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

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

Information Processing Letters, cilt.147, ss.61-68, 2019 (SCI-Expanded, Scopus) 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, Diffusion layer, Involutory matrices, MDS matrices
  • Trakya Üniversitesi Adresli: Evet

Özet

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.