Paper 2016/685

Overlaying Circuit Clauses for Secure Computation

W. Sean Kennedy, Vladimir Kolesnikov, and Gordon Wilfong

Abstract

Given a set S = {C_1,...,C_k } of Boolean circuits, we show how to construct a universal for S circuit C_0, which is much smaller than Valiant’s universal circuit or a circuit incorporating all C_1,...,C_k. Namely, given C_1,...,C_k and viewing them as directed acyclic graphs (DAGs) D_1,...,D_k, we embed them in a new graph D_0. The embedding is such that a GC garbling of any of C_1,...,C_k could be implemented by a corresponding garbling of a circuit corresponding to D_0. We show how to improve Garbled Circuit (GC) and GMW-based secure function evaluation (SFE) of circuits with if/switch clauses using such S-universal circuit. The most interesting case here is the application to the GMW approach. We provide a novel observation that in GMW the cost of processing a gate is almost the same for 5 (or more) Boolean inputs, as it is for the usual case of 2 Boolean inputs. While we expect this observation to greatly improve general GMW-based computation, in our context this means that GMW gates can be programmed almost for free, based on the secret-shared programming of the clause. Our approach naturally and cheaply supports nested clauses. Our algorithm is a heuristic; we show that solving the circuit embedding problem is NP-hard. Our algorithms are in the semi-honest model and are compatible with Free-XOR. We report on experimental evaluations and discuss achieved performance in detail. For 32 diverse circuits in our experiment, our construction results 6.1x smaller circuit than prior techniques.

Note: slightly changed flow for clarity