run https://ideone.com/f0GVgV

RandomWordMatch.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Security.Cryptography;
using System.Text;

namespace Util
{
    public class RandomWordMatch
    {
        private readonly string baseChars = "1234567890";
        private readonly string defaultMatchWord = "114514";

        private bool _ProgressDisplay = true;
        public bool ProgressDisplay { get { return _ProgressDisplay; } set { _ProgressDisplay = value; } }

        public RandomWordMatch()
        {
        }

        public RandomWordMatch(string baseChars, string defaultMatchWord = "114514")
        {
            if (string.IsNullOrWhiteSpace(baseChars))
                throw new ArgumentNullException("baseChars");
            else if (string.IsNullOrWhiteSpace(defaultMatchWord))
                throw new ArgumentNullException("defaultMatchWord");

            this.baseChars = baseChars;
            this.defaultMatchWord = defaultMatchWord;
        }


        public void Start(string matchWord = null, int limit = int.MaxValue)
        {
            if (string.IsNullOrWhiteSpace(matchWord))
                matchWord = defaultMatchWord;

            var wordQueue = new Queue<char>();

            foreach (var c in GetRandomString(matchWord.Count()))
                wordQueue.Enqueue(c);

            int count = 0;
            while (count < limit)
            {
                if (wordQueue.SequenceEqual(matchWord))
                {
                    foreach (var c in wordQueue)
                        Console.Write(c);

                    Console.WriteLine(
                        "\n\n    ＨＩＴ！！！ \n    {0}回目で「{1}」！！！",
                        (count + matchWord.Count()),
                        matchWord);

                    break;
                }

                count++;

                if (ProgressDisplay)
                {
                    Console.Write(wordQueue.Dequeue());
                }
                else
                {
                    wordQueue.Dequeue();
                }

                wordQueue.Enqueue(GetRandomString(1)[0]);
            }
        }

        private string GetRandomString(int length)
        {
            var sb = new StringBuilder(length);
            for (int i = 0; i < length; i++)
                sb.Append(baseChars[GetRandomNumber()]);
            return sb.ToString();
        }

        private int GetRandomNumber()
        {
            var bs = new byte[4];
            var rng = new RNGCryptoServiceProvider();
            rng.GetBytes(bs);
            var num = BitConverter.ToInt32(bs, 0);
            return Math.Abs(num % baseChars.Length);
        }
    }
}