Password Based Key Exchange with Mutual Authentication

A reasonably efficient password based key exchange (KE) protocol with provable security without random oracle was recently proposed by Katz, et al. [18] and later by Gennaro and Lindell [13]. However, these protocols do not support mutual authentication (MA). The authors explained that this could be achieved by adding an additional flow. But then this protocol turns out to be 4-round. As it is known that a high entropy secret based key exchange protocol with MA is optimally 3round (otherwise, at least one entity is not authenticated since a replay attack is applicable), it is quite interesting to ask whether such a protocol in the password setting (without random oracle) is achievable or not. In this paper, we provide an affirmative answer with an efficient construction in the common reference string (CRS) model. Our protocol is even simpler than that of Katz, et al. Furthermore, we show that our protocol is secure under the DDH assumption (without random oracle).