A novel golden π-ratio scaling chaotification model for securing medical internet of things applications

Abstract The rapid advancement of the Medical Internet of Things (MIoT) technology has enabled remote monitoring, real-time data exchange, and personalized treatment; however, it has also introduced critical security challenges that demand efficient, robust frameworks to safeguard sensitive data. One-dimensional (1D) discrete chaotic maps provide a simple yet effective approach for securing low-end applications. However, their limited dynamics and narrow control parameter ranges significantly restrict their practical usability. The paper proposes a Golden π-Ratio Scaling Chaotification Model (GPRS-CM) that extends the control parameter range of any 1D discrete chaotic map to infinity. The model has been tested for six maps, including Cubic Logistic, Chebyshev, Cubic, Logistic, Renyi, and Sine maps. The enhanced maps have been evaluated for chaos complexity in terms of bifurcation diagram, Lyapunov exponent, time sensitivity analysis, 0–1 test, cobweb plots, approximate and sample entropies, and 2D and 3D phase plots. The results show that the enhanced maps exhibit chaotic behavior with no blank regions, persistently positive Lyapunov exponents, larger approximate and sample entropy values, near ideal 0 - 1 test indicator values, linear $$\:M-T$$ and random $$\:P-Q$$ plots, intricate cobweb plots, and 2D and 3D plots that fill the entire phase space. Additionally, a fast, operationally efficient Pseudo-Random Bit Generator (PRBG) is designed, leveraging the GPRS-CM-based enhanced chaotic maps. The PRBG demonstrates small operation count, high speed, and large throughput in addition to qualifying the fifteen NIST4statistical tests for randomness. Performance efficiency of the PRBG is compared on an ARM Cortex-M4-based LPC4357 IoT platform, with and without Floating Point Unit (FPU) usage. The FPU version outperforms the non-FPU version, showing improvements of 5.749%, 20.421%, 2.231%, and 25.438% in memory, time, power, and energy consumption, respectively. Overall, the results confirm that the proposed GPRS-CM chaotification model and the enhanced map-based PRBG offer a highly robust and resource-efficient security solution for MIoT systems.