A Convex Optimization Approach for Addressing Storage-Communication Tradeo s in Multicast Encryption

In Eurocrypt'99, Canetti, Malkin, and Nissim 1] presented a new tree based key distribution algorithm that required O(log n) (n is the group size) key update communications and key storage of O(n log n). The results in 1] are known to be the rst results presenting the sub-linear storage among the family of tree based key distribution schemes. The question of whether this storage was the possible optimal value while keeping the communication as O(log n) was posed as a problem. We show that the storage-communication tradeoo can be formulated as a convex optimization problem in terms of the size of the minimal storage parameter deened in 1]. In particular, we show that the optimal solution is parameterizable by the ratio of the communication and storage costs denoted , the degree of the tree denoted a, and the group size n. Using this design triplet (a; n;), we show that not only the results in 1] but also the results of the basic scheme of Wallner, Harder, and Agee 2] can be derived as speciic Pareto optimal points for speciic choice of the triplet (a; n;). We also present an exact design procedure for feasibility testing and constructing optimal key distribution tree of the type in 1]. We also show that if the communication and the storage are equally weighted, then the optimal value for storage and communication is O(p n), a value noted in 1].