Higher-degree supersingular group actions - Département d'informatique Accéder directement au contenu
Article Dans Une Revue Mathematical Cryptology Année : 2022

Higher-degree supersingular group actions

Résumé

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.
Fichier principal
Vignette du fichier
hal.pdf (293.35 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03288075 , version 1 (16-07-2021)

Identifiants

Citer

Mathilde Chenu, Benjamin Smith. Higher-degree supersingular group actions. Mathematical Cryptology, 2022, 1 (2), pp.85-101. ⟨hal-03288075⟩
166 Consultations
170 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More