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Award ID contains: 1701567

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  1. ; (, ANTS)
    We introduce a special class of supersingular curves over Fp2 , 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. 
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    Accepted Manuscript Full Text Available
  2. ; (, Algorithmic number theory symposium (ANTS))
    We introduce a special class of supersingular curves over Fp2 , 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. 
    more » « less
    Accepted Manuscript Full Text Available