Splittings and Endomorphism Rings

Péter Kutas; Min-Yi Shen

Paper 2026/1198

Splittings and Endomorphism Rings

Péter Kutas

, University of Birmingham, Eötvös Loránd University

Min-Yi Shen

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.
Keywords: Reductions Splitting Problems Endomorphism Problems
Contact author(s): kutasp @ gmail com
min yi shen0403106 @ gmail com
History: 2026-06-10: approved; 2026-06-08: received; See all versions
Short URL: https://ia.cr/2026/1198
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1198,
      author = {Péter Kutas and Min-Yi Shen},
      title = {Splittings and Endomorphism Rings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1198},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1198}
}