Secure cross-realm client-to-client password-based authenticated key exchange against undetectable on-line dictionary attacks

The cross-realm client-to-client password-based authenticated key exchange (C2C-PAKE) is protocol which two clients in two different realms with different passwords exchange a session key through their corresponding servers. Recently, a provably secure cross-realm C2C-PAKE scheme with the optimal number of rounds for a client is pointed out that the scheme is insecure against an undetectable on-line dictionary attack and an unknown-key share attack. In this paper, we propose a new cross-realm C2C-PAKE scheme with the optimal number of rounds for a client, which has resistances to previously considered attacks which should be prevented, including undetectable on-line dictionary attacks and unknown-key share attacks. Moreover, our scheme assumes no pre-established secure channels between different realms, but just basic setups of ID-based systems.