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On the Round Complexity of Black-Box Secure MPC

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Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12826))

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Abstract

We consider the question of minimizing the round complexity of secure multiparty computation (MPC) protocols that make a black-box use of simple cryptographic primitives with security against any number of malicious parties. In the plain model, previous black-box protocols required a high constant number of rounds (>15). This is far from the known lower bound of 4 rounds for protocols with black-box simulators.

When allowing random oblivious transfer (OT) correlations, 2-round protocols making black-box use of a pseudorandom generator were known. However, such protocols were obtained via a round-collapsing “protocol garbling” technique that has poor concrete efficiency and makes non-black-box use of an underlying maliciously secure protocol.

We improve this state of affairs by presenting the following types of black-box protocols.

  • 4-round “pairwise MPC” in the plain model. This round-optimal protocol enables each ordered pair of parties to compute a function of both inputs whose output is delivered to the second party. The protocol makes black-box use of any public-key encryption (\(\mathsf {PKE}\)) with pseudorandom public keys. As a special case, we get a black-box round-optimal realization of secure (copies of) OT between every ordered pair of parties.

  • 2-round MPC from OT correlations. This round-optimal protocol makes a black-box use of any general 2-round MPC protocol satisfying an augmented notion of semi-honest security. In the two-party case, this yields new kinds of 2-round black-box protocols.

  • 5-round MPC in the plain model. This protocol makes a black-box use of \(\mathsf {PKE}\) with pseudorandom public keys, and 2-round oblivious transfer with “semi-malicious” security.

A key technical tool for the first result is a novel combination of split-state non-malleable codes (Dziembowski, Pietrzak, and Wichs, JACM’18) with standalone secure two-party protocols to construct non-malleable two-party protocols. The second result is based on a new round-optimized variant of the “IPS compiler” (Ishai, Prabhakaran and Sahai, Crypto’08). The third result is obtained via a specialized combination of these two techniques.

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Notes

  1. 1.

    As we noted before, for the case of constant number of parties, watchlist correlations reduces to standard OT correlations.

  2. 2.

    Note that this corresponds to the programmability requirement.

  3. 3.

    Actually, the \(\mathsf {MIM}\) may also output \((\widetilde{\mathsf {L}}_0,\widetilde{\mathsf {L}}_1)\) as a function of only \((\mathsf {m}_{\widetilde{\mathsf {b}}}, \mathsf {R}_0, \mathsf {R}_1)\), and \((\widetilde{\mathsf {R}}_0,\widetilde{\mathsf {R}}_1)\) as a function of only \((\mathsf {m}_{\widetilde{\mathsf {b}}}, \mathsf {L}_0, \mathsf {L}_1)\). We use codes satisfying an additional symmetric decoding property to account for this case.

  4. 4.

    We show in Sect. 5.1 of the full version that 1-rewind secure 2PC for \(\mathsf {NC1}\) circuits suffices to obtain non-malleable OT.

  5. 5.

    This property guarantees parallel composability, and is satisfied by most natural rewinding-based protocols.

  6. 6.

    If any of these is not well-defined, we denote it by \(\bot \).

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Acknowledgements

Y. Ishai was supported by ERC Project NTSC (742754), NSF-BSF grant 2015782, BSF grant 2018393, and ISF grant 2774/20. D. Khurana was supported from a DARPA SIEVE award. A. Sahai was supported in part from a DARPA SIEVE award, NTT Research, NSF Frontier Award 1413955, BSF grant2012378, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024. Work done in part when A. Srinivasan was at UC Berkeley and supported in part by AFOSR Award FA9550-19-1-0200, AFOSR YIP Award, NSF CNS Award 1936826, DARPA/ARL SAFEWARE Award W911NF15C0210, a Hellman Award and research grants by the Sloan Foundation, Okawa Foundation, Visa Inc., and Center for Long-Term Cybersecurity (CLTC, UC Berkeley). The views expressed are those of the authors and do not reflect the official policy or position of the funding agencies.

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Authors and Affiliations

  1. Technion, Haifa, Israel

    Yuval Ishai

  2. UIUC, Champaign, US

    Dakshita Khurana

  3. UCLA, Los Angeles, US

    Amit Sahai

  4. Tata Institute of Fundamental Research, Mumbai, India

    Akshayaram Srinivasan

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  1. Columbia University, New York City, NY, USA

    Tal Malkin

  2. University of Michigan, Ann Arbor, MI, USA

    Chris Peikert

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Ishai, Y., Khurana, D., Sahai, A., Srinivasan, A. (2021). On the Round Complexity of Black-Box Secure MPC. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12826. Springer, Cham. https://doi.org/10.1007/978-3-030-84245-1_8

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