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Many emerging network applications are based upon a group communications model. As a result, securing group communications, i.e., providing confidentiality, authenticity, and integrity of messages delivered between group members, will become a critical networking issue. We present, in this paper, a novel solution to the scalability problem of group/multicast key management. We formalize the notion of a secure group as a triple (U,K,R) where U denotes a set of users, K a set of keys held by the users, and R a user-key relation. We then introduce key graphs to specify secure groups. For a special class of key graphs, we present three strategies for securely distributing rekey messages after a join/leave and specify protocols for joining and leaving a secure group. The rekeying strategies and join/leave protocols are implemented in a prototype key server we have built. We present measurement results from experiments and discuss performance comparisons. We show that our group key management service, using any of the three rekeying strategies, is scalable to large groups with frequent joins and leaves. In particular, the average measured processing time per join/leave increases linearly with the logarithm of group size.