On the Algebraic Immunity of Boolean Function

In view of the construction requirements of Boolean functions with many good cryptography properties, through the analysis of the relationship between the function values on the vectors with weight not more than d and the algebraic immunity, a method to determine the higher order algebraic immunity function is given. Meanwhile, a method that appropriate change in the function value without reducing algebraic immunity is produced, and using it, an example to construct Boolean function with optimal properties in the algebraic immunity, nonlinearity, balance and correlation immunity etc is presented.