Supersingular Curves With Small Non-integer Endomorphisms

We introduce a special class of supersingular curves over \(\mathbb{F}_{p^2}\), characterized by the existence of non-integer endomorphisms of small degree. A number of properties of this set is proved. Most notably, we show that when this set partitions into subsets in such a way that curves within...

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Bibliographic Details
Published inarXiv.org
Main Authors Love, Jonathan, Boneh, Dan
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 24.06.2020
Subjects
Integers
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Summary:We introduce a special class of supersingular curves over \(\mathbb{F}_{p^2}\), characterized by the existence of non-integer endomorphisms of small degree. A number of properties of this set is proved. Most notably, we show that when this set partitions into subsets in such a way that curves within each subset have small-degree isogenies between them, but curves in distinct subsets have no small-degree isogenies between them. Despite this, we show that isogenies between these curves can be computed efficiently, giving a technique for computing isogenies between certain prescribed curves that cannot be reasonably connected by searching on \(\ell\)-isogeny graphs.
ISSN:2331-8422