Abstract
The \((r + 1)\)th order Gowers norm of a Boolean function is a measure of its resistance to rth order approximations. Gowers, Green, and Tao presented the connection between Gowers uniformity norm of a function and its correlation with polynomials of a certain degree. Gowers \(U_2\) and \(U_3\) norms measure the resistance of a Boolean function against linear and quadratic approximations, respectively. This paper presents computational results on the Gowers \(U_2\) and \(U_3\) norms of some known 4, 5, and 6-bit S-Boxes used in the present-day block ciphers. It is observed that there are S-Boxes having the same algebraic degree, differential uniformity, and linearity, but their Gowers norms values are different. Equivalently, they possess different strengths against linear and quadratic cryptanalysis.
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Kumar, V., Mandal, B., Gangopadhyay, A.K., Gangopadhyay, S. (2023). Computational Results on Gowers \(U_2\) and \(U_3\) Norms of Known S-Boxes. In: El Hajji, S., Mesnager, S., Souidi, E.M. (eds) Codes, Cryptology and Information Security. C2SI 2023. Lecture Notes in Computer Science, vol 13874. Springer, Cham. https://doi.org/10.1007/978-3-031-33017-9_10
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DOI: https://doi.org/10.1007/978-3-031-33017-9_10
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