X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ef5f48103e83977bda6ef4d7d1aacbb66a629b10..c65df27983057ec76ed0e72bb370f9a5ae7dad28:/mpmont.c

diff --git a/mpmont.c b/mpmont.c
index d061934..39f51ed 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 1.19 2004/04/08 01:36:15 mdw Exp $
  *
  * Montgomery reduction
  *
@@ -27,34 +27,6 @@
  * MA 02111-1307, USA.
  */
 
-/*----- Revision history --------------------------------------------------* 
- *
- * $Log: mpmont.c,v $
- * 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"
@@ -70,7 +42,7 @@
 
 /* #define MPMONT_DISABLE */
 
-/*----- Main code ---------------------------------------------------------*/
+/*----- Reduction and multiplication --------------------------------------*/
 
 /* --- @mpmont_create@ --- *
  *
@@ -91,58 +63,40 @@ 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)
 {
-  /* --- 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));
+  size_t n = MP_LEN(m);
+  mp *r2 = mp_new(2 * n + 1, 0);
+  mp r;
 
   /* --- Take a copy of the modulus --- */
 
-  mp_shrink(m);
+  assert(MP_ISPOS(m) && MP_ISODD(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_modinv(MP_NEW, m, &r);
+  mm->mi = mp_sub(mm->mi, &r, mm->mi);
 
   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
 
-  {
-    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 +116,7 @@ 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 +140,68 @@ 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 > MPK_THRESH * 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;
+
+    /* --- Initial conditioning of the arguments --- */
+
+    a = MP_COPY(a);
+    if (d)
+      MP_DROP(d);
+    d = a;
+    MP_DEST(d, 2 * n + 1, a->f);
+
+    dv = d->v; dvl = d->vl;
+    mv = mm->m->v; mvl = mm->m->vl;
 
-  /* --- Let's go to work --- */
+    /* --- Let's go to work --- */
 
-  while (n--) {
-    mpw u = MPW(*dv * mm->mi);
-    MPX_UMLAN(dv, dvl, mv, mvl, u);
-    dv++;
+    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 +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 (MP_LEN(a) > KARATSUBA_CUTOFF && MP_LEN(b) > KARATSUBA_CUTOFF) {
+  if (mm->n > MPK_THRESH * 3) {
     d = mp_mul(d, a, b);
     d = mpmont_reduce(mm, d, d);
   } else {
@@ -257,6 +239,7 @@ 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 +250,7 @@ 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 +261,10 @@ 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 +274,7 @@ 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 +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);
   }
@@ -313,69 +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, %$a^e R \bmod m$%.
- */
-
-mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
-{
-  mpscan sc;
-  mp *ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
-  mp *x = MP_COPY(mm->r);
-  mp *spare = MP_NEW;
-
-  mp_scan(&sc, e);
-
-  if (MP_STEP(&sc)) {
-    size_t 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))
-	break;
-    }
-  }
-  MP_DROP(ar);
-  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 ----------------------------------------------------------*/
 
 #ifdef TEST_RIG
@@ -392,15 +315,15 @@ 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 +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);
@@ -442,7 +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);
@@ -461,7 +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);
@@ -485,46 +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 } },
 };