Cryptology ePrint Archive: Report 2021/376

On the Impossibility of Post-Quantum Black-Box Zero-Knowledge in Constant Rounds

Nai-Hui Chia and Kai-Min Chung and Qipeng Liu and Takashi Yamakawa

Abstract: We investigate the existence of constant-round post-quantum black-box zero-knowledge protocols for $\mathbf{NP}$. As a main result, we show that there is no constant-round post-quantum black-box zero-knowledge argument for $\mathbf{NP}$ unless $\mathbf{NP}\subseteq \mathbf{BQP}$. As constant-round black-box zero-knowledge arguments for $\mathbf{NP}$ exist in the classical setting, our main result points out a fundamental difference between post-quantum and classical zero-knowledge protocols. Combining previous results, we conclude that unless $\mathbf{NP}\subseteq \mathbf{BQP}$, constant-round post-quantum zero-knowledge protocols for $\mathbf{NP}$ exist if and only if we use non-black-box techniques or relax certain security requirements such as relaxing standard zero-knowledge to $\epsilon$-zero-knowledge. Additionally, we also prove that three-round and public-coin constant-round post-quantum black-box $\epsilon$-zero-knowledge arguments for $\mathbf{NP}$ do not exist unless $\mathbf{NP}\subseteq \mathbf{BQP}$.

Category / Keywords: foundations / zero knowledge, quantum cryptography

Date: received 20 Mar 2021

Contact author: nchia at umd edu,kmchung@iis sinica edu tw,qipengl@cs princeton edu,takashi yamakawa obf@gmail com

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Version: 20210322:193720 (All versions of this report)

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