public static Signature Sign(SecretKey secretKey, string message)
{
var numberK = Utils.GenerateNumber().Mod(Static.Q - 2) + 2; // Crete 1 < k < q
var matrixR =
secretKey.MatrixD.Pow(secretKey.NumberW).Inverse() *
secretKey.MatrixG.Pow(numberK) *
secretKey.MatrixU.Pow(secretKey.NumberT);
byte[] hash;
using (SHA512 shaM = new SHA512Managed())
{
var bytes = Utils.ConcatBytes(Encoding.Unicode.GetBytes(message), matrixR.ToBytes());
hash = shaM.ComputeHash(bytes);
}
var numberE = new BigInteger(hash);
var numberEModed = numberE.Mod();
Static.NumberE = numberEModed;
var numberS = (numberK + numberEModed * secretKey.NumberX).Mod(Static.Q);
return(new Signature {
NumberE = numberEModed, NumberS = numberS
});
}
public static (PublicKey, SecretKey) GenerateKeys()
{
(Static.P, Static.Q) = Static.PrimeGenerator.GeneratePair();
var g = Utils.GenerateNonInvertibleMatrix();
var gPow = g.Pow(Static.Q + 1);
while (gPow != g)
{
var m = (Static.P - 1) / Static.Q;
g = g.Pow(m);
gPow = g.Pow(Static.Q + 1);
}
var d = Utils.GenerateMatrix();
while (!d.IsInvertible() || !d.IsNonMultipliableBothSide(g))
{
d = Utils.GenerateMatrix();
}
var u = Utils.GenerateMatrix();
while (!u.IsInvertible() || !u.IsNonMultipliableBothSide(g) || !u.IsNonMultipliableBothSide(d))
{
u = Utils.GenerateMatrix();
}
var numberW = Utils.GenerateNumber();
var numberT = Utils.GenerateNumber();
var numberX = Utils.GenerateNumber().Mod(Static.Q - 2) + 2; // Crete 1 < x < q
var e = Utils.GenerateRightUnit(g);
var dPowW = d.Pow(numberW);
var dPowWInversed = dPowW.Inverse();
var uPowT = u.Pow(numberT);
var uPowTInversed = uPowT.Inverse();
var l = dPowWInversed * e * uPowT;
var y = dPowWInversed * g.Pow(numberX) * dPowW;
var z = uPowTInversed * g * uPowT;
return(new PublicKey
{
Modulus = Static.P,
PrimeNumber = Static.Q,
MatrixL = l,
MatrixY = y,
MatrixZ = z
}, new SecretKey
{
MatrixD = d,
MatrixG = g,
MatrixU = u,
NumberW = numberW,
NumberX = numberX,
NumberT = numberT
});
}