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This paper proposes an efficient protocol and associate algorithm for group key management in secure multicast. This protocol is based on a hierarchy approach in which the group is logically divided into subgroups. The group key is organized using member secrets assigned to each member and server secrets assigned to each subgroup, and the inverse value of the member secrets are also used to manage the group key when a member leaves. In this case, each member in a single subgroup needs to store the inverse values of the other members in that subgroup with the exception of its own. When a member joins the group, after updating the previous group key in the server, the new key is sent to all existing group members, and the inverse value of the new member is sent to subgroup members (where there is a join), by exploiting IP multicast. Most importantly, the server just sends the inverse value of the leaving member to the subgroups when a member leaves. Then, the group key is updated by each remaining member in the subgroups by using that inverse value. Consequently, the benefits are two-fold. First, only one key needs to be generated by the server at each event. Second, not only the computational overhead is reduced but also new key information can be multicast to all members simultaneously. This paper describes the details of our novel protocol and the related algorithm.