Signing and verifying signatures with RSA C#

I recently posted about issues with encrypting large data with RSA, I am finally done with that and now I am moving on to implementing signing with a user's private key and verifying with the corresponding public key. However, whenever I compare the signed data and the original message I basically just get false returned. I am hoping some of your could see what I am doing wrong.

Here is the code:

public static string SignData(string message, RSAParameters privateKey)
    {
        //// The array to store the signed message in bytes
        byte[] signedBytes;
        using (var rsa = new RSACryptoServiceProvider())
        {
            //// Write the message to a byte array using UTF8 as the encoding.
            var encoder = new UTF8Encoding();
            byte[] originalData = encoder.GetBytes(message);
            
            try
            {
                //// Import the private key used for signing the message
                rsa.ImportParameters(privateKey);

                //// Sign the data, using SHA512 as the hashing algorithm 
                signedBytes = rsa.SignData(originalData, CryptoConfig.MapNameToOID("SHA512"));
            }
            catch (CryptographicException e)
            {
                Console.WriteLine(e.Message);
                return null;
            }
            finally
            {
                //// Set the keycontainer to be cleared when rsa is garbage collected.
                rsa.PersistKeyInCsp = false;
            }
        }
        //// Convert the a base64 string before returning
        return Convert.ToBase64String(signedBytes);
    }

So that is the first step, to sign the data, next I move on to verifying the data:

public static bool VerifyData(string originalMessage, string signedMessage, RSAParameters publicKey)
    {
        bool success = false;
        using (var rsa = new RSACryptoServiceProvider())
        {
            byte[] bytesToVerify = Convert.FromBase64String(originalMessage);
            byte[] signedBytes = Convert.FromBase64String(signedMessage);
            try
            {
                rsa.ImportParameters(publicKey);

                SHA512Managed Hash = new SHA512Managed();

                byte[] hashedData = Hash.ComputeHash(signedBytes);

                success = rsa.VerifyData(bytesToVerify, CryptoConfig.MapNameToOID("SHA512"), signedBytes);
            }
            catch (CryptographicException e)
            {
                Console.WriteLine(e.Message);
            }
            finally
            {
                rsa.PersistKeyInCsp = false;
            }
        }
        return success;
    }

And here is the test client:

public static void Main(string[] args)
    {
        PublicKeyInfrastructure pki = new PublicKeyInfrastructure();
        Cryptograph crypto = new Cryptograph();
        RSAParameters privateKey = crypto.GenerateKeys("[email protected]");

        const string PlainText = "This is really sent by me, really!";

        RSAParameters publicKey = crypto.GetPublicKey("[email protected]");

        string encryptedText = Cryptograph.Encrypt(PlainText, publicKey);

        Console.WriteLine("This is the encrypted Text:" + "\n " + encryptedText);

        string decryptedText = Cryptograph.Decrypt(encryptedText, privateKey);

        Console.WriteLine("This is the decrypted text: " + decryptedText);

        string messageToSign = encryptedText;

        string signedMessage = Cryptograph.SignData(messageToSign, privateKey);

        //// Is this message really, really, REALLY sent by me?
        bool success = Cryptograph.VerifyData(messageToSign, signedMessage, publicKey);

        Console.WriteLine("Is this message really, really, REALLY sent by me? " + success);
        
    }

Am I missing a step here? According to the Cryptography API and the examples there, I shouldn't manually compute any hashes, since I supply the algorithm within the method call itself.

Any help will be greatly appreciated.

Your problem is at the beginning of the VerifyData method:

public static bool VerifyData(string originalMessage, string signedMessage, RSAParameters publicKey)
{
    bool success = false;
    using (var rsa = new RSACryptoServiceProvider())
    {
        //Don't do this, do the same as you did in SignData:
        //byte[] bytesToVerify = Convert.FromBase64String(originalMessage);
        var encoder = new UTF8Encoding();
        byte[] bytesToVerify = encoder.GetBytes(originalMessage);

        byte[] signedBytes = Convert.FromBase64String(signedMessage);
        try
        ...

For some reason you switched to FromBase64String instead of UTF8Encoding.GetBytes.