NEQRX: A Quantum Image Encryption and Reversible Data Hiding Scheme with Reduced Circuit Complexity

The development of image processing requires advanced cryptographic and embedding techniques to ensure data security and efficiency. However, existing approaches suffer from high quantum circuit complexity, limited scalability, and increased vulnerability to both classical and quantum threats. Therefore, we introduce NEQRX, an efficient quantum image encryption and reversible data hiding (RDH) scheme that combines the Generalized Affine Transform (GAT) and Logistic Map (LM) to enhance security and data embedding capacity while significantly reducing quantum circuit complexity and cost. We introduce a novel two-stage optimization framework that first applies the classical Espresso algorithm and then uses the ancillary qubit compression technique. This hybrid approach achieves cumulative reductions exceeding 60% in quantum cost and 64% in time complexity, significantly outperforming optimization from the Espresso algorithm alone while maintaining both security and efficiency. Comprehensive experimental evaluations on Qiskit's quantum simulators validate the practical realization of our approach. NEQRX outperforms other state-of-the-art techniques in data embedding capacity and image recovery fidelity. Furthermore, our RDH algorithm maintains high image quality and embedding capacity, outperforming other approaches in terms of peak signal-to-noise ratio (PSNR) as the embedding rate increases. Finally, the security and robustness analysis of NEQRX demonstrates its resilience against various noise models, ensuring a scalable and efficient framework that enhances the security of digital image processing.