public static EllipticCurvePoint addPoints(EllipticCurve curve, EllipticCurvePoint point1, EllipticCurvePoint point2)
{
BigInteger xResult = calculateX(curve, point1, point2);
return(new EllipticCurvePoint {
x = xResult, y = calculateY(curve, point1, point2, xResult)
});
}
public static EllipticCurvePoint doublePoint(EllipticCurve curve, EllipticCurvePoint point)
{
BigInteger xResult = calculateX(curve, point);
return(new EllipticCurvePoint {
x = xResult, y = calculateY(curve, point, xResult)
});
}
private static BigInteger calculateYDenominator(EllipticCurve curve, EllipticCurvePoint point)
{
BigInteger yDenominator = 2 * point.y;
return(ModulusLogic.inverseModuloN(ModulusLogic.convertToModulus(yDenominator, curve.n), curve.n));
}
private static BigInteger calculateYNumerator(EllipticCurve curve, EllipticCurvePoint point, BigInteger xResult)
{
BigInteger yNumerator = (3 * point.x * point.x + curve.a) * (point.x - xResult) - 2 * point.y * point.y;
return(ModulusLogic.convertToModulus(yNumerator, curve.n));
}
/*---------------------------------------------------------------------------------------------------------------------------
* Y
* ---------------------------------------------------------------------------------------------------------------------------*/
private static BigInteger calculateY(EllipticCurve curve, EllipticCurvePoint point, BigInteger xResult)
{
return(ModulusLogic.convertToModulus(calculateYNumerator(curve, point, xResult) * calculateYDenominator(curve, point), curve.n));
}
private static BigInteger calculateXNumerator(EllipticCurve curve, EllipticCurvePoint point)
{
BigInteger xNumerator = 9 * point.x * point.x * point.x * point.x + 6 * curve.a * point.x * point.x + curve.a * curve.a - 8 * point.x * point.y * point.y;
return(ModulusLogic.convertToModulus(xNumerator, curve.n));
}
/*---------------------------------------------------------------------------------------------------------------------------
* X
* ---------------------------------------------------------------------------------------------------------------------------*/
private static BigInteger calculateX(EllipticCurve curve, EllipticCurvePoint point)
{
return(ModulusLogic.convertToModulus((calculateXNumerator(curve, point) * calculateXDenominator(curve, point)), curve.n));
}
private static BigInteger calculateYNumerator(EllipticCurve curve, EllipticCurvePoint point1, EllipticCurvePoint point2, BigInteger xResult)
{
BigInteger yNumerator = (point2.y - point1.y) * (point1.x - xResult) - point1.y * (point2.x - point1.x);
return(ModulusLogic.convertToModulus(yNumerator, curve.n));
}
private static BigInteger calculateXDenominator(EllipticCurve curve, EllipticCurvePoint point1, EllipticCurvePoint point2)
{
BigInteger xDenominator = (point2.x - point1.x) * (point2.x - point1.x);
return(ModulusLogic.inverseModuloN(ModulusLogic.convertToModulus(xDenominator, curve.n), curve.n));
}
private static BigInteger calculateXNumerator(EllipticCurve curve, EllipticCurvePoint point1, EllipticCurvePoint point2)
{
BigInteger xNumerator = (point2.y - point1.y) * (point2.y - point1.y) - (point1.x + point2.x) * (point2.x - point1.x) * (point2.x - point1.x);
return(ModulusLogic.convertToModulus(xNumerator, curve.n));
}
public static EllipticCurvePoint calculatePublicKey(BigInteger prk, EllipticCurve curve)
{
return(PointMultiplication.multiplyPoint(prk, curve.G, curve));
}
public static EllipticCurvePoint calculateMasterKey(BigInteger prk, EllipticCurvePoint theirPublicKey, EllipticCurve curve)
{
return(PointAddition.addPoints(curve, theirPublicKey, PointMultiplication.multiplyPoint(prk, curve.G, curve)));
}