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The More the Merrier: Reducing the Cost of Large Scale MPC

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Advances in Cryptology – EUROCRYPT 2021 (EUROCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12697))

Abstract

Secure multi-party computation (MPC) allows multiple parties to perform secure joint computations on their private inputs. Today, applications for MPC are growing with thousands of parties wishing to build federated machine learning models or trusted setups for blockchains. To address such scenarios we propose a suite of novel MPC protocols that maximize throughput when run with large numbers of parties. In particular, our protocols have both communication and computation complexity that decrease with the number of parties. Our protocols buildon prior protocolsbased on packed secret-sharing, introducing new techniques to build more efficient computation for general circuits. Specifically, we introduce a new approach for handling linear attacks that arise in protocols using packed secret-sharing and we propose a method for unpacking shared multiplication triples without increasing the asymptotic costs. Compared with prior work, we avoid the \(\log |C|\) overhead required when generically compiling circuits of size |C| for use in a SIMD computation, and we improve over folklore “committee-based” solutions by a factor of O(s), the statistical security parameter. In practice, our protocol is up to 10X faster than any known construction, under a reasonable set of parameters.

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Notes

  1. 1.

    We are ignoring terms that do not depend on |C| or n.

  2. 2.

    Sometimes such experiments are run in cloud environments, which is useful for tens or hundreds of participants. However, we are interested in deployments involving tens or hundreds of thousands of participants. AWS has only 64 data centers, so testing with more parties than this would provide an inaccurate simulation of the network environment.

  3. 3.

    This estimate is for a malicious-secure protocol that generates unauthenticated triples, which suffice for semi-honest computation in the online phase. In Sect. 4.1, we present a known result for converting these to authenticated triples. The throughput in that setting is closer to 70 million triples per second.

  4. 4.

    Or commanded by Google.

  5. 5.

    There are advantages and disadvantages to varying the size of this committee, which we will discuss in depth in what follows. For now, we can assume that the online committee is in fact the entire network of n parties. In the “standard” approach to executing the online phase with n parties, the communication complexity is O(|C|) per party. We will address this as well.

  6. 6.

    Technically, since we are selecting many such committees, to guarantee that they all have at least one honest party requires a union bound over the number of committees, resulting in committees of size \(O(s + \log {n})\). However, since \(s > \log {n}\), we drop this \(\log {n}\) term in our asymptotic notation. However, we point out that our experimental results in Sect. 6 do account for this union bound.

  7. 7.

    This can be done regardless of the circuit structure, and does not require a wide circuit.

  8. 8.

    When analyzing total or average communication, there is no need to consider receiving complexity as the number of bits sent by all parties equals the number of bits received. But, when considering bottleneck complexity, one must make a distinction between the two. For example, if many parties send messages to one party, that party’s receiving bandwidth becomes the bottleneck. In fact, there are MPC protocols such as [37] that are bottlenecked by the receiving bandwidth of some of the parties.

  9. 9.

    Note that when we assume \(t < n/3\), we cannot construct committees of size O(s) that have the same corruption threshold. We therefore do not consider running Furukawa and Lindell in parallel. We could do so with larger, committees, or we could consider a smaller threshold, but we feel the current set of comparisons suffices for demonstrating the value of our protocol.

  10. 10.

    For example, to compute \([\alpha a]\) from \([\alpha ]\) and [a] using triple (x, y, z), the parties open \(a + x\) and \(\alpha + y\). Each locally fixes its share by computing \((a+x)[\alpha ] + (\alpha + y)[a] - (a+x)(\alpha + y) + [z]\).

  11. 11.

    Note that our offline phase has a computational bottleneck, so reducing the communication cost per triple might not lead to large improvement in runtime, though it still may reduce the dollar cost of communicating. Reducing the number of triples needed will reduce end-to-end runtime.

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Acknowledgments

The authors would like to thank the anonymous reviewers for many helpful comments. Arkady Yerukhimovich and Dov Gordon are supported by NSF grant 1955264. Arkady Yerukhimovich is also supported by a Facebook Research Award.

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Authors and Affiliations

  1. George Mason University, Fairfax, USA

    S. Dov Gordon

  2. Perspecta Labs, Basking Ridge, USA

    Daniel Starin

  3. George Washington University, Washington, D.C., USA

    Arkady Yerukhimovich

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Correspondence to S. Dov Gordon .

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    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Gordon, S.D., Starin, D., Yerukhimovich, A. (2021). The More the Merrier: Reducing the Cost of Large Scale MPC. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12697. Springer, Cham. https://doi.org/10.1007/978-3-030-77886-6_24

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