Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We prove several results concerning permutation resemblance and show how it can be used to produce low differentially uniform bijections. We also study the permutation resemblance of planar functions, which over fields of odd characteristic are known not to be bijections and to have the optimal differential uniformity.

翻译：我们的动机是,以低差异统一性构建双向图的问题为动因,我们引入了功能的变异相似性概念,该概念旨在测量某一地图与变异性之间的距离。我们证明了关于变异性相似性的若干结果,并展示了如何利用它产生低差异统一的双向分布。我们还研究了平面功能的变异性相似性,在奇特特征领域,人们知道,平面的变异性不是双向的,而是最佳的差异统一性。