Paper 2011/135 Original: eprint.iacr.org/2011/135 ↗
On isogeny classes of Edwards curves over finite fields
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.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2011-03-21: last updated
- 2011-03-21: published
- Short URL
- https://ia.cr/2011/135
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}