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m + k,m)-functions with good cryptographic properties when 1 ≤ k < m play an important role in several block ciphers. In this paper, based on the method introduced by Carlet et al. in 2018, we construct infinite families of (m + k,m)-functions with low differential uniformity by constructing a class of pairwise disjoint special subsets in Fk 2 . Such class of subsets Ui are chosen to generate multisets such that all elements in Fk 2 appears as many times as possible in each of these multisets. We construct explicitly such kind of special subsets by linearized polynomials, and provide differentially ∆-uniform (m + k,m)-functions with ∆ < 2k+1, k ≤ m − 2. Specifically when k = m − 2, the differential uniformity of our functions are lower than the function constructed by Carlet et al. The constructed functions provide more choices for the design of Feistel ciphers. key words: substitution boxes, Feistel structures, differential uniformity

ieice transactions on fundamentals of electronics, communications and computer sciences/ieice transactions on fundamentals of electronics, communications and computer science

A New Construction of (<i>m</i>+<i>k</i>,<i>m</i>)-Functions with Low Differential Uniformity