New differentially 4-uniform permutations from modifications of the inverse function

Abstract

Finding permutations with good cryptographic parameters is a good research topic about constructing a secure S-box in substitution-permutation networks. In particular constructing differentially 4-uniform permutations has made considerable progress in recent years. In this paper, we present new differentially 4-uniform permutations from the inverse function composed by disjoint cycles. Our new differentially 4-uniform permutations have high nonlinearity and low differential-linear uniformity. We give the differential spectrum and the extended Walsh spectrum of some of our differentially 4-uniform permutations, and then we can see that they are CCZ-inequivalent to some permutations whose differential spectrum and extended Walsh spectrum are known.