On Some Algebraic Structures in the AES Round Function

In this paper, we show that all the coordinate functions of the Advanced Encryption Standard (AES) round function are equivalent under an aane transformation of the input to the round function. In other words, let fi and fj be any two distinct output coordinates of the AES round function, then there exists a nonsingular matrix Aji over GF(2) such that fj(Ajix) + bji = fi(x); bji 2 GF(2). We also show that such linear relations will always exist if the Rijndael s-box is replaced by any bijective monomial over GF(2 8).