Low c-differential uniformity for functions modified on subfields

12/06/2021

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by   Daniele Bartoli, et al.

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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 β_i (a basis of 𝔽_q^n over 𝔽_q), some functions f_i of c-differential uniformities δ_i, and L_i (specific linearized polynomials defined in terms of β_i), 1≤ i≤ n, then F(x)=∑_i=1^nβ_i f_i(L_i(x)) has c-differential uniformity equal to ∏_i=1^n δ_i.