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 proceedingForeword / postscriptScientificpeer-review

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 verticesand edges have a very simple representation as two-by-two matrices, which, as we show, is usefulfor understanding certain aspects of the corresponding elliptic curves and isogenies. MoreoverBruhat–Tits trees can be given an orientation and a notion of depth that we translate into thesetting of supersingular isogeny graphs. We give some suggestions towards using Bruhat–Titstrees as a tool for cryptanalysis of certain cryptosystems based on supersingular isogeny graphs.
Original languageEnglish
Title of host publicationProceedings of the Women in Numbers Europe 3 Conference
EditorsAlina Carmen Cojocaru, Sorina Ionica, Elisa Lorenzo Garcia
Number of pages34
Publication statusAccepted/In press - 17 Sep 2020
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

Workshop

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

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