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Journal Articles Mathematical Cryptology Year : 2022

Higher-degree supersingular group actions


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



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