public mpz_t Multiply(mpz_t a, mpz_t b, PaillierKey key)
{
var nsquare = key.N * key.N;
var res = (a * b) % nsquare;
return(res);
}
public mpz_t DecryptNumber(mpz_t encryptedNumber, PaillierKey key)
{
var nsquare = key.N * key.N;
var m = encryptedNumber.PowerMod(key.Lambda, nsquare).Subtract(1).Divide(key.N).Multiply(key.Mu).Mod(key.N);
return(m);
}
public mpz_t EncryptNumber(int number, PaillierKey key)
{
mpz_t r = RandomZStarN(key.N);
var nsq = key.N * key.N;
// c = g^m * r^n mod n^2
return((key.G.PowerMod(number, nsq).Multiply(r.PowerMod(key.N, nsq))).Mod(nsq));
}
public PaillierKey GenerateKey()
{
var p = new PrimeNumber();
var q = new PrimeNumber();
GeneratePrimes(out p, out q);
// lambda = lcm(p-1, q-1) = (p-1)*(q-1)/gcd(p-1, q-1)
var lambda = ((p.GetPrimeNumber() - 1) * (q.GetPrimeNumber() - 1)) /
mpz_t.Gcd(p.GetPrimeNumber() - 1, q.GetPrimeNumber() - 1);
var n = p.GetPrimeNumber() * q.GetPrimeNumber(); // n = p*q
var nsquare = n * n; // nsquare = n*n
mpz_t g;
do
{
// generate g, a random integer in Z*_{n^2}
g = RandomZStarNSquare(nsquare);
}
// verify g, the following must hold: gcd(L(g^lambda mod n^2), n) = 1, where L(u) = (u-1)/n
while (mpz_t.Gcd(g.PowerMod(lambda, nsquare).Subtract(1).Divide(n), n) != 1);
// mu = (L(g^lambda mod n^2))^{-1} mod n, where L(u) = (u-1)/n
var mu = g.PowerMod(lambda, nsquare).Subtract(1).Divide(n).InvertMod(n);
var key = new PaillierKey
{
N = n,
G = g,
Lambda = lambda,
Mu = mu
};
return(key);
}
