public (BigInteger, BigInteger, BigInteger) AlicePass()
{
p = NumberTheoryUtils.RandomPrimeInRange(10, 10000000000000000);
g = NumberTheoryUtils.GetGroupGenerator(p, true);
a = NumberTheoryUtils.RandomIntegerInRange(10, 10000000000000000);
A = BigInteger.ModPow(g, a, p);
return(g, p, A);
}
public static (BigInteger, BigInteger, BigInteger, BigInteger) GetElgamalKeys()
{
var p = NumberTheoryUtils.RandomPrime(1);
var g = NumberTheoryUtils.GetGroupGenerator(p, isPrime: true);
var x = NumberTheoryUtils.RandomIntegerInRange(1, p);
var y = BigInteger.ModPow(g, x, p);
return(p, g, x, y);
}
public (BigInteger, BigInteger) Sign(byte[] M)
{
var m = GetDigest(M);
var k = NumberTheoryUtils.RandomPrimeInRange(1, p - 1);
var r = BigInteger.ModPow(g, k, p);
var s = ((m - x * r) * k.ModInverse(p - 1)).EuclidianMod(p - 1);
Check(M, (r, s));
return(r, s);
}
public static (BigInteger, BigInteger, BigInteger) GetRsaKeys()
{
var p = NumberTheoryUtils.RandomPrime();
var q = NumberTheoryUtils.RandomPrime();
var n = p * q;
var phi = (p - 1) * (q - 1);
var e = NumberTheoryUtils.RandomIntegerInRange(2, phi);
while (BigInteger.GreatestCommonDivisor(e, phi) != 1)
{
e = NumberTheoryUtils.RandomIntegerInRange(2, phi);
}
var d = e.ModInverse(phi, isCoPrime: true);
return(n, e, d);
}