A quantum classical hybrid image encryption method and system

Abstract

The present invention belongs to the field of image encryption technology, and discloses a quantum classical hybrid image encryption method based on quantum walk and chaotic mapping. The method of the present invention does not need to encode the image, nor does it need to perform quantum walk operations multiple times. On the contrary, the method of the present invention directly uses plaintext information as parameters of quantum walk, Henon map and Catmap. Therefore, even if the same initial conditions are used to encrypt multiple images, the random matrix generated by the quantum walk and the initial parameters used by the chaotic system are almost completely different, achieving an approximate "one-time one-key" effect. The method of the present invention only needs to perform one quantum walk, which improves the encryption efficiency. Numerical simulation and performance analysis show that the encryption scheme of the present invention has the following characteristics: weak correlation between adjacent pixel points, high sensitivity to small changes in plaintext images, large key space, and uniform ciphertext histogram. This shows that the scheme of the present invention can resist various noise attacks and differential attacks.

Description

Technical Field

[0001] The present invention belongs to the technical field of image encryption, and in particular relates to a quantum classical hybrid image encryption method based on quantum walk and chaotic mapping. Background Art

[0002] With the rapid development of digital photography technology, people are increasingly using digital cameras, smartphones, scanners and other devices to create and capture images. These images can be easily edited, disseminated and stored on the Internet. However, the large amount of image data disseminated and stored on the Internet also increases the risk of unauthorized access and misappropriation. Image leakage and misappropriation cause serious intellectual property infringement problems and potential losses to creators, research institutions and enterprises. In this case, people often use image encryption to protect intellectual property. The purpose of image encryption is to convert image data into an unreadable form using complex algorithms and keys to ensure security during transmission and storage. It provides intellectual property creators with an effective tool to safely share and store image data without worrying about infringement issues.

[0003] Traditional image encryption algorithms include chaos theory, DNA computing, cellular automata (CA), etc. Chaotic system is a dynamic system with complexity, high sensitivity to initial conditions and control parameters, and nonlinear characteristics. Therefore, it is widely used in the field of image encryption to improve the security and anti-attack ability of encryption algorithms.

[0004] However, with the development of quantum computing technology, the security of traditional image encryption algorithms is facing severe challenges. Therefore, in order to resist the attacks of quantum computing and ensure the security of images in the context of the quantum era, quantum image encryption technology has become an emerging technology in the field of image encryption.

[0005] Existing research on quantum image encryption technology can be roughly divided into two categories. One is to first quantize the classical image into a quantum image and then encrypt the quantum image. XHSong, et al proposed an image encryption scheme based on restricted geometry and color transformation. The encryption scheme is divided into two stages: permutation and diffusion. The permutation stage is to permute the encoding of the pixel position through restricted geometric transformation. The diffusion stage is to implement quantum diffusion operations on the permuted quantum image through restricted color transformation. The encryption keys of the two stages are generated by two chaotic maps. Li-Hua, et al proposed a quantum bit XOR encryption scheme based on chaotic sequence. The scheme uses Chen's hyper-chaotic system and Runge-Kutta method to generate quantum bit XOR sequence. A.El-Latif, et al proposed a quantum encryption scheme using Gray code and chaotic mapping. The scheme generates quantum bit XOR sequence through logical sine mapping. The main problem of these schemes is that their keys are all generated by classical mathematical algorithms. The key stream generated by classical methods has security limitations and predictability problems. Hao, et al proposed a quantum encryption scheme related to the original image. The key generated by this scheme is related to the original image. A random matrix is ​​generated through the key, and then the original image and the random matrix are bit-XORed and then bit-cyclically shifted. The advantage of this type of scheme is that it can improve the image processing speed. The disadvantage is that a certain number of quantum bits are required to represent the image. For example, if a grayscale image with a grayscale value of is is encoded into a quantum state, quantum bits are required. However, under current technical conditions, the more quantum bits are required for encryption, the greater the cost and difficulty of implementation.

[0006] Another type of quantum image encryption technology is to use the randomness of quantum technology to directly encrypt classical images. Zhao, et al proposed an image encryption scheme based on quantum walk and controlled Rubik's Cube. The scheme first randomly maps each pixel of the image to the Rubik's Cube, then determines the rotation operation of the Rubik's Cube through the random sequence generated by quantum walk, and finally performs bit XOR operation on the Rubik's Cube. Abd EL-Latif, et al proposed an image encryption scheme that uses quantum walk to permute and arrange. The scheme uses two quantum walks to generate substitution matrix and permutation matrix. First, the substitution matrix and the original image are bit XORed, and then the pixel position is disturbed by the permutation matrix. Liu, et al proposed an image encryption scheme that combines quantum walk technology with AES encryption technology. The scheme replaces some components in the AES encryption scheme with the probability matrix of quantum walk to improve the security of the traditional AES encryption scheme. Ma, el al proposed an encryption scheme based on quantum walk and discrete cosine transform. The scheme generates multiple probability distribution matrices through multiple quantum walks, and these probability matrices are used to replace the random phase mask in the traditional double random phase encoding. In the spatial domain, XOR operation is used to encrypt the input image. In the discrete cosine transform domain, random phase mask is used to complete image encryption. Abd el-Latif, et al. proposed an encryption scheme of cascade quantum walk logical mapping. The scheme cascades the random sequence generated by quantum walk and the random sequence generated by logical mapping to obtain S-boxes and random numbers with higher security. Abd-El-Atty, et al. proposed a dual image encryption scheme based on quantum walk. The scheme performs a hash operation on the original image to divide the image into two parts. Then the probability matrix generated by quantum walk is used to encrypt the first part of the image, and the second part of the image is encrypted by logical mapping. The above scheme has a problem of fixed encryption parameters, which means that when encrypting multiple batches of pictures, if the encryption parameters are not changed, then these batches of pictures will be encrypted with the same key. This situation leads to problems such as reduced security, data association and inadaptability to dynamic environments. Liu, et al. proposed a 3D rectangular encryption scheme using quantum walk. The scheme first divides the original image into blocks and integrates them into a cuboid, and then performs a hash operation to obtain the quantum walk parameters. The original image is encrypted using the probability matrix and quantum hash sequence generated by quantum walk. Zhang, et al proposed an image encryption scheme using quantum walk and controlled zigzag transformation. The scheme performs SHA-256 on the original image to obtain the parameters of quantum walk, and obtains the probability matrix of quantum distribution through multiple walk measurements; then, a controlled zigzag transformation is performed on the original image. Finally, the probability matrix is ​​bit-XORed with the transformed image.The above scheme uses multiple quantum walks to generate multiple probability matrices, but due to the large overhead of quantum walks, the efficiency of the scheme is not high. Abd-El-Atty, et al proposed an image encryption scheme using quantum walks and Henon maps. The scheme first encodes and accumulates the original image using Gray code to obtain the parameters of the quantum walk. Next, the image is encrypted using the probability matrix and Henon map generated by the quantum walk. However, this scheme does not take into account that Gray code encoding will increase the complexity and computational cost of image processing. In addition, the generated key still has security limitations and predictability issues.

[0007] Through the above analysis, the problems and defects of the prior art are as follows:

[0008] The existing technology uses multiple quantum walks to generate multiple probability matrices, but due to the large overhead of quantum walks, the efficiency of the solution is not high. Summary of the invention

[0009] In view of the problems existing in the prior art, the present invention provides a quantum classical hybrid image encryption method based on quantum walk and chaos mapping.

[0010] The present invention is implemented in this way: a quantum classical hybrid image encryption method based on quantum walk and chaos mapping includes:

[0011] S1: Receive the image to be encrypted; calculate the pixel ratios q1, q2, q3 of the three channels of the image to be encrypted;

[0012] S2: Execute the quantum walk module with initial parameters (s, N, q, q1, q2) to obtain a probability matrix P N′N ; Then enlarge the probability matrix to the same size as the image to be encrypted L′W′C ;

[0013] S3: The encrypted image O1 and the matrix RP L′W′C Perform bit XOR operation to obtain the intermediate ciphertext C1;

[0014] S4: Execute the Henon map module with parameters (a, b, q3) on the intermediate ciphertext C1 to obtain the intermediate ciphertext C2;

[0015] S5: Execute a cyclic shift module with parameters (q1, q2, q3) on the intermediate ciphertext C2 to obtain the intermediate ciphertext C3;

[0016] S6: Execute the Arnold Cat map module with parameters (q1, q2, q3) on the intermediate ciphertext C3 to obtain the final ciphertext C;

[0017] S7: Evaluate the encryption capability of the algorithm through evaluation indicators.

[0018] The present invention also provides a quantum classical hybrid image encryption system based on quantum walk and chaotic mapping, including: a quantum walk module, a Henon map module, a cyclic shift module, and an Arnold Cat map module.

[0019] Furthermore, the quantum walk module is used to perform a quantum walk operation with parameters (s, N, q, q1, q2) according to the initial parameters of the algorithm to obtain a probability matrix P N′N ; According to the size of the image to be encrypted, the probability matrix P N′N Enlarge the matrix RP to the same size as the image to be encrypted L′W′C .

[0020] Furthermore, the Henon map module is used to perform a Henon map operation with parameters (a, b, q3) on the image that has been processed by the quantum walk module to perform pixel replacement according to the relevant parameter q3 of the image to be encrypted.

[0021] Furthermore, the cyclic shift module is used to perform a cyclic shift operation on each pixel of the image processed by the Henon map module according to relevant parameters (q1, q2, q3) of the image to be encrypted.

[0022] Furthermore, the Arnold Cat map module is used to perform an Arnold Cat map operation on the image processed by the cyclic shift module according to relevant parameters (q1, q2, q3) of the image to be encrypted, perform pixel replacement, and obtain the final ciphertext.

[0023] Furthermore, the image to be encrypted is O1, and its size is L′W′C; L, W, C represent the length, width and number of channels of the image; the initial parameters of the algorithm are (s, N, a, b, q); and the parameters related to the image to be encrypted are (q1, q2, q3).

[0024] The present invention also provides a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the quantum-classical hybrid image encryption method based on quantum walk and chaotic mapping.

[0025] The present invention also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the quantum-classical hybrid image encryption method based on quantum walk and chaotic mapping.

[0026] The present invention also provides an information data processing terminal, which is used to implement the quantum classical hybrid image encryption system based on quantum walk and chaotic mapping.

[0027] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0028] First, this algorithm proposes a quantum classical hybrid image encryption scheme based on quantum walk, Henon map and Arnold Cat map, which uses these complex and nonlinear mappings to protect image data. This algorithm does not need to encode the original image, but directly calculates the pixel ratio as part of the parameters required for the encryption scheme, which improves the efficiency of the encryption scheme. In addition, the initial conditions of the Henon map, the number of iterations of the Arnold Cat map, and the coin operator parameters of the quantum walk are related to the plaintext image, making the image encryption scheme very sensitive to small changes in the pixels of the plaintext image. Therefore, this encryption method can be regarded as an encryption method that approximates "one-time one-pad".

[0029] (1) More efficient encryption method: Compared with traditional encryption algorithms, this algorithm does not need to encode the image or perform multiple quantum walks, which reduces the time and resources required for encryption. Images can be encrypted more efficiently.

[0030] (2) More secure encryption method: Compared with the pseudo-random key stream generated by classical methods, this algorithm uses the special properties of quantum and quantum walk technology to generate a truly random key stream, which increases the security of the encryption scheme.

[0031] (3) More sensitive encryption scheme: Compared with the encryption algorithm with fixed parameters, the parameters of the key stream generated by this algorithm are related to the image to be encrypted. Therefore, this algorithm is more sensitive to the key than the encryption algorithm with fixed parameters.

[0032] The quantum classical hybrid image encryption method based on quantum walk and chaotic mapping has the advantages of being more efficient, safer and more sensitive, and can have broad application prospects in image encryption.

[0033] Third, as auxiliary evidence of the inventiveness of the claims of the present invention, it is also reflected in the following important aspects:

[0034] (1) The expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0035] 1. Demand for security solutions: With the development of the digital age, the demand for data security is increasing. Especially in the fields of finance, medical care, government and military, the requirements for data security and privacy protection are very strict. The encryption scheme of quantum walk and chaos mapping hybrid can provide high security and meet the demand for security solutions in these fields.

[0036] 2. Market competitive advantage: Most of the encryption technologies on the market are based on classical algorithms and models, while the encryption scheme that combines quantum walk and chaos mapping is an emerging and more cutting-edge technology. Therefore, this scheme has the potential to gain a competitive advantage in the market and attract more customers to choose it.

[0037] 3. Enhanced brand value: The investment and efforts of enterprises in data security can enhance the reputation and value of their brands. By adopting highly secure encryption solutions, enterprises can establish a good brand image, enhance customer trust, and thus promote business development and increase revenue.

[0038] 4. Launch of new products and services: Quantum walk and chaos mapping hybrid encryption solutions can be introduced to the market as new products or services, creating new business opportunities and revenue sources for enterprises. Enterprises can integrate the encryption solution into their existing product portfolio or provide customized encryption solutions to expand their market share and profitability.

[0039] Third, the quantum classical hybrid image encryption method based on quantum walk and chaos mapping proposed in this invention mainly solves the technical problems of low security and high computational complexity of image encryption algorithms in the prior art. By introducing quantum walk and chaos theory, this method not only improves encryption security, but also optimizes the efficiency and complexity of the encryption process, meeting the dual requirements of modern communications for high security and high efficiency.

[0040] The present invention solves the technical problems of the prior art:

[0041] 1. Improve security: Existing image encryption technologies often rely on traditional encryption algorithms, which face potential threats from quantum computing and will be cracked by future quantum computers. This invention introduces quantum walks, takes advantage of their randomness and unpredictability, and combines the sensitivity and dynamic complexity of classical chaotic mapping to significantly improve encryption security and enhance the ability to resist quantum computing attacks.

[0042] 2. Optimize computational complexity: Traditional image encryption methods often involve complex mathematical operations or require long computational time, which is particularly evident when processing large-scale data. In the present invention, the probability matrix generated by the quantum walk module directly performs a simple bit XOR operation with the image data, simplifying the complex computational process in traditional encryption algorithms. In addition, the introduction of chaotic mapping further increases the nonlinear characteristics of the system without significantly increasing the computational burden.

[0043] The technical progress of the present invention:

[0044] 1. Effective fusion of quantum and classical encryption: This invention effectively combines the advantages of quantum computing with the maturity of classical encryption technology, providing a new type of high-security image encryption solution. Quantum walk provides uncertainty and randomness based on the principles of quantum mechanics, while chaos mapping utilizes the high sensitivity and complex dynamic behavior of classical chaotic systems. The combination of the two ensures the practicality and efficiency of the algorithm while ensuring security.

[0045] 2. Improve the performance and evaluation system of image encryption: By introducing multi-layer encryption strategies and comprehensively utilizing different chaotic mappings, the present invention not only enhances the ciphertext's ability to resist attacks, but also quantitatively evaluates the encryption effect through systematic evaluation indicators (such as information entropy, contrast, etc.), providing users with a highly reliable and easy-to-implement encryption tool, which is particularly suitable for industrial applications that require high security protection, such as military communications, financial transaction data transmission and other fields.

[0046] The present invention provides significant technical progress in improving the security and computational efficiency of image encryption, solves some key technical problems existing in the prior art, and is of great significance for promoting the technological development of related industrial applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a quantum classical hybrid image encryption method based on quantum walk and chaotic mapping provided by an embodiment of the present invention.

[0048] Figure 2 It is a structural block diagram of a quantum classical hybrid image encryption system based on quantum walk and chaotic mapping provided by an embodiment of the present invention.

[0049] Figure 3 It is a flow chart of a quantum classical hybrid encryption algorithm based on quantum walk and chaos mapping provided by an embodiment of the present invention.

[0050] Figure 4 This is a classic image encryption result diagram provided by an embodiment of the present invention.

[0051] Figure 5 is a correlation diagram of the red channel provided by an embodiment of the present invention.

[0052] Figure 6 It is a correlation diagram of the green channel provided by an embodiment of the present invention.

[0053] Figure 7 is a correlation diagram of the blue channel provided by an embodiment of the present invention.

[0054] Figure 8 are histograms of five encrypted images provided by the embodiments of the present invention.

[0055] Fig. 9 This is the final decryption effect diagram provided by the embodiment of the present invention.

[0056] Fig.10 This is a result diagram of a cropping attack provided by an embodiment of the present invention.

[0057] Fig.11 This is an image decrypted by the Gaussian noise attack provided by an embodiment of the present invention.

[0058] Fig.12 This is an image decrypted by the salt and pepper noise attack provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0060] Application Example 1: Secure Transmission of Medical Images

[0061] In the medical field, image data such as X-rays, MRIs, and CT scans contain sensitive personal health information. Therefore, it is crucial to ensure the security and privacy of these medical images during transmission.

[0062] 1) Receive a medical image to be encrypted: for example, receive an MRI scan image.

[0063] 2) Quantum walk generates a probability matrix: Based on specific initial parameters, a quantum walk is performed to generate a probability matrix of the same size as the MRI image.

[0064] 3) Perform bitwise XOR operation: Perform bitwise XOR operation on the pixels of the MRI image and the probability matrix to generate an intermediate ciphertext.

[0065] 4) Henon map transformation: The intermediate ciphertext is further encrypted through the Henon map to increase the randomness and security of the ciphertext.

[0066] 5) Cyclic shift processing: Cyclic shift is performed on the intermediate ciphertext processed by the Henon map to confuse the image structure.

[0067] 6) Arnold Cat map transformation: Perform Arnold Cat map on the final processed intermediate ciphertext to obtain the final ciphertext image.

[0068] 7) Encryption capability assessment: Evaluate the security of encrypted images through methods such as differential attacks and statistical analysis.

[0069] Application effect:

[0070] Encrypted medical images can be securely sent to remote clinics or hospitals via the Internet or other electronic means without worrying about the data being stolen or tampered with during transmission.

[0071] Application Example 2: Digital Watermarking for Copyright Protection

[0072] For artworks, photos, and other digital media where copyright protection is particularly important, the use of digital watermarking technology can effectively prevent unauthorized copying and dissemination.

[0073] 1) Receiving a digital media image to be encrypted: for example, receiving a high-definition photograph.

[0074] 2) Quantum walk generates probability matrix: Generate a probability matrix of the same size as the original image through quantum walk technology.

[0075] 3) Perform bit XOR operation: perform bit XOR operation on the original image and the probability matrix to integrate the digital watermark.

[0076] 4) Henon map transformation: Perform Henon map encryption on the intermediate ciphertext with watermark to ensure the invisibility of the watermark.

[0077] 5) Circular shift processing: The circular shift technology is used to further confuse the image content and increase the concealment of the watermark.

[0078] 6) Arnold Cat map transformation: Arnold Cat map is finally used to ensure the uniform distribution and difficulty of removing the watermark.

[0079] 7) Encryption capability evaluation: Evaluate the robustness, invisibility and minimization of the impact of the watermark on the original image.

[0080] Application effect:

[0081] Through this encryption and watermarking technology, the copyright of photographic works or artworks is effectively protected, and even if the works are illegally copied or downloaded, the watermark can help track and prove the copyright ownership of the original creator.

[0082] These two embodiments show the practical application potential of the image encryption method based on quantum walk and chaos mapping in protecting information security and copyright.

[0083] Example 1: Image encryption system based on quantum walk and Henon mapping

[0084] In military communication systems, it is crucial to ensure the confidentiality and integrity of transmitted image data. This embodiment aims to provide a highly secure encryption method for military image data by combining quantum walk and Henon mapping technology.

[0085] 1. Image reception: The system first receives the military image data that needs to be encrypted.

[0086] 2. Quantum walk processing: Using the set initial state parameters, a quantum walk operation is performed to generate a probability matrix, which is then expanded to the same size as the image to be encrypted.

[0087] 3. Preliminary encryption operation: Generate preliminary encrypted image data by performing a bitwise XOR operation on the expanded probability matrix and the original image.

[0088] 4. Henon mapping obfuscation: Apply Henon mapping to the initially encrypted image to increase the encryption depth and generate intermediate ciphertext.

[0089] 5. Final encrypted output: Perform additional image chaos mapping processing, such as Arnold Cat mapping, and finally output the ciphertext.

[0090] High security: The combination of quantum walk and Henon mapping not only ensures high randomness and irreversibility, but also greatly enhances the ability to resist statistical analysis and differential attacks.

[0091] Fast processing: Compared with traditional image encryption methods, this system can process large-size image data faster while ensuring security.

[0092] Example 2: Medical image encryption system based on quantum walk and cyclic shift

[0093] In medical information systems, protecting patient privacy is a legal and ethical requirement. This embodiment provides a secure medical image encryption solution by combining quantum walk and cyclic shift technology to ensure the security of medical record images during transmission.

[0094] 1. Receiving medical images: The system first receives the medical images that need to be encrypted.

[0095] 2. Quantum walk generation matrix: Use specific initial parameters to perform quantum walk and generate a probability matrix based on the image size.

[0096] 3. Perform preliminary encryption: Combine the probability matrix with the medical image through a bitwise XOR operation to generate a primary encrypted image.

[0097] 4. Apply cyclic shift: Perform cyclic shift processing on the primary encrypted image to increase the complexity of decryption.

[0098] 5. Output the final ciphertext: Perform the final chaotic mapping encryption processing on the cyclically shifted image, complete the encryption process and output the ciphertext.

[0099] Personalized security: Create a unique encryption mode for each patient or medical institution by personalizing the quantum walk parameters and cyclic shift step length.

[0100] Wide applicability: The system is designed to be compatible with medical images of various types and sizes and can be easily integrated into existing medical information systems.

[0101] These two embodiments demonstrate the specific implementation methods of the encryption method of the present invention in different application scenarios, both of which can achieve high-security and high-efficiency encryption effects.

[0102] like Figure 1 As shown, a quantum classical hybrid image encryption method based on quantum walk and chaotic mapping provided by an embodiment of the present invention includes the following steps:

[0103] S1: Receive the image to be encrypted; calculate the pixel ratios q1, q2, q3 of the three channels of the image to be encrypted;

[0104] S2: Execute the quantum walk module with initial parameters (s, N, q, q1, q2) to obtain a probability matrix P N′N ; Then enlarge the probability matrix to the same size as the image to be encrypted L′W′C ;

[0105] S3: The encrypted image O1 and the matrix RP L′W′C Perform bit XOR operation to obtain the intermediate ciphertext C1;

[0106] S4: Execute the Henon map module with parameters (a, b, q3) on the intermediate ciphertext C1 to obtain the intermediate ciphertext C2;

[0107] S5: Execute a cyclic shift module with parameters (q1, q2, q3) on the intermediate ciphertext C2 to obtain the intermediate ciphertext C3;

[0108] S6: Execute the Arnold Cat map module with parameters (q1, q2, q3) on the intermediate ciphertext C3 to obtain the final ciphertext C;

[0109] S7: Evaluate the encryption capability of the algorithm through evaluation indicators.

[0110] The following is the detailed signal data processing process of the quantum classical hybrid image encryption method based on quantum walk and chaos mapping:

[0111] S1: Receive the image to be encrypted; calculate the pixel ratio of the three channels of the image to be encrypted

[0112] 1) Image reception:

[0113] An image to be encrypted is received, including a red channel (R), a green channel (G), and a blue channel (B).

[0114] 2) Pixel ratio calculation:

[0115] The pixels of each channel are statistically analyzed to calculate the pixel ratio of each channel (eg, number of R channel pixels / total number of pixels).

[0116] S2: Execute the quantum walk module with initial parameters to obtain a probability matrix; then enlarge the probability matrix to a matrix of the same size as the image to be encrypted.

[0117] 1) Quantum walk module:

[0118] A quantum walk operation is performed using the initial parameters to generate a probability matrix that contains the randomness of the image.

[0119] 2) Probability matrix amplification:

[0120] The generated probability matrix is ​​enlarged to the same size as the image to be encrypted to ensure that it can be bitwise XORed with the image.

[0121] S3: Perform bitwise XOR operation on the image to be encrypted and the matrix to obtain the intermediate ciphertext

[0122] 1) Bit XOR operation:

[0123] Perform a bitwise XOR operation on each pixel of the image to be encrypted and the corresponding position of the probability matrix to generate an intermediate ciphertext.

[0124] S4: Execute the Henon map module with parameter on the intermediate ciphertext to obtain the intermediate ciphertext

[0125] 1) Henon map module:

[0126] Use the Henon map module with parameter to perform chaotic mapping operation on the intermediate ciphertext to increase the encryption strength.

[0127] S5: Execute the cyclic shift module with parameter on the intermediate ciphertext to obtain the intermediate ciphertext

[0128] 1) Circular shift module:

[0129] Use a cyclic shift module with parameter to perform cyclic shift operation on the intermediate ciphertext to further increase obfuscation and security.

[0130] S6: Execute the Arnold Cat map module with parameter on the intermediate ciphertext to obtain the final ciphertext

[0131] 1) Arnold Cat map module:

[0132] Use the Arnold Cat map module with parameters to perform Arnold Cat mapping on the intermediate ciphertext to generate the final ciphertext.

[0133] S7: Evaluate the encryption capability of the algorithm through evaluation indicators

[0134] 1) Evaluation indicators:

[0135] The encrypted image is evaluated using evaluation indicators (such as information entropy, pixel change rate, uniform change intensity, peak signal-to-noise ratio, etc.) to evaluate the encryption strength and effect of the algorithm.

[0136] The above steps describe the detailed signal data processing process of the quantum classical hybrid image encryption method based on quantum walk and chaotic mapping. By combining quantum walk and chaotic mapping, this method can provide high encryption strength and security, protecting the privacy and confidentiality of the image.

[0137] like Figure 2 As shown, a quantum classical hybrid image encryption system based on quantum walk and chaotic mapping provided by an embodiment of the present invention includes: a quantum walk module, a Henon map module, a cyclic shift module, and an Arnold Cat map module.

[0138] The quantum classical hybrid image encryption system based on quantum walk and chaos mapping, the working principles of each module are as follows:

[0139] 1. Quantum Walk Module: Quantum walk, also known as quantum walk, is an important computational model in the field of quantum computing. It is based on the basic principles of quantum mechanics and corresponds to the classical random walk. The quantum walk module uses the superposition and interference properties of quantum particles to generate complex random paths in multidimensional space. This randomness can generate a large number of random sequences for key generation in image encryption. Since quantum walk is sensitive to initial states and non-periodic states, it can theoretically generate infinite spatial keys, greatly increasing the complexity and unpredictability of the keys.

[0140] 2. Henon map module: Henon map is a typical chaotic mapping method, which has complex chaotic behavior and high sensitivity. In image encryption, the Henon map module generates a large number of random sequences through chaotic mapping, which are combined with the sequences generated by the quantum walk module to form the final encryption key. The characteristics of chaotic mapping make the key sequence highly random and unpredictable, thereby enhancing the security of encryption.

[0141] 3. Circular shift module: The main function of the circular shift module is to change the position of pixels in the image. It stores and reads image data according to certain rules to achieve circular shift of pixels. Through circular shift, the original arrangement order of pixels in the image can be broken, making the encrypted image visually unrecognizable.

[0142] 4. Arnold Cat map module: Arnold Cat map is an encryption algorithm based on scrambling and diffusion. The scrambling step disperses the image information into a larger space through a specific permutation matrix, increasing the difficulty of encryption. The diffusion step further confuses the scrambled information through complex calculations, making the encrypted image more difficult to crack. The ArnoldCat map module achieves deep encryption of the image through these two steps.

[0143] In summary, these four modules work together to use the characteristics of quantum walk and chaotic mapping to generate complex random sequences and pixel arrangements, thereby achieving deep encryption of images. This encryption method has high security and complexity and can resist various brute force attacks and cracking attempts.

[0144] The quantum walk module provided in the embodiment of the present invention is used to perform a quantum walk operation with parameters (s, N, q, q1, q2) according to the initial parameters of the algorithm to obtain a probability matrix P N′N ; According to the size of the image to be encrypted, the probability matrix P N′N Enlarge the matrix RP to the same size as the image to be encrypted L′W′C .

[0145] The Henon map module provided in the embodiment of the present invention is used to perform a Henon map operation with parameters (a, b, q3) on the image that has been processed by the quantum walk module to perform pixel replacement according to the relevant parameter q3 of the image to be encrypted.

[0146] The cyclic shift module provided in the embodiment of the present invention is used to perform a cyclic shift operation on each pixel point of the image processed by the Henon map module according to relevant parameters (q1, q2, q3) of the image to be encrypted.

[0147] The Arnold Cat map module provided in the embodiment of the present invention is used to perform an Arnold Cat map operation on the image processed by the cyclic shift module according to relevant parameters (q1, q2, q3) of the image to be encrypted, perform pixel replacement, and obtain the final ciphertext.

[0148] The image to be encrypted provided by the embodiment of the present invention is O1, and its size is L′W′C; L, W, C represent the length, width and number of channels of the image; the initial parameters of the algorithm are (s, N, a, b, q); and the parameters related to the image to be encrypted are (q1, q2, q3).

[0149] A computer device provided by an embodiment of the present invention includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the quantum-classical hybrid image encryption method based on quantum walk and chaotic mapping.

[0150] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the quantum-classical hybrid image encryption method based on quantum walk and chaotic mapping.

[0151] An embodiment of the present invention provides an information data processing terminal, which is used to implement the quantum classical hybrid image encryption system based on quantum walk and chaotic mapping.

[0152] like Figure 3 As shown, the above algorithm steps are detailed through simulation experiments, and the specific program implementation is consistent with the algorithm steps.

[0153] The technical solution of the present invention is applied to image data. In this application embodiment, the technical solution of the present invention can protect the secure transmission of images.

[0154] It should be noted that the embodiments of the present invention can be simulated through a software platform. The software platform can choose to use Google Colab or anaconda, install and call library functions required by various programs on this platform, and use an open source cross-platform python library to implement the image encryption algorithm of the present invention.

[0155] The embodiments of the present invention have achieved some positive effects during the development or use process, and indeed have great advantages over the prior art. The following content is described in conjunction with data, charts, etc. of the test process.

[0156] The quantum classical hybrid image encryption method based on quantum walk and chaotic mapping provided by the embodiment of the present invention;

[0157] This application is to verify the feasibility and effectiveness of the quantum classical hybrid image encryption method based on quantum walk and chaos mapping;

[0158] Five public images, Lena, Mandrill, Sailboat, House, and Airplane, are used for verification. The image size is 512′512. The image encryption effect is as follows: Figure 4 shown.

[0159] In order to prove that the proposed encryption algorithm can resist statistical analysis, adjacent pixel correlation analysis, histogram analysis, information entropy analysis and sensitivity analysis were carried out.

[0160] The correlation between adjacent pixels refers to the correlation between pixels that are close in position in the image space. The correlation coefficient is used to measure the correlation between adjacent pixels. A good encryption algorithm can make the correlation coefficient of the image close to zero.

[0161] Here, 10,000 pairs of adjacent pixels are randomly selected to calculate the correlation coefficient. Take "Sailboat.tiff" and its corresponding ciphertext correlation distribution as an example. The correlations of the red, green, and blue channels are Figure 5-7 It can be seen that the plaintext image shows a strong correlation in the three channels, while the pixels of the encrypted image show a uniform distribution in the three channels, which shows that the encryption scheme can resist correlation analysis attacks. The correlation coefficient results of all test images are shown in Table 1.

[0162] Table 1: Correlation coefficients in different directions

[0163]

[0164]

[0165] It can be seen that the correlation coefficients of the ciphertexts are close to zero, which proves that the encryption scheme has the ability to resist statistical attacks.

[0166] A histogram is a statistical graph used to show the distribution of pixel values ​​in an image. A good encryption scheme will make the histogram of the ciphertext image show uniform characteristics. For an image, the smaller the histogram coefficient, the more uniform the pixel distribution. Here, the chi-square distribution with a confidence level of a=0.05 is selected to detect whether the pixels of the ciphertext image are uniformly distributed. If the histogram coefficient of the ciphertext image can be Test, then it means that the pixel distribution histogram of the image is uniform. The specific test results are shown in Table 3. The histograms of the five encrypted images are shown in Figure 8 shown.

[0167] Table 3 performs the ciphertext Test results

[0168]

[0169] In information theory, information entropy is used to describe the uncertainty of random variables. Here, information entropy is used to represent the uncertainty of images.

[0170] For a color image, each pixel contains multiple color channels, and each color channel is regarded as a discrete random variable with a symbol set size of 256. Therefore, for a color image, if the information entropy of each color channel is closer to log2(256)=8, it means that the encryption algorithm has better performance. Here, the information entropy of each test image and its corresponding ciphertext image is calculated, as shown in Table 4. At the same time, the average information entropy of other schemes is also compared, as shown in Table V.

[0171] Table 4: Information entropy of plaintext and ciphertext

[0172]

[0173] Table 5: Comparison results of information entropy of different schemes

[0174]

[0175] It can be seen that the information entropy of all ciphertexts is very close to 8. This shows that the encryption scheme can resist information entropy attacks, and its information entropy performance is better than other schemes.

[0176] If a small change in the plaintext can significantly change the ciphertext, then it means that the scheme has good sensitivity to the plaintext. In order to test the sensitivity of the encryption scheme to small changes in the plaintext image, the pixel change rate (NPCR) and the uniform average change intensity (UACI) are used for measurement. NPCR measures the number of different pixels in two images, which is used to indicate the degree of similarity or difference between them. A higher NPCR value means that there are more different pixels between the two images, while a lower NPCR value means that they are more similar. UACI measures the average intensity of the difference between the two images. The specific NPCR values ​​and UACI values ​​are shown in Table VI and Table VII.

[0177] Table 6 NPCR value of ciphertext

[0178]

[0179] Table 7 UACI values ​​of ciphertext

[0180]

[0181] Table 8 Comparison of the average NPCR values ​​between this paper and references [4], [1, 2, 5, 6]

[0182]

[0183] Table 9 Comparison of the average UACI values ​​of this paper and references [4], [1, 2, 5, 6]

[0184]

[0185] Reference [7] points out that for a 512*512 image, when the confidence a=0.05, the theoretical lower bound of NPCR is 99.5893%, and the range of UACI is 33.3730%-33.5541%. It can be seen that the encryption scheme meets the theoretical requirements. Therefore, the encryption scheme is very sensitive to slight changes in the original image and can resist differential attacks. In addition, the UACI and NPCR values ​​of different schemes are compared. Since the encrypted images selected by each scheme are different, the average values ​​of each scheme are selected for comparison. Table 8 and Table 9 are the comparison results of respectively. It can be seen that the scheme performs well in terms of NPCR and UACI values.

[0186] In order to prove that the proposed encryption scheme has sufficient security, key space analysis is performed to ensure that the scheme can resist brute force attacks.

[0187] Key space analysis: The initial key is (m, N, q, a, b), which corresponds to the string of alternating quantum walks, the number of nodes, the initial state of the coin, and the initial parameters of the Henon map. For m, theoretically it can be infinitely long, representing an infinite key space. In the experiment, the length of m is 47. By analyzing m alone, we can get the key space size of 2 47 >>10 14 Assume that the calculation precision is 10 -16 , then the initial key space size is 10 64 . Then calculate other parameters (q1, q2, q3), we can get the key space size is 10 48 Therefore, the total key space size is 10 126 . This key space is sufficient to resist brute force attacks.

[0188] Key sensitivity analysis: Key sensitivity refers to the degree to which an encryption algorithm responds to key changes. Specifically, it measures the degree of difference in the encryption result when the encryption key changes slightly. If the encryption algorithm is very sensitive to key changes, even if the key changes slightly, the difference in the encryption result will be very obvious. On the contrary, if the encryption algorithm is not sensitive to key changes, even if the key changes slightly, the difference in the encryption result will not be so significant. Here, the initial key composition is (m, N, q, a, b, q1, q2, q3), and eight experiments were conducted, respectively changing the last bit of m, adjusting the number of nodes N, changing the initial state q of the coin, changing the constants a and b of the Henon map, and changing the three angles q1, q2, q3. The final decryption effect is as follows: Fig. 9 As shown. It can be seen that the scheme is very sensitive to the key, which also shows that if the malicious attacker does not know all the initial parameters, he will not be able to decipher the correct image.

[0189] During data transmission, noise interferes with data transmission and causes partial loss of data. In order to evaluate the proposed encryption method, cropping attack and noise attack are performed on the encrypted image to ensure that the proposed encryption system has the ability to resist noise and cropping attacks.

[0190] Cropping attack: Image cropping attack refers to a method in which the attacker breaks the encryption algorithm by cutting or cropping the digital image. Here, PSNR (Peak Signal-to-Noise Ratio) is introduced to measure the image quality, which is used to compare the similarity between the original image and the processed image. The larger the PSNR value, the higher the image quality. It is generally believed that when the PSNR value is higher than 40, the image quality is excellent (that is, very close to the original image), 30-40 indicates good image quality (that is, the distortion is noticeable but acceptable), 20-30 indicates poor image quality, and below 20 indicates unacceptable image. The results of the cropping attack are shown in Figure 2. Fig.10 The PSNR values ​​after cropping are shown in Table 10.

[0191] Table 10 PSNR values ​​of the decrypted images after cropping

[0192]

[0193] It can be seen that the PSNR values ​​of the encryption scheme under different degrees of cropping are between 40 and 30, indicating that the image quality is good. Therefore, the encryption scheme can resist cropping attacks.

[0194] Gaussian noise attack: Gaussian noise attack is a common attack method in digital image processing. In this attack, random noise from Gaussian distribution is added to each pixel value of the original image to change the pixel value of the image. Here, the mean value of the added Gaussian noise is 0, and the variance is 0.001, 0.01, 0.1, and 0.15 respectively. The decrypted image is as follows Fig.11 As shown. It can be seen that the decrypted image is still visible. In addition, Table 11 gives the PSNR values ​​of the decrypted image after adding different variances.

[0195] Table 11: PSNR values ​​of decrypted images after adding Gaussian noise with different variances

[0196]

[0197] It can be observed that after adding different degrees of Gaussian noise, the scheme shows a PSNR value between 40-30, indicating that the image quality is good. This shows that the encryption scheme is able to resist Gaussian noise attacks.

[0198] Salt and pepper noise attack: Salt and pepper noise attack is a common attack method in digital image processing. In this attack, random black and white pixels are added to the original image to change the pixel values ​​of the image. In this experiment, salt and pepper noise with intensities of 0.1, 0.2, 0.3, and 0.4 were added. The decrypted image is as follows Fig.12 As shown. It can be observed that the decrypted image still maintains visibility. In addition, Table 12 gives the PSNR value of the decrypted image after adding salt and pepper noise. This shows that the encryption scheme can resist the salt and pepper noise attack.

[0199] Table 12 PSNR values ​​of decrypted images after adding salt and pepper noise

[0200]

[0201] It can be seen that when adding 0.1 salt and pepper noise, the PSNR value of the decrypted image is higher than 40, which indicates that the decrypted image quality is very good. The PSNR value of the decrypted image at other intensities is between 40-30, which indicates that the decrypted image quality is good. This shows that the encryption scheme can resist the salt and pepper noise attack.

[0202] Complexity analysis: For the convenience of analysis, assume that the image size is h′w and the number of nodes of quantum walk is N. Then the time complexity of the encryption scheme can be divided into three parts: the time complexity of the first part, quantum walk, is O(N 2), the time complexity of the second part bit XOR is O(h′w), and the time complexity of the third part to execute Henon map and Cat map is O(h′w). In summary, the time complexity of the above solution is O(max(N 2 ,h′w)).

[0203] NIST Testing: NIST SP 800-22 testing consists of a set of standardized test procedures published by the National Institute of Standards and Technology (NIST) for evaluating randomness and the efficacy of random number generators. These tests are designed to evaluate various characteristics of random number generators, including randomness, consistency, and independence, to determine their reliability in security and cryptographic environments. NIST SP 800-22 testing typically includes a number of statistical evaluations that can be used to verify the reliability and suitability of random number generators. Table 13 shows the NIST success rates for the schemes.

[0204] Table 13: NIST success rate.

[0205]

[0206] The above simulation experiments verified and applied the proposed algorithm, proving the feasibility and effectiveness of the algorithm.

[0207] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0208] In order to prove the creativity and technical value of the technical solution of the present invention, this section provides application examples of the claimed technical solution on specific products or related technologies.

[0209] Healthcare: Apply encryption schemes in medical image transmission and storage to protect patients’ privacy information, such as medical images, patient photos, etc.

[0210] Apply encryption solutions to the transmission and storage of medical images such as X-rays, CT scans, MRIs, etc. to ensure that only authorized personnel can access these sensitive data.

[0211] Military and Intelligence: Apply encryption schemes to the transmission and storage of military images (such as satellite images, reconnaissance images) to ensure their security and confidentiality.

[0212] In the field of intelligence and security, encryption schemes are used to encrypt and protect sensitive image information to prevent hostile forces from obtaining confidential information.

[0213] Business and Finance: In the financial sector, encryption schemes are applied to the transmission and storage of sensitive image information such as transaction data and customer information to prevent data leakage and theft.

[0214] Confidential image assets in the business field, such as design drawings, product prototypes, etc., can also be protected by encryption schemes to prevent competitors from obtaining sensitive information.

[0215] E-government: In government agencies, encryption schemes are applied to the transmission and storage of sensitive information such as government image materials to ensure the security and confidentiality of government data.

[0216] Education and research: In educational and research institutions, encryption solutions are applied to the transmission and storage of sensitive image information such as scientific research data and academic paper data to protect intellectual property rights and research results.

[0217] The embodiments of the present invention have achieved some positive effects during the development or use process, and indeed have great advantages over the prior art. The following content is described in conjunction with data, charts, etc. of the test process.

[0218] In order to prove that the proposed encryption algorithm can resist statistical analysis, adjacent pixel correlation analysis, histogram analysis, information entropy analysis and sensitivity analysis were carried out.

[0219] The correlation coefficient results of all test images are shown in Table 1.

[0220] Table 1: Correlation coefficients in different directions

[0221]

[0222]

[0223] It can be seen that the correlation coefficients of the ciphertexts are close to zero, which proves that the encryption scheme has the ability to resist statistical attacks.

[0224] For an image, the smaller the histogram coefficient, the more uniform the pixel distribution. Here, the chi-square distribution with a confidence level of a = 0.05 is selected to detect whether the pixels of the ciphertext image are uniformly distributed. Test, then it means that the pixel distribution histogram of the image is uniform. The specific test results are shown in Table 3. The histograms of the five encrypted images are shown in Figure 8 shown.

[0225] Table 3 performs the ciphertext Test results

[0226]

[0227] It can be seen that our solution passed the histogram analysis test.

[0228] Therefore, for a color image, if the information entropy of each color channel is closer to log2(256)=8, it means that the encryption algorithm has better performance. Here, the information entropy of each test image and its corresponding ciphertext image is calculated, as shown in Table 4. At the same time, the average information entropy of other schemes is also compared, as shown in Table 5.

[0229] Table 4: Information entropy of plaintext and ciphertext

[0230]

[0231] Table 5: Comparison results of information entropy of different schemes

[0232]

[0233] It can be seen that the information entropy of all ciphertexts is very close to 8. This shows that the encryption scheme can resist information entropy attacks, and its information entropy performance is better than other schemes.

[0234] If a small change in the plaintext can significantly change the ciphertext, then it means that the scheme has good sensitivity to the plaintext. The specific NPCR values ​​and UACI values ​​are shown in Table VI and Table VII.

[0235] Table 6 NPCR value of ciphertext

[0236]

[0237] Table 7 UACI values ​​of ciphertext

[0238]

[0239] Table 8 Comparison of the average NPCR values ​​between this paper and references [4], [1, 2, 5, 6]

[0240]

[0241] Table 9 Comparison of the average UACI values ​​of this paper and references [4], [1, 2, 5, 6]

[0242]

[0243] Reference [7] points out that for a 512*512 image, when the confidence a=0.05, the theoretical lower bound of NPCR is 99.5893%, and the range of UACI is 33.3730%-33.5541%. It can be seen that the encryption scheme meets the theoretical requirements. Therefore, the encryption scheme is very sensitive to slight changes in the original image and can resist differential attacks. In addition, the UACI and NPCR values ​​of different schemes are compared. Since the encrypted images selected by each scheme are different, the average values ​​of each scheme are selected for comparison. Table 8 and Table 9 are the comparison results of respectively. It can be seen that the scheme performs well in terms of NPCR and UACI values.

[0244] In order to prove that the proposed encryption scheme has sufficient security, key space analysis is performed to ensure that the scheme can resist brute force attacks.

[0245] Key space analysis: The initial key is (m, N, q, a, b), which corresponds to the string of alternating quantum walks, the number of nodes, the initial state of the coin, and the initial parameters of the Henon map. For m, theoretically it can be infinitely long, representing an infinite key space. In the experiment, the length of m is 47. By analyzing m alone, we can get the key space size of 2 47 >>10 14 Assume that the calculation precision is 10 -16 , then the initial key space size is 10 64 . Then calculate other parameters (q1, q2, q3), we can get the key space size is 10 48 Therefore, the total key space size is 10 126 . This key space is sufficient to resist brute force attacks.

[0246] Key sensitivity analysis: Key sensitivity refers to the degree to which an encryption algorithm responds to key changes. Specifically, it measures the degree of difference in the encryption result when the encryption key changes slightly. If the encryption algorithm is very sensitive to key changes, even if the key changes slightly, the difference in the encryption result will be very obvious. On the contrary, if the encryption algorithm is not sensitive to key changes, even if the key changes slightly, the difference in the encryption result will not be so significant. Here, the initial key composition is (m, N, q, a, b, q1, q2, q3), and eight experiments were conducted, respectively changing the last bit of m, adjusting the number of nodes N, changing the initial state q of the coin, changing the constants a and b of the Henon map, and changing the three angles q1, q2, q3. The final decryption effect is as follows: Fig. 9 As shown. It can be seen that the scheme is very sensitive to the key, which also shows that if the malicious attacker does not know all the initial parameters, he will not be able to decipher the correct image.

[0247] During data transmission, noise interferes with data transmission and causes partial loss of data. In order to evaluate the proposed encryption method, cropping attack and noise attack are performed on the encrypted image to ensure that the proposed encryption system has the ability to resist noise and cropping attacks.

[0248] Cropping attack: Image cropping attack refers to a method in which the attacker breaks the encryption algorithm by cutting or cropping the digital image. Here, PSNR (Peak Signal-to-Noise Ratio) is introduced to measure the image quality, which is used to compare the similarity between the original image and the processed image. The larger the PSNR value, the higher the image quality. It is generally believed that when the PSNR value is higher than 40, the image quality is excellent (that is, very close to the original image), 30-40 indicates good image quality (that is, the distortion is noticeable but acceptable), 20-30 indicates poor image quality, and below 20 indicates unacceptable image. The results of the cropping attack are shown in Figure 2. Fig.10 The PSNR values ​​after cropping are shown in Table 10.

[0249] Table 10 PSNR values ​​of the decrypted images after cropping

[0250]

[0251] It can be seen that the PSNR values ​​of the encryption scheme under different degrees of cropping are between 40 and 30, indicating that the image quality is good. Therefore, the encryption scheme can resist cropping attacks.

[0252] Gaussian noise attack: Gaussian noise attack is a common attack method in digital image processing. In this attack, random noise from Gaussian distribution is added to each pixel value of the original image to change the pixel value of the image. Here, the mean value of the added Gaussian noise is 0, and the variance is 0.001, 0.01, 0.1, and 0.15 respectively. The decrypted image is as follows Fig.11 As shown. It can be seen that the decrypted image is still visible. In addition, Table 11 gives the PSNR values ​​of the decrypted image after adding different variances.

[0253] Table 11: PSNR values ​​of decrypted images after adding Gaussian noise with different variances

[0254]

[0255] It can be observed that after adding different degrees of Gaussian noise, the scheme shows a PSNR value between 40-30, indicating that the image quality is good. This shows that the encryption scheme is able to resist Gaussian noise attacks.

[0256] Salt and pepper noise attack: Salt and pepper noise attack is a common attack method in digital image processing. In this attack, random black and white pixels are added to the original image to change the pixel values ​​of the image. In this experiment, salt and pepper noise with intensities of 0.1, 0.2, 0.3, and 0.4 were added. The decrypted image is as follows Fig.12 As shown. It can be observed that the decrypted image still maintains visibility. In addition, Table 12 gives the PSNR value of the decrypted image after adding salt and pepper noise. This shows that the encryption scheme can resist the salt and pepper noise attack.

[0257] Table 12 PSNR values ​​of decrypted images after adding salt and pepper noise

[0258]

[0259] It can be seen that when adding 0.1 salt and pepper noise, the PSNR value of the decrypted image is higher than 40, which indicates that the decrypted image quality is very good. The PSNR value of the decrypted image at other intensities is between 40-30, which indicates that the decrypted image quality is good. This shows that the encryption scheme can resist the salt and pepper noise attack.

[0260] Complexity analysis: For the convenience of analysis, assume that the image size is h′w and the number of nodes of quantum walk is N. Then the time complexity of the encryption scheme can be divided into three parts: the time complexity of the first part, quantum walk, is O(N 2), the time complexity of the second part bit XOR is O(h′w), and the time complexity of the third part to execute Henon map and Cat map is O(h′w). In summary, the time complexity of the above solution is O(max(N 2 ,h′w)).

[0261] NIST Testing: NIST SP 800-22 testing consists of a set of standardized test procedures published by the National Institute of Standards and Technology (NIST) for evaluating randomness and the efficacy of random number generators. These tests are designed to evaluate various characteristics of random number generators, including randomness, consistency, and independence, to determine their reliability in security and cryptographic environments. NIST SP 800-22 testing typically includes a number of statistical evaluations that can be used to verify the reliability and suitability of random number generators. Table 13 shows the NIST success rates for the schemes.

[0262] Table 13: NIST success rate.

[0263]

[0264]

[0265] The above simulation experiments verified and applied the proposed algorithm, proving the feasibility and effectiveness of the algorithm.

[0266] References

[0267] [1] Gan, Z.-h., Chai, X.-l., Han, D.-j., Chen, Y.-r.: A chaotic image encryption algorithm based on 3-d bit-plane permutation. Neural Computing and Applications 31, 7111–7130 (2019). The article mainly proposes a chaotic color image encryption algorithm based on 3-d bit-plane permutation.

[0268] [2] Askar, SS, Karawia, AA, Al-Khedhairi, A., Al-Ammar, FS: An algorithm of image encryption using logistic and two-dimensional chaotic economic maps. Entropy 21(1), 44(2019). The article mainly proposes an image encryption algorithm combining one-dimensional and two-dimensional chaotic maps.

[0269] [3] Abd EL-Latif, AA, Abd-El-Atty, B., Abou-Nassar, EM, Venegas-Andraca, SE: Controlled alternate quantum walks based privacy preserving healthcare images in internet of things. Optics & Laser Technology 124, 105942 (2020). This paper mainly proposes an image encryption scheme based on quantum walks.

[0270] [4] Abd-El-Atty, B., ElAffendi, M., El-Latif, AAA: A novel image cryptosystem using gray code, quantum walks, and henon map for cloud applications. Complex & Intelligent Systems 9(1), 609–624(2023). The article mainly proposes an image encryption scheme using quantum walks and classical chaotic maps.

[0271] [5] Xian, Y., Wang, X.: Fractal sorting matrix and its application on chaotic image encryption. Information Sciences 547, 1154–1169 (2021). This paper proposes a sorting matrix with fractal characteristics and a new global pixel diffusion method with two chaotic sequences.

[0272] [6] Wang, X., Feng, L., Zhao, H.: Fast image encryption algorithm based on parallel computing system. Information Sciences 486, 340–358 (2019). The article mainly proposes a permutation algorithm and a parallel diffusion method.

[0273] [7] Wu, Y., Noonan, JP, Agaian, S., et al.: Npcr and uaci randomness tests for image encryption. Cyber ​​journals: multidisciplinary journals in science and technology, Journal of Selected Areas in Telecommunications (JSAT) 1(2), 31–38 (2011). The article mathematically analyzes the security indicators of image encryption algorithms.

[0274] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A quantum classical hybrid image encryption method based on quantum walk and chaos mapping, characterized in that: The following steps are involved: S1: Receive the image to be encrypted; calculate the pixel ratios q1, q2, q3 of the three channels of the image to be encrypted; S2: Execute the quantum walk module with initial parameters (s, N, q, q1, q2) to obtain a probability matrix P N×N ; Then enlarge the probability matrix to the same size as the image to be encrypted L×W×C ; S3: The encrypted image O1 and the matrix RP L×W×C Perform bit XOR operation to obtain the intermediate ciphertext C1; S4: Execute the Henonmap module with parameters (a, b, q3) on the intermediate ciphertext C1 to obtain the intermediate ciphertext C2; S5: Execute a cyclic shift module with parameters (q1, q2, q3) on the intermediate ciphertext C2 to obtain the intermediate ciphertext C3; S6: Execute the Arnold Catmap module with parameters (q1, q2, q3) on the intermediate ciphertext C3 to obtain the final ciphertext C; S7: Evaluate the encryption capability of the algorithm through evaluation indicators.

2. A quantum classical hybrid image encryption system based on quantum walk and chaos mapping for implementing the quantum classical hybrid image encryption method as claimed in claim 1, characterized in that: include: Quantum Walk module, used to generate random sequences based on the quantum walk principle as part of the encryption key; Henonmap module, which is used to generate random sequences based on chaotic maps and combine them with the random sequences generated by the quantum walk module to form a complete encryption key; A cyclic shift module, used for cyclically shifting pixels of the image according to an encryption key to change the arrangement order of the pixels; as well as Arnold Catmap module is used to perform scrambling and diffusion operations on the cyclically shifted image to further confuse the image information.

3. The quantum classical hybrid image encryption system based on quantum walk and chaos mapping as claimed in claim 2, characterized in that: The quantum walk module is used to perform a quantum walk operation with parameters (s, N, q, q1, q2) according to the initial parameters of the algorithm to obtain a probability matrix P N×N ; According to the size of the image to be encrypted, the probability matrix P N×N Enlarge the matrix RP to the same size as the image to be encrypted L×W×C .

4. The quantum classical hybrid image encryption system based on quantum walk and chaos mapping as claimed in claim 2, characterized in that: The Henonmap module is used to perform a Henonmap operation with parameters (a, b, q3) on the image that has been processed by the quantum walk module to perform pixel replacement according to the relevant parameter q3 of the image to be encrypted.

5. The quantum classical hybrid image encryption system based on quantum walk and chaos mapping as claimed in claim 2, characterized in that: The cyclic shift module is used to perform a cyclic shift operation on each pixel of the image processed by the Henonmap module according to relevant parameters (q1, q2, q3) of the image to be encrypted.

6. The quantum classical hybrid image encryption system based on quantum walk and chaos mapping as claimed in claim 2, characterized in that: The Arnold Cat map module is used to perform an Arnold Catmap operation on the image processed by the cyclic shift module according to relevant parameters (q1, q2, q3) of the image to be encrypted, perform pixel replacement, and obtain the final ciphertext.

7. The quantum classical hybrid image encryption system based on quantum walk and chaos mapping as claimed in claim 3, characterized in that: The image to be encrypted is O1, and its size is L×W×C; L, W, C represent the length, width and number of channels of the image; the initial parameters of the algorithm are (s, N, a, b, q); and the parameters related to the image to be encrypted are (q1, q2, q3).

8. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the quantum classical hybrid image encryption method based on quantum walk and chaotic mapping as claimed in claim 1.

9. A medical image encryption method based on quantum walk and chaos mapping that implements the quantum classical hybrid image encryption method as claimed in claim 1, characterized in that: The following steps are involved: (a) receiving a medical image to be encrypted; (b) Use quantum walk to generate a probability matrix of the same size as the image; (c) performing bitwise XOR operation on the medical image and the probability matrix to generate an intermediate ciphertext; (d) performing Henonmap, cyclic shift and Arnold Catmap module encryption on the intermediate ciphertext; (e) Save the final ciphertext and evaluate the encryption effect.

10. A digital media image copyright protection method based on quantum walk and chaos mapping that implements the quantum classical hybrid image encryption method as claimed in claim 1, characterized in that: The following steps are involved: (a) receiving a digital media image to be encrypted; (b) Use quantum walk to generate a probability matrix of the same size as the image; (c) Performing bitwise XOR operation on the digital media image and the probability matrix to integrate into the digital watermark to generate an intermediate ciphertext; (d) Perform Henon map, cyclic shift and Arnold Cat map module encryption on the intermediate ciphertext with watermark; (e) Save the final ciphertext and evaluate the concealment and robustness of the watermark.

Images