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Constructing Isogenies on Extended Jacobi Quartic Curves

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Book cover Information Security and Cryptology (Inscrypt 2016)

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Abstract

Isogenies are widely used in elliptic curves. Since Moody and Shumow [20] proposed isogenies on Edwards and Huff curves analogues of Vélu’s formulas, they have pointed out a new way to construct isogenies. However, hardly any isogeny on Jacobi quartic curves has been designed, this paper extends their work to construct isogenies on extended Jacobi quartic curves for the first time including a 2-isogeny and a generalized l-isogeny for any odd l as well as an improved l-isogeny. This paper also estimates the time complexity of the improved l-isogeny. If the constants are carefully chosen, the Jacobi quartic isogeny is about to catch up with Huff isogeny.

This work is supported in part by National Research Foundation of China under Grant No. 61502487, 61272040, and in part by National Basic Research Program of China (973) under Grant No. 2013CB338001.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Xiu Xu, Wei Yu, Kunpeng Wang & Xiaoyang He

  2. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, China

    Xiu Xu, Wei Yu, Kunpeng Wang & Xiaoyang He

  3. University of Chinese Academy of Sciences, Beijing, China

    Xiu Xu, Kunpeng Wang & Xiaoyang He

Authors
  1. Xiu Xu
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  2. Wei Yu
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  3. Kunpeng Wang
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  4. Xiaoyang He
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Correspondence to Wei Yu .

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Editors and Affiliations

  1. School of Science, Hangzhou Normal University, Hangzhou, China

    Kefei Chen

  2. Institute of Information Engineering, SKLOIS, Beijing, China

    Dongdai Lin

  3. Snapchat Inc., Columbia University, New York, New York, USA

    Moti Yung

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Xu, X., Yu, W., Wang, K., He, X. (2017). Constructing Isogenies on Extended Jacobi Quartic Curves. In: Chen, K., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2016. Lecture Notes in Computer Science(), vol 10143. Springer, Cham. https://doi.org/10.1007/978-3-319-54705-3_26

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  • DOI: https://doi.org/10.1007/978-3-319-54705-3_26

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-54705-3

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