Effective Linear Transformation Matrices for Block Cipher Based on Bi-regular Matrix

Abstract

Although the separation matrix with maximum distance (MDS matrix) has been widely used in the cipher and hash function, the implementation of the linear transformation based on MDS matrix in many current block ciphers is not effective because the number of occurrences of 1 in matrices is not much and the number of different elements in the matrices is quite large. In this paper, we propose a method to develop the effective MDS matrices based on the bi-regular matrix that maximizes the number of occurrences of 1 and minimizes the number of different elements in MDS matrices. By using the proposed method, we will construct the square MDS matrices 4 × 4, 8 × 8, 16 × 16 for using in the block ciphers.