Stronger security model of group key agreement

In PKC 2009, Gorantla, Boyd and González Nieto presented a nice result on modelling security for group key agreement (GKA) protocols. They proposed a novel security model (GBG model) that better supports the adversaries' queries than previous models for GKA protocols by considering KCI resilience. However, ephemeral key leakage attack resistance has been left outside the scope of the GBG model. In this paper, we demonstrate an ephemeral key leakage on an existing GKA protocol which has been shown secure in the GBG model. We then extend the GBG model by allowing the adversary greater attack powers of leaking ephemeral keys in GKA protocol session. We also apply the well known NAX-OS trick to propose an improvement to an existing GKA protocol, which can resist the ephemeral key leakage attack. The security of the improved protocol has been argued under the our new model.