Yazar "Karaahmetoglu, Osman" seçeneğine göre listele

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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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    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.