Annihilators and Algebraic Immunity of Symmetric Boolean Functions

概要

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In this paper, we deal with the algebraic immunity of the symmetric Boolean functions. The algebraic immunity is a property which measures the resistance against the algebraic attacks on symmetric ciphers. It is well known that the algebraic immunity of the symmetric Boolean functions is completely determined by a narrow class of annihilators with low degree which is denoted by $G(n,\\lceil\\frac{n}{2}\\rceil)$. We study and determine the weight support of part of these functions. Basing on this, we obtain some relations between the algebraic immunity of a symmetric Boolean function and its simplified value vector. For applications, we put forward an upper bound on the number of the symmetric Boolean functions with algebraic immunity at least d and prove that the algebraic immunity of the symmetric palindromic functions is not high.
（社）電子情報通信学会の論文
2011-06-01