Perfect Secret Sharing Schemes on Five Participants

A perfect secret sharing scheme is a system for the protection of a secret among a number of participants in such a way that only certain subsets of these participants can reconstruct the secret, and the remaining subsets can obtain no additional information about the secret. The efficiency of a perfect secret sharing scheme can be assessed in terms of its information rates. In this paper we discuss techniques for obtaining bounds on the information rates of perfect secret sharing schemes and illustrate these techniques using the set of monotone access structures on five participants. We give a full listing of the known information rate bounds for all the monotone access structures on five participants.