Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees

Laia Amoros Carafi, Annamaria Iezzi, Kristin Lauter, Chloe Martindale, Jana Sotáková

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

Abstract

In this paper 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.

Original languageEnglish
Title of host publicationWomen in Numbers Europe III
Subtitle of host publicationResearch Directions in Number Theory
EditorsAlina Carmen Cojocaru, Sorina Ionica, Elisa Lorenzo Garcia
PublisherSPRINGER
Pages39-73
Number of pages35
Edition1
ISBN (Electronic)978-3-030-77700-5
ISBN (Print)978-3-030-77699-2
DOIs
Publication statusPublished - 2021
MoE publication typeA3 Part of a book or another research book
EventWomen in Numbers Europe - La Hublais Center, Rennes, France
Duration: 26 Aug 201930 Aug 2019
Conference number: 3
http://www.claymath.org/events/women-numbers-europe-3

Publication series

NameAssociation for Women in Mathematics Series
PublisherSpringer
ISSN (Print)2364-5733
ISSN (Electronic)2364-5741

Workshop

WorkshopWomen in Numbers Europe
Country/TerritoryFrance
CityRennes
Period26/08/201930/08/2019
Internet address

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