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 (Formula presented.). These functions attain the maximum absolute value in the autocorrelation spectra (without considering the zero point) less than (Formula presented.) 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 (Formula presented.) have nonlinearity greater than (Formula presented.). In the process, our search strategy produces balanced Boolean functions with the best-known nonlinearity for (Formula presented.).