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The notion of $c$-differential uniformity has recently received a lot ofattention since its proposal~\cite{Ellingsen}, and recently a characterizationof perfect $c$-nonlinear functions in terms of difference sets in somequasigroups was obtained in~\cite{AMS22}. Independent of their applications asa measure for certain statistical biases, the construction of functions,especially permutations, with low $c$-differential uniformity is an interestingmathematical problem in this area, and recent work has focused heavily in thisdirection. We provide a few classes of permutation polynomials with low$c$-differential uniformity. The used technique involves handling various Weilsums, as well as analyzing some equations in finite fields, and we believethese can be of independent interest.

Differential uniformity properties of some classes of permutation polynomials