Towards post-quantum secure PAKE - A tight security proof for OCAKE in the BPR model

. We revisit OCAKE (ACNS 23), a generic recipe that constructs password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEMs) in a black-box way. This allows to potentially achieve post-quantum security by instantiating the KEM with a post-quantum KEM like KYBER. It was left as an open problem to further adapt the proof such that it also holds against quantum attackers. The security proof is given in the universal composability (UC) framework, which is common for PAKE. So far, however, it is not known how to model or prove computational UC security against quantum adversarieslet alone if the proof uses idealized primitives like random oracles or ideal ciphers. To pave the way towards reasoning post-quantum security, we therefore resort to a (still classical) game-based security proof in the BPR model (EUROCRYPT 2000). We consider this a crucial stepping stone towards a full proof of post-quantum security. We prove security of (a minor variation of) OCAKE, assuming the underlying KEM sat-isfies notions of ciphertext indistinguishability, anonymity, and (computational) public-key uniformity. To achieve tight security bounds, we use multi-user variants of the aforementioned properties. We provide a full detailed proof – something often omitted in publications on game-based security of PAKE. As a side-contribution, we demonstrate in detail how to handle password guesses, which is something we were unable to find in the existing literature on game-based PAKE proofs.