Efficient Ate-Based Pairing over the Attractive Classes of BN Curves

  • Yuki NanjoEmail author
  • Md. Al-Amin Khandaker
  • Masaaki Shirase
  • Takuya Kusaka
  • Yasuyuki Nogami
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11402)


This paper proposes two attractive classes of Barreto-Naehrig curve for ate-based pairing by imposing certain condition Open image in new window on the integer \(\chi \) that parameterizes the curve settings. The restriction results in an unparalleled way to determine a BN curve, its twisted curve coefficients, and obvious generator points. The proposed \(\chi \equiv 11~(\bmod ~12)\) are found to be more efficient than \(\chi \equiv 7~(\bmod ~12)\) together with pseudo 8-sparse multiplication in Miller’s algorithm. The authors also provide comparative implementations for the proposal.


Pairing Tower of extension field Barreto-Naehrig curve 



This work was supported by the Strategic Information and Communications R&D Promotion Programme (SCOPE) of Ministry of Internal Affairs and Communications, Japan.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graduate School of Natural Science and TechnologyOkayama UniversityOkayamaJapan
  2. 2.Future University HakodateHakodateJapan

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