Quantum Image Encryption Algorithms Based On Measured Alternate Quantum Walks And Short Memory Fractional-Order Cellular Neural Network

The image is one of the information media commonly used in the communication process and computers.To ensure the security of image information,image encryption is one of the most intuitive methods of protection.Relying on the powerful computational abilities of quantum computer,many quantum image encryption algorithms have been proposed,which mainly encrypt plaintext images into a noise-like ciphertext image.However,such image tends to attract the attention of attackers,inviting more attacks and failing to achieve visual security.In addition,some complex chaotic systems are introduced into image encryption to improve the security of the algorithm,generating pseudo-random sequences through multiple iterations of the chaotic systems,yet improving the security of the algorithm at the expense of encryption time.Based on the above two issues,two quantum image encryption algorithms are proposed,and the specific research contents are as follows:Since the probability distribution generated by alternate quantum walk may appear zero-probability at multiple positions,inspired by compressive sensing,measured alternate quantum walks（MAQW）are designed.And quantum logistic mixed linear-nonlinear coupled mapping lattice（QLMLNCML）with good dynamic characteristics is presented.A visually meaningful quantum color image encryption algorithm is proposed based on the MAQW and the QLMLNCML.The algorithm includes encryption process and embedding process.During the encryption process,the plaintext image is transformed into quantum form with quantum representation for color digital images（NCQI）.Subsequently,the quantum image is divided into two sub-blocks,on which permutation and diffusion operations are respectively implemented with the probability distribution generated by the MAQW.The pseudo-random sequences are iteratively generated by the QLMLNCML and converted into quantum key images.The two encryption sub-blocks are combined and then XORed with the quantum key images to acquire the secret image.During the embedding process,the coefficient matrices of the carrier image are obtained with the integer Haar wavelet transform（Haar IWT）,after that,the secret image is embedded into the scrambled coefficient matrices by means of the embedding technique,the visually meaningful ciphertext image is achieved by transforming the modified coefficient matrices into spatial domain with the inverse integer Haar wavelet transform（Haar IIWT）.Numerical simulations and analyses show that the algorithm has good robustness and can achieve visual security.Since fractional-order cellular neural network for image encryption consumes much encryption time,a short memory fractional-order cellular neural network（SMFr CNN）is proposed by optimizing its algorithm,which can improve the security of the algorithm and significantly save the encryption time.Quantum operators are the essential devices for designing quantum circuits,the complexity of quantum adder and quantum multiplier on the finite field F_2n are O（n）and O（n ³）,respectively,if the finite fieldF₂n contains an optimal normal basis,the complexity of quantum multiplier on the finite field F_2n can be reduced to O（n ²）.In this paper,the quantum circuit of discrete Henon map on the finite field F_2n is designed,and its complexity is O（n ³）,which can be reduced to O（n ²）provided that the finite field F_2ncontains an optimal normal basis.A fast quantum color image encryption algorithm is proposed by combining the SMFr CNN with the quantum discrete Henon map on the finite field F_2n.The plaintext image is stored as quantum state by means of the NCQI.To improve the security of the algorithm,a plaintext correlation mechanism is introduced to generate the key associated with the plaintext image.The pixel position information of the quantum image is scrambled by quantum discrete Henon map on the finite field F_2n,and the pixel color information of scrambled quantum image is diffused by three sets of pseudo-random sequences generated by the SMFr CNN.Numerical simulations and analyses show that the algorithm can achieve fast and secure encryption,and can be resistant to various attack analyses.