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Title:
Higher-degree supersingular group actions
Authors: Mathilde Chenu, 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.
ePrint: https://eprint.iacr.org/2021/955
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