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A password-authenticated key exchange scheme allows two entities, who only share a memorable password, to authenticate each other and to agree on a cryptographic session key. Instead of considering it in the classic client and server scenarios, Byun et al. recently proposed a password-authenticated key exchange protocol in a cross-realm setting where two clients in different realms obtain a secret session key as well as mutual authentication, with the help of respective servers. In this paper, we first point out that the proposed protocol is not secure, due to the choice of invalid parameters (say, subgroup generator). Furthermore, we show in detail that, even with properly chosen parameters, the protocol has still some secure flaws. We provide three attacks to illustrate the insecurity of the protocol. Finally, countermeasures are also given, which are believed able to withstand our attacks.

Weaknesses of a Password-Authenticated Key Exchange Protocol between Clients with Different Passwords