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

   1 /* -*-c-*-
   2  *
   3  * Miller-Rabin primality test
   4  *
   5  * (c) 1999 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  12  * Catacomb is free software; you can redistribute it and/or modify
  13  * it under the terms of the GNU Library General Public License as
  14  * published by the Free Software Foundation; either version 2 of the
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  22  * You should have received a copy of the GNU Library General Public
  23  * License along with Catacomb; if not, write to the Free
  24  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Header files ------------------------------------------------------*/
  29
  30 #include "mp.h"
  31 #include "mpbarrett.h"
  32 #include "mpmont.h"
  33 #include "pgen.h"
  34 #include "rabin.h"
  35
  36 /*----- Main code ---------------------------------------------------------*/
  37
  38 /* --- @rabin_create@ --- *
  39  *
  40  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  41  *              @mp *m@ = pointer to number to test
  42  *
  43  * Returns:     Zero on success, nonzero on failure.
  44  *
  45  * Use:         Precomputes some useful values for performing the
  46  *              Miller-Rabin probabilistic primality test.
  47  */
  48
  49 int rabin_create(rabin *r, mp *m)
  50 {
  51   mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
  52   if (mpmont_create(&r->mm, m)) {
  53     MP_DROP(m1);
  54     return (-1);
  55   }
  56   r->r = mp_odd(MP_NEW, m1, &r->s);
  57   r->m1 = mp_sub(MP_NEW, m, r->mm.r);
  58   mp_drop(m1);
  59   return (0);
  60 }
  61
  62 /* --- @rabin_destroy@ --- *
  63  *
  64  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  65  *
  66  * Returns:     ---
  67  *
  68  * Use:         Disposes of a Rabin-Miller context when it's no longer
  69  *              needed.
  70  */
  71
  72 void rabin_destroy(rabin *r)
  73 {
  74   mp_drop(r->r);
  75   mp_drop(r->m1);
  76   mpmont_destroy(&r->mm);
  77 }
  78
  79 /* --- @rabin_test@, @rabin_rtest@ --- *
  80  *
  81  * Arguments:   @rabin *r@ = pointer to Rabin-Miller context
  82  *              @mp *g@ = base to test the number against
  83  *
  84  * Returns:     Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
  85  *              if it succeeded.
  86  *
  87  * Use:         Performs a single iteration of the Rabin-Miller primality
  88  *              test.  The @rtest@ variant assumes that %$g$% is either
  89  *              already in Montgomery representation, or you don't care.
  90  */
  91
  92 int rabin_rtest(rabin *r, mp *g)
  93 {
  94   mp *y;
  95   mp *dd, *spare = MP_NEW;
  96   size_t j;
  97   int rc = PGEN_FAIL;
  98
  99   /* --- Calculate %$y R = g^r R \bmod m$% --- *
 100    *
 101    * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime.  If course, note that
 102    * @y@ here has an extra factor of %$R$%.
 103    */
 104
 105   y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
 106   if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) {
 107     rc = PGEN_PASS;
 108     goto done;
 109   }
 110
 111   /* --- Now for the main loop --- *
 112    *
 113    * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
 114    * composite.  Of course, %$j = 0$% has already been tested.
 115    */
 116
 117   for (j = 1; j < r->s; j++) {
 118     dd = mp_sqr(spare, y);
 119     dd = mpmont_reduce(&r->mm, dd, dd);
 120     spare = y; y = dd;
 121     if (MP_EQ(y, r->mm.r))
 122       break;
 123     if (MP_EQ(y, r->m1)) {
 124       rc = PGEN_PASS;
 125       break;
 126     }
 127   }
 128
 129   /* --- Done --- */
 130
 131 done:
 132   if (spare != MP_NEW)
 133     MP_DROP(spare);
 134   MP_DROP(y);
 135   return (rc);
 136 }
 137
 138 int rabin_test(rabin *r, mp *g)
 139 {
 140   int rc;
 141   g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2);
 142   rc = rabin_rtest(r, g);
 143   mp_drop(g);
 144   return (rc);
 145 }
 146
 147 /* --- @rabin_iters@ --- *
 148  *
 149  * Arguments:   @unsigned len@ = number of bits in value
 150  *
 151  * Returns:     Number of iterations recommended.
 152  *
 153  * Use:         Returns the recommended number of iterations to ensure that a
 154  *              number with @len@ bits is really prime.
 155  */
 156
 157 int rabin_iters(unsigned len)
 158 {
 159   static const struct {
 160     unsigned b;
 161     int i;
 162   } *p, *q, tab[] = {
 163     { 100, 27 },
 164     { 150, 18 },
 165     { 200, 15 },
 166     { 250, 12 },
 167     { 300, 9 },
 168     { 350, 8 },
 169     { 400, 7 },
 170     { 450, 6 },
 171     { 550, 5 },
 172     { 650, 4 },
 173     { 850, 3 },
 174     { 1300, 2 }
 175   };
 176
 177   unsigned i;
 178
 179   /* --- Binary search through the table --- */
 180
 181   p = tab;
 182   q = tab + (sizeof(tab)/sizeof(tab[0]));
 183   for (;;) {
 184     i = (q - p) / 2;
 185     if (!i)
 186       break;
 187     if (len >= p[i].b && len < p[i + 1].b)
 188       break;
 189     if (len > p[i].b)
 190       p = p + i;
 191     else
 192       q = p + i;
 193   }
 194   return (p[i].i);
 195 }
 196
 197 /*----- That's all, folks -------------------------------------------------*/