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On extended algebraic immunity

机译:关于扩展代数免疫

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Algebraic immunity (AI) measures the resistance of a Boolean function f against algebraic attack. Extended algebraic immunity (EAI) extends the concept of algebraic immunity, whose point is that a Boolean function f may be replaced by another Boolean function f c called the algebraic complement of f. In this paper, we study the relation between different properties (such as weight, nonlinearity, etc.) of Boolean function f and its algebraic complement f c . For example, the relation between annihilator sets of f and f c provides a faster way to find their annihilators than previous report. Next, we present a necessary condition for Boolean functions to be of the maximum possible extended algebraic immunity. We also analyze some Boolean functions with maximum possible algebraic immunity constructed by known existing construction methods for their extended algebraic immunity.
机译:代数免疫(AI)测量布尔函数f对代数攻击的抵抗力。扩展代数免疫(EAI)扩展了代数免疫的概念,其要点是布尔函数f可以被称为f的代数补码的另一个布尔函数f c 代替。在本文中,我们研究了布尔函数f的不同属性(例如权重,非线性等)与其代数补数f c 之间的关系。例如,f和f c 的an灭者集合之间的关系提供了比以前的报告更快的找到其an灭者的方法。接下来,我们提出布尔函数具有最大可能的扩展代数免疫性的必要条件。我们还分析了一些布尔函数,这些布尔函数通过已知的现有构造方法为其扩展的代数免疫度构建了最大可能的代数免疫度。

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