排列相似性
Permutation resemblance
摘要：
受构造具有低微分一致性的双射映射的问题的启发，我们引入了函数的置换相似性的概念，它看起来度量给定映射从成为置换的距离。我们证明了几个结果置换相似性，并显示它如何可以用来产生低差分均匀双射。我们还研究了平面函数的置换相似性，这在域上的奇特征是已知的不是双射，并有最佳的微分一致性。
英文摘要：
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.
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