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SUMMARY:Daniel J. Bernstein (Eindhoven University of Technology)\, Luca De
  Feo (Université de Versailles)\, Antonin Leroux (LIX - École polytechni
 que)\, and Benjamin Smith (LIX - École polytechnique)
DTSTART:20200702T160000Z
DTEND:20200702T163000Z
DTSTAMP:20260423T200955Z
UID:ANTS14/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS14/15/">
 Faster computation of isogenies of large prime degree</a>\nby Daniel J. Be
 rnstein (Eindhoven University of Technology)\, Luca De Feo (Université de
  Versailles)\, Antonin Leroux (LIX - École polytechnique)\, and Benjamin 
 Smith (LIX - École polytechnique) as part of Algorithmic Number Theory Sy
 mposium (ANTS XIV)\n\n\nAbstract\nLet $E/\\F_q$ be an elliptic curve\, and
  $P$ a point in $E(\\F_q)$ of prime order $\\ell$. Vélu's formulae let us
  compute a quotient curve $E' = E/\\langle P \\rangle$ and rational maps d
 efining the quotient isogeny $\\phi\\colon E \\to E'$ in $\\tilde{O}(\\ell
 )$ $\\F_q$-operations\, where the $\\tilde{O}$ is uniform in $q$. This art
 icle shows how to compute $E'$\, and $\\phi(Q)$ for $Q$ in $E(\\F_q)$\, us
 ing only $\\tilde{O}(\\sqrt{\\ell})$ $\\F_q$-operations\, where the $\\til
 de{O}$ is again uniform in $q$. As an application\, we speed up some compu
 tations used in the isogeny-based cryptosystems CSIDH and CSURF.\n\nChairs
 : Wouter Castryck and Chloe Martindale\n
LOCATION:https://researchseminars.org/talk/ANTS14/15/
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