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 language | English |
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Title of host publication | Women in Numbers Europe III |
Subtitle of host publication | Research Directions in Number Theory |
Editors | Alina Carmen Cojocaru, Sorina Ionica, Elisa Lorenzo Garcia |
Publisher | SPRINGER |
Pages | 39-73 |
Number of pages | 35 |
Edition | 1 |
ISBN (Electronic) | 978-3-030-77700-5 |
ISBN (Print) | 978-3-030-77699-2 |
DOIs | |
Publication status | Published - 2021 |
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 |
Publication series
Name | Association for Women in Mathematics Series |
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Publisher | Springer |
ISSN (Print) | 2364-5733 |
ISSN (Electronic) | 2364-5741 |
Workshop
Workshop | Women in Numbers Europe |
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Country/Territory | France |
City | Rennes |
Period | 26/08/2019 → 30/08/2019 |
Internet address |