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In many remote user authentication schemes, there was no scheme to resist the power analysis attack. As far as we know, this is the first remote user authentication scheme which considers power analysis attack. In this paper, we propose a new efficient and secure remote authentication scheme. Compared with other smart card-based schemes, our scheme has more merits as follows: 1) the system does not keep the password table of the users; 2) user can choose their password freely; 3) mutual authentication is provided between the user and the remote system; 4) the communication cost and the computational cost are very low; 5) the nonce-based scheme does not require a timestamp to solve the serious time synchronization problem; 6) the scheme can resist the power analysis attack and other several attacks.