--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: strongprime.c,v 1.1 1999/12/22 15:51:22 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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: strongprime.c,v $
+ * Revision 1.1 1999/12/22 15:51:22 mdw
+ * Find `strong' RSA primes using Gordon's algorithm.
+ *
+ */
+
+/*----- 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@ --- *
+ *
+ * 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)
+{
+ mp *s, *t, *q, *p = 0;
+ dstr dn = DSTR_INIT;
+
+ mp *rr = MP_NEW;
+ pgen_filterctx c;
+ pgen_jumpctx cj;
+ 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 10
+
+ /* --- Choose two primes %$s$% and %$t$% of half the required size --- */
+
+ 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_NEW, rr, event, ectx, n, pgen_filter, &c,
+ rabin_iters(nbits), pgen_test, &rb)) == 0)
+ goto fail_s;
+ mp_burn(s);
+
+ rr = mprand(rr, nbits, r, 1);
+ DRESET(&dn); dstr_putf(&dn, "%s [t]", name);
+ if ((t = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_filter, &c,
+ rabin_iters(nbits), pgen_test, &rb)) == 0)
+ goto fail_t;
+ mp_burn(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);
+ cj.j = &c.f;
+ nbits += BITSLOP;
+ if ((q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &cj,
+ rabin_iters(nbits), pgen_test, &rb)) == 0)
+ goto fail_r;
+ pfilt_destroy(&c.f);
+
+ /* --- 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(&c.f, x);
+ x = mp_lsl(x, x, BITSLOP - 1);
+ rr = mp_add(rr, rr, x);
+ mp_drop(x);
+ }
+
+ if ((p = pgen(name, d, rr, event, ectx, n, pgen_jump, &cj,
+ rabin_iters(nbits * 2), pgen_test, &rb)) == 0)
+ goto fail_p;
+
+ /* --- Tidy up because we've finished --- */
+
+fail_p:
+ mp_drop(q);
+fail_r:
+ pfilt_destroy(&c.f);
+ mp_drop(t);
+fail_t:
+ mp_drop(s);
+fail_s:
+ mp_drop(rr);
+ dstr_destroy(&dn);
+
+ return (p);
+
+#undef BITSLOP
+}
+
+/*----- That's all, folks -------------------------------------------------*/
--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: strongprime.h,v 1.1 1999/12/22 15:51:22 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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: strongprime.h,v $
+ * Revision 1.1 1999/12/22 15:51:22 mdw
+ * Find `strong' RSA primes using Gordon's algorithm.
+ *
+ */
+
+#ifndef CATACOMB_STRONGPRIME_H
+#define CATACOMB_STRONGPRIME_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#ifndef CATACOMB_GRAND_H
+# include "grand.h"
+#endif
+
+#ifndef CATACOMB_PGEN_H
+# include "pgen.h"
+#endif
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @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.
+ */
+
+extern mp *strongprime(const char */*name*/, mp */*d*/, unsigned /*nbits*/,
+ grand */*r*/, unsigned /*n*/,
+ pgen_proc */*event*/, void */*ectx*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif