| With the rapid development of digital technology,digital images have become an indispensable part of people’s daily lives,profoundly affecting our lifestyle and social media habits.Image information not only contains rich content,but also reflects important information about individuals,businesses,and society.The widespread use of digital images has made their security issues increasingly important.Classic encryption methods,such as AES,DES,RSA,and SM4,can effectively protect the security of textual information.However,digital image information typically has the characteristics of high information content and strong correlation between adjacent information.Using traditional encryption methods to encrypt digital images does not yield ideal results in terms of encryption efficiency and security.In recent years,the application scope of quantum algorithms has been expanding,and some algorithms can now be directly applied to classical computing,including quantum random walks.Quantum random walks are a type of chaotic system that have the advantages of chaotic systems in image encryption,but the probability distribution matrix they generate does not have short-term periodic responses,which poses a trade-off between accuracy and confidentiality.Despite their many advantages,the probability distribution matrix generated by them does not perform well as a key matrix for image encryption in terms of statistical effect,and other encryption auxiliary technologies are needed to further optimize the key matrix and improve its statistical effect.Most machine learning algorithms have inherent non-linear characteristics,and leveraging this characteristic can effectively enhance the statistical effect of the key matrix,making it a potentially powerful encryption auxiliary technology.This paper combines quantum random walks with machine learning to propose two image encryption schemes.(1)A image encryption scheme that combines quantum random walk and Hopfield network pseudo attractors is proposed to address the encryption needs of conventional pixel images.The probability distribution matrix of quantum random walk is used as the input matrix of the Hopfield network.The pseudo attractor generated by the Hopfield network is processed through tensor operation and numerical scaling,and is used as the key matrix for image encryption.Although this scheme increases the time required to prepare the key matrix,only three rounds of pixel scrambling and confusion operations are needed to complete the encryption,as the key matrix has excellent statistical properties.The scheme is tested on a 512x512 pixel Lena image for statistical security and key sensitivity analysis,achieving an average information entropy of 7.9994,an average NPCR of 99.6218%,an average UACI of 33.5379%,and an average correlation of0.0039.The scheme is also subjected to various noise simulation tests to verify its robustness against common noise and attack interference in practical applications,and the results meet the expected ideal standards.(2)An image encryption scheme that combines quantum random walk and long short-term memory(LSTM)network is proposed to address the encryption needs of high pixel images.The probability distribution matrix of quantum random walk is used as the training matrix of LSTM,and the output gate of LSTM is used to prepare the key matrix.The efficiency of generating the key matrix is greatly improved while ensuring the encryption quality.The scheme is tested on a 2000x2000 pixel Lena image for statistical security and key sensitivity analysis,achieving an average information entropy of 7.9992,an average NPCR of99.6149%,an average UACI of 33.5234%,and an average correlation of 0.0024.When encrypting high pixel images,the scheme achieves similar indicators as the conventional pixel image encryption scheme mentioned above,while greatly improving the efficiency of generating the quantum random walk probability distribution matrix.This scheme provides a new feasible option for the encryption of high pixel images. |
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