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Paper: Sublinear GMW-Style Compiler for MPC with Preprocessing

Authors:
Elette Boyle , IDC Herzliya
Niv Gilboa , Ben-Gurion University
Yuval Ishai , Technion Israel Institute of Technology
Ariel Nof , Technion Israel Institute of Technology
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Conference: CRYPTO 2021
Abstract: We consider the efficiency of protocols for secure multiparty computation (MPC) with a dishonest majority. A popular approach for the design of such protocols is to employ {\em preprocessing}. Before the inputs are known, the parties generate correlated secret randomness, which is consumed by a fast and ``information-theoretic'' online protocol. A powerful technique for securing such protocols against malicious parties uses {\em homomorphic MACs} to authenticate the values produced by the online protocol. Compared to a baseline protocol, which is only secure against semi-honest parties, this involves a significant increase in the size of the correlated randomness, by a factor of up to a statistical security parameter. Different approaches for partially mitigating this extra storage cost come at the expense of increasing the online communication. In this work we propose a new technique for protecting MPC with preprocessing against malicious parties. We show that for circuit evaluation protocols that satisfy mild security and structural requirements, that are met by almost all standard protocols with semi-honest security, the extra {\em additive} storage and online communication costs are both {\em logarithmic} in the circuit size. This applies to Boolean circuits and to arithmetic circuits over fields or rings, and to both information-theoretic and computationally secure protocols. Our protocol can be viewed as a sublinear information-theoretic variant of the celebrated ``GMW compiler'' that applies to MPC with preprocessing. Our compiler makes a novel use of the techniques of Boneh et al. (Crypto 2019) for sublinear distributed zero knowledge, which were previously only used in the setting of {\em honest-majority} MPC.
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BibTeX
@inproceedings{crypto-2021-31260,
  title={Sublinear GMW-Style Compiler for MPC with Preprocessing},
  publisher={Springer-Verlag},
  author={Elette Boyle and Niv Gilboa and Yuval Ishai and Ariel Nof},
  year=2021
}