Generating Multi-Dimensional Chaotic Sequences and Application in True Random S-Boxes Design

This paper introduces an innovative approach for generating true random multi-dimensional chaotic sequences employing physical unclonable functions (PUFs) and applies them to construct robust S-boxes. While conventional chaotic maps have found utility in random number generation, their susceptibility to issues like chaotic space discontinuity and predictable sequence numbers limits their broader application. To address these shortcomings, we present a multi-dimensional exponential chaotic map with extendable dimensions. Our empirical analysis reveals that the 3D instantiation of this map exhibits robust nonlinear dynamics, rendering it well-suited for random number generation. In constructing PUFs, we capitalize on inherent variations in physical behavior resulting from process errors and other factors in integrated circuit components, ensuring distinctiveness even when identification parameters remain identical. Leveraging the properties of chaotic maps and PUFs, we design a true random number generator that successfully passes randomness tests, showcasing exceptional randomness. Subsequently, we utilize these generated chaotic sequences to craft potent permutation boxes free from vulnerabilities like fixed points, reverse-fixed points, and short periods. These S-boxes demonstrate remarkable strength, positioning them as effective tools for enhancing existing block encryption algorithms.