /* --- @rabin_destroy@ --- *
  92  *
  93  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  94  *
  95  * Returns:     ---
  96  *
  97  * Use:         Disposes of a Rabin-Miller context when it's no longer
  98  *              needed.
  99  */
 100
 101 void rabin_destroy(rabin *r)
 102 {
 103   mp_drop(r->r);
 104   mp_drop(r->m1);
 105   mpmont_destroy(&r->mm);
 106 }
 107
 108 /* --- @rabin_test@, @rabin_rtest@ --- *
 109  *
 110  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
 111  *              @mp *g@ = base to test the number against
 112  *
 113  * Returns:     Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
 114  *              if it succeeded.
 115  *
 116  * Use:         Performs a single iteration of the Rabin-Miller primality
 117  *              test.  The @rtest@ variant assumes that %$g$% is either
 118  *              already in Montgomery representation, or you don't care.
 119  */
 120
 121 int rabin_rtest(rabin *r, mp *g)
 122 {
 123   mp *y;
 124   mp *dd, *spare = MP_NEW;
 125   size_t j;
 126   int rc = PGEN_FAIL;
 127
 128   /* --- Calculate %$y R = g^r R \bmod m$% --- *
 129    *
 130    * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime.  If course, note that
 131    * @y@ here has an extra factor of %$R$%.
 132    */
 133
 134   y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
 135   if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) {
 136     rc = PGEN_PASS;
 137     goto done;
 138   }
 139
 140   /* --- Now for the main loop --- *
 141    *
 142    * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
 143    * composite.  Of course, %$j = 0$% has already been tested.
 144    */
 145
 146   for (j = 1; j < r->s; j++) {
 147     dd = mp_sqr(spare, y);
 148     dd = mpmont_reduce(&r->mm, dd, dd);
 149     spare = y; y = dd;
 150     if (MP_EQ(y, r->mm.r))
 151       break;
 152     if (MP_EQ(y, r->m1)) {
 153       rc = PGEN_PASS;
 154       break;
 155     }
 156   }
 157
 158   /* --- Done --- */
 159
 160 done:
 161   if (spare != MP_NEW)
 162     MP_DROP(spare);
 163   MP_DROP(y);
 164   return (rc);
 165 }
 166
 167 int rabin_test(rabin *r, mp *g)
 168 {
 169   int rc;
 170   g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2);
 171   rc = rabin_rtest(r, g);
 172   mp_drop(g);
 173   return (rc);
 174 }
 175
 176 /* --- @rabin_iters@ --- *
 177  *
 178  * Arguments:   @unsigned len@ = number of bits in value
 179  *
 180  * Returns:     Number of iterations recommended.
 181  *
 182  * Use:         Returns the recommended number of iterations to ensure that a
 183  *              number with @len@ bits is really prime.
 184  */
 185
 186 int rabin_iters(unsigned len)
 187 {
 188   static const struct {
 189     unsigned b;
 190     int i;
 191   } *p, *q, tab[] = {
 192     { 100, 27 },
 193     { 150, 18 },
 194     { 200, 15 },
 195     { 250, 12 },
 196     { 300, 9 },
 197     { 350, 8 },
 198     { 400, 7 },
 199     { 450, 6 },
 200     { 550, 5 },
 201     { 650, 4 },
 202     { 850, 3 },
 203     { 1300, 2 }
 204   };
 205
 206   unsigned i;
 207
 208   /* --- Binary search through the table --- */
 209
 210   p = tab;
 211   q = tab + (sizeof(tab)/sizeof(tab[0]));
 212   for (;;) {
 213     i = (q - p) / 2;
 214     if (!i)
 215       break;
 216     if (len >= p[i].b && len < p[i + 1].b)
 217       break;
 218     if (len > p[i].b)
 219       p = p + i;
 220     else
 221       q = p + i;
 222   }
 223   return (p[i].i);
 224 }
 225
 226 /*----- That's all, folks -------------------------------------------------*/