private static bool CheckSignature(BigInteger m, BigInteger s, BigInteger d, BigInteger N)
{
BigInteger h = CalculateHash(m);
BigInteger w = CryptoTools.ModuloPower(s, d, N);
return(w == h);
}
private static void SimulateShamirExchange(BigInteger p, BigInteger cA, BigInteger cB, BigInteger m)
{
BigInteger dA, dB;
dA = ShamirTools.GenerateShamirPrivateKeyUsingAnother(p, cA);
Console.WriteLine($"dA = {dA}");
dB = ShamirTools.GenerateShamirPrivateKeyUsingAnother(p, cB);
Console.WriteLine($"dB = {dB}");
BigInteger x = m;
Console.WriteLine($"Message is {x}");
BigInteger y = CryptoTools.ModuloPower(x, cA, p);
Console.WriteLine($"Alice calculated y = {y} and sent it to Bob");
BigInteger z = CryptoTools.ModuloPower(y, cB, p);
Console.WriteLine($"Bob calculated z = {z} and sent it to Alice");
BigInteger u = CryptoTools.ModuloPower(z, dA, p);
Console.WriteLine($"Alice calculated u = {u} and sent it to Bob");
BigInteger w = CryptoTools.ModuloPower(u, dB, p);
Console.WriteLine($"Bob calculated w = {w}");
}
private static void EncryptMessage(BigInteger g, BigInteger receiverPublicKey, BigInteger p, BigInteger message, out BigInteger y, out BigInteger k)
{
BigInteger r = CryptoTools.GenerateRandomBigInteger(1, p - 1);
k = CryptoTools.ModuloPower(g, r, p);
y = (message * CryptoTools.ModuloPower(receiverPublicKey, r, p)) % p;
}
private static void SimulateDiffieHellmanExchange(BigInteger p, BigInteger g)
{
Console.WriteLine("Alice starts exchange");
BigInteger xA = CryptoTools.GenerateDiffieHellmanPrivateKey(g, p);
Console.WriteLine("Alice generated private key xA = {0}", xA);
BigInteger yA = CryptoTools.GenerateDiffieHellmanPublicKey(g, xA, p);
Console.WriteLine("Alice generated public key yA = {0} and sent it to Bob", yA);
BigInteger xB = CryptoTools.GenerateDiffieHellmanPrivateKey(g, p);
Console.WriteLine("Bob generated private key xB = {0}", xB);
BigInteger yB = CryptoTools.GenerateDiffieHellmanPublicKey(g, xB, p);
Console.WriteLine("Bob generated public key yB = {0} and sent it to Alice", yB);
BigInteger zAB = CryptoTools.ModuloPower(yB, xA, p);
Console.WriteLine($"Alice calculated zAB = {zAB} - common private key");
BigInteger zBA = CryptoTools.ModuloPower(yA, xB, p);
Console.WriteLine($"Bob calculated zBA = {zBA} - common private key");
}
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);
}
private static bool CheckBanknoteSignature(BigInteger n, BigInteger s, BigInteger d, BigInteger N)
{
if (n == CryptoTools.ModuloPower(s, d, N))
{
return(true);
}
return(false);
}
//private static List<NumberIndex> babyList = new List<NumberIndex>(), giantList = new List<NumberIndex>();
internal static BigInteger SolveEquation(BigInteger y, BigInteger a, BigInteger p)
{
List <NumberIndex> commonList = new List <NumberIndex>();
BigInteger k, m;
k = m = (BigInteger)Math.Ceiling(Math.Sqrt((double)p));
for (BigInteger i = 0; i < m; i++)
{
commonList.Add(new NumberIndex((y * CryptoTools.ModuloPower(a, i, p)) % p, i, true));
}
for (BigInteger j = 1; j <= k; j++)
{
commonList.Add(new NumberIndex(CryptoTools.ModuloPower(a, j * m, p), j, false));
}
commonList.Sort();
NumberIndex prev = null, cur = null;
BigInteger iX = 0, jX = 0;
foreach (var element in commonList)
{
if (cur != null)
{
prev = cur;
}
cur = element;
if (prev != null)
{
if (prev.Number == cur.Number)
{
if (prev.IsBaby != cur.IsBaby)
{
if (prev.IsBaby == false)
{
iX = prev.Index;
jX = cur.Index;
}
else
{
jX = prev.Index;
iX = cur.Index;
}
break;
}
else
{
}
}
}
}
return(iX * m - jX);
}
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($"Alice sent message {m} and signature {s} to Bob");
Console.WriteLine("Bob received them and checked if signature is correct");
SimulateRSAChecking(m, s, d, N);
}
public static void GenerateShamirPrivateKeys(BigInteger p, out BigInteger c, out BigInteger d)
{
Random r = new Random();
BigInteger cCandidate, dCandidate, ret;
do
{
BigInteger temp;
cCandidate = r.Next(1, (int)p);
ret = CryptoTools.EuclidAlgorithm(p - 1, cCandidate, out temp, out dCandidate);
} while (ret != 1); //крутимся пока не найдём такое cCandidate: (cCandidate, p - 1) = 1. тогда dCandidate обратное к cCandidate с точностью до модуля
c = cCandidate;
if (dCandidate < 0)
{
dCandidate += (p - 1);
}
d = dCandidate;
}
public static void SimulateMoneyExchange(BigInteger p, BigInteger q)
{
Console.WriteLine($"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);
}
}
private static void SimulateShamirExchange(BigInteger p)
{
BigInteger cA, dA, cB, dB;
ShamirTools.GenerateShamirPrivateKeys(p, out cA, out dA);
Console.WriteLine($"Alice generated private keys cA = {cA}, dA = {dA}");
ShamirTools.GenerateShamirPrivateKeys(p, out cB, out dB);
Console.WriteLine($"Bob generated private keys cB = {cB}, dB = {dB}");
BigInteger x = -1;
do
{
Console.WriteLine("Please enter message, x < p");
string s = Console.ReadLine();
try
{
x = BigInteger.Parse(s);
}
catch (FormatException)
{
x = -1;
}
}while (x < 0 || x >= p);
Console.WriteLine($"Message is {x}");
BigInteger y = CryptoTools.ModuloPower(x, cA, p);
Console.WriteLine($"Alice calculated y = {y} and sent it to Bob");
BigInteger z = CryptoTools.ModuloPower(y, cB, p);
Console.WriteLine($"Bob calculated z = {z} and sent it to Alice");
BigInteger u = CryptoTools.ModuloPower(z, dA, p);
Console.WriteLine($"Alice calculated u = {u} and sent it to Bob");
BigInteger w = CryptoTools.ModuloPower(u, dB, p);
Console.WriteLine($"Bob calculated w = {w}");
}
public static void SimulateElGamalSigning(BigInteger p, BigInteger g, BigInteger m)
{
Console.WriteLine($"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));
}
private static bool CheckSignature(BigInteger m, BigInteger r, BigInteger s, BigInteger p, BigInteger y, BigInteger g)
{
BigInteger h = CalculateHash(m);
return((CryptoTools.ModuloPower(y, r, p) * CryptoTools.ModuloPower(r, s, p)) % p == CryptoTools.ModuloPower(g, h, p));
}
private static BigInteger GenerateKey(int n)
{
return(CryptoTools.GenerateUnsignedRandomBigInteger(0, BigInteger.Pow(2, n)));
}
internal static void SimulatePokerExchange(BigInteger p)
{
BigInteger cA, dA, cB, dB;
GeneratePokerPrivateKeys(p, out cA, out dA);
Console.WriteLine($"Alice's private keys are cA = {cA} and dA = {dA}");
GeneratePokerPrivateKeys(p, out cB, out dB);
Console.WriteLine($"Bob's private keys are cB = {cB} and dB = {dB}");
BigInteger alpha, beta, gamma; //карты
GenerateCardNumbers(p, out alpha, out beta, out gamma);
Console.WriteLine($"Alice generated numbers for cards and told Bob that alpha is {alpha}, beta is {beta}, gamma is {gamma}");
Console.WriteLine("START OF THE EXCHANGE");
Triplet cards = new Triplet(new Card(alpha, "ALPHA"), new Card(beta, "BETA"), new Card(gamma, "GAMMA"));
Triplet encryptedCardsForBob = cards.ModuloPower(cA, p);
Console.WriteLine($"Alice encrypted card numbers: alpha to {encryptedCardsForBob.X}, beta to {encryptedCardsForBob.Y}, gamma to {encryptedCardsForBob.Z}...");
encryptedCardsForBob.Mix();
Console.WriteLine($"...And then mixed them: {encryptedCardsForBob.X}, {encryptedCardsForBob.Y}, {encryptedCardsForBob.Z} and sent to Bob");
BigInteger cardAEncryptedNumber = encryptedCardsForBob.ChooseRandom3();
Console.WriteLine($"Bob chose {cardAEncryptedNumber} and sent to Alice");
BigInteger cardANumber = CryptoTools.ModuloPower(cardAEncryptedNumber, dA, p);
Console.WriteLine($"Alice decrypted it; her card number is {cardANumber} and it's {cards.FindName(cardANumber)}!");
encryptedCardsForBob.RemoveUsedCard();
Triplet encryptedCardsForAlice = encryptedCardsForBob.ModuloPower(cB, p);
encryptedCardsForAlice.Mix();
Console.Write($"Bob encrypted card numbers, mixed them and sent to Alice: ");
for (int i = 0; i < 3; i++)
{
if (encryptedCardsForAlice[i].Number != 0)
{
Console.Write($"{encryptedCardsForAlice[i].Name} to {encryptedCardsForAlice[i].Number} ");
}
}
Console.WriteLine();
BigInteger cardBEncryptedNumber = encryptedCardsForAlice.ChooseRandom2();
BigInteger cardBPartiallyDecryptedNumber = CryptoTools.ModuloPower(cardBEncryptedNumber, dA, p);
Console.WriteLine($"Alice chose {cardBEncryptedNumber}, found its power {cardBPartiallyDecryptedNumber} and sent to Bob");
BigInteger cardBNumber = CryptoTools.ModuloPower(cardBPartiallyDecryptedNumber, dB, p);
Console.WriteLine($"Bob decrypted it; his card number is {cardBNumber} and it's {cards.FindName(cardBNumber)}!");
encryptedCardsForBob.RemoveUsedCard();
for (int i = 0; i < 3; i++)
{
if (cards[i].Number != cardANumber && cards[i].Number != cardBNumber)
{
Console.WriteLine($"The third card has number {cards[i].Number} and is {cards[i].Name} ");
}
}
}
private static BigInteger GenerateElGamalPublicKey(BigInteger g, BigInteger privateKey, BigInteger p)
{
return(CryptoTools.ModuloPower(g, privateKey, p));
}
private static BigInteger DecryptMessage(BigInteger receiverPrivateKey, BigInteger p, BigInteger y, BigInteger k)
{
return(y * CryptoTools.ModuloPower(k, p - receiverPrivateKey - 1, p) % p);
}
private static BigInteger SignMessage(BigInteger y, BigInteger c, BigInteger N)
{
return(CryptoTools.ModuloPower(y, c, N));
}