Two Classes of Symmetric Boolean Functions With Optimum Algebraic Immunity: Construction and Analysis

This paper discusses two classes of symmetric Boolean functions. For each class, a necessary and sufficient condition for having optimum algebraic immunity is proposed. The algebraic degree and nonlinearity of the Boolean functions are also completely determined. And then we prove several of Braeken's conjectures about the algebraic degree and nonlinearity of the Boolean functions with optimum algebraic immunity in the two classes.

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