Create short GUIDs with a custom alphabet

ShortGUID.cs

using System;
using System.Numerics;

namespace Cuppster
{
  /// <summary>
  /// converted from the python version at https://github.com/stochastic-technologies/shortuuid
  /// </summary>
  class ShortUUID
  {
    private char[] _alphabet = "23456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz".ToCharArray();
    private int _alphaLen;

    public ShortUUID()
    {
      _alphaLen = _alphabet.Length;
    }

    public ShortUUID(char[] alphabet)
    {
      _alphabet = alphabet;
      _alphaLen = _alphabet.Length;
    }

    public string Uuid()
    {
      var uuid = Guid.NewGuid();
      return Encode(uuid);
    }

    private string Encode(Guid uuid)
    {
      var uuidBytes = uuid.ToByteArray();

      // ensure that the most-significant bit of the last byte (because it's little endian) is zero
      // see: http://stackoverflow.com/questions/6141745/shift-a-128-bit-signed-biginteger-to-always-be-positive
      byte[] padded = new byte[uuidBytes.Length + 1];
      uuidBytes.CopyTo(padded, 0);
      padded[uuidBytes.Length] = 0;

      BigInteger big = new BigInteger(padded);
      return NumToString(big);
    }

    private string NumToString(BigInteger number)
    {
      var output = string.Empty;
      var len = new BigInteger(_alphaLen);
      BigInteger digit;
      while (0 <  number)
      {        
        number = BigInteger.DivRem(number, len, out digit);
        output += _alphabet[(int)digit];
      }
      return output;
    }
  }
}