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research article

On isogeny classes of Edwards curves over finite fields

Ahmadi, Omran
•
Granger, Robert  
2012
Journal of Number Theory

We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\em complete} Edwards curve, and that an Edwards curve is isogenous to an {\em original} Edwards curve over $\mathbb{F}_q$ if and only if its group order is divisible by $8$ if $q \equiv -1 \pmod{4}$, and $16$ if $q \equiv 1 \pmod{4}$. Furthermore, we give formulae for the proportion of $d \in \mathbb{F}_q$ \ {0,1} for which the Edwards curve $E_d$ is complete or original, relative to the total number of $d$ in each isogeny class.

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Type
research article
DOI
10.1016/j.jnt.2011.12.013
Author(s)
Ahmadi, Omran
Granger, Robert  
Date Issued

2012

Publisher

Elsevier

Published in
Journal of Number Theory
Volume

132

Issue

6

Start page

1337

End page

1358

Subjects

Edwards curves

•

Legendre curves

•

Isogeny classes

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
IIF  
Available on Infoscience
January 18, 2016
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/122303
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