Find `strong' RSA primes using Gordon's algorithm.

diff --git a/strongprime.c b/strongprime.c
new file mode 100644 (file)
index 0000000..4a7ddb8
--- /dev/null
+++ b/strongprime.c
@@ -0,0 +1,180 @@
+/* -*-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 -------------------------------------------------*/

diff --git a/strongprime.h b/strongprime.h
new file mode 100644 (file)
index 0000000..6f06cda
--- /dev/null
+++ b/strongprime.h
@@ -0,0 +1,89 @@
+/* -*-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