internal FPoint AddS(FPoint b)
{
if (this.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
FieldElement x2 = (FieldElement)b.X;
FieldElement y2 = (FieldElement)b.Y;
if (this.x.Equals(x2))
{
if (this.y.Equals(y2))
{
return((FPoint)this.Twice());
}
return((FPoint)this.curve.Infinity);
}
ECFieldElement xSum = this.x.Add(x2);
FieldElement lambda = (FieldElement)(this.y.Add(y2)).Divide(xSum);
FieldElement x3 = (FieldElement)lambda.Square().Add(lambda).Add(xSum).Add(this.curve.A);
FieldElement y3 = (FieldElement)lambda.Multiply(this.x.Add(x3)).Add(x3).Add(this.y);
return(new FPoint(curve, x3, y3));
}
static void Main(string[] args)
{
int m = 163;
int k1 = 3;
int k2 = 6;
int k3 = 7;
var a = new BigInteger("1", 16);
var b = new BigInteger("5FF6108462A2DC8210AB403925E638A19C1455D21", 16);
var n = new BigInteger("400000000000000000002BEC12BE2262D39BCF14D", 16);
//var basePoint = computeBasePoint();
var x = new BigInteger("72D867F93A93AC27DF9FF01AFFE74885C8C540420", 16);
var y = new BigInteger("0224A9C3947852B97C5599D5F4AB81122ADC3FD9B", 16);
//var x = basePoint.X.ToBigInteger();
//var y = basePoint.Y.ToBigInteger();
var curve = new FCurve(m, k1, k2, k3, a, b);
var x_element = new FieldElement(m, k1, k2, k3, x);
var y_element = new FieldElement(m, k1, k2, k3, y);
var P = new FPoint(curve, x_element, y_element);
var d = getRandom();
var Q = (FPoint)P.Multiply(d).Negate();
Console.WriteLine("Q (x, y) = ({0}, {1})", Q.X.ToBigInteger().ToString(16), Q.Y.ToBigInteger().ToString(16));
var M = new BigInteger("1263612ABD726", 16);
var e = getRandom();
var eP = P.Multiply(e);
Console.WriteLine("eP (x, y) = ({0}, {1})", eP.X.ToBigInteger().ToString(16), eP.Y.ToBigInteger().ToString(16));
var F_e = eP.X.ToBigInteger();
Console.WriteLine("F_e = {0}", F_e.ToString(16));
var M_temp = new FieldElement(m, k1, k2, k3, M);
var F_temp = new FieldElement(m, k1, k2, k3, F_e);
ECFieldElement y_temp = M_temp.Multiply(F_temp);
var r = y_temp.ToBigInteger();
Console.WriteLine("y = {0}", r.ToString(16));
var s = (e.Add(d.Multiply(r))).Remainder(n);
Console.WriteLine("s = {0}", s.ToString(16));
// Validation
var R = P.Multiply(s).Add(Q.Multiply(r));
Console.WriteLine("R (x, y) = ({0}, {1})", R.X.ToBigInteger().ToString(16), R.Y.ToBigInteger().ToString(16));
var M2 = new FieldElement(m, k1, k2, k3, M);
var R_x = new FieldElement(m, k1, k2, k3, R.X.ToBigInteger());
var y2 = M2.Multiply(R_x);
Console.WriteLine("y2 = {0}", y_temp.ToBigInteger().ToString(16));
}
static FPoint computeRandomPoint()
{
int m = 163;
int k1 = 3;
int k2 = 6;
int k3 = 7;
var a = new BigInteger("1", 16);
var b = new BigInteger("5FF6108462A2DC8210AB403925E638A19C1455D21", 16);
var curve = new FCurve(m, k1, k2, k3, a, b);
BigInteger u = getRandom();
var u_element = new FieldElement(m, k1, k2, k3, u);
var a_element = new FieldElement(m, k1, k2, k3, a);
var b_element = new FieldElement(m, k1, k2, k3, b);
var au = u_element.Multiply(u_element).Multiply(a_element);
var w = u_element.Multiply(u_element).Multiply(u_element).Add(au).Add(b_element);
var z = quadraticEquation(u_element.ToBigInteger(), w.ToBigInteger());
var point = new FPoint(curve, u_element, z);
return(point);
}
static FieldElement quadraticEquation(BigInteger u, BigInteger w)
{
int m = 163;
int k1 = 3;
int k2 = 6;
int k3 = 7;
var w1 = new FieldElement(m, k1, k2, k3, w);
var u1 = new FieldElement(m, k1, k2, k3, u);
var u2 = u1.Invert().Square();
var v = (FieldElement)w1.Multiply(u2);
var tr = trace(v);
var t = halfTrace(v);
var z = (FieldElement)t.Multiply(u1);
return(z);
}