Grey Wolf Optimizer and Discrete Chaotic Map for Substitution Boxes Design and Optimization

Abstract

A metaheuristic approach based on the nature-inspired and well-known Grey Wolf Optimization algorithm (GWO) was employed in this study to design an approach for retrieving strong designs of $8\times 8$ substitution boxes (S-boxes). The GWO was developed as a novel metaheuristic based on inspiration from grey wolves and how they hunt. The ability of the GWO to quickly explore the search space for the near/optimal feature subsets that maximize any given fitness function (in consideration of its distinctive hierarchical structure) aids in the construction of strong S-boxes that can satisfy the required criteria. However, when tackling optimization problems, GWO may experience the problem of premature convergence. Therefore, a variant of GWO called Crossover Grey Wolf Optimizer (XGWO) has been proposed in this study. The performance of the proposed novel approach was evaluated using numerous cryptographic performance metrics, including bijective property, bit independence, strict avalanche, linear probability, and I/O XOR distribution and the result was contrasted with a couple of existing S-box creation techniques. Overall, the results of the experiment showed that the suggested S-box design had adequate cryptographic features.

Keywords

• Substitution boxes
• optimization
• nature-inspired algorithms
• Grey Wolf Optimizer
• cryptology