Paper 2022/1446
Radical isogenies and modular curves
, University of ZagrebAbstract
This article explores the connection between radical isogenies and modular curves. Radical isogenies are formulas designed for the computation of chains of isogenies of fixed small degree $N$, introduced by Castryck, Decru, and Vercauteren at Asiacrypt 2020. One significant advantage of radical isogeny formulas over other formulas with a similar purpose is that they eliminate the need to generate a point of order $N$ that generates the kernel of the isogeny. While radical isogeny formulas were originally developed using elliptic curves in Tate normal form, Onuki and Moriya have proposed radical isogeny formulas of degrees $3$ and $4$ on Montgomery curves and attempted to obtain a simpler form of radical isogenies using enhanced elliptic and modular curves. In this article, we translate the original setup of radical isogenies in Tate normal form into the language of modular curves. Additionally, we solve an open problem introduced by Onuki and Moriya regarding radical isogeny formulas on $X_0(N).$
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Minor revision. Advances in Mathematics of Communications
- DOI
- 10.3934/amc.2023019
- Keywords
- radical isogeniesisogeny-based cryptographymodular curves
- Contact author(s)
- valentina pribanic @ gmail com
- History
- 2023-07-16: last of 2 revisions
- 2022-10-23: received
- See all versions
- Short URL
- https://ia.cr/2022/1446
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2022/1446,
author = {Valentina Pribanić},
title = {Radical isogenies and modular curves},
howpublished = {Cryptology ePrint Archive, Paper 2022/1446},
year = {2022},
doi = {10.3934/amc.2023019},
note = {\url{https://eprint.iacr.org/2022/1446}},
url = {https://eprint.iacr.org/2022/1446}
}
