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Erschienen in:
2019 | OriginalPaper | Buchkapitel
Efficient Ate-Based Pairing over the Attractive Classes of BN Curves
verfasst von : Yuki Nanjo, Md. Al-Amin Khandaker, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami
Erschienen in: Information Security Applications
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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.
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.