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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2021: Advances in Cryptology – EUROCRYPT 2021 pp 663–693Cite as

Order-C Secure Multiparty Computation for Highly Repetitive Circuits

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

Abstract

Running secure multiparty computation (MPC) protocols with hundreds or thousands of players would allow leveraging large volunteer networks (such as blockchains and Tor) and help justify honest majority assumptions. However, most existing protocols have at least a linear (multiplicative) dependence on the number of players, making scaling difficult. Known protocols with asymptotic efficiency independent of the number of parties (excluding additive factors) require expensive circuit transformations that induce large overheads.

We observe that the circuits used in many important applications of MPC such as training algorithms used to create machine learning models have a highly repetitive structure. We formalize this class of circuits and propose an MPC protocol that achieves \(O(|\mathsf {C}|)\) total complexity for this class. We implement our protocol and show that it is practical and outperforms \(O(n|\mathsf {C}|)\) protocols for modest numbers of players.

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Notes

  1. 1.

    For sake of simplicity, throughout the introduction, we omit a linear multiplicative factor of the security parameter in all asymptotic notations.

  2. 2.

    SIMD circuits are arithmetic circuits that simultaneously evaluate \(\ell \) copies of the same arithmetic circuit on different inputs. Genkin et al. [20] showed that it is possible to design an \(O(|\mathsf {C}|)\) MPC protocol for SIMD circuits, where \(\ell =\varTheta (n)\).

  3. 3.

    We note that for more commonly used corruption thresholds \(n/2>t>n/4\), the overhead incurred by our compiler is somewhere between 2.5–3.

  4. 4.

    The choice of the leader can be rotated amongst the players to divide the total computation.

  5. 5.

    In this toy example only one vector is distributed back to the parties. If layers are approximately of the same size, an approximately equal number of vectors will be returned.

  6. 6.

    For simplicity we assume that each party has only one input. But our protocol can be trivially extended to accommodate scenarios where each party has multiple inputs.

  7. 7.

    We remark that for notational convenience we describe this step as consisting of \(4|\mathsf {C}|/\ell \) multiplications (and hence these many degree reduction steps), it can be done with just two degree reduction step, where the parties first locally multiply and add their respective shares to compute \(\langle \mathbf {v}\rangle \) and \(\langle \mathbf {u}\rangle \) and then communicate to obtain shares of \([\mathbf {v}]\) and \([\mathbf {u}]\) respectively.

  8. 8.

    The only protocol to be run on large numbers of parties rests on incomparable assumptions like CRS [38].

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Acknowledgements

The first and second authors are supported in part by NSF under awards CNS-1653110 and CNS-1801479 and the Office of Naval Research under contract N00014-19-1-2292. The first author is also supported in part by DARPA under Contract No. HR001120C0084. The second and third authors are supported in part by an NSF CNS grant 1814919, NSF CAREER award 1942789 and Johns Hopkins University Catalyst award. The third author is additionally partly supported by Office off Naval Research grant N00014-19-1-2294. The forth author is supported by the National Science Foundation under Grant #2030859 to the Computing Research Association for the CIFellows Project. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government or DARPA.

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Authors and Affiliations

  1. Johns Hopkins University, Baltimore, USA

    Gabrielle Beck, Aarushi Goel & Abhishek Jain

  2. Boston University, Boston, USA

    Gabriel Kaptchuk

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  1. Gabrielle Beck
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Correspondence to Gabrielle Beck .

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  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Beck, G., Goel, A., Jain, A., Kaptchuk, G. (2021). Order-C Secure Multiparty Computation for Highly Repetitive Circuits. 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_23

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  • DOI: https://doi.org/10.1007/978-3-030-77886-6_23

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