A multiplicative extension for discrete logarithms on ordinary pairing-friendly curves of embedding degree

Yasuyuki Nogami, Erika Yanagi, Taichi Sumo, Tomoko Matsushima, Satoshi Uehara

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

Abstract

This paper deals with r-torsion rational points on ordinary pairing-friendly curves such that the embedding degree k divides r + 1, where r is the order of rational points. Especially, its group structure is focused on. In this case, the twisted characteristic polynomial f′(πd) becomes irreducible over double-struck Fr, where πd is the skew Frobenius map with twist degree d such as quadratic, cubic, quartic, and sextic. Then, using the irreducible polynomial f′(πd), this paper considers a multiplicative representation of r?torsion rational points.

Original languageEnglish
Title of host publicationProceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011
Pages603-606
Number of pages4
DOIs
Publication statusPublished - Sep 8 2011
Event2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011 - Seoul, Korea, Republic of
Duration: Jun 30 2011Jul 2 2011

Publication series

NameProceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011

Other

Other2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011
CountryKorea, Republic of
CitySeoul
Period6/30/117/2/11

Keywords

  • group structure
  • pairing
  • torsion point

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications

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    Nogami, Y., Yanagi, E., Sumo, T., Matsushima, T., & Uehara, S. (2011). A multiplicative extension for discrete logarithms on ordinary pairing-friendly curves of embedding degree. In Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011 (pp. 603-606). [5976282] (Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011). https://doi.org/10.1109/IMIS.2011.61