On the complexity of hyperelliptic discrete logarithm problem

Hiroki Shizuya, Toshiya Itoh, Kouichi Sakurai

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

5 Citations (Scopus)

Abstract

We give a characterization for the intractability of hyperelliptic discrete logarithm problem from a viewpoint of computational complexity theory. It is shown that the language of which complexity is equivalent to that of the hyperelliptic discrete logarithm problem is in NP ∩ co-AM, and that especially for elliptic curves, the corresponding language is in NP ∩ co-NP. It should be noted here that the language of which complexity is equivalent to that of the discrete logarithm problem defined over the multiplicative group of a finite field is also characterized as in NP ∩ co-NP.

Original languageEnglish
Title of host publicationAdvances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
EditorsDonald W. Davies
PublisherSpringer Verlag
Pages337-351
Number of pages15
ISBN (Print)9783540546207
DOIs
Publication statusPublished - Jan 1 1991
Externally publishedYes
EventWorkshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991 - Brighton, United Kingdom
Duration: Apr 8 1991Apr 11 1991

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume547 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherWorkshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991
CountryUnited Kingdom
CityBrighton
Period4/8/914/11/91

Fingerprint

Discrete Logarithm Problem
Computational complexity
Complexity Theory
Elliptic Curves
Galois field
Multiplicative
Computational Complexity
Language

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Shizuya, H., Itoh, T., & Sakurai, K. (1991). On the complexity of hyperelliptic discrete logarithm problem. In D. W. Davies (Ed.), Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings (pp. 337-351). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 547 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-46416-6_29

On the complexity of hyperelliptic discrete logarithm problem. / Shizuya, Hiroki; Itoh, Toshiya; Sakurai, Kouichi.

Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. ed. / Donald W. Davies. Springer Verlag, 1991. p. 337-351 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 547 LNCS).

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

Shizuya, H, Itoh, T & Sakurai, K 1991, On the complexity of hyperelliptic discrete logarithm problem. in DW Davies (ed.), Advances in Cryptology—EUROCRYPT 1991 - 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. 547 LNCS, Springer Verlag, pp. 337-351, Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991, Brighton, United Kingdom, 4/8/91. https://doi.org/10.1007/3-540-46416-6_29
Shizuya H, Itoh T, Sakurai K. On the complexity of hyperelliptic discrete logarithm problem. In Davies DW, editor, Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Springer Verlag. 1991. p. 337-351. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-46416-6_29
Shizuya, Hiroki ; Itoh, Toshiya ; Sakurai, Kouichi. / On the complexity of hyperelliptic discrete logarithm problem. Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. editor / Donald W. Davies. Springer Verlag, 1991. pp. 337-351 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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