The Industrial Internet of Things (IIoT) has revolutionized automation and data analytics across various industries. However, the exponential growth of connected devices has introduced significant security challenges that traditional cryptographic techniques fail to address. One promising solution is the use of one-dimensional (1D) discrete chaotic maps, which provide lightweight and effective security to IIoT systems. Despite their potential, these maps exhibit a limited range of chaotic control parameter ranges, limiting their effectiveness. The paper proposes a novel generic Irrational Scaling Chaotification Model (ISCM) for improving the chaotic dynamics of one-dimensional discrete chaotic maps to infinity. The model is rigorously tested across ten 1D maps, including Cubic Logistic, Chebyshev, Coupled Sine, Cubic, Logistic, Renyi, Sine, Singer, Sine-Sinh-Sine, and Tent maps. The evaluation of the enhanced chaotic maps was conducted using a range of chaos dynamical tests such as bifurcation diagrams, Lyapunov exponents, cobweb plots, time sensitivity analysis, \(0-1\) test, 2D and 3D phase plots, and approximate and sample entropies. The results show consistent chaotic regimes in the bifurcation diagram without blank regions, consistently positive Lyapunov exponents, significantly higher approximate and sample entropies, intricate and dense cobweb plots, and fully populated 2D and 3D phase trajectory plots. Moreover, the \(0-1\) test provided an indicator value close to the ideal of 1, with \(M-t\) plots showing linear trends and \(p-q\) plots demonstrating the erratic, diffusive patterns characteristic of chaotic Brownian motion. To further explore the practical application of the enhanced maps, a lightweight high-performance Pseudorandom Bit Generator (PRBG) is designed using the enhanced maps and evaluated against standard NIST security tests. Performance metrics, including throughput, execution time, and operation count, have been computed in MATLAB, with results showing a marked improvement over traditional PRBGs. Moreover, the proposed PRBG is implemented on the IIoT hardware platform, and its performance is compared in terms of memory, execution time, power consumption, and energy efficiency, both with and without the Floating-Point Unit (FPU) in use. Experimental results demonstrate a significant reduction in all key metrics, particularly when the FPU is utilized. Thus, the overall results highlight the effectiveness of the enhanced ISCM chaotic model in addressing the security and performance demands of modern IIoT systems, paving the way for more resilient and efficient cryptographic solutions in the IIoT landscape.
