Point.java

    public Point copy(){
        Point point = new Point(this.x,this.y,this.a,this.p);
        return point;
    }

    public Point inverse(){
        Point point = new Point(this.x,this.y.negate().mod(p),this.a,this.p);
        return point;
    }
    /*Point Operation*/
    //Addition (P + Q)
    public Point addition(Point q){
        if(this.isEqual(O)){
            return q;
        }else if(q.isEqual(O)){
            return this.copy();
        }else if(this.inverse().isEqual(q)){
            return O;
        }else if(this.isEqual(q)){
            return this.doubling();
        }else if(this.x.compareTo(q.getX()) == 0){
            return O;
        }else{
            BigInteger m = ((this.y.subtract(q.getY())).multiply((this.x.subtract(q.getX())).modInverse(p))).mod(p);  //Calculate the slope of line
            BigInteger x3 = (m.pow(2).subtract(this.x)).subtract(q.getX());
            BigInteger y3 = (m.multiply(this.x.subtract(x3))).subtract(this.y);
            Point rPoint = new Point(x3.mod(p),y3.mod(p),this.a,this.p);
            return rPoint;
        }
    }

    //Subtraction (P + (-Q))
    public Point substraction(Point q){
        Point rPoint = new Point();
        rPoint = this.addition(q.inverse());
        return rPoint;
    }

    //Doubling
    public Point doubling(){
        if(this.y.compareTo(BigInteger.ZERO) == 0){
            return O;
        }else{
            BigInteger m = ((this.x.pow(2).multiply(BigInteger.valueOf(3))).add(this.a)).multiply((this.y.multiply(BigInteger.valueOf(2))).modInverse(p));
            BigInteger x3 = (m.pow(2)).subtract(this.x.multiply(BigInteger.valueOf(2)));
            BigInteger y3 = (m.multiply(this.x.subtract(x3))).subtract(this.y);
            Point rPoint = new Point(x3.mod(p),y3.mod(p),this.a,this.p);
            return rPoint;
        }
    }

    //k multiplication
    public Point multiplication(BigInteger k){
        Point rPoint = new Point();
        if(k.compareTo(BigInteger.ZERO) == 0){
            return O;
        }else if(k.compareTo(BigInteger.ONE) == 0){
            return this.copy();
        }else if(k.mod(BigInteger.valueOf(2)).compareTo(BigInteger.ONE) == 0){
            rPoint = this.addition(this.multiplication(k.subtract(BigInteger.ONE)));
            return rPoint;
        }else{
            Point temp = this.doubling();
            rPoint = temp.multiplication(k.divide(BigInteger.valueOf(2)));
            return rPoint;
        }
    }