We consider a system where each user is in one or more elementary groups. In this system, arbitrary groups of users can be specified using the operations of union, intersection, and complement over the elementary groups in the system. Each elementary group in the system is provided with a security key that is known only to the users in the elementary group and to the system server. Thus, for any user u to securely multicast a data item d to every user in an arbitrary group G, u first forwards d to the system server which encrypts it using the keys of the elementary groups that comprise G before multicasting the encrypted d to every user in G. Every elementary group is also provided with a key tree to ensure that the cost of changing the key of the elementary group, when a user leaves the group, is small. We describe two methods for packing the key trees of elementary groups into key bundles and into key parcels. Packing into key bundles has the advantage of reducing the number of encryptions needed to multicast a data item to the complement of an elementary group. Packing into key parcels has the advantage of reducing the total number of keys in the system. We apply these two methods to a class of synthetic systems: each system has 10000 users and 500 elementary groups, and each user is in 2 elementary groups on average. Simulations of these systems show that our proposals to pack key trees into key bundles and key parcels live up to their promises.
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