The most important concerns is how to minimize the communication overhead when the shared GK is updated among the subscribers. Treebased KM, one class of GKM, has received considerable attention from many researchers since the amount of overhead for group rekeying is proportional to the logarithm of the group size. Many researchers have proposed new GKM schemes with tree-based structure such as logical key hierarchy(LKH), one-way function tree(OFT), and one-way key derivation(OKD). Next-generation mobile communication, multicast service will be a key application for suporting a large group of subscribers simultaneously. Because multicast transmits data to the group simultaneously, it reduces the communication cost significantly. They since multicast may be vulnerable to an overhearing attack, this efficiency can be achieved only when security or access control is guaranteed; i.e., only authorized group members can read the data properly. Because smart phones are becoming popular, many mobile applications which need group communication such as DMB, video conference, and online game have emerged. For both security and efficiency, a group key (GK) which is shared only by a group of mobile devices has been employed for access control. A message for the group is encrypted by the GK and transmitted only once. The GK is updated whenever the group membership changes for forward and backward secrecy, which can cause a serious problem with rekeying overhead. Although many GKM proposals have been made since BR was proposed, they have some fundamental limitations to be adopted to the mobile environment.