Guzel, Gulsum GozdeSakalli, Muharrem TolgaAkleylek, SedatRijmen, VincentCengellenmis, Yasemin2024-06-122024-06-1220190020-01901872-6119https://doi.org/10.1016/j.ipl.2019.02.013https://hdl.handle.net/20.500.14551/20251In 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.en10.1016/j.ipl.2019.02.013info:eu-repo/semantics/openAccessCryptographyMDS MatricesDiffusion LayerInvolutory MatricesArticle1476168Q4WOS:0004678925000132-s2.0-85063406209Q3