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The password based authentication schemes are commonly used for authenticating remote users. Many password based schemes both with and without smart card have been proposed; each scheme has its merits and demerits. In this paper we propose an efficient scheme for remote user authentication which does not maintain verifier table and allows the user to freely choose and change their passwords. Also the proposed scheme achieves mutual authentication which is essential for many applications. The scheme is secure against id theft, guessing attack, insider attack, stolen verifier attack, replay attack, impersonation attack, and reflection attack