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 PcN (or not) function via an arbitrary Boolean function is PcN. The affine, extended affine and CCZ-equivalence is also looked at, as it relates to c-differential uniformity.

中文翻译：

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关于有限域上某些映射的 c 微分均匀性

对于 c = -1，我们给出了在奇特性的有限域上具有低 c 微分均匀性的一些类别的功率图。此外，我们给出了线性化多项式成为完美 c 非线性函数的充分必要条件，并研究了通过任意布尔函数对 PcN（或非）函数的扰动为 PcN 时的条件。还考虑了仿射、扩展仿射和 CCZ 等价，因为它与 c 微分均匀性有关。