Bivariate functions with low $c$-differential uniformity

Yanan Wu; Pantelimon Stănică; Chunlei Li; Nian Li; Xiangyong Zeng

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arXiv · 2212.12903

Bivariate functions with low $c$-differential uniformity

Yanan Wu·Pantelimon Stănică·Chunlei Li·Nian Li·Xiangyong Zeng

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Abstract

Starting with the multiplication of elements in $\mathbb{F}_{q}^2$ which is consistent with that over $\mathbb{F}_{q^2}$, where $q$ is a prime power, via some identification of the two environments, we investigate the $c$-differential uniformity for bivariate functions $F(x,y)=(G(x,y),H(x,y))$. By carefully choosing the functions $G(x,y)$ and $H(x,y)$, we present several constructions of bivariate functions with low $c$-differential uniformity. Many P$c$N and AP$c$N functions can be produced from our constructions.

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Yanan Wu, Pantelimon Stănică, Chunlei Li, Nian Li, Xiangyong Zeng. 2022-12-25. Bivariate functions with low $c$-differential uniformity. https://arxiv.org/abs/2212.12903

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