public static FpVector3 <Fp12> Twist(FpVector3 <Fp2> point)
{
// If the point isn't properly initialize
if (point == null)
{
return(null);
}
// Place the items at the start and half way point
BigInteger[] xcoefficients = new BigInteger[12] {
point.X.Coefficients.ElementAt(0) - (point.X.Coefficients.ElementAt(1) * 9), 0, 0, 0, 0, 0, point.X.Coefficients.ElementAt(1), 0, 0, 0, 0, 0
};
BigInteger[] ycoefficients = new BigInteger[12] {
point.Y.Coefficients.ElementAt(0) - (point.Y.Coefficients.ElementAt(1) * 9), 0, 0, 0, 0, 0, point.Y.Coefficients.ElementAt(1), 0, 0, 0, 0, 0
};
BigInteger[] zcoefficients = new BigInteger[12] {
point.Z.Coefficients.ElementAt(0) - (point.Z.Coefficients.ElementAt(1) * 9), 0, 0, 0, 0, 0, point.Z.Coefficients.ElementAt(1), 0, 0, 0, 0, 0
};
// Instantiate fp12s from the extended fp2
Fp12 newx = new Fp12(xcoefficients);
Fp12 newy = new Fp12(ycoefficients);
Fp12 newz = new Fp12(zcoefficients);
// Return a twisted point from fp2 to fp12.
return(new FpVector3 <Fp12>(newx * _twistPoint.Pow(2), newy * _twistPoint.Pow(3), newz));
}
public static Fp12 FinalExponentiate(Fp12 p)
{
return(p.Pow((BigInteger.Pow(Bn128Curve.P, 12) - 1) / Bn128Curve.N));
}
