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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • 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