Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3

Sabrina Kunzweiler; Luciano Maino; Tomoki Moriya; Christophe Petit; Giacomo Pope; Damien Robert; Miha Stopar; Yan Bo Ti

Paper 2024/1732

Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3

Sabrina Kunzweiler

, Inria Bordeaux - Sud-Ouest Research Centre, Institut de Mathématiques de Bordeaux

Luciano Maino, University of Bristol

Tomoki Moriya, University of Birmingham

Christophe Petit, Université Libre de Bruxelles

Giacomo Pope, NCC group, UK, University of Bristol

Damien Robert, Inria Bordeaux - Sud-Ouest Research Centre, Institut de Mathématiques de Bordeaux

Miha Stopar, Université Libre de Bruxelles, Ethereum Foundation

Yan Bo Ti, DSO National Laboratories, National University of Singapore

Abstract

We provide explicit descriptions for radical 2-isogenies in dimensions one, two and three using theta coordinates. These formulas allow us to efficiently navigate in the corresponding isogeny graphs. As an application of this, we implement different versions of the CGL hash func- tion. Notably, the three-dimensional version is fastest, which demonstrates yet another potential of using higher dimensional isogeny graphs in cryptography.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint.
Keywords: isogenies cryptographic hash functions abelian varieties
Contact author(s): sabrina kunzweiler @ math u-bordeaux fr
luciano maino @ bristol ac uk
t moriya @ bham ac uk
christophe petit @ ulb be
giacomo pope @ nccgroup com
damien robert @ inria fr
stopar miha @ gmail com
yanbo ti @ gmail com
History: 2024-10-25: approved; 2024-10-22: received; See all versions
Short URL: https://ia.cr/2024/1732
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1732,
      author = {Sabrina Kunzweiler and Luciano Maino and Tomoki Moriya and Christophe Petit and Giacomo Pope and Damien Robert and Miha Stopar and Yan Bo Ti},
      title = {Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1732},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1732}
}