Interactive Diffie-Hellman Assumptions with Applications to Password-Based Authentication

The area of password-based authenticated key exchange protocols has been the subject of a vast amount of work in the last few years due to its practical aspects. In these protocols, the goal is to enable users communicating over an unreliable channel to establish a secure session key even when the secret key that they share is drawn from a small set of values. Despite the attention given to it, it was only recently that this problem has been formally addressed in the three-party setting. In this setting, the users trying to establish a secret session key are only required to share a password with a trusted server and not directly among themselves. In this paper, we introduce a new three-party password-based authenticated key exchange protocol based on the two-party encrypted key exchange of Bellovin and Merritt. Our protocol is reasonably efficient and has a per-user computational cost that is comparable to that of the underlying two-party encrypted key exchange. The proof of security is in the random oracle model and is based on new and apparently stronger variants of the decisional Diffie-Hellman problem which are of independent interest.