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The concept of differential uniformity was recently extended to the$c$-differential uniformity. An interesting problem in this area is theconstruction of functions with low $c$-differential uniformity and a lot ofresearch has been done in this direction in the recent past. Here, we presentthree classes of (almost) perfect $c$-nonlinear permutations over finite fieldsof even characteristic.

Some new classes of (almost) perfect $c$-nonlinear permutations