Efficiently deciding and recovering CCZ and EA equivalence for arbitrary vectorial Boolean functions using the partition refinement framework

Nikolay Kaleyski; Joakim Sunde

Paper 2026/940

Efficiently deciding and recovering CCZ and EA equivalence for arbitrary vectorial Boolean functions using the partition refinement framework

Nikolay Kaleyski

, University of Bergen

Joakim Sunde, University of Bergen

Abstract

We propose an algorithm based on the partition refinement framework for testing and recovering CCZ and EA equivalence between a pair of vectorial Boolean functions. In contrast to existing approaches, our method can be used for any pair of functions regardless of their algebraic degree, image size and other properties, and it outperforms all currently known algorithms in terms of time and memory. The algorithm can also compute the automorphism group of the functions efficiently. Our implementation is available at https://github.com/zskiley/CCZ-EA-equivalence

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
Keywords: CCZ-equivalence EA-equivalence Sboxes affine equivalence Classification
Contact author(s): Nikolay Kaleyski @ uib no
joakim sunde @ uib no
History: 2026-05-14: approved; 2026-05-12: received; See all versions
Short URL: https://ia.cr/2026/940
License: CC BY

BibTeX

@misc{cryptoeprint:2026/940,
      author = {Nikolay Kaleyski and Joakim Sunde},
      title = {Efficiently deciding and recovering {CCZ} and {EA} equivalence for arbitrary vectorial Boolean functions using the partition refinement framework},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/940},
      year = {2026},
      url = {https://eprint.iacr.org/2026/940}
}