/// <summary>
/// S (N) parameter
/// </summary>
/// <returns>return Lcm between Legendre</returns>
private BigInteger GetLcm()
{
BigInteger d = GetD();
LegendreNumbers legendresNumbers = new LegendreNumbers(d, PrimeNumbers.Q, PrimeNumbers.P);
int a = PrimeNumbers.P - legendresNumbers.Dp;
int b = PrimeNumbers.Q - legendresNumbers.Dq;
return(MathNet.Numerics.Euclid.LeastCommonMultiple(a, b));
}
public void PrivateKey()
{
LucPrime lucPrime = new LucPrime(p: 1949, q: 2089);
BigInteger message = 11111;
LucPublicKey publicKey = new LucPublicKey(1103, 4071461);
LegendreNumbers legend = new LucasSequences.LegendreNumbers(lucPrime, message);
LucPrivateKey key = new LucPrivateKey(publicKey, legend);
Assert.AreEqual <BigInteger>(key.d, 24017);
}
public void LegandNumbers()
{
//int
LucPrime lucPrime = new LucPrime(p: 1949, q: 2089);
BigInteger message = 11111;
LegendreNumbers legend = new LucasSequences.LegendreNumbers(lucPrime, message);
Assert.AreEqual <Int32>(lucPrime.N, 4071461);
Assert.AreEqual <BigInteger>(legend.D, 123454317);
Assert.AreEqual <int>(legend.Dp, -1);
Assert.AreEqual <int>(legend.Dq, -1);
Assert.AreEqual(legend.Sn, 407550);
}
public void EncryptMessageMod()
{
AAtkin a = new AAtkin(1350);
LucPrime lucPrime = new LucPrime(a.RandomPrime, a.RandomPrime);
BigInteger message = 11111;
LegendreNumbers legendreNumbers = new LucasSequences.LegendreNumbers(primeNumbers: lucPrime, message: message);
LucPublicKey publicKey = new LucPublicKey(lucPrime);
LucPrivateKey privateKey = new LucPrivateKey(publicKey, legendreNumbers);
var seqPublic = new LucasSequences.LucasSequence(message, 1);
var ciphertext = seqPublic[publicKey.e, publicKey.N];
var seqPrivate = new LucasSequences.LucasSequence(ciphertext, 1);
var result = seqPrivate[privateKey.d, privateKey.N];
Assert.AreEqual <BigInteger>(result, message);
}
public LucPrivateKey(LucPublicKey publicKey, LegendreNumbers legendreNumbers)
{
d = BigInteger.ModPow(publicKey.e, (int)(legendreNumbers.Sn.Eyler() - 1), legendreNumbers.Sn);
N = publicKey.N;
}