Rho method with period k on non-symmetric ordinary pairings of embedding degree k - Especially for Barreto-Naehrig curves

Yasuyuki Nogami; Yusuke Takai; Tomoko Matsushima; Satoshi Uehara

doi:10.1109/IMIS.2011.62

Rho method with period k on non-symmetric ordinary pairings of embedding degree k - Especially for Barreto-Naehrig curves

Yasuyuki Nogami, Yusuke Takai, Tomoko Matsushima, Satoshi Uehara

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Pollard's ρ method is well known as an efficient method for solving elliptic curve discrete logarithm problem (ECDLP). This paper applies it to non-super singular pairing-friendly curves, especially to Barreto-Naehrig curves, together with Frobenius endomorphism. Then, it is shown that the list of rational points can be reduced with norms of their x and y coordinates without loss of theoretic uniqueness.

Original language	English
Title of host publication	Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011
Pages	618-621
Number of pages	4
DOIs	https://doi.org/10.1109/IMIS.2011.62
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

Pollard's ρ method
non-symmetric pairing group

ASJC Scopus subject areas

Computer Networks and Communications
Computer Science Applications

Access to Document

10.1109/IMIS.2011.62

Cite this

Nogami, Y., Takai, Y., Matsushima, T., & Uehara, S. (2011). Rho method with period k on non-symmetric ordinary pairings of embedding degree k - Especially for Barreto-Naehrig curves. In Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011 (pp. 618-621). [5976285] (Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011). https://doi.org/10.1109/IMIS.2011.62

Rho method with period k on non-symmetric ordinary pairings of embedding degree k - Especially for Barreto-Naehrig curves. / Nogami, Yasuyuki; Takai, Yusuke; Matsushima, Tomoko et al.

Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011. 2011. p. 618-621 5976285 (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, Takai, Y, Matsushima, T & Uehara, S 2011, Rho method with period k on non-symmetric ordinary pairings of embedding degree k - Especially for Barreto-Naehrig curves. in Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011., 5976285, Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011, pp. 618-621, 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.2011.62

Nogami Y, Takai Y, Matsushima T, Uehara S. Rho method with period k on non-symmetric ordinary pairings of embedding degree k - Especially for Barreto-Naehrig curves. In Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011. 2011. p. 618-621. 5976285. (Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011). doi: 10.1109/IMIS.2011.62

Nogami, Yasuyuki ; Takai, Yusuke ; Matsushima, Tomoko et al. / Rho method with period k on non-symmetric ordinary pairings of embedding degree k - Especially for Barreto-Naehrig curves. Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011. 2011. pp. 618-621 (Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011).

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abstract = "Pollard's ρ method is well known as an efficient method for solving elliptic curve discrete logarithm problem (ECDLP). This paper applies it to non-super singular pairing-friendly curves, especially to Barreto-Naehrig curves, together with Frobenius endomorphism. Then, it is shown that the list of rational points can be reduced with norms of their x and y coordinates without loss of theoretic uniqueness.",

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Rho method with period k on non-symmetric ordinary pairings of embedding degree k - Especially for Barreto-Naehrig curves

Abstract

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Keywords

ASJC Scopus subject areas

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