Welcome to the resource topic for 2011/135
Title:
On isogeny classes of Edwards curves over finite fields
Authors: Omran Ahmadi, Robert Granger
Abstract: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 \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 \F_q \setminus \{0,1\} for which the Edwards curve E_d is complete or original, relative to the total number of d in each isogeny class.
ePrint: https://eprint.iacr.org/2011/135
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