Bent Functions and Strongly Regular Graphs

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 \(srg(v,k,\lambda,\mu)\), with \(\lambda=\mu\). 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.