Received: July 5, 2023. Revised: August 27, 2023. 249 International Journal of Intelligent Engineering and Systems, Vol.16, No.6, 2023 DOI: 10.22266/ijies2023.1231.21 BH-Sbox: A Substitution Box Generating Algorithm Based on Chaotic Black Hole Algorithm Samer Saeed Issa 1 Abdullah Hasan Ali 2 Sinan Q. Salih 3 * Faris Hasan Taha 4 1 Computer science department, Al-Rafidain University College, Baghdad, Iraq 2 Supervision & Scientific Education, Ministry of Higher Education and Scientific Research, Baghdad, Iraq 3 Technical College of Engineering, Al-Bayan University, Baghdad, Iraq 4 Department of Medical Equipment Technology Engineering, College of Engineering Technology, Al-Kitab University, Kirkuk, Iraq * Corresponding author’s Email: sinan.salih@albayan.edu.iq Abstract: This paper introduces a novel approach for generating strong substitution boxes (S-Boxes) using the black hole algorithm (BHA) integrated with Arnold chaotic map (ACM) and Henon chaotic map (HCM). The ACM is employed for enhanced initialization of the BHA, while the HCM is utilized for generating new stars during the searching process. The proposed algorithm, named BH-SBOX, aims to enhance the nonlinearity and cryptographic properties of the generated S-Boxes. Experimental evaluations further demonstrate that the BH-SBOX algorithm produces S-Boxes with excellent nonlinearity, strict avalanche criteria, bit independence criteria, differential uniformity, and the maximum expected linear probability. The proposed method demonstrated a high nonlinearity property, achieving a value of 108.25, which is considered successful and effective. This exceptional nonlinearity can be attributed to the utilization of the Henon map, which enables good exploration of the solution space during the search process. The chaotic and unpredictable nature of the Henon map contributes significantly to the algorithm's ability to discover S-Boxes with enhanced nonlinearity and robust cryptographic characteristics. The average bit independence criteria (BIC) and strict avalanche criteria (SAC) were found to be 102.85 and 0.50392, respectively. These results indicate that the proposed method successfully generated S-boxes with strong cryptographic properties, ensuring robustness and resistance against various attacks. Keywords: Cryptography, Operational researches, Optimization, S-box, Chaotic map, Black hole algorithm. 1. Introduction In the realm of modern cryptography, the protection of message confidentiality is a critical aspect, typically achieved through the use of block ciphers. One crucial component that drives the selection of block ciphers for ensuring data integrity is the substitution box (S-box). S-boxes are non- linear substitution mapping functions that provide the necessary confusion property to the corresponding block cipher [1–4]. S-boxes play a fundamental role in modern cryptographic applications. The impact of S-boxes on the security properties of cryptographic algorithms cannot be overstated. They are specifically responsible for providing the confusion property to block ciphers, and directly affecting the level of security in an encryption process. By introducing complexity and nonlinearity, S-boxes ensure that the relationship between the input and output values remains obscured, which enhances the overall security and resilience of cryptographic algorithms [5, 6]. In symmetric-key algorithms, S-boxes are primarily employed to obscure the key-output relationship, making them a crucial component in ensuring the security of the system. The task of creating S-boxes that satisfy the requirements of symmetric-key cryptography has consistently posed a significant challenge [7, 8]. The concept of confusion is integral to the design of secure cryptosystems. S-boxes, as nonlinear