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Implementing optimized pairings with elliptic nets

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Abstract

In this paper, we use elliptic nets to implement the optimized Ate pairings and optimal pairings on the Barreto-Naehrig curves with embedding degree 12. In order to do the arithmetic of elliptic curves over finite fields with elliptic nets, we first give some basic properties of elliptic nets associated to elliptic curves over finite fields and the expression of Miller function in terms of elliptic nets. Then we give formulae to compute some optimized pairings with elliptic nets, which is a new method to implement pairings. This method with elliptic nets has time complexity comparable to Miller’s algorithm and it can be optimized.

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Authors and Affiliations

  1. School of Mathematics and Information, China West Normal University, Nanchong, 637002, China

    ChunMing Tang

  2. LMAM, Chinese Ministry of Education, Peking University, Beijing, 100871, China

    ChunMing Tang, DongMei Ni, MaoZhi Xu & YanFeng Qi

  3. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    ChunMing Tang, DongMei Ni, MaoZhi Xu & YanFeng Qi

  4. Aisino Corporation Inc., Beijing, 100195, China

    BaoAn Guo & YanFeng Qi

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  1. ChunMing Tang
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  2. DongMei Ni
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  3. MaoZhi Xu
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  4. BaoAn Guo
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  5. YanFeng Qi
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Correspondence to YanFeng Qi.

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Tang, C., Ni, D., Xu, M. et al. Implementing optimized pairings with elliptic nets. Sci. China Inf. Sci. 57, 1–10 (2014). https://doi.org/10.1007/s11432-013-4840-7

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  • DOI: https://doi.org/10.1007/s11432-013-4840-7

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