两类具有最优代数免疫阶的奇变元布尔函数

Two classes of boolean functions with optimum algebraic immunity in odd number of variables

奇变元的对称布尔函数中达到最优代数免疫阶的有且仅有两个:f0和f0+1.在此基础上构造了两类奇变元的具有最优代数免疫阶,有较高代数次数,并且非线性度等于2n-1-〔n-1 (n-1)/2〕的平衡非对称布尔函数.

For an odd integer n≥3, f0 and f0 ＋ 1 are the only n-variable symmetric boolean functions with maximum algebraic immunity（n＋ 1）/2. This paper constructs two classes of balanced boolean functions in odd number of variables, having optimum algebraic immunity and algebraic high degree, and their nonlinearities are equal to 2^n-1-（n-1（n-1）/2）.These functions are symmetric.