ECPoint.java

package org.bouncycastle.math.ec;

import java.math.BigInteger;

/**
 * base class for points on elliptic curves.
 */
public abstract class ECPoint
{
    ECCurve        curve;
	ECFieldElement x;
	ECFieldElement y;

	protected ECPoint(ECCurve curve, ECFieldElement x, ECFieldElement y)
	{
        this.curve = curve;
		this.x = x;
		this.y = y;
	}
		
	public ECFieldElement getX()
	{
		return x;
	}

	public ECFieldElement getY()
	{
		return y;
	}

    public boolean equals(
        Object  other)
    {
        if ( other == this )
            return true;

        if ( !(other instanceof ECPoint) )
            return false;

        ECPoint o = (ECPoint)other;

        return x.equals(o.x) && y.equals(o.y);
    }

	public abstract byte[] getEncoded();

	public abstract ECPoint add(ECPoint b);
	public abstract ECPoint subtract(ECPoint b);
	public abstract ECPoint twice();
	public abstract ECPoint multiply(BigInteger b);

    /**
     * Elliptic curve points over Fp
     */
    public static class Fp extends ECPoint
    {
        public Fp(ECCurve curve, ECFieldElement x, ECFieldElement y)
        {
            super(curve, x, y);
        }

        /**
         * return the field element encoded with point compression. (S 4.3.6)
         */
        public byte[] getEncoded()
        {
            byte    PC;

            if (this.getY().toBigInteger().testBit(0))
            {
                PC = 0x02;
            }
            else
            {
                PC = 0x03;
            }

            byte[]  X = this.getX().toBigInteger().toByteArray();
            byte[]  PO = new byte[X.length + 1];

            PO[0] = PC;
            System.arraycopy(X, 0, PO, 1, X.length);

            return PO;
        }

        // B.3 pg 62
        public ECPoint add(ECPoint b)
        {
            ECFieldElement gamma = b.y.subtract(y).divide(b.x.subtract(x));

            ECFieldElement x3 = gamma.multiply(gamma).subtract(x).subtract(b.x);
            ECFieldElement y3 = gamma.multiply(x.subtract(x3)).subtract(y);

            return new ECPoint.Fp(curve, x3, y3);
        }

        // B.3 pg 62
        public ECPoint twice()
        {
            ECFieldElement TWO = curve.fromBigInteger(BigInteger.valueOf(2));
            ECFieldElement THREE = curve.fromBigInteger(BigInteger.valueOf(3));
            ECFieldElement gamma = x.multiply(x).multiply(THREE).add(curve.a).divide(y.multiply(TWO));

            ECFieldElement x3 = gamma.multiply(gamma).subtract(x.multiply(TWO));
            ECFieldElement y3 = gamma.multiply(x.subtract(x3)).subtract(y);
                
            return new ECPoint.Fp(curve, x3, y3);
        }

        // D.3.2 pg 102 (see Note:)
        public ECPoint subtract(ECPoint p2)
        {
            return add(new ECPoint.Fp(curve, p2.x, p2.y.negate()));
        }

        // D.3.2 pg 101
        public ECPoint multiply(BigInteger k)
        {
            // BigInteger e = k.mod(n); // n == order this
            BigInteger e = k;

            BigInteger h = e.multiply(BigInteger.valueOf(3));

            ECPoint R = this;

            for (int i = h.bitLength() - 2; i > 0; i--)
            {             
                R = R.twice();       

                if ( h.testBit(i) && !e.testBit(i) )
                {                    
                    //System.out.print("+");
                    R = R.add(this);
                }
                else if ( !h.testBit(i) && e.testBit(i) )
                {
                    //System.out.print("-");
                    R = R.subtract(this);
                }
                // else
                // System.out.print(".");
            }
            // System.out.println();

            return R;
        }
    }
}