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   1 /* -*-c-*-
   2  *
   3  * $Id: rabin.c,v 1.2 1999/12/10 23:29:48 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 1.2  1999/12/10 23:29:48  mdw
  34  * Change header file guard names.
  35  *
  36  * Revision 1.1  1999/11/19 13:17:57  mdw
  37  * Prime number generator and tester.
  38  *
  39  */
  40
  41 /*----- Header files ------------------------------------------------------*/
  42
  43 #include "mp.h"
  44 #include "mpmont.h"
  45 #include "pgen.h"
  46 #include "rabin.h"
  47
  48 /*----- Main code ---------------------------------------------------------*/
  49
  50 /* --- @rabin_create@ --- *
  51  *
  52  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  53  *              @mp *m@ = pointer to number to test
  54  *
  55  * Returns:     ---
  56  *
  57  * Use:         Precomputes some useful values for performing the
  58  *              Miller-Rabin probabilistic primality test.
  59  */
  60
  61 void rabin_create(rabin *r, mp *m)
  62 {
  63   mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
  64   mpscan sc;
  65   size_t s;
  66
  67   /* --- Find @r@ and @s@ --- */
  68
  69   mpmont_create(&r->mm, m);
  70   mp_scan(&sc, m1);
  71   s = 0;
  72   while (mp_step(&sc)) {
  73     if (mp_bit(&sc))
  74       break;
  75     s++;
  76   }
  77   r->s = s;
  78   r->r = mp_lsr(MP_NEW, m1, s);
  79
  80   /* --- Compute %$(m - 1)R \bmod m$% --- */
  81
  82   r->m1 = mpmont_mul(&r->mm, MP_NEW, m1, r->mm.r2);
  83   mp_drop(m1);
  84 }
  85
  86 /* --- @rabin_destroy@ --- *
  87  *
  88  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  89  *
  90  * Returns:     ---
  91  *
  92  * Use:         Disposes of a Rabin-Miller context when it's no longer
  93  *              needed.
  94  */
  95
  96 void rabin_destroy(rabin *r)
  97 {
  98   mp_drop(r->r);
  99   mp_drop(r->m1);
 100   mpmont_destroy(&r->mm);
 101 }
 102
 103 /* --- @rabin_test@ --- *
 104  *
 105  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
 106  *              @mp *g@ = base to test the number against
 107  *
 108  * Returns:     Either @PGEN_COMPOSITE@ if the test failed, or @PGEN_MAYBE@
 109  *              if it succeeded.
 110  *
 111  * Use:         Performs a single iteration of the Rabin-Miller primality
 112  *              test.
 113  */
 114
 115 int rabin_test(rabin *r, mp *g)
 116 {
 117   mp *y;
 118   mp *dd, *spare = MP_NEW;
 119   size_t j;
 120   int rc = PGEN_COMPOSITE;
 121
 122   /* --- Calculate %$y R = g^r R \bmod m$% --- *
 123    *
 124    * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime.  If course, note that
 125    * @y@ here has an extra factor of %$R$%.
 126    */
 127
 128   y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
 129   if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) {
 130     rc = PGEN_MAYBE;
 131     goto done;
 132   }
 133
 134   /* --- Now for the main loop --- *
 135    *
 136    * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
 137    * composite.  Of course, %$j = 0$% has already been tested.
 138    */
 139
 140   for (j = 1; j < r->s; j++) {
 141     dd = mpmont_mul(&r->mm, spare, y, y); spare = y; y = dd;
 142     if (MP_CMP(y, ==, r->mm.r))
 143       break;
 144     if (MP_CMP(y, ==, r->m1)) {
 145       rc = PGEN_MAYBE;
 146       break;
 147     }
 148   }
 149
 150   /* --- Done --- */
 151
 152 done:
 153   if (spare != MP_NEW)
 154     MP_DROP(spare);
 155   MP_DROP(y);
 156   return (rc);
 157 }
 158
 159 /*----- That's all, folks -------------------------------------------------*/