Universally Composable Relaxed Password Authenticated Key Exchange

Protocols for password authenticated key exchange (PAKE) allow two parties who share only a weak password to agree on a cryptographically strong key. We revisit the notion of PAKE in the framework of universal composability, and propose a relaxation of the PAKE functionality of Canetti et al. that we call lazy-extraction PAKE (lePAKE). Roughly, our relaxation allows the ideal-world adversary to postpone its password guess even until after a session is complete. We argue that this relaxed notion still provides meaningful security in the password-only setting.

As our main result, we show that several PAKE protocols that were previously only proven secure with respect to a "game-based" definition can in fact be shown to realize the lePAKE functionality in the random-oracle model. These include SPEKE, SPAKE2, and TBPEKE, the most efficient PAKE schemes currently known.