Abstract: As the only nonlinear structures in most block ciphers, S-boxes account for the block ciphers' secruity. A detail analysis of the cryptographic properties of teh AES S-box is made in this paper. A new simple and universal method, the Lagrange Interpolating Fundamental Polynomial is used to get the algebraic expression for teh S-box. Eight algebraic properties of S-boxes such as balanceness, strict avalanche criterion, differential uniformance, algebraic order, and so on are calculated and proved.

Key words: AES algorithm, S-boxes, differential cryptanalysis, linear cryptanalysis, multi-output Boolean function