International Association
for Cryptologic Research

Constructing S-boxes with low differential uniformity and high

nonlinearity is of cardinal significance in cryptography. In the

present paper, we show that numerous differentially 4-uniform

permutations over GF(2^{2k}) can be constructed by composing

the inverse function and cycles over GF(2^{2k}). Two sufficient

conditions are given, which ensure that the differential uniformity

of the corresponding compositions equals 4. A lower bound on

nonlinearity is also given for permutations constructed with the

method in the present paper. Moreover, up to CCZ-equivalence, a new

differentially 4-uniform permutation with the best known

nonlinearity over GF(2^{2k}) with $k$ odd is constructed. For

some special cycles, necessary and sufficient conditions are given

such that the corresponding compositions are differentially

4-uniform.