From: mdw <mdw>
Date: Sat, 29 Jul 2000 17:05:43 +0000 (+0000)
Subject: (mpmont_expr): Use sliding window exponentiation, with a drop-through
X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/commitdiff_plain/c9d4c30b618d250d16676a9db4ef225cee9ec77c

(mpmont_expr): Use sliding window exponentiation, with a drop-through
for small exponents to use a simple left-to-right bitwise routine.  This
can reduce modexp times by up to a quarter.
---

diff --git a/mpmont.c b/mpmont.c
index e7b9bb7..be7d00e 100644
--- a/mpmont.c
+++ b/mpmont.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpmont.c,v 1.9 2000/06/17 11:45:09 mdw Exp $
+ * $Id: mpmont.c,v 1.10 2000/07/29 17:05:43 mdw Exp $
  *
  * Montgomery reduction
  *
@@ -30,6 +30,11 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mpmont.c,v $
+ * Revision 1.10  2000/07/29 17:05:43  mdw
+ * (mpmont_expr): Use sliding window exponentiation, with a drop-through
+ * for small exponents to use a simple left-to-right bitwise routine.  This
+ * can reduce modexp times by up to a quarter.
+ *
  * Revision 1.9  2000/06/17 11:45:09  mdw
  * Major memory management overhaul.  Added arena support.  Use the secure
  * arena for secret integers.  Replace and improve the MP management macros
@@ -349,35 +354,63 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
  * Returns:	Result, %$a^e R \bmod m$%.
  */
 
-mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
+#define WINSZ 5
+#define TABSZ (1 << (WINSZ - 1))
+
+#define THRESH (((MPW_BITS / WINSZ) << 2) + 1)
+
+static mp *exp_simple(mpmont *mm, mp *d, mp *a, mp *e)
 {
   mpscan sc;
-  mp *ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
+  mp *ar;
   mp *x = MP_COPY(mm->r);
   mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
-
-  mp_scan(&sc, e);
-
-  if (MP_STEP(&sc)) {
-    size_t sq = 0;
+  unsigned sq = 0;
+
+  mp_rscan(&sc, e);
+  if (!MP_RSTEP(&sc))
+    goto exit;
+  while (!MP_RBIT(&sc))
+    MP_RSTEP(&sc);
+
+  /* --- Do the main body of the work --- */
+  
+  ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
+  for (;;) {
+    sq++;
+    while (sq) {
+      mp *y;
+      y = mp_sqr(spare, x);
+      y = mpmont_reduce(mm, y, y);
+      spare = x; x = y;
+      sq--;
+    }
+    { mp *y = mpmont_mul(mm, spare, x, ar); spare = x; x = y; }
+    sq = 0;
     for (;;) {
-      mp *dd;
-      if (MP_BIT(&sc)) {
-	while (sq) {
-	  dd = mp_sqr(spare, ar);
-	  dd = mpmont_reduce(mm, dd, dd);
-	  spare = ar; ar = dd;
-	  sq--;
-	}
-	dd = mpmont_mul(mm, spare, x, ar);
-	spare = x; x = dd;
-      }
-      sq++;
-      if (!MP_STEP(&sc))
+      if (!MP_RSTEP(&sc))
+	goto done;
+      if (MP_RBIT(&sc))
 	break;
+      sq++;
     }
   }
+
+  /* --- Do a final round of squaring --- */
+
+done:
+  while (sq) {
+    mp *y;
+    y = mp_sqr(spare, x);
+    y = mpmont_reduce(mm, y, y);
+    spare = x; x = y;
+    sq--;
+  }
+
+  /* --- Done --- */
+
   MP_DROP(ar);
+exit:
   if (spare != MP_NEW)
     MP_DROP(spare);
   if (d != MP_NEW)
@@ -385,6 +418,131 @@ mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
   return (x);
 }
 
+mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
+{
+  mp **tab;
+  mp *ar, *a2;
+  mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
+  mp *x = MP_COPY(mm->r);
+  unsigned i, sq = 0;
+  mpscan sc;
+
+  /* --- Do we bother? --- */
+
+  MP_SHRINK(e);
+  if (MP_LEN(e) == 0)
+    goto exit;
+  if (MP_LEN(e) < THRESH) {
+    x->ref--;
+    return (exp_simple(mm, d, a, e));
+  }
+
+  /* --- Do the precomputation --- */
+
+  ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
+  a2 = mp_sqr(MP_NEW, ar);
+  a2 = mpmont_reduce(mm, a2, a2);
+  tab = xmalloc(TABSZ * sizeof(mp *));
+  tab[0] = ar;
+  for (i = 1; i < TABSZ; i++)
+    tab[i] = mpmont_mul(mm, MP_NEW, tab[i - 1], a2);
+  mp_drop(a2);
+  mp_rscan(&sc, e);
+
+  /* --- Skip top-end zero bits --- *
+   *
+   * If the initial step worked, there must be a set bit somewhere, so keep
+   * stepping until I find it.
+   */
+
+  MP_RSTEP(&sc);
+  while (!MP_RBIT(&sc)) {
+    MP_RSTEP(&sc);
+  }
+
+  /* --- Now for the main work --- */
+
+  for (;;) {
+    unsigned l = 0;
+    unsigned z = 0;
+
+    /* --- The next bit is set, so read a window index --- *
+     *
+     * Reset @i@ to zero and increment @sq@.  Then, until either I read
+     * @WINSZ@ bits or I run out of bits, scan in a bit: if it's clear, bump
+     * the @z@ counter; if it's set, push a set bit into @i@, shift it over
+     * by @z@ bits, bump @sq@ by @z + 1@ and clear @z@.  By the end of this
+     * palaver, @i@ is an index to the precomputed value in @tab@.
+     */
+
+    i = 0;
+    sq++;
+    for (;;) {
+      l++;
+      if (l >= WINSZ || !MP_RSTEP(&sc))
+	break;
+      if (!MP_RBIT(&sc))
+	z++;
+      else {
+	i = ((i << 1) | 1) << z;
+	sq += z + 1;
+	z = 0;
+      }
+    }
+
+    /* --- Do the squaring --- *
+     *
+     * Remember that @sq@ carries over from the zero-skipping stuff below.
+     */
+
+    while (sq) {
+      mp *y;
+      y = mp_sqr(spare, x);
+      y = mpmont_reduce(mm, y, y);
+      spare = x; x = y;
+      sq--;
+    }
+
+    /* --- Do the multiply --- */
+
+    { mp *y = mpmont_mul(mm, spare, x, tab[i]); spare = x; x = y; }
+
+    /* --- Now grind along through the rest of the bits --- */
+
+    sq = z;
+    for (;;) {
+      if (!MP_RSTEP(&sc))
+	goto done;
+      if (MP_RBIT(&sc))
+	break;
+      sq++;
+    }
+  }
+
+  /* --- Do a final round of squaring --- */
+
+done:
+  while (sq) {
+    mp *y;
+    y = mp_sqr(spare, x);
+    y = mpmont_reduce(mm, y, y);
+    spare = x; x = y;
+    sq--;
+  }
+
+  /* --- Done --- */
+
+  for (i = 0; i < TABSZ; i++)
+    mp_drop(tab[i]);
+  xfree(tab);
+exit:
+  if (d != MP_NEW)
+    mp_drop(d);
+  if (spare)
+    mp_drop(spare);
+  return (x);
+}
+
 /* --- @mpmont_exp@ --- *
  *
  * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context