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arXiv · 2007.03996

A complete characterization of the APN property of a class of quadrinomials

Kangquan Li·Chunlei Li·Tor Helleseth·Longjiang Qu
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Abstract

In this paper, by the Hasse-Weil bound, we determine the necessary and sufficient condition on coefficients $a_1,a_2,a_3\in\mathbb{F}_{2^n}$ with $n=2m$ such that $f(x) = {x}^{3\cdot2^m} + a_1x^{2^{m+1}+1} + a_2 x^{2^m+2} + a_3x^3$ is an APN function over $\mathbb{F}_{2^n}$. Our result resolves the first half of an open problem by Carlet in International Workshop on the Arithmetic of Finite Fields, 83-107, 2014.

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Kangquan Li, Chunlei Li, Tor Helleseth, Longjiang Qu. 2020-07-08. A complete characterization of the APN property of a class of quadrinomials. https://arxiv.org/abs/2007.03996

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