A Key for John Doe: Modeling and Designing Anonymous Password-Authenticated Key Exchange Protocols

Anonymous Password-Authenticated Key Exchange (\sf APAKEAPAKE) can be seen as the hybrid offspring of standard key exchange and anonymous password authentication protocols. \sf APAKEAPAKE allows a client holding a low-entropy password to establish a session key with a server, provided that the client's password is in the server's set. Moreover, no information about the password input by the client or the set of valid passwords held by the server should leak to the other party-beyond whether the client's password lies or not in the server's password database. To the best of our knowledge, all \sf APAKEAPAKE proposals to date either assume client storage or force the client to remember the index assigned to its password in the server's database. Furthermore, earlier works either provide only informal definitions or fail in some sense to properly model the primitive. In this paper, we provide a formal security model for \sf APAKEAPAKE, capturing security and anonymity provisions for both clients and servers. In addition, we present two \sf APAKEAPAKE protocols that only require clients to remember a password and that attain our sought key secrecy and anonymity guarantees. Our first protocol leverages oblivious pseudo-random functions, while the second one builds upon a special type of identity-based encryption scheme.