Several classes of permutation polynomials and their differential uniformity properties
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The notion of c-differential uniformity has recently received a lot of popularity because of its potential applications in cryptography (we point out that a connection with difference sets in some quasigroups is already realized for perfect c-nonlinear functions, in a recent manuscript <cit.>). The construction of functions, especially permutations, with low c-differential uniformity is an interesting problem in this area, and recent work has focused heavily in this direction. We provide a few classes of permutation polynomials with low c-differential uniformity. The used technique involves handling various Weil sums, as well as analyzing some equations in finite fields, and we believe these can be of independent interest.
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