Ejemplo n.º 1
0
        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));
        }
Ejemplo n.º 2
0
        //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;
        }
Ejemplo n.º 3
0
        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));
        }
Ejemplo n.º 4
0
        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);
        }
Ejemplo n.º 5
0
        // 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));
        }
Ejemplo n.º 6
0
        //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);
        }
Ejemplo n.º 7
0
        //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));
        }
Ejemplo n.º 8
0
        //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;
        }
Ejemplo n.º 9
0
 private JacobPoint Negate(JacobPoint p)
 {
     return(new JacobPoint(p.X, (BigInt)this.field.Negate(p.Y), p.Z));
 }