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;
}
}
/**
* Elliptic curve points over Fp
*/
public static class F2m extends ECPoint
{
/**
* @param curve
* @param x
* @param y
*/
protected F2m(ECCurve curve, ECFieldElement x, ECFieldElement y)
{
super(curve, x, y);
}
/* (non-Javadoc)
* @see org.bouncycastle.math.ec.ECPoint#getEncoded()
*/
public byte[] getEncoded()
{
// TODO Auto-generated method stub
return null;
}
/* (non-Javadoc)
* @see org.bouncycastle.math.ec.ECPoint#add(org.bouncycastle.math.ec.ECPoint)
*/
public ECPoint add(ECPoint b)
{
// TODO Auto-generated method stub
return null;
}
/* (non-Javadoc)
* @see org.bouncycastle.math.ec.ECPoint#subtract(org.bouncycastle.math.ec.ECPoint)
*/
public ECPoint subtract(ECPoint b)
{
// TODO Auto-generated method stub
return null;
}
/* (non-Javadoc)
* @see org.bouncycastle.math.ec.ECPoint#twice()
*/
public ECPoint twice()
{
// TODO Auto-generated method stub
return null;
}
/* (non-Javadoc)
* @see org.bouncycastle.math.ec.ECPoint#multiply(java.math.BigInteger)
*/
public ECPoint multiply(BigInteger b)
{
// TODO Auto-generated method stub
return null;
}
}
}