+++ /dev/null
-/* -*-c-*-
- *
- * $Id: strongprime.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
- *
- * Generate `strong' prime numbers
- *
- * (c) 1999 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include <mLib/dstr.h>
-
-#include "grand.h"
-#include "rand.h"
-#include "mp.h"
-#include "mpmont.h"
-#include "mprand.h"
-#include "pgen.h"
-#include "pfilt.h"
-#include "rabin.h"
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @strongprime_setup@ --- *
- *
- * Arguments: @const char *name@ = pointer to name root
- * @mp *d@ = destination for search start point
- * @pfilt *f@ = where to store filter jump context
- * @unsigned nbits@ = number of bits wanted
- * @grand *r@ = random number source
- * @unsigned n@ = number of attempts to make
- * @pgen_proc *event@ = event handler function
- * @void *ectx@ = argument for the event handler
- *
- * Returns: A starting point for a `strong' prime search, or zero.
- *
- * Use: Sets up for a strong prime search, so that primes with
- * particular properties can be found. It's probably important
- * to note that the number left in the filter context @f@ is
- * congruent to 2 (mod 4).
- */
-
-mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
- grand *r, unsigned n, pgen_proc *event, void *ectx)
-{
- mp *s, *t, *q;
- dstr dn = DSTR_INIT;
-
- mp *rr = d;
- pgen_filterctx c;
- pgen_jumpctx j;
- rabin rb;
-
- /* --- The bitslop parameter --- *
- *
- * There's quite a lot of prime searching to be done. The constant
- * @BITSLOP@ is a (low) approximation to the base-2 log of the expected
- * number of steps to find a prime number. Experimentation shows that
- * numbers around 10 seem to be good.
- */
-
-#define BITSLOP 12
-
- /* --- Choose two primes %$s$% and %$t$% of half the required size --- */
-
- assert(((void)"nbits too small in strongprime_setup", nbits/2 > BITSLOP));
- nbits = nbits/2 - BITSLOP;
- c.step = 1;
-
- rr = mprand(rr, nbits, r, 1);
- DRESET(&dn); dstr_putf(&dn, "%s [s]", name);
- if ((s = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c,
- rabin_iters(nbits), pgen_test, &rb)) == 0)
- goto fail_s;
-
- rr = mprand(rr, nbits, r, 1);
- DRESET(&dn); dstr_putf(&dn, "%s [t]", name);
- if ((t = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c,
- rabin_iters(nbits), pgen_test, &rb)) == 0)
- goto fail_t;
-
- /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */
-
- rr = mp_lsl(rr, t, 1);
- pfilt_create(&c.f, rr);
- rr = mp_lsl(rr, rr, BITSLOP - 1);
- rr = mp_add(rr, rr, MP_ONE);
- DRESET(&dn); dstr_putf(&dn, "%s [r]", name);
- j.j = &c.f;
- nbits += BITSLOP;
- q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &j,
- rabin_iters(nbits), pgen_test, &rb);
- pfilt_destroy(&c.f);
- if (!q)
- goto fail_r;
-
- /* --- Select a suitable starting-point for finding %$p$% --- *
- *
- * This computes %$p_0 = 2(s^{r - 2} \bmod r)s - 1$%.
- */
-
- {
- mpmont mm;
-
- mpmont_create(&mm, q);
- rr = mp_sub(rr, q, MP_TWO);
- rr = mpmont_exp(&mm, rr, s, rr);
- mpmont_destroy(&mm);
- rr = mp_mul(rr, rr, s);
- rr = mp_lsl(rr, rr, 1);
- rr = mp_sub(rr, rr, MP_ONE);
- }
-
- /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */
-
- {
- mp *x;
- x = mp_mul(MP_NEW, q, s);
- x = mp_lsl(x, x, 1);
- pfilt_create(f, x);
- x = mp_lsl(x, x, BITSLOP - 1);
- rr = mp_add(rr, rr, x);
- mp_drop(x);
- }
-
- /* --- Return the result --- */
-
- mp_drop(q);
- mp_drop(t);
- mp_drop(s);
- dstr_destroy(&dn);
- return (rr);
-
- /* --- Tidy up if something failed --- */
-
-fail_r:
- mp_drop(t);
-fail_t:
- mp_drop(s);
-fail_s:
- mp_drop(rr);
- dstr_destroy(&dn);
- return (0);
-
-#undef BITSLOP
-}
-
-/* --- @strongprime@ --- *
- *
- * Arguments: @const char *name@ = pointer to name root
- * @mp *d@ = destination integer
- * @unsigned nbits@ = number of bits wanted
- * @grand *r@ = random number source
- * @unsigned n@ = number of attempts to make
- * @pgen_proc *event@ = event handler function
- * @void *ectx@ = argument for the event handler
- *
- * Returns: A `strong' prime, or zero.
- *
- * Use: Finds `strong' primes. A strong prime %$p$% is such that
- *
- * * %$p - 1$% has a large prime factor %$r$%,
- * * %$p + 1$% has a large prime factor %$s$%, and
- * * %$r - 1$% has a large prime factor %$t$%.
- *
- * The numbers produced may be slightly larger than requested,
- * by a few bits.
- */
-
-mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r,
- unsigned n, pgen_proc *event, void *ectx)
-{
- pfilt f;
- pgen_jumpctx j;
- rabin rb;
-
- d = strongprime_setup(name, d, &f, nbits, r, n, event, ectx);
- j.j = &f;
- d = pgen(name, d, d, event, ectx, n, pgen_jump, &j,
- rabin_iters(nbits), pgen_test, &rb);
- pfilt_destroy(&f);
- return (d);
-}
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff