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arXiv · 2212.11325

Bent functions and strongly regular graphs

Valentino Smaldore
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Abstract

The family of bent functions is a known class of Boolean functions, which have a great importance in cryptography. The Cayley graph defined on $\mathbb{Z}_{2}^{n}$ by the support of a bent function is a strongly regular graph $srg(v,kλ,μ)$, with $λ=μ$. In this note we list the parameters of such Cayley graphs. Moreover, it is given a condition on $(n,m)$-bent functions $F=(f_1,\ldots,f_m)$, involving the support of their components $f_i$, and their $n$-ary symmetric differences.

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Valentino Smaldore. 2024-03-09. Bent functions and strongly regular graphs. https://arxiv.org/abs/2212.11325

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