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

Rohit Chatterjee, Xiao Liang, Omkant Pandey, Takashi Yamakawa

TL;DR

The first black-box, constant-round post-quantum commitment is introduced, achieving a weaker version of 1-many non-malleability, from post-quantum one-way functions.

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 $ε$-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 $ω(1)$ 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 $ε$-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.

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

TL;DR

The first black-box, constant-round post-quantum commitment is introduced, achieving a weaker version of 1-many non-malleability, from post-quantum one-way functions.

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 . 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 -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 rounds. These results have already been applied in the oracle separation between classical-communication quantum MPC and in Kretschmer, Qian, and Tal [STOC'25]. As for -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.

Paper Structure

This paper contains 73 sections, 53 theorems, 139 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Our Results
  3. Black-Box PQ-2PC and PQ-MPC with Full Simulation
  4. Application I: LOCC MPC without OWFs
  5. Constant-Round Black-Box PQ-MPC with $\varepsilon$-Simulation
  6. Application II: Quantum Parallel Repetition Lower Bound
  7. More Related Work on Non-Black-Box Constructions
  8. Technical Overview
  9. Reduction to Post-Quantum 1-Many Non-Malleability
  10. PQ-NMC from FOCS:LPY23
  11. Our Black-Box Construction: 1-1 Setting
  12. Quantum-Exclusive Challenges
  13. One-Many Non-Malleability
  14. Simultaneous Extraction
  15. Black-Box Post-Quantum 2PC and MPC with Full Simulation
  16. ...and 58 more sections

Key Result

theorem 1.1

There exists a $\omega(1)$-round,While the term $\omega(1)$ is typically used for lower bounds, in our context, we use it to mean that "any super-constant value suffices." black-box construction of PQ-2PC (with full simulation), from the minimal assumption of post-quantum, semi-honest oblivious tran

Figures (1)

  • Figure 1:

Theorems & Definitions (118)

  • theorem 1.1
  • lemma thmcounterlemma
  • theorem 1.2
  • corollary thmcountercorollary: STOC:KreQiaTal25, strengthened
  • theorem 1.3
  • theorem 1.4
  • corollary thmcountercorollary
  • corollary thmcountercorollary
  • lemma thmcounterlemma: Simultaneous extraction lemma (informal)
  • definition thmcounterdefinition: Post-Quantum Commitments
  • ...and 108 more