On the c-differential uniformity of certain maps over finite fields

Abstract

We give some classes of power maps with low c-differential uniformity over finite fields of odd characteristic, for c= - 1. Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect c-nonlinear function and investigate conditions when perturbations of perfect c-nonlinear (or not) function via an arbitrary Boolean or p-ary function is perfect c-nonlinear. In the process, we obtain a class of polynomials that are perfect c-nonlinear for all c≠ 1 , in every characteristic. The affine, extended affine and CCZ-equivalence is also looked at, as it relates to c-differential uniformity. © 2020, This is a U.S. Government work and not under copyright protection in the US

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