Paper 2026/276 Original: eprint.iacr.org/2026/276 ↗
On the conversion of module representations for higher dimensional supersingular isogenies
Abstract
We expand the well developed toolbox between quaternionic ideals and supersingular elliptic curves into its higher dimensional version, namely (Hermitian) modules and maximal supersingular principally polarized abelian varieties. One of our main result is an efficient algorithm to compute an unpolarized isomorphism $A \simeq E_0^g$ given the abstract module representation of $A$. This algorithm relies on a subroutine that solves the Principal Ideal Problem in matrix rings over quaternion orders, combined with a higher dimensional generalisation of the Clapotis algorithm. To illustrate the flexibility of our framework, we also use it to reduce the degree of the output of the KLPT$^2$ algorithm, from $O(p^{25})$ to $O(p^{15.5})$.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2026-06-05: last updated
- 2026-02-16: published
- Short URL
- https://ia.cr/2026/276
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/276,
author = {Aurel Page and Damien Robert and Julien Soumier},
title = {On the conversion of module representations for higher dimensional supersingular isogenies},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/276},
year = {2026},
url = {https://eprint.iacr.org/2026/276}
}