private static void EncryptMessage(BigInteger g, BigInteger receiverPublicKey, BigInteger p, BigInteger message, out BigInteger y, out BigInteger k)
{
BigInteger r = CryptoTools.GenerateRandomBigInteger(1, p - 1);
k = CryptoTools.ModuloPower(g, r, p);
y = (message * CryptoTools.ModuloPower(receiverPublicKey, r, p)) % p;
}
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);
}
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 SimulateMoneyExchange(BigInteger p, BigInteger q)
{
Console.WriteLine($"Bank's private p is {p}");
Console.WriteLine($"Bank's private q is {q}");
BigInteger N = p * q, phi = (p - 1) * (q - 1);
Console.WriteLine($"Bank's public N is {N}, phi(N) = {phi}");
BigInteger c, d;
CryptoTools.GenerateInverseNumbers(phi, out c, out d);
Console.WriteLine($"Bank's private c is {c} and public d is {d}");
Console.WriteLine("START OF EXCHANGE");
BigInteger n = CryptoTools.GenerateRandomBigInteger(2, N);
BigInteger r, rInv;
CryptoTools.GenerateInverseNumbers(N, out r, out rInv);
BigInteger n_ = n * CryptoTools.ModuloPower(r, d, N) % N;
Console.WriteLine("Client wants to purchase an item.");
Console.WriteLine($"Client generated private n = {n}, random r = {r}: (r, N) = 1, then calculated n_ = (n * r^d) mod N = {n_} and sent it to bank");
BigInteger s_ = CryptoTools.ModuloPower(n_, c, N);
Console.WriteLine($"Bank calculated s_ = {s_}, withdrew money from client's account and sent s_ to client");
BigInteger s = (s_ * rInv) % N;
Console.WriteLine($"Client calculated s = {s} - this is bank's signature. Client's banknote is <n = {n}, s = {s}>");
Console.WriteLine("Client sends banknote to shop");
SimulateBanknoteChecking(n, s, d, N);
Console.WriteLine("Do you want to try to use the same banknote again? y - yes, else - no");
ConsoleKeyInfo cki = Console.ReadKey();
Console.WriteLine();
if (cki.KeyChar == 'y')
{
SimulateBanknoteChecking(n, s, d, N);
}
}
public static void SimulateElGamalSigning(BigInteger p, BigInteger g, BigInteger m)
{
Console.WriteLine($"Alice gonna sign messsage m = {m} and send it to Bob");
BigInteger x = CryptoTools.GenerateRandomBigInteger(2, p - 1);
BigInteger y = CryptoTools.ModuloPower(g, x, p);
Console.WriteLine($"Alice generated her private key x = {x} and calculated her public key y = {y}");
BigInteger h = CalculateHash(m);
Console.WriteLine($"Hash function of message {m} is {h} (h(m) = m)");
BigInteger r, s;
SignMessage(h, g, p, x, out r, out s);
Console.WriteLine($"Alice signed her message and sent <m = {m}, r = {r}, s = {s}> to Bob");
Console.WriteLine("Bob received them and checked if signature is correct:");
SimulateElGamalChecking(m, r, s, p, y, g);
}
internal static void SimulateRSAExchange(BigInteger p, BigInteger q, BigInteger d, BigInteger x)
{
BigInteger N = p * q;
BigInteger phi = (p - 1) * (q - 1);
BigInteger c, temp;
BigInteger ret = CryptoTools.EuclidAlgorithm(phi, d, out temp, out c);
if (ret != 1)
{
Console.WriteLine($"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}");
}
private static BigInteger GenerateElGamalPrivateKey(BigInteger g, BigInteger p)
{
return(CryptoTools.GenerateRandomBigInteger(2, p - 1));
}