Quantum-inspired image encryption based on QZS, chaotic umbrella mapping and unequal modulus decomposition

This paper proposes a pioneering quantum-inspired asymmetric image encryption scheme for biometric iris images, integrating quantum state vector representation, chaotic umbrella map, the QZS algorithm and unequal modulus decomposition in the fractional Fourier transform (frFT) domain. The scheme has asymmetric and non-linear characteristics, making it more robust and key management-friendly, and provides an enlarged key space consisting of fractional order of the fractional Fourier transform, umbrella map initial conditions and control parameters, mask from unequal modulus decomposition and private keys of QZS. In the proposed scheme, the normalized iris images are first converted to state vectors, which are similar to quantum states, followed by encoding using the chaotic umbrella map, QZS algorithm, fractional Fourier transform and unequal modulus decomposition to realize robust and secure encoding of these images. Numerical simulation results show that the encryption speed is 0.3472s, the statistical performance is good (NPCR = 99.6104%, UACI = 33.3205%, entropy = 7.99545 bits), the reconstruction is perfect (MSE = 0, CC = 1), and it has strong resistance against brute force attack, noise attack, traditional transform-based attack and iterative transform-based attack. This work is novel in its first-time combination of quantum-like state-based preprocessing, QZS, chaotic umbrella mapping and unequal modulus decomposition in frFT domain, providing a great size of key space, key sensitivity and resistance to cryptanalysis, which makes it a practical and secure approach to protect biometric images.