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Öğe Affine equivalence in S-boxes(IEEE, 2006) Sakalli, M. Tolga; Bulus, Ercan; Sahin, Andac; Buyuksaracogcu, FatmaNowadays, 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.Öğe 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, FatmaRecently 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.