Which Languages Have 4-Round Fully Black-Box Zero-Knowledge Arguments from One-Way Functions?

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12107)


We prove that if a language \(\mathcal{L}\) has a 4-round fully black-box zero-knowledge argument with negligible soundness based on one-way functions, then \(\overline{\mathcal{L}} \in \mathsf {MA}\). Since \(\mathsf {coNP}\subseteq \mathsf {MA}\) implies that the polynomial hierarchy collapses, our result implies that \(\mathsf {NP}\)-complete languages are unlikely to have 4-round fully black-box zero-knowledge arguments based on one-way functions. In TCC 2018, Hazay and Venkitasubramaniam, and Khurana, Ostrovsky, and Srinivasan demonstrated 4-round fully black-box zero-knowledge arguments for all languages in \(\mathsf {NP}\) based on injective one-way functions. Their results also imply a 5-round protocol based on one-way functions. In essence, our result resolves the round complexity of fully black-box zero-knowledge arguments based on one-way functions.


One-way functions Zero-knowledge arguments Black-box constructions 



The first author is supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, and by ISF grant 1316/18. The second author is supported in part by NSF Award SATC-1704788, NSF Award RI-1703846, and AFOSR Award FA9550-18-1-0267, and in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2019-19-020700006. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. The third author is supported by Google Faculty Research Grant and NSF Award CNS-1618884. The views expressed are those of the authors and do not reflect the official policy or position of Google, the Department of Defense, the National Science Foundation, or the U.S. Government.


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Copyright information

© International Association for Cryptologic Research 2020

Authors and Affiliations

  1. 1.Bar-Ilan UniversityRamat GanIsrael
  2. 2.Cornell TechNew YorkUSA
  3. 3.University of RochesterRochesterUSA

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