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

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

doi:10.1109/IMIS.2011.61

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 proceeding › Conference 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′(π_d) becomes irreducible over double-struck F_r, where π_d is the skew Frobenius map with twist degree d such as quadratic, cubic, quartic, and sextic. Then, using the irreducible polynomial f′(π_d), this paper considers a multiplicative representation of r?torsion rational points.

Original language	English
Title of host publication	Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011
Pages	603-606
Number of pages	4
DOIs	https://doi.org/10.1109/IMIS.2011.61
Publication status	Published - Sept 8 2011
Event	2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011 - Seoul, Korea, Republic of Duration: Jun 30 2011 → Jul 2 2011

Publication series

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

Other

Other	2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011
Country/Territory	Korea, Republic of
City	Seoul
Period	6/30/11 → 7/2/11

Keywords

group structure
pairing
torsion point

ASJC Scopus subject areas

Computer Networks and Communications
Computer Science Applications

Access to Document

10.1109/IMIS.2011.61

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). Article 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

A multiplicative extension for discrete logarithms on ordinary pairing-friendly curves of embedding degree. / Nogami, Yasuyuki; Yanagi, Erika; Sumo, Taichi et al.
Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011. 2011. p. 603-606 5976282 (Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011).

Research output: Chapter in Book/Report/Conference proceeding › Conference 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, Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011, 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. (Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011). doi: 10.1109/IMIS.2011.61

Nogami, Yasuyuki ; Yanagi, Erika ; Sumo, Taichi et al. / 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 (Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011).

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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.",

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

Abstract

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