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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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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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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