From: mdw <mdw>
Date: Sat, 16 Jun 2001 13:00:20 +0000 (+0000)
Subject: Use the generic exponentiation functions.
X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/commitdiff_plain/4640a0dd947f422cfda780c62da342792af27b7b

Use the generic exponentiation functions.
---

diff --git a/mpbarrett.c b/mpbarrett.c
index 889b268..b38aa91 100644
--- a/mpbarrett.c
+++ b/mpbarrett.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpbarrett.c,v 1.7 2001/04/19 18:25:26 mdw Exp $
+ * $Id: mpbarrett.c,v 1.8 2001/06/16 13:00:20 mdw Exp $
  *
  * Barrett modular reduction
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mpbarrett.c,v $
+ * Revision 1.8  2001/06/16 13:00:20  mdw
+ * Use the generic exponentiation functions.
+ *
  * Revision 1.7  2001/04/19 18:25:26  mdw
  * Use sliding-window exponentiation.
  *
@@ -61,6 +64,7 @@
 
 #include "mp.h"
 #include "mpbarrett.h"
+#include "mpbarrett-exp.h"
 
 /*----- Main code ---------------------------------------------------------*/
 
@@ -199,189 +203,18 @@ mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
  * Returns:     Result, %$a^e \bmod m$%.
  */
 
-#define WINSZ 5
-#define TABSZ (1 << (WINSZ - 1))
-
-#define THRESH (((MPW_BITS / WINSZ) << 2) + 1)
-
-static mp *exp_simple(mpbarrett *mb, mp *d, mp *a, mp *e)
-{
-  mpscan sc;
-  mp *x = MP_ONE;
-  mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
-  unsigned sq = 0;
-
-  a = MP_COPY(a);
-  mp_rscan(&sc, e);
-  if (!MP_RSTEP(&sc))
-    goto exit;
-  while (!MP_RBIT(&sc))
-    MP_RSTEP(&sc);
-
-  /* --- Do the main body of the work --- */
-
-  for (;;) {
-    sq++;
-    while (sq) {
-      mp *y;
-      y = mp_sqr(spare, x);
-      y = mpbarrett_reduce(mb, y, y);
-      spare = x; x = y;
-      sq--;
-    }
-    {
-      mp *y = mp_mul(spare, x, a);
-      y = mpbarrett_reduce(mb, y, y);
-      spare = x; x = y;
-    }
-    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 = mpbarrett_reduce(mb, y, y);
-    spare = x; x = y;
-    sq--;
-  }  
-
-exit:
-  MP_DROP(a);
-  if (spare != MP_NEW)
-    MP_DROP(spare);
-  if (d != MP_NEW)
-    MP_DROP(d);
-  return (x);
-}
-
 mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
 {
-  mp **tab;
-  mp *a2;
-  mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
   mp *x = MP_ONE;
-  unsigned i, sq = 0;
-  mpscan sc;
-
-  /* --- Do we bother? --- */
+  mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
 
   MP_SHRINK(e);
-  if (MP_LEN(e) == 0)
-    goto exit;
-  if (MP_LEN(e) < THRESH) {
-    x->ref--;
-    return (exp_simple(mb, d, a, e));
-  }
-
-  /* --- Do the precomputation --- */
-
-  a2 = mp_sqr(MP_NEW, a);
-  a2 = mpbarrett_reduce(mb, a2, a2);
-  tab = xmalloc(TABSZ * sizeof(mp *));
-  tab[0] = MP_COPY(a);
-  for (i = 1; i < TABSZ; i++) {
-    mp *x = mp_mul(MP_NEW, tab[i - 1], a2);
-    tab[i] = mpbarrett_reduce(mb, x, x);
-  }
-  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 = mpbarrett_reduce(mb, y, y);
-      spare = x; x = y;
-      sq--;
-    }
-
-    /* --- Do the multiply --- */
-
-    { mp *y = mp_mul(spare, x, tab[i]); spare = x;
-      x = mpbarrett_reduce(mb, y, 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 = mpbarrett_reduce(mb, y, y);
-    spare = x; x = y;
-    sq--;
-  }
-
-  /* --- Done --- */
-
-  for (i = 0; i < TABSZ; i++)
-    mp_drop(tab[i]);
-  xfree(tab);
-exit:
+  if (!MP_LEN(e))
+    ;
+  else if (MP_LEN(e) < EXP_THRESH)
+    EXP_SIMPLE(x, a, e);
+  else
+    EXP_WINDOW(x, a, e);
   mp_drop(d);
   mp_drop(spare);
   return (x);
diff --git a/mpmont-mexp.c b/mpmont-mexp.c
index c0ede4d..fabac3e 100644
--- a/mpmont-mexp.c
+++ b/mpmont-mexp.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpmont-mexp.c,v 1.5 2000/10/08 12:11:22 mdw Exp $
+ * $Id: mpmont-mexp.c,v 1.6 2001/06/16 13:00:20 mdw Exp $
  *
  * Multiple simultaneous exponentiations
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mpmont-mexp.c,v $
+ * Revision 1.6  2001/06/16 13:00:20  mdw
+ * Use the generic exponentiation functions.
+ *
  * Revision 1.5  2000/10/08 12:11:22  mdw
  * Use @MP_EQ@ instead of @MP_CMP@.
  *
@@ -55,157 +58,44 @@
 #include "mp.h"
 #include "mpmont.h"
 
+#define EXP_WINSZ 3
+#include "mpmont-exp.h"
+
 /*----- Main code ---------------------------------------------------------*/
 
 /* --- @mpmont_mexpr@ --- *
  *
  * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
  *		@mp *d@ = fake destination
- *		@mpmont_factor *f@ = pointer to array of factors
+ *		@mp_expfactor *f@ = pointer to array of factors
  *		@size_t n@ = number of factors supplied
  *
  * Returns:	If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the
  *		exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result
  *		is:
  *
- *		%$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} R \bmod m$%
+ *		%$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
+ *
+ *		except that the %$g_i$% and result are in Montgomery form.
  */
 
-typedef struct scan {
-  size_t len;
-  mpw w;
-} scan;
-
-mp *mpmont_mexpr(mpmont *mm, mp *d, mpmont_factor *f, size_t n)
+mp *mpmont_mexpr(mpmont *mm, mp *d, mp_expfactor *f, size_t n)
 {
-  size_t vn = 1 << n;
-  mp **v = xmalloc(vn * sizeof(mp *));
-  scan *s;
-  size_t o;
-  unsigned b;
-  mp *a = MP_COPY(mm->r);
-  mp *spare = MP_NEW;
-
-  /* --- Perform the precomputation --- */
-
-  {
-    size_t i, j;
-    size_t mask;
-
-    /* --- Fill in the rest of the array --- *
-     *
-     * Zero never gets used.
-     */
-
-    j = 0;
-    mask = 0;
-    for (i = 1; i < vn; i++) {
-
-      /* --- Check for a new bit entering --- *
-       *
-       * If a bit gets set that wasn't set before, then all the lower bits
-       * are zeroes and I've got to introduce a new base into the array.
-       */
-
-      if ((i & mask) == 0) {
-	v[i] = mpmont_mul(mm, MP_NEW, f[j++].base, mm->r2);
-	mask = i;
-      }
-
-      /* --- Otherwise I can get away with a single multiplication --- *
-       *
-       * In particular, if %$i$% has more than one bit set, then I only need
-       * to calculate %$v_i = v_{\mathit{mask}} v_{i - \mathit{mask}}$%.
-       * Since both are less than %$i$%, they must have already been
-       * computed.
-       */
-
-      else
-	v[i] = mpmont_mul(mm, MP_NEW, v[mask], v[i & ~mask]);
-    }
-  }
-
-  /* --- Set up the bitscanners --- *
-   *
-   * I must scan the exponents from left to right, which is a shame.  It
-   * means that I can't use the standard @mpscan@ stuff, in particular.
-   *
-   * If any of the exponents are considered secret then make the accumulator
-   * automatically set the secret bit.
-   */
-
-  {
-    size_t i;
-
-    s = xmalloc(n * sizeof(scan));
-    o = 0;
-    for (i = 0; i < n; i++) {
-      s[i].len = MP_LEN(f[i].exp);
-      if (s[i].len > o)
-	o = s[i].len;
-      if (f[i].exp->f & MP_BURN)
-	spare = MP_NEWSEC;
-    }
-    b = 0;
-  }
+  mp *a = mp_copy(mm->r);
+  mp *spare;
+  size_t i;
 
-  /* --- Now do the actual calculation --- */
-
-  b = 0;
-  for (;;) {
-    size_t i;
-    size_t j;
-    mp *dd;
-
-    /* --- If no more bits, get some more --- */
-
-    if (!b) {
-      if (!o)
-	break;
-      o--;
-      b = MPW_BITS;
-    }
-
-    /* --- Work out the next index --- */
-
-    j = 0;
-    b--;
-    for (i = 0; i < n; i++) {
-      if (o < s[i].len)
-	j |= (((f[i].exp->v[o] >> b) & 1) << i);
-    }
-
-    /* --- Accumulate the result --- */
-
-    if (spare) {
-      dd = mp_sqr(spare, a);
-      dd = mpmont_reduce(mm, dd, dd);
-      spare = a;
-      a = dd;
-    }
-    
-    if (j) {
-      dd = mpmont_mul(mm, spare, a, v[j]);
-      spare = a;
-      a = dd;
+  spare = MP_NEW;
+  for (i = 0; i < n; i++) {
+    if (f[i].exp->f & MP_BURN) {
+      spare = MP_NEWSEC;
+      break;
     }
   }
 
-  /* --- Tidy up afterwards --- */
-
-  {
-    size_t i;
-    for (i = 1; i < vn; i++)
-      MP_DROP(v[i]);
-    if (spare)
-      MP_DROP(spare);
-    free(v);
-    free(s);
-  }
-
-  if (d != MP_NEW)
-    MP_DROP(d);
-
+  EXP_SIMUL(a, f, n);
+  mp_drop(d);
+  mp_drop(spare);
   return (a);
 }
 
@@ -213,7 +103,7 @@ mp *mpmont_mexpr(mpmont *mm, mp *d, mpmont_factor *f, size_t n)
  *
  * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
  *		@mp *d@ = fake destination
- *		@mpmont_factor *f@ = pointer to array of factors
+ *		@mp_expfactor *f@ = pointer to array of factors
  *		@size_t n@ = number of factors supplied
  *
  * Returns:	Product of bases raised to exponents, all mod @m@.
@@ -221,9 +111,19 @@ mp *mpmont_mexpr(mpmont *mm, mp *d, mpmont_factor *f, size_t n)
  * Use:		Convenient interface over @mpmont_mexpr@.
  */
 
-mp *mpmont_mexp(mpmont *mm, mp *d, mpmont_factor *f, size_t n)
+mp *mpmont_mexp(mpmont *mm, mp *d, mp_expfactor *f, size_t n)
 {
-  d = mpmont_mexpr(mm, d, f, n);
+  mp_expfactor *v = xmalloc(sizeof(*v) * n);
+  size_t i;
+
+  for (i = 0; i < n; i++) {
+    v[i].base = mpmont_mul(mm, MP_NEW, f[i].base, mm->r2);
+    v[i].exp = f[i].exp;
+  }
+  d = mpmont_mexpr(mm, d, v, n);
+  for (i = 0; i < n; i++)
+    MP_DROP(v[i].base);
+  xfree(v);
   d = mpmont_reduce(mm, d, d);
   return (d);
 }
@@ -237,7 +137,7 @@ mp *mpmont_mexp(mpmont *mm, mp *d, mpmont_factor *f, size_t n)
 static int verify(size_t n, dstr *v)
 {
   mp *m = *(mp **)v[0].buf;
-  mpmont_factor *f = xmalloc(n * sizeof(*f));
+  mp_expfactor *f = xmalloc(n * sizeof(*f));
   mp *r, *rr;
   size_t i, j;
   mpmont mm;
diff --git a/mpmont.c b/mpmont.c
index d051778..2371de8 100644
--- a/mpmont.c
+++ b/mpmont.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpmont.c,v 1.14 2001/02/22 09:04:26 mdw Exp $
+ * $Id: mpmont.c,v 1.15 2001/06/16 13:00:20 mdw Exp $
  *
  * Montgomery reduction
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mpmont.c,v $
+ * Revision 1.15  2001/06/16 13:00:20  mdw
+ * Use the generic exponentiation functions.
+ *
  * Revision 1.14  2001/02/22 09:04:26  mdw
  * Cosmetic fix.
  *
@@ -88,6 +91,7 @@
 
 #include "mp.h"
 #include "mpmont.h"
+#include "mpmont-exp.h"
 
 /*----- Tweakables --------------------------------------------------------*/
 
@@ -99,7 +103,7 @@
 
 /* #define MPMONT_DISABLE */
 
-/*----- Main code ---------------------------------------------------------*/
+/*----- Reduction and multiplication --------------------------------------*/
 
 /* --- @mpmont_create@ --- *
  *
@@ -363,6 +367,8 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 
 #endif
 
+/*----- Exponentiation ----------------------------------------------------*/
+
 /* --- @mpmont_expr@ --- *
  *
  * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
@@ -370,190 +376,21 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
  *		@mp *a@ = base
  *		@mp *e@ = exponent
  *
- * Returns:	Result, %$a^e R \bmod m$%.
+ * Returns:	Result, %$(a R^{-1})^e R \bmod m$%.
  */
 
-#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;
-  mp *x = MP_COPY(mm->r);
-  mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
-  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 (;;) {
-      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)
-    MP_DROP(d);
-  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 *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
 
   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:
+    ;
+  else if (MP_LEN(e) < EXP_THRESH)
+    EXP_SIMPLE(x, a, e);
+  else
+    EXP_WINDOW(x, a, e);
   mp_drop(d);
   mp_drop(spare);
   return (x);
@@ -571,7 +408,8 @@ exit:
 
 mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e)
 {
-  d = mpmont_expr(mm, d, a, e);
+  d = mpmont_mul(mm, d, a, mm->r2);
+  d = mpmont_expr(mm, d, d, e);
   d = mpmont_reduce(mm, d, d);
   return (d);
 }