Constructing Pairing-Friendly Elliptic Curves Using Global Number Fields

Takanori Yasuda, Tsuyoshi Takagi, Kouichi Sakurai

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

1 Citation (Scopus)

Abstract

Efficient implementation of pairing-based cryptography requires construction of a pairing-friendly curve and its corresponding twisted curve. In this paper, we give a formula which determines the twisted curve. The formula are obtained by using technique in the algebraic number theory such as the complex multiplication theory. Applying the formula, we present an easy method for constructing pairing-friendly curves for BN-family. In fact, our method does not require the process of elliptic curve construction and finite field construction, but only requires searching an integer satisfying some conditions. Using our construction method, we implemented an optimal ate pairing for BN-family which is usable at various security levels, and investigated the time efficiency of the pairing computation for various security levels.

Original languageEnglish
Title of host publicationProceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages477-483
Number of pages7
ISBN (Electronic)9781467397971
DOIs
Publication statusPublished - Mar 2 2016
Event3rd International Symposium on Computing and Networking, CANDAR 2015 - Sapporo, Hokkaido, Japan
Duration: Dec 8 2015Dec 11 2015

Publication series

NameProceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015

Other

Other3rd International Symposium on Computing and Networking, CANDAR 2015
CountryJapan
CitySapporo, Hokkaido
Period12/8/1512/11/15

Fingerprint

Number theory
Cryptography

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computer Networks and Communications

Cite this

Yasuda, T., Takagi, T., & Sakurai, K. (2016). Constructing Pairing-Friendly Elliptic Curves Using Global Number Fields. In Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015 (pp. 477-483). [7424760] (Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDAR.2015.28

Constructing Pairing-Friendly Elliptic Curves Using Global Number Fields. / Yasuda, Takanori; Takagi, Tsuyoshi; Sakurai, Kouichi.

Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015. Institute of Electrical and Electronics Engineers Inc., 2016. p. 477-483 7424760 (Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015).

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

Yasuda, T, Takagi, T & Sakurai, K 2016, Constructing Pairing-Friendly Elliptic Curves Using Global Number Fields. in Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015., 7424760, Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015, Institute of Electrical and Electronics Engineers Inc., pp. 477-483, 3rd International Symposium on Computing and Networking, CANDAR 2015, Sapporo, Hokkaido, Japan, 12/8/15. https://doi.org/10.1109/CANDAR.2015.28
Yasuda T, Takagi T, Sakurai K. Constructing Pairing-Friendly Elliptic Curves Using Global Number Fields. In Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015. Institute of Electrical and Electronics Engineers Inc. 2016. p. 477-483. 7424760. (Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015). https://doi.org/10.1109/CANDAR.2015.28
Yasuda, Takanori ; Takagi, Tsuyoshi ; Sakurai, Kouichi. / Constructing Pairing-Friendly Elliptic Curves Using Global Number Fields. Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 477-483 (Proceedings - 2015 3rd International Symposium on Computing and Networking, CANDAR 2015).
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