Differentially $2^t$-uniform quadrinomials with high nonlinearity

Niki Spithaki; Enrico Piccione; Lilya Budaghyan; Alexander Kholosha

Paper 2026/2742

Differentially $2^t$-uniform quadrinomials with high nonlinearity

Niki Spithaki

, University of Bergen

Enrico Piccione

, Ruhr University Bochum

Lilya Budaghyan, University of Bergen

Alexander Kholosha, University of Bergen

Abstract

In this paper, we discuss some cryptographic properties of a family of quadrinomials constructed as a generalization of a known family of APN quadrinomials. In particular, we show that this family produces differentially $2^t$-uniform quadrinomials with the same Walsh spectrum as the Gold power function $x^{2^t+1}$ over $\mathbb{F}_{2^n}$. We also discuss whether this family provides permutations.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Differential uniformity Nonlinearity Walsh spectrum S-boxes Vectorial Boolean functions Permutation
Contact author(s): niki spithaki @ uib no
enrico piccione @ rub de
lilya budaghyan @ uib no
oleksandr kholosha @ uib no
History: 2026-11-05: approved; 2026-11-03: received; See all versions
Short URL: https://ia.cr/2026/2742
License: CC BY

BibTeX

@misc{cryptoeprint:2026/2742,
      author = {Niki Spithaki and Enrico Piccione and Lilya Budaghyan and Alexander Kholosha},
      title = {Differentially $2^t$-uniform quadrinomials with high nonlinearity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/2742},
      year = {2026},
      url = {https://eprint.iacr.org/2026/2742}
}