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We introduce and analyze a scalable re-keying scheme for implementing secure group communications over IP multicast. We show that our scheme incurs constant processing, message, and storage overhead for a re-key operation when a single member joins or leaves the group, and logarithmic overhead for bulk simultaneous changes to the group membership. These bounds hold even when group dynamics are not known a priori. Our re-keying algorithm requires a particular clustering of the members of the secure multicast group. We describe a protocol to achieve such clustering and show that it is feasible to efficiently cluster members over realistic Internet-like topologies. We evaluate the overhead of our own re-keying scheme and also of previously published schemes via simulation over an Internet topology map containing over 280,000 routers. Through analysis and detailed simulations, we show that this re-keying scheme performs better than previous schemes for a single change to group membership. Further, for bulk changes, our algorithm outperforms all previously known schemes by several orders of magnitude in terms of actual bandwidth usage, processing costs and storage requirements.