X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/c9d4c30b618d250d16676a9db4ef225cee9ec77c..c65df27983057ec76ed0e72bb370f9a5ae7dad28:/mpmont.c

diff --git a/mpmont.c b/mpmont.c
index be7d00e..39f51ed 100644
--- a/mpmont.c
+++ b/mpmont.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpmont.c,v 1.10 2000/07/29 17:05:43 mdw Exp $
+ * $Id: mpmont.c,v 1.19 2004/04/08 01:36:15 mdw Exp $
  *
  * Montgomery reduction
  *
@@ -27,50 +27,6 @@
  * MA 02111-1307, USA.
  */
 
-/*----- 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
- * (e.g., replace MP_MODIFY by MP_DEST).
- *
- * Revision 1.8  1999/12/22 15:55:00  mdw
- * Adjust Karatsuba parameters.
- *
- * Revision 1.7  1999/12/11 01:51:14  mdw
- * Use a Karatsuba-based reduction for large moduli.
- *
- * Revision 1.6  1999/12/10 23:18:39  mdw
- * Change interface for suggested destinations.
- *
- * Revision 1.5  1999/11/22 13:58:40  mdw
- * Add an option to disable Montgomery reduction, so that performance
- * comparisons can be done.
- *
- * Revision 1.4  1999/11/21 12:27:06  mdw
- * Remove a division from the Montgomery setup by calculating
- * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
- * %$R^2$%.
- *
- * Revision 1.3  1999/11/21 11:35:10  mdw
- * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
- * @mpmont_mul@ for squaring in exponentiation.
- *
- * Revision 1.2  1999/11/19 13:17:26  mdw
- * Add extra interface to exponentiation which returns a Montgomerized
- * result.
- *
- * Revision 1.1  1999/11/17 18:02:16  mdw
- * New multiprecision integer arithmetic suite.
- *
- */
-
 /*----- Header files ------------------------------------------------------*/
 
 #include "mp.h"
@@ -86,7 +42,7 @@
 
 /* #define MPMONT_DISABLE */
 
-/*----- Main code ---------------------------------------------------------*/
+/*----- Reduction and multiplication --------------------------------------*/
 
 /* --- @mpmont_create@ --- *
  *
@@ -118,15 +74,9 @@ void mpmont_create(mpmont *mm, mp *m)
   mp *r2 = mp_new(2 * n + 1, 0);
   mp r;
 
-  /* --- Validate the arguments --- */
-
-  assert(((void)"Montgomery modulus must be positive",
-	  (m->f & MP_NEG) == 0));
-  assert(((void)"Montgomery modulus must be odd", m->v[0] & 1));
-
   /* --- Take a copy of the modulus --- */
 
-  mp_shrink(m);
+  assert(MP_ISPOS(m) && MP_ISODD(m));
   mm->m = MP_COPY(m);
 
   /* --- Determine %$R^2$% --- */
@@ -138,8 +88,7 @@ void mpmont_create(mpmont *mm, mp *m)
   /* --- Find the magic value @mi@ --- */
 
   mp_build(&r, r2->v + n, r2->vl);
-  mm->mi = MP_NEW;
-  mp_gcd(0, 0, &mm->mi, &r, m);
+  mm->mi = mp_modinv(MP_NEW, m, &r);
   mm->mi = mp_sub(mm->mi, &r, mm->mi);
 
   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
@@ -195,7 +144,7 @@ mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 
   /* --- Check for serious Karatsuba reduction --- */
 
-  if (n > KARATSUBA_CUTOFF * 3) {
+  if (n > MPK_THRESH * 3) {
     mp al;
     mpw *vl;
     mp *u;
@@ -246,8 +195,12 @@ mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 
   memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
   d->vl -= n;
-  if (MP_CMP(d, >=, mm->m))
-    d = mp_sub(d, d, mm->m);
+  if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
+    mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
+  if (d->f & MP_NEG) {
+    mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
+    d->f &= ~MP_NEG;
+  }
   MP_SHRINK(d);
   return (d);
 }
@@ -276,7 +229,7 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 
 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 {
-  if (mm->n > KARATSUBA_CUTOFF * 3) {
+  if (mm->n > MPK_THRESH * 3) {
     d = mp_mul(d, a, b);
     d = mpmont_reduce(mm, d, d);
   } else {
@@ -331,10 +284,12 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 
     memmove(d->v, dv, MPWS(dvl - dv));
     d->vl -= dv - d->v;
+    if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
+      mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
+    if ((a->f ^ b->f) & MP_NEG)
+      mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
     MP_SHRINK(d);
     d->f = (a->f | b->f) & MP_BURN;
-    if (MP_CMP(d, >=, mm->m))
-      d = mp_sub(d, d, mm->m);
     MP_DROP(a);
     MP_DROP(b);
   }
@@ -344,222 +299,6 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 
 #endif
 
-/* --- @mpmont_expr@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@mp *d@ = fake destination
- *		@mp *a@ = base
- *		@mp *e@ = exponent
- *
- * Returns:	Result, %$a^e R \bmod m$%.
- */
-
-#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_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
- *		@mp *d@ = fake destination
- *		@mp *a@ = base
- *		@mp *e@ = exponent
- *
- * Returns:	Result, %$a^e \bmod m$%.
- */
-
-mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e)
-{
-  d = mpmont_expr(mm, d, a, e);
-  d = mpmont_reduce(mm, d, d);
-  return (d);
-}
-
 /*----- Test rig ----------------------------------------------------------*/
 
 #ifdef TEST_RIG
@@ -584,7 +323,7 @@ static int tcreate(dstr *v)
     ok = 0;
   }
 
-  if (MP_CMP(mm.r, !=, r)) {
+  if (!MP_EQ(mm.r, r)) {
     fputs("\n*** bad r", stderr);
     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
@@ -593,7 +332,7 @@ static int tcreate(dstr *v)
     ok = 0;
   }
 
-  if (MP_CMP(mm.r2, !=, r2)) {
+  if (!MP_EQ(mm.r2, r2)) {
     fputs("\n*** bad r2", stderr);
     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
@@ -626,7 +365,7 @@ static int tmul(dstr *v)
     mp *qr = mp_mul(MP_NEW, a, b);
     mp_div(0, &qr, qr, m);
 
-    if (MP_CMP(qr, !=, r)) {
+    if (!MP_EQ(qr, r)) {
       fputs("\n*** classical modmul failed", stderr);
       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
@@ -645,7 +384,7 @@ static int tmul(dstr *v)
     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
     mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
     mr = mpmont_reduce(&mm, mr, mr);
-    if (MP_CMP(mr, !=, r)) {
+    if (!MP_EQ(mr, r)) {
       fputs("\n*** montgomery modmul failed", stderr);
       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
@@ -669,46 +408,9 @@ static int tmul(dstr *v)
   return ok;
 }
 
-static int texp(dstr *v)
-{
-  mp *m = *(mp **)v[0].buf;
-  mp *a = *(mp **)v[1].buf;
-  mp *b = *(mp **)v[2].buf;
-  mp *r = *(mp **)v[3].buf;
-  mp *mr;
-  int ok = 1;
-
-  mpmont mm;
-  mpmont_create(&mm, m);
-
-  mr = mpmont_exp(&mm, MP_NEW, a, b);
-
-  if (MP_CMP(mr, !=, r)) {
-    fputs("\n*** montgomery modexp failed", stderr);
-    fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
-    fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
-    fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
-    fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
-    fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
-    fputc('\n', stderr);
-    ok = 0;
-  }
-
-  MP_DROP(m);
-  MP_DROP(a);
-  MP_DROP(b);
-  MP_DROP(r);
-  MP_DROP(mr);
-  mpmont_destroy(&mm);
-  assert(mparena_count(MPARENA_GLOBAL) == 0);
-  return ok;
-}
-
-
 static test_chunk tests[] = {
   { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
   { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
-  { "exp", texp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
   { 0, 0, { 0 } },
 };