Paper 2021/372 Original: eprint.iacr.org/2021/372 ↗
Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees
Abstract
We give an exposition of supersingular isogeny graphs, quaternion ideal graphs and Bruhat–Tits trees, and of their connections. Bruhat–Tits trees are combinatorial objects whose vertices and edges have a very simple representation as two-by-two matrices, which, as we show, is useful for understanding certain aspects of the corresponding elliptic curves and isogenies. Moreover Bruhat–Tits trees can be given an orientation and a notion of depth that we translate into the setting of supersingular isogeny graphs. We give some suggestions towards using Bruhat–Tits trees as a tool for cryptanalysis of certain cryptosystems based on supersingular isogeny graphs.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2021-03-22: last updated
- 2021-03-22: published
- Short URL
- https://ia.cr/2021/372
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2021/372,
author = {Laia Amorós and Annamaria Iezzi and Kristin Lauter and Chloe Martindale and Jana Sotáková},
title = {Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/372},
year = {2021},
url = {https://eprint.iacr.org/2021/372}
}