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10-Party Sublinear Secure Computation from Standard Assumptions

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Advances in Cryptology – CRYPTO 2024 (CRYPTO 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14928))

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Abstract

Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocols – in particular, when communication can be sublinear in the circuit representation size of the desired function. While several techniques have demonstrated the viability of sublinear secure computation in the two-party setting, known methods for the corresponding multi-party setting rely either on fully homomorphic encryption, non-standard hardness assumptions, or are limited to a small number of parties. In this work, we expand the study of multi-party sublinear secure computation by demonstrating sublinear-communication 10-party computation from various combinations of standard hardness assumptions. In particular, our contributions show:

  • 8-party homomorphic secret sharing under the hardness of (DDH or DCR), the superpolynomial hardness of LPN, and the existence of constant-depth pseudorandom generators;

  • A general framework for achieving \((N+M)\)-party sublinear secure computation using M-party homomorphic secret sharing for \(\ensuremath {\textsf{NC}} ^1\) and correlated symmetric PIR.

Together, our constructions imply the existence of a 10-party MPC protocol with sublinear computation. At the core of our techniques lies a novel series of computational approaches based on homomorphic secret sharing.

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Notes

  1. 1.

    With a few exceptions that either required exponential computation [5, 37], or were limited to simple functions such as point functions [21, 22, 35].

  2. 2.

    A distributed point function allows sharing a point function \(f_{\alpha ,\beta }\) (that is, \(f_{\alpha ,\beta }(\alpha )=\beta \) and \(f_{\alpha ,\beta }(x) = 0\) else) such that (1) the shares computationally hide \(f_{\alpha ,\beta }\), and (2) given shares of \(f_{\alpha ,\beta }\), the parties can locally obtain additive shares of \(f_{\alpha ,\beta }(x)\) for any x.

  3. 3.

    Since the receiver knows the positions of the noise, using a puncturable pseudorandom function actually suffices. Using the Doerner-shelat protocol [27], securely distributing the punctured key of a puncturable PRF can be done in two rounds.

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Acknowledgements

Part of this work was done while the second author was visiting Université Paris Cité and supported by the ReLaX program (CNRS, IRL2000). The first and second author acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-20-CE39-0001 (project SCENE). This work was also supported by the France 2030 ANR Project ANR-22-PECY-003 SecureCompute.

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Authors and Affiliations

  1. Université Paris Cité, CNRS, IRIF, Paris, France

    Geoffroy Couteau

  2. Oregon State University, Corvallis, USA

    Naman Kumar

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Correspondence to Geoffroy Couteau .

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  1. Boston University, Boston, MA, USA

    Leonid Reyzin

  2. University of Waterloo, Waterloo, ON, Canada

    Douglas Stebila

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Couteau, G., Kumar, N. (2024). 10-Party Sublinear Secure Computation from Standard Assumptions. In: Reyzin, L., Stebila, D. (eds) Advances in Cryptology – CRYPTO 2024. CRYPTO 2024. Lecture Notes in Computer Science, vol 14928. Springer, Cham. https://doi.org/10.1007/978-3-031-68400-5_2

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