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Optimized Method for Computing Odd-Degree Isogenies on Edwards Curves

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Advances in Cryptology – ASIACRYPT 2019 (ASIACRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11922))

Abstract

In this paper, we present an efficient method to compute arbitrary odd-degree isogenies on Edwards curves. By using the w-coordinate, we optimized the isogeny formula on Edwards curves by Moody and Shumow. We demonstrate that Edwards curves have an additional benefit when recovering the coefficient of the image curve during isogeny computation. For \(\ell \)-degree isogeny where \(\ell =2s+1\), our isogeny formula on Edwards curves outperforms Montgomery curves when \(s \ge 2\). To better represent the performance improvements when w-coordinate is used, we implement CSIDH using our isogeny formula. Our implementation is about 20% faster than the previous implementation. The result of our work opens the door for the usage of Edwards curves in isogeny-based cryptography, especially for CSIDH which requires higher degree isogenies.

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2017R1A2B4011599).

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Acknowledgement

We thank the anonymous reviewers for their useful and constructive comments.

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Authors and Affiliations

  1. Center for Information Security Technologies (CIST), Korea University, Seoul, Republic of Korea

    Suhri Kim & Seokhie Hong

  2. NSHC Inc., Uiwang, Republic of Korea

    Kisoon Yoon

  3. Sejong Cyber University, Seoul, Republic of Korea

    Young-Ho Park

Authors
  1. Suhri Kim
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  2. Kisoon Yoon
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  3. Young-Ho Park
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  4. Seokhie Hong
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Corresponding author

Correspondence to Young-Ho Park .

Editor information

Editors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Steven D. Galbraith

  2. Security Fundamentals Lab, NICT, Tokyo, Japan

    Shiho Moriai

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© 2019 International Association for Cryptologic Research

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Kim, S., Yoon, K., Park, YH., Hong, S. (2019). Optimized Method for Computing Odd-Degree Isogenies on Edwards Curves. In: Galbraith, S., Moriai, S. (eds) Advances in Cryptology – ASIACRYPT 2019. ASIACRYPT 2019. Lecture Notes in Computer Science(), vol 11922. Springer, Cham. https://doi.org/10.1007/978-3-030-34621-8_10

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  • DOI: https://doi.org/10.1007/978-3-030-34621-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34620-1

  • Online ISBN: 978-3-030-34621-8

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