static FieldElement halfTrace(FieldElement x)
{
int m = 163;
FieldElement t = x;
for (int i = 1; i <= ((m - 1) / 2); i++)
{
t = (FieldElement)t.Square().Square().Add(x);
}
return(t);
}
static FieldElement trace(FieldElement x)
{
int m = 163;
FieldElement t = x;
for (int i = 1; i < m; i++)
{
t = (FieldElement)t.Square().Add(x);
}
return(t);
}
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);
}
public override bool Equals(
object obj)
{
if (obj == this)
{
return(true);
}
FieldElement other = obj as FieldElement;
if (other == null)
{
return(false);
}
return(Equals(other));
}
public override ECPoint Twice()
{
if (this.IsInfinity)
{
return(this);
}
if (this.x.ToBigInteger().SignValue == 0)
{
return(this.curve.Infinity);
}
FieldElement bX2 = (FieldElement)x.Invert().Square().Multiply(this.curve.B);
FieldElement x2 = (FieldElement)x.Square().Add(bX2);
FieldElement ydX = (FieldElement)x.Invert().Multiply(y);
FieldElement by2 = (FieldElement)x.Add(ydX).Multiply(x2);
FieldElement y2 = (FieldElement)x.Square().Add(by2).Add(x2);
return(new FPoint(this.curve, x2, y2));
}
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);
}