Security analysis of a password-based authentication protocol proposed to IEEE 1363

Abstract

In recent years, several protocols for password-based authenticated key exchange have been proposed. These protocols aim to be secure even though the sample space of passwords may be small enough to be enumerated by an off-line adversary. In Eurocrypt 2000, Bellare, Pointcheval and Rogaway (BPR) presented a model and security definition for authenticated key exchange. They claimed that in the ideal-cipher model (random oracles), the two-flow protocol at the core of Encrypted Key Exchange (EKE) is secure. Bellare and Rogaway suggested several instantiations of the ideal cipher in their proposal to the IEEE P1363.2 working group. Since then there has been an increased interest in proving the security of password-based protocols in the ideal-cipher model. For example, Bresson, Chevassut, and Pointcheval have recently showed that the One-Encryption-Key-Exchange (OEKE) protocol is secure in the ideal cipher model. In this paper, we present examples of real (NOT ideal) ciphers (including naive implementations of the instantiations proposed to IEEE P1363.2) that would result in broken instantiations of the idealised AuthA protocol and OEKE protocol. Our result shows that the AuthA protocol can be instantiated in an insecure way, and that there are no well defined (let alone rigorous) ways to distinguish between secure and insecure instantiations. Thus, without a rigorous metric for ideal-ciphers, the value of provable security in ideal cipher model is limited.