Paper 2011/135
On isogeny classes of Edwards curves over finite fields
Omran Ahmadi and 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.
Note: Comments welcome.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. preprint
- Keywords
- number theory
- Contact author(s)
- rgranger @ computing dcu ie
- History
- 2011-03-21: received
- Short URL
- https://ia.cr/2011/135
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2011/135, author = {Omran Ahmadi and Robert Granger}, title = {On isogeny classes of Edwards curves over finite fields}, howpublished = {Cryptology {ePrint} Archive, Paper 2011/135}, year = {2011}, url = {https://eprint.iacr.org/2011/135} }