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首页> 外文会议>International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes(AAECC-16); 20060220-24; Las Vegas, NV(US) >On Bent and Highly Nonlinear Balanced/Resilient Functions and Their Algebraic Immunities
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On Bent and Highly Nonlinear Balanced/Resilient Functions and Their Algebraic Immunities

机译：关于弯曲和高度非线性平衡/弹性函数及其代数免疫

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摘要

Since the introduction of the notions of nonlinearity in the mid-70's (the term has been in fact introduced later), of correlation immunity and resiliency in the mid-80's, and of algebraic immunity recently, the problem of efficiently constructing Boolean functions satisfying, at high levels, one or several of these criteria has received much attention. Only few primary constructions are known, and secondary constructions are also necessary to obtain functions achieving or approaching the best possible cryptographic characteristics. After recalling the background on cryptographic criteria and making some general observations, we try to give a survey of all these constructions and their properties. We then show that a nice and simple property of Boolean functions leads to a general secondary construction building an n-variable function from three known n-variable functions. This construction generalizes secondary constructions recently obtained for Boolean bent functions and also leads to secondary constructions of highly nonlinear balanced or resilient functions, with potentially better algebraic immunities than the three functions used as building blocks.
机译：自从70年代中期开始引入非线性概念（该术语实际上已在稍后介绍），80年代中期引入了相关免疫和弹性以及代数免疫以来，有效构造满足以下条件的布尔函数的问题就解决了：在较高级别上，这些标准中的一项或多项受到了广泛关注。只有很少的一级构造是已知的，并且二级构造对于获得实现或接近最佳可能的密码特性的功能也是必需的。在回顾了加密标准的背景并进行了一些一般性观察之后，我们尝试对所有这些构造及其性质进行调查。然后，我们表明布尔函数的一个好而简单的属性导致了一个一般的二级构造，该构造从三个已知的n变量函数构建一个n变量函数。这种构造概括了最近为布尔弯曲函数获得的二次构造，并且还导致了高度非线性的平衡或弹性函数的二次构造，与用作构造块的三个函数相比，具有潜在更好的代数免疫性。

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