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Round-Optimal Black-Box MPC in the Plain Model

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

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Abstract

We give the first construction of a (fully) black-box round-optimal secure multiparty computation protocol in the plain model. Our protocol makes black-box use of a sub-exponentially secure two-message statistical sender private oblivious transfer (SSP-OT), which in turn can be based on (sub-exponential variants of) most of the standard cryptographic assumptions known to imply public-key cryptography.

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Notes

  1. 1.

    By simultaneous message exchange we mean that in each round, every party can send a message over a broadcast channel. However, we allow the adversarial parties to be rushing, meaning that they can wait until they receive all the honest party messages in each round before sending their own messages.

  2. 2.

    Recently, SSP-OT was constructed from low-noise LPN and a standard derandomization assumption [BF22] (building on [DGH+20]). However, this construction is only secure against quasi-polynomial sized adversaries.

  3. 3.

    Recall that semi-malicious adversaries are stronger than the standard semi-honest adversaries and are allowed to fix the random tape of adversarial parties to arbitrary values. However, like in the semi-honest setting, they are forced to follow the protocol specification.

  4. 4.

    We note that any protocol, even one in the bidirectional communication model, can be reduced to this setting.

  5. 5.

    For technical reasons, we actually need the inner protocol to run in three rounds instead of four rounds. However, to keep the exposition simple, we will ignore this in the overview. In the main body, we give a black-box construction of such a three-round inner protocol based on two-round semi-malicious OT protocol (which is implied by two-round SSP OT). This construction builds on the protocols given in [GS18, PS21].

  6. 6.

    Specifically, the set of watched executions of the adversarial parties correspond to a subset of the corrupted servers in the outer protocol. To invoke the security of the outer protocol, we need to extract this information from the watchlist messages.

  7. 7.

    Recall that a split-state non-malleable code \((\textsf{enc},\textsf{dec})\) encodes any message m into multiple states, such that the distribution of the tampered message obtained by tampering the each state individually is independent of m.

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Acknowledgment

Y. Ishai was supported in part by ERC Project NTSC (742754), BSF grant 2018393, ISF grant 2774/20, and a Google Faculty Research Award. D. Khurana was supported in part by NSF CAREER CNS-2238718 and DARPA SIEVE. A. Sahai was supported in part from a Simons Investigator Award, DARPA SIEVE award, NTT Research, NSF Frontier Award 1413955, BSF grant 2012378, a Xerox Faculty Research Award, a Google Faculty Research Award, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024. A. Srinivasan was supported in part by a SERB startup grant and Google India Research Award.

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Authors and Affiliations

  1. Technion, Haifa, Israel

    Yuval Ishai

  2. UIUC, Champaign, USA

    Dakshita Khurana

  3. UCLA, Los Angeles, USA

    Amit Sahai

  4. Tata Institute of Fundamental Research, Bengaluru, India

    Akshayaram Srinivasan

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  1. Yuval Ishai
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  2. Dakshita Khurana
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Correspondence to Yuval Ishai .

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  1. Rambus Inc., San Jose, CA, USA

    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Ishai, Y., Khurana, D., Sahai, A., Srinivasan, A. (2023). Round-Optimal Black-Box MPC in the Plain Model. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14081. Springer, Cham. https://doi.org/10.1007/978-3-031-38557-5_13

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