Combinatorial bounds for broadcast encryption

A broadcast encryption system allows a center to communicate securely over a broadcast channel with selected sets of users. Each time the set of privileged users changes, the center enacts a protocol to establish a new broadcast key that only the privileged users can obtain, and subsequent transmissions by the center are encrypted using the new broadcast key. We study the inherent trade-off between the number of establishment keys held by each user and the number of transmissions needed to establish a new broadcast key. For every given upper bound on the number of establishment keys held by each user, we prove a lower bound on the number of transmissions needed to establish a new broadcast key. We show that these bounds are essentially tight, by describing broadcast encryption systems that come close to these bounds.