private static void SignMessage(BigInteger h, BigInteger g, BigInteger p, BigInteger x, out BigInteger r, out BigInteger s)
{
BigInteger k, kRev, ret;
do
{
k = CryptoTools.GenerateRandomBigInteger(2, p - 1);
ret = CryptoTools.EuclidAlgorithm(p - 1, k, out _, out kRev);
} while (ret != 1);
if (kRev < 0)
{
kRev += (p - 1);
}
r = CryptoTools.ModuloPower(g, k, p);
BigInteger u = (h - x * r) % (p - 1);
if (u < 0)
{
u += (p - 1);
}
s = (kRev * u) % (p - 1);
}
public static BigInteger GenerateShamirPrivateKeyUsingAnother(BigInteger p, BigInteger c)
{
BigInteger temp, d, ret = CryptoTools.EuclidAlgorithm(p - 1, c, out temp, out d);
if (d < 0)
{
d += (p - 1);
}
return(d);
}
internal static void SimulateRSASigning(BigInteger p, BigInteger q, BigInteger d, BigInteger m)
{
Console.WriteLine($"Alice gonna sign messsage m = {m} and send it to Bob");
BigInteger N = p * q;
BigInteger phi = (p - 1) * (q - 1);
BigInteger c, temp;
BigInteger ret = CryptoTools.EuclidAlgorithm(phi, d, out temp, out c);
if (ret != 1)
{
Console.WriteLine($"d = {d} isn't mutually prime with phi(N)! A new one will be generated");
BigInteger cCandidate, dCandidate;
do
{
dCandidate = CryptoTools.GenerateRandomBigInteger(1, phi);
ret = CryptoTools.EuclidAlgorithm(phi, dCandidate, out temp, out cCandidate);
} while (ret != 1);
c = cCandidate;
d = dCandidate;
}
if (c < 0)
{
c += phi;
}
Console.WriteLine($"Alice's public keys are N = {N} and d = {d}");
Console.WriteLine($"Alice's private key is c = {c}");
BigInteger y = CalculateHash(m);
Console.WriteLine($"Hash function of message {m} is {y} (h(m) = m)");
BigInteger s = SignMessage(y, c, N);
Console.WriteLine($"Alice sent message {m} and signature {s} to Bob");
Console.WriteLine("Bob received them and checked if signature is correct");
SimulateRSAChecking(m, s, d, N);
}
public static void GenerateShamirPrivateKeys(BigInteger p, out BigInteger c, out BigInteger d)
{
Random r = new Random();
BigInteger cCandidate, dCandidate, ret;
do
{
BigInteger temp;
cCandidate = r.Next(1, (int)p);
ret = CryptoTools.EuclidAlgorithm(p - 1, cCandidate, out temp, out dCandidate);
} while (ret != 1); //крутимся пока не найдём такое cCandidate: (cCandidate, p - 1) = 1. тогда dCandidate обратное к cCandidate с точностью до модуля
c = cCandidate;
if (dCandidate < 0)
{
dCandidate += (p - 1);
}
d = dCandidate;
}
internal static void SimulateRSAExchange(BigInteger p, BigInteger q, BigInteger d, BigInteger x)
{
BigInteger N = p * q;
BigInteger phi = (p - 1) * (q - 1);
BigInteger c, temp;
BigInteger ret = CryptoTools.EuclidAlgorithm(phi, d, out temp, out c);
if (ret != 1)
{
Console.WriteLine($"d = {d} isn't mutually prime with phi(N)! A new one will be generated");
BigInteger cCandidate, dCandidate;
do
{
dCandidate = CryptoTools.GenerateRandomBigInteger(1, phi);
ret = CryptoTools.EuclidAlgorithm(phi, dCandidate, out temp, out cCandidate);
} while (ret != 1);
c = cCandidate;
d = dCandidate;
}
if (c < 0)
{
c += phi;
}
Console.WriteLine($"Receiver's public keys are N = {N} and d = {d}");
Console.WriteLine($"Receiver's private key is c = {c}");
BigInteger y = CryptoTools.ModuloPower(x, d, N);
Console.WriteLine($"Sender encrypted message and sent y = {y} to receiver");
BigInteger w = CryptoTools.ModuloPower(y, c, N);
Console.WriteLine($"Receiver decrypted y and got w = {w}");
}