X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/0f5ec153dcb1c20a765d0420cc189ebac1b9682d..962dd3329d51f1d18313a17eb0cb4695ee4421a0:/rabin.c

diff --git a/rabin.c b/rabin.c
index 095c21d..915dc14 100644
--- a/rabin.c
+++ b/rabin.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: rabin.c,v 1.1 1999/11/19 13:17:57 mdw Exp $
+ * $Id: rabin.c,v 1.7 2002/01/13 13:42:53 mdw Exp $
  *
  * Miller-Rabin primality test
  *
@@ -30,6 +30,26 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: rabin.c,v $
+ * Revision 1.7  2002/01/13 13:42:53  mdw
+ * More efficient Rabin-Miller test: with random witnesses, skip redundant
+ * Montgomerization.  (Being bijective, it can't affect the distribution.)
+ *
+ * Revision 1.6  2001/06/16 12:56:38  mdw
+ * Fixes for interface change to @mpmont_expr@ and @mpmont_mexpr@.
+ *
+ * Revision 1.5  2000/10/08 12:11:22  mdw
+ * Use @MP_EQ@ instead of @MP_CMP@.
+ *
+ * Revision 1.4  2000/06/22 19:03:02  mdw
+ * Use the new @mp_odd@ function.
+ *
+ * Revision 1.3  1999/12/22 15:50:29  mdw
+ * Reworking for new prime-search system.  Add function for working out how
+ * many iterations to use for a particular number.
+ *
+ * Revision 1.2  1999/12/10 23:29:48  mdw
+ * Change header file guard names.
+ *
  * Revision 1.1  1999/11/19 13:17:57  mdw
  * Prime number generator and tester.
  *
@@ -38,6 +58,7 @@
 /*----- Header files ------------------------------------------------------*/
 
 #include "mp.h"
+#include "mpbarrett.h"
 #include "mpmont.h"
 #include "pgen.h"
 #include "rabin.h"
@@ -58,25 +79,9 @@
 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);
+  r->r = mp_odd(MP_NEW, m1, &r->s);
+  r->m1 = mp_sub(MP_NEW, m, r->mm.r);
   mp_drop(m1);
 }
 
@@ -97,24 +102,25 @@ void rabin_destroy(rabin *r)
   mpmont_destroy(&r->mm);
 }
 
-/* --- @rabin_test@ --- *
+/* --- @rabin_test@, @rabin_rtest@ --- *
  *
  * 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@
+ * Returns:	Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
  *		if it succeeded.
  *
  * Use:		Performs a single iteration of the Rabin-Miller primality
- *		test.
+ *		test.  The @rtest@ variant assumes that %$g$% is either
+ *		already in Montgomery representation, or you don't care.
  */
 
-int rabin_test(rabin *r, mp *g)
+int rabin_rtest(rabin *r, mp *g)
 {
   mp *y;
   mp *dd, *spare = MP_NEW;
   size_t j;
-  int rc = PGEN_COMPOSITE;
+  int rc = PGEN_FAIL;
 
   /* --- Calculate %$y R = g^r R \bmod m$% --- *
    *
@@ -122,9 +128,9 @@ int rabin_test(rabin *r, mp *g)
    * @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;
+  y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
+  if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) {
+    rc = PGEN_PASS;
     goto done;
   }
 
@@ -135,11 +141,13 @@ int rabin_test(rabin *r, mp *g)
    */
 
   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))
+    dd = mp_sqr(spare, y);
+    dd = mpmont_reduce(&r->mm, dd, dd);
+    spare = y; y = dd;
+    if (MP_EQ(y, r->mm.r))
       break;
-    if (MP_CMP(y, ==, r->m1)) {
-      rc = PGEN_MAYBE;
+    if (MP_EQ(y, r->m1)) {
+      rc = PGEN_PASS;
       break;
     }
   }
@@ -153,4 +161,63 @@ done:
   return (rc);
 }
 
+int rabin_test(rabin *r, mp *g)
+{
+  int rc;
+  g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2);
+  rc = rabin_rtest(r, g);
+  mp_drop(g);
+  return (rc);
+}
+
+/* --- @rabin_iters@ --- *
+ *
+ * Arguments:	@unsigned len@ = number of bits in value
+ *
+ * Returns:	Number of iterations recommended.
+ *
+ * Use:		Returns the recommended number of iterations to ensure that a
+ *		number with @len@ bits is really prime.
+ */
+
+int rabin_iters(unsigned len)
+{
+  static struct {
+    unsigned b;
+    int i;
+  } *p, *q, tab[] = {
+    { 100, 27 },
+    { 150, 18 },
+    { 200, 15 },
+    { 250, 12 },
+    { 300, 9 },
+    { 350, 8 },
+    { 400, 7 },
+    { 450, 6 },
+    { 550, 5 },
+    { 650, 4 },
+    { 850, 3 },
+    { 1300, 2 }
+  };
+
+  unsigned i;
+
+  /* --- Binary search through the table --- */
+
+  p = tab;
+  q = tab + (sizeof(tab)/sizeof(tab[0]));
+  for (;;) {
+    i = (q - p) / 2;
+    if (!i)
+      break;
+    if (len >= p[i].b && len < p[i + 1].b)
+      break;
+    if (len > p[i].b)
+      p = p + i;
+    else
+      q = p + i;
+  }
+  return (p[i].i);
+}
+
 /*----- That's all, folks -------------------------------------------------*/