Supersingular curves with small noninteger endomorphisms Article Swipe
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Jonathan Love
,
Dan Boneh
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.2140/obs.2020.4.7
· OA: W3116436840
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.2140/obs.2020.4.7
· OA: W3116436840
We introduce a special class of supersingular curves over ކ p 2 , characterized by the existence of noninteger endomorphisms of small degree.We prove a number of properties about this set.Most notably, we can partition this set into subsets such 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 distinct subsets can heuristically be computed efficiently, giving a technique for computing isogenies between certain prescribed curves that cannot be efficiently found by searching on -isogeny graphs.
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