Efficient algorithms for the construction of hyperelliptic cryptosystems

Tatsuaki Okamoto, Kouichi Sakurai

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

6 被引用数 (Scopus)

抄録

The jacobian of hyperelliptic curves, including elliptic curves as a special case, offers a good primitive for cryptosystems, since cryptosystems (discrete logarithms) based on the jacobians seem to be more intractable than those based on conventional multiplicative groups. In this paper, we show that the problem to determine the group structure of the jacobian can be characterized to be in NP ∩ co-NP, when the jacobian is a non-degenerate type (“non-half-degenerate”). We also show that the hyperelliptic discrete logarithm can be characterized to be in NP ∩ co-NP, when the group structure is non-half-degenerate. Moreover, we imply the reducibility of the hyperelliptic discrete logarithm to a multiplicative discrete logarithm. The extended Weil pairing over the jacobian is the key tool for these algorithms.

本文言語英語
ホスト出版物のタイトルAdvances in Cryptology — CRYPTO 1991, Proceedings
編集者Joan Feigenbaum
出版社Springer Verlag
ページ267-278
ページ数12
ISBN(印刷版)9783540551881
DOI
出版ステータス出版済み - 1992
外部発表はい
イベント11th Confrence on Advances in Cryptology, CRYPTO 1991 - Santa Barbara, 米国
継続期間: 8 11 19918 15 1991

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)
576 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他11th Confrence on Advances in Cryptology, CRYPTO 1991
国/地域米国
CitySanta Barbara
Period8/11/918/15/91

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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