Construction of Boolean functions with optimal algebraic immunity based on the maximal linear orthomorphic permutations

How to construct Boolean functions with good cryptographic characteristics is an interesting and significant problem in cryptography. Based on the maximal linear orthomorphic permutations, a method is proposed in this paper to construct a large class of Boolean functions with optimal algebraic immunity. Moreover, we demonstrate that the Boolean functions construct by Wang are contained in ours. The Boolean functions constructed in this paper can be balanced. At the end, based on the examples, we also give two conjectures on the construction of Boolean functions with optimal algebraic immunity.