public (CurvePoint, BigInteger) CreateKeys()
{
var closeKey = Algos.GenerateRandom(1, Curve.n - 1);
var openKey = Curve.G.MulOnScalar(closeKey);
return(openKey, closeKey);
}
public (ElGamalKey, ElGamalKey) GenerateKeys()
{
BigInteger prime, safePrime, generator;
while (true)
{
prime = Algos.GenetateRandomPrime(
BigInteger.Pow(2, dimension / 4),
BigInteger.Pow(2, dimension - 1),
Algos.MillerRabin
);
safePrime = 2 * prime + 1;
if (Algos.MillerRabin(safePrime))
{
break;
}
}
while (true)
{
generator = Algos.GenetateRandomPrime(3, safePrime - 2, Algos.MillerRabin);
if (BigInteger.ModPow(generator, 2, safePrime) != 1 && BigInteger.ModPow(generator, prime, safePrime) != 1)
{
break;
}
}
var closeKey = new ElGamalKey(Algos.GenerateRandom(2, safePrime - 2), generator, safePrime);
var openKey = new ElGamalKey(BigInteger.ModPow(generator, closeKey.Key, safePrime), generator, safePrime);
return(openKey, closeKey);
}
public ElGamalSignature CreateSignature(ElGamalKey closeKey)
{
using var sHA256 = SHA256.Create();;
using var file = File.OpenRead(fileName);
var hash = new BigInteger(sHA256.ComputeHash(file), true);
var k = Algos.GenerateRandomCoprime(closeKey.Prime - 1);
var r = BigInteger.ModPow(closeKey.Generator, k, closeKey.Prime);
var s = ((hash - closeKey.Key * r) * Algos.ReverseByMod(k, closeKey.Prime - 1)) % (closeKey.Prime - 1);
return(new ElGamalSignature(r, s));
}
public static BigInteger GenerateRandomCoprime(BigInteger other)
{
for (var i = 0; i < 100; ++i)
{
var result = GenetateRandomPrime(2, other - 1, MillerRabin);
if (Algos.EuclidExtended(other, result, out BigInteger temp1, out BigInteger temp2) == 1)
{
return(result);
}
}
return(65537);
}
static public BigInteger Inverse(BigInteger n, BigInteger m)
{
if (n < 0)
{
return(m - Inverse(-n, m));
}
var gcd = Algos.EuclidExtended(n, m, out BigInteger x, out BigInteger y);
if ((n * x + m * y) % m != gcd || gcd != 1)
{
throw new InvalidProgramException("Inverse don't exist");
}
return(x % m);
}
public Signature CreateSignature(BigInteger closeKey)
{
var z = GetHash();
while (true)
{
var k = Algos.GenerateRandom(1, Curve.n - 1);
var P = Curve.G.MulOnScalar(k);
var r = P.x % Curve.n;
if (r == 0)
{
continue;
}
var s = (Inverse(k, Curve.n) * (z + r * closeKey)) % Curve.n;
if (s == 0)
{
continue;
}
return(new Signature(r, s));
}
}