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One-Way Functions vs. TFNP: Simpler and Improved

Authors Lukáš Folwarczný , Mika Göös, Pavel Hubáček , Gilbert Maystre , Weiqiang Yuan

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LIPIcs.ITCS.2024.50.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Oracles and decision trees
Keywords
  • TFNP
  • One-Way Functions
  • Oracle
  • Separation
  • Black-Box

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Abstract

Simon (1998) proved that it is impossible to construct collision-resistant hash functions from one-way functions using a black-box reduction. It is conjectured more generally that one-way functions do not imply, via a black-box reduction, the hardness of any total NP search problem (collision-resistant hash functions being just one such example). We make progress towards this conjecture by ruling out a large class of "single-query" reductions. In particular, we improve over the prior work of Hubáček et al. (2020) in two ways: our result is established via a novel simpler combinatorial technique and applies to a broader class of semi black-box reductions.

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Lukáš Folwarczný, Mika Göös, Pavel Hubáček, Gilbert Maystre, and Weiqiang Yuan. One-Way Functions vs. TFNP: Simpler and Improved. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITCS.2024.50

Author Details

Lukáš Folwarczný
  • Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic
  • Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Mika Göös
  • EPFL, Lausanne, Switzerland
Pavel Hubáček
  • Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic
  • Charles University, Faculty of Mathematics and Physics, Czech Republic
Gilbert Maystre
  • EPFL, Lausanne, Switzerland
Weiqiang Yuan
  • EPFL, Lausanne, Switzerland

Funding

  • Folwarczný, Lukáš: Supported by the Academy of Sciences of the Czech Republic (RVO 67985840) and by the Grant Agency of the Czech Republic (19-27871X).
  • Göös, Mika: Supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number MB22.00026.
  • Hubáček, Pavel: Supported by the Academy of Sciences of the Czech Republic (RVO 67985840).
  • Maystre, Gilbert: supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number MB22.00026.
  • Yuan, Weiqiang: Supported by the Swiss National Science Foundation project 200021-184656

Acknowledgements

We thank anonymous reviewers for their helpful comments.

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