Paper 2025/136
Computing Isomorphisms between Products of Supersingular Elliptic Curves
, Université de Lorraine, CNRS, Inria, Université de Lorraine, CNRS, InriaAbstract
The Deligne-Ogus-Shioda theorem guarantees the existence of isomorphisms between products of supersingular elliptic curves over finite fields. In this paper, we present methods for explicitly computing these isomorphisms in polynomial time, given the endomorphism rings of the curves involved. Our approach leverages the Deuring correspondence, enabling us to reformulate computational isogeny problems into algebraic problems in quaternions. Specifically, we reduce the computation of isomorphisms to solving systems of quadratic and linear equations over the integers derived from norm equations. We develop $\ell$-adic techniques for solving these equations when we have access to a low discriminant subring. Combining these results leads to the description of an efficient probabilistic Las Vegas algorithm for computing the desired isomorphisms. Under GRH, it is proved to run in expected polynomial time.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- IsogeniesSuperspecial abelian surfaces
- Contact author(s)
-
pierrick gaudry @ loria fr
julien soumier @ inria fr
pierre-jean spaenlehauer @ inria fr - History
- 2025-03-28: last of 2 revisions
- 2025-01-28: received
- See all versions
- Short URL
- https://ia.cr/2025/136
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2025/136,
author = {Pierrick Gaudry and Julien Soumier and Pierre-Jean Spaenlehauer},
title = {Computing Isomorphisms between Products of Supersingular Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/136},
year = {2025},
url = {https://eprint.iacr.org/2025/136}
}
