Paper 2026/2259
Supersingularity and Superspeciality Verification of Abelian Surfaces
, École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, KU Leuven, KU LeuvenAbstract
Supersingular abelian surfaces are essential in isogeny-based cryptography. Despite this, we have no efficient algorithm to verify if a given abelian surface is supersingular. In this work, we initiate this research topic by giving an efficient Monte Carlo algorithm to verify if an abelian surface over $\mathbb{F}_p$ is supersingular in $O(\log p)$ with negligible failure probability, and an efficient conclusive algorithm if the order is smooth. We derive this algorithm by a careful analysis on the structure of supersingular Jacobians over $\mathbb{F}_p$. Furthermore, we derive efficient algorithms to verify if an abelian variety of any dimension is minimal or maximal, and to verify if a Jacobian of any dimension is superspecial.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- post-quantum cryptographyisogeniesJacobianssupersingularity
- Contact author(s)
-
maria corte_real_santos @ ens-lyon fr
gioella lorenzon @ esat kuleuven be
crypto krijn @ gmail com - History
- 2026-09-30: approved
- 2026-09-29: received
- See all versions
- Short URL
- https://ia.cr/2026/2259
- License
-
CC BY-SA
BibTeX
@misc{cryptoeprint:2026/2259,
author = {Maria Corte-Real Santos and Gioella Lorenzon and Krijn Reijnders},
title = {Supersingularity and Superspeciality Verification of Abelian Surfaces},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2259},
year = {2026},
url = {https://eprint.iacr.org/2026/2259}
}
