Abstract
The best known n party unconditional multiparty computation protocols with an optimal corruption threshold communicates O(n) field elements per gate. This has been the case even in the semi-honest setting despite over a decade of research on communication complexity in this setting. Going to the slightly sub-optimal corruption setting, the work of Damgård, Ishai, and Krøigaard (EUROCRYPT 2010) provided the first protocol for a single circuit achieving communication complexity of \(O(\log |C|)\) elements per gate. While a number of works have improved upon this result, obtaining a protocol with O(1) field elements per gate has been an open problem.
In this work, we construct the first unconditional multi-party computation protocol evaluating a single arithmetic circuit with amortized communication complexity of O(1) elements per gate.
V. Goyal and Y. Song—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.
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.
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- 1.
While the semi-honest version of the protocol in [GIP15] can use a field \(\mathbb {F}\) of size O(n), the maliciously secure protocol requires to use a large enough field since the error probability is proportional to the field size.
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Goyal, V., Polychroniadou, A., Song, Y. (2021). Unconditional Communication-Efficient MPC via Hall’s Marriage Theorem. 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_10
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