Quantum Image Encryption Algorithms Based On Transform Theory

As a branch of quantum information field, quantum image processing has drawn great attention of research scholars. More and more methods to represent quantum images have been proposed, and the various algorithms of combining the classical image processing techniques with quantum mechanics have been widely applied to quantum image encryption. Image encryption methods based on quantum information theory have unique advantages. However, its research is still in the preliminary stage internationally, and these methods are imperfect from the perspective of information theory. The classical image encryption algorithms have slow processing speed and the security analyses of the existing quantum image encryption algorithms are insufficient. To solve these problems, the classical encryption algorithms, quantum encryption algorithms and the application of quantum image encryption techniques combining classical with quantum encryption algorithms will be researched by using the representation of quantum image. According to the cryptography and information theory, quantum transformation theory as a new tool is applied to quantum image encryption technology. Three security and effective quantum image encryption algorithms are designed based on quantum image correlation decomposition, the generalized Arnold transform, Hadamard transform and quantum image XOR operations. In addition, in order to ensure that the algorithms have classical and quantum information theory security and better performance compared with the classical image encryption system, the theoretical analyses and experimental simulations are performed. The main research results are achieved as follows:A novel quantum gray-level image encryption and decryption algorithm based on image correlation decomposition is proposed. The correlation among image pixels is established by utilizing the superposition and measurement principle of quantum states. And a whole quantum image is divided into a series of sub-images. These sub-images are stored into a complete binary tree array constructed previously and then randomly performed by one of the operations of quantum random-phase gate,quantum revolving gate and Hadamard transform. The encrypted image can be obtained by superimposing the resulting sub-images with the superposition principle of quantum states. The proposed encryption algorithm can resist brute force attack due to its very large key space and has lower computational complexity than its classical counterparts. Moreover, the encrypted image is stored and transmitted in theform of quantum states. So quantum encryption algorithm has better performance than the classical image encryption algorithm and can greatly improve the security.A quantum realization of the generalized Arnold transform is designed. A novel quantum image encryption algorithm based on generalized Arnold transform and double random-phase encoding is proposed. The pixels are scrambled by the generalized Arnold transform and the gray-level information of images is encoded by the double random phase operations. The keys of the encryption algorithm include the independent parameters of coefficients matrix, iterative times and classical binary sequences, thus the key space is extremely large. Numerical simulations and theoretical analysis demonstrate that the proposed algorithm is against to common attacks, sensitive to keys and has lower computational complexity than its classical counterparts.Quantum image XOR operations are constructed based on the novel enhanced quantum image representation, and a novel encryption scheme for quantum image based on hyper-chaotic system is proposed. The chaotic sequences are generated by Chen’s hyper-chaotic system. The quantum image XOR operations are designed by using chaotic sequences construct the control NOT operation, which are used to encode gray-level information. The initial conditions of the hyper-chaotic system have the very high sensitivity as the keys, which guarantee the security of the proposed algorithm. Numerical simulations and theoretical analysis demonstrate the feasibility, effectiveness and security of the proposed algorithm.