Paper 2025/736
Superglue: Fast formulae for (2,2)-gluing isogenies
, École Polytechnique Fédérale de LausanneAbstract
Following Mumford's theory, theta structures on products of elliptic curves are induced by symmetries whose eigenvectors correspond to 4-torsion points on the Kummer line. These symmetries introduce a rich pattern of self-similarities within the theta structure that we exploit to enhance the computation of gluing isogenies. Focusing on the dimension-2 case, we show how theta structures can be computed projectively, thereby avoiding costly modular inversions. Moreover, by leveraging the sparsity of certain specific 4-torsion points and the action of the canonical 2-torsion points in the Kummer line, we derive new formulae for the evaluation of (2,2)-gluing isogenies. These formulae require significantly fewer precomputations and arithmetic operations than previous methods. Additionally, our formulae also support the evaluation of points on the quadratic twist at negligible additional cost, without requiring operations in an extended field.
Note: Fixed typos and added implementations
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- A minor revision of an IACR publication in ASIACRYPT 2025
- Keywords
- High-dimensional isogeniesTheta structuresGluing isogenies
- Contact author(s)
- max duparc @ epfl ch
- History
- 2025-09-16: last of 3 revisions
- 2025-04-24: received
- See all versions
- Short URL
- https://ia.cr/2025/736
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2025/736,
author = {Max Duparc},
title = {Superglue: Fast formulae for (2,2)-gluing isogenies},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/736},
year = {2025},
url = {https://eprint.iacr.org/2025/736}
}
