Multi-round secure light-weight broadcast exclusion protocol with pre-processing

A broadcast exclusion protocol allows a broadcaster to transmit a encrypted message to a set of n users over a broadcast channel so that all but some specified small group of k excluded users can decrypt the message, even if these excluded users collude with each other in an arbitrary manner. Recently, Matsuzaki et al. pointed out a potential problem in the earlier works regarding the number of modular exponentiation, and proposed an extended scheme in which decryption requires only two modular exponentiations regardless of n and k. However, our analysis shows this scheme has a limitation of the number of rounds. The contribution of this paper is to present a new broadcast exclusion protocol maintaining security within a virtually unlimited number of rounds without spoiling the efficiency. First, we demonstrate a limitation of the rounds of the previous work by showing how a user can derive the system secret parameters after more than a certain number of rounds. Then, we present a new protocol for which we can provide rigorous security proof under the Computational Diffie-Hellman (CDH) assumption. We note that even if we point out some limitation of the previous work, we still consider it nevertheless significant. In particular, we derived our new protocol by modifying some of their fundamental techniques.