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

抄録

(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 $gf_2^k$. Such class of subsets U_i are chosen to generate multisets such that all elements in $gf_2^k$ 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 Δ-uniform (m+k,m)-functions with Δ<2^k+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.