International Association for Cryptologic Research

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

Authors:
Sabrina Kunzweiler , Inria and IMB France
Luciano Maino , University of Bristol, UK
Tomoki Moriya , University of Birmingham, UK
Christophe Petit , University of Birmingham, UK; Université libre de Bruxelles, Belgium
Giacomo Pope , University of Bristol, UK; NCC Group, UK
Damien Robert , Inria and IMB France
Miha Stopar , Université libre de Bruxelles, Belgium, Ethereum Foundation
Yan Bo Ti , DSO National Laboratories, Singapore; National University of Singapore, Singapore
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Conference: PKC 2025
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 function. Notably, the three-dimensional version is fastest, which demonstrates yet another potential of using higher dimensional isogeny graphs in cryptography.
BibTeX
@inproceedings{pkc-2025-35202,
  title={Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3},
  publisher={Springer-Verlag},
  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},
  year=2025
}