1. Overlaying Circuit Clauses for Secure Computation 2017 Asiacrypt GarbledCircuits MPC
    W. Sean Kennedy and Vladimir Kolesnikov and Gordon Wilfong
    [View PDF on eprint.iacr.org]
    [Show BibTex Citation]

    @misc{cryptoeprint:2016:685,
    author = {W. Sean Kennedy and Vladimir Kolesnikov and Gordon Wilfong},
    title = {Overlaying Circuit Clauses for Secure Computation},
    howpublished = {Cryptology ePrint Archive, Report 2016/685},
    year = {2016},
    note = {\url{https://eprint.iacr.org/2016/685}},
    }

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.

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