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

Takanori Yasuda, Tsuyoshi Takagi, Kouichi Sakurai

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

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationAdvances in Information and Computer Security - 7th International Workshop on Security, IWSEC 2012, Proceedings
Pages19-36
Number of pages18
Volume7631 LNCS
DOIs
Publication statusPublished - 2012
Event7th International Workshop on Security, IWSEC 2012 - Fukuoka, Japan
Duration: Nov 7 2012Nov 9 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7631 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th International Workshop on Security, IWSEC 2012
CountryJapan
CityFukuoka
Period11/7/1211/9/12

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Theoretical Computer Science

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