using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using Org.BouncyCastle.Math;

namespace secret
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Bartłomiej Wolnik, gr.A");
            string secretString = getRandomSecretString(secretSize());
            Console.WriteLine("Sekret: " + secretString);
            Console.WriteLine("--------");
            int[] senatorNumbers = { 6, 4, 10 };
            int[] requiredAcceptances = { 3, 3, 6 };
            BigInteger[] regionSecrets = new BigInteger[3];

            for (int i = 0; i < 3; i++)
            {
                string regionSecretString = secretString.Substring(i * (secretString.Length / 3), secretString.Length / 3);
                regionSecrets[i] = new BigInteger(regionSecretString);
            }

            for (int i = 0; i < 3; i++)
            {
                BigInteger secret = regionSecrets[i];
                BigInteger prime = secret.NextProbablePrime();
                Console.WriteLine();
                Console.WriteLine("Sekret dla regionu " + i + ":");
                Console.WriteLine(secret);
                Console.WriteLine("prime: " + prime);
                BigInteger[] elements = new BigInteger[requiredAcceptances[i] - 1];
                BigInteger[] shares = new BigInteger[senatorNumbers[i]];

                for (int j = 0; j < requiredAcceptances[i] - 1; j++)
                {
                    BigInteger randomBigInteger;
                    do
                    {
                        randomBigInteger = new BigInteger(getRandomSecretString(secretSize()/3));
                    } while (randomBigInteger.CompareTo(secret) > 0);
                    elements[j] = randomBigInteger;
                }
                Console.WriteLine("Udziały: ");
                for (int x = 1; x <= senatorNumbers[i]; x++)
                {
                    BigInteger W = new BigInteger("0");
                    for (int power = 1; power < requiredAcceptances[i]; power++)
                    {
                        BigInteger xBigInt = new BigInteger(x.ToString());
                        BigInteger el = xBigInt.Pow(power).Multiply(elements[power - 1]);
                        W = W.Add(el);
                    }
                    W = W.Add(secret);
                    shares[x - 1] = W.Mod(prime);
                    Console.WriteLine(x + ", " + shares[x-1]);
                }
                BigInteger M = new BigInteger("0");
                Console.WriteLine("Odtworzony sekret: ");
                for (int x = 1; x <= requiredAcceptances[i]; x++)
                {
                    BigInteger xBigInt = new BigInteger(x.ToString());
                    BigInteger part = shares[x-1];
                    for (int xup = x+1; xup <= requiredAcceptances[i]; xup++)
                    {
                        BigInteger xupBigInt = new BigInteger(xup.ToString());
                        BigInteger tmp = xupBigInt.Multiply(new BigInteger("-1")).Mod(prime);
                        BigInteger tmp2 = xBigInt.Subtract(xupBigInt).Mod(prime);
                        part = part.Multiply(tmp.Multiply(tmp2));
                    }
                    for (int xdown = x-1; xdown >= 1; xdown--)
                    {
                        BigInteger xdownBigInt = new BigInteger(xdown.ToString());
                        BigInteger tmp = xdownBigInt.Multiply(new BigInteger("-1").Mod(prime));
                        BigInteger tmp2 = xBigInt.Subtract(xdownBigInt).ModInverse(prime);
                        part = part.Multiply(tmp.Multiply(tmp2));
                    }
                    M = M.Add(part.Mod(prime));
                }
                M = M.Mod(prime);
                Console.WriteLine(M);
            }
            Console.ReadLine();
            return;
        }

        private static Random random = new Random();

        static int secretSize()
        {
            return 6;
        }
        static string getRandomSecretString(int length)
        {
            const string chars = "0123456789";
            return new string(Enumerable.Repeat(chars, length).Select(s => s[random.Next(s.Length)]).ToArray());
        }
    }
}