Application of scalar multiplication of edwards curves to pairing-based cryptography

Takanori Yasuda, Tsuyoshi Takagi, Kouichi Sakurai

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

1 引用 (Scopus)

抜粋

Edwards curves have efficient scalar multiplication algorithms, and their application to pairing-based cryptography has been studied. In particular, if a pairing-friendly curve used in a pairing-based protocol is isomorphic to an Edwards curve, all the scalar multiplication appearing in the protocol can be computed efficiently. In this paper, we extend this idea to pairing-friendly curves not isomorphic but isogenous to Edwards curves, and add to pairing-friendly curves to which Edwards curves can be applied. Above all, pairing-friendly curves with smaller ρ-values provide more efficient pairing computation. Therefore, we investigate whether pairing-friendly curves with the minimal ρ-values are isogenous to Edwards curves for embedding degree up to 50. Based on the investigation, we present parameters of pairing-friendly curves with 160-bit and 256-bit security level at embedding degree 16 and 24, respectively. These curves have the minimal ρ-values and are not isomorphic but isogenous to Edwards curves, and thus our proposed method is effective for these curves.

元の言語英語
ホスト出版物のタイトルAdvances in Information and Computer Security - 7th International Workshop on Security, IWSEC 2012, Proceedings
ページ19-36
ページ数18
7631 LNCS
DOI
出版物ステータス出版済み - 2012
イベント7th International Workshop on Security, IWSEC 2012 - Fukuoka, 日本
継続期間: 11 7 201211 9 2012

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)
7631 LNCS
ISSN(印刷物)03029743
ISSN(電子版)16113349

その他

その他7th International Workshop on Security, IWSEC 2012
日本
Fukuoka
期間11/7/1211/9/12

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Theoretical Computer Science

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  • これを引用

    Yasuda, T., Takagi, T., & Sakurai, K. (2012). Application of scalar multiplication of edwards curves to pairing-based cryptography. : Advances in Information and Computer Security - 7th International Workshop on Security, IWSEC 2012, Proceedings (巻 7631 LNCS, pp. 19-36). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 7631 LNCS). https://doi.org/10.1007/978-3-642-34117-5-2