Computing endomorphisms of superspecial principally polarized abelian surfaces in time and memory $p^{4/5+o(1)}$

Marc Houben; Lam L. Pham

Paper 2026/2530

Computing endomorphisms of superspecial principally polarized abelian surfaces in time and memory $p^{4/5+o(1)}$

Marc Houben

, Université Libre de Bruxelles

Lam L. Pham

, Université Libre de Bruxelles

Abstract

We present an algorithm for computing endomorphisms of superspecial principally polarized abelian surfaces over finite fields. Under a standard heuristic, we obtain a non-scalar polarized endomorphism in expected time and memory $p^{4/5 + o(1)}$.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Keywords: Isogeny-based cryptography superspecial abelian surfaces
Contact author(s): houben mr @ gmail com
lam pham @ ulb be
History: 2026-10-19: approved; 2026-10-18: received; See all versions
Short URL: https://ia.cr/2026/2530
License: CC BY

BibTeX

@misc{cryptoeprint:2026/2530,
      author = {Marc Houben and Lam L. Pham},
      title = {Computing endomorphisms of superspecial principally polarized abelian surfaces in time and memory \(p^{4/5+o(1)}\)},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/2530},
      year = {2026},
      url = {https://eprint.iacr.org/2026/2530}
}