Bob and Alice use a cryptosystem in which their private key

Bob and Alice use a cryptosystem in which their private key is a (large) prime k and their plaintexts and ciphertexts are integers. Bob encrypts a message m by computing the product c = km. Eve intercepts the following two ciphertexts:

c1 = 12849217045006222, c2 = 6485880443666222

Solution

public class DataEncryptor
{
TripleDESCryptoServiceProvider symm;

  
public DataEncryptor()
{
this.symm = new TripleDESCryptoServiceProvider();
this.symm.Padding = PaddingMode.PKCS7;
}
public DataEncryptor(TripleDESCryptoServiceProvider keys)
{
this.symm = keys;
}

public DataEncryptor(byte[] key, byte[] iv)
{
this.symm = new TripleDESCryptoServiceProvider();
this.symm.Padding = PaddingMode.PKCS7;
this.symm.Key = key;
this.symm.IV = iv;
}

public TripleDESCryptoServiceProvider Algorithm
{
get { return symm; }
set { symm = value; }
}
public byte[] Key
{
get { return symm.Key; }
set { symm.Key = value; }
}
public byte[] IV
{
get { return symm.IV; }
set { symm.IV = value; }
}

#endregion

#region Crypto

public byte[] Encrypt(byte[] data) { return Encrypt(data, data.Length); }
public byte[] Encrypt(byte[] data, int length)
{
try
{
// Create a MemoryStream.
var ms = new MemoryStream();

// Create a CryptoStream using the MemoryStream
// and the passed key and initialization vector (IV).
var cs = new CryptoStream(ms,
symm.CreateEncryptor(symm.Key, symm.IV),
CryptoStreamMode.Write);

// Write the byte array to the crypto stream and flush it.
cs.Write(data, 0, length);
cs.FlushFinalBlock();

// Get an array of bytes from the
// MemoryStream that holds the
// encrypted data.
byte[] ret = ms.ToArray();

// Close the streams.
cs.Close();
ms.Close();

// Return the encrypted buffer.
return ret;
}
catch (CryptographicException ex)
{
Console.WriteLine(\"A cryptographic error occured: {0}\", ex.Message);
}
return null;
}

public string EncryptString(string text)
{
return Convert.ToBase64String(Encrypt(Encoding.UTF8.GetBytes(text)));
}

public byte[] Decrypt(byte[] data) { return Decrypt(data, data.Length); }
public byte[] Decrypt(byte[] data, int length)
{
try
{
// Create a new MemoryStream using the passed
// array of encrypted data.
MemoryStream ms = new MemoryStream(data);

// Create a CryptoStream using the MemoryStream
// and the passed key and initialization vector (IV).
CryptoStream cs = new CryptoStream(ms,
symm.CreateDecryptor(symm.Key, symm.IV),
CryptoStreamMode.Read);

// Create buffer to hold the decrypted data.
byte[] result = new byte[length];

// Read the decrypted data out of the crypto stream
// and place it into the temporary buffer.
cs.Read(result, 0, result.Length);
return result;
}
catch (CryptographicException ex)
{
Console.WriteLine(\"A cryptographic error occured: {0}\", ex.Message);
}
return null;
}

public string DecryptString(string data)
{
return Encoding.UTF8.GetString(Decrypt(Convert.FromBase64String(data))).TrimEnd(\'\\0\');
}

}