Study on Test for Structure of S-boxes in Rijndael

This paper constructs 30 different S-boxes of Rijndael algorithm by MATLAB using 30 irreducible polynomials the maximum power of which is eight in GF(28). Then, through taking four kinds of cryptographic properties tests and fifteen kinds of cryptograph randomness tests on 30 different S-boxes, we find that the S-box which is constructed by No.22 irreducible polynomial is better than the original S-box of Rijndael algorithm.