Analysis of the Role of Algebraic Structures in Enhancing Cryptographic Security and Encryption Techniques

The arithmetic characteristics of a finite field significantly influence the security attributes of both symmetric and asymmetric encryption systems. Contemporary symmetric-key encryption systems utilize a Galois field with 256 components derived from a singular 8th-degree primitive indeterminate polynomials over Z to construct an S-box, the primary nonlinear factor in AES. The efficacy of S-box-based picture encryption techniques is inferior to that of chaotic system-oriented solutions. This work enhances S-box-based picture encryption methods by using all 16 unique degree 8 fundamental reductive polynomials over Z and using a novel function of the ring Zn of integers times n in the permutations processes. The efficacy of this unique 2-algebraic structures-based encryption of images system is assessed by various statistical analyses, resulting in a notable efficiency level. The comparison of encrypting quality among current chaos-based picture encryption techniques demonstrates that the newly introduced scheme exhibits greater efficiency. This recent advancement in picture encryption techniques offers a replacement for chaos-based encryption of images.