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This paper concerns methods by which a trusted authoritycan distribute keys and/or broadcast a message over a network,so that each member of a privileged subset of users can computea specified key or decrypt the broadcast message. Moreover, thisis done in such a way that no coalition is able to recover anyinformation on a key or broadcast message they are not supposedto know. The problems are studied using the tools of informationtheory, so the security provided is unconditional (i.e., notbased on any computational assumption).In a recent paper st95a, Stinson described a method of constructingkey predistribution schemes by combining Mitchell-Piper key distributionpatterns with resilient functions; and also presented a constructionmethod for broadcast encryption schemes that combines Fiat-Naorkey predistribution schemes with ideal secret sharing schemes.In this paper, we further pursue these two themes, providingseveral nice applications of these techniques by using combinatorialstructures such as orthogonal arrays, perpendicular arrays, Steinersystems and universal hash families.