A new cost function for heuristic search of nonlinear substitutions

This work investigates the development of an improved cost function specifically designed for the rapid generation of highly nonlinear substitution or S-boxes, a key component in modern symmetric key ciphers. The S-boxes are generated via a tailored hill-climbing algorithm, a heuristic search method typically employed in solving complex computational problems. The novel cost function proposed in this paper is shown to expedite this generation process, reducing the iteration count by 25% relative to the best-known prior result, which required about 65,000 iterations. Furthermore, the approach enhances the likelihood of obtaining target S-boxes, with a threefold increase in successful outcomes compared to existing methods. Our method yields S-boxes that adhere to critical cryptographic measures, such as delta-uniformity, algebraic immunity, and others. This study emphasizes the specific application of the cost function to the generation of S-boxes, noting that its effectiveness may vary in other combinatorial optimization problems.