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

   1 /* -*-c-*-
   2  *
   3  * $Id: rabin.c,v 1.9 2004/04/08 01:36:15 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 /*----- 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:     ---
  46  *
  47  * Use:         Precomputes some useful values for performing the
  48  *              Miller-Rabin probabilistic primality test.
  49  */
  50
  51 void rabin_create(rabin *r, mp *m)
  52 {
  53   mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
  54   mpmont_create(&r->mm, m);
  55   r->r = mp_odd(MP_NEW, m1, &r->s);
  56   r->m1 = mp_sub(MP_NEW, m, r->mm.r);
  57   mp_drop(m1);
  58 }
  59
  60 /* --- @rabin_destroy@ --- *
  61  *
  62  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  63  *
  64  * Returns:     ---
  65  *
  66  * Use:         Disposes of a Rabin-Miller context when it's no longer
  67  *              needed.
  68  */
  69
  70 void rabin_destroy(rabin *r)
  71 {
  72   mp_drop(r->r);
  73   mp_drop(r->m1);
  74   mpmont_destroy(&r->mm);
  75 }
  76
  77 /* --- @rabin_test@, @rabin_rtest@ --- *
  78  *
  79  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  80  *              @mp *g@ = base to test the number against
  81  *
  82  * Returns:     Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
  83  *              if it succeeded.
  84  *
  85  * Use:         Performs a single iteration of the Rabin-Miller primality
  86  *              test.  The @rtest@ variant assumes that %$g$% is either
  87  *              already in Montgomery representation, or you don't care.
  88  */
  89
  90 int rabin_rtest(rabin *r, mp *g)
  91 {
  92   mp *y;
  93   mp *dd, *spare = MP_NEW;
  94   size_t j;
  95   int rc = PGEN_FAIL;
  96
  97   /* --- Calculate %$y R = g^r R \bmod m$% --- *
  98    *
  99    * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime.  If course, note that
 100    * @y@ here has an extra factor of %$R$%.
 101    */
 102
 103   y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
 104   if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) {
 105     rc = PGEN_PASS;
 106     goto done;
 107   }
 108
 109   /* --- Now for the main loop --- *
 110    *
 111    * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
 112    * composite.  Of course, %$j = 0$% has already been tested.
 113    */
 114
 115   for (j = 1; j < r->s; j++) {
 116     dd = mp_sqr(spare, y);
 117     dd = mpmont_reduce(&r->mm, dd, dd);
 118     spare = y; y = dd;
 119     if (MP_EQ(y, r->mm.r))
 120       break;
 121     if (MP_EQ(y, r->m1)) {
 122       rc = PGEN_PASS;
 123       break;
 124     }
 125   }
 126
 127   /* --- Done --- */
 128
 129 done:
 130   if (spare != MP_NEW)
 131     MP_DROP(spare);
 132   MP_DROP(y);
 133   return (rc);
 134 }
 135
 136 int rabin_test(rabin *r, mp *g)
 137 {
 138   int rc;
 139   g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2);
 140   rc = rabin_rtest(r, g);
 141   mp_drop(g);
 142   return (rc);
 143 }
 144
 145 /* --- @rabin_iters@ --- *
 146  *
 147  * Arguments:   @unsigned len@ = number of bits in value
 148  *
 149  * Returns:     Number of iterations recommended.
 150  *
 151  * Use:         Returns the recommended number of iterations to ensure that a
 152  *              number with @len@ bits is really prime.
 153  */
 154
 155 int rabin_iters(unsigned len)
 156 {
 157   static const struct {
 158     unsigned b;
 159     int i;
 160   } *p, *q, tab[] = {
 161     { 100, 27 },
 162     { 150, 18 },
 163     { 200, 15 },
 164     { 250, 12 },
 165     { 300, 9 },
 166     { 350, 8 },
 167     { 400, 7 },
 168     { 450, 6 },
 169     { 550, 5 },
 170     { 650, 4 },
 171     { 850, 3 },
 172     { 1300, 2 }
 173   };
 174
 175   unsigned i;
 176
 177   /* --- Binary search through the table --- */
 178
 179   p = tab;
 180   q = tab + (sizeof(tab)/sizeof(tab[0]));
 181   for (;;) {
 182     i = (q - p) / 2;
 183     if (!i)
 184       break;
 185     if (len >= p[i].b && len < p[i + 1].b)
 186       break;
 187     if (len > p[i].b)
 188       p = p + i;
 189     else
 190       q = p + i;
 191   }
 192   return (p[i].i);
 193 }
 194
 195 /*----- That's all, folks -------------------------------------------------*/