A new matrix form to generate all 3 × 3 involutory MDS matrices over F2m
Information Processing Letters, vol.147, pp.61-68, 2019 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 147
- Publication Date: 2019
- Doi Number: 10.1016/j.ipl.2019.02.013
- Journal Name: Information Processing Letters
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.61-68
- Keywords: Cryptography, Diffusion layer, Involutory matrices, MDS matrices
- Trakya University Affiliated: Yes
Abstract
In this paper, we propose a new matrix form to generate all 3×3 involutory and MDS matrices over F2m and prove that the number of all 3×3 involutory and MDS matrices over F2m is (2m−1)2⋅(2m−2)⋅(2m−4), where m>2. Moreover, we give 3×3 involutory and MDS matrices over F23 , F24 and F28 defined by the irreducible polynomials x3+x+1, x4+x+1 and x8+x7+x6+x+1, respectively, by considering the minimum XOR count, which is a metric used in the estimation of hardware implementation cost. Finally, we provide the maximum number of 1s in 3×3 involutory MDS matrices.