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

Tatsuaki Okamoto, Kouichi Sakurai, Hiroki Shizuya

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

3 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトルAdvances in Cryptology – EUROCRYPT 1992 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
編集者Rainer A. Rueppel
出版社Springer Verlag
ページ420-428
ページ数9
ISBN(印刷版)9783540564133
DOI
出版ステータス出版済み - 1 1 1993
外部発表はい
イベントWorkshop on the Theory and Application of Cryptographic Technique, EUROCRYPT 1992 - Balatonfured, ハンガリー
継続期間: 5 24 19925 28 1992

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
658 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他Workshop on the Theory and Application of Cryptographic Technique, EUROCRYPT 1992
国/地域ハンガリー
CityBalatonfured
Period5/24/925/28/92

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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