Cryptology ePrint Archive: Report 2018/163

We initiate the study of "Strong aPAKE" protocols that are secure as aPAKE's but are also secure against pre-computation attacks. We formalize this notion in the Universally Composable (UC) settings and present two modular constructions using an Oblivious PRF as a main tool. The first builds a Strong aPAKE from any aPAKE (which in turn can be constructed from any PAKE [GMR'06]) while the second builds a Strong aPAKE from any authenticated key-exchange protocol secure against reverse impersonation (a.k.a. KCI). Using the latter transformation, we show a practical instantiation of a UC-secure Strong aPAKE in the Random Oracle model. The protocol ("OPAQUE") consists of 2 messages (3 with mutual authentication), requires 3 and 4 exponentiations for server and client, respectively (2 to 4 of which can be fixed-base depending on optimizations), provides forward secrecy, is PKI-free, supports user-side hash iterations, has a built-in facility for password-based storage and retrieval of secrets and credentials, and accommodates a user-transparent server-side threshold implementation.