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Lecture notes in computer science

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

Seung Hwan Lee, Jaesang Noh, Taejeong Kim, Dohyuk Kim, Dong‐Joon Shin

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.1007/978-3-032-01884-7_4

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Secure multiparty computation (MPC) over Z2kis more efficient than computations over fields, and studying MPC protocols under malicious security has practical application value. Malicious security with a dishonest majority over rings remains challenging. The most popular approach is SPDZ2k, however, this is a specific protocol that does not support the transformation of any existing semi-honest MPC protocols into malicious security protocols. The zero knowledge proof (ZKP)-based compiler satisfies this requirement. Existing state-of-the-art protocols have logarithmic online communication overhead in terms of the circuit size |C|, and their direct application to rings is nontrivial as they were originally designed for finite fields. In this work, we investigate the communication overhead to develop malicious security protocols. We bridge the gap between malicious security with abort and semi-honest security, by constructing a “GMW-style” verification protocol to achieve malicious security in a dishonest majority setting. This approach incurs a constant online communication overhead by enhancing the machinery of zero-knowledge fully linear interactive oracle proof (zk-FLIOP). Additionally, we extend the zk-FLIOP to work over any ring by invoking reverse multiplication friendly embeddings (RMFEs). Our results show that the online communication complexity of the verification process depends on only the security parameter, the number of parties, and the ring size. Furthermore, for small-scale circuits over Z2, we designed a distributed lookup table argument where both the total communication complexity and the computational cost are independent of the circuit size but of the input wires.
The Fluid multiparty computation (MPC) model, introduced in (Choudhuri et al. CRYPTO 2021), addresses dynamic scenarios where participants can join or leave computations between rounds. Communication complexity initially stood at Ω ( n 2 ) elements per gate, where n is the number of parties in a committee online at a time. This held for both statistical security (honest majority) and computational security (dishonest majority) in (Choudhuri et al. CRYPTO'21) and (Rachuri and Scholl, CRYPTO'22), respectively. The work of (Bienstock et al. CRYPTO'23) improved communication to O ( n ) elements per gate. However, it's important to note that the perfectly secure setting with one-third corruptions per committee has only recently been addressed in the work of (David et al. CRYPTO'23). Notably, their contribution marked a significant advancement in the Fluid MPC literature by introducing guaranteed output delivery. However, this achievement comes at the cost of prohibitively expensive communication, which scales to Ω ( n 9 ) elements per gate. In this work, we study the realm of perfectly secure Fluid MPC under one-third active corruptions. Our primary focus lies in proposing efficient protocols that embrace the concept of security with abort. Towards this, we design a protocol for perfectly secure Fluid MPC that requires only linear communication of O ( n ) elements per gate, matching the communication of the non-Fluid setting. Our results show that, as in the case of computational and statistical security, perfect security with abort for Fluid MPC comes “for free” (asymptotically linear in n ) with respect to traditional non-Fluid MPC, marking a substantial leap forward in large scale dynamic computations, such as Fluid MPC.