Design techniques for maximum distance separable semi involutory matrices

Linear transformation layers are the fundamental building blocks that implement the diffusion principle in modern block cipher algorithms. Maximum Distance Separable (MDS) matrices are preferred in the design of these layers since they offer strong diffusion properties with the maximum branch number. On the other hand, linear transformation layers that are involutory, equal to their inverses, provide an advantage by allowing encryption and decryption operations to be implemented at the same cost. Semi-involutory MDS matrices, which are equal to the multiplication of an involutory matrix by a scalar c in F_(2^m) - {0,1}, offer a broader design space by enabling the inversion process to be carried out through simple matrix multiplications. In this thesis, an algebraic method is proposed that enables the construction of semi-involutory MDS matrices from involutory MDS matrices using irreducible polynomials defined over the finite fields F_(2^3) and F_(2^4). Additionally, comparative analyses with four different XOR optimization algorithms were conducted to enhance the hardware implementability of the developed matrices.