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