A combinatory approach of non-chain ring and henon map for image encryption application

Algebraic structures play a vital role in securing important data. These structures are utilized to construct the non-linear components of block ciphers. Since constructing non-linear components through algebraic structures is crucial for the confusion aspects of encryption schemes, relying solely on these structures can result in limited key spaces. To address this issue, a complex non-chain ring with combination of Henon map based algorithm is presented. This proposed work aims to enhance both security and key space by utilizing complex algebraic structures. In this study, we investigate the use of unit elements from non-chain rings, establishing a mapping from the group of units to Galois fields to enhance the algebraic robustness of the scheme. A substitution box is constructed from Galois field and is applied in image processing. For pixel mixing, the Henon map is employed, and the exclusive OR operation is performed using a key generated from image pixels and the substitution box. The algorithm's performance is evaluated using standard parameters such as histograms, Structural Similarity Index Measure (SSIM), correlation analysis, and National Institute of Standards and Technology (NIST) tests. For S-box analysis, we apply the strict avalanche criterion (SAC), bit independence criterion (BIC), linear approximation probability (LAP), and differential approximation probability (DAP). This algebraic approach utilizes a robust and state-of-the-art image encryption system that is highly effective against potential attackers.