BH-Sbox: A Substitution Box Generating Algorithm Based on Chaotic Black Hole Algorithm

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.