Akleylek, SedatSakalli, Muharrem TolgaOzturk, EmirMesut, Andac SahinTuncay, Gokhan2024-06-122024-06-1220161939-01141939-0122https://doi.org/10.1002/sec.1561https://hdl.handle.net/20.500.14551/20499In this paper, we propose a new method to generate n x n binary matrices (for n = k . 2(t) where k and t are positive integers) with a maximum/high of branch numbers and a minimum number of fixed points by using 2(t) x 2(t) Hadamard (almost) maximum distance separable matrices and k x k cyclic binary matrix groups. By using the proposed method, we generate n x n (for n = 6, 8, 12, 16, and 32) binary matrices with a maximum of branch numbers, which are efficient in software implementations. The proposed method is also applicable with m x m circulant matrices to generate n x n (for n = k . m) binary matrices with a maximum/high of branch numbers. For this case, some examples for 16 x 16, 48 x 48, and 64 x 64 binary matrices with branch numbers of 8, 15, and 18, respectively, are presented. Copyright (C) 2016 John Wiley & Sons, Ltd.en10.1002/sec.1561info:eu-repo/semantics/openAccessDiffusion LayerBlock CiphersBranch NumberBinary MatrixMDS MatrixAlgebraic ConstructionLinear TransformationsBlock CipherMatrixArticle91635583569Q4WOS:0003892501000412-s2.0-84978114982Q2