/*---------------------------------------------------------------------------------------------------------------------------
X
---------------------------------------------------------------------------------------------------------------------------*/
private static BigInteger calculateX(EllipticCurve curve, EllipticCurvePoint point)
{
return ModulusLogic.convertToModulus(
(calculateXNumerator(curve, point) * calculateXDenominator(curve, point)),
curve.n
);
}
private static BigInteger calculateXDenominator(EllipticCurve curve, EllipticCurvePoint point)
{
BigInteger xDenominator = 4 * point.y * point.y;
return ModulusLogic.inverseModuloN(
ModulusLogic.convertToModulus(xDenominator, curve.n),
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);
}
public static bool verifyMessage(Signature signature, string message, EllipticCurvePoint publicKey, EllipticCurve theCurve)
{
//step 2+3
BigInteger z = Common.computeZ(Common.getHash(message), theCurve);
//step 4
BigInteger u1 = ModulusLogic.convertToModulus(z * ModulusLogic.inverseModuloN(signature.s, theCurve.p), theCurve.p);
BigInteger u2 = ModulusLogic.convertToModulus(signature.r * ModulusLogic.inverseModuloN(signature.s, theCurve.p), theCurve.p);
//step 5
return(getPoint(u1, u2, publicKey, theCurve).x == signature.r);
}
//step 6
private static BigInteger calculateS(BigInteger privateKey, BigInteger k, BigInteger z, BigInteger r, EllipticCurve theCurve)
{
BigInteger inverseK = ModulusLogic.inverseModuloN(k, theCurve.p);
return(ModulusLogic.convertToModulus(inverseK * (z + (r * privateKey)), theCurve.p));
}
private static BigInteger calculateYDenominator(EllipticCurve curve, EllipticCurvePoint point1, EllipticCurvePoint point2)
{
BigInteger yDenominator = point2.x - point1.x;
return(ModulusLogic.inverseModuloN(ModulusLogic.convertToModulus(yDenominator, curve.n), 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));
}
/*---------------------------------------------------------------------------------------------------------------------------
* Y
* ---------------------------------------------------------------------------------------------------------------------------*/
private static BigInteger calculateY(EllipticCurve curve, EllipticCurvePoint point1, EllipticCurvePoint point2, BigInteger xResult)
{
return(ModulusLogic.convertToModulus(calculateYNumerator(curve, point1, point2, xResult) * calculateYDenominator(curve, point1, point2), 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));
}
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));
}