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

   1 /* -*-c-*-
   2  *
   3  * $Id: strongprime.c,v 1.4 2000/07/01 11:24:52 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 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: strongprime.c,v $
  33  * Revision 1.4  2000/07/01 11:24:52  mdw
  34  * Remove old debugging code.
  35  *
  36  * Revision 1.3  2000/06/17 12:10:09  mdw
  37  * Add some argument checking.  Use MP secure memory interface.
  38  *
  39  * Revision 1.2  2000/02/12 18:21:03  mdw
  40  * Overhaul of key management (again).
  41  *
  42  * Revision 1.1  1999/12/22 15:51:22  mdw
  43  * Find `strong' RSA primes using Gordon's algorithm.
  44  *
  45  */
  46
  47 /*----- Header files ------------------------------------------------------*/
  48
  49 #include <mLib/dstr.h>
  50
  51 #include "grand.h"
  52 #include "rand.h"
  53 #include "mp.h"
  54 #include "mpmont.h"
  55 #include "mprand.h"
  56 #include "pgen.h"
  57 #include "pfilt.h"
  58 #include "rabin.h"
  59
  60 /*----- Main code ---------------------------------------------------------*/
  61
  62 /* --- @strongprime_setup@ --- *
  63  *
  64  * Arguments:   @const char *name@ = pointer to name root
  65  *              @mp *d@ = destination for search start point
  66  *              @pfilt *f@ = where to store filter jump context
  67  *              @unsigned nbits@ = number of bits wanted
  68  *              @grand *r@ = random number source
  69  *              @unsigned n@ = number of attempts to make
  70  *              @pgen_proc *event@ = event handler function
  71  *              @void *ectx@ = argument for the event handler
  72  *
  73  * Returns:     A starting point for a `strong' prime search, or zero.
  74  *
  75  * Use:         Sets up for a strong prime search, so that primes with
  76  *              particular properties can be found.  It's probably important
  77  *              to note that the number left in the filter context @f@ is
  78  *              congruent to 2 (mod 4).
  79  */
  80
  81 mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
  82                       grand *r, unsigned n, pgen_proc *event, void *ectx)
  83 {
  84   mp *s, *t, *q;
  85   dstr dn = DSTR_INIT;
  86
  87   mp *rr = d;
  88   pgen_filterctx c;
  89   pgen_jumpctx j;
  90   rabin rb;
  91
  92   /* --- The bitslop parameter --- *
  93    *
  94    * There's quite a lot of prime searching to be done.  The constant
  95    * @BITSLOP@ is a (low) approximation to the base-2 log of the expected
  96    * number of steps to find a prime number.  Experimentation shows that
  97    * numbers around 10 seem to be good.
  98    */
  99
 100 #define BITSLOP 12
 101
 102   /* --- Choose two primes %$s$% and %$t$% of half the required size --- */
 103
 104   assert(((void)"nbits too small in strongprime_setup", nbits/2 > BITSLOP));
 105   nbits = nbits/2 - BITSLOP;
 106   c.step = 1;
 107
 108   rr = mprand(rr, nbits, r, 1);
 109   DRESET(&dn); dstr_putf(&dn, "%s [s]", name);
 110   if ((s = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c,
 111            rabin_iters(nbits), pgen_test, &rb)) == 0)
 112     goto fail_s;
 113
 114   rr = mprand(rr, nbits, r, 1);
 115   DRESET(&dn); dstr_putf(&dn, "%s [t]", name);
 116   if ((t = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c,
 117                 rabin_iters(nbits), pgen_test, &rb)) == 0)
 118     goto fail_t;
 119
 120   /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */
 121
 122   rr = mp_lsl(rr, t, 1);
 123   pfilt_create(&c.f, rr);
 124   rr = mp_lsl(rr, rr, BITSLOP - 1);
 125   rr = mp_add(rr, rr, MP_ONE);
 126   DRESET(&dn); dstr_putf(&dn, "%s [r]", name);
 127   j.j = &c.f;
 128   nbits += BITSLOP;
 129   q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &j,
 130            rabin_iters(nbits), pgen_test, &rb);
 131   pfilt_destroy(&c.f);
 132   if (!q)
 133     goto fail_r;
 134
 135   /* --- Select a suitable starting-point for finding %$p$% --- *
 136    *
 137    * This computes %$p_0 = 2(s^{r - 2} \bmod r)s - 1$%.
 138    */
 139
 140   {
 141     mpmont mm;
 142
 143     mpmont_create(&mm, q);
 144     rr = mp_sub(rr, q, MP_TWO);
 145     rr = mpmont_exp(&mm, rr, s, rr);
 146     mpmont_destroy(&mm);
 147     rr = mp_mul(rr, rr, s);
 148     rr = mp_lsl(rr, rr, 1);
 149     rr = mp_sub(rr, rr, MP_ONE);
 150   }
 151
 152   /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */
 153
 154   {
 155     mp *x;
 156     x = mp_mul(MP_NEW, q, s);
 157     x = mp_lsl(x, x, 1);
 158     pfilt_create(f, x);
 159     x = mp_lsl(x, x, BITSLOP - 1);
 160     rr = mp_add(rr, rr, x);
 161     mp_drop(x);
 162   }
 163
 164   /* --- Return the result --- */
 165
 166   mp_drop(q);
 167   mp_drop(t);
 168   mp_drop(s);
 169   dstr_destroy(&dn);
 170   return (rr);
 171
 172   /* --- Tidy up if something failed --- */
 173
 174 fail_r:
 175   mp_drop(t);
 176 fail_t:
 177   mp_drop(s);
 178 fail_s:
 179   mp_drop(rr);
 180   dstr_destroy(&dn);
 181   return (0);
 182
 183 #undef BITSLOP
 184 }
 185
 186 /* --- @strongprime@ --- *
 187  *
 188  * Arguments:   @const char *name@ = pointer to name root
 189  *              @mp *d@ = destination integer
 190  *              @unsigned nbits@ = number of bits wanted
 191  *              @grand *r@ = random number source
 192  *              @unsigned n@ = number of attempts to make
 193  *              @pgen_proc *event@ = event handler function
 194  *              @void *ectx@ = argument for the event handler
 195  *
 196  * Returns:     A `strong' prime, or zero.
 197  *
 198  * Use:         Finds `strong' primes.  A strong prime %$p$% is such that
 199  *
 200  *                * %$p - 1$% has a large prime factor %$r$%,
 201  *                * %$p + 1$% has a large prime factor %$s$%, and
 202  *                * %$r - 1$% has a large prime factor %$t$%.
 203  *
 204  *              The numbers produced may be slightly larger than requested,
 205  *              by a few bits.
 206  */
 207
 208 mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r,
 209                 unsigned n, pgen_proc *event, void *ectx)
 210 {
 211   pfilt f;
 212   pgen_jumpctx j;
 213   rabin rb;
 214
 215   d = strongprime_setup(name, d, &f, nbits, r, n, event, ectx);
 216   j.j = &f;
 217   d = pgen(name, d, d, event, ectx, n, pgen_jump, &j,
 218            rabin_iters(nbits), pgen_test, &rb);
 219   pfilt_destroy(&f);
 220   return (d);
 221 }
 222
 223 /*----- That's all, folks -------------------------------------------------*/