This study presents a novel two-dimensional hyperchaotic map, referred to as the 2D exponent-logarithm-sine chaotic map (2D-ELSCM), which is intricately designed through the interplay of exponential, logarithmic, and sine functions. To comprehensively evaluate the chaotic performance of the 2D-ELSCM, several critical metrics are employed, including the largest Lyapunov exponent (LLE), permutation entropy (PE), sample entropy (SE), Kolmogorov entropy (KE), and the results of the 0–1 test, which yield values of 8.3175, 0.9998, 1.9826, 2.1117, and 0.9970, respectively. Furthermore, the 2D-ELSCM successfully passes the NIST randomness tests, collectively confirming its exceptional randomness and complexity. Building upon this robust chaotic map, we develop a distinctive chaotic image encryption scheme that employs an improved Knuth-Durstenfeld shuffle (IKDS) to rearrange pixel positions, effectively disrupting the correlation between adjacent pixels. Complementing this, we introduce a dynamic diffusion mechanism that integrates DNA encoding with the Zigzag transform, thereby promoting global pixel diffusion and enhancing encryption security. The initial conditions of the chaotic map are generated from the SHA-512 hash of the plaintext image in conjunction with an external key, which not only expands the key space but also significantly improves key sensitivity. Simulation results demonstrate that the proposed encryption scheme achieves correlation coefficients approaching 0 in the encrypted test images, with an average NPCR of 99.6090% and UACI of 33.4707%. These findings indicate a strong resistance to various attacks and showcase excellent encryption quality, thereby underscoring the scheme’s potential for secure image transmission and storage.

Although promising in terms of its applications in many facets of science and engineering; notably, in laser technology and remote sensing, ghost imaging is primarily impeded by its intense demands related to computational overhead, which impacts on the quality of output images. Advances in imaging and computing technologies have seen many efforts to overcome this perceived shortcoming. This study contributes towards ameliorating the earlier mentioned costs via implementation of ghost imaging from the perspective of quantum computing. Specifically, a quantum circuit implementation of ghost imaging is proposed wherein the speckle patterns and phase mask are encoded by utilizing the quantum representation of images. To accomplish this, we formulated several quantum modules, i.e. quantum accumulator, quantum multiplier, and quantum divider, and suffused them into our quantum ghost imaging (QGI) mechanism. Our study provides a new impetus to explore the implementation of ghost imaging using quantum computing resources.