Yazar "Bulus, Ercan" seçeneğine göre listele

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    Affine equivalence in S-boxes
    (IEEE, 2006) Sakalli, M. Tolga; Bulus, Ercan; Sahin, Andac; Buyuksaracogcu, Fatma
    Nowadays, Linear redundancy has been identified in all S-boxes generated from finite field inversion and power mappings. That means it may be used in a new cryptanalytic attack in the future. In our study, we have developed an application to show that all output functions of an S-box are equivalent under an affine transformation of the input bits. To realize this application, we have used 4-bit input and 4-bit output S-box which has similar design technique with AES S-box. This application shows that S-boxes generated with the same tecnique of AES S-box has a vulnerability.
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    Arithmatic of elliptic curves and use in cryptography
    (IEEE, 2006) Yerlikaya, Tarik; Bulus, Ercan; Bulus, Nusret
    In this study, first of all, we categorized encryption algorithms and exposed the structure and specifications of the symmetric and asymmetric algorithms. We explained that asymmetric encryption algorithms are based on hard problems (NP) and explained what these problems are. In addition, we showed how addition and doubling are realized on the elliptic curves and which theorems are used for that. We also showed how we can use Elliptic curves, which are very important development for asymmetric cryptosystems, in encryption process and explained how ECC algorithm using elliptic curves realize encryption and decryption process. As a result, we developed ECC application showing numerical results to compare with other asymmetric encryption algorithms in view of security
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    Classifying 8-bit to 8-bit S-boxes based on power mappings from the point of DDT and LAT distributions
    (Springer-Verlag Berlin, 2008) Aslan, Bora; Sakalli, M. Tolga; Bulus, Ercan
    S-boxes are vital elements in the design of symmetric ciphers. To date, the techniques for the construction of S-boxes have included pseudo-random generation, finite field inversion, power mappings and heuristic techniques. From these techniques, the use of finite field inversion in the construction of an S-box is so popular because it presents good cryptographic properties. On the other hand, while S-boxes such as AES, Shark, Square and Hierocrypt that are based on inversion mapping over GF(2(n)) use an affine transformation after the output of the S-box, in some ciphers like Camellia, an additional affine transformation is used before the input. In this paper, we classify 8-bit to 8-bit S-boxes based on power mappings into classes according to DDT and LAT distributions. Moreover, a formula is given for the calculation of the number of terms in the algebraic expression for a power mapping based S-box according to the given three probable cases.
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    Infrastructure of a Wireless Local Area Network: TU Mehmet Akif Ersoy Lecture Center
    (Fac Teacher Education, 2012) Gezgin, Deniz Mertkan; Bulus, Ercan
    Wireless Local Area Networks (WLAN), is a network structure which is used primarily for establishing connections between servers, printers and other endpoint devices found within smaller scale areas, such as a building or a group of buildings. These structures offer the superior advantages of shared access for applications and devices, means of file-transfer and electronic mail communication to users found within areas which include cafeterias, dormitories or miscellaneous intracampus applications. The use of WLAN applications has become increasingly common with the integration of these structures into wired networks -especially with intra-campus wired infrastructures- and of new wireless devices that support high-speed communication, thanks to the introduction of the Institute of Electrical and Electronics Engineers (IEEE) 802.11n standard. In this paper the network infrastructure of T.U. Mehmet Akif Ersoy Lecture Center -and the established WLAN structure therein- shall be discussed. Experiences and examples obtained from this application will be given along with samples from wireless security policies employed.
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    A new method to determine algebraic expression of power mapping based S-boxes
    (Elsevier, 2013) Karaahmetoglu, Osman; Sakalli, Muharrem Tolga; Bulus, Ercan; Tutanescu, Ion
    Power mapping based S-boxes, especially those with finite field inversion, have received significant attention by cryptographers. S-boxes designed by finite field inversion provide good cryptographic properties and are used in most ciphers' design such as Advanced Encryption Standard (AES), Camellia, Shark and others. However, such an S-box consists of a simple algebraic expression, thus the S-box design is completed by adding an affine transformation before the input of the S-box, or after the output of the S-box or both in order to make the overall S-box description more complex in a finite field. In the present study, a new method of computation of the algebraic expression (as a polynomial function over GF(2(8))) of power mapping based S-boxes designed by three different probable cases is described in which the place of the affine transformation differs. The proposed method is compared with the Lagrange interpolation formula with respect to the number of polynomial operations needed. The new method (based on the square-and-multiply technique) is found to reduce time and polynomial operation complexity in the computation of the algebraic expression of S-boxes. (C) 2013 Elsevier B.V. All rights reserved.
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    Obtaining algebraic expression of an S-box based on inversion mapping using finite field theory
    (IEEE, 2007) Sakalli, M. Tolga; Bulus, Ercan; Sahin, Andac; Bueyueksaracoglu, Fatma
    Recently proposed block ciphers like AES, Square, Shark use S-boxes that are based on inversion mapping over a finite field F=GF(p(n)). Because of the simple algebraic structure of S-boxes generated in this way, these ciphers usually use a bitwise affine transformation after the inversion mapping. In this study, we show how we obtain algebraic expression of an S-box based on inversion mapping using finite field theory and trace function combined with theoretical preliminaries related with this theory.
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    On the Algebraic Expression of the AES S-Box Like S-Boxes
    (Springer-Verlag Berlin, 2010) Sakalli, M. Tolga; Aslan, Bora; Bulus, Ercan; Mesut, Andac Sahin; Buyuksaracoglu, Fatma; Karaahmetoglu, Osman
    In the literature, there are several proposed block ciphers like ADS, Square, Shark and Hierocrypt which use S-boxes that are based on inversion mapping over a finite field. Because of the simple algebraic structure of S-boxes generated in this way, these ciphers usually use a bitwise affine transformation after the inversion mapping. In some ciphers like Camellia, an additional affine transformation is used before the input of the S-box as well. In this paper, we study algebraic expressions of S-boxes based on power mappings with the aid of finite field theory and show that the number of terms in the algebraic expression of an S-box based on power mappings changes according to the place an affine transformation is added. Moreover, a new method is presented to resolve the algebraic expression of the AES S-box like S-boxes according to the given three probable cases.
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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.