Using search algorithm of affine equivalent S-boxes set for their quality assessment
Abstract— The article focuses on the problem of quality assessment of S-boxes by evaluating the search complexity of the set of S-boxes that are affine equivalent to the specified S-box. It is known, that S-boxes with linear and close to them coordinate functions are considered to be cryptologically weak and vice versa. That is, in good S-boxes coordinate Boolean functions must be maximum remote from linear ones. However, S-boxes possessing maximum nonlinearity are notable for the strength of their set of affine equivalence class that under other equal conditions enables to present the given S-box as a large (or less) number of S-boxes that are affine equivalent to it.
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References [1]. Alex Birykov, Christophe De Cannere, An Braeken, and Barn Prenell, “A Toolbox for Cryptanalysis: Linear and Affine Equivalent Algorithms”, EUROCRYPTO’2003. Springer, vol. 2656, pp. 33-50, 2003. [2]. O. A.Logachev, A. A. Salnikov, S. V. Smyshlyaev [and another], “Boolean functions in coding theory and cryptology”, Moscow : LENAND, pp. 576, 2015. |
Nikolay Pavlovich Borisenko
