Abstract: It was pointed out that a good cryptographic 13oolcan function should also be complex enough after it is changed a little. The generalized normality of Boolean functions based on this theory was introduced. The relation between the normality and generalized normality of Boolean functions, and the relation between the generalized normality and the generalized algebraic immunity were proposed. Finally, the normality and algebraic immunity of 13oolcan funclions from the point of algebraic normal form of Boolean functions were presented, which proposed a new way to analyzing the normality and algebraic immunity of Boolean functions.

Key words: Cryptographic boolcan ,functions.Algebraic immunity, Normality, Algebraic normal form