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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2022: Advances in Cryptology – EUROCRYPT 2022 pp 427–457Cite as

Secure Multiparty Computation with Sublinear Preprocessing

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13275))

Abstract

A common technique for enhancing the efficiency of secure multiparty computation (MPC) with dishonest majority is via preprocessing: In an offline phase, parties engage in an input-independent protocol to securely generate correlated randomness. Once inputs are known, the correlated randomness is consumed by a “non-cryptographic” and highly efficient online protocol.

The correlated randomness in such protocols traditionally comes in two flavors: multiplication triples (Beaver, Crypto ’91), which suffice for security against semi-honest parties, and authenticated multiplication triples (Bendlin et al., Eurocrypt ’11, Damgård et al., Crypto ’12) that yield efficient protocols against malicious parties.

Recent constructions of pseudorandom correlation generators (Boyle et al., Crypto ’19, ’20) enable concretely efficient secure generation of multiplication triples with sublinear communication complexity. However, these techniques do not efficiently apply to authenticated triples, except in the case of secure two-party computation of arithmetic circuits over large fields.

In this work, we propose the first concretely efficient approach for (malicious) MPC with preprocessing in which the offline communication is sublinear in the circuit size. More specifically, the offline communication scales with the square root of the circuit size.

From a feasibility point of view, our protocols can make use of any secure protocol for generating (unauthenticated) multiplication triples together with any additive homomorphic encryption. We propose concretely efficient instantiations (based on strong but plausible “linear-only” assumptions) from existing homomorphic encryption schemes and pseudorandom correlation generators.

Our technique is based on a variant of a recent protocol of Boyle et al. (Crypto ’21) for MPC with preprocessing. As a result, our protocols inherit the succinct correlated randomness feature of the latter protocol.

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Notes

  1. 1.

    This can be formalized by requiring the existence of alternative correlated randomness, which is computationally indistinguishable from the one generated by the offline protocol, and given which the entire protocol is information-theoretically secure.

  2. 2.

    While these limitations can in some cases be circumvented [9, 25, 40], this comes at a big additional cost.

  3. 3.

    Implied, e.g., by any of the Quadratic Residuosity, Learning with Errors, or Decisional Composite Residuosity assumptions.

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Acknowledgments

We thank the Eurocrypt reviewers for helpful comments. E. Boyle supported by a Google Research Scholar Award, AFOSR Award FA9550-21-1-0046, ERC Project HSS (852952), and ERC Project NTSC (742754). N. Gilboa supported by ISF grant 2951/20, ERC grant 876110, and a grant by the BGU Cyber Center. Y. Ishai supported by ERC Project NTSC (742754), BSF grant 2018393, and ISF grant 2774/20. A. Nof supported by ERC Project NTSC (742754).

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Authors and Affiliations

  1. Reichman University (IDC Herzliya), and NTT Research, Herzliya, Israel

    Elette Boyle

  2. Ben-Gurion University, Beersheba, Israel

    Niv Gilboa

  3. Technion, Haifa, Israel

    Yuval Ishai & Ariel Nof

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  1. Elette Boyle
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  2. Niv Gilboa
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  3. Yuval Ishai
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  4. Ariel Nof
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Correspondence to Elette Boyle .

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Editors and Affiliations

  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Boyle, E., Gilboa, N., Ishai, Y., Nof, A. (2022). Secure Multiparty Computation with Sublinear Preprocessing. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13275. Springer, Cham. https://doi.org/10.1007/978-3-031-06944-4_15

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