Provably secure three-party password-based authenticated key exchange protocol

A three-party password-based authenticated key exchange (3PAKE) protocol is a useful mechanism to establish a secure session key in a network. However, most current 3PAKE protocols only achieve “heuristic” security; the underlying hardness assumptions of these protocols are not perfect. We propose a 3PAKE protocol which is provably secure if the Diffie–Hellman problem is computationally infeasible (the CDH assumption), even in the 3eCK model where the adversary is allowed to make more queries and have more freedom than previous models. In our formal proof, we use the trapdoor test technique introduced by Cash, Kiltz and Shoup to construct an efficient decision oracle. As far as we know, our protocol is the first provably secure 3PAKE protocol based on the CDH assumption and the first 3PAKE protocol using the trapdoor test technique for the security proof.