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Efficient Algorithms for Isogeny Sequences and Their Cryptographic Applications

  • Katsuyuki TakashimaEmail author
Chapter
Part of the Mathematics for Industry book series (MFI, volume 29)

Abstract

We summarize efficient isogeny sequence computations on elliptic and genus 2 Jacobians. For cryptographic purposes, sequences of low-degree isogenies are important. Then we focus on sequences of 2- and 3-isogenies on elliptic curves and (2, 2)- and (3, 3)-isogenies on genus 2 Jacobians. Our aim is to explicitly describe the low-degree isogeny sequence computations and improve them for cryptographic applications such as post-quantum cryptosystems and random self-reducibility of discrete logarithm problem (DLP).

Keywords

Isogeny Expander graph Post-quantum cryptography Random self-reducibility of dlp 

Notes

Acknowledgements

The author would like to thank Kazuto Matsuo for his valuable comments on genus 2 division polynomials given in Sect. 4.3.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Mitsubishi ElectricKamakuraJapan

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