An Information Theoretic Analysis of Rooted-Tree Based Secure Multicast Key Distribution Schemes

Several variations of rooted tree based solutions have been recently proposed for member revocation in multicast communications [18, 19, 20, 21]. In this paper, we show that by assigning probabilities for member revocations, the optimality, correctness, and the system requirements of some of these schemes [18, 19, 20, 21] can be systematically studied using information theoretic concepts. Specifically, we show that the optimal average number of keys per member in a rooted tree is related to the entropy of the member revocation event. Using our derivations we show that (a) the key assignments in [18, 21, 20, 19] correspond to the maximum entropy solution, (b) and direct application of source coding will lead to member collusion (we present recently proposed solutions [21, 20] as examples of this) and a general criteria that admits member collusion. We also show the relationship between entropy of member revocation event and key length.