Machine learning based metaheuristic hybrids for S-box optimization

Recent research has consistently shown that the concurrence between exploration and exploitation can significantly limit the effectiveness of exploration on heuristic search. This has led to the design of hybrid algorithms that separate both task and alleviate this limitation. Many of these hybrids are based on the Leaders and Followers metaheuristic, which is specifically designed to avoid this concurrence and achieve an unbiased exploration. In this paper we adapt Leaders and Followers to a combinatorial domain in order to optimize the non-linearity and transparency order of S-boxes. Hybrid algorithms are then presented using Hill-climbing to perform exploitation. Using machine learning techniques these hybrids are further improved by automatically identifying the optimum transition point between exploration and exploitation. The solutions found are among the best S-boxes reported in literature.