public static BigPoint addPoint(BigPoint left, BigPoint right) {
if (left == right.getNegativePoint())
throw new IllegalArgumentException("Für Punktaddition von P und Q muss P != -Q sein!");
BigInteger s = BigInteger.ZERO, xR, yR;
// s = (Y_P - Y_Q) / (X_P - X_Q) mod p = (Y_P - Y_Q) * (X_P - X_Q)^-1
// mod p
s =
left.Y
.subtract(right.Y)
.multiply(
ECCField.GetInverseValue(
left.X.subtract(right.X), Configuration._ellipticCurveParamP))
.mod(Configuration._ellipticCurveParamP);
// -> Berechnungen aufgedröselt:
// BigInteger s1, s2, s3, s4, s5;
// s1 = BigInteger.Subtract(left.Y, right.Y);
// s2 = BigInteger.Subtract(left.X, right.X);
// s3 = GetInverseValue(s2, Configuration._ellipticCurveParamP);
// s4 = BigInteger.Multiply(s1, s3);
// s5 = BigInteger.ModPow(s4, 1, Configuration._ellipticCurveParamP);
// s = s5;
// Normalisieren
if (s.compareTo(BigInteger.ZERO) < 0) s = s.add(Configuration._ellipticCurveParamP);
xR =
s.modPow(new BigInteger("2"), Configuration._ellipticCurveParamP)
.subtract(left.X)
.subtract(right.X)
.mod(Configuration._ellipticCurveParamP);
// Normalisieren
if (xR.compareTo(BigInteger.ZERO) < 0) xR = xR.add(Configuration._ellipticCurveParamP);
yR =
left.Y
.negate()
.add(s.multiply(left.X.subtract(xR)))
.mod(Configuration._ellipticCurveParamP);
// Normalisieren
if (yR.compareTo(BigInteger.ZERO) < 0) yR = yR.add(Configuration._ellipticCurveParamP);
return new BigPoint(xR, yR);
}
public static boolean equals(BigPoint left, BigPoint right) {
return ((left.X.compareTo(right.X) == 0) && (left.Y.abs().compareTo(right.Y.abs())) == 0);
}