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Higher-degree supersingular group actions

Mathilde Chenu 1 Benjamin Smith 1 
1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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.
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https://hal.inria.fr/hal-03288075
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Submitted on : Friday, July 16, 2021 - 10:18:54 AM
Last modification on : Friday, April 1, 2022 - 3:56:00 AM

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  • HAL Id : hal-03288075, version 1
  • ARXIV : 2107.08832

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Mathilde Chenu, Benjamin Smith. Higher-degree supersingular group actions. Mathematical Cryptology, Florida Online Journals, inPress. ⟨hal-03288075⟩

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