Open Access

ARTICLE

Hybrid Metaheuristic Lion and Firefly Optimization Algorithm with Chaotic Map for Substitution S-Box Design

by Arkan Kh Shakr Sabonchi^*

Department of Mathematics, Open Educational College, Kirkuk Branch, Kirkuk, 36001, Iraq

* Corresponding Author: Arkan Kh Shakr Sabonchi. Email:

Journal of Information Hiding and Privacy Protection 2024, 6, 21-45. https://doi.org/10.32604/jihpp.2024.058954

Received 25 September 2024; Accepted 11 December 2024; Issue published 31 December 2024

Abstract

Substitution boxes (S-boxes) are key components of symmetrical cryptosystems, acting as nonlinear substitution functions that hide the relationship between the encrypted text and input key. This confusion mechanism is vital for cryptographic security because it prevents attackers from intercepting the secret key by analyzing the encrypted text. Therefore, the S-box design is essential for the robustness of cryptographic systems, especially for the data encryption standard (DES) and advanced encryption standard (AES). This study focuses on the application of the firefly algorithm (FA) and metaheuristic lion optimization algorithm (LOA), thereby proposing a hybrid approach called the metaheuristic lion firefly (ML-F) algorithm. FA, inspired by the blinking behavior of fireflies, is a relatively new calculation technique that is effective for various optimization problems. However, FA often experiences early convergence, limiting the ability to determine the global optimal solution in complex search areas. To address this problem, the ML-F algorithm was developed by combining the strengths of FA and LOA. This study identifies a research gap in enhancing S-box nonlinearity and resistance to differential attacks, which the proposed ML-F aims to address. The main contributions of this paper are the enhanced cryptographic robustness of the S-boxes developed with ML-F, consistently outperforming those generated by FA and other methods regarding nonlinearity and overall cryptographic properties. The LOA, inspired by the social hunting behavior of lions, uses the collective intelligence of a pride of lions to explore and exploit the search space more effectively. The experimental analysis of this study focused on the main encryption criteria, namely, nonlinearity, the bit independence criterion (BIC), strict avalanche criterion (SAC), differential probability (DP), and maximum expected linear probability (MELP). These criteria ensure that the S-boxes provide robust security against various cryptanalytic attacks. The ML-F algorithm consistently surpassed the FA and other optimization algorithms in generating S-boxes with higher nonlinearity and better overall cryptographic properties. In case of ML-F-based S-boxes, the results indicated a better average nonlinear score and more resistance against several cryptographic attacks for quite a number of criteria. Therefore, they were considered more reliable while dealing with secured encryption. The values generated by the ML-F S-boxes are near ideal in both SAC and BIC, indicating better diffusion properties and consequently, enhanced security. The DP analysis further showed that the ML-F-generated S-boxes are highly resistant to differential attacks, which is a crucial requirement for secure encryption systems.

---

Keywords

---