Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph

Enric Florit; Benjamin Smith

doi:10.1090/conm/779/15672

Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph

Enric Florit
, Benjamin Smith

University of Barcelona

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

4 Citations (Scopus)

Résumé

We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular. We give theoretical and experimental results on the spectral and statistical properties of (2, 2)-isogeny graphs of superspecial abelian surfaces, including stationary distributions for random walks, bounds on eigenvalues and diameters, and a proof of the connectivity of the Jacobian subgraph of the (2, 2)-isogeny graph. Our results improve our understanding of the performance and security of some recently-proposed cryptosystems, and are also a concrete step towards a better understanding of general superspecial isogeny graphs in arbitrary dimension.

langue originale	Anglais
titre	Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021
rédacteurs en chef	Samuele Anni, Valentijn Karemaker, Elisa Lorenzo García
Editeur	American Mathematical Society
Pages	103-132
Nombre de pages	30
ISBN (imprimé)	9781470467944
Les DOIs	https://doi.org/10.1090/conm/779/15672
état	Publié - 1 janv. 2022
Evénement	18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AGC2T 2021 - Virtual, Online Durée: 31 mai 2021 → 4 juin 2021

Série de publications

Nom	Contemporary Mathematics
Volume	779
ISSN (imprimé)	0271-4132
ISSN (Electronique)	1098-3627

Une conférence

Une conférence	18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AGC2T 2021
La ville	Virtual, Online
période	31/05/21 → 4/06/21

Accès au document

10.1090/conm/779/15672

Contient cette citation

Florit, E., & Smith, B. (2022). Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph. Dans S. Anni, V. Karemaker, & E. L. García (eds.), Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021 (p. 103-132). (Contemporary Mathematics; Vol 779). American Mathematical Society. https://doi.org/10.1090/conm/779/15672

Florit, Enric ; Smith, Benjamin. / Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph. Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021. Editeur / Samuele Anni ; Valentijn Karemaker ; Elisa Lorenzo García. American Mathematical Society, 2022. p. 103-132 (Contemporary Mathematics).

@inproceedings{7a372e169b0749299f7df9571d97a266,

title = "Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph",

abstract = "We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular. We give theoretical and experimental results on the spectral and statistical properties of (2, 2)-isogeny graphs of superspecial abelian surfaces, including stationary distributions for random walks, bounds on eigenvalues and diameters, and a proof of the connectivity of the Jacobian subgraph of the (2, 2)-isogeny graph. Our results improve our understanding of the performance and security of some recently-proposed cryptosystems, and are also a concrete step towards a better understanding of general superspecial isogeny graphs in arbitrary dimension.",

keywords = "Superspecial abelian varieties, isogeny graphs, isogeny-based cryptography",

author = "Enric Florit and Benjamin Smith",

note = "Publisher Copyright: {\textcopyright} 2022 Copyright by the authors.; 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AGC2T 2021 ; Conference date: 31-05-2021 Through 04-06-2021",

year = "2022",

month = jan,

day = "1",

doi = "10.1090/conm/779/15672",

language = "English",

isbn = "9781470467944",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "103--132",

editor = "Samuele Anni and Valentijn Karemaker and Garc{\'i}a, \{Elisa Lorenzo\}",

booktitle = "Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021",

}

Florit, E & Smith, B 2022, Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph. Dans S Anni, V Karemaker & EL García (eds), Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021. Contemporary Mathematics, VOL. 779, American Mathematical Society, p. 103-132, 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AGC2T 2021, Virtual, Online, 31/05/21. https://doi.org/10.1090/conm/779/15672

Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph. / Florit, Enric; Smith, Benjamin.
Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021. Ed. / Samuele Anni; Valentijn Karemaker; Elisa Lorenzo García. American Mathematical Society, 2022. p. 103-132 (Contemporary Mathematics; Vol 779).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

TY - GEN

T1 - Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph

AU - Florit, Enric

AU - Smith, Benjamin

PY - 2022/1/1

Y1 - 2022/1/1

N2 - We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular. We give theoretical and experimental results on the spectral and statistical properties of (2, 2)-isogeny graphs of superspecial abelian surfaces, including stationary distributions for random walks, bounds on eigenvalues and diameters, and a proof of the connectivity of the Jacobian subgraph of the (2, 2)-isogeny graph. Our results improve our understanding of the performance and security of some recently-proposed cryptosystems, and are also a concrete step towards a better understanding of general superspecial isogeny graphs in arbitrary dimension.

AB - We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular. We give theoretical and experimental results on the spectral and statistical properties of (2, 2)-isogeny graphs of superspecial abelian surfaces, including stationary distributions for random walks, bounds on eigenvalues and diameters, and a proof of the connectivity of the Jacobian subgraph of the (2, 2)-isogeny graph. Our results improve our understanding of the performance and security of some recently-proposed cryptosystems, and are also a concrete step towards a better understanding of general superspecial isogeny graphs in arbitrary dimension.

KW - Superspecial abelian varieties

KW - isogeny graphs

KW - isogeny-based cryptography

U2 - 10.1090/conm/779/15672

DO - 10.1090/conm/779/15672

M3 - Conference contribution

AN - SCOPUS:85130498835

SN - 9781470467944

T3 - Contemporary Mathematics

SP - 103

EP - 132

BT - Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021

A2 - Anni, Samuele

A2 - Karemaker, Valentijn

A2 - García, Elisa Lorenzo

PB - American Mathematical Society

T2 - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AGC2T 2021

Y2 - 31 May 2021 through 4 June 2021

ER -

Florit E, Smith B. Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph. Dans Anni S, Karemaker V, García EL, rédacteurs en chef, Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021. American Mathematical Society. 2022. p. 103-132. (Contemporary Mathematics). doi: 10.1090/conm/779/15672

Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph

Résumé

Série de publications

Une conférence

Accès au document

Empreinte digitale

Contient cette citation