On Composability of Game-Based Password Authenticated Key Exchange
2018 IEEE European Symposium on Security and Privacy (EuroS&P)
It is standard practice that the secret key derived from an execution of a Password Authenticated Key Exchange (PAKE) protocol is used to authenticate and encrypt some data payload using a Symmetric Key Protocol (SKP). Unfortunately, most PAKEs of practical interest are studied using so-called game-based models, which -unlike simulation models -do not guarantee secure composition per se. However, Brzuska et al. (CCS 2011) have shown that a middle ground is possible in the case of authenticated
... ey exchange that relies on Public-Key Infrastructure (PKI): the game-based models do provide secure composition guarantees when the class of higher-level applications is restricted to SKPs. The question that we pose in this paper is whether or not a similar result can be exhibited for PAKE. Our work answers this question positively. More specifically, we show that PAKE protocols secure according to the game-based Real-or-Random (RoR) definition with the weak forward secrecy of Abdalla et al. (S&P 2015) allow for safe composition with arbitrary, higher-level SKPs. Since there is evidence that most PAKEs secure in the Find-then-Guess (FtG) model are in fact secure according to RoR definition, we can conclude that nearly all provably secure PAKEs enjoy a certain degree of composition, one that at least covers the case of implementing secure channels. In this paper, we answer this question positively by essentially adapting the framework in  to the passwordbased case. More specifically, our findings are as follows: • First of all, we demonstrate in Sect. 1.3 that the composition theorem of Brzuska et al.  can not be directly applied in PAKE setting. Namely, the FtG definition that was used in  to show that PKI-KE securely composes with an arbitrary Symmetric Key Protocol (SKP), does not seem to be sufficient in the case of PAKE. Fortunately, we show that PAKE enjoys similar composition properties when satisfying a stronger security notion, i.e. RoR. 6. This model assumes that the passwords setup procedure is private. 7. The description of the internal state and the definitions of partnering and freshness can be found below.