On the Construction of Boolean Functions With Optimal Algebraic Immunity
Na Li, Longjiang Qu, Wen‐Feng Qi, GuoZhu Feng, Chao Li, DuanQiang Xie · IEEE Transactions on Information Theory · 2008
In this correspondence, we introduce a method to construct Boolean functions in any number of variables, with optimal algebraic immunity. Remarkably, all functions of this type with an odd number of variables can be obtained in this way. We study some cryptographic properties, such as balancedness, algebraic degree of the constructed functions. Moreover, a lower bound of the number of Boolean functions with optimal algebraic immunity is given.