Endomorphisms via splittings

Sabrina Kunzweiler; Min-Yi Shen

Paper 2026/215

Endomorphisms via splittings

Sabrina Kunzweiler

, Centre Inria de l'université de Bordeaux, Université de Bordeaux

Min-Yi Shen

Abstract

One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. We show that this problem is related to the problem of finding a good splitting of a principally polarized superspecial abelian surface. We provide formal security reductions, as well as a proof-of-concept implementation of an algorithm to compute endomorphisms of elliptic curves by solving the splitting problem.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Published elsewhere. PQCrypto 2026
Keywords: Isogeny-based cryptography abelian varieties security assumptions implementation
Contact author(s): sabrina kunzweiler @ math u-bordeaux fr
min yi shen0403106 @ gmail com
History: 2026-02-12: revised; 2026-02-10: received; See all versions
Short URL: https://ia.cr/2026/215
License: CC BY

BibTeX

@misc{cryptoeprint:2026/215,
      author = {Sabrina Kunzweiler and Min-Yi Shen},
      title = {Endomorphisms via splittings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/215},
      year = {2026},
      url = {https://eprint.iacr.org/2026/215}
}