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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2021: Advances in Cryptology – EUROCRYPT 2021 pp 812–841Cite as

Constant-Overhead Unconditionally Secure Multiparty Computation Over Binary Fields

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12697))

Abstract

We study the communication complexity of unconditionally secure multiparty computation (MPC) protocols in the honest majority setting. Despite tremendous efforts in achieving efficient protocols for binary fields under computational assumptions, there are no efficient unconditional MPC protocols in this setting. In particular, there are no n-party protocols with constant overhead admitting communication complexity of O(n) bits per gate. Cascudo, Cramer, Xing and Yuan (CRYPTO 2018) were the first ones to achieve such an overhead in the amortized setting by evaluating \(O(\log n)\) copies of the same circuit in the binary field in parallel. In this work, we construct the first unconditional MPC protocol secure against a malicious adversary in the honest majority setting evaluating just a single boolean circuit with amortized communication complexity of O(n) bits per gate.

A. Polychroniadou—This paper was prepared in part for information purposes by the Artificial Intelligence Research group of JPMorgan Chase & Co and its affiliates (“JP Morgan”), and is not a product of the Research Department of JP Morgan. JP Morgan makes no representation and warranty whatsoever and disclaims all liability, for the completeness, accuracy or reliability of the information contained herein. This document is not intended as investment research or investment advice, or a recommendation, offer or solicitation for the purchase or sale of any security, financial instrument, financial product or service, or to be used in any way for evaluating the merits of participating in any transaction, and shall not constitute a solicitation under any jurisdiction or to any person, if such solicitation under such jurisdiction or to such person would be unlawful. 2020 JPMorgan Chase & Co. All rights reserved.

Y. Song—Work done in part while at J.P. Morgan AI Research. Supported in part by the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.

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Notes

  1. 1.

    In [CCXY18], Cascudo, et al. show that the requirement \(q\ge 2n\) of using hyper-invertible matrices can be relaxed to any field size. However, \(q>n\) is still necessary to use Shamir secret sharing in [BTH08].

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Authors and Affiliations

  1. J.P. Morgan AI Research, New York, USA

    Antigoni Polychroniadou

  2. Carnegie Mellon University, Pittsburgh, USA

    Yifan Song

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  1. Antigoni Polychroniadou
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Correspondence to Yifan Song .

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Editors and Affiliations

  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Polychroniadou, A., Song, Y. (2021). Constant-Overhead Unconditionally Secure Multiparty Computation Over Binary Fields. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12697. Springer, Cham. https://doi.org/10.1007/978-3-030-77886-6_28

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  • DOI: https://doi.org/10.1007/978-3-030-77886-6_28

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