Selective chaotic maps Tiki-Taka algorithm for the S-box generation and optimization

• Published in: Neural computing & applications Vol. 33; no. 23; pp. 16641 - 16658
• Main Authors: Zamli, Kamal Z., Kader, Abdul, Din, Fakhrud, Alhadawi, Hussam S.
• Format: Journal Article
• Language: English
• Published: London Springer London 01.12.2021; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Chaos theory; Chebyshev approximation; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Cryptography; Data Mining and Knowledge Discovery; Encryption; Heuristic methods; Image Processing and Computer Vision; Optimization; Original Article; Probability and Statistics in Computer Science; Search process; Substitutes; Tiki-Taka algorithm; Chaotic maps; Substitution-box
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-021-06260-8

Cryptography often involves substituting (and converting) the secret information into dummy data so that it could reach the desired destination without leakage. Within symmetric key cryptography, substitution-box (S-box) is often adopted to perform the actual block cipher substitution. To address the nonlinear requirement of cryptography (i.e., ensuring the generated S-box is sufficiently robust against linear and differential cryptanalysis attacks), many chaos-based metaheuristic algorithms have been developed in the literature. This paper introduces a new variant of a metaheuristic algorithm based on Tiki-Taka algorithm, called selective chaotic maps Tiki-Taka algorithm (SCMTTA). Unlike competing works (which typically integrates a single chaotic map into a particular metaheuristic algorithm), SCMTTA assembles five chaotic maps (i.e., tent map, logistic map, Chebyshev map, singer map and sine map) as part of the algorithm itself in order to further enhance ergodicity and unpredictability of the generated solution. Based on a simple penalized and reward mechanism, one best performing chaotic map will be selected in the current cycle, while the poor performing one will miss its current turn. Experimental results on the case study related to the generation of 8 × 8 substitution-box demonstrate that the proposed SCMTTA gives competitive performance against other existing works due to its ability to adaptively modify its chaotic behavior based on the performance feedback of the current search process.