An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve

Yuki Kono, Yasuyuki Nogami

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

Abstract

This paper considers the discrete logarithm problem (DLP) appeared in the context of pairing - based cryptography with Barreto - Naehrig (BN) curve. Since the embedding degree of BN curve is 12, the DLP is defined in the extension field Fp12, where p is the characteristic. This paper first points out that efficient and compact subgroup trace representation (ECSTR:XTR) is available for representing the DLP. Then, XTR-based rho method for solving the DLP is proposed. After that, its efficiency with and without tag tracing technique is evaluated by a small experiment.

Original languageEnglish
Title of host publicationProceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages519-524
Number of pages6
ISBN (Electronic)9781479941520
DOIs
Publication statusPublished - Feb 27 2015
Event2nd International Symposium on Computing and Networking, CANDAR 2014 - Shizuoka, Japan
Duration: Dec 10 2014Dec 12 2014

Publication series

NameProceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014

Other

Other2nd International Symposium on Computing and Networking, CANDAR 2014
CountryJapan
CityShizuoka
Period12/10/1412/12/14

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Keywords

  • BarretoNaehrig curve
  • Discrete logarithm
  • Elliptic curve
  • Pairing
  • Tagtracing
  • XTR

ASJC Scopus subject areas

  • Computer Networks and Communications

Cite this

Kono, Y., & Nogami, Y. (2015). An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve. In Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014 (pp. 519-524). [7052239] (Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDAR.2014.60