public FieldElement Compute(Point P, Point Q)
{
FieldElement f = new Complex((Fp)this.field, BigInt.ONE);
JacobPoint V = this.ec.AToJ(P);
BigInt n = this.order.Subtract(BigInt.ONE);
Point nP = ec.Negate(P);
//byte[] ba =n.toByteArray();
sbyte[] r = Naf(this.order, (byte)2);
//Point T;
//BigInt [] lamda= new BigInt[1];;
FieldElement u;
for (int i = r.Length - 2; i >= 0; i--)
{
u = EncDbl(V, Q);
//f=f.square().multiply(u);
f = this.gt.Multiply(this.gt.Square(f), u);
if (r[i] == 1)
{
u = EncAdd(V, P, Q);
f = this.gt.Multiply(f, u);
}
if (r[i] == -1) //this is probably going to fail!
{
u = EncAdd(V, nP, Q);
f = this.gt.Multiply(f, u);
}
}
f = ((Complex)f).Conjugate().Divide((Complex)f);
return(this.gt.Pow(f, this.finalExponent));
}
//add two point, save result in the first argument
public void JAddMut(JacobPoint P, Point Q)
{
if (P.IsInfinity())
{
P.X = (BigInt)Q.X;
P.Y = (BigInt)Q.Y;
P.Z = (BigInt)this.field.GetOne();
return;
}
if (Q.IsInfinity())
{
return;
}
FieldElement x1 = P.X;
FieldElement y1 = P.Y;
FieldElement z1 = P.Z;
FieldElement x = Q.X;
FieldElement y = Q.Y;
//t1=z1^2
FieldElement t1 = this.field.Square(z1);
//t2=z1t1
FieldElement t2 = this.field.Multiply(z1, t1);
//t3=xt1
FieldElement t3 = this.field.Multiply(x, t1);
//t4=Yt2
FieldElement t4 = this.field.Multiply(y, t2);
//t5=t3-x1
FieldElement t5 = this.field.Subtract(t3, x1);
//t6=t4-y1
FieldElement t6 = this.field.Subtract(t4, y1);
//t7=t5^2
FieldElement t7 = this.field.Square(t5);
//t8=t5t7
FieldElement t8 = this.field.Multiply(t5, t7);
//t9=x1t7
FieldElement t9 = this.field.Multiply(x1, t7);
//x3=t6^2-(t8+2t9)
FieldElement x3 = this.field.Square(t6);
x3 = this.field.Subtract(x3, this.field.Add(t8, this.field.Add(t9, t9)));
//y3=t6(t9-x3)-y1t8
FieldElement y3 = this.field.Multiply(t6, this.field.Subtract(t9, x3));
y3 = this.field.Subtract(y3, this.field.Multiply(y1, t8));
//z3=z1t5
FieldElement z3 = this.field.Multiply(z1, t5);
P.X = (BigInt)x3;
P.Y = (BigInt)y3;
P.Z = (BigInt)z3;
return;
}
public Complex EncAdd(JacobPoint A, Point P, Point Q)
{
BigInt x1 = A.X;
BigInt y1 = A.Y;
BigInt z1 = A.Z;
FieldElement x = P.X;
FieldElement y = P.Y;
//t1=z1^2
FieldElement t1 = this.field.Square(z1);
//t2=z1t1
FieldElement t2 = this.field.Multiply(z1, t1);
//t3=xt1
FieldElement t3 = this.field.Multiply(x, t1);
//t4=Yt2
FieldElement t4 = this.field.Multiply(y, t2);
//t5=t3-x1
FieldElement t5 = this.field.Subtract(t3, x1);
//t6=t4-y1
FieldElement t6 = this.field.Subtract(t4, y1);
//t7=t5^2
FieldElement t7 = this.field.Square(t5);
//t8=t5t7
FieldElement t8 = this.field.Multiply(t5, t7);
//t9=x1t7
FieldElement t9 = this.field.Multiply(x1, t7);
//x3=t6^2-(t8+2t9)
FieldElement x3 = this.field.Square(t6);
x3 = this.field.Subtract(x3, this.field.Add(t8, this.field.Add(t9, t9)));
//y3=t6(t9-x3)-y1t8
FieldElement y3 = this.field.Multiply(t6, this.field.Subtract(t9, x3));
y3 = this.field.Subtract(y3, this.field.Multiply(y1, t8));
//z3=z1t5
FieldElement z3 = this.field.Multiply(z1, t5);
A.X = (BigInt)x3;
A.Y = (BigInt)y3;
A.Z = (BigInt)z3;
//z3yqi -(z3Y-t6(xq+x))
FieldElement imag = this.field.Multiply(z3, Q.Y);
FieldElement real = this.field.Add(Q.X, x);
real = this.field.Multiply(real, t6);
real = this.field.Subtract(real, this.field.Multiply(z3, y));
return(new Complex((Fp)this.field, (BigInt)real, (BigInt)imag));
}
public override bool Equals(Object obj)
{ //this could fail
if (this == obj)
{
return(true);
}
if (obj == null)
{
return(false);
}
//if ( != obj.getClass())
// return false;
JacobPoint other = (JacobPoint)obj;
if (x == null)
{
if (other.x != null)
{
return(false);
}
}
else if (!x.Equals(other.x))
{
return(false);
}
if (y == null)
{
if (other.y != null)
{
return(false);
}
}
else if (!y.Equals(other.y))
{
return(false);
}
if (z == null)
{
if (other.z != null)
{
return(false);
}
}
else if (!z.Equals(other.z))
{
return(false);
}
return(true);
}
// convert Jacobian to Affine
public Point JToA(JacobPoint P)
{
if (P.IsInfinity())
{
return(Point.INFINITY);
}
FieldElement bi = P.Z;
FieldElement zInverse = this.field.Inverse(P.Z);
FieldElement square = this.field.Square(zInverse);
//x =X/Z^2
FieldElement x = this.field.Multiply(P.X, square);
//y=Y/Z^3
FieldElement y = this.field.Multiply(P.Y, this.field.Multiply(square, zInverse));
return(new Point(x, y));
}
//multiplication using Jacobian coordinates
public JacobPoint JMultiplyMut(Point p, BigInt k)
{
if (!(this.field.IsValidElement(p.X)) || !(this.field.IsValidElement(p.Y)))
{
throw new ArgumentException("The input point must be taken over the field.");
}
if (p.IsInfinity())
{
return(this.AToJ(p));
}
if (k.Equals(BigInt.ZERO))
{
return(JacobPoint.INFINITY);
}
if (k.Equals(BigInt.ONE))
{
return(this.AToJ(p));
}
if (k.Signum() == -1)
{
k = k.Abs();
p = this.Negate(p);
}
//byte [] ba =k.toByteArray();
int degree = k.BitLength() - 2;
JacobPoint result = this.AToJ(p);
for (int i = degree; i >= 0; i--)
{
this.JDblMut(result);
if (k.TestBit(i)) ///AQUI TE QUEDASTE IMPLEMENTAR TESTBIT
{
this.JAddMut(result, p);
}
}
return(result);
}
//used by tate pairing, point doubling in Jacobian coordinates, and return the value of f
public Complex EncDbl(JacobPoint P, Point Q)
{
//if(P.isInfinity())
// return;
BigInt x = P.X;
BigInt y = P.Y;
BigInt z = P.Z;
//t1=y^2
FieldElement t1 = this.field.Square(y);
//t2=4xt1
FieldElement t2 = this.field.Multiply(x, t1);
//t2=this.field.multiply(t2, 4);
t2 = this.field.Add(t2, t2);
t2 = this.field.Add(t2, t2);
//t3=8t1^2
FieldElement t3 = this.field.Square(t1);
//t3 = this.field.multiply(t3, 8);
t3 = this.field.Add(t3, t3);
t3 = this.field.Add(t3, t3);
t3 = this.field.Add(t3, t3);
//t4=z^2
FieldElement t4 = this.field.Square(z);
FieldElement t5;
//if a==-3
if (this.ec.Opt)
{
t5 = this.field.Multiply(this.field.Subtract(x, t4), this.field.Add(x, t4));
t5 = this.field.Add(t5, this.field.Add(t5, t5));
}
else
{
//t5=3x^2+aZ^4
t5 = this.field.Square(x);
t5 = this.field.Add(t5, this.field.Add(t5, t5));
t5 = this.field.Add(t5, this.field.Multiply(this.ec.A4, this.field.Square(t4)));
// FieldElement temp =this.field.square(this.field.square(z));
// temp=this.field.multiply(this.ec.getA4(), temp);
//
// t5=this.field.add(t5,temp);
}
//x3=t5^2-2t2
FieldElement x3 = this.field.Square(t5);
x3 = this.field.Subtract(x3, this.field.Add(t2, t2));
//y3=t5(t2-x3)-t3
FieldElement y3 = this.field.Multiply(t5, this.field.Subtract(t2, x3));
y3 = this.field.Subtract(y3, t3);
//z3=2y1z1
FieldElement z3 = this.field.Multiply(y, z);
z3 = this.field.Add(z3, z3);
P.X = (BigInt)x3;
P.Y = (BigInt)y3;
P.Z = (BigInt)z3;
//Z3t4yQi-(2t1-t5(t4Xq+x1))
FieldElement real = this.field.Multiply(t4, Q.X);
real = this.field.Add(real, x);
real = this.field.Multiply(t5, real);
real = this.field.Subtract(real, t1);
real = this.field.Subtract(real, t1);
FieldElement imag = this.field.Multiply(z3, t4);
imag = this.field.Multiply(imag, Q.Y);
return(new Complex((Fp)this.field, (BigInt)real, (BigInt)imag));
}
//point doubling in Jacobian coordinates, result is saving in the input point
public void JDblMut(JacobPoint P)
{
if (P.IsInfinity())
{
return;
}
BigInt x = P.X;
BigInt y = P.Y;
BigInt z = P.Z;
//t1=y^2
FieldElement t1 = this.field.Square(y);
//t2=4xt1
FieldElement t2 = this.field.Multiply(x, t1);
//t2=this.field.multiply(t2, 4);
t2 = this.field.Add(t2, t2);
t2 = this.field.Add(t2, t2);
//t3=8t1^2
FieldElement t3 = this.field.Square(t1);
//t3 = this.field.multiply(t3, 8);
t3 = this.field.Add(t3, t3);
t3 = this.field.Add(t3, t3);
t3 = this.field.Add(t3, t3);
//t4=z^2
FieldElement t4 = this.field.Square(z);
FieldElement t5;
//if a==-3
if (opt)
{
t5 = this.field.Multiply(this.field.Subtract(x, t4), this.field.Add(x, t4));
t5 = this.field.Add(t5, this.field.Add(t5, t5));
}
else
{
//t5=3x^2+aZ^4 =3x^2+at4^2
t5 = this.field.Square(x);
t5 = this.field.Add(t5, this.field.Add(t5, t5));
t5 = this.field.Add(t5, this.field.Multiply(this.A4, this.field.Square(t4)));
}
//x3=t5^2-2t2
FieldElement x3 = this.field.Square(t5);
x3 = this.field.Subtract(x3, this.field.Add(t2, t2));
//y3=t5(t2-x3)-t3
FieldElement y3 = this.field.Multiply(t5, this.field.Subtract(t2, x3));
y3 = this.field.Subtract(y3, t3);
//z3=2y1z1
FieldElement z3 = this.field.Multiply(y, z);
z3 = this.field.Add(z3, z3);
P.X = (BigInt)x3;
P.Y = (BigInt)y3;
P.Z = (BigInt)z3;
return;
}
private JacobPoint Negate(JacobPoint p)
{
return(new JacobPoint(p.X, (BigInt)this.field.Negate(p.Y), p.Z));
}