I took the array approach which should be still faster because it avoids the hash calculations. Just build an array Char[65536] containing at every index i the character the character i should be mapped to. Rotator.Rotate() then simply becomes the following where Rotator.map is the precomputed array. Probably very similar to an implementation using a hash table. I also got rid of the string builder but did not profile the difference. If one uses a string builder it would most likely help to specify the capacity in the constructor call so that the internal array does not have to be resized repeatedly as the result is constructed and grows in length.

  public static String Rotate(String input)
  {
    var result = new Char[input.Length];

    for (var index = 0; index < input.Length; index++)
    {
      result[index] = Rotator.map[input[index]];
    }

    return new String(result);
  }