Low c-differential uniformity for functions modified on subfields

Abstract

In this paper, we construct some piecewise defined functions, and study their c-differential uniformity. As a by-product, we improve upon several prior results. Further, we look at concatenations of functions with low differential uniformity and show several results. For example, we prove that given \(\beta _i\) (a basis of \(\mathbb {F}_{q^n}\) over \(\mathbb {F}_q\)), some functions \(f_i\) of c-differential uniformities \(\delta _i\), and \(L_i\) (specific linearized polynomials defined in terms of \(\beta _i\)), \(1\le i\le n\), then \(F(x)=\sum _{i=1}^n\beta _i f_i(L_i(x))\) has c-differential uniformity equal to \(\prod _{i=1}^n \delta _i\).