Paper 2019/110
Optimized Method for Computing Odd-Degree Isogenies on Edwards Curves
Suhri Kim, Kisoon Yoon, Young-Ho Park, and Seokhie Hong
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 $s \geq 2$. 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.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- IsogenyPost-quantum cryptographyMontgomery curvesEdwards curvesSIDHCSIDH
- Contact author(s)
- suhrikim @ gmail com
- History
- 2019-12-07: last of 2 revisions
- 2019-02-05: received
- See all versions
- Short URL
- https://ia.cr/2019/110
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/110,
author = {Suhri Kim and Kisoon Yoon and Young-Ho Park and Seokhie Hong},
title = {Optimized Method for Computing Odd-Degree Isogenies on Edwards Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/110},
year = {2019},
url = {https://eprint.iacr.org/2019/110}
}
