论文标题
在有限场上某些地图的C-差异均匀性上
On the c-differential uniformity of certain maps over finite fields
论文作者
论文摘要
我们提供了一些类别的功率图，而低$ c $ -Differential均匀性比有限特征的有限字段，{for $ c = -1 $}。此外，我们为线性化的多项式提供了必要和充分的条件，使其成为完美的$ c $ - nlininarear功能，并在通过任意的boolean或$ p $ - yar-ary功能是完美的$ c $ nonalinear的扰动时调查条件。在此过程中，我们将获得一类多项式，对于所有特征，对于所有$ c \ neq 1 $来说都是完美的$ c $ - nonilinear。还查看了仿射，扩展的仿射和CCZ等效性，因为它涉及$ c $差异均匀性。
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 $c\neq 1$, in every characteristic. The affine, extended affine and CCZ-equivalence is also looked at, as it relates to $c$-differential uniformity.
