git.distorted.org.uk Git - u/mdw/catacomb/blob - rabin.c

   1 /* -*-c-*-
   2  *
   3  * $Id: rabin.c,v 1.3 1999/12/22 15:50:29 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 1.3  1999/12/22 15:50:29  mdw
  34  * Reworking for new prime-search system.  Add function for working out how
  35  * many iterations to use for a particular number.
  36  *
  37  * Revision 1.2  1999/12/10 23:29:48  mdw
  38  * Change header file guard names.
  39  *
  40  * Revision 1.1  1999/11/19 13:17:57  mdw
  41  * Prime number generator and tester.
  42  *
  43  */
  44
  45 /*----- Header files ------------------------------------------------------*/
  46
  47 #include "mp.h"
  48 #include "mpbarrett.h"
  49 #include "mpmont.h"
  50 #include "pgen.h"
  51 #include "rabin.h"
  52
  53 /*----- Main code ---------------------------------------------------------*/
  54
  55 /* --- @rabin_create@ --- *
  56  *
  57  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  58  *              @mp *m@ = pointer to number to test
  59  *
  60  * Returns:     ---
  61  *
  62  * Use:         Precomputes some useful values for performing the
  63  *              Miller-Rabin probabilistic primality test.
  64  */
  65
  66 void rabin_create(rabin *r, mp *m)
  67 {
  68   mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
  69   mpscan sc;
  70   size_t s;
  71
  72   /* --- Find @r@ and @s@ --- */
  73
  74   mpmont_create(&r->mm, m);
  75   mp_scan(&sc, m1);
  76   s = 0;
  77   while (mp_step(&sc)) {
  78     if (mp_bit(&sc))
  79       break;
  80     s++;
  81   }
  82   r->s = s;
  83   r->r = mp_lsr(MP_NEW, m1, s);
  84
  85   /* --- Compute %$(m - 1)R \bmod m$% --- */
  86
  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@ --- *
 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.
 118  */
 119
 120 int rabin_test(rabin *r, mp *g)
 121 {
 122   mp *y;
 123   mp *dd, *spare = MP_NEW;
 124   size_t j;
 125   int rc = PGEN_FAIL;
 126
 127   /* --- Calculate %$y R = g^r R \bmod m$% --- *
 128    *
 129    * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime.  If course, note that
 130    * @y@ here has an extra factor of %$R$%.
 131    */
 132
 133   y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
 134   if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) {
 135     rc = PGEN_PASS;
 136     goto done;
 137   }
 138
 139   /* --- Now for the main loop --- *
 140    *
 141    * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
 142    * composite.  Of course, %$j = 0$% has already been tested.
 143    */
 144
 145   for (j = 1; j < r->s; j++) {
 146     dd = mp_sqr(spare, y);
 147     dd = mpmont_reduce(&r->mm, dd, dd);
 148     spare = y; y = dd;
 149     if (MP_CMP(y, ==, r->mm.r))
 150       break;
 151     if (MP_CMP(y, ==, r->m1)) {
 152       rc = PGEN_PASS;
 153       break;
 154     }
 155   }
 156
 157   /* --- Done --- */
 158
 159 done:
 160   if (spare != MP_NEW)
 161     MP_DROP(spare);
 162   MP_DROP(y);
 163   return (rc);
 164 }
 165
 166 /* --- @rabin_iters@ --- *
 167  *
 168  * Arguments:   @unsigned len@ = number of bits in value
 169  *
 170  * Returns:     Number of iterations recommended.
 171  *
 172  * Use:         Returns the recommended number of iterations to ensure that a
 173  *              number with @len@ bits is really prime.
 174  */
 175
 176 int rabin_iters(unsigned len)
 177 {
 178   static struct {
 179     unsigned b;
 180     int i;
 181   } *p, *q, tab[] = {
 182     { 100, 27 },
 183     { 150, 18 },
 184     { 200, 15 },
 185     { 250, 12 },
 186     { 300, 9 },
 187     { 350, 8 },
 188     { 400, 7 },
 189     { 450, 6 },
 190     { 550, 5 },
 191     { 650, 4 },
 192     { 850, 3 },
 193     { 1300, 2 }
 194   };
 195
 196   unsigned i;
 197
 198   /* --- Binary search through the table --- */
 199
 200   p = tab;
 201   q = tab + (sizeof(tab)/sizeof(tab[0]));
 202   for (;;) {
 203     i = (q - p) / 2;
 204     if (!i)
 205       break;
 206     if (len >= p[i].b && len < p[i + 1].b)
 207       break;
 208     if (len > p[i].b)
 209       p = p + i;
 210     else
 211       q = p + i;
 212   }
 213   return (p[i].i);
 214 }
 215
 216 /*----- That's all, folks -------------------------------------------------*/