On isogeny classes of Edwards curves over finite fields

Details On isogeny classes of Edwards curves over finite fields On isogeny classes of Edwards curves over finite fields

2011-03-17

arxiv.org/abs/1103.3381v1

Mathematics

Number Theory

27 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On isogeny classes of Edwards curves over finite fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On isogeny classes of Edwards curves over finite fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On isogeny classes of Edwards curves over finite fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-247989