Affine equivalence in the AES round function (Q2486749)

Several questions and concerns have been raised about the algebraic structure of the advanced encryption standard (AES). Fuller and Millan (2003) have shown that all the coordinate functions of the Rijndael \(S\)-box can be mapped to each other using an affine transformation of the input variables. The main concern of this paper is to extend their result by using the algebraic properties of the Rijndael \(S\)-box. In particular, it is shown that all the coordinate functions of the Rijndael round function (and not just the \(S\)-box) are equivalent under an affine transformation of the input to the round function.