Paper 2021/955

Higher-degree supersingular group actions

Mathilde Chenu and Benjamin Smith

Abstract

We investigate the isogeny graphs of supersingular elliptic curves over \(\mathbb{F}_{p^2}\) equipped with a \(d\)-isogeny to their Galois conjugate. These curves are interesting because they are, in a sense, a generalization of curves defined over \(\mathbb{F}_p\), and there is an action of the ideal class group of \(\mathbb{Q}(\sqrt{-dp})\) on the isogeny graphs. We investigate constructive and destructive aspects of these graphs in isogeny-based cryptography, including generalizations of the CSIDH cryptosystem and the Delfs--Galbraith algorithm.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. MathCrypt 2021 - Mathematical Cryptology
Keywords
Isogeny-based cryptographySupersingular elliptic curvesEndomorphisms
Contact author(s)
smith @ lix polytechnique fr
mathilde chenu @ inria fr
History
2021-07-22: received
Short URL
https://ia.cr/2021/955
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2021/955,
      author = {Mathilde Chenu and Benjamin Smith},
      title = {Higher-degree supersingular group actions},
      howpublished = {Cryptology ePrint Archive, Paper 2021/955},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/955}},
      url = {https://eprint.iacr.org/2021/955}
}
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