Genetic Approach to Improve Cryptographic Properties of Balanced Boolean Functions Using Bent Functions

Abstract

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 2n2 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−1−2n2. In the process, our search strategy produces balanced Boolean functions with the best-known nonlinearity for 8≤n≤16.