Supersingular Curves With Small Non-integer Endomorphisms Article Swipe

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Jonathan Love , Dan Boneh ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1910.03180 · OA: W2979341815

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.