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

   1 /* -*-c-*-
   2  *
   3  * $Id$
   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 /*----- Header files ------------------------------------------------------*/
  31
  32 #include "mp.h"
  33 #include "mpbarrett.h"
  34 #include "mpmont.h"
  35 #include "pgen.h"
  36 #include "rabin.h"
  37
  38 /*----- Main code ---------------------------------------------------------*/
  39
  40 /* --- @rabin_create@ --- *
  41  *
  42  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  43  *              @mp *m@ = pointer to number to test
  44  *
  45  * Returns:     Zero on success, nonzero on failure.
  46  *
  47  * Use:         Precomputes some useful values for performing the
  48  *              Miller-Rabin probabilistic primality test.
  49  */
  50
  51 int rabin_create(rabin *r, mp *m)
  52 {
  53   mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
  54   if (mpmont_create(&r->mm, m)) {
  55     MP_DROP(m1);
  56     return (-1);
  57   }
  58   r->r = mp_odd(MP_NEW, m1, &r->s);
  59   r->m1 = mp_sub(MP_NEW, m, r->mm.r);
  60   mp_drop(m1);
  61   return (0);
  62 }
  63
  64 /* --- @rabin_destroy@ --- *
  65  *
  66  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  67  *
  68  * Returns:     ---
  69  *
  70  * Use:         Disposes of a Rabin-Miller context when it's no longer
  71  *              needed.
  72  */
  73
  74 void rabin_destroy(rabin *r)
  75 {
  76   mp_drop(r->r);
  77   mp_drop(r->m1);
  78   mpmont_destroy(&r->mm);
  79 }
  80
  81 /* --- @rabin_test@, @rabin_rtest@ --- *
  82  *
  83  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  84  *              @mp *g@ = base to test the number against
  85  *
  86  * Returns:     Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
  87  *              if it succeeded.
  88  *
  89  * Use:         Performs a single iteration of the Rabin-Miller primality
  90  *              test.  The @rtest@ variant assumes that %$g$% is either
  91  *              already in Montgomery representation, or you don't care.
  92  */
  93
  94 int rabin_rtest(rabin *r, mp *g)
  95 {
  96   mp *y;
  97   mp *dd, *spare = MP_NEW;
  98   size_t j;
  99   int rc = PGEN_FAIL;
 100
 101   /* --- Calculate %$y R = g^r R \bmod m$% --- *
 102    *
 103    * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime.  If course, note that
 104    * @y@ here has an extra factor of %$R$%.
 105    */
 106
 107   y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
 108   if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) {
 109     rc = PGEN_PASS;
 110     goto done;
 111   }
 112
 113   /* --- Now for the main loop --- *
 114    *
 115    * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
 116    * composite.  Of course, %$j = 0$% has already been tested.
 117    */
 118
 119   for (j = 1; j < r->s; j++) {
 120     dd = mp_sqr(spare, y);
 121     dd = mpmont_reduce(&r->mm, dd, dd);
 122     spare = y; y = dd;
 123     if (MP_EQ(y, r->mm.r))
 124       break;
 125     if (MP_EQ(y, r->m1)) {
 126       rc = PGEN_PASS;
 127       break;
 128     }
 129   }
 130
 131   /* --- Done --- */
 132
 133 done:
 134   if (spare != MP_NEW)
 135     MP_DROP(spare);
 136   MP_DROP(y);
 137   return (rc);
 138 }
 139
 140 int rabin_test(rabin *r, mp *g)
 141 {
 142   int rc;
 143   g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2);
 144   rc = rabin_rtest(r, g);
 145   mp_drop(g);
 146   return (rc);
 147 }
 148
 149 /* --- @rabin_iters@ --- *
 150  *
 151  * Arguments:   @unsigned len@ = number of bits in value
 152  *
 153  * Returns:     Number of iterations recommended.
 154  *
 155  * Use:         Returns the recommended number of iterations to ensure that a
 156  *              number with @len@ bits is really prime.
 157  */
 158
 159 int rabin_iters(unsigned len)
 160 {
 161   static const struct {
 162     unsigned b;
 163     int i;
 164   } *p, *q, tab[] = {
 165     { 100, 27 },
 166     { 150, 18 },
 167     { 200, 15 },
 168     { 250, 12 },
 169     { 300, 9 },
 170     { 350, 8 },
 171     { 400, 7 },
 172     { 450, 6 },
 173     { 550, 5 },
 174     { 650, 4 },
 175     { 850, 3 },
 176     { 1300, 2 }
 177   };
 178
 179   unsigned i;
 180
 181   /* --- Binary search through the table --- */
 182
 183   p = tab;
 184   q = tab + (sizeof(tab)/sizeof(tab[0]));
 185   for (;;) {
 186     i = (q - p) / 2;
 187     if (!i)
 188       break;
 189     if (len >= p[i].b && len < p[i + 1].b)
 190       break;
 191     if (len > p[i].b)
 192       p = p + i;
 193     else
 194       q = p + i;
 195   }
 196   return (p[i].i);
 197 }
 198
 199 /*----- That's all, folks -------------------------------------------------*/