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, cilt.147, ss.61-68, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 147
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.ipl.2019.02.013
  • Dergi Adı: INFORMATION PROCESSING LETTERS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.61-68
  • Anahtar Kelimeler: Cryptography, MDS matrices, Diffusion layer, Involutory matrices
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.