EllipticCurve.java

//package ecc.elliptic;

/**An implementation of an elliptic curve over a -finite- field.
 *
*/
import java.io.*;
import java.math.BigInteger;

public class EllipticCurve {

    private BigInteger a, b, p, order;
    private ECPoint generator;
    public BigInteger ppodbf;
    private int pointcmpsize;
    private String name;

    public static final BigInteger COEFA = new BigInteger("4");
    public static final BigInteger COEFB = new BigInteger("27");
    public static final int PRIMESECURITY = 500;

    /** Constructs an elliptic curve over the finite field of 'mod' elements.
     *The equation of the curve is on the form : y^2 = x^3 + ax + b.
     *@param a the value of 'a' where y^2 = x^3 + ax + b
     *@param b the value of 'b' where y^2 = x^3 + ax + b
     *@param mod The number of elements in the field. 
     IMPORTANT: Must a prime number!
    *@exception InsecureCurveException if the curve defined by a and b are singular, 
    *supersingular, trace one/anomalous. 
    *This ensures well defined operations and security.*/
    public EllipticCurve(BigInteger a, BigInteger b, BigInteger p) throws InsecureCurveException {

	this.a = a;
	this.b = b;
	this.p = p;
	if (!p.isProbablePrime(PRIMESECURITY)) {
	    //System.out.println("THIS CANNOT HAPPEN!!! "+p+" is not a prime!");
	    //throw new InsecureCurveException(InsecureCurveException.NONPRIMEMODULUS,this);
	}
	if (isSingular()) throw new InsecureCurveException(InsecureCurveException.SINGULAR, this);
	
	byte[] pb = p.toByteArray();
	if(pb[0] == 0) pointcmpsize = pb.length;
	else pointcmpsize = pb.length + 1;
	//ppodbf = (p.add(BigInteger.ONE)).shiftRight(2);
	name = "";


	//FIXME compute the order of the group
	//FIXME compute a generator for the group
    }

    public EllipticCurve(ECParameters ecp) throws InsecureCurveException {
	this(ecp.a(),ecp.b(),ecp.p());
	order = ecp.order();
	name = ecp.toString();
	try{
	    generator = new ECPoint(this, ecp.generatorX(), ecp.generatorY());
	    generator.fastCache();
	}
	catch (NotOnMotherException e){
	    System.out.println("Error defining EllipticCurve: generator not on mother!");
	}
    }

    public void writeCurve(DataOutputStream output) throws IOException {
	byte[] ab = a.toByteArray();
	output.writeInt(ab.length);
	output.write(ab);
	byte[] bb = b.toByteArray();
	output.writeInt(bb.length);
	output.write(bb);
	byte[] pb = p.toByteArray();
	output.writeInt(pb.length);
	output.write(pb);
	byte[] ob = order.toByteArray();
	output.writeInt(ob.length);
	output.write(ob);
	byte[] gb = generator.compress();
	output.writeInt(gb.length);
	output.write(gb);
	byte[] ppb = getPPODBF().toByteArray();
	output.writeInt(ppb.length);
	output.write(ppb);
	output.writeInt(pointcmpsize);
	output.writeUTF(name);
    }

    protected EllipticCurve(DataInputStream input) throws IOException {
	byte[] ab = new byte[input.readInt()];
	input.read(ab);
	a = new BigInteger(ab);
	byte[] bb = new byte[input.readInt()];
	input.read(bb);
	b = new BigInteger(bb);
	byte[] pb = new byte[input.readInt()];
	input.read(pb);
	p = new BigInteger(pb);
	byte[] ob = new byte[input.readInt()];
	input.read(ob);
	order = new BigInteger(ob);
	byte[] gb = new byte[input.readInt()];
	input.read(gb);
	generator = new ECPoint(gb, this);
	byte[] ppb = new byte[input.readInt()];
	input.read(ppb);
	ppodbf = new BigInteger(ppb);
	pointcmpsize = input.readInt();
	name = input.readUTF();
	generator.fastCache();
    }

    public boolean isSingular(){

	BigInteger aa = a.pow(3);
	BigInteger bb = b.pow(2);

	BigInteger result = ((aa.multiply(COEFA)).add(bb.multiply(COEFB) ) ).mod(p);

	if ( result.compareTo(BigInteger.ZERO) == 0 ) return true;
	else return false;

    }

    //FIXME!!!!!!!!!!
    public BigInteger calculateOrder(){
	return null;
    }

    //FIXME!!!!!!!!
    public ECPoint calculateGenerator(){
	return null;
    }

    public boolean onCurve(ECPoint q){

	if (q.isZero()) return true;
	BigInteger y_square = (q.gety()).modPow(new BigInteger("2"),p);
	BigInteger x_cube = (q.getx()).modPow(new BigInteger("3"),p);
	BigInteger x = q.getx();

	BigInteger dum = ((x_cube.add(a.multiply(x))).add(b)).mod(p);
			      
	if (y_square.compareTo(dum) == 0) return true;
	else return false;

    }

    /** Returns the order of the group */
    public BigInteger getOrder(){
	return order;
    }

    public ECPoint getZero(){
	return new ECPoint(this);
    }

    public BigInteger geta(){
	return a;
    }

    public BigInteger getb(){
	return b;
    }

    public BigInteger getp(){
	return p;
    }

    public int getPCS() {
	return pointcmpsize;
    }

    /** Returns a generator for this EllipticCurve.*/
    public ECPoint getGenerator(){
	return generator;
    }

    public String toString(){
	if (name == null) return "y^2 = x^3 + "  + a + "x + " + b + " ( mod " + p + " )";
	else if (name.equals("")) return "y^2 = x^3 + "  + a + "x + " + b + " ( mod " + p + " )";
	else return name;
    }

    public BigInteger getPPODBF(){
	if(ppodbf == null) {
	    ppodbf = p.add(BigInteger.ONE).shiftRight(2);
	}
	return ppodbf;
    }
}