NEQRX: Efficient Quantum Image Encryption with Reduced Circuit Complexity

Abstract: Cryptography plays an important role in ensuring data security and authentication within information processing systems. As the prevalence of digital imagery continues to grow, safeguarding this form of data becomes increasingly crucial. However, existing security protocols, reliant on complex mathematical models, exhibit vulnerabilities in effectively protecting information from both internal and external threats. Moreover, the forthcoming advent of quantum computing poses a significant challenge, as it could decrypt data encrypted by classical. In this paper, we propose an efficient implementation scheme for a quantum image encryption algorithm combining the generalized affine transform and logistic map. We evaluated developed quantum circuits using qiskit and quantum devices to validate the encryption technique. Through comprehensive performance analysis, we have demonstrated the efficiency of the chosen encryption algorithm across various criteria. Furthermore, we introduce a hybrid methodology aimed at mitigating circuit complexity and reducing quantum cost. Leveraging the Espresso algorithm and incorporating an ancilla qubit into the circuitry, we achieve a remarkable 50\% reduction in cost while maintaining security and efficiency. Finally, we conducted robustness and security analyses to assess the resilience of our encryption method against diverse noise attacks. The results confirm that our proposed quantum image encryption technique provides a secure solution and offers precise and measurable quantum image processing capabilities.