Paper 2025/1495

Pairwise independence of AES-like block ciphers

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.

@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}
}