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 Ī²_i (a basis of š½_q^n over š½_q), some functions f_i of c-differential uniformities Ī“_i, and L_i (specific linearized polynomials defined in terms of Ī²_i), 1ā¤ iā¤ n, then F(x)=ā_i=1^nĪ²_i f_i(L_i(x)) has c-differential uniformity equal to ā_i=1^n Ī“_i.
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