Standard curves and curve checking.

[u/mdw/catacomb] / f-prime.c

diff --git a/f-prime.c b/f-prime.c
index a9673b8..a82f3a0 100644 (file)
--- a/f-prime.c
+++ b/f-prime.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: f-prime.c,v 1.2 2002/01/13 13:48:44 mdw Exp $
+ * $Id: f-prime.c,v 1.7 2004/03/27 17:54:11 mdw Exp $
  *
  * Prime fields with Montgomery arithmetic
  *
@@ -30,6 +30,30 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: f-prime.c,v $
+ * Revision 1.7  2004/03/27 17:54:11  mdw
+ * Standard curves and curve checking.
+ *
+ * Revision 1.6  2004/03/23 15:19:32  mdw
+ * Test elliptic curves more thoroughly.
+ *
+ * Revision 1.5  2004/03/23 12:08:26  mdw
+ * Random field-element selection.
+ *
+ * Revision 1.4  2004/03/21 22:52:06  mdw
+ * Merge and close elliptic curve branch.
+ *
+ * Revision 1.3.4.3  2004/03/21 22:39:46  mdw
+ * Elliptic curves on binary fields work.
+ *
+ * Revision 1.3.4.2  2004/03/20 00:13:31  mdw
+ * Projective coordinates for prime curves
+ *
+ * Revision 1.3.4.1  2003/06/10 13:43:53  mdw
+ * Simple (non-projective) curves over prime fields now seem to work.
+ *
+ * Revision 1.3  2003/05/15 23:25:59  mdw
+ * Make elliptic curve stuff build.
+ *
  * Revision 1.2  2002/01/13 13:48:44  mdw
  * Further progress.
  *
@@ -44,6 +68,7 @@
 
 #include "field.h"
 #include "mpmont.h"
+#include "mprand.h"
 
 /*----- Data structures ---------------------------------------------------*/
 
@@ -63,10 +88,17 @@ static void fdestroy(field *ff)
   DESTROY(f);
 }
 
+static mp *frand(field *ff, mp *d, grand *r)
+{
+  fctx *f = (fctx *)ff;
+  return (mprand_range(d, f->mm.m, r, 0));
+}
+
 static mp *fin(field *ff, mp *d, mp *x)
 {
   fctx *f = (fctx *)ff;
-  return (mpmont_mul(&f->mm, d, x, f->mm.r2));
+  mp_div(0, &d, x, f->mm.m);
+  return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 }
 
 static mp *fout(field *ff, mp *d, mp *x)
@@ -75,6 +107,11 @@ static mp *fout(field *ff, mp *d, mp *x)
   return (mpmont_reduce(&f->mm, d, x));
 }
 
+static int fzerop(field *ff, mp *x)
+{
+  return (!MP_LEN(x));
+}
+
 static mp *fneg(field *ff, mp *d, mp *x)
 {
   fctx *f = (fctx *)ff;
@@ -83,12 +120,24 @@ static mp *fneg(field *ff, mp *d, mp *x)
 
 static mp *fadd(field *ff, mp *d, mp *x, mp *y)
 {
-  return (mp_add(d, x, y));
+  fctx *f = (fctx *)ff;
+  d = mp_add(d, x, y);
+  if (d->f & MP_NEG)
+    d = mp_add(d, d, f->mm.m);
+  else if (MP_CMP(d, >, f->mm.m))
+    d = mp_sub(d, d, f->mm.m);
+  return (d);
 }
 
 static mp *fsub(field *ff, mp *d, mp *x, mp *y)
 {
-  return (mp_sub(d, x, y));
+  fctx *f = (fctx *)ff;
+  d = mp_sub(d, x, y);
+  if (d->f & MP_NEG)
+    d = mp_add(d, d, f->mm.m);
+  else if (MP_CMP(d, >, f->mm.m))
+    d = mp_sub(d, d, f->mm.m);
+  return (d);
 }
 
 static mp *fmul(field *ff, mp *d, mp *x, mp *y)
@@ -107,7 +156,7 @@ static mp *fsqr(field *ff, mp *d, mp *x)
 static mp *finv(field *ff, mp *d, mp *x)
 {
   fctx *f = (fctx *)ff;
-  d = mpmont_reduce(&f->mm, x);
+  d = mpmont_reduce(&f->mm, d, x);
   mp_gcd(0, 0, &d, f->mm.m, d);
   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 }
@@ -119,10 +168,23 @@ static mp *freduce(field *ff, mp *d, mp *x)
   return (d);
 }
 
+static mp *fsqrt(field *ff, mp *d, mp *x)
+{
+  fctx *f = (fctx *)ff;
+  d = mpmont_reduce(&f->mm, d, x);
+  d = mp_modsqrt(d, d, f->mm.m);
+  if (!d)
+    return (d);
+  return (mpmont_mul(&f->mm, d, d, f->mm.r2));
+}
+
 static mp *fdbl(field *ff, mp *d, mp *x)
 {
   fctx *f = (fctx *)ff;
-  return (mp_lsl(d, x, 1));
+  d = mp_lsl(d, x, 1);
+  if (MP_CMP(d, >, f->mm.m))
+    d = mp_sub(d, d, f->mm.m);
+  return (d);
 }
 
 static mp *ftpl(field *ff, mp *d, mp *x)
@@ -130,24 +192,44 @@ static mp *ftpl(field *ff, mp *d, mp *x)
   fctx *f = (fctx *)ff;
   MP_DEST(d, MP_LEN(x) + 1, x->f);
   MPX_UMULN(d->v, d->vl, x->v, x->vl, 3);
+  while (MP_CMP(d, >, f->mm.m))
+    d = mp_sub(d, d, f->mm.m);
   return (d);
 }
 
-static mp *fsqrt(field *ff, mp *d, mp *x)
+static mp *fqdl(field *ff, mp *d, mp *x)
 {
   fctx *f = (fctx *)ff;
-  d = mpmont_reduce(&f->mm, x);
-  d = mp_modsqrt(d, d, f->mm.m);
-  return (mpmont_mul(&f->mm, d, d, f->mm.r2));
+  d = mp_lsl(d, x, 2);
+  while (MP_CMP(d, >, f->mm.m))
+    d = mp_sub(d, d, f->mm.m);
+  return (d);
+}
+
+static mp *fhlv(field *ff, mp *d, mp *x)
+{
+  fctx *f = (fctx *)ff;
+  if (!MP_LEN(x)) {
+    MP_COPY(x);
+    MP_DROP(d);
+    return (x);
+  }
+  if (x->v[0] & 1) {
+    d = mp_add(d, x, f->mm.m);
+    x = d;
+  }
+  return (mp_lsr(d, x, 1));
 }
 
 /* --- Field operations table --- */
 
 static field_ops fops = {
-  fdestroy,
+  FTY_PRIME, "prime",
+  fdestroy, frand,
   fin, fout,
-  fneg, fadd, fsub, fmul, fsqr, finv, freduce,
-  fdbl, ftpl, fsqrt
+  fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
+  0,
+  fdbl, ftpl, fqdl, fhlv
 };
 
 /* --- @field_prime@ --- *
@@ -162,11 +244,14 @@ static field_ops fops = {
 
 field *field_prime(mp *p)
 {
-  ftcx *f = CREATE(fctx);
+  fctx *f = CREATE(fctx);
   f->f.ops = &fops;
   mpmont_create(&f->mm, p);
-  f->zero = MP_ZERO;
-  f->one = &f->mm.r;
+  f->f.zero = MP_ZERO;
+  f->f.one = f->mm.r;
+  f->f.m = f->mm.m;
+  f->f.nbits = mp_bits(p);
+  f->f.noctets = (f->f.nbits + 7) >> 3;
   return (&f->f);
 }