Paper 2026/276
On the conversion of module representations for higher dimensional supersingular isogenies
, Centre Inria de l'Université de Bordeaux, Centre Inria de l'Université de BordeauxAbstract
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.
- Keywords
- IsogenyAbelian varietiesModules
- Contact author(s)
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aurel page @ inria fr
damien robert @ inria fr
julien soumier @ inria fr - History
- 2026-02-24: last of 2 revisions
- 2026-02-16: received
- See all versions
- Short URL
- https://ia.cr/2026/276
- License
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CC BY
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}
}
