math/strongprime.c: Replace inexplicable exponentiation with extended-gcd.

For some reason, I calculated s^-1 as s^{r-2} (mod r).  This code isn't
even slightly constant-time, and gcd is faster than modexp.  Also, this
bit isn't time-critical anyway, and the code is way simpler like this.

diff --git a/math/strongprime.c b/math/strongprime.c
index 9eab8b2..5b13653 100644 (file)
--- a/math/strongprime.c
+++ b/math/strongprime.c
@@ -140,17 +140,10 @@ mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
    * This computes %$p_0 = 2 s (s^{r - 2} \bmod r) - 1$%.
    */
 
-  {
-    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);
-  }
+  rr = mp_modinv(rr, s, q);
+  rr = mp_mul(rr, rr, s);
+  rr = mp_lsl(rr, rr, 1);
+  rr = mp_sub(rr, rr, MP_ONE);
 
   /* --- Pick a starting point for the search --- *
    *