Advances in Cryptology — CRYPTO’ 88

Abstract

We introduce new theoretical measures for the qualitative and quantitative assessment of encryption schemes designed for broad- cast transmissions. The goal is to allow a central broadcast site to broad- cast secure transmissions to an arbitrary set of recipients while minimiz- ing key management related transmissions. We present several schemes that allow a center to broadcast a secret to any subset of privileged users out of a universe of size n so that coalitions of k users not in the privileged set cannot learn the secret. The most interesting scheme requires every user to store O(klogklogn)keys and the center to broad- cast O(k2log' k logn) messages regardless of the size of the privileged set. This scheme is resilient to any coalition of k users. We also present a scheme that is resilient with probability p against a random subset of k users. This scheme requires every user to store O(1og k log(l/p)) keys and the center to broadcast O(klog2klog(l/p)) messages.