A New Involutory MDS Matrix for the AES

This paper proposes a new, large diffusion layer for the AES block cipher. This new layer replaces the ShiftRows and MixColumns operations by a new involutory matrix in every round. The objective is to provide complete diffusion in a single round, thus sharply improving the overall cipher security. Moreover, the new matrix elements have low Hamming-weight in order to provide equally good performance for both the encryption and decryption operations. We use the Cauchy matrix construction instead of circulant matrices such as in the AES. The reason is that circulant matrices cannot be simultaneously MDS and involutory.