A new involutory 4×4 MDS matrix for the AES-like block ciphers

Abstract

Maximum Distance Separable (MDS) codes are used as diffusion layers in the design of the well known block ciphers like the Advanced Encryption Standard (AES) and Khazad. The reason for the use of MDS codes in the design of block ciphers is that they provide optimal diffusion effect to meet security of a round function of a block cipher. On the other hand, the constructions of these diffusion layers are various. For example, while the AES use a 4×4 MDS matrix over GF(28), Khazad use an 8×8 involutory MDS matrix over GF(28). In this study, a new involutory 4×4 MDS matrix for the AES-like block ciphers is proposed and an efficient software implementation of this matrix is given. The new involutory matrix replaces Mix Columns operation used in the AES cipher in order to provide equally good performance for both encryption and decryption operations. In the design of our involutory MDS matrix, we use Hadamard matrix construction instead of circulant matrices such as in the AES. © 2011 Praise Worthy Prize S.r.l.