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Robustness for Space-Bounded Statistical Zero Knowledge

Authors Eric Allender , Jacob Gray, Saachi Mutreja, Harsha Tirumala , Pengxiang Wang

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Author Details

Eric Allender
  • Rutgers University, Piscataway, NJ, USA
Jacob Gray
  • University of Massachusetts, Amherst, MA, USA
Saachi Mutreja
  • University of California, Berkeley, CA, USA
Harsha Tirumala
  • Rutgers University, Piscataway, NJ, USA
Pengxiang Wang
  • University of Michigan, Ann Arbor, MI, USA

Funding

  • Allender, Eric: Supported in part by NSF Grants CCF-1909216 and CCF-1909683.
  • Gray, Jacob: Supported in part by NSF grants CNS-215018 and CCF-1852215
  • Mutreja, Saachi: Supported in part by NSF grants CNS-215018 and CCF-1852215
  • Tirumala, Harsha: Supported in part by NSF Grants CCF-1909216 and CCF-1909683.
  • Wang, Pengxiang: Supported in part by NSF grants CNS-215018 and CCF-1852215

Acknowledgements

This work was done in part while EA and HT were visiting the Simons Institute for the Theory of Computing. This work was carried out while JG, SM, and PW were participants in the 2022 DIMACS REU program at Rutgers University. We thank Yuval Ishai for helpful conversations about SREN, and we thank Markus Lohrey, Sam Buss, and Dave Barrington for useful discussions about Lemma 34. We also thank the anonymous referees for helpful comments.

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Eric Allender, Jacob Gray, Saachi Mutreja, Harsha Tirumala, and Pengxiang Wang. Robustness for Space-Bounded Statistical Zero Knowledge. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 56:1-56:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.56

Abstract

We show that the space-bounded Statistical Zero Knowledge classes SZK_L and NISZK_L are surprisingly robust, in that the power of the verifier and simulator can be strengthened or weakened without affecting the resulting class. Coupled with other recent characterizations of these classes [Eric Allender et al., 2023], this can be viewed as lending support to the conjecture that these classes may coincide with the non-space-bounded classes SZK and NISZK, respectively.

Subject Classification

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

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References

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