Actively Secure MPC in the Dishonest Majority Setting: Achieving Constant Complexity in Online Communication, Computation Per Gate, Rounds, and Private Input Size

Abstract

SPDZ-style and BMR-style protocols are widely known as practical MPC protocols that achieve active security in the dishonest majority setting. However, to date, SPDZ-style protocols have not achieved constant rounds, and BMR-style protocols have struggled to achieve scalable communication or computation. Additionally, there exists fully homomorphic encryption (FHE)-based MPC protocols that achieve both constant rounds and scalable communication, but they face challenges in achieving active security in the dishonest majority setting and are considered impractical due to computational inefficiencies. In this work, we propose an MPC framework that constructs an efficient and scalable FHE-based MPC protocol by integrating a linear secret sharing scheme (LSSS)-based MPC and FHE. The resulting FHE-based MPC protocol achieves active security in the dishonest majority setting and constant complexity in online communication, computation per gate, rounds, and private input size. Notably, by instantiating the proposed framework with the SPDZ protocol and gate FHE, the resulting FHE-based MPC protocol efficiently achieves active security in the dishonest majority setting by using SPDZ-style MAC and ensures the computation per gate time within 3 ms. Moreover, its offline phase achieves scalable communication and computation, both of which grow linearly with the number of parties n. In other words, the proposed FHE-based MPC preserves the key advantages of existing FHE-based MPCs and simultaneously overcomes the weaknesses of them. As a result, the proposed FHE-based MPC is highly practical and secure like both SPDZ-style and BMR-style protocols. For the first time, we introduce the concept of circuit-private MPC, which ensures that external adversaries who eavesdrop on communications do not obtain information about the circuit being evaluated. We rigorously prove that our construction inherently satisfy circuit-private MPC, thereby extending a security definition for MPC.