A novel finite rings based algebraic scheme of evolving secure S-boxes for images encryption

Abstract

Substitution-boxes have significant role in block ciphers as they are the only component which offers nonlinearity in the anticipated symmetric encryption systems. This paper proposed to present a novel algebraic scheme to generate secure 8 × 8 substitution-boxes. We find the finite rings of integers with exactly 256 unit elements which are utilized to construct S-boxes. Firstly, the unit elements of the selected rings are used to create the initial random sequence of 256 elements. Secondly, the newly defined bijective polynomial maps are applied to create two initial seed S-boxes of decent cryptographic strength. Lastly, appropriate permutations of a symmetric group of degree 16 are employed to evolve two more S-boxes. The performances of the generated S-boxes are tested through the standard analyses consisting of criterions such as nonlinearity test, probability tests (linear and differential approximation), strictly avalanche criteria, and output bits independence criteria. Moreover, we examine the strength of generated S-boxes for symmetric image encryption applications through various performance measures. The simulation outcomes confirm the effectiveness of proposed scheme for secure communication.