RSA signature sample code without RSACryptoServiceProvider

RSASIGNATURE.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;
using System.Security.Cryptography;
using Newtonsoft.Json;
using Newtonsoft.Json.Linq;
using System.Globalization;

//RSA signature sample example

namespace RSASIGNATURE
{
    public class RSASIGNATURE
    {
        public BigInteger e, p, q, n, phi;



        private BigInteger Encrypt(BigInteger m, BigInteger e, BigInteger n)          //encryption
        {
            return BigInteger.ModPow(m, e, n);
        }

        private BigInteger Decrypt(BigInteger cResult, BigInteger d, BigInteger n)    //decryption
        {
            return BigInteger.ModPow(cResult, d, n);
        }


        private void generateParams(string p_str, string q_str)
        {

            p = BigInteger.Parse(p_str);

            q = BigInteger.Parse(q_str);

            e = BigInteger.Parse("65537");

            n = p * q;

            phi = (p - 1) * (q - 1);
        }

        private Tuple<BigInteger, BigInteger, BigInteger> generatePrivateKey()
        {

            return egcd(e, phi);
        }

        Tuple<BigInteger, BigInteger, BigInteger> egcd(BigInteger a, BigInteger b)
        {
            BigInteger x = 0, y = 1, u = 1, v = 0, gcd = 0;


            while (a != 0)
            {
                q = b / a;
                BigInteger r = b % a;
                BigInteger m = x - u * q;
                BigInteger n = y - v * q;
                b = a;
                a = r;
                x = u;
                y = v;
                u = m;
                v = n;
                gcd = b;
            }

            if (x < 0) x += phi;
            if (y < 0) y += phi;


            return Tuple.Create(gcd, x, y);
        }



        public string Sign(string message, string privatekey)
        {
            string hash = CalculateMD5Hash(message);

            var pr_object = JObject.Parse(GZIP.DecompressString(privatekey));

            var big = BigInteger.Parse(hash, NumberStyles.HexNumber); //new BigInteger(Encoding.ASCII.GetBytes(hash));


            var signature = this.Encrypt(big, BigInteger.Parse(pr_object.GetValue("d").ToString()), BigInteger.Parse(pr_object.GetValue("n").ToString())); // to hex



            return signature.ToString("X");
        }


        public string[] encodeKeys()
        {

            

            var gcd_d_y = this.generatePrivateKey();


            var pk = new
            {
                n = this.n,
                e = this.e
            };

            var pr = new
            {
                n = this.n,
                d = gcd_d_y.Item2
            };



            return new String[] { GZIP.CompressString(JsonConvert.SerializeObject(pk)), GZIP.CompressString(JsonConvert.SerializeObject(pr)) };
        }



        public JObject[] decodeKeys(string pk, string pr)
        {
            var pk_object = JObject.Parse(GZIP.DecompressString(pk));
            var pr_object = JObject.Parse(GZIP.DecompressString(pr));
            return new JObject[] { pk_object, pr_object };
        }




        public bool Verify(string message, string publickey, string signature)
        {

            var pk_object = JObject.Parse(GZIP.DecompressString(publickey));

            string hash = this.CalculateMD5Hash(message);

            var signatureBig = BigInteger.Parse(signature, NumberStyles.HexNumber);


            var dec = this.Decrypt(signatureBig, BigInteger.Parse(pk_object.GetValue("e").ToString()), BigInteger.Parse(pk_object.GetValue("n").ToString()));



            return dec.ToString("X") == hash;

        }


        public string CalculateMD5Hash(string input)
        {
            // step 1, calculate MD5 hash from input
            MD5 md5 = System.Security.Cryptography.MD5.Create();
            byte[] inputBytes = System.Text.Encoding.ASCII.GetBytes(input);
            byte[] hash = md5.ComputeHash(inputBytes);

            // step 2, convert byte array to hex string
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < hash.Length; i++)
            {
                sb.Append(hash[i].ToString("X2"));
            }
            return sb.ToString();
        }

    }
}



//main.cs

RSASIGNATURE rsa = new RSASIGNATURE();
// p , q params
BigInteger p = "1090660992520643446103273789680343";
BigInteger q = "1162435056374824133712043309728653";
rsa.generateParams(p, q);

//encode private and public keys 

string[] keyspair = rsa.encodeKeys();

Console.WriteLine("Public key: "+ keyspair[0]); //<e,n>
Console.WriteLine("Private key: "+ keyspair[1]); //<d,n>


string message = "by safi";

//generate signature
string signature = rsa.Sign(message,keyspair[1]);

Console.WriteLine("Signature: "+ signature);

//verify signature
bool verfied = rsa.Verify(message,keyspair[0],signature)

Assert.isTrue(verfied);