Radical isogenies and modular curves

Valentina Pribanić

Paper 2022/1446

Radical isogenies and modular curves

Valentina Pribanić

, University of Zagreb

Abstract

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

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 isogenies isogeny-based cryptography modular 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},
      url = {https://eprint.iacr.org/2022/1446}
}