Optimum Dynamic Diffusion of Block Cipher Based on Maximum Distance Separable Matrices

Abstract

Maximum Distance Separable matrices became the state of the art as a diffusion component in block cipher design for example those MDS matrices used in algorithms such as AES and Twofish. This paper firstly reviews the relation between coding theory and cryptography in the context of providing optimal diffusion. Secondly, The Vandermonde and Cauchy based methodologies introduced by Mahdi Sajadieh et al. and J. Nakahara respectively for generating Involutory MDS matrices that are proposed to provide full block diffusion in order to decrease number of rounds of a block cipher were assessed. Finally Punctured MDS matrices are proposed to provide dynamicity of a block cipher, which guaranteed to provide optimum diffusion that should be considered in security proof against Linear and Differential Cryptanalysis of a block cipher.