Abstract
Cryptography is commonly used to secure communication and data transmission over insecure networks through the use of cryptosystems. A cryptosystem is a set of cryptographic algorithms offering security facilities for maintaining more cover-ups. A substitution-box (S-box) is the lone component in a cryptosystem that gives rise to a nonlinear mapping between inputs and outputs, thus providing confusion in data. An S-box that possesses high nonlinearity and low linear and differential probability is considered cryptographically secure. In this study, a new technique is presented to construct cryptographically strong 8×8 S-boxes by applying an adjacency matrix on the Galois field GF(28). The adjacency matrix is obtained corresponding to the coset diagram for the action of modular group on a projective line PL(F7) over a finite field F7. The strength of the proposed S-boxes is examined by common S-box tests, which validate their cryptographic strength. Moreover, we use the majority logic criterion to establish an image encryption application for the proposed S-boxes. The encryption results reveal the robustness and effectiveness of the proposed S-box design in image encryption applications.
Highlights
The significance of information security is expanding with time and the areas of communication and data transformation are becoming more and more complicated
We proposed a novel and efficient technique for designing 8×8 S-boxes based on the action of modular group PSLð2; ZÞ on a projective line PL(F7) over a finite field F7
We inspect the cryptographic strength of the proposed S-boxes based on the National Institute of Standards and Technology (NIST) criteria using algebraic analyses such as nonlinearity, strict avalanche criterion, bit independent criterion, differential approximation probability, and linear approximation probability
Summary
The significance of information security is expanding with time and the areas of communication and data transformation are becoming more and more complicated. In [13], the authors proposed a new S-box based on fractional linear transformation on the Galois field GF (28), which can create confusion in the data. In [33], the authors proposed a hybrid scheme based on chaotic map and affine transformation to generate multiple S-boxes using rotational matrices. The research work in [34] utilized a chaotic map along with algebraic groups to proposed another hybrid method for generating non-linear S-boxes. We inspect the cryptographic strength of the proposed S-boxes based on the NIST criteria using algebraic analyses such as nonlinearity, strict avalanche criterion, bit independent criterion, differential approximation probability, and linear approximation probability.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
