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   1 /* -*-c-*-
   2  *
   3  * $Id: rabin.c,v 1.5 2000/10/08 12:11:22 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 1.5  2000/10/08 12:11:22  mdw
  34  * Use @MP_EQ@ instead of @MP_CMP@.
  35  *
  36  * Revision 1.4  2000/06/22 19:03:02  mdw
  37  * Use the new @mp_odd@ function.
  38  *
  39  * Revision 1.3  1999/12/22 15:50:29  mdw
  40  * Reworking for new prime-search system.  Add function for working out how
  41  * many iterations to use for a particular number.
  42  *
  43  * Revision 1.2  1999/12/10 23:29:48  mdw
  44  * Change header file guard names.
  45  *
  46  * Revision 1.1  1999/11/19 13:17:57  mdw
  47  * Prime number generator and tester.
  48  *
  49  */
  50
  51 /*----- Header files ------------------------------------------------------*/
  52
  53 #include "mp.h"
  54 #include "mpbarrett.h"
  55 #include "mpmont.h"
  56 #include "pgen.h"
  57 #include "rabin.h"
  58
  59 /*----- Main code ---------------------------------------------------------*/
  60
  61 /* --- @rabin_create@ --- *
  62  *
  63  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  64  *              @mp *m@ = pointer to number to test
  65  *
  66  * Returns:     ---
  67  *
  68  * Use:         Precomputes some useful values for performing the
  69  *              Miller-Rabin probabilistic primality test.
  70  */
  71
  72 void rabin_create(rabin *r, mp *m)
  73 {
  74   mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
  75   mpmont_create(&r->mm, m);
  76   r->r = mp_odd(MP_NEW, m1, &r->s);
  77   r->m1 = mp_sub(MP_NEW, m, r->mm.r);
  78   mp_drop(m1);
  79 }
  80
  81 /* --- @rabin_destroy@ --- *
  82  *
  83  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  84  *
  85  * Returns:     ---
  86  *
  87  * Use:         Disposes of a Rabin-Miller context when it's no longer
  88  *              needed.
  89  */
  90
  91 void rabin_destroy(rabin *r)
  92 {
  93   mp_drop(r->r);
  94   mp_drop(r->m1);
  95   mpmont_destroy(&r->mm);
  96 }
  97
  98 /* --- @rabin_test@ --- *
  99  *
 100  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
 101  *              @mp *g@ = base to test the number against
 102  *
 103  * Returns:     Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
 104  *              if it succeeded.
 105  *
 106  * Use:         Performs a single iteration of the Rabin-Miller primality
 107  *              test.
 108  */
 109
 110 int rabin_test(rabin *r, mp *g)
 111 {
 112   mp *y;
 113   mp *dd, *spare = MP_NEW;
 114   size_t j;
 115   int rc = PGEN_FAIL;
 116
 117   /* --- Calculate %$y R = g^r R \bmod m$% --- *
 118    *
 119    * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime.  If course, note that
 120    * @y@ here has an extra factor of %$R$%.
 121    */
 122
 123   y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
 124   if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) {
 125     rc = PGEN_PASS;
 126     goto done;
 127   }
 128
 129   /* --- Now for the main loop --- *
 130    *
 131    * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
 132    * composite.  Of course, %$j = 0$% has already been tested.
 133    */
 134
 135   for (j = 1; j < r->s; j++) {
 136     dd = mp_sqr(spare, y);
 137     dd = mpmont_reduce(&r->mm, dd, dd);
 138     spare = y; y = dd;
 139     if (MP_EQ(y, r->mm.r))
 140       break;
 141     if (MP_EQ(y, r->m1)) {
 142       rc = PGEN_PASS;
 143       break;
 144     }
 145   }
 146
 147   /* --- Done --- */
 148
 149 done:
 150   if (spare != MP_NEW)
 151     MP_DROP(spare);
 152   MP_DROP(y);
 153   return (rc);
 154 }
 155
 156 /* --- @rabin_iters@ --- *
 157  *
 158  * Arguments:   @unsigned len@ = number of bits in value
 159  *
 160  * Returns:     Number of iterations recommended.
 161  *
 162  * Use:         Returns the recommended number of iterations to ensure that a
 163  *              number with @len@ bits is really prime.
 164  */
 165
 166 int rabin_iters(unsigned len)
 167 {
 168   static struct {
 169     unsigned b;
 170     int i;
 171   } *p, *q, tab[] = {
 172     { 100, 27 },
 173     { 150, 18 },
 174     { 200, 15 },
 175     { 250, 12 },
 176     { 300, 9 },
 177     { 350, 8 },
 178     { 400, 7 },
 179     { 450, 6 },
 180     { 550, 5 },
 181     { 650, 4 },
 182     { 850, 3 },
 183     { 1300, 2 }
 184   };
 185
 186   unsigned i;
 187
 188   /* --- Binary search through the table --- */
 189
 190   p = tab;
 191   q = tab + (sizeof(tab)/sizeof(tab[0]));
 192   for (;;) {
 193     i = (q - p) / 2;
 194     if (!i)
 195       break;
 196     if (len >= p[i].b && len < p[i + 1].b)
 197       break;
 198     if (len > p[i].b)
 199       p = p + i;
 200     else
 201       q = p + i;
 202   }
 203   return (p[i].i);
 204 }
 205
 206 /*----- That's all, folks -------------------------------------------------*/