X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ef5f48103e83977bda6ef4d7d1aacbb66a629b10..22bab86c9df047bdd258283c6567821319ba7a6f:/mpmont.c

diff --git a/mpmont.c b/mpmont.c
index d061934..4868bff 100644
--- a/mpmont.c
+++ b/mpmont.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpmont.c,v 1.6 1999/12/10 23:18:39 mdw Exp $
+ * $Id: mpmont.c,v 1.11 2000/10/08 12:04:27 mdw Exp $
  *
  * Montgomery reduction
  *
@@ -30,6 +30,25 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mpmont.c,v $
+ * Revision 1.11  2000/10/08 12:04:27  mdw
+ * (mpmont_reduce, mpmont_mul): Cope with negative numbers.
+ *
+ * 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.
  *
@@ -91,12 +110,17 @@ void mpmont_create(mpmont *mm, mp *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",
@@ -108,41 +132,25 @@ void mpmont_create(mpmont *mm, mp *m)
   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 = MP_NEW;
-    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(2 * l + 1);
-
-    mm->shift = l * MPW_BITS;
-    MPX_ZERO(r->v, r->vl - 1);
-    r->vl[-1] = 1;
-    mm->r2 = MP_NEW;
-    mp_div(0, &mm->r2, r, m);
-    mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
-    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
@@ -162,6 +170,7 @@ void mpmont_destroy(mpmont *mm)
   MP_DROP(mm->m);
   MP_DROP(mm->r);
   MP_DROP(mm->r2);
+  MP_DROP(mm->mi);
 }
 
 /* --- @mpmont_reduce@ --- *
@@ -185,41 +194,68 @@ mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 
 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 {
-  mpw *dv, *dvl;
-  mpw *mv, *mvl;
-  size_t n;
-
-  /* --- Initial conditioning of the arguments --- */
+  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 + 1);
   else {
-    MP_MODIFY(d, 2 * n + 1);
-    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;
 
-  /* --- Let's go to work --- */
+    /* --- Initial conditioning of the arguments --- */
+
+    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 (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);
-  d->f = a->f & MP_BURN;
-  if (MP_CMP(d, >=, mm->m))
-    d = mp_sub(d, d, mm->m);
   return (d);
 }
 
@@ -247,7 +283,7 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 
 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 {
-  if (MP_LEN(a) > KARATSUBA_CUTOFF && MP_LEN(b) > KARATSUBA_CUTOFF) {
+  if (mm->n > KARATSUBA_CUTOFF * 3) {
     d = mp_mul(d, a, b);
     d = mpmont_reduce(mm, d, d);
   } else {
@@ -257,6 +293,7 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
     mpw *mv, *mvl;
     mpw y;
     size_t n, i;
+    mpw mi;
 
     /* --- Initial conditioning of the arguments --- */
 
@@ -267,7 +304,7 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 
     a = MP_COPY(a);
     b = MP_COPY(b);
-    MP_MODIFY(d, 2 * n + 1);
+    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;
@@ -278,9 +315,10 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
     /* --- Montgomery multiplication phase --- */
 
     i = 0;
+    mi = mm->mi->v[0];
     while (i < n && av < avl) {
       mpw x = *av++;
-      mpw u = MPW((*dv + x * y) * mm->mi);
+      mpw u = MPW((*dv + x * y) * mi);
       MPX_UMLAN(dv, dvl, bv, bvl, x);
       MPX_UMLAN(dv, dvl, mv, mvl, u);
       dv++;
@@ -290,7 +328,7 @@ mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
     /* --- Simpler Montgomery reduction phase --- */
 
     while (i < n) {
-      mpw u = MPW(*dv * mm->mi);
+      mpw u = MPW(*dv * mi);
       MPX_UMLAN(dv, dvl, mv, mvl, u);
       dv++;
       i++;
@@ -300,10 +338,12 @@ 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);
   }
@@ -323,35 +363,63 @@ 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 = MP_NEW;
-
-  mp_scan(&sc, e);
-
-  if (MP_STEP(&sc)) {
-    size_t sq = 0;
+  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 (;;) {
-      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)
@@ -359,6 +427,131 @@ 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
@@ -392,15 +585,15 @@ 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;
   }
 
-  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);
@@ -409,7 +602,7 @@ 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);
@@ -442,7 +635,7 @@ 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);
@@ -461,7 +654,7 @@ 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);
@@ -499,7 +692,7 @@ static int texp(dstr *v)
 
   mr = mpmont_exp(&mm, MP_NEW, a, b);
 
-  if (MP_CMP(mr, !=, r)) {
+  if (!MP_EQ(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);