X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb/blobdiff_plain/540ff246b952bd91381bfe4fdfbc613983326379..373641eaacc86b56715a2ebf0b603fce25c16051:/math/strongprime.c

diff --git a/math/strongprime.c b/math/strongprime.c
index e8834925..9eab8b20 100644
--- a/math/strongprime.c
+++ b/math/strongprime.c
@@ -55,7 +55,14 @@
  * Use:		Sets up for a strong prime search, so that primes with
  *		particular properties can be found.  It's probably important
  *		to note that the number left in the filter context @f@ is
- *		congruent to 2 (mod 4).
+ *		congruent to 2 (mod 4); that the jump value is twice the
+ *		product of two large primes; and that the starting point is
+ *		at least %$3 \cdot 2^{N-2}$%.  (Hence, if you multiply two
+ *		such numbers, the product is at least
+ *
+ *			%$9 \cdot 2^{2N-4} > 2^{2N-1}$%
+ *
+ *		i.e., it will be (at least) a %$2 N$%-bit value.
  */
 
 mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
@@ -128,7 +135,7 @@ mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
   if (!q)
     goto fail_r;
 
-  /* --- Select a suitable starting-point for finding %$p$% --- *
+  /* --- Select a suitable congruence class for %$p$% --- *
    *
    * This computes %$p_0 = 2 s (s^{r - 2} \bmod r) - 1$%.
    */
@@ -145,14 +152,19 @@ mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
     rr = mp_sub(rr, rr, MP_ONE);
   }
 
-  /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */
+  /* --- Pick a starting point for the search --- *
+   *
+   * Select %$3 \cdot 2^{N-2} < p_1 < 2^N$% at random, only with
+   * %$p_1 \equiv p_0 \pmod{2 r s}$.
+   */
 
   {
     mp *x, *y;
     x = mp_mul(MP_NEW, q, s);
     x = mp_lsl(x, x, 1);
-    pfilt_create(f, x);
-    y = mp_lsl(MP_NEW, MP_ONE, nbits - 1);
+    pfilt_create(f, x); /* %$2 r s$% */
+    y = mprand(MP_NEW, nbits, r, 0);
+    y = mp_setbit(y, y, nbits - 2);
     rr = mp_leastcongruent(rr, y, rr, x);
     mp_drop(x); mp_drop(y);
   }