The Black-Box Simulation Barrier Persists in a Fully Quantum World

2024-09-10

IACR Cryptology ePrint Archive

AI Summary

This work investigates the feasibility boundary of constant-round black-box simulation zero-knowledge (BBZK) arguments in a fully quantum setting. Addressing the open question—“Which languages admit constant-round fully quantum BBZK arguments?”—the paper establishes the first rigorous complexity-theoretic barrier: it proves that a language admits such an argument if and only if it lies in BQP; consequently, if NP ⊈ BQP, then no NP language admits a constant-round fully quantum BBZK argument. This result uncovers an intrinsic connection between fully quantum BBZK and the BQP vs QMA problem, explaining why existing quantum zero-knowledge protocols rely on non-black-box techniques or weakened security definitions. The analysis integrates quantum interactive proofs, black-box simulation theory, and fine-grained complexity class reasoning. As the first tight impossibility result for quantum BBZK, it provides a fundamental theoretical limit for quantum cryptographic protocol design.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: Discourse, Pragmatics & Argument Mining

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

Abstract

Zero-Knowledge (ZK) protocols have been intensely studied due to their fundamental importance and versatility. However, quantum information's inherent differences significantly alter the landscape, necessitating a re-examination of ZK designs. A crucial aspect is round complexity, linked to $ extit{simulation}$, which forms the foundation of ZK definition and security proofs. In the $ extit{post-quantum}$ setting, where honest parties and channels are classical but adversaries quantum, Chia et al. [FOCS'21] showed constant-round $ extit{black-box-simulatable}$ ZK arguments (BBZK) for $mathbf{NP}$ are impossible unless $mathbf{NP} subseteq mathbf{BQP}$. But this problem remains open when all parties and communication are quantum. Indeed, this problem interests the broader theory of quantum computing. Investigating how quantum power alters tasks like the $ extit{unconditional}$ security of QKD and incorporating OT in MiniQCrypt has been crucial. Moreover, quantum communication has enabled round compression for commitments and interactive arguments. Along this line, understanding if quantum computing could fundamentally change ZK protocols is vital. We resolved this problem by proving that only languages in $mathbf{BQP}$ admit constant-round $ extit{fully-quantum}$ BBZK. This result holds significant implications. Firstly, it illuminates the nature of quantum zero-knowledge and provides valuable insights for designing future protocols in the quantum realm. Secondly, it relates ZK round complexity with the intriguing problem of $mathbf{BQP}$ vs $mathbf{QMA}$, which is out of the reach of previous analogue impossibility results in the classical or post-quantum setting. Lastly, it justifies the need for the $ extit{non-black-box}$ simulation techniques or the relaxed security notions employed in existing constant-round fully-quantum BBZK protocols.

Problem

• Examine Zero-Knowledge protocols in quantum settings
• Determine round complexity for quantum BBZK arguments
• Assess impact of quantum power on ZK security

Innovation

• Proved constant-round fully-quantum BBZK limitations
• Linked ZK round complexity to BQP vs QMA
• Highlighted need for non-black-box simulation techniques