Universally composable anonymous password authenticated key exchange

Anonymous password authenticated key exchange（APAKE） is an important cryptographic primitive, through which a client holding a password can establish a session key with a server both authentically and anonymously. Although the server is guaranteed that the client in communication is from a pre-determined group, but the client＇s actual identity is protected. Because of their convenience, APAKE protocols have been widely studied and applied to the privacy protection research. However, all existing APAKE protocols are handled in stand-alone models and do not adequately settle the problem of protocol composition, which is a practical issue for protocol implementation. In this paper, we overcome this issue by formulating and realizing an ideal functionality for APAKE within the well-known universal composability（UC） framework, which thus guarantees security under the protocol composition operations. Our formulation captures the essential security requirements of APAKE such as off-line dictionary attack resistance, client anonymity and explicit mutual authentication. Moreover, it addresses the arbitrary probabilistic distribution of passwords. The construction of our protocol, which utilizes SPHF-friendly commitments and CCA2-secure encryption schemes, can be instantiated and proven secure in the standard model, i.e., without random oracle heuristics.