On 2k-Variable Symmetric Boolean Functions with Maximum Algebraic Immunity k

2011/11/09 by Wang, Hui, Peng, Jie, Li, Yuan +1
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.1111.2121

Abstract

Algebraic immunity of Boolean function f is defined as the minimal degree of a nonzero g such that fg=0 or (f+1)g=0. Given a positive even integer n, it is found that the weight distribution of any n-variable symmetric Boolean function with maximum algebraic immunity (n)/(2) is determined by the binary expansion of n. Based on the foregoing, all n-variable symmetric Boolean functions with maximum algebraic immunity are constructed. The amount is (2\wt(n)+1)2^{\lfloor log₂ n \rfloor}

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