Diff: math/numtheory/fp_prime_miller_rabin.c

Revision:

0:35aa5be3b78d

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/math/numtheory/fp_prime_miller_rabin.c	Fri Jun 06 10:49:02 2014 +0000
@@ -0,0 +1,77 @@
+/* TomsFastMath, a fast ISO C bignum library.
+ * 
+ * This project is meant to fill in where LibTomMath
+ * falls short.  That is speed ;-)
+ *
+ * This project is public domain and free for all purposes.
+ * 
+ * Tom St Denis, tomstdenis@gmail.com
+ */
+#include <tfm.h>
+
+/* Miller-Rabin test of "a" to the base of "b" as described in 
+ * HAC pp. 139 Algorithm 4.24
+ *
+ * Sets result to 0 if definitely composite or 1 if probably prime.
+ * Randomly the chance of error is no more than 1/4 and often 
+ * very much lower.
+ */
+void fp_prime_miller_rabin (fp_int * a, fp_int * b, int *result)
+{
+  fp_int  n1, y, r;
+  int     s, j;
+
+  /* default */
+  *result = FP_NO;
+
+  /* ensure b > 1 */
+  if (fp_cmp_d(b, 1) != FP_GT) {
+     return;
+  }     
+
+  /* get n1 = a - 1 */
+  fp_init_copy(&n1, a);
+  fp_sub_d(&n1, 1, &n1);
+
+  /* set 2**s * r = n1 */
+  fp_init_copy(&r, &n1);
+
+  /* count the number of least significant bits
+   * which are zero
+   */
+  s = fp_cnt_lsb(&r);
+
+  /* now divide n - 1 by 2**s */
+  fp_div_2d (&r, s, &r, NULL);
+
+  /* compute y = b**r mod a */
+  fp_init(&y);
+  fp_exptmod(b, &r, a, &y);
+
+  /* if y != 1 and y != n1 do */
+  if (fp_cmp_d (&y, 1) != FP_EQ && fp_cmp (&y, &n1) != FP_EQ) {
+    j = 1;
+    /* while j <= s-1 and y != n1 */
+    while ((j <= (s - 1)) && fp_cmp (&y, &n1) != FP_EQ) {
+      fp_sqrmod (&y, a, &y);
+
+      /* if y == 1 then composite */
+      if (fp_cmp_d (&y, 1) == FP_EQ) {
+         return;
+      }
+      ++j;
+    }
+
+    /* if y != n1 then composite */
+    if (fp_cmp (&y, &n1) != FP_EQ) {
+       return;
+    }
+  }
+
+  /* probably prime now */
+  *result = FP_YES;
+}
+
+/* $Source: /cvs/libtom/tomsfastmath/src/numtheory/fp_prime_miller_rabin.c,v $ */
+/* $Revision: 1.1 $ */
+/* $Date: 2007/01/24 21:25:19 $ */