Generating MDS Matrices in Toeplitz Form by Using Generalised Hadamard Form

In this paper, hardware efficient diffusion layers are generated. Non-involutory and new 8×8 MDS matrices over GF(28) with the best-known XOR counts are constructed by using a new matrix form, which is developed by circulant matrix form and the idea used in developing Generalised Hadamard (GHadamard) matrix form. Then, it is shown that the proposed matrix form is a subset of Toeplitz matrix form.