A new matrix form to generate all 3 x 3 involutory MDS matrices over F2m

© 2019 Elsevier B.V. In this paper, we propose a new matrix form to generate all 3×3 involutory and MDS matrices over F 2 m and prove that the number of all 3×3 involutory and MDS matrices over F 2 m is (2 m −1) 2 ⋅(2 m −2)⋅(2 m −4), where m>2. Moreover, we give 3×3 involutory and MDS matrices over F 2 3 , F 2 4 and F 2 8 defined by the irreducible polynomials x 3 +x+1, x 4 +x+1 and x 8 +x 7 +x 6 +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.

Jaar van publicatie:2019

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:0.1

CSS-citation score:1

Auteurs:International

Authors from:Government, Higher Education

Toegankelijkheid:Open