User Authentication in computer systems is an important cornerstone in today's computer era. The concept of a user id and password is one of the easiest ways for authentication. It is not only the easiest way, but also cost effective and highly efficient. Today, the authors can see the password cracking and hacking in everywhere. At present, they are using the single server system for this sort of password based authentication. Traditional protocols for password-based authentication assume a single server which stores all the information (e.g., the password) necessary to authenticate a user.