A design of multiple color image encryption scheme based on finite algebraic structures

This article introduces an innovative method for constructing substitution and permutation boxes and their application in image encryption. In encryption, the essential component that creates confusion is the substitution box(S-box). S-boxes can be constructed using different mathematical structures. An S-box with high nonlinearity enhances confusion in encryption. The nonlinearity of the S-box depends on its mathematical structure; the more nonlinear the structure, the higher the quality of the S-box. Quality can be measured using differential, linear, and statistical attacks. Another main component in image encryption is the permutation box(P-box), which creates confusion by scrambling the image pixels. The proposed scheme is based on the algebraic structure of the Galois field. In this scheme, we utilize the group action over an 8-bit finite field and then apply a bi-linear transformation to construct S-boxes and P-boxes. The proposed encryption scheme satisfies standard cryptographic requirements. Experimental results show that, in comparison with other well-known existing schemes, the method successfully generates many unique, uncorrelated, and secure S-boxes. A security study of the proposed scheme indicates that multiple color-encrypted images can swiftly and effectively mitigate numerous risks, rendering them suitable for real-time applications with stringent security demands.