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Genetic Approach to Improve Cryptographic Properties of Balanced Boolean Functions Using Bent Functions
(Mdpi, 2023) Ozcekic, Erol; Kavut, Selcuk; Kutucu, Hakan
Recently, balanced Boolean functions with an even number n of variables achieving very good autocorrelation properties have been obtained for 12 <= n <= 26. These functions attain the maximum absolute value in the autocorrelation spectra (without considering the zero point) less than 2 n2 and are found by using a heuristic search algorithm that is based on the design method of an infinite class of such functions for a higher number of variables. Here, we consider balanced Boolean functions that are closest to the bent functions in terms of the Hamming distance and perform a genetic algorithm efficiently aiming to optimize their cryptographic properties, which provides better absolute indicator values for all of those values of n for the first time. We also observe that among our results, the functions for 16 <= n <= 26 have nonlinearity greater than 2n 1 2 n2. In the process, our search strategy produces balanced Boolean functions with the best-known nonlinearity for 8 <= n <= 16.