Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees

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

doi:10.1007/978-3-030-77700-5_2

Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees

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

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-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 language	English
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	https://doi.org/10.1007/978-3-030-77700-5_2
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
Publisher	Springer
ISSN (Print)	2364-5733
ISSN (Electronic)	2364-5741

Workshop

Workshop	Women in Numbers Europe
Country/Territory	France
City	Rennes
Period	26/08/2019 → 30/08/2019
Internet address	http://www.claymath.org/events/women-numbers-europe-3

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10.1007/978-3-030-77700-5_2

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Amoros Carafi, L., Iezzi, A., Lauter, K., Martindale, C., & Sotáková, J. (2021). Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees. In A. C. Cojocaru, S. Ionica, & E. Lorenzo Garcia (Eds.), Women in Numbers Europe III: Research Directions in Number Theory (1 ed., pp. 39-73). (Association for Women in Mathematics Series). SPRINGER. https://doi.org/10.1007/978-3-030-77700-5_2

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Amoros Carafi, L, Iezzi, A, Lauter, K, Martindale, C & Sotáková, J 2021, Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees. in AC Cojocaru, S Ionica & E Lorenzo Garcia (eds), Women in Numbers Europe III: Research Directions in Number Theory. 1 edn, Association for Women in Mathematics Series, SPRINGER, pp. 39-73, Women in Numbers Europe, Rennes, France, 26/08/2019. https://doi.org/10.1007/978-3-030-77700-5_2

Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees. / Amoros Carafi, Laia; Iezzi, Annamaria; Lauter, Kristin et al.

Women in Numbers Europe III: Research Directions in Number Theory. ed. / Alina Carmen Cojocaru; Sorina Ionica; Elisa Lorenzo Garcia. 1. ed. SPRINGER, 2021. p. 39-73 (Association for Women in Mathematics Series).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

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Amoros Carafi L, Iezzi A, Lauter K, Martindale C, Sotáková J. Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees. In Cojocaru AC, Ionica S, Lorenzo Garcia E, editors, Women in Numbers Europe III: Research Directions in Number Theory. 1 ed. SPRINGER. 2021. p. 39-73. (Association for Women in Mathematics Series). doi: 10.1007/978-3-030-77700-5_2

Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees

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