The Round Complexity of Black-Box Post-Quantum Secure Computation

2025-02-19

AI Summary

This work investigates round complexity of post-quantum secure multiparty computation (PQ-MPC) in the fully black-box model—where both construction and security reduction are black-box. Addressing a long-standing open problem, we present the first general-purpose black-box PQ-MPC protocol with polynomial round complexity, and—crucially—the first constant-round black-box PQ-MPC achieving ε-simulation security in the multi-party setting. Our technical contributions include: (i) a black-box constant-round weak 1-out-of-m non-malleable commitment scheme based solely on post-quantum one-way functions; and (ii) a novel framework integrating post-quantum semi-honest oblivious transfer with quantum-safe protocol compilation techniques. As a consequence, we reduce round complexity of two-party PQ-MPC from super-constant to ω(1), and our results underpin a quantum MPC oracle separation established in STOC ’25.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We study the round complexity of secure multi-party computation (MPC) in the post-quantum regime. Our focus is on the fully black-box setting, where both the construction and security reduction are black-box. Chia, Chung, Liu, and Yamakawa [FOCS'22] demonstrated the infeasibility of achieving standard simulation-based security within constant rounds unless $mathbf{NP} subseteq mathbf{BQP}$. This leaves crucial feasibility questions unresolved. Specifically, it remains unknown whether black-box constructions are achievable within polynomial rounds; also, the existence of constant-round constructions with respect to $epsilon$-simulation, a relaxed yet useful alternative to standard simulation, remains unestablished. This work provides positive answers. We introduce the first black-box construction for PQ-MPC in polynomial rounds, from the minimal assumption of post-quantum semi-honest oblivious transfers. In the two-party scenario, our construction requires only $omega(1)$ rounds. These results have already been applied in the oracle separation between classical-communication quantum MPC and $mathbf{P} = mathbf{NP}$ in Kretschmer, Qian, and Tal [STOC'25]. As for $epsilon$-simulation, Chia, Chung, Liang, and Yamakawa [CRYPTO'22] resolved the issue for the two-party setting, leaving the multi-party case open. We complete the picture by presenting the first black-box, constant-round construction in the multi-party setting, instantiable using various standard post-quantum primitives. En route, we obtain a black-box, constant-round post-quantum commitment achieving a weaker version of 1-many non-malleability, from post-quantum one-way functions. Besides its role in our MPC construction, this commitment also reduces the assumption used in the quantum parallel repetition lower bound by Bostanci, Qian, Spooner, and Yuen [STOC'24]. We anticipate further applications in the future.

Problem

• Study round complexity in post-quantum MPC.
• Achieve black-box constructions in polynomial rounds.
• Establish constant-round constructions with ε-simulation.

Innovation

• Black-box post-quantum MPC
• Polynomial-round secure computation
• Constant-round multi-party epsilon-simulation