Constructing and Cryptanalysis of a 16 × 16 Binary Matrix as a Diffusion Layer

Abstract

In this paper, we construct a 16 × 16 involution binary matrix of branch number 8 and estimate security of an 128-bit SPN(a substitution and permutation encrypion network) block cipher which uses the matrix as a diffusion layer in a round function. We show how to construct such an involution binary matrix of branch number 8, and use some mathematical techniques to find a form in product of matrices, which is for increasing efficiency in software implementations. We also show that the cryptanalytic properties such as the resistance to differential, linear, impossible differential, and truncated differential cryptanalysis.