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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.
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