Low c-differential uniformity for functions modified on subfields

2021/12/06 by Daniele Bartoli, Bartoli, Daniele, Marco Calderini +5 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Polynomial and algebraic computation #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2112.02987

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 β_i (a basis of \mathbbF_qⁿ over \mathbbF_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=1ⁿβ_i f_i(L_i(x)) has c-differential uniformity equal to ∏_i=1ⁿ δ_i.

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