Construction of Involution Cauchy-Hadamard Type MDS Matrices

MDS matrices and involution MDS matrices are widely used in block ciphers. This paper deals with those MDS matrices which are Hadamard matrices and Cauchy matrices simultaneously. Then the structure, the method of constructing and the count value of this kind of matrices are presented. By this, a new method for constructing MDS matrices is obtained. Additionally, this paper proves that a Cauchy-Hadamard type MDS matrix can be transformed into an involution Cauchy-Hadamard type MDS, and then proposes a new method to construct an involution Cauchy-Hadamard type MDS matrix from a Cauchy-Hadamard type MDS matrix.