Higher-degree supersingular group actions

Mathilde Chenu; Benjamin Smith

Paper 2021/955

Higher-degree supersingular group actions

Mathilde Chenu and Benjamin Smith

Abstract

We investigate the isogeny graphs of supersingular elliptic curves over $F_{p^{2}}$ 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 $F_{p}$ , and there is an action of the ideal class group of $Q (\sqrt{- d p})$ 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 cryptography Supersingular elliptic curves Endomorphisms
Contact author(s): smith @ lix polytechnique fr
mathilde chenu @ inria fr
History: 2021-07-22: received
Short URL: https://ia.cr/2021/955
License: 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},
      url = {https://eprint.iacr.org/2021/955}
}