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 proceedingConference 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 languageEnglish
Title of host publicationProceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011
Pages618-621
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

Keywords

  • non-symmetric pairing group
  • Pollard's ρ method

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications

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] 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; Uehara, Satoshi.

Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011. 2011. p. 618-621 5976285.

Research output: Chapter in Book/Report/Conference proceedingConference 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, 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 https://doi.org/10.1109/IMIS.2011.62
Nogami, Yasuyuki ; Takai, Yusuke ; Matsushima, Tomoko ; Uehara, Satoshi. / 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
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