/* -*-apcalc-*-
*
- * $Id: ecp.cal,v 1.1 2000/10/08 16:01:37 mdw Exp $
+ * $Id: ecp.cal,v 1.2 2004/03/21 22:52:06 mdw Exp $
*
* Testbed for elliptic curve arithmetic over prime fields
*
/*----- Revision history --------------------------------------------------*
*
* $Log: ecp.cal,v $
+ * Revision 1.2 2004/03/21 22:52:06 mdw
+ * Merge and close elliptic curve branch.
+ *
+ * Revision 1.1.4.2 2004/03/20 00:13:31 mdw
+ * Projective coordinates for prime curves
+ *
+ * Revision 1.1.4.1 2003/06/10 13:43:53 mdw
+ * Simple (non-projective) curves over prime fields now seem to work.
+ *
* Revision 1.1 2000/10/08 16:01:37 mdw
* Prototypes of various bits of code.
*
obj ecp_curve { a, b, p };
obj ecp_pt { x, y, e };
+obj ecpp_pt { x, y, z, e };
/*----- Main code ---------------------------------------------------------*/
return (p);
}
+define ecpp_pt(p)
+{
+ local obj ecpp_pt pp;
+ if (istype(p, 1))
+ return (0);
+ pp.x = p.x;
+ pp.y = p.y;
+ pp.z = 1;
+ pp.e = p.e;
+ return (pp);
+}
+
+define ecpp_fix(pp)
+{
+ local obj ecp_pt p;
+ local e, zi, z2, z3;
+ if (istype(pp, 1) || pp.z == 0)
+ return (0);
+ e = pp.e;
+ zi = minv(pp.z, e.p);
+ z2 = zi * zi;
+ z3 = zi * z2;
+ p.x = pp.x * z2 % e.p;
+ p.y = pp.y * z3 % e.p;
+ p.e = e;
+ return (p);
+}
+
+define ecpp_dbl(a)
+{
+ local m, s, t, y2;
+ local e;
+ local obj ecpp_pt d;
+ if (istype(a, 1) || a.y == 0)
+ return (0);
+ e = a.e;
+ if (e.a % e.p == e.p - 3) {
+ m = a.z^3 % e.p;
+ m = 3 * (a.x + t4) * (a.x - t4) % e.p;
+ } else {
+ m = (3 * a.x^2 - e.a * a.z^4) % e.p;
+ }
+ d.z = 2 * a.y * a.z % e.p;
+ y2 = a.y^2 % e.p;
+ s = 4 * a.x * a.y % e.p;
+ d.x = (m^2 - 2 * s) % e.p;
+ d.y = (m * (s - d.x) - y * y2^2) % e.p;
+ d.e = e;
+ return (d);
+}
+
+define ecpp_add(a, b)
+{
+ if (a == 0)
+ d = b;
+ else if (b == 0)
+ d = a;
+ else if (!istype(a, b))
+ quit "bad type arguments to ecp_pt_add";
+ else if (a.e != b.e)
+ quit "points from different curves in ecp_pt_add";
+ else {
+ e = a.e;
+
+}
+
define ecp_pt_print(a)
{
print "(" : a.x : ", " : a.y : ")" :;
return (d);
}
+define ecp_pt_dbl(a)
+{
+ local e, alpha;
+ local obj ecp_pt d;
+ if (istype(a, 1))
+ return (0);
+ e = a.e;
+ alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p;
+ d.x = (alpha^2 - 2 * a.x) % e.p;
+ d.y = (-a.y + alpha * (a.x - d.x)) % e.p;
+ d.e = e;
+ return (d);
+}
+
define ecp_pt_neg(a)
{
local obj ecp_pt d;
return (d);
}
+define ecp_pt_check(a)
+{
+ local e;
+
+ e = a.e;
+ if (a.y^2 % e.p != (a.x^3 + e.a * a.x + e.b) % e.p)
+ quit "bad curve point";
+}
+
define ecp_pt_mul(a, b)
{
local p, n;
if (n & 1)
d += p;
n >>= 1;
- p += p;
+ p = ecp_pt_dbl(p);
}
return (d);
}
+/*----- FIPS186-2 standard curves -----------------------------------------*/
+
+p192 = ecp_curve(-3, 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1,
+ 6277101735386680763835789423207666416083908700390324961279);
+p192_r = 6277101735386680763835789423176059013767194773182842284081;
+p192_g = ecp_pt(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012,
+ 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p192);
+
/*----- That's all, folks -------------------------------------------------*/