Higher-degree supersingular group actions

2021/07/19 by Mathilde Chenu, Benjamin Smith, Chenu, Mathilde +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2107.08832

openalex publication_date 2021/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the isogeny graphs of supersingular elliptic curves over\n mathbbF_p² equipped with a d-isogeny to their Galois conjugate. These\ncurves are interesting because they are, in a sense, a generalization of curves\ndefined over mathbbF_p, and there is an action of the ideal class group of\n\ℚ(\√(-dp)) on the isogeny graphs. We investigate constructive and\ndestructive aspects of these graphs in isogeny-based cryptography, including\ngeneralizations of the CSIDH cryptosystem and the Delfs-Galbraith algorithm.\n

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