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 - 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

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

Fingerprint

Torsional stress
Polynomials

Keywords

  • group structure
  • pairing
  • torsion point

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications

Cite this

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] https://doi.org/10.1109/IMIS.2011.61

A multiplicative extension for discrete logarithms on ordinary pairing-friendly curves of embedding degree. / Nogami, Yasuyuki; Yanagi, Erika; Sumo, Taichi; Matsushima, Tomoko; Uehara, Satoshi.

Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011. 2011. p. 603-606 5976282.

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

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., 5976282, pp. 603-606, 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011, Seoul, Korea, Republic of, 6/30/11. https://doi.org/10.1109/IMIS.2011.61
Nogami Y, Yanagi E, Sumo T, Matsushima T, Uehara S. 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. 2011. p. 603-606. 5976282 https://doi.org/10.1109/IMIS.2011.61
Nogami, Yasuyuki ; Yanagi, Erika ; Sumo, Taichi ; Matsushima, Tomoko ; Uehara, Satoshi. / A multiplicative extension for discrete logarithms on ordinary pairing-friendly curves of embedding degree. Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011. 2011. pp. 603-606
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