Yazar "Rijmen, Vincent" seçeneğine göre listele

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    Efficient methods to generate cryptographically significant binary diffusion layers
    (Inst Engineering Technology-Iet, 2017) Akleylek, Sedat; Rijmen, Vincent; Sakalli, Muharrem Tolga; Ozturk, Emir
    In 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.
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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 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, Yasemin
    In 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.
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    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, Vincent
    In 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.