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Cryptography entails the practice of designing mathematical algorithms to secure data communication over insecure networks in the presence of adversaries. In this aspect, a cryptographic algorithm encrypts the confidential data and converts it into a non-readable text for adversaries. Advanced Encryption Standard (AES) is the most effective encryption algorithm proposed till now. Substitution-box (S-box) is the most crucial and only nonlinear component in AES (or any cryptographic algorithm), which provides data confusion. A highly nonlinear S-box offers high confidentiality and security against cryptanalysis attacks; hence, the design of S-box is very crucial in any encryption algorithm. To address this challenge, we propose the action of matrices (conforming to the basis of P7 [Z2]) on the Galois field GF (28). Consequently, a novel algebraic technique for S-box construction to generate highly nonlinear 8 &#x00D7; 8 S-boxes based on by our proposed algorithm, we obtain 1.324&#x00D7;1014 different S-boxes. Standard S-box tests analyze the cryptographic strength of our proposed S-boxes. The examined results show that the proposed S-boxes possess state-of-the-art cryptographic properties. Moreover, we also demonstrate the effectiveness of the proposed S-boxes in image encryption applications using the majority logic criterion.

A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field