A new encoding for generating highly nonlinear eight-variables Boolean functions using multi-parent genetic algorithms

Balanced Boolean functions are a critical component in cryptographic systems, as they provide the necessary nonlinearity to resist linear attacks. Generating such functions with high nonlinearity is a challenging task, especially for functions with a large number of variables. In this work, we employ genetic algorithms to generate eight-variable Boolean functions with high nonlinearity. Unlike traditional algebraic methods, which often explore only a limited portion of the search space, genetic algorithms leverage stochastic search techniques to explore a broader and more diverse set of solutions. We introduce a novel encoding scheme for the genetic algorithm that enhances flexibility and efficiency, enabling the generation of highly nonlinear Boolean functions in a shorter time frame. This approach not only produces Boolean functions with high nonlinearity but also introduces an element of randomness, making the generated functions less predictable and more resistant to cryptographic attacks. Furthermore, the generated functions can be used to personalize cryptographic algorithms, enhancing their security and adaptability to specific use cases.