A note on broadcast encryption key management with applications to large scale emergency alert systems

Emergency alerting capability is crucial for the prompt response to natural disasters and terrorist attacks. The emerging network infrastructure and secure broadcast techniques enable prompt and secure delivery of emergency notification messages. With the ubiquitous deployment of alert systems, scalability and heterogeneity pose new challenges for the design of secure broadcast schemes. In this paper, we discuss the key generation problem with the goal of minimizing the total number of keys which need to be generated by the alert center and distributed to the users. Two encryption schemes, zero message scheme and extended header scheme, are modeled formally. For both schemes we show the equivalence of the general optimal key generation (OKG) problem and the bipartite clique cover (BCC) problem, and show that OKG problem is NP-hard. The result is then generalized to the case with resource constraints, and we provide a heuristic algorithm for solving the restricted BCC (and OKG) problem.