Determining the Minimum Degree of an S-box

S-boxes are important building blocks in block ciphers. For secure design one should not choose an S-box that has low degree. In this work we consider minimum degree of an S-box which is the minimum value of the degree of the nonzero component functions of the S-box. For an S-box F : F2 → F2 , there are 2m−1 nonzero component functions, we show that there is a better way to determine the minimum degree of an S-box which does not require to check all the 2m − 1 component functions. To the best of our knowledge, this is the best algorithm for determining the minimum degree of an S-box in the literature. keyword: Boolean function, S-box, degree, row echelon form, linear span.