Isogeny-based Cryptography using Isomorphisms of Superspecial Abelian Surfaces

Pierrick Gaudry; Julien Soumier; Pierre-Jean Spaenlehauer

Paper 2025/136

Isogeny-based Cryptography using Isomorphisms of Superspecial Abelian Surfaces

Pierrick Gaudry

, Université de Lorraine, CNRS, Inria

Julien Soumier, Université de Lorraine, CNRS, Inria

Pierre-Jean Spaenlehauer

, Université de Lorraine, CNRS, Inria

Abstract

We investigate the algorithmic problem of computing isomorphisms between products of supersingular elliptic curves, given their endomorphism rings. This computational problem seems to be difficult when the domain and codomain are fixed, whereas we provide efficient algorithms to compute isomorphisms when part of the codomain is built during the construction. We propose an authentication protocol whose security relies on this asymmetry. Its most prominent feature is that the endomorphism rings of the elliptic curves are not hidden. Furthermore, it does not require a trusted setup. Quickly after this preprint was published, Benjamin Wesolowski found a way to solve efficiently Problem 5.1 that we assumed to be hard. This kills our authentication protocol.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Contact author(s): pierrick gaudry @ loria fr
julien soumier @ inria fr
pierre-jean spaenlehauer @ inria fr
History: 2025-01-29: revised; 2025-01-28: received; See all versions
Short URL: https://ia.cr/2025/136
License: CC BY

BibTeX

@misc{cryptoeprint:2025/136,
      author = {Pierrick Gaudry and Julien Soumier and Pierre-Jean Spaenlehauer},
      title = {Isogeny-based Cryptography using Isomorphisms of Superspecial Abelian Surfaces},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/136},
      year = {2025},
      url = {https://eprint.iacr.org/2025/136}
}