Affine subspace and algebraic immunity

The algebraic immunity of Boolean functions is an important index to determine its ability to resist algebraic attack.To caculate the algebraic immunity of Boolean functions fastly and make algebraic attack on a cipher,the relationship between the character matrix of a Boolean function and its algebraic degree was researched to get the relationship between normality and the algebraic immunity of Boolean functions.It was suggested that n variables Boolean function satisfied that AI(f)≤min{degf,n-k} if the function was k-normal.The sufficient condition under which Boolean functions algebraic immunity was 1 and 2 was obtained.The research provides some proof to ensure that a Boolean function has annilator of low degree.