Enhancing Post-Quantum Information Security: A Novel Two-Dimensional Chaotic System for Quantum Image Encryption

Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing. To address these concerns, this paper presents the mathematical and computer modeling of a novel two-dimensional (2D) chaotic system for secure key generation in quantum image encryption (QIE). The proposed map employs trigonometric perturbations in conjunction with rational-saturation functions and hence, named as Trigonometric-Rational-Saturation (TRS) map. Through rigorous mathematical analysis and computational simulations, the map is extensively evaluated for bifurcation behaviour, chaotic trajectories, and Lyapunov exponents. The security evaluation validates the map’s non-linearity, unpredictability, and sensitive dependence on initial conditions. In addition, the proposed TRS map has further been tested by integrating it in a QIE scheme. The QIE scheme first quantum-encodes the classic image using the Novel Enhanced Quantum Representation (NEQR) technique, the TRS map is used for the generation of secure diffusion key, which is XOR-ed with the quantum-ready image to obtain the encrypted images. The security evaluation of the QIE scheme demonstrates superior security of the encrypted images in terms of statistical security attacks and also against Differential attacks. The encrypted images exhibit zero correlation and maximum entropy with demonstrating strong resilience due to 99.62% and 33.47% results for Number of Pixels Change Rate (NPCR) and Unified Average Changing Intensity (UACI). The results validate the effectiveness of TRS-based quantum encryption scheme in securing digital images against emerging quantum threats, making it suitable for secure image encryption in IoT and edge-based applications.