Using Evolutionary Algorithms for the Search of 16-Variable Weight-Wise Perfectly Balanced Boolean Functions with High Non-linearity

New methods to construct adequate Boolean functions for use in cryptography have had to evolve in accordance with the requirements of continually proposed cryptosystems. Among the desired properties in Boolean functions are balancedness, high non-linearity, algebraic immunity, and resilience, all of which contribute to making the cryptosystem more resistant to various attacks. In 2016, the FLIP steam-cipher was proposed, which requires weight-wise perfectly balanced Boolean functions. As the field of cryptography evolves, so does the need for new methods of constructing Boolean functions. Our research contributes to this ongoing exploration. Evolutionary algorithms are among the explored approaches. However, much of the work has focused on 8-variable functions. In this investigation, previous work done on 8-variable functions is revisited and applied to the search for 16-variable WPB Boolean functions. The investigation yielded promising results, finding 16-variable WPB Boolean functions with high general non-linearity and weight-wise non-linearities that surpassed previous results. This marks a significant advancement in the exploration of EAs’ potential in cryptography.