As an important mechanism to guarantee secure communication, the authentication scheme has attracted wide attention. Recently, Xu et al. proposed a new authentication scheme and show their scheme is provably secure in the random oracle model under the computational Diffie-Hellman assumption. Unfortunately, in this paper, we will demonstrate that Xu et al.'s scheme is vulnerable to the impersonation attack and the privileged insider attack. We also propose an improved scheme to eliminate the security vulnerability.
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