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

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Abstract

Confidential Content-Based Publish/Subscribe (C-CBPS) is an interaction model that allows parties to exchange content while 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 confidentially computed by a broker while guaranteeing perfect information-theoretic security. Previous work could handle only strictly shallower circuits (e.g. those with depth O(ℑ)). We present three protocols—UGP-Match, FSGP-Match and OFSGP-Match—based on 2-decomposable randomized encodings of group programs for circuits in NC1. UGP-Match is conceptually simple and has a clean proof of correctness but its running time is a polynomial with a high exponent and hence impractical. FSGP-Match uses a “fixed structure” construction that reduces the exponent drastically and achieves efficiency and scalability. OFSGP-Match optimizes the group programs further to shave off a linear factor.

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