X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/d3409d5ecf2492cff862616de72a580d1a8e8dc0..d34decd2b2b88240cf4ca68a2a5feb7bf36de6e7:/mpmont.c

diff --git a/mpmont.c b/mpmont.c
index d924009..e7b9bb7 100644
--- a/mpmont.c
+++ b/mpmont.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpmont.c,v 1.1 1999/11/17 18:02:16 mdw Exp $
+ * $Id: mpmont.c,v 1.9 2000/06/17 11:45:09 mdw Exp $
  *
  * Montgomery reduction
  *
@@ -30,6 +30,37 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mpmont.c,v $
+ * 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.
  *
@@ -40,6 +71,16 @@
 #include "mp.h"
 #include "mpmont.h"
 
+/*----- Tweakables --------------------------------------------------------*/
+
+/* --- @MPMONT_DISABLE@ --- *
+ *
+ * Replace all the clever Montgomery reduction with good old-fashioned long
+ * division.
+ */
+
+/* #define MPMONT_DISABLE */
+
 /*----- Main code ---------------------------------------------------------*/
 
 /* --- @mpmont_create@ --- *
@@ -50,53 +91,62 @@
  * Returns:	---
  *
  * Use:		Initializes a Montgomery reduction context ready for use.
+ *		The argument @m@ must be a positive odd integer.
  */
 
+#ifdef MPMONT_DISABLE
+
 void mpmont_create(mpmont *mm, mp *m)
 {
+  mp_shrink(m);
+  mm->m = MP_COPY(m);
+  mm->r = MP_ONE;
+  mm->r2 = MP_ONE;
+  mm->mi = MP_ONE;
+}
+
+#else
+
+void mpmont_create(mpmont *mm, mp *m)
+{
+  size_t n = MP_LEN(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);
   mm->m = MP_COPY(m);
 
-  /* --- Find the magic value @mi@ --- *
-   *
-   * This is a slightly grungy way of solving the problem, but it does work.
-   */
+  /* --- Determine %$R^2$% --- */
 
-  {
-    mpw av[2] = { 0, 1 };
-    mp a, b;
-    mp *i;
-    mpw mi;
+  mm->n = n;
+  MPX_ZERO(r2->v, r2->vl - 1);
+  r2->vl[-1] = 1;
 
-    mp_build(&a, av, av + 2);
-    mp_build(&b, m->v, m->v + 1);
-    mp_gcd(0, 0, &i, &a, &b);
-    mi = i->v[0];
-    if (!(i->f & MP_NEG))
-      mi = MPW(-mi);
-    mm->mi = mi;
-    MP_DROP(i);
-  }
+  /* --- 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_sub(mm->mi, &r, mm->mi);
 
   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
 
-  {
-    size_t l = MP_LEN(m);
-    mp *r = mp_create(l + 1);
-
-    mm->shift = l * MPW_BITS;
-    MPX_ZERO(r->v, r->vl - 1);
-    r->vl[-1] = 1;
-    mm->r = mm->r2 = MP_NEW;
-    mp_div(0, &mm->r, r, m);
-    r = mp_sqr(r, mm->r);
-    mp_div(0, &mm->r2, r, m);
-    MP_DROP(r);
-  }
+  mm->r2 = MP_NEW;
+  mp_div(0, &mm->r2, r2, m);
+  mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
+  MP_DROP(r2);
 }
 
+#endif
+
 /* --- @mpmont_destroy@ --- *
  *
  * Arguments:	@mpmont *mm@ = pointer to a Montgomery reduction context
@@ -112,152 +162,244 @@ void mpmont_destroy(mpmont *mm)
   MP_DROP(mm->m);
   MP_DROP(mm->r);
   MP_DROP(mm->r2);
+  MP_DROP(mm->mi);
 }
 
 /* --- @mpmont_reduce@ --- *
  *
  * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
  *		@mp *d@ = destination
- *		@const mp *a@ = source, assumed positive
+ *		@mp *a@ = source, assumed positive
  *
  * Returns:	Result, %$a R^{-1} \bmod m$%.
  */
 
-mp *mpmont_reduce(mpmont *mm, mp *d, const mp *a)
+#ifdef MPMONT_DISABLE
+
+mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 {
-  mpw *dv, *dvl;
-  const mpw *mv, *mvl;
-  size_t n;
+  mp_div(0, &d, a, mm->m);
+  return (d);
+}
 
-  /* --- Initial conditioning of the arguments --- */
+#else
+
+mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
+{
+  size_t n = mm->n;
+
+  /* --- Check for serious Karatsuba reduction --- */
+
+  if (n > KARATSUBA_CUTOFF * 3) {
+    mp al;
+    mpw *vl;
+    mp *u;
+
+    if (MP_LEN(a) >= n)
+      vl = a->v + n;
+    else
+      vl = a->vl;
+    mp_build(&al, a->v, vl);
+    u = mp_mul(MP_NEW, &al, mm->mi);
+    if (MP_LEN(u) > n)
+      u->vl = u->v + n;
+    u = mp_mul(u, u, mm->m);
+    d = mp_add(d, a, u);
+    mp_drop(u);
+  }
 
-  n = MP_LEN(mm->m);
+  /* --- Otherwise do it the hard way --- */
 
-  if (d == a)
-    MP_MODIFY(d, 2 * n);
   else {
-    MP_MODIFY(d, 2 * n);
-    memcpy(d->v, a->v, MPWS(MP_LEN(a)));
-    memset(d->v + MP_LEN(a), 0, MPWS(MP_LEN(d) - MP_LEN(a)));
-  }
-    
-  dv = d->v; dvl = d->vl;
-  mv = mm->m->v; mvl = mm->m->vl;
+    mpw *dv, *dvl;
+    mpw *mv, *mvl;
+    mpw mi;
+    size_t k = n;
+
+    /* --- Initial conditioning of the arguments --- */
 
-  /* --- Let's go to work --- */
+    a = MP_COPY(a);
+    if (d)
+      MP_DROP(d);
+    d = a;
+    MP_DEST(d, 2 * n + 1, a->f);
 
-  while (n--) {
-    mpw u = MPW(*dv * mm->mi);
-    MPX_UMLAN(dv, dvl, mv, mvl, u);
-    dv++;
+    dv = d->v; dvl = d->vl;
+    mv = mm->m->v; mvl = mm->m->vl;
+
+    /* --- Let's go to work --- */
+
+    mi = mm->mi->v[0];
+    while (k--) {
+      mpw u = MPW(*dv * mi);
+      MPX_UMLAN(dv, dvl, mv, mvl, u);
+      dv++;
+    }
   }
 
-  /* --- Done --- */
+  /* --- Wrap everything up --- */
 
-  memmove(d->v, dv, MPWS(dvl - dv));
-  d->vl -= dv - d->v;
+  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);
   MP_SHRINK(d);
-  d->f = a->f & MP_BURN;
   return (d);
 }
 
+#endif
+
 /* --- @mpmont_mul@ --- *
  *
  * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
  *		@mp *d@ = destination
- *		@const mp *a, *b@ = sources, assumed positive
+ *		@mp *a, *b@ = sources, assumed positive
  *
  * Returns:	Result, %$a b R^{-1} \bmod m$%.
  */
 
-mp *mpmont_mul(mpmont *mm, mp *d, const mp *a, const mp *b)
+#ifdef MPMONT_DISABLE
+
+mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 {
-  mpw *dv, *dvl;
-  const mpw *av, *avl;
-  const mpw *bv, *bvl;
-  const mpw *mv, *mvl;
-  mpw y;
-  size_t n, i;
+  d = mp_mul(d, a, b);
+  mp_div(0, &d, d, mm->m);
+  return (d);
+}
 
-  /* --- Initial conditioning of the arguments --- */
+#else
 
-  if (MP_LEN(a) > MP_LEN(b)) {
-    const mp *t = a; a = b; b = t;
-  }
-  n = MP_LEN(mm->m);
-    
-  MP_MODIFY(d, 2 * n + 1);
-  dv = d->v; dvl = d->vl;
-  MPX_ZERO(dv, dvl);
-  av = a->v; avl = a->vl;
-  bv = b->v; bvl = b->vl;
-  mv = mm->m->v; mvl = mm->m->vl;
-  y = *bv;
-
-  /* --- Montgomery multiplication phase --- */
-
-  i = 0;
-  while (i < n && av < avl) {
-    mpw x = *av++;
-    mpw u = MPW((*dv + x * y) * mm->mi);
-    MPX_UMLAN(dv, dvl, bv, bvl, x);
-    MPX_UMLAN(dv, dvl, mv, mvl, u);
-    dv++;
-    i++;
-  }
+mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
+{
+  if (mm->n > KARATSUBA_CUTOFF * 3) {
+    d = mp_mul(d, a, b);
+    d = mpmont_reduce(mm, d, d);
+  } else {
+    mpw *dv, *dvl;
+    mpw *av, *avl;
+    mpw *bv, *bvl;
+    mpw *mv, *mvl;
+    mpw y;
+    size_t n, i;
+    mpw mi;
 
-  /* --- Simpler Montgomery reduction phase --- */
+    /* --- Initial conditioning of the arguments --- */
 
-  while (i < n) {
-    mpw u = MPW(*dv * mm->mi);
-    MPX_UMLAN(dv, dvl, mv, mvl, u);
-    dv++;
-    i++;
-  }
+    if (MP_LEN(a) > MP_LEN(b)) {
+      mp *t = a; a = b; b = t;
+    }
+    n = MP_LEN(mm->m);
+
+    a = MP_COPY(a);
+    b = MP_COPY(b);
+    MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
+    dv = d->v; dvl = d->vl;
+    MPX_ZERO(dv, dvl);
+    av = a->v; avl = a->vl;
+    bv = b->v; bvl = b->vl;
+    mv = mm->m->v; mvl = mm->m->vl;
+    y = *bv;
+
+    /* --- Montgomery multiplication phase --- */
+
+    i = 0;
+    mi = mm->mi->v[0];
+    while (i < n && av < avl) {
+      mpw x = *av++;
+      mpw u = MPW((*dv + x * y) * mi);
+      MPX_UMLAN(dv, dvl, bv, bvl, x);
+      MPX_UMLAN(dv, dvl, mv, mvl, u);
+      dv++;
+      i++;
+    }
 
-  /* --- Done --- */
+    /* --- Simpler Montgomery reduction phase --- */
+
+    while (i < n) {
+      mpw u = MPW(*dv * mi);
+      MPX_UMLAN(dv, dvl, mv, mvl, u);
+      dv++;
+      i++;
+    }
+
+    /* --- Done --- */
+
+    memmove(d->v, dv, MPWS(dvl - dv));
+    d->vl -= dv - d->v;
+    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);
+  }
 
-  memmove(d->v, dv, MPWS(dvl - dv));
-  d->vl -= dv - d->v;
-  MP_SHRINK(d);
-  d->f = (a->f | b->f) & MP_BURN;
   return (d);
 }
 
-/* --- @mpmont_exp@ --- *
+#endif
+
+/* --- @mpmont_expr@ --- *
  *
  * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@const mp *a@ = base
- *		@const mp *e@ = exponent
+ *		@mp *d@ = fake destination
+ *		@mp *a@ = base
+ *		@mp *e@ = exponent
  *
- * Returns:	Result, %$a^e \bmod m$%.
+ * Returns:	Result, %$a^e R \bmod m$%.
  */
 
-mp *mpmont_exp(mpmont *mm, const mp *a, const mp *e)
+mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
 {
   mpscan sc;
   mp *ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
-  mp *d = MP_COPY(mm->r);
+  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;
     for (;;) {
       mp *dd;
       if (MP_BIT(&sc)) {
-	dd = mpmont_mul(mm, MP_NEW, d, ar);
-	MP_DROP(d);
-	d = dd;
+	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))
 	break;
-      dd = mpmont_mul(mm, MP_NEW, ar, ar);
-      MP_DROP(ar);
-      ar = dd;
     }
   }
   MP_DROP(ar);
-  return (mpmont_reduce(mm, d, d));
+  if (spare != MP_NEW)
+    MP_DROP(spare);
+  if (d != MP_NEW)
+    MP_DROP(d);
+  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 ----------------------------------------------------------*/
@@ -276,9 +418,9 @@ static int tcreate(dstr *v)
 
   mpmont_create(&mm, m);
 
-  if (mm.mi != mi->v[0]) {
+  if (mm.mi->v[0] != mi->v[0]) {
     fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
-	    (unsigned long)mm.mi, (unsigned long)mi->v[0]);
+	    (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
     fputc('\n', stderr);
     ok = 0;
@@ -288,7 +430,7 @@ static int tcreate(dstr *v)
     fputs("\n*** bad r", stderr);
     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
-    fputs("\n   found ", stderr); mp_writefile(r, stderr, 10);
+    fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
     fputc('\n', stderr);
     ok = 0;
   }
@@ -297,7 +439,7 @@ static int tcreate(dstr *v)
     fputs("\n*** bad r2", stderr);
     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
-    fputs("\n   found ", stderr); mp_writefile(r2, stderr, 10);
+    fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
     fputc('\n', stderr);
     ok = 0;
   }
@@ -307,6 +449,7 @@ static int tcreate(dstr *v)
   MP_DROP(r);
   MP_DROP(r2);
   mpmont_destroy(&mm);
+  assert(mparena_count(MPARENA_GLOBAL) == 0);
   return (ok);
 }
 
@@ -316,52 +459,55 @@ static int tmul(dstr *v)
   mp *a = *(mp **)v[1].buf;
   mp *b = *(mp **)v[2].buf;
   mp *r = *(mp **)v[3].buf;
-  mp *mr, *qr;
   int ok = 1;
 
   mpmont mm;
   mpmont_create(&mm, m);
 
   {
+    mp *qr = mp_mul(MP_NEW, a, b);
+    mp_div(0, &qr, qr, m);
+
+    if (MP_CMP(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);
+      fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
+      fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
+      fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
+      fputc('\n', stderr);
+      ok = 0;
+    }
+
+    mp_drop(qr);
+  }
+
+  {
     mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
-    mr = mpmont_mul(&mm, MP_NEW, ar, br);
+    mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
     mr = mpmont_reduce(&mm, mr, mr);
+    if (MP_CMP(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);
+      fputs("\n b = ", 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(ar); MP_DROP(br);
+    mp_drop(mr);
   }
 
-  qr = mp_mul(MP_NEW, a, b);
-  mp_div(0, &qr, qr, m);
-
-  if (MP_CMP(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);
-    fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
-    fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
-    fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
-    fputc('\n', stderr);
-    ok = 0;
-  }
-
-  if (MP_CMP(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);
-    fputs("\n b = ", 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);
-  MP_DROP(qr);
   mpmont_destroy(&mm);
+  assert(mparena_count(MPARENA_GLOBAL) == 0);
   return ok;
 }
 
@@ -377,7 +523,7 @@ static int texp(dstr *v)
   mpmont mm;
   mpmont_create(&mm, m);
 
-  mr = mpmont_exp(&mm, a, b);
+  mr = mpmont_exp(&mm, MP_NEW, a, b);
 
   if (MP_CMP(mr, !=, r)) {
     fputs("\n*** montgomery modexp failed", stderr);
@@ -396,14 +542,15 @@ static int texp(dstr *v)
   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 } },
-  { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp } },
-  { "exp", texp, { &type_mp, &type_mp, &type_mp, &type_mp } },
+  { "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 } },
 };