X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/41cb1beba35c8a69ee7ae1298f51711995011b5c..ceb3f0c0a3b7bb3fa3250d31b04c382894095e52:/ec-prime.c

diff --git a/ec-prime.c b/ec-prime.c
index 4611855..40f487e 100644
--- a/ec-prime.c
+++ b/ec-prime.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: ec-prime.c,v 1.3 2003/05/15 23:25:59 mdw Exp $
+ * $Id: ec-prime.c,v 1.3.4.3 2004/03/21 22:39:46 mdw Exp $
  *
  * Elliptic curves over prime fields
  *
@@ -30,6 +30,15 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: ec-prime.c,v $
+ * 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.
  *
@@ -54,14 +63,37 @@ typedef struct ecctx {
   mp *a, *b;
 } ecctx;
 
-/*----- Main code ---------------------------------------------------------*/
+/*----- Simple prime curves -----------------------------------------------*/
 
-static const ec_ops ec_primeops;
+static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops;
 
 static ec *ecneg(ec_curve *c, ec *d, const ec *p)
 {
   EC_COPY(d, p);
-  d->y = F_NEG(c->f, d->y, d->y);
+  if (d->y)
+    d->y = F_NEG(c->f, d->y, d->y);
+  return (d);
+}
+
+static ec *ecfind(ec_curve *c, ec *d, mp *x)
+{
+  mp *p, *q;
+  ecctx *cc = (ecctx *)c;
+  field *f = c->f;
+
+  q = F_SQR(f, MP_NEW, x);
+  p = F_MUL(f, MP_NEW, x, q);
+  q = F_MUL(f, q, x, cc->a);
+  p = F_ADD(f, p, p, q);
+  p = F_ADD(f, p, p, cc->b);
+  MP_DROP(q);
+  p = F_SQRT(f, p, p);
+  if (!p)
+    return (0);
+  EC_DESTROY(d);
+  d->x = MP_COPY(x);
+  d->y = p;
+  d->z = MP_COPY(f->one);
   return (d);
 }
 
@@ -69,7 +101,7 @@ static ec *ecdbl(ec_curve *c, ec *d, const ec *a)
 {
   if (EC_ATINF(a))
     EC_SETINF(d);
-  else if (!MP_LEN(a->y))
+  else if (F_ZEROP(c->f, a->y))
     EC_COPY(d, a);
   else {
     field *f = c->f;
@@ -77,19 +109,19 @@ static ec *ecdbl(ec_curve *c, ec *d, const ec *a)
     mp *lambda;
     mp *dy, *dx;
 
-    dx = F_SQR(f, MP_NEW, a->x);
-    dy = F_DBL(f, MP_NEW, a->y);
-    dx = F_TPL(f, dx, dx);
-    dx = F_ADD(f, dx, dx, cc->a);
-    dy = F_INV(f, dy, dy);
-    lambda = F_MUL(f, MP_NEW, dx, dy);
+    dx = F_SQR(f, MP_NEW, a->x);	/* %$x^2$% */
+    dy = F_DBL(f, MP_NEW, a->y);	/* %$2 y$% */
+    dx = F_TPL(f, dx, dx);		/* %$3 x^2$% */
+    dx = F_ADD(f, dx, dx, cc->a);	/* %$3 x^2 + A$% */
+    dy = F_INV(f, dy, dy);		/* %$(2 y)^{-1}$% */
+    lambda = F_MUL(f, MP_NEW, dx, dy);	/* %$\lambda = (3 x^2 + A)/(2 y)$% */
 
-    dx = F_SQR(f, dx, lambda);
-    dy = F_DBL(f, dy, a->x);
-    dx = F_SUB(f, dx, dx, dy);
-    dy = F_SUB(f, dy, a->x, dx);
-    dy = F_MUL(f, dy, lambda, dy);
-    dy = F_SUB(f, dy, dy, a->y);
+    dx = F_SQR(f, dx, lambda);		/* %$\lambda^2$% */
+    dy = F_DBL(f, dy, a->x);		/* %$2 x$% */
+    dx = F_SUB(f, dx, dx, dy);		/* %$x' = \lambda^2 - 2 x */
+    dy = F_SUB(f, dy, a->x, dx);	/* %$x - x'$% */
+    dy = F_MUL(f, dy, lambda, dy);	/* %$\lambda (x - x')$% */
+    dy = F_SUB(f, dy, dy, a->y);	/* %$y' = \lambda (x - x') - y$% */
 
     EC_DESTROY(d);
     d->x = dx;
@@ -100,6 +132,94 @@ static ec *ecdbl(ec_curve *c, ec *d, const ec *a)
   return (d);
 }
 
+static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a)
+{
+  if (EC_ATINF(a))
+    EC_SETINF(d);
+  else if (F_ZEROP(c->f, a->y))
+    EC_COPY(d, a);
+  else {
+    field *f = c->f;
+    ecctx *cc = (ecctx *)c;
+    mp *p, *q, *m, *s, *dx, *dy, *dz;
+
+    p = F_SQR(f, MP_NEW, a->z);		/* %$z^2$% */
+    q = F_SQR(f, MP_NEW, p);		/* %$z^4$% */
+    p = F_MUL(f, p, q, cc->a);		/* %$A z^4$% */
+    m = F_SQR(f, MP_NEW, a->x);		/* %$x^2$% */
+    m = F_TPL(f, m, m);			/* %$3 x^2$% */
+    m = F_ADD(f, m, m, p);		/* %$m = 3 x^2 + A z^4$% */
+
+    q = F_DBL(f, q, a->y);		/* %$2 y$% */
+    dz = F_MUL(f, MP_NEW, q, a->z);	/* %$z' = 2 y z$% */
+
+    p = F_SQR(f, p, q);			/* %$4 y^2$% */
+    s = F_MUL(f, MP_NEW, p, a->x);	/* %$s = 4 x y^2$% */
+    q = F_SQR(f, q, p);			/* %$16 y^4$% */
+    q = F_HLV(f, q, q);			/* %$t = 8 y^4$% */
+
+    p = F_DBL(f, p, s);			/* %$2 s$% */
+    dx = F_SQR(f, MP_NEW, m);		/* %$m^2$% */
+    dx = F_SUB(f, dx, dx, p);		/* %$x' = m^2 - 2 s$% */
+
+    s = F_SUB(f, s, s, dx);		/* %$s - x'$% */
+    dy = F_MUL(f, p, m, s);		/* %$m (s - x')$% */
+    dy = F_SUB(f, dy, dy, q);		/* %$y' = m (s - x') - t$% */
+
+    EC_DESTROY(d);
+    d->x = dx;
+    d->y = dy;
+    d->z = dz;
+    MP_DROP(m);
+    MP_DROP(q);
+    MP_DROP(s);
+  }
+  return (d);
+}
+
+static ec *ecprojxdbl(ec_curve *c, ec *d, const ec *a)
+{
+  if (EC_ATINF(a))
+    EC_SETINF(d);
+  else if (F_ZEROP(c->f, a->y))
+    EC_COPY(d, a);
+  else {
+    field *f = c->f;
+    mp *p, *q, *m, *s, *dx, *dy, *dz;
+
+    m = F_SQR(f, MP_NEW, a->z);		/* %$z^2$% */
+    p = F_SUB(f, MP_NEW, a->x, m);	/* %$x - z^2$% */
+    q = F_ADD(f, MP_NEW, a->x, m);	/* %$x + z^2$% */
+    m = F_MUL(f, m, p, q);		/* %$x^2 - z^4$% */
+    m = F_TPL(f, m, m);			/* %$m = 3 x^2 - 3 z^4$% */
+
+    q = F_DBL(f, q, a->y);		/* %$2 y$% */
+    dz = F_MUL(f, MP_NEW, q, a->z);	/* %$z' = 2 y z$% */
+
+    p = F_SQR(f, p, q);			/* %$4 y^2$% */
+    s = F_MUL(f, MP_NEW, p, a->x);	/* %$s = 4 x y^2$% */
+    q = F_SQR(f, q, p);			/* %$16 y^4$% */
+    q = F_HLV(f, q, q);			/* %$t = 8 y^4$% */
+
+    p = F_DBL(f, p, s);			/* %$2 s$% */
+    dx = F_SQR(f, MP_NEW, m);		/* %$m^2$% */
+    dx = F_SUB(f, dx, dx, p);		/* %$x' = m^2 - 2 s$% */
+
+    s = F_SUB(f, s, s, dx);		/* %$s - x'$% */
+    dy = F_MUL(f, p, m, s);		/* %$m (s - x')$% */
+    dy = F_SUB(f, dy, dy, q);		/* %$y' = m (s - x') - t$% */
+
+    EC_DESTROY(d);
+    d->x = dx;
+    d->y = dy;
+    d->z = dz;
+    MP_DROP(m);
+    MP_DROP(q);
+    MP_DROP(s);
+  }
+  return (d);
+}
+
 static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b)
 {
   if (a == b)
@@ -114,29 +234,31 @@ static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b)
     mp *dy, *dx;
 
     if (!MP_EQ(a->x, b->x)) {
-      dy = F_SUB(f, MP_NEW, a->y, b->y);
-      dx = F_SUB(f, MP_NEW, a->x, b->x);
-      dx = F_INV(f, dx, dx);
+      dy = F_SUB(f, MP_NEW, a->y, b->y); /* %$y_0 - y_1$% */
+      dx = F_SUB(f, MP_NEW, a->x, b->x); /* %$x_0 - x_1$% */
+      dx = F_INV(f, dx, dx);		/* %$(x_0 - x_1)^{-1}$% */
       lambda = F_MUL(f, MP_NEW, dy, dx);
-    } else if (!MP_LEN(a->y) || !MP_EQ(a->y, b->y)) {
+				   /* %$\lambda = (y_0 - y1)/(x_0 - x_1)$% */
+    } else if (F_ZEROP(c->f, a->y) || !MP_EQ(a->y, b->y)) {
       EC_SETINF(d);
       return (d);
     } else {
       ecctx *cc = (ecctx *)c;
-      dx = F_SQR(f, MP_NEW, a->x);
-      dx = F_TPL(f, dx, dx);
-      dx = F_ADD(f, dx, dx, cc->a);
-      dy = F_DBL(f, MP_NEW, a->y);
-      dy = F_INV(f, dy, dy);
+      dx = F_SQR(f, MP_NEW, a->x);	/* %$x_0^2$% */
+      dx = F_TPL(f, dx, dx);		/* %$3 x_0^2$% */
+      dx = F_ADD(f, dx, dx, cc->a);	/* %$3 x_0^2 + A$% */
+      dy = F_DBL(f, MP_NEW, a->y);	/* %$2 y_0$% */
+      dy = F_INV(f, dy, dy);		/* %$(2 y_0)^{-1}$% */
       lambda = F_MUL(f, MP_NEW, dx, dy);
+				    /* %$\lambda = (3 x_0^2 + A)/(2 y_0)$% */
     }
 
-    dx = F_SQR(f, dx, lambda);
-    dx = F_SUB(f, dx, dx, a->x);
-    dx = F_SUB(f, dx, dx, b->x);
-    dy = F_SUB(f, dy, b->x, dx);
-    dy = F_MUL(f, dy, lambda, dy);
-    dy = F_SUB(f, dy, dy, b->y);
+    dx = F_SQR(f, dx, lambda);		/* %$\lambda^2$% */
+    dx = F_SUB(f, dx, dx, a->x);	/* %$\lambda^2 - x_0$% */
+    dx = F_SUB(f, dx, dx, b->x);	/* %$x' = \lambda^2 - x_0 - x_1$% */
+    dy = F_SUB(f, dy, b->x, dx);	/* %$x_1 - x'$% */
+    dy = F_MUL(f, dy, lambda, dy);	/* %$\lambda (x_1 - x')$% */
+    dy = F_SUB(f, dy, dy, b->y);      /* %$y' = \lambda (x_1 - x') - y_1$% */
 
     EC_DESTROY(d);
     d->x = dx;
@@ -147,6 +269,98 @@ static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b)
   return (d);
 }
 
+static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b)
+{
+  if (a == b)
+    c->ops->dbl(c, d, a);
+  else if (EC_ATINF(a))
+    EC_COPY(d, b);
+  else if (EC_ATINF(b))
+    EC_COPY(d, a);
+  else {
+    field *f = c->f;
+    mp *p, *q, *r, *w, *u, *s, *dx, *dy, *dz;
+
+    q = F_SQR(f, MP_NEW, a->z);		/* %$z_0^2$% */
+    u = F_MUL(f, MP_NEW, q, b->x);	/* %$u = x_1 z_0^2$% */
+    p = F_MUL(f, MP_NEW, q, b->y);	/* %$y_1 z_0^2$% */
+    s = F_MUL(f, q, p, a->z);		/* %$s = y_1 z_0^3$% */
+
+    w = F_SUB(f, p, a->x, u);		/* %$w = x_0 - u$% */
+    r = F_SUB(f, MP_NEW, a->y, s);	/* %$r = y_0 - s$% */
+    if (F_ZEROP(f, w)) {
+      MP_DROP(w);
+      MP_DROP(u);
+      MP_DROP(s);
+      if (F_ZEROP(f, r)) {
+	MP_DROP(r);
+	return (c->ops->dbl(c, d, a));
+      } else {
+	MP_DROP(r);
+	EC_SETINF(d);
+	return (d);
+      }
+    }
+    u = F_ADD(f, u, u, a->x);		/* %$t = x_0 + u$% */
+    s = F_ADD(f, s, s, a->y);		/* %$m = y_0 + r$% */
+
+    dz = F_MUL(f, MP_NEW, a->z, w);	/* %$z' = z_0 w$% */
+
+    p = F_SQR(f, MP_NEW, w);		/* %$w^2$% */
+    q = F_MUL(f, MP_NEW, p, u);		/* %$t w^2$% */
+    u = F_MUL(f, u, p, w);		/* %$w^3$% */
+    p = F_MUL(f, p, u, s);		/* %$m w^3$% */
+    
+    dx = F_SQR(f, u, r);		/* %$r^2$% */
+    dx = F_SUB(f, dx, dx, q);		/* %$x' = r^2 - t w^2$% */
+
+    s = F_DBL(f, s, dx);		/* %$2 x'$% */
+    q = F_SUB(f, q, q, s);		/* %$v = t w^2 - 2 x'$% */
+    dy = F_MUL(f, s, q, r);		/* %$v r$% */
+    dy = F_SUB(f, dy, dy, p);		/* %$v r - m w^3$% */
+    dy = F_HLV(f, dy, dy);		/* %$y' = (v r - m w^3)/2$% */
+
+    EC_DESTROY(d);
+    d->x = dx;
+    d->y = dy;
+    d->z = dz;
+    MP_DROP(p);
+    MP_DROP(q);
+    MP_DROP(r);
+    MP_DROP(w);
+  }
+  return (d);
+}
+
+static int eccheck(ec_curve *c, const ec *p)
+{
+  ecctx *cc = (ecctx *)c;
+  field *f = c->f;
+  int rc;
+  mp *l = F_SQR(f, MP_NEW, p->y);
+  mp *x = F_SQR(f, MP_NEW, p->x);
+  mp *r = F_MUL(f, MP_NEW, x, p->x);
+  x = F_MUL(f, x, cc->a, p->x);
+  r = F_ADD(f, r, r, x);
+  r = F_ADD(f, r, r, cc->b);
+  rc = MP_EQ(l, r) ? 0 : -1;
+  mp_drop(l);
+  mp_drop(x);
+  mp_drop(r);
+  return (rc);
+}
+
+static int ecprojcheck(ec_curve *c, const ec *p)
+{
+  ec t = EC_INIT;
+  int rc;
+  
+  c->ops->fix(c, &t, p);
+  rc = eccheck(c, &t);
+  EC_DESTROY(&t);
+  return (rc);
+}
+
 static void ecdestroy(ec_curve *c)
 {
   ecctx *cc = (ecctx *)c;
@@ -157,7 +371,7 @@ static void ecdestroy(ec_curve *c)
 
 /* --- @ec_prime@, @ec_primeproj@ --- *
  *
- * Arguments:	@field *f@ = the underyling field for this elliptic curve
+ * Arguments:	@field *f@ = the underlying field for this elliptic curve
  *		@mp *a, *b@ = the coefficients for this curve
  *
  * Returns:	A pointer to the curve.
@@ -172,13 +386,42 @@ extern ec_curve *ec_prime(field *f, mp *a, mp *b)
   ecctx *cc = CREATE(ecctx);
   cc->c.ops = &ec_primeops;
   cc->c.f = f;
-  cc->a = MP_COPY(a);
-  cc->b = MP_COPY(b);
+  cc->a = F_IN(f, MP_NEW, a);
+  cc->b = F_IN(f, MP_NEW, b);
+  return (&cc->c);
+}
+
+extern ec_curve *ec_primeproj(field *f, mp *a, mp *b)
+{
+  ecctx *cc = CREATE(ecctx);
+  mp *ax;
+
+  ax = mp_add(MP_NEW, a, MP_THREE);
+  ax = F_IN(f, ax, ax);
+  if (F_ZEROP(f, ax))
+    cc->c.ops = &ec_primeprojxops;
+  else
+    cc->c.ops = &ec_primeprojops;
+  MP_DROP(ax);
+  cc->c.f = f;
+  cc->a = F_IN(f, MP_NEW, a);
+  cc->b = F_IN(f, MP_NEW, b);
   return (&cc->c);
 }
 
 static const ec_ops ec_primeops = {
-  ecdestroy, ec_idin, ec_idout, 0, ecneg, ecadd, ec_stdsub, ecdbl
+  ecdestroy, ec_idin, ec_idout, ec_idfix,
+  0, ecneg, ecadd, ec_stdsub, ecdbl, eccheck
+};
+
+static const ec_ops ec_primeprojops = {
+  ecdestroy, ec_projin, ec_projout, ec_projfix,
+  0, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
+};
+
+static const ec_ops ec_primeprojxops = {
+  ecdestroy, ec_projin, ec_projout, ec_projfix,
+  0, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck
 };
 
 /*----- Test rig ----------------------------------------------------------*/
@@ -187,33 +430,48 @@ static const ec_ops ec_primeops = {
 
 #define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
 
-int main(void)
+int main(int argc, char *argv[])
 {
   field *f;
   ec_curve *c;
   ec g = EC_INIT, d = EC_INIT;
   mp *p, *a, *b, *r;
+  int i, n = argc == 1 ? 1 : atoi(argv[1]);
 
+  printf("ec-prime: ");
+  fflush(stdout);
   a = MP(-3);
   b = MP(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1);
   p = MP(6277101735386680763835789423207666416083908700390324961279);
-  r = MP(6277101735386680763835789423176059013767194773182842284081);
+  r = MP(6277101735386680763835789423176059013767194773182842284080);
 
   f = field_prime(p);
-  c = ec_prime(f, a, b);
+  c = ec_primeproj(f, a, b);
   
   g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012);
   g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811);
 
-  ec_mul(c, &d, &g, r);
-  MP_PRINT("d.x", d.x);
-  MP_PRINT("d.y", d.y);
-
-  ec_destroy(&d);
+  for (i = 0; i < n; i++) { 
+    ec_mul(c, &d, &g, r);
+    if (EC_ATINF(&d)) {
+      fprintf(stderr, "zero too early\n");
+      return (1);
+    }
+    ec_add(c, &d, &d, &g);
+    if (!EC_ATINF(&d)) {
+      fprintf(stderr, "didn't reach zero\n");
+      MP_EPRINT("d.x", d.x);
+      MP_EPRINT("d.y", d.y);
+      return (1);
+    }
+    ec_destroy(&d);
+  }
   ec_destroy(&g);
   ec_destroycurve(c);
   F_DESTROY(f);
-
+  MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r);
+  assert(!mparena_count(&mparena_global));
+  printf("ok\n");
   return (0);
 }