Construction of $(n,n)$-functions with low differential-linear uniformity

Xi Xie; Nian Li; Qiang Wang; Xiangyong Zeng; Yinglong Du

doi:10.1016/j.ffa.2025.102710

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arXiv · 2508.01190

Construction of $(n,n)$-functions with low differential-linear uniformity

Xi Xie·Nian Li·Qiang Wang·Xiangyong Zeng·Yinglong Du

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Abstract

The differential-linear connectivity table (DLCT), introduced by Bar-On et al. at EUROCRYPT'19, is a novel tool that captures the dependency between the two subciphers involved in differential-linear attacks. This paper is devoted to exploring the differential-linear properties of $(n,n)$-functions. First, by refining specific exponential sums, we propose two classes of power functions over $\mathbb{F}_{2^n}$ with low differential-linear uniformity (DLU). Next, we further investigate the differential-linear properties of $(n,n)$-functions that are polynomials by utilizing power functions with known DLU. Specifically, by combining a cubic function with quadratic functions, and employing generalized cyclotomic mappings, we construct several classes of $(n,n)$-functions with low DLU, including some that achieve optimal or near-optimal DLU compared to existing results.

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Xi Xie, Nian Li, Qiang Wang, Xiangyong Zeng, Yinglong Du. 2025-08-02. Construction of $(n,n)$-functions with low differential-linear uniformity. https://doi.org/10.1016/j.ffa.2025.102710

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