Pairwise independence of AES-like block ciphers

Tim Beyne; Gregor Leander; Immo Schütt

Paper 2025/1495

Pairwise independence of AES-like block ciphers

Tim Beyne

, KU Leuven

Gregor Leander

, Ruhr University Bochum

Immo Schütt, Ruhr University Bochum

Abstract

We prove that $4r + 4$ rounds of an AES variant with independent and uniform random round keys are $\varepsilon$-close to pairwise independent with $\varepsilon = 2^{14}\, 2^{-40r}$. This result follows from a near-optimal bound for a two-norm version of pairwise independence for the Shark construction, depending on the third singular value of the difference-distribution table of the S-boxes. Our analysis combines insights from cryptanalysis — in particular, truncated differentials — and linear algebra over the reals.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published by the IACR in EUROCRYPT 2026
Keywords: Pairwise independence AES SHARK Truncated differentials
Contact author(s): tim beyne @ esat kuleuven be
gregor leander @ rub de
immo schuett @ ruhr-uni-bochum de
History: 2026-02-01: last of 4 revisions; 2025-08-19: received; See all versions
Short URL: https://ia.cr/2025/1495
License: CC BY

BibTeX

@misc{cryptoeprint:2025/1495,
      author = {Tim Beyne and Gregor Leander and Immo Schütt},
      title = {Pairwise independence of {AES}-like block ciphers},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1495},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1495}
}