The cryptographic properties of a class of Boolean functions with maximum algebraic immunity are investigated. Its algebraic normal form is described, its Walsh spectrum is determined and its resistance to fast algebraic attacks is observed by computer experiments. The maximum algebraic degree of this class of Boolean functions is n -1. It has always the same nonlinearity, which is the minimum nonlinearity of Boolean functions with the maximum algebraic immunity. There may not exist a suboptimal Boolean function against fast algebraic attacks in this class of Boolean functions.
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