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

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Book cover Information Security Applications (WISA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11402))

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Abstract

This paper proposes two attractive classes of Barreto-Naehrig curve for ate-based pairing by imposing certain condition 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.

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Notes

  1. 1.

    http://github.com/YukiNanjo/BN12_attractive.

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Acknowledgement

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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Authors and Affiliations

  1. Graduate School of Natural Science and Technology, Okayama University, Okayama, Japan

    Yuki Nanjo, Md. Al-Amin Khandaker, Takuya Kusaka & Yasuyuki Nogami

  2. Future University Hakodate, Hakodate, Hokkaido, Japan

    Masaaki Shirase

Authors
  1. Yuki Nanjo
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  2. Md. Al-Amin Khandaker
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  3. Masaaki Shirase
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  4. Takuya Kusaka
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  5. Yasuyuki Nogami
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Corresponding author

Correspondence to Yuki Nanjo .

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Editors and Affiliations

  1. Korea Advanced Institute of Science and Technology, Daejeon, Korea (Republic of)

    Brent ByungHoon Kang

  2. Korea Advanced Institute of Science and Technology, Daejeon, Korea (Republic of)

    JinSoo Jang

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Nanjo, Y., Khandaker, M.AA., Shirase, M., Kusaka, T., Nogami, Y. (2019). Efficient Ate-Based Pairing over the Attractive Classes of BN Curves. In: Kang, B., Jang, J. (eds) Information Security Applications. WISA 2018. Lecture Notes in Computer Science(), vol 11402. Springer, Cham. https://doi.org/10.1007/978-3-030-17982-3_5

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  • DOI: https://doi.org/10.1007/978-3-030-17982-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-17981-6

  • Online ISBN: 978-3-030-17982-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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