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On isogeny classes of Edwards curves over finite fields

Ahmadi, Omran and Granger, Robert (2012) On isogeny classes of Edwards curves over finite fields Journal of Number Theory, 132 (6). pp. 1337-1358.

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Abstract

We count the number of isogeny classes of Edwards curves over odd characteristic finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a complete Edwards curve, and that an Edwards curve is isogenous to an original Edwards curve over Fq if and only if its group order is divisible by 8 if q ≡ −1 (mod 4), and 16 if q ≡ 1 (mod 4). Furthermore, we give formulae for the proportion of d ∈ Fq \ {0, 1} for which the Edwards curve Ed is complete or original, relative to the total number of d in each isogeny class

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Computing Science
Authors :
NameEmailORCID
Ahmadi, Omran
Granger, Robertr.granger@surrey.ac.uk
Date : 18 February 2012
DOI : 10.1016/j.jnt.2011.12.013
Uncontrolled Keywords : Edwards curves; Legendre curves; Isogeny classes
Depositing User : Clive Harris
Date Deposited : 06 Feb 2019 16:29
Last Modified : 06 Feb 2019 16:29
URI: http://epubs.surrey.ac.uk/id/eprint/850392

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