Enhanced logistic map with infinite chaos and its applicability in lightweight and high-speed pseudo-random bit generation
Mir Nazish, Munika Javid, M. Tariq Banday
Abstract
Abstract Chaotic maps are employed in cryptography and secure communications due to their unpredictable and complex dynamics. However, existing chaotic maps, specifically the one-dimensional chaotic maps, often have limited chaotic control parameter ranges, which restricts their effectiveness and applicability in practical low-end applications. This paper proposes an enhanced Logistic map with an infinite chaotic control parameter range to address these limitations. The performance of the proposed map has been comprehensively evaluated using various chaos dynamical tests, including the bifurcation diagram, Lyapunov exponent, cobweb plots, 2D and 3D phase plots, approximate entropy, and sample entropy, time sensitivity analysis, and the 0–1 test. The results demonstrate that the improved Logistic map significantly outperforms its seed map across all evaluation metrics. Additionally, the enhanced Logistic map-based pseudorandom bit generator (PRBG) has been designed and evaluated for resource efficiency and security. The findings validate that the PRBG achieves significant implementation efficiency while also successfully qualifying the fifteen NIST tests, validating its statistical randomness. Thus, the proposed map and the PRBG position themselves as lightweight, highly secure solutions for safeguarding resource-limited smart IoT applications.