Prime number generator and tester.

[u/mdw/catacomb] / rabin.c

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+/* -*-c-*-
+ *
+ * $Id: rabin.c,v 1.1 1999/11/19 13:17:57 mdw Exp $
+ *
+ * Miller-Rabin primality test
+ *
+ * (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: rabin.c,v $
+ * Revision 1.1  1999/11/19 13:17:57  mdw
+ * Prime number generator and tester.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+#include "mpmont.h"
+#include "pgen.h"
+#include "rabin.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @rabin_create@ --- *
+ *
+ * Arguments:  @rabin *r@ = pointer to Rabin-Miller context
+ *             @mp *m@ = pointer to number to test
+ *
+ * Returns:    ---
+ *
+ * Use:                Precomputes some useful values for performing the
+ *             Miller-Rabin probabilistic primality test.
+ */
+
+void rabin_create(rabin *r, mp *m)
+{
+  mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
+  mpscan sc;
+  size_t s;
+
+  /* --- Find @r@ and @s@ --- */
+
+  mpmont_create(&r->mm, m);
+  mp_scan(&sc, m1);
+  s = 0;
+  while (mp_step(&sc)) {
+    if (mp_bit(&sc))
+      break;
+    s++;
+  }
+  r->s = s;
+  r->r = mp_lsr(MP_NEW, m1, s);
+
+  /* --- Compute %$(m - 1)R \bmod m$% --- */
+
+  r->m1 = mpmont_mul(&r->mm, MP_NEW, m1, r->mm.r2);
+  mp_drop(m1);
+}
+
+/* --- @rabin_destroy@ --- *
+ *
+ * Arguments:  @rabin *r@ = pointer to Rabin-Miller context
+ *
+ * Returns:    ---
+ *
+ * Use:                Disposes of a Rabin-Miller context when it's no longer
+ *             needed.
+ */
+
+void rabin_destroy(rabin *r)
+{
+  mp_drop(r->r);
+  mp_drop(r->m1);
+  mpmont_destroy(&r->mm);
+}
+
+/* --- @rabin_test@ --- *
+ *
+ * Arguments:  @rabin *r@ = pointer to Rabin-Miller context
+ *             @mp *g@ = base to test the number against
+ *
+ * Returns:    Either @PGEN_COMPOSITE@ if the test failed, or @PGEN_MAYBE@
+ *             if it succeeded.
+ *
+ * Use:                Performs a single iteration of the Rabin-Miller primality
+ *             test.
+ */
+
+int rabin_test(rabin *r, mp *g)
+{
+  mp *y;
+  mp *dd, *spare = MP_NEW;
+  size_t j;
+  int rc = PGEN_COMPOSITE;
+
+  /* --- Calculate %$y R = g^r R \bmod m$% --- *
+   *
+   * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime.  If course, note that
+   * @y@ here has an extra factor of %$R$%.
+   */
+
+  y = mpmont_expr(&r->mm, g, r->r);
+  if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) {
+    rc = PGEN_MAYBE;
+    goto done;
+  }
+
+  /* --- Now for the main loop --- *
+   *
+   * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
+   * composite.  Of course, %$j = 0$% has already been tested.
+   */
+
+  for (j = 1; j < r->s; j++) {
+    dd = mpmont_mul(&r->mm, spare, y, y); spare = y; y = dd;
+    if (MP_CMP(y, ==, r->mm.r))
+      break;
+    if (MP_CMP(y, ==, r->m1)) {
+      rc = PGEN_MAYBE;
+      break;
+    }
+  }
+
+  /* --- Done --- */
+
+done:
+  if (spare != MP_NEW)
+    MP_DROP(spare);
+  MP_DROP(y);
+  return (rc);
+}
+
+/*----- That's all, folks -------------------------------------------------*/