The performance assessments demonstrate that the proposed scheme and S-box have excellent features, and are thus capable of offering high nonlinearity in the cryptosystem. The proposed scheme is able to evolve an S-box having mean nonlinearity of 111.25, strict avalanche criteria value of 0.5007, and differential uniformity of 10. The cryptographic performance of the evolved S-box is assessed by using standard security parameters, including nonlinearity, strict avalanche criterion, bits independence criterion, differential uniformity, linear approximation probability, etc. The proposed scheme involves the evolution of initially generated S-box for improved nonlinearity based on the fractional-order time-delayed Hopfield neural network. This paper proposes to present the construction of key-dependent dynamic S-boxes having high nonlinearity. However, key-dependent dynamic substitution-boxes (S-boxes) assume to improve the security and robustness of the whole cryptosystem. Static substitution-boxes in fixed structured block ciphers may make the system vulnerable to cryptanalysis. Moreover, they are also applied for image encryption to demonstrate their suitability for multimedia security applications. The features of proposed S-boxes are compared with most of the recent S-boxes to validate the superior performance. Few of such proposed S-boxes are reported and assessed against standard performance parameters to validate the effectiveness of proposed findings. In addition, a specific group is designed the action of whose pairs of permutations has the ability to generate as many as 462422016 strong S-boxes. Firstly, a strong S-box is generated with the help of orbits of coset graphs and the action of proposed powerful permutation of symmetric group S256. With an aim to fulfill the mentioned requirement of robustness, a novel group theoretic and graphical method is proposed to construct S-box with optimal features. It is because they are solely responsible to decide the robustness of cryptosystem against linear and differential cryptanalyses. The success of AES encryption standard created challenges for the cryptographers to construct strong substitution-boxes using different underlying approaches. Keywords: Advanced encryption standard Avalanche effect Cryptography algorithm Information security S-box This is an open access article under the CC BY-SA license. Results indicate that the 16×16 S-box with a 52% AE ratio is the superior S-box. A robust and strong cryptography algorithm should be able to confirm the AEs. The AE is the main criterion used in choosing the best S-box. Subsequently, this research selects the best S-box by comparing different sizes (4×4, 8×8, and 16×16) and measuring them on the basis of the million-bit encryption. However, when information is shared between different devices in an authorized manner, the algorithm should be able to combine a sufficient number of confusion layers to guarantee the avalanche effect (AE). The S-box represents the confusion part in the AES. This research presents the S-box, one of the fundamental parts of the advanced encryption standard (AES) algorithm. Each element of the state in a S-box is nonlinearly replaced using a lookup table.

They also play a significant role in the security area because of their robustness to different linear cryptanalysis. Substitution boxes are essential nonlinear modules that are popular in block cipher algorithms.

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