Optimized CSIDH Implementation Using a 2-torsion Point

Donghoe Heo; Suhri Kim; Kisoon Yoon; Young-Ho Park; Seokhie Hong

Paper 2020/391

Optimized CSIDH Implementation Using a 2-torsion Point

Donghoe Heo, Suhri Kim, Kisoon Yoon, Young-Ho Park, and Seokhie Hong

Abstract

The implementation of isogeny-based cryptography mainly use Montgomery curves as they offer fast elliptic curve arithmetic and isogeny compuation. However, although Montgomery curves have efficient 3- and 4-isogenies, it becomes inefficient when recovering the coefficient of the image curve for large degree isogenies. This is the main bottleneck of using a Montgomery curve for CSIDH as it requires odd-degree isogenies up to at least 587. In this paper, we present a new optimization method for faster CSIDH protocols entirely on Montgomery curves. To this end, we present a new parameter for CSIDH in which the rational 2-torsion points are defined over . By using the proposed parameters the CSIDH moves around the surface. The curve coefficient of the image curve can be recovered by a 2-torsion point. We also proved that the CSIDH using the proposed parameter guarantees a free and transitive group action. Additionally, we present the implementation result using our method. We demonstrated that our method is 6.1% faster than the original CSIDH. Our works show that quite higher performance of CSIDH is achieved using only Montgomery curves.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Post-quantum cryptography Isogeny Montgomery curves 2-torsion points CSIDH.
Contact author(s): dong5641 @ korea ac kr
History: 2020-04-28: revised; 2020-04-09: received; See all versions
Short URL: https://ia.cr/2020/391
License: CC BY

BibTeX

@misc{cryptoeprint:2020/391,
      author = {Donghoe Heo and Suhri Kim and Kisoon Yoon and Young-Ho Park and Seokhie Hong},
      title = {Optimized {CSIDH} Implementation Using a 2-torsion Point},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/391},
      year = {2020},
      url = {https://eprint.iacr.org/2020/391}
}