LAUSR

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 a novel algebraic technique for S-box construction to generate highly nonlinear $8\times 8$ S-boxes based on the action of matrices (conforming to the basis of $\mathrm {P}_{7}\left [{ \mathrm {Z}_{2} }\right]$ ) on the Galois field $\mathrm {GF}\left ({2^{8} }\right)$ . Consequently, by our proposed algorithm, we obtain $\mathrm {1.324\times }{10}^{14}$ 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.