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Öğe Bi-GISIS KE: Modified key exchange protocol with reusable keys for IoT security(Elsevier, 2021) Seyhan, Kubra; Tu N Nguyen; Akleylek, Sedat; Cengiz, Korhan; Islam, S. K. HafizulWe propose a new bilateral generalization inhomogeneous short integer solution (Bi-GISIS)-based key exchange protocol with reusable key feature for post-quantum IoT security. It is aimed to reduce the time consumption in the key generation of key exchange protocols to be used in IoT devices. To obtain reusable key, we define modified bilateral pasteurization in the random oracle model. By ensuring reusable keys, the same key becomes available in several executions of the proposed protocol. This feature allows efficient usage of reusable keys in resource-constrained IoT architectures. The proposed scheme is suitable for quantum secure key exchange in D2D-aided fog computing environment. A key exchange protocol with improved key management process is constructed for D2D.Öğe Binary Finite Field Extensions for Diffusion Matrices over the Finite Field F2m(IEEE, 2021) Pehlivanoglu, Meltem Kurt; Sakalli, Fatma Buyuksaracoglu; Akleylek, Sedat; Sakalli, Muharrem TolgaIn 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.Öğe Efficient methods to generate cryptographically significant binary diffusion layers(Inst Engineering Technology-Iet, 2017) Akleylek, Sedat; Rijmen, Vincent; Sakalli, Muharrem Tolga; Ozturk, EmirIn this study, the authors propose new methods using a divide-and-conquer strategy to generate n x n binary matrices ( for composite n) with a high/maximum branch number and the same Hamming weight in each row and column. They introduce new types of binary matrices: namely, (BHwC)(t,m) and (BCwC)(q,m) types, which are a combination of Hadamard and circulant matrices, and the recursive use of circulant matrices, respectively. With the help of these hybrid structures, the search space to generate a binary matrix with a high/maximum branch number is drastically reduced. By using the proposed methods, they focus on generating 12 x 12, 16 x 16 and 32 x 32 binary matrices with a maximum or maximum achievable branch number and the lowest implementation costs (to the best of their knowledge) to be used in block ciphers. Then, they discuss the implementation properties of binary matrices generated and present experimental results for binary matrices in these sizes. Finally, they apply the proposed methods to larger sizes, i.e. 48 x 48, 64 x 64 and 80 x 80 binary matrices having some applications in secure multi-party computation and fully homomorphic encryption.Öğe 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, VincentIn 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.Öğe Generating binary diffusion layers with maximum/high branch numbers and low search complexity(Wiley-Hindawi, 2016) Akleylek, Sedat; Sakalli, Muharrem Tolga; Ozturk, Emir; Mesut, Andac Sahin; Tuncay, GokhanIn 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.Öğe Lattice-based cryptosystems for the security of resource-constrained IoT devices in post-quantum world: a survey(Springer, 2022) Seyhan, Kubra; Nguyen, Tu N.; Akleylek, Sedat; Cengiz, KorhanThe concept of the Internet of Things (IoT) arises due to the change in the characteristics and numbers of smart devices. Communication of things makes it important to ensure security in this interactive architecture. One of the developments that are subject to change in IoT environments is post-quantum cryptography. This evolution, which includes the change of asymmetric cryptosystems, affects the security of IoT devices. In this paper, fundamental characteristics and layered architecture of IoT environments are examined. Basic security requirements and solution technologies for IoT architecture are remembered. Some important open problems in the literature for IoT device security are recalled. From these open problems, the post-quantum security of IoT devices with limited resources is focused. The main purpose of this paper is to improve the constrained resource classification and give a point of view for post-quantum IoT security. In this context, a sensitive classification is proposed by improving the limited resource classification of IETF. The cryptosystem efficiency definition is made for the analysis of resource-constrained device security. Using the proposed classification and efficiency definition, the usage of lattice-based cryptosystems in resource-constrained IoT device security is analyzed.Öğe 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 TolgaThis 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.Öğe A new matrix form to generate all 3 x 3 involutory MDS matrices over F2m(Elsevier Science Bv, 2019) Guzel, Gulsum Gozde; Sakalli, Muharrem Tolga; Akleylek, Sedat; Rijmen, Vincent; Cengellenmis, YaseminIn 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.Öğe On the automorphisms and isomorphisms of MDS matrices and their efficient implementations(Tubitak Scientific & Technological Research Council Turkey, 2020) Sakalli, Muharrem Tolga; Akleylek, Sedat; Akkanat, Kemal; Rijmen, VincentIn this paper, we explicitly define the automorphisms of MDS matrices over the same binary extension field. By extending this idea, we present the isomorphisms between MDS matrices over F-2m and MDS matrices over F-2mt, where t >= 1 and m > 1, which preserves the software implementation properties in view of XOR operations and table lookups of any given MDS matrix over F-2m. Then we propose a novel method to obtain distinct functions related to these automorphisms and isomorphisms to be used in generating isomorphic MDS matrices (new MDS matrices in view of implementation properties) using the existing ones. The comparison with the MDS matrices used in AES, ANUBIS, and subfield-Hadamard construction shows that we generate an involutory 4 x 4 MDS matrix over F-28 (from an involutory 4 x 4 MDS matrix over F-24) whose required number of XOR operations is the same as that of ANUBIS and the subfield-Hadamard construction, and better than that of AES. The proposed method, due to its ground field structure, is intended to be a complementary method for the current construction methods in the literature.Öğe 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 BuyuksaracogluWe 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.Öğe 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 TolgaMaximum 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.Öğe 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, NevcihanIn 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.
