A new matrix form to generate all 3 x 3 involutory MDS matrices over F-2(m)

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Guzel G. G., SAKALLI M. T., Akleylek S., Rijmen V., ÇENGELLENMİŞ Y.

INFORMATION PROCESSING LETTERS, vol.147, pp.61-68, 2019 (SCI-Expanded) identifier identifier

  • 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, MDS matrices, Diffusion layer, Involutory matrices
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we propose a new matrix form to generate all 3 x 3 involutory and MDS matrices over F-2(m) and prove that the number of all 3 x 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 x 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 x 3 involutory MDS matrices. (C) 2019 Elsevier B.V. All rights reserved.