Paper 2026/454 Original: eprint.iacr.org/2026/454 ↗
The principal ideal problem for endomorphism rings of superspecial abelian varieties
Abstract
We describe a Las Vegas algorithm for the principal ideal problem in matrix rings $M_g(O)$ for $g \geq 2$, over maximal orders $O$ in the rational quaternion algebra $B_{p, \infty}$ ramified at $\infty$ and a prime number $p$. Under plausible heuristic assumptions, the method has expected polynomial runtime. An implementation in SageMath shows that it runs very efficiently in practice, with compact output. Our main auxiliary result is a method for finding endomorphisms of superspecial abelian varieties (i.e., powers of supersingular elliptic curves) with a prescribed kernel.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2026-09-28: last updated
- 2026-03-04: published
- Short URL
- https://ia.cr/2026/454
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/454,
author = {Wouter Castryck and Jonathan Komada Eriksen and Riccardo Invernizzi and Frederik Vercauteren},
title = {The principal ideal problem for endomorphism rings of superspecial abelian varieties},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/454},
year = {2026},
url = {https://eprint.iacr.org/2026/454}
}