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SUMMARY:Jonathan Love (Stanford) and Dan Boneh (Stanford)
DTSTART:20200629T211000Z
DTEND:20200629T214000Z
DTSTAMP:20260423T150057Z
UID:ANTS14/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS14/1/">S
 upersingular curves with small non-integer endomorphisms</a>\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 <a href="http://math.mit.edu/~drew/ANTSXI
 V/SupersingularCurvesVideoSlides.pdf">here</a>.\n\nChairs: Steven Galbrait
 h and Christophe Petit\n
LOCATION:https://researchseminars.org/talk/ANTS14/1/
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