Modern block ciphers are cascades of several rounds and each round consists of confusion and diffusion layers. In many block ciphers, non-linear substitution boxes (S-boxes) form the confusion layer, and a linear transformation provides the required diffusion. The diffusion layer plays an efficacious role in providing resistance against the most well-known attacks on block ciphers, such as differential cryptanalysis (DC) and linear cryptanalysis. In this thesis, first we propose a new involutory construction for diffusion layer where be replaced in the diffusion layer of the block cipher Hierocrypt to increase their performance without decrease of security. The new diffusion layer are based on the invertibility of some simple linear functions in GF(2). According to the new method, recursive diffusion layers are designed and these properties are studied. In the last, the method is proposed that makes an involutory MDS matrix from the Vandermonde matrices. Then we propose another method for the construction of 2 n × 2 n Hadamard MDS matrices in the finite field GF(2 q ). In addition to introduce this method, we present a direct method for the inversion of a special 0cm 0cm 0pt; mso-layout-grid-align: none" Key words: Block cipher, Diffusion layer, Branch number, MDS matrix.
