论文标题
$ c $ - 不同的弯曲功能和完美的非线性
$C$-differential bent functions and perfect nonlinearity
论文作者
论文摘要
从Nyberg的论文〜\ Cite {Nyb91}中汲取灵感，以及我们在〜\ cite {efrst20}中定义的$ c $ -Differential概念，在本文中，我们介绍了$ c $ c $ -diftiality bent bent bent bent的概念，以两种不同的方式（从而扩展了kumar et exterdend kumar et logess）。我们进一步扩展了在〜\ cite {efrst20}中引入的完美$ c $ -nonlinear的概念，也以两种不同的方式表明，在这两种情况下，在这两种情况下，$ c $ differential弯曲的概念和完美的$ c $ -c $ - noninlineareare是等效的（在某些自然限制的参数下）。还提供了具有这些属性的功能的某些构造；其中一种构造提供了有关该领域某个子场的所有$ c $的大量PCN功能。我们还表明，我们的两个类别的$ 0 $不同的款式都是置换多项式的超集，并且Maiorana-Mcfarland弯曲函数不是差异的（第一类）。
Drawing inspiration from Nyberg's paper~\cite{Nyb91} on perfect nonlinearity and the $c$-differential notion we defined in~\cite{EFRST20}, in this paper we introduce the concept of $c$-differential bent functions in two different ways (thus extending Kumar et al.~\cite{Ku85} classical definition). We further extend the notion of perfect $c$-nonlinear introduced in~\cite{EFRST20}, also in two different ways, and show that, in both cases, the concepts of $c$-differential bent and perfect $c$-nonlinear are equivalent (under some natural restriction of the parameters). Some constructions of functions with these properties are also provided; one such construction provides a large class of PcN functions with respect to all $c$ in some subfield of the field under consideration. We also show that both our classes of $0$-differential bents are supersets of permutation polynomials, and that Maiorana-McFarland bent functions are not differential bent (of the first kind).
