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Many enterprise networks require flexible dynamic group communications on the Internet. When we develop these systems on multicast communication framework, various types of security threats will occur. As a result, construction of secure group communication that protects users from intrusion and eavesdropping are very important matters. We propose an efficient key distribution method for a secure group communication over multicast communication framework. In this method, we use IP multicast mechanism to shorten rekeying time to minimize adverse effect on communication. In addition, we introduce a proxy mechanism for replies from group members to the group manager to reduce traffic generated by rekeying. We define a multicast communication network model and evaluate the proposed method by computations using the model. From results of the evaluation, the proposed method shortens the rekeying time and reduces concentration of traffic to the group management server in large systems.