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 - 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

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

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] (Proceedings - 2011 5th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS 2011). https://doi.org/10.1109/IMIS.2011.62