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

Enric Florit and Benjamin Smith

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.

Metadata
Available format(s)
Publication info
Published elsewhere. Proceedings of AGC2T 18
Keywords
Isogeniespost-quantum cryptographyabelian varietieshyperelliptic-curve cryptography
Contact author(s)
smith @ lix polytechnique fr
History
2022-01-17: revised
2021-01-06: received
See all versions
Short URL
https://ia.cr/2021/012
License

CC BY

BibTeX

@misc{cryptoeprint:2021/012,
author = {Enric Florit and Benjamin Smith},
title = {Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph},
howpublished = {Cryptology ePrint Archive, Paper 2021/012},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/012}},
url = {https://eprint.iacr.org/2021/012}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.