Cryptology ePrint Archive: Report 2021/955

Higher-degree supersingular group actions

Mathilde Chenu and 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.

Category / Keywords: public-key cryptography / Isogeny-based cryptography, Supersingular elliptic curves, Endomorphisms

Original Publication (in the same form): MathCrypt 2021 - Mathematical Cryptology

Date: received 15 Jul 2021

Contact author: smith at lix polytechnique fr, mathilde chenu@inria fr

Available format(s): PDF | BibTeX Citation

Version: 20210722:090536 (All versions of this report)

Short URL: ia.cr/2021/955


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