The success of AES encryption standard created challenges for the cryptographers to construct strong substitution-boxes using different underlying approaches. It is because they are solely responsible to decide the robustness of cryptosystem against linear and differential cryptanalyses. 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. 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. 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. Few of such proposed S-boxes are reported and assessed against standard performance parameters to validate the effectiveness of proposed findings. The features of proposed S-boxes are compared with most of the recent S-boxes to validate the superior performance. Moreover, they are also applied for image encryption to demonstrate their suitability for multimedia security applications.

This paper presents a hybrid method for the construction of cryptographically strong bijective substitution-boxes by utilizing the merits of chaotic map and algebraic groups. The hybrid method first generates the key-dependent dynamic S-boxes using chaotic heuristic search strategy and then the S-boxes are evolved with the help of potent proposed algebraic group structures. This paper proposes a new improved combination chaotic map to operate initial search strategy. To augment the strength of generated S-boxes, the algebraic group structures are discovered which have the power to improve their cryptographic strength. The performance assessments using standard criterions are rendered to quantify the strengths of proposed bijective S-boxes. The experimental results and comparisons with recent S-box research findings justify the effectiveness and competence of the proposed bijective S-boxes and anticipated hybrid generation method.

This paper proposes to present a novel group theoretic approach of improvising the cryptographic features of substitution-boxes. The approach employs a proposed finite Abelian group of order 3720 with three generators and six relations. The pre and post-action of the new Abelian group on some nonlinear schemes is analyzed and investigated. It has been found that post-action is competent to construct substitution-boxes whose cryptographic strengths are quite better compared to them before the group action. The S-box strength improvisation has been perceived on multiple performance parameters including nonlinearity, differential uniformity, bits independent criteria, linear approximation probability, and auto-correlation functions along with the satisfaction of strict avalanche criteria. The suitability of proposed improved S-box is tested for image encryption applications under the majority logic criterions and differential analyses. The conducted statistical investigations demonstrated the proficiency of anticipated group action approach and its suitability for cryptographic usages.