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SUMMARY:Jonathan Love (Stanford) and Dan Boneh (Stanford)
DTSTART;VALUE=DATE-TIME:20200629T211000Z
DTEND;VALUE=DATE-TIME:20200629T214000Z
DTSTAMP;VALUE=DATE-TIME:20220528T083010Z
UID:ANTS14/1
DESCRIPTION:Title: S
upersingular curves with small non-integer endomorphisms\nby Jonathan
Love (Stanford) and Dan Boneh (Stanford) as part of Algorithmic Number The
ory Symposium (ANTS XIV)\n\n\nAbstract\nWe introduce a special class of su
persingular curves over $\\mathbb{F}_{p^2}$\, characterized by the existen
ce 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-degre
e isogenies between them\, but curves in distinct subsets have no small-de
gree isogenies between them. Despite this\, we show that isogenies between
these curves can be computed efficiently\, giving a technique for computi
ng isogenies between certain prescribed curves that cannot be reasonably c
onnected by searching on $\\ell$-isogeny graphs.\n\nThe slides used in the
pre-recorded video can be found here.\n\nChairs: Steven Galbrait
h and Christophe Petit\n
LOCATION:https://researchseminars.org/talk/ANTS14/1/
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