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In this paper, we mainly investigate anonymous user authentication scheme using smart card. We first demonstrate security weaknesses still exist in two such schemes recently propose by Wang et al. and Tsai et al., respectively according to Wang et al.'s criteria. Thereafter, we propose an enhanced smart-card-based authentication scheme with user anonymity for providing all the admired requirements at the same time. Compared with the previous schemes, our scheme is yet efficient both in computation and communication cost. Moreover, we can prove the security of the proposed scheme in the random oracle model. Copyright © 2011 John Wiley & Sons, Ltd. (We demonstrate security weaknesses still exist in two such schemes recently propose by Wang et al. and Tsai et al. respectively according to Wang et al.'s criteria. And we propose an enhanced smart-card-based authentication scheme with user anonymity for providing all the admired requirements at the same time.)