Welcome to the resource topic for 2021/372
Title:
Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees
Authors: Laia Amorós, Annamaria Iezzi, Kristin Lauter, Chloe Martindale, Jana Sotáková
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.
ePrint: https://eprint.iacr.org/2021/372
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