Construction of algebraic complex 9-bit lookup tables using non-chain-ring and its applications in data security

A substitution box (S-box) is the only nonlinear component of a symmetric key encryption cipher that directly affects an encryption scheme's performance and security level. So it is appealing to produce S-boxes with good performance and efficiency. Customarily, in algebra, Galois fields are used to generate such structures. It requires the storage memory of size 8 x 28 bits. Similarly, in GF(29) this figure reaches to 9 x 29 bits. In this study, a novel construction of lookup tables over the algebraic structure of non-chain ring R = Z8[u] of cardinality 512 is presented that holds 9 x 28 computer memory calls. Moreover, the use of non-chain ring operations in the building of lookup tables results in a more complex S-box. Afterward, we use this nonlinear layer to produce confusion in a novel image-enciphering scheme. A nonlinear encryption scheme such as a nonchain-ring S-box construction is susceptible to adversaries because of its complex connections between key ciphertexts and cryptographic primitives. With non-chain ring encryption, you can benefit from enhanced security, complexity of algorithm, resistance to modern attacks, as well as improved computing performance. Texture, algebraic, and statistical analyses were performed on the suggested S-box encryption technique. A comparison of the encryption data using the proposed S-box with the literature available S-boxes demonstrates that the suggested S-box is superior and can be employed in various ciphers. The results of the statistical, differential, and security analyses also reveal that our approach is more effective for image encryption.

Automated summary

A substitution box (S-box) is a crucial component in symmetric key encryption, and its performance and security level have a direct impact on the encryption scheme. The conventional approach to generate S-boxes involves using Galois fields. This study presents a novel construction of lookup tables using the non-chain ring structure of cardinality 512, which results in a more complex S-box. The use of non-chain ring encryption enhances security, algorithm complexity, resistance to attacks, and computational performance. The proposed S-box encryption technique is statistically, differentially, and security-wise superior to existing methods, making it more effective for image encryption.