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Symmetric Boolean functions depending on an odd number of variables with maximum algebraic immunity

机译:对称布尔函数,取决于奇数个变量,具有最大的代数免疫力

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摘要

To resist algebraic attacks, Boolean functions should possess high algebraic immunity. In 2003, Courtois and Meier showed that the algebraic immunity of an n-variable Boolean function is upper bounded by /spl lceil/2/spl rceil/. And then several papers studied how to find symmetric Boolean functions with maximum algebraic immunity. In this correspondence, we prove that for each odd n, there is exactly one trivially balanced n-variable symmetric Boolean function achieving the maximum algebraic immunity.
机译:为了抵抗代数攻击,布尔函数应具有较高的代数免疫力。在2003年,Courtoois和Meier表明,n变量布尔函数的代数免疫上限是/ spl lceil / n / 2 / spl rceil /。然后几篇论文研究了如何找到具有最大代数免疫力的对称布尔函数。在这种对应关系中,我们证明了对于每个奇数n,只有一个微不足道的平衡n变量对称布尔函数可实现最大的代数免疫性。

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