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SUMMARY:Sarah Arpin (Leiden University)
DTSTART:20230315T160000Z
DTEND:20230315T170000Z
DTSTAMP:20260418T065554Z
UID:LNTS/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/91/">Ad
 ding Level Structure to Supersingular Elliptic Curve Isogeny Graphs</a>\nb
 y Sarah Arpin (Leiden University) as part of London number theory seminar\
 n\nLecture held in Rm. 706\, UCL Department of Mathematics (UCL Union Buil
 ding).\n\nAbstract\nThe classical Deuring correspondence provides a roadma
 p between supersingular elliptic curves and the maximal orders which are i
 somorphic to their endomorphism rings. Building on this idea\, we add the 
 information of a cyclic subgroup of prime order $N$ to supersingular ellip
 tic curves\, and prove a generalisation of the Deuring correspondence for 
 these objects. We also study the resulting $\\ell$-isogeny graphs supersin
 gular elliptic curve with level-$N$ structure\, and the corresponding grap
 hs in the realm of quaternion algebras. The structure of the supersingular
  elliptic curve ell-isogeny graph underlies the security of a new cryptogr
 aphic signature protocol\, SQISign\, which is proposed to be resistant aga
 inst both classical and quantum attack.\n
LOCATION:https://researchseminars.org/talk/LNTS/91/
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