A Novel Cosine-Modulated-Polynomial Chaotic Map to Strengthen Image Encryption Algorithms in IoT Environments

With the widespread use of the Internet of Things (IoT), securing the storage and transmission of multimedia content across IoT devices is a critical concern. Chaos-based Pseudo-Random Number Generators (PRNGs) play an essential role in enhancing the security of image encryption algorithms. This paper introduces a novel 1-dimensional cosine-modulated-polynomial chaotic map to be used as a PRNG in image encryption algorithms. The proposed map utilizes a cosine function to modulate the outcome of a polynomial expression, resulting in complex chaotic behaviour. The designed map acts as a self-modulating system and offers a larger chaotic range, reduced structural complexity, and enhanced chaotic properties, such as aperiodicity, unpredictability, ergodicity, and sensitivity to control parameters and initial conditions, in comparison to the traditional 1-dimensional chaotic maps. An extensive evaluation is performed to gauge the chaotic behaviour of the proposed map, including bifurcation diagrams, chaotic trajectory analysis, fixed point and stability analysis, Lyapunov Exponent, Kolmogorov Entropy and NIST SP800-22 tests demonstrating its effectiveness to be used as a secure PRNG in image encryption algorithms.