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

Abstract

Confidential Content-Based Publish/Subscribe (C-CBPS) is an interaction (pub/sub) model that allows parties to exchange data while still protecting their security and privacy interests. In this paper we advance the state of the art 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 perfect information-theoretic security. Previous work could handle only strictly shallower circuits (e.g. those with depth O(\sqrt{\lg n}) [SYY99, V76]. We present three protocols -- UGP-Match, FSGP-Match and OFSGP-Match -- all three are based on (2-decomposable randomized encodings of) group programs and handle circuits in NC1. UGP-Match is conceptually simple and has a clean proof of correctness but it is inefficient and impractical. FSGP-Match uses a "fixed structure" 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 prototype implementation.