Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees

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

Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees

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

Tietotekniikan laitos

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Foreword / postscript › vertaisarvioitu

Abstrakti

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.

Alkuperäiskieli	Englanti
Otsikko	Proceedings of the Women in Numbers Europe 3 Conference
Toimittajat	Alina Carmen Cojocaru, Sorina Ionica, Elisa Lorenzo Garcia
Sivumäärä	34
Tila	Hyväksytty/In press - 17 syyskuuta 2020
OKM-julkaisutyyppi	A3 Kirjan osa tai toinen tutkimuskirja
Tapahtuma	Women in Numbers Europe - La Hublais Center, Rennes, Ranska Kesto: 26 elokuuta 2019 → 30 elokuuta 2019 Konferenssinumero: 3 http://www.claymath.org/events/women-numbers-europe-3

Workshop

Workshop	Women in Numbers Europe
Maa	Ranska
Kaupunki	Rennes
Ajanjakso	26/08/2019 → 30/08/2019
www-osoite	http://www.claymath.org/events/women-numbers-europe-3

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Siteeraa tätä

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title = "Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees",

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.",

author = "{Amoros Carafi}, Laia and Annamaria Iezzi and Kristin Lauter and Chloe Martindale and Jana Sot{\'a}kov{\'a}",

year = "2020",

month = sep,

day = "17",

language = "English",

editor = "Cojocaru, {Alina Carmen} and Sorina Ionica and {Lorenzo Garcia}, Elisa",

booktitle = "Proceedings of the Women in Numbers Europe 3 Conference",

note = "Women in Numbers Europe ; Conference date: 26-08-2019 Through 30-08-2019",

url = "http://www.claymath.org/events/women-numbers-europe-3",

}

Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees. / Amoros Carafi, Laia; Iezzi, Annamaria; Lauter, Kristin; Martindale, Chloe; Sotáková, Jana.

Proceedings of the Women in Numbers Europe 3 Conference. toim. / Alina Carmen Cojocaru; Sorina Ionica; Elisa Lorenzo Garcia. 2020.

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Foreword / postscript › vertaisarvioitu

TY - CHAP

T1 - Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees

AU - Amoros Carafi, Laia

AU - Iezzi, Annamaria

AU - Lauter, Kristin

AU - Martindale, Chloe

AU - Sotáková, Jana

N1 - Conference code: 3

PY - 2020/9/17

Y1 - 2020/9/17

N2 - 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.

AB - 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.

M3 - Foreword / postscript

BT - Proceedings of the Women in Numbers Europe 3 Conference

A2 - Cojocaru, Alina Carmen

A2 - Ionica, Sorina

A2 - Lorenzo Garcia, Elisa

T2 - Women in Numbers Europe

Y2 - 26 August 2019 through 30 August 2019

ER -