Higher-degree supersingular group actions


Isogeny-based cryptography
Supersingular elliptic curves

How to Cite

Chenu, M., & Smith, B. (2022). Higher-degree supersingular group actions. Mathematical Cryptology, 1(2), 85–101. Retrieved from https://journals.flvc.org/mathcryptology/article/view/130604


We investigate the isogeny graphs of supersingular elliptic curves over GF(p2) 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 GF(p), and there is an action of the ideal class group of Q(√︁-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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Copyright (c) 2022 Mathilde Chenu, Benjamin Smith