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Generalized Plateaued Functions and Admissible (Plateaued) Functions

机译：广义平稳函数和允许（平稳）函数

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摘要

Plateaued functions are very important crypto- graphic functions due to their various desirable cryptographic characteristics. We point out that plateaued functions are more general than bent functions (that is, functions with maximum nonlinearity). Some Boolean plateaued functions have large nonlinearity, which provides protection against fast correlation attacks when they are used as combiners or filters in stream ciphers, and contributes, when they are the component functions of the substitution boxes in block ciphers, to protection against linear cryptanalysis. P-ary plateaued functions have attracted recently some attention in the literature, and many activities on generalized -ary functions have been carried out. This paper increases our knowledge on plateaued functions in the general context of generalized -ary functions. We first introduce two new versions of plateaued functions, which we shall call generalized plateaued functions and admissible plateaued functions. The generalized plateaued functions extend the standard notion of plateaued -ary functions to those whose outputs are in the ring . Next, we study the generalized plateaued functions and use admissible plateaued functions to characterize the generalized plateaued functions by means of their components. Finally, we provide for the first time two constructions of generalized plateaued functions. In particular, we generalize a known secondary construction of binary generalized bent functions and derive constructions of binary generalized plateaued functions with different amplitudes.
机译：平稳功能由于其各种所需的密码特性而成为非常重要的密码功能。我们指出，平稳函数比弯曲函数（即具有最大非线性度的函数）更通用。某些布尔平稳函数具有较大的非线性，当它们用作流密码中的组合器或过滤器时，可以提供针对快速相关攻击的保护，并且当它们作为分组密码中的替换框的组成函数时，有助于防止线性密码分析。 Pary平稳函数最近在文献中引起了一些注意，并且已经进行了关于广义ary函数的许多活动。本文在广义泛函的一般上下文中增加了对平稳函数的知识。我们首先介绍两个高原函数的新版本，我们将其称为广义高原函数和可容许的高原函数。广义平稳函数将平稳二进制函数的标准概念扩展到输出在环中的那些函数。接下来，我们研究广义平稳函数，并使用可允许的平稳函数通过其组件来表征广义平稳函数。最后，我们首次提供了广义平稳函数的两种构造。特别地，我们推广了二进制广义弯曲函数的已知二次构造，并推导了具有不同幅度的二进制广义平稳函数的构造。

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