How intractable is the discrete logarithm for a general finite group?

Tatsuaki Okamoto, Kouichi Sakurai, Hiroki Shizuya

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

GDL is the discrete logarithm problem for a general finitc group G. This paper gives a characterization for the intractability of GDL from the viewpoint of computational complexity theory. It is shown that GDL ∈ NP ∩ co-AM, assuming that G is in NP ∩ co-NP, and that the group law operation of G can be exccuted in a polynomial time of the element size. Furthermore, as a natural probabilistic extension, the complexity of GDL is investigated under the assumption that the group law operation is executed in an expected polynomial time of the element size. In this case, it is shown that GDL ∈ MA ∩ co-AM if G ∈ NP ∩ co-NP. Finally, we show that GDL is less intractable than NP-complete problems unless the polynomial time hierarchy collapses to the second level.

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 1992 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
EditorsRainer A. Rueppel
PublisherSpringer Verlag
Pages420-428
Number of pages9
ISBN (Print)9783540564133
DOIs
Publication statusPublished - Jan 1 1993
Externally publishedYes
EventWorkshop on the Theory and Application of Cryptographic Technique, EUROCRYPT 1992 - Balatonfured, Hungary
Duration: May 24 1992May 28 1992

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume658 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherWorkshop on the Theory and Application of Cryptographic Technique, EUROCRYPT 1992
CountryHungary
CityBalatonfured
Period5/24/925/28/92

Fingerprint

Discrete Logarithm
Polynomial time
Finite Group
Polynomials
Computational complexity
Discrete Logarithm Problem
Complexity Theory
Computational Complexity
NP-complete problem

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Okamoto, T., Sakurai, K., & Shizuya, H. (1993). How intractable is the discrete logarithm for a general finite group? In R. A. Rueppel (Ed.), Advances in Cryptology – EUROCRYPT 1992 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings (pp. 420-428). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 658 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-47555-9_34

How intractable is the discrete logarithm for a general finite group? / Okamoto, Tatsuaki; Sakurai, Kouichi; Shizuya, Hiroki.

Advances in Cryptology – EUROCRYPT 1992 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. ed. / Rainer A. Rueppel. Springer Verlag, 1993. p. 420-428 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 658 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Okamoto, T, Sakurai, K & Shizuya, H 1993, How intractable is the discrete logarithm for a general finite group? in RA Rueppel (ed.), Advances in Cryptology – EUROCRYPT 1992 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 658 LNCS, Springer Verlag, pp. 420-428, Workshop on the Theory and Application of Cryptographic Technique, EUROCRYPT 1992, Balatonfured, Hungary, 5/24/92. https://doi.org/10.1007/3-540-47555-9_34
Okamoto T, Sakurai K, Shizuya H. How intractable is the discrete logarithm for a general finite group? In Rueppel RA, editor, Advances in Cryptology – EUROCRYPT 1992 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Springer Verlag. 1993. p. 420-428. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-47555-9_34
Okamoto, Tatsuaki ; Sakurai, Kouichi ; Shizuya, Hiroki. / How intractable is the discrete logarithm for a general finite group?. Advances in Cryptology – EUROCRYPT 1992 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. editor / Rainer A. Rueppel. Springer Verlag, 1993. pp. 420-428 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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