A Secure Construction for Threshold Anonymous Password-Authenticated Key Exchange

At Indocrypt 2005, Viet et al., [21] 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 $n\leq 2 \sqrt{N-1} -1$, where N is a dictionary size of passwords. We rigorously prove that the TAP protocol has semantic security of session keys in the random oracle model by showing the reduction to the computational Diffie-Hellman problem. In addition, the TAP protocol provides unconditional 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 [21].