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 language | English |
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Title of host publication | Proceedings of the Women in Numbers Europe 3 Conference |
Editors | Alina Carmen Cojocaru, Sorina Ionica, Elisa Lorenzo Garcia |
Number of pages | 34 |
Publication status | Accepted/In press - 17 Sep 2020 |
MoE publication type | A3 Part of a book or another research book |
Event | Women in Numbers Europe - La Hublais Center, Rennes, France Duration: 26 Aug 2019 → 30 Aug 2019 Conference number: 3 http://www.claymath.org/events/women-numbers-europe-3 |
Workshop
Workshop | Women in Numbers Europe |
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Country | France |
City | Rennes |
Period | 26/08/2019 → 30/08/2019 |
Internet address |