1 Search Results for "Václavek, Jan"


Document
On Search Complexity of Discrete Logarithm

Authors: Pavel Hubáček and Jan Václavek

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
In this work, we study the discrete logarithm problem in the context of TFNP - the complexity class of search problems with a syntactically guaranteed existence of solutions for all instances. Our main results establish that suitable variants of the discrete logarithm problem are complete for the complexity class PPP, respectively PWPP, i.e., the subclasses of TFNP capturing total search problems with a solution guaranteed by the pigeonhole principle, respectively the weak pigeonhole principle. Besides answering an open problem from the recent work of Sotiraki, Zampetakis, and Zirdelis (FOCS’18), our completeness results for PPP and PWPP have implications for the recent line of work proving conditional lower bounds for problems in TFNP under cryptographic assumptions. In particular, they highlight that any attempt at basing average-case hardness in subclasses of TFNP (other than PWPP and PPP) on the average-case hardness of the discrete logarithm problem must exploit its structural properties beyond what is necessary for constructions of collision-resistant hash functions. Additionally, our reductions provide new structural insights into the class PWPP by establishing two new PWPP-complete problems. First, the problem Dove, a relaxation of the PPP-complete problem Pigeon. Dove is the first PWPP-complete problem not defined in terms of an explicitly shrinking function. Second, the problem Claw, a total search problem capturing the computational complexity of breaking claw-free permutations. In the context of TFNP, the PWPP-completeness of Claw matches the known intrinsic relationship between collision-resistant hash functions and claw-free permutations established in the cryptographic literature.

Cite as

Pavel Hubáček and Jan Václavek. On Search Complexity of Discrete Logarithm. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 60:1-60:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{hubacek_et_al:LIPIcs.MFCS.2021.60,
  author =	{Hub\'{a}\v{c}ek, Pavel and V\'{a}clavek, Jan},
  title =	{{On Search Complexity of Discrete Logarithm}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{60:1--60:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.60},
  URN =		{urn:nbn:de:0030-drops-145006},
  doi =		{10.4230/LIPIcs.MFCS.2021.60},
  annote =	{Keywords: discrete logarithm, total search problems, completeness, TFNP, PPP, PWPP}
}
  • Refine by Author
  • 1 Hubáček, Pavel
  • 1 Václavek, Jan

  • Refine by Classification
  • 1 Theory of computation → Problems, reductions and completeness

  • Refine by Keyword
  • 1 PPP
  • 1 PWPP
  • 1 TFNP
  • 1 completeness
  • 1 discrete logarithm
  • Show More...

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2021

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail