Yazar "Pehlivanoglu, Meltem Kurt" 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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    Generalisation of Hadamard matrix to generate involutory MDS matrices for lightweight cryptography
    (Inst Engineering Technology-Iet, 2018) Pehlivanoglu, Meltem Kurt; Sakalli, Muharrem Tolga; Akleylek, Sedat; Duru, Nevcihan; Rijmen, Vincent
    In this study, the authors generalise Hadamard matrix over F-2m and propose a new form of Hadamard matrix, which they call generalised Hadamard (GHadamard) matrix. Then, they focus on generating lightweight (involutory) maximum distance separable (MDS) matrices. They also extend this idea to any k x k matrix form, where k is not necessarily a power of 2. The new matrix form, GHadamard matrix, is used to generate new 4 x 4 involutory MDS matrices over F-24 and F-28, and 8 x 8 involutory/non- involutory MDS matrices over F-24 by considering the minimum exclusive OR (XOR) count, which is a metric defined to estimate the hardware implementation cost. In this context, they improve the best-known results of XOR counts for 8 x 8 involutory/non-involutory MDS matrices over F-24.
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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 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.
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    On the Design Strategies of Diffusion Layers and Key Schedule in Lightweight Block Ciphers
    (IEEE, 2017) Pehlivanoglu, Meltem Kurt; Akleylek, Sedat; Sakalli, M. Tolga; Duru, Nevcihan
    In recent years, lightweight cryptography has become essential especially for the resource-constrained devices to ensure data protection and security. The selection of suitable cryptographic algorithm which is directly linked to requirements of the system will have dynamically effect on following such metrics like performance of the device, hardware resource cost, the area, speed, efficiency, computation latency, communication bandwidth. This paper aims to provide a comprehensive survey on the lightweight block ciphers that were given in the literature and throw a light on the future research directions. Then, the focus is given to the diffusion layers in view of construction methods and efficiency. A new metric based on the order of the matrix to measure the security of diffusion layer consisting MDS matrix over a finite field extension is proposed and related experimental results are given. Key schedule of the lightweight block ciphers is analyzed.