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In this paper, a bilinear mapping based password-based access control scheme with remote user authentication scheme using smart cards is presented. The proposed scheme enables one user to choose his password freely in the registration phase and easily change it as needed. We take the novel technique of binding one user's private key to his identity, which enables the AS (authentication server) to be unnecessary to maintain a password table to verify the login request and thus enhances the practicality and reliability of the system. Additionally, based on the difficulty of Elliptic Curve Discrete Logarithm (ECDL) problem, the proposed scheme can efficiently withstand replaying attacks, forgery attacks, Masquerade attacks, guessing and stolen verifier attacks and insider attacks.