关键词: 布尔函数, plateaued函数, 代数免疫, Walsh谱, 非线性度

Abstract: The plateaued function is a larger class of Boolean functions which include all partially bent functions and bent functions as a proper subset. The plateaued function has many cryptographically desirable properties. The algebraic immunity（a new criteria for evaluating the property of the Boolean function） of the plateaued function in odd variables is studied in this paper. Based on the relationship between the nonlinearity and algebraic immunity of the Boolean functions and by means of Walsh spectrum and other tools, a sufficient condition is given on which the plateaued function can not posses the optimized algebraic immunity, that is, there exists some annihilators of low degree. Moreover, an inequality is given to describe the relationship between n（the number of the variables） and the function’s degree r. According to this inequality, the upper bound of the function’s algebraic immunity can be determined.

Key words: Boolean functions, plateaued functions, algebraic immunity, Walsh spectrum, nonlinearity