At Indocrypt 2005, Viet et al., [20] have proposed an anonymous password-authenticated key exchange (PAKE) protocol and its threshold construction both of which are designed for client’s password-based authentication and anonymity against a passive server, who does not deviate the protocol. In this paper, we first point out that their threshold construction is completely insecure against off-line dictionary attacks. For the threshold t?>?1, we propose a secure threshold anonymous PAKE (for short, TAP) protocol with the number of clients n upper-bounded, such that , where N is a dictionary size of passwords. We also show that the TAP protocol provides semantic security of session keys in the random oracle model, with the reduction to the computational Diffie-Hellman problem, as well as anonymity against a passive server. For the threshold t?=?1, we propose an efficient anonymous PAKE protocol that significantly improves efficiency in terms of computation costs and communication bandwidth compared to the original (not threshold) anonymous PAKE protocol [20].
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