Many emerging applications in both wired and wireless networks need support of secure group communications. There have been many secure group communication schemes in the setting of wired networks. These schemes can be directly adopted in, or appropriately adapted to, the setting of wireless networks such as mobile ad hoc networks (MANETs) and sensor networks. In this paper we show that the popular group communication schemes that we have examined are vulnerable to the following attack: An outsider adversary who compromises a certain legitimate group member could obtain all past and present group keys; this is in sharp contrast to the widely-accepted belief that a such adversary can only obtain the present group key. This attack is very powerful also because it provides the adversary the following flexibility: There are possibly many legitimate group members such that compromising any of them leads to the exposure of those past and present group keys. In order to understand and deal ...