Tuncay, GokhanSakalli, Fatma BuyuksaracogluPehlivanoglu, Meltem KurtYilmazguc, Gulsum GozdeAkleylek, SedatSakalli, Muharrem Tolga2024-06-122024-06-1220232376-5992https://doi.org/10.7717/peerj-cs.1577https://hdl.handle.net/20.500.14551/22319This article presents a new hybrid method (combining search based methods and direct construction methods) to generate all 4 x 4 involutory maximum distance separable (MDS) matrices over F2m. The proposed method reduces the search space complexity at the level of root n, where n represents the number of all 4 x 4 invertible matrices over F-2m to be searched for. Hence, this enables us to generate all 4 x 4 involutory MDS matrices over F(2)3 and F(2)4. After applying global optimization technique that supports higher Exclusive-OR (XOR) gates (e.g., XOR3, XOR4) to the generated matrices, to the best of our knowledge, we generate the lightest involutory/ non-involutory MDS matrices known over F(2)3, F(2)4 and F(2)8 in terms of XOR count. In this context, we present new 4 x 4 involutory MDS matrices over F(2)3, F(2)4 and F(2)8, which can be implemented by 13 XOR operations with depth 5, 25 XOR operations with depth 5 and 42 XOR operations with depth 4, respectively. Finally, we denote a new property of Hadamard matrix, i.e., (involutory and MDS) Hadamard matrix form is, in fact, a representative matrix form that can be used to generate a small subset of all 2(k) x 2(k) involutory MDS matrices, where k > 1. For k = 1, Hadamard matrix form can be used to generate all involutory MDS matrices.en10.7717/peerj-cs.1577info:eu-repo/semantics/openAccessMDS MatricesInvolutory MatricesDiffusion LayerA New Hybrid MethodLightweight CryptographyArticle9N/AWOS:0011504372000012-s2.0-8517222559037810342Q2