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Leakage Resilience, Targeted Pseudorandom Generators, and Mild Derandomization of Arthur-Merlin Protocols

Authors Dieter van Melkebeek, Nicollas Mocelin Sdroievski

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Author Details

Dieter van Melkebeek
  • University of Wisconsin-Madison, WI, USA
Nicollas Mocelin Sdroievski
  • University of Wisconsin-Madison, WI, USA

Funding

Partial support for this research was provided by the University of Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation, and by the National Science Foundation under Grant No. 2312540.

Cite AsGet BibTex

Dieter van Melkebeek and Nicollas Mocelin Sdroievski. Leakage Resilience, Targeted Pseudorandom Generators, and Mild Derandomization of Arthur-Merlin Protocols. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.FSTTCS.2023.29

Abstract

Many derandomization results for probabilistic decision processes have been ported to the setting of Arthur-Merlin protocols. Whereas the ultimate goal in the first setting consists of efficient simulations on deterministic machines (BPP vs. P problem), in the second setting it is efficient simulations on nondeterministic machines (AM vs. NP problem). Two notable exceptions that have not yet been ported from the first to the second setting are the equivalence between whitebox derandomization and leakage resilience (Liu and Pass, 2023), and the equivalence between whitebox derandomization and targeted pseudorandom generators (Goldreich, 2011). We develop both equivalences for mild derandomizations of Arthur-Merlin protocols, i.e., simulations on Σ₂-machines. Our techniques also apply to natural simulation models that are intermediate between nondeterministic machines and Σ₂-machines.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • Hardness versus randomness tradeoff
  • leakage resilience
  • Arthur-Merlin protocol
  • targeted hitting set generator

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References

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