Yazar "Sakalli, Fatma Buyuksaracoglu" seçeneğine göre listele

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    Binary Finite Field Extensions for Diffusion Matrices over the Finite Field F2m
    (IEEE, 2021) Pehlivanoglu, Meltem Kurt; Sakalli, Fatma Buyuksaracoglu; Akleylek, Sedat; Sakalli, Muharrem Tolga
    In this paper, a new software tool has been developed that computes the corresponding m x m binary matrix over the finite field F-2 of each element which is defined over F-2m (where 3 <= m <= 8) generated by different primitive irreducible polynomials. This extension process is necessary for the optimization of XOR (exclusive OR) counts of diffusion matrices whose elements are defined over the finite field, which are used especially in the diffusion layers of block ciphers. Therefore, the corresponding binary matrices given in this study can be used directly for the construction of new diffusion matrices.
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    A new hybrid method combining search and direct based construction ideas to generate all 4 x 4 involutory maximum distance separable (MDS) matrices over binary field extensions
    (Peerj Inc, 2023) Tuncay, Gokhan; Sakalli, Fatma Buyuksaracoglu; Pehlivanoglu, Meltem Kurt; Yilmazguc, Gulsum Gozde; Akleylek, Sedat; Sakalli, Muharrem Tolga
    This 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.
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    On the Construction of 20 x 20 and 24 x 24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions
    (Hindawi Ltd, 2014) Sakalli, Muharrem Tolga; Akleylek, Sedat; Aslan, Bora; Bulus, Ercan; Sakalli, Fatma Buyuksaracoglu
    We present an algebraic construction based on state transform matrix (companion matrix) for n x n (where n + 2(k), k being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for 20 x 20 and 24 x 24 binary matrices having advantages on implementation issues in lightweight block ciphers and hash functions. The powers of the companion matrix for an irreducible polynomial over GF(2) with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct 20 x 20 and 24 x 24 binary matrices, respectively. Moreover, the binary matrices are constructed to have good software and hardware implementation properties. To the best of our knowledge, this is the first study for n x n (where n not equal 2(k), k being a positive integer) binary matrices with high branch number and low number of fixed points.
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    On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form
    (IEEE-Inst Electrical Electronics Engineers Inc, 2023) Pehlivanoglu, Meltem Kurt; Sakalli, Fatma Buyuksaracoglu; Akleylek, Sedat; Sakalli, Muharrem Tolga
    Maximum Distance Separable (MDS) matrices are used as the main component of diffusion layers in block ciphers. MDS matrices have the optimal diffusion properties and the maximum branch number, which is a criterion to measure diffusion rate and security against linear and differential crypt analysis. However, it is a challenging problem to construct hardware-friendly MDS matrices with optimal or close to optimal circuits, especially for involutory ones. In this paper, we consider the generalized subfield construction method from the global optimization perspective and then give new 4 x 4 involutory MDS matrices over F-2(3) and F-2(5). After that, we present 1,176 (= 28 x 42) new 4 x 4 involutory and MDS diffusion matrices by 33 XORs and depth 3. This new record also improves the previously best-known cost of 38 XOR gates.