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. In this paper, we show that by assigning probabilities for member revocations, the optimality, correctness, and the system requirements of some of these schemes 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 correspond to the maximum entropy solution, (b) and direct application of source coding will lead to member collusion (we present recently proposed solutions 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.Crypto '99 :: 19th Annual IACR Crypto Conference</i