LA-ring based non-linear components: Application to image security

The prevalent utilization of symmetric block ciphers in contemporary information security systems reinforces the need for immediate action to increase their effectiveness. This task is considered crucial in the synthesis of high-quality cryptographic primitives, particularly S-boxes. In accordance with this requirement, the current article demonstrates a strategy for generating an 8 × 8 S-box drawing over an LA-ring of order 1024, which is considered a substantial class of non-associative rings. For the purpose of investigating LA-ring and their practical uses, it is essential to have illustrative examples. However, obtaining such examples using current methods is tedious and yields limited results. Therefore, this research explores an intriguing opportunity for an extensive exploration of LA-ring, far exceeding the limitations previously established and offering a valuable analytical approach for creating examples of higher-order LA-ring by drawing upon lower orders. The manuscript also performs a variety of standard evaluation tests based on five core indicators, which highlight their potential as parallels to the existing frameworks. By using the crafted S-box, an image encryption approach is launched that aims to enhance security measures. It is therefore seen that the recommended S-box has shown a high potential for causing confusion during the substitution phase, and a 3D chaotic map is implemented for the pixel permutation in order to create diffusion into the colour image. Certainly, the discovery is leading to a foundational framework among academics and is expected to serve as the basis for numerous implementations in the future.