Gate Evaluation Secret Sharing and Secure One-Round Two-Party Computation

We propose Gate Evaluation Secret Sharing (GESS) – a new kind of secret sharing, designed for use in secure function evaluation (SFE) with minimal interaction. The resulting simple and powerful GESS approach to SFE is a generalization of Yao’s garbled circuit technique. We give efficient GESS schemes for evaluating binary gates and prove (almost) matching lower bounds. We give a more efficient informationtheoretic reduction of SFE of a boolean formula F to oblivious transfer. Its complexity is ≈ di , where di is the depth of the i-th leaf of F .