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arXiv · 2411.15750

A Novel Approach for Bent Functions with Dillon-like Exponents and Characterizing Three Classes of Bent Functions via Kloosterman Sums

Ziran Tu·Sihem Mesnager·Xiangyong Zeng·Nian Li·Yupeng Jiang·Yanan Deng
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Abstract

Dillon-like Boolean functions are known, in the literature, to be those trace polynomial functions from $\mathbb{F}_{2^{2n}}$ to $\mathbb{F}_{2}$, with all the exponents being multiples of $2^n-1$ often called Dillon-like exponents. This paper is devoted to bent functions in which we study the bentness of some classes of Dillon-like Boolean functions connected with rational trace functions. Specifically, we introduce a special infinite family of trace rational functions. We shall use these functions as building blocks and generalise notably a criterion due to Li et al. published in [IEEE Trans. Inf. Theory 59(3), pp. 1818-1831, 2013] on the bentness of Dillon-like functions in the binary case, we explicitly characterize three classes of bent functions. These characterizations are expressed in terms of the well-known binary Kloosterman sums. Furthermore, analysis and experiments indicate that new functions not EA-equivalent to all known classes of monomial functions are included in our classes.

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Ziran Tu, Sihem Mesnager, Xiangyong Zeng, Nian Li, Yupeng Jiang, Yanan Deng. 2024-11-24. A Novel Approach for Bent Functions with Dillon-like Exponents and Characterizing Three Classes of Bent Functions via Kloosterman Sums. https://arxiv.org/abs/2411.15750

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