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Confidential Content-Based Publish/Subscribe (C-CBPS) is an interaction(pub/sub) model that allows parties to exchange data while still protectingtheir security and privacy interests. In this paper we advance the state of theart in C-CBPS by showing how all predicate circuits in NC1 (logarithmic-depth,bounded fan-in) can be securely computed by a broker while guaranteeing perfectinformation-theoretic security. Previous work could handle only strictlyshallower circuits (e.g. those with depth O(\sqrt{\lg n}) [SYY99, V76]. Wepresent three protocols -- UGP-Match, FSGP-Match and OFSGP-Match -- all threeare based on (2-decomposable randomized encodings of) group programs and handlecircuits in NC1. UGP-Match is conceptually simple and has a clean proof ofcorrectness but it is inefficient and impractical. FSGP-Match uses a "fixedstructure" trick to achieve efficiency and scalability. And, finally,OFSGP-Match uses hand-optimized group programs to wring greater efficiencies.We complete our investigation with an experimental evaluation of a prototypeimplementation.

Secure and scalable match: overcoming the universal circuit bottleneck using group programs