Sparse Permutations with Low Differential Uniformity
Abstract
We study the functions View the $F_{s,t,\gamma}(x)=x^s+\gamma Tr(x^t)$ on $F_{2^n}$. We describe the set of such permutations and the explicit expressions of their compositional inverses. Further we consider special classes of such functions, for which we determine the size of their image set, the algebraic degree and the differential uniformity.