Low c-differential uniformity for functions modified on subfields

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 βi (a basis of Fqn over Fq), some functions fi of c-differential uniformities δi, and Li (specific linearized polynomials defined in terms of βi), 1 ≤ i≤ n, then F(x)=∑i=1nβifi(Li(x)) has c-differential uniformity equal to ∏i=1nδi.