Paper 2026/2259 Original: eprint.iacr.org/2026/2259 ↗
Supersingularity and Superspeciality Verification of Abelian Surfaces
Abstract
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.
- History
- 2026-09-29: last updated
- 2026-09-29: published
- Short URL
- https://ia.cr/2026/2259
- License
- https://creativecommons.org/licenses/by-sa/4.0/
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}
}