Abstract
In the last few years, the efficiency of secure multi-party computation (MPC) in the dishonest majority setting has increased by several orders of magnitudes starting with the SPDZ protocol family which offers a speedy information-theoretic online phase in the prepossessing model. However, state-of-the-art n-party MPC protocols in the dishonest majority setting incur online communication complexity per multiplication gate which is linear in the number of parties, i.e. O(n), per gate across all parties. In this work, we construct the first MPC protocols in the preprocessing model for dishonest majority with sub-linear communication complexity per gate in the number of parties n. To achieve our results, we extend the use of packed secret sharing to the dishonest majority setting. For a constant fraction of corrupted parties (i.e. if 99 percent of the parties are corrupt), we can achieve a communication complexity of O(1) field elements per multiplication gate across all parties.
At the crux of our techniques lies a new technique called sharing transformation. The sharing transformation technique allows us to transform shares under one type of linear secret sharing scheme into another, and even perform arbitrary linear maps on the secrets of (packed) secret sharing schemes with optimal communication complexity. This technique can be of independent interest since transferring shares from one type of scheme into another (e.g., for degree reduction) is ubiquitous in MPC. Furthermore, we introduce what we call sparsely packed Shamir sharing which allows us to address the issue of network routing efficiently, and packed Beaver triples which is an extension of the widely used technique of Beaver triples for packed secret sharing (for dishonest majority).
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Notes
- 1.
To be more precise, our protocol achieves linear communication complexity in the summation of the sharing sizes of the two secret sharing schemes in the transformation. This is optimal (up to a constant factor) since it matches the communication complexity of using an ideal functionality to do sharing transformation: the size of the input is the sharing size of the first secret sharing scheme, the size of the output is the sharing size of the second secret sharing scheme, and the communication complexity is the size of the input and output.
- 2.
In this work, we only focus on deterministic functions. A randomized function can be transformed to a deterministic function by taking as input an additional random tape from each party. The XOR of the input random tapes of all parties is used as the randomness of the randomized function.
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Acknowledgement
V. Goyal, Y. Song—Supported by the NSF award 1916939, DARPA SIEVE program under Agreement No. HR00112020025, 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. Y. Song was also supported by a Cylab Presidential Fellowship.
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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Goyal, V., Polychroniadou, A., Song, Y. (2022). Sharing Transformation and Dishonest Majority MPC with Packed Secret Sharing. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13510. Springer, Cham. https://doi.org/10.1007/978-3-031-15985-5_1
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