X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb/blobdiff_plain/0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a..f4ed788cf4e6bf263a417eb8d7832c269b7a9db7:/math/strongprime.c

diff --git a/math/strongprime.c b/math/strongprime.c
index 6acac174..fc20bfea 100644
--- a/math/strongprime.c
+++ b/math/strongprime.c
@@ -63,58 +63,74 @@ mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
 {
   mp *s, *t, *q;
   dstr dn = DSTR_INIT;
+  unsigned slop, nb, u, i;
 
   mp *rr = d;
   pgen_filterctx c;
   pgen_jumpctx j;
   rabin rb;
 
-  /* --- The bitslop parameter --- *
+  /* --- Figure out how large the smaller primes should be --- *
    *
-   * There's quite a lot of prime searching to be done.  The constant
-   * @BITSLOP@ is a (low) approximation to the base-2 log of the expected
-   * number of steps to find a prime number.  Experimentation shows that
-   * numbers around 10 seem to be good.
+   * We want them to be `as large as possible', subject to the constraint
+   * that we produce a number of the requested size at the end.  This is
+   * tricky, because the final prime search is going to involve quite large
+   * jumps from its starting point; the size of the jumps are basically
+   * determined by our choice here, and if they're too big then we won't find
+   * a prime in time.
+   *
+   * Let's suppose we're trying to make an %$N$%-bit prime.  The expected
+   * number of steps tends to increase linearly with size, i.e., we need to
+   * take about %2^k N$% steps for some %$k$%.  If we're jumping by a
+   * %$J$%-bit quantity each time, from an %$N$%-bit starting point, then we
+   * will only be able to find a match if %$2^k N 2^{J-1} \le 2^{N-1}$%,
+   * i.e., if %$J \le N - (k + \log_2 N)$%.
+   *
+   * Experimentation shows that taking %$k + \log_2 N = 12$% works well for
+   * %$N = 1024$%, so %$k = 2$%.
    */
 
-#define BITSLOP 12
+  for (i = 1; i && nbits >> i; i <<= 1); assert(i);
+  for (slop = 2, nb = nbits; nb > 1; i >>= 1) {
+    u = nb >> i;
+    if (u) { slop += i; nb = u; }
+  }
+  if (nbits/2 <= slop) return (0);
 
   /* --- Choose two primes %$s$% and %$t$% of half the required size --- */
 
-  assert(((void)"nbits too small in strongprime_setup", nbits/2 > BITSLOP));
-  nbits = nbits/2 - BITSLOP;
+  nb = nbits/2 - slop;
   c.step = 1;
 
-  rr = mprand(rr, nbits, r, 1);
+  rr = mprand(rr, nb, r, 1);
   DRESET(&dn); dstr_putf(&dn, "%s [s]", name);
   if ((s = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c,
-	   rabin_iters(nbits), pgen_test, &rb)) == 0)
+		rabin_iters(nb), pgen_test, &rb)) == 0)
     goto fail_s;
 
-  rr = mprand(rr, nbits, r, 1);
+  rr = mprand(rr, nb, r, 1);
   DRESET(&dn); dstr_putf(&dn, "%s [t]", name);
   if ((t = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c,
-		rabin_iters(nbits), pgen_test, &rb)) == 0)
+		rabin_iters(nb), pgen_test, &rb)) == 0)
     goto fail_t;
 
   /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */
 
   rr = mp_lsl(rr, t, 1);
   pfilt_create(&c.f, rr);
-  rr = mp_lsl(rr, rr, BITSLOP - 1);
+  rr = mp_lsl(rr, rr, slop - 1);
   rr = mp_add(rr, rr, MP_ONE);
   DRESET(&dn); dstr_putf(&dn, "%s [r]", name);
   j.j = &c.f;
-  nbits += BITSLOP;
   q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &j,
-	   rabin_iters(nbits), pgen_test, &rb);
+	   rabin_iters(nb + slop), pgen_test, &rb);
   pfilt_destroy(&c.f);
   if (!q)
     goto fail_r;
 
   /* --- Select a suitable starting-point for finding %$p$% --- *
    *
-   * This computes %$p_0 = 2(s^{r - 2} \bmod r)s - 1$%.
+   * This computes %$p_0 = 2 s (s^{r - 2} \bmod r) - 1$%.
    */
 
   {
@@ -132,13 +148,13 @@ mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits,
   /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */
 
   {
-    mp *x;
+    mp *x, *y;
     x = mp_mul(MP_NEW, q, s);
     x = mp_lsl(x, x, 1);
     pfilt_create(f, x);
-    x = mp_lsl(x, x, BITSLOP - 1);
-    rr = mp_add(rr, rr, x);
-    mp_drop(x);
+    y = mp_lsl(MP_NEW, MP_ONE, nbits - 1);
+    rr = mp_leastcongruent(rr, y, rr, x);
+    mp_drop(x); mp_drop(y);
   }
 
   /* --- Return the result --- */
@@ -159,8 +175,6 @@ fail_s:
   mp_drop(rr);
   dstr_destroy(&dn);
   return (0);
-
-#undef BITSLOP
 }
 
 /* --- @strongprime@ --- *
@@ -180,24 +194,26 @@ fail_s:
  *		  * %$p - 1$% has a large prime factor %$r$%,
  *		  * %$p + 1$% has a large prime factor %$s$%, and
  *		  * %$r - 1$% has a large prime factor %$t$%.
- *
- *		The numbers produced may be slightly larger than requested,
- *		by a few bits.
  */
 
 mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r,
 		unsigned n, pgen_proc *event, void *ectx)
 {
+  mp *p;
   pfilt f;
   pgen_jumpctx j;
   rabin rb;
 
-  d = strongprime_setup(name, d, &f, nbits, r, n, event, ectx);
+  if (d) mp_copy(d);
+  p = strongprime_setup(name, d, &f, nbits, r, n, event, ectx);
+  if (!p) { mp_drop(d); return (0); }
   j.j = &f;
-  d = pgen(name, d, d, event, ectx, n, pgen_jump, &j,
+  p = pgen(name, p, p, event, ectx, n, pgen_jump, &j,
 	   rabin_iters(nbits), pgen_test, &rb);
+  if (mp_bits(p) != nbits) { mp_drop(p); return (0); }
   pfilt_destroy(&f);
-  return (d);
+  mp_drop(d);
+  return (p);
 }
 
 /*----- That's all, folks -------------------------------------------------*/