Paper 2025/608
On some non-linear recurrences over finite fields linked to isogeny graphs
, vicente.munoz@ucm.esAbstract
This paper presents new results that establish connections between isogeny graphs and nonlinear recurrences over finite fields. Specifically, we prove several theorems that link these two areas, offering deeper insights into the structure of isogeny graphs and their relationship with nonlinear recurrence sequences. We further provide two related conjectures which may be worth of further research. These findings contribute to a better understanding of the endomorphism ring of a curve, advancing progress toward the resolution of the Endomorphism Ring Problem, which aims to provide a computational characterization of the endomorphism ring of a supersingular elliptic curve.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Isogeny Graphsinvariantsrecurrencesenomorphism ring of a curve
- Contact author(s)
- jjleon @ gmv com
- History
- 2025-04-08: approved
- 2025-04-03: received
- See all versions
- Short URL
- https://ia.cr/2025/608
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2025/608,
author = {Juan Jesús León and Vicente Muñoz},
title = {On some non-linear recurrences over finite fields linked to isogeny graphs},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/608},
year = {2025},
url = {https://eprint.iacr.org/2025/608}
}
