Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
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In this paper, we study the construction of (2t+1)-variable Boolean functions with maximum algebraic immunity, and we also analyze some other cryptographic properties of this kind of functions, such as nonlinearity, resilience. We first identify several classes of this kind of functions. Further, some necessary conditions of this kind of functions which also have higher nonlinearity are obtained. In this way, a modified construction method is proposed to possibly obtain (2t+1)-variable Boolean functions which have maximum algebraic immunity and higher nonlinearity, and a class of such functions is also obtained. Finally, we present a sufficient and necessary condition of (2t+1)-variable Boolean functions with maximum algebraic immunity which are also 1-resilient.