A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm

Abstract

Substitution-boxes (S-boxes) are unique nonlinear elements, which are used to achieve the property of confusion in modern symmetric ciphers and offer resistance to cryptanalysis. The construction of strong S-boxes has gained considerable attention in the area of cryptography. In fact, the security of transmitted data is highly dependent on the strength of the S-boxes for the prevention of unauthorised access. Therefore, the creation of strong S-box with high nonlinearity score has been considered a significant challenge. This study presented a novel method for the designing of 8 × 8 S-boxes with selected cryptographic characteristics based on a cuckoo search (CS) algorithm and discrete-space chaotic map. Notably, the advantage of the proposed approach is indicated through the efficient randomisation and lower adjustable parameters in CS compared to GA and PSO. Also, this approach utilised a 1D discrete-space chaotic map with virtually unlimited key space to design initial S-boxes, which is another advantage over the methods based on continuous-space chaotic maps, which consist of the limited key space. Moreover, chaotic maps have a potential to overcome the trapping problem of a standard CS in the local optima, and they were used to generate initial S-boxes to achieve the desired quality and facilitate the metaheuristic search. Accordingly, the metaheuristic CS was used to find a notable S-box configuration which fulfilled the established criteria. This objective was achieved by searching for the optimal or near-optimal features which maximised the given fitness function. The performance of the proposed method was evaluated based on the established performance evaluation criteria, including bijectivity, nonlinearity, strict avalanche criteria, bit independence criteria, differential uniformity, and linear probability. Based on the results of proposed method performance was benchmarked against the results of the recently developed S-boxes, it was indicated that the S-boxes exhibited good cryptographic features and could resist various cryptanalysis attacks.