BCConsoleApp.cs

using System;
using System.Security.Cryptography;
using System.Text;
using Org.BouncyCastle.Crypto;
using Org.BouncyCastle.Crypto.Digests;
using Org.BouncyCastle.Crypto.Encodings;
using Org.BouncyCastle.Crypto.Engines;
using Org.BouncyCastle.Crypto.Generators;
using Org.BouncyCastle.Crypto.Parameters;
using Org.BouncyCastle.Security;

namespace BCConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            SHA512Managed hash = new SHA512Managed();
            SecureRandom randomNumber = new SecureRandom();
            byte[] encodingParam = hash.ComputeHash(Encoding.UTF8.GetBytes(randomNumber.ToString()));
            string inputMessage = "Test Message";
            UTF8Encoding utf8enc = new UTF8Encoding();

            byte[] inputBytes = utf8enc.GetBytes(inputMessage);

            RsaKeyPairGenerator rsaKeyPairGnr = new RsaKeyPairGenerator();
            rsaKeyPairGnr.Init(new KeyGenerationParameters(new SecureRandom(), 2048));
            AsymmetricCipherKeyPair keyPair = rsaKeyPairGnr.GenerateKeyPair();
            RsaKeyParameters publicKey = (RsaKeyParameters)keyPair.Public;
            RsaKeyParameters privateKey = (RsaKeyParameters)keyPair.Private;

            IAsymmetricBlockCipher cipher = new OaepEncoding(new RsaEngine(), new Sha512Digest(), encodingParam);
            cipher.Init(true, publicKey);
            byte[] ciphered = cipher.ProcessBlock(inputBytes, 0, inputMessage.Length);
           
            cipher.Init(false, privateKey);
            byte[] deciphered = cipher.ProcessBlock(ciphered, 0, ciphered.Length);
            string decipheredText = utf8enc.GetString(deciphered);

            if (decipheredText == "Test Message")
                Console.WriteLine("Encrypt / decrypt works");
            else
                Console.WriteLine("Encrypt / decrypt fails");

            var result = Sign(inputMessage, privateKey);

            bool result1 = Verify(inputMessage, result, publicKey);

            if (result1)
                Console.WriteLine("Signing works");
            else
                Console.WriteLine("Signing fails");

            Console.ReadLine();
        }

        public static String Sign(String data, RsaKeyParameters privateKey)
        {
            ISigner sign = SignerUtilities.GetSigner("SHA512withRSA");
            sign.Init(true, privateKey);
            var bytes = Encoding.UTF8.GetBytes(data);
            sign.BlockUpdate(bytes, 0, bytes.Length);
            byte[] signature = sign.GenerateSignature();
            var signed = Convert.ToBase64String(signature);
            return signed;
        }

        public static bool Verify(String data, String expectedSignature, RsaKeyParameters publicKey)
        {
            ISigner sign = SignerUtilities.GetSigner("SHA512withRSA");
            sign.Init(false, publicKey);
            var expectedSign = Convert.FromBase64String(expectedSignature);
            var bytes = Encoding.UTF8.GetBytes(data);
            sign.BlockUpdate(bytes, 0, bytes.Length);
            return sign.VerifySignature(expectedSign);
        }
    }
}

https://medium.com/the-new-control-plane/bouncycastle-cryptography-ce2a41bf1c92