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 S 256 . 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.
The substitution box is a basic tool to convert the plaintext into an enciphered format. In this paper, we use coset diagram for the action of (2, Z) on projective line over the finite field (2 9 ) to construct proposed S-box. The vertices of the cost diagram are elements of (2 9 ) which can be represented by powers of , where is the root of irreducible polynomial ( ) = 9 + 4 + 1 over Z 2 . Let * (2 9 ) denote the elements of (2 9 ) which are of the form of even powers of . In the first step, we construct a 16 × 16 matrix with the elements of * (2 9 ) in a specific order, determined by the coset diagram. Next, we consider ℎ :2 ) = to destroy the structure of (2 8 ). In the last step, we apply a bijective map on each element of the matrix to evolve proposed S-box. The ability of the proposed S-box is examined by different available algebraic and statistical analyses. The results are then compared with the familiar S-boxes. We get encouraging statistics of the proposed box after comparison.
In this study, we presents the idea of η-intuitionistic fuzzy subgroup (IFSG) defined on ηintuitionistic fuzzy set (IFS). Furthermore, we prove that every IFSG is an η-IFSG. Also, we extend the study of this notion to define η-intuitionistic fuzzy cosets and η-intuitionistic fuzzy normal subgroups of a given group and investigate some of their fundamental algebraic features. Besides, we define the η-intuitionistic fuzzy homomorphism between two η-IFSG's and show that an η-intuitionistic fuzzy homomorphic image (inverse image) of the η-IFSG is an η-IFSG.
In this study, we propose the concept of t-intuitionistic fuzzy order of an element of a tintuitionistic fuzzy subgroup (t-IFSG) of a finite group and examine different important algebraic properties of this phenomena. We also prove many useful algebraic aspects of this notion for a cyclic group. Moreover, we extend this ideology to define t-intuitionistic fuzzy order and index of a t-IFSG of group. In addition, we establish t-intuitionistic fuzzification of Langrange's theorem. INDEX TERMS t-intuitionistic fuzzy subgroup (t-IFSG), t-intuitionistic fuzzy order of an element of t-IFSG, t-intuitionistic fuzzy order of t-IFSG, t-intuitionistic fuzzy quotient group, index of t-IFSG.
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