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Kolmogorov Complexity Characterizes Statistical Zero Knowledge

Authors Eric Allender , Shuichi Hirahara , Harsha Tirumala

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Author Details

Eric Allender
  • Rutgers University, Piscataway, NJ, USA
Shuichi Hirahara
  • National Institute of Informatics, Tokyo, Japan
Harsha Tirumala
  • Rutgers University, Piscataway, NJ, USA

Funding

  • Allender, Eric: Supported in part by NSF Grants CCF-1909216 and CCF-1909683.
  • Hirahara, Shuichi: Supported in part by JST, PRESTO Grant Number JPMJPR2024, Japan.
  • Tirumala, Harsha: Supported in part by NSF Grants CCF-1909216 and CCF-1909683.

Acknowledgements

We thank Sam Buss, Johannes Köbler, and Uwe Schöning for discussions concerning Boolean formula reducibility.

Cite AsGet BibTex

Eric Allender, Shuichi Hirahara, and Harsha Tirumala. Kolmogorov Complexity Characterizes Statistical Zero Knowledge. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ITCS.2023.3

Abstract

We show that a decidable promise problem has a non-interactive statistical zero-knowledge proof system if and only if it is randomly reducible via an honest polynomial-time reduction to a promise problem for Kolmogorov-random strings, with a superlogarithmic additive approximation term. This extends recent work by Saks and Santhanam (CCC 2022). We build on this to give new characterizations of Statistical Zero Knowledge SZK, as well as the related classes NISZK_L and SZK_L.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
  • Theory of computation → Circuit complexity
Keywords
  • Kolmogorov Complexity
  • Interactive Proofs

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