Paper 2026/1198 Original: eprint.iacr.org/2026/1198 ↗
A Note on Splittings and Endomorphisms
Abstract
Finding a nontrivial endomorphism of a given supersingular elliptic curve is a hardness assumption of isogeny-based cryptography. We prove the reduction from it to the problem of finding a splitting of a given principally polarized abelian surface. By using this new reduction, we also prove the heuristic equivalence of the splitting problem with a degree restriction and the endomorphism ring problem in dimension two.
Metadata
- Available format(s)
PDF- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- History
- 2026-10-12: last updated
- 2026-06-08: published
- Short URL
- https://ia.cr/2026/1198
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/1198,
author = {Péter Kutas and Min-Yi Shen},
title = {A Note on Splittings and Endomorphisms},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1198},
year = {2026},
url = {https://eprint.iacr.org/2026/1198}
}