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Unconditionally Secure Multiparty Computation for Symmetric Functions with Low Bottleneck Complexity

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Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14438))

Abstract

Bottleneck complexity is an efficiency measure of secure multiparty computation (MPC) introduced by Boyle et al. (ICALP 2018) to achieve load-balancing. Roughly speaking, it is defined as the maximum communication complexity required by any player within the protocol execution. Since it was shown to be impossible to achieve sublinear bottleneck complexity in the number of players n for all functions, a prior work constructed MPC protocols with low bottleneck complexity for specific functions. However, the previous protocol for symmetric functions needs to assume a computational primitive of garbled circuits and its unconditionally secure variant has exponentially large bottleneck complexity in the depth of an arithmetic formula computing the function, which limits the class of symmetric functions the protocol can compute with sublinear bottleneck complexity in n. In this work, we make the following contributions to unconditionally secure MPC protocols for symmetric functions with sublinear bottleneck complexity in n.

  • We propose for the first time unconditionally secure MPC protocols computing any symmetric function with sublinear bottleneck complexity in n. Technically, our first protocol is inspired by the one-time truth-table protocol by Ishai et al. (TCC 2013) but our second and third protocols use a novel technique to express the one-time truth-table as an array of two or higher dimensions and achieve better trade-offs.

  • We propose an unconditionally secure protocol tailored to the AND function with lower bottleneck complexity. It avoids pseudorandom functions used by the previous protocol for the AND function, preserving bottleneck complexity up to a logarithmic factor in n.

  • By combining our protocol for the AND function with Bloom filters, we construct an unconditionally secure protocol for private set intersection (PSI), which computes the intersection of players’ private sets. This is the first PSI protocol with sublinear bottleneck complexity in n and to the best of our knowledge, there has been no such protocol even under cryptographic assumptions.

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Notes

  1. 1.

    An independent work [41] show an unconditionally secure MPC protocol for symmetric functions but our second and third protocols achieve better offline bottleneck complexity than [41].

  2. 2.

    We here assume that there is an injective map from the universe U containing all the \(X_i\)’s to some finite field.

  3. 3.

    The original protocol in [48] computes the AND function. The functionalities are equivalent since \(\textrm{OR}(x_1,\ldots ,x_n)=1-\textrm{AND}(1-x_1,\ldots ,1-x_n)\).

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Acknowledgements

We thank anonymous reviewers of ASIACRYPT 2023 for their helpful comments. Especially, one of the reviewers kindly showed us a more round-efficient protocol for computing the sum. This optimization reduces the round complexity of our protocols to \(O(\log n)\), which appears in the full version [22]. We really appreciate his or her great solution. We also thank Koji Nuida and Takahiro Matsuda for helpful discussions and suggestions. This work was partially supported by JST AIP Acceleration Research JPMJCR22U5, Japan and JST CREST Grant Number JPMJCR22M1, Japan.

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  1. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Reo Eriguchi

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  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

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Eriguchi, R. (2023). Unconditionally Secure Multiparty Computation for Symmetric Functions with Low Bottleneck Complexity. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14438. Springer, Singapore. https://doi.org/10.1007/978-981-99-8721-4_11

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