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Summary: We introduce new theoretical measures for the qualitative and quantitative assessment of encryption schemes designed for broadcast transmissions. The goal is to allow a central broadcast site to broadcast secure transmissions to an arbitrary set of recipients while minimizing 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 $$O(k \log k \log n)$$ keys and the center to broadcast $$O(k^2 \log^2 k \log n)$$ 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 $$O(\log k \log(1/p))$$ keys and the center to broadcast $$O(k \log^2 k \log (1/p))$$ messages.