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Round-Optimal and Communication-Efficient Multiparty Computation

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Advances in Cryptology – EUROCRYPT 2022 (EUROCRYPT 2022)

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

Abstract

Typical approaches for minimizing the round complexity of multiparty computation (MPC) come at the cost of increased communication complexity (CC) or the reliance on setup assumptions. A notable exception is the recent work of Ananth et al. [TCC 2019], which used Functional Encryption (FE) combiners to obtain a round optimal (two-round) semi-honest MPC in the plain model with a CC proportional to the depth and input-output length of the circuit being computed—we refer to such protocols as circuit scalable. This leaves open the question of obtaining communication efficient protocols that are secure against malicious adversaries in the plain model, which we present in this work. Concretely, our two main contributions are:

1) We provide a round-preserving black-box compiler that compiles a wide class of MPC protocols into circuit-scalable maliciously secure MPC protocols in the plain model, assuming (succinct) FE combiners.

2) We provide a round-preserving black-box compiler that compiles a wide class of MPC protocols into circuit-independent—i.e., with a CC that depends only on the input-output length of the circuit—maliciously secure MPC protocols in the plain model, assuming Multi-Key Fully-Homomorphic Encryption (MFHE). Our constructions are based on a new compiler that turns a wide class of MPC protocols into k-delayed-input function MPC protocols (a notion we introduce), where the function that is being computed is specified only in the k-th round of the protocol.

As immediate corollaries of our two compilers, we derive (1) the first round-optimal and circuit-scalable maliciously secure MPC, and (2) the first round-optimal and circuit-independent maliciously secure MPC in the plain model. The latter MPC achieves the best to-date CC for a round-optimal malicious MPC protocol. In fact, it is even communication-optimal when the output size of the function being evaluated is smaller than its input size (e.g., for boolean functions). All of our results are based on standard polynomial time assumptions.

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Notes

  1. 1.

    A malicious adversary attacks the protocol following an arbitrary probabilistic polynomial-time strategy. Unless stated differently, when we talk about the security of an MPC protocol against semi-honest or malicious adversaries we assume that up to \(n-1\) parties can be corrupted, where n is the number of parties.

  2. 2.

    We stress that in our work the size of the circuit is always related to the security parameter via a polynomial p. We use the term circuit-independent for MPC protocols whose communication complexity depend on the security parameter, the size of the input and output, and does not depend on p. The same argument holds for circuit-scalable MPC protocols.

  3. 3.

    In the communication model used in [33] in each round only one party can speak. Hence they obtain the best possible security guarantees in such a communication model.

  4. 4.

    Unless otherwise specified, all our results are proved secure in the dishonest majority setting.

  5. 5.

    We require the first 2 rounds of the MPC protocol to be independent from the inputs.

  6. 6.

    We recall that a semi-malicious adversary behaves like a semi-honest adversary with the exception that it decides the randomness and the input used to run the protocol.

  7. 7.

    All our result are with respect to black-box simulation.

  8. 8.

    R is parsed as n strings and each of the strings is used to generate a different master secret key.

  9. 9.

    Note that only the committed message is sent, not the randomness \(\rho _{i}^{1-i}\).

  10. 10.

    We recall that \(P_0^i\) and \(P_1^i\) do not need to use the input to compute the first \(k-1\) rounds, nonetheless we can specify the input of \(P_i^1\) at the very beginning of the protocol.

  11. 11.

    Any \(k'\)-delayed-input function MPC with \(k'>3\) can be turned into a 3-delayed-input function MPC protocol since the function received in round 2 can be ignored up to round \(k'-1\).

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Acknowledgments

Work done in part while the fourth author was at the University of Edinburgh.

The first author is supported in part by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement 780477 (PRIVILEDGE). The second author is supported in part by DARPA under Cooperative Agreement HR0011-20-2-0025, NSF grant CNS-2001096, US-Israel BSF grant 2015782, Cisco Research Award, Google Faculty Award, JP Morgan Faculty Award, IBM Faculty Research Award, Xerox Faculty Research Award, OKAWA Foundation Research Award, B. John Garrick Foundation Award, Teradata Research Award, Lockheed-Martin Research Award and Sunday Group. The third author is supported in part by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement 780108 (FENTEC). The fourth author is supported in part by NSF grant no. 2055599 and by Sunday Group.

The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of DARPA, the Department of Defense, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes not withstanding any copyright annotation therein.

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Authors and Affiliations

  1. The University of Edinburgh, Edinburgh, UK

    Michele Ciampi & Hendrik Waldner

  2. University of California, Los Angeles, CA, USA

    Rafail Ostrovsky

  3. Purdue University, West Lafayette, IN, USA

    Vassilis Zikas

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  1. Michele Ciampi
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Correspondence to Hendrik Waldner .

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  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Ciampi, M., Ostrovsky, R., Waldner, H., Zikas, V. (2022). Round-Optimal and Communication-Efficient Multiparty Computation. 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_3

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