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

   1 /* -*-c-*-
   2  *
   3  * $Id: strongprime.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
   4  *
   5  * Generate `strong' prime numbers
   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 <mLib/dstr.h>
  33
  34 #include "grand.h"
  35 #include "rand.h"
  36 #include "mp.h"
  37 #include "mpmont.h"
  38 #include "mprand.h"
  39 #include "pgen.h"
  40 #include "pfilt.h"
  41 #include "rabin.h"
  42
  43 /*----- Main code ---------------------------------------------------------*/
  44
  45 /* --- @strongprime_setup@ --- *
  46  *
  47  * Arguments:   @const char *name@ = pointer to name root
  48  *              @mp *d@ = destination for search start point
  49  *              @pfilt *f@ = where to store filter jump context
  50  *              @unsigned nbits@ = number of bits wanted
  51  *              @grand *r@ = random number source
  52  *              @unsigned n@ = number of attempts to make
  53  *              @pgen_proc *event@ = event handler function
  54  *              @void *ectx@ = argument for the event handler
  55  *
  56  * Returns:     A starting point for a `strong' prime search, or zero.
  57  *
  58  * Use:         Sets up for a strong prime search, so that primes with
  59  *              particular properties can be found.  It's probably important
  60  *              to note that the number left in the filter context @f@ is
  61  *              congruent to 2 (mod 4).
  62  */
  63
  64 mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
  65                       grand *r, unsigned n, pgen_proc *event, void *ectx)
  66 {
  67   mp *s, *t, *q;
  68   dstr dn = DSTR_INIT;
  69
  70   mp *rr = d;
  71   pgen_filterctx c;
  72   pgen_jumpctx j;
  73   rabin rb;
  74
  75   /* --- The bitslop parameter --- *
  76    *
  77    * There's quite a lot of prime searching to be done.  The constant
  78    * @BITSLOP@ is a (low) approximation to the base-2 log of the expected
  79    * number of steps to find a prime number.  Experimentation shows that
  80    * numbers around 10 seem to be good.
  81    */
  82
  83 #define BITSLOP 12
  84
  85   /* --- Choose two primes %$s$% and %$t$% of half the required size --- */
  86
  87   assert(((void)"nbits too small in strongprime_setup", nbits/2 > BITSLOP));
  88   nbits = nbits/2 - BITSLOP;
  89   c.step = 1;
  90
  91   rr = mprand(rr, nbits, r, 1);
  92   DRESET(&dn); dstr_putf(&dn, "%s [s]", name);
  93   if ((s = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c,
  94            rabin_iters(nbits), pgen_test, &rb)) == 0)
  95     goto fail_s;
  96
  97   rr = mprand(rr, nbits, r, 1);
  98   DRESET(&dn); dstr_putf(&dn, "%s [t]", name);
  99   if ((t = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c,
 100                 rabin_iters(nbits), pgen_test, &rb)) == 0)
 101     goto fail_t;
 102
 103   /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */
 104
 105   rr = mp_lsl(rr, t, 1);
 106   pfilt_create(&c.f, rr);
 107   rr = mp_lsl(rr, rr, BITSLOP - 1);
 108   rr = mp_add(rr, rr, MP_ONE);
 109   DRESET(&dn); dstr_putf(&dn, "%s [r]", name);
 110   j.j = &c.f;
 111   nbits += BITSLOP;
 112   q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &j,
 113            rabin_iters(nbits), pgen_test, &rb);
 114   pfilt_destroy(&c.f);
 115   if (!q)
 116     goto fail_r;
 117
 118   /* --- Select a suitable starting-point for finding %$p$% --- *
 119    *
 120    * This computes %$p_0 = 2(s^{r - 2} \bmod r)s - 1$%.
 121    */
 122
 123   {
 124     mpmont mm;
 125
 126     mpmont_create(&mm, q);
 127     rr = mp_sub(rr, q, MP_TWO);
 128     rr = mpmont_exp(&mm, rr, s, rr);
 129     mpmont_destroy(&mm);
 130     rr = mp_mul(rr, rr, s);
 131     rr = mp_lsl(rr, rr, 1);
 132     rr = mp_sub(rr, rr, MP_ONE);
 133   }
 134
 135   /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */
 136
 137   {
 138     mp *x;
 139     x = mp_mul(MP_NEW, q, s);
 140     x = mp_lsl(x, x, 1);
 141     pfilt_create(f, x);
 142     x = mp_lsl(x, x, BITSLOP - 1);
 143     rr = mp_add(rr, rr, x);
 144     mp_drop(x);
 145   }
 146
 147   /* --- Return the result --- */
 148
 149   mp_drop(q);
 150   mp_drop(t);
 151   mp_drop(s);
 152   dstr_destroy(&dn);
 153   return (rr);
 154
 155   /* --- Tidy up if something failed --- */
 156
 157 fail_r:
 158   mp_drop(t);
 159 fail_t:
 160   mp_drop(s);
 161 fail_s:
 162   mp_drop(rr);
 163   dstr_destroy(&dn);
 164   return (0);
 165
 166 #undef BITSLOP
 167 }
 168
 169 /* --- @strongprime@ --- *
 170  *
 171  * Arguments:   @const char *name@ = pointer to name root
 172  *              @mp *d@ = destination integer
 173  *              @unsigned nbits@ = number of bits wanted
 174  *              @grand *r@ = random number source
 175  *              @unsigned n@ = number of attempts to make
 176  *              @pgen_proc *event@ = event handler function
 177  *              @void *ectx@ = argument for the event handler
 178  *
 179  * Returns:     A `strong' prime, or zero.
 180  *
 181  * Use:         Finds `strong' primes.  A strong prime %$p$% is such that
 182  *
 183  *                * %$p - 1$% has a large prime factor %$r$%,
 184  *                * %$p + 1$% has a large prime factor %$s$%, and
 185  *                * %$r - 1$% has a large prime factor %$t$%.
 186  *
 187  *              The numbers produced may be slightly larger than requested,
 188  *              by a few bits.
 189  */
 190
 191 mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r,
 192                 unsigned n, pgen_proc *event, void *ectx)
 193 {
 194   pfilt f;
 195   pgen_jumpctx j;
 196   rabin rb;
 197
 198   d = strongprime_setup(name, d, &f, nbits, r, n, event, ectx);
 199   j.j = &f;
 200   d = pgen(name, d, d, event, ectx, n, pgen_jump, &j,
 201            rabin_iters(nbits), pgen_test, &rb);
 202   pfilt_destroy(&f);
 203   return (d);
 204 }
 205
 206 /*----- That's all, folks -------------------------------------------------*/