Analysis of Two Pairing - based Three - party Password

Password-Authenticated Key Exchange (PAKE) protocols allow parties to share secret keys in an authentic manner based on an easily memorizable password. Recently, Nam et al. showed that a provably secure three-party passwordbased authenticated key exchange protocol using Weil pairing by Wen et al. is vulnerable to a man-in-the-middle attack. In doing so, Nam et al. showed the flaws in the proof of Wen et al. and described how to fix the problem so that their attack no longer works. In this paper, we show that both Wen et al. and Nam et al. variants fall to key compromise impersonation by any adversary. Our results underline the fact that although the provable security approach is necessary to designing PAKEs, gaps still exist between what can be proven and what are really secure in practice. Keywords-Password-authenticated key exchange; cryptanalysis; attacks; provable security; three-party; key compromise impersonation; Weil pairing