A set theoretic approach to broadcast encryption

Broadcast Encryption allows a centre to send information over a broadcast channel to a dynamically changing group of users. The performance is rated by the bandwidth required for the broadcast and the amount of secret information needed to be stored at the user end. It can also be rated by the computational overhead. In the “Stateless Receiver” model, receivers are incapable of storing any new information, or updating themselves, between broadcasts. We look at two Stateless Receiver schemes by Naor et al., the Complete Subtree Revocation Scheme and the Subset Difference Revocation Scheme. We improve the bound on the bandwidth for the Complete Subtree Revocation Scheme given by Naor from tmax(n, r) ≤ r(k − log2(r)) to tmax(n, r) = r(k − j)− 2(r − 2), where j = blog2(r)c. We prove a similar bound on the maximum bandwidth for the Subset Difference Revocation Scheme. We also derive formula for the average bandwidth for both schemes. The schemes of Naor et al. are each based on a single binary tree. We construct some variations of the Complete Subtree Revocation Scheme, the first has more than one tree, the other is based on an a-ary tree. We calculate the improved performance in bandwidth (traded off against an increase in storage). We make meaningful comparisons between these schemes and existing ones. Finally, we show how to reduce the storage requirement of the Complete Subtree Revocation Scheme from O(log2(n)) to a constant term.