A novel exposine chaotic map for secure image encryption with applications in adaptive cruise control

— Chaotic maps in one dimension often fail to exhibit topological complexity, demonstrating insufficient statistical unpredictability, and deteriorate under finite-precision, producing limited dynamical characteristics, thereby limiting their applicability for lightweight, protected data transmission and control in cost-limited conditions. To address these limitations, we propose a novel one-dimensional Exposine Chaotic Map (ECM) that incorporates sinusoidal-driven variations, exponential reformations, and a dynamic scaling factor to broaden the chaotic band, enhance reactivity to initial conditions, and amplify overall nonlinearity. Moreover, we have also introduced a polynomial approximate version of the proposed ECM using Taylor’s and Padé approximations, retaining its chaotic properties while further refining it for utilization in hardware-resource-effective environments. The novel ECM and AECM achieve positive Lyapunov Exponent throughout parameter space, pass all NIST SP 800-22 tests, achieve high correlation dimension, equiform bifurcation, nearly zero autocorrelation, optimum level of entropy, finite-precision adaptability, and robust sensitivity by means of indeterminate, irregular cobweb dynamics. In addition, a Look-Up Table-driven realization strategy is presented to optimize real-time complexity and advance finite-precision interoperability for cost-efficient hardware deployment. Moreover, this work demonstrates the dual applicability of the proposed Exposine map and its approximation in ensuring unpredictability, secure encryption, and cost-efficient dynamic cruise control for intelligent transportation systems. In image cryptosystem, the methodology attains a typical entropy value of 7.9973, NPCR of 99.61%, UACI of 33.47%, a correlation coefficient of 0.0016, key space , asymptotic intricacy of O(n), and a throughput of 1.0417 MB/sec, with runtime of 0.06 seconds for a 256×256 image. In the cruise control implementation, the system acquires an average speed of 60.2915, an approximate entropy of 1.4751, a correlation dimension of 0.1639, a standard deviation of 0.6207, and Shannon entropy of 5.2977, confirming its deterministic chaos, adaptability, and compatibility for real-time adaptive control. • Novel Exposine map with sine–exponential modulation and nonlinear scaling proposed. • We have tuned parameters of Novel map to boost sensitivity and widen chaotic range. • Approximation of Novel Exposine map via Taylor–Padé enables low-cost hardware. • Extensive analysis confirms both maps maintain robust unpredictability traits. • Both maps demonstrated effectiveness for secure IIoT and IoMT applications.