Paper 2022/650
Supersingular Non-Superspecial Abelian Surfaces in Cryptography
Abstract
We consider the use of supersingular abelian surfaces in cryptography. Several generalisations of well-known cryptographic schemes and constructions based on supersingular elliptic curves to the 2-dimensional setting of superspecial abelian surfaces have been proposed. The computational assumptions in the superspecial 2-dimensional case can be reduced to the corresponding 1-dimensional problems via a product decomposition by observing that every superspecial abelian surface is non-simple and separably isogenous to a product of supersingular elliptic curves. Instead, we propose to use supersingular non-superspecial isogeny graphs where such a product decomposition does not have a computable description via separable isogenies. We study the advantages and investigate security concerns of the move to supersingular non-superspecial abelian surfaces.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Isogenies Genus 2
- Contact author(s)
-
jason legrow @ auckland ac nz
yanbo ti @ gmail com
lukas zobernig @ auckland ac nz - History
- 2022-05-28: approved
- 2022-05-26: received
- See all versions
- Short URL
- https://ia.cr/2022/650
- License
-
CC BY-SA
BibTeX
@misc{cryptoeprint:2022/650,
author = {Jason T. LeGrow and Yan Bo Ti and Lukas Zobernig},
title = {Supersingular Non-Superspecial Abelian Surfaces in Cryptography},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/650},
year = {2022},
url = {https://eprint.iacr.org/2022/650}
}
