An image encryption and decryption method based on switching chaotic neural network anti-interference synchronization

Abstract

The application discloses an image encryption and decryption method based on switching chaotic neural network anti-interference synchronization, which comprises the following steps: obtaining a pre-processed image to be encrypted; constructing a pair of structure-matched switching chaotic time-delay neural network master system and slave system; establishing a switching synchronization error system; designing a disturbance observer, and then forming an augmented synchronization error system; establishing a disturbance compensation controller to realize anti-interference synchronization of the switching chaotic time-delay neural network master system and slave system; generating an encryption key, and encrypting the pre-processed image to be encrypted by using the encryption key; generating a decryption key based on the synchronized slave system, and performing a decryption operation on the encrypted image. The application provides an image encryption solution with simple structure, easy hardware implementation, outstanding anti-interference capability and excellent security in engineering practice, ensures encryption and decryption reliability in complex application scenarios, and provides efficient technical support for safe storage and transmission of image data.

Description

Technical Field

[0001] This invention relates to the field of image encryption technology, and in particular to an image encryption and decryption method based on switching chaotic neural network anti-interference synchronization. Background Technology

[0002] Chaotic time-delay neural networks, due to their extreme sensitivity to initial conditions and quasi-stochastic nonlinear dynamic behavior, have become an important technological support in the field of image encryption. Their complex evolutionary process can generate highly secure keys and, through mechanisms such as chaotic mapping and synchronization, can scramble and transform image pixels, effectively resisting common attack methods such as statistical analysis. They have gained widespread attention and application in engineering fields such as image processing, secure communication, and automated control.

[0003] On the other hand, under the influence of practical factors such as sudden changes in the external environment, information latching, and dynamic switching of system tasks, time-delay neural networks often exhibit switching characteristics. Switching signals play a crucial role in their dynamic behavior analysis. A reasonable switching strategy can improve the network's adaptability to environmental changes, balance the performance of different sub-networks, and overcome the bottleneck of a single mode, thereby enhancing the system's complexity and security in secure communication. This switching mechanism can increase the unpredictability of the network's dynamic behavior, prevent attackers from reverse-engineering network patterns, and further expand the key space by designing switching signals related to the initial state, thus promoting the in-depth development of chaotic neural network encryption technology.

[0004] However, most current research neglects the actual impact of external perturbations on the synchronization performance of switching time-delay neural networks, leading to a significant discrepancy between theory and practical application. Especially in secure communication scenarios, perturbations can disrupt the accuracy of master-slave system synchronization, weaken the system's sensitivity to initial values ​​and parameters, reduce the encryption scheme's resistance to attacks, and cause problems such as key mismatch and decryption failure. This makes it difficult to meet the high security requirements of image data in complex transmission or storage environments, thus limiting the practical application value and promotion potential of switching time-delay neural networks in the field of image encryption.

[0005] Existing research has proposed synchronization control techniques based on H∞ and L∞ disturbance suppression theories for time-delay neural networks affected by disturbances. While these methods can mitigate the impact of disturbances on system performance to some extent, they impose explicit constraints on the type of disturbance, typically requiring it to satisfy bounded energy or peak bounded conditions. In reality, the types of disturbances faced by switching neural networks are often uncertain and may not satisfy the boundedness assumption, thus limiting the anti-interference effectiveness and application scope of existing methods. Summary of the Invention

[0006] This invention provides an image encryption and decryption method based on switching chaotic neural network anti-interference synchronization to overcome the technical problems of weak anti-interference ability, insufficient synchronization stability and poor adaptability to complex disturbances in existing image encryption schemes.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] An image encryption / decryption method based on switching chaotic neural network anti-interference synchronization, the specific steps of which include:

[0009] S1. Obtain the image to be encrypted and preprocess the image to be encrypted to obtain the preprocessed image to be encrypted;

[0010] S2. Construct a pair of structurally matched switching chaotic time-delay neural network master and slave systems, and in the presence of external disturbances in the channel, use anti-interference synchronization control technology to enable the state of the slave system to asymptotically synchronize with the state of the master system, specifically including:

[0011] S21. Establish a switching synchronization error system that includes external disturbances and can transform the synchronization problem between the master system and slave system of the switching chaotic time-delay neural network into a stability problem for analysis, and design a combined switching strategy for the switching synchronization error system accordingly.

[0012] S22. Design a disturbance observer for estimating external disturbances in the switching synchronization error system, thereby forming an augmented synchronization error system;

[0013] S23. Based on the disturbance observer, a disturbance compensation controller is established. The disturbance compensation controller can ensure that the augmented synchronization error system asymptotically converges to zero, thereby realizing anti-interference synchronization of the switching chaotic time-delay neural network master system and slave system.

[0014] S3. Based on the synchronous switching chaotic time-delay neural network master system, an encryption key for the preprocessed image to be encrypted is generated, and the encryption key is used to encrypt the preprocessed image to be encrypted to obtain an encrypted image.

[0015] S4. A synchronous switching chaotic time-delay neural network generates a decryption key from the system and uses the decryption key to perform the inverse operation on the encrypted image to achieve image decryption.

[0016] Furthermore, the established switching chaotic neural network master system is represented as follows:

[0017] ;

[0018] in, and These represent the switching states and outputs of the time-delay neural network master system, respectively. for The derivative; It is an external input vector; Indicates a switching signal. Represents a set , It is a positive integer; and It is a known constant matrix. Is affected Indicates the subsystem index; Represents the initialization function; This represents the activation function of a continuously bounded neuron. ,and , s =1,2,…, n , n This indicates the number of neurons in a neural network;

[0019] It is time-varying and time-delayed, and satisfies the following constraints:

[0020] ;

[0021] in, Given constants, for The derivative;

[0022] at the same time, Must meet:

[0023] ;

[0024] in, and It is a known constant.

[0025] Furthermore, the established switching chaotic time-delay neural network is represented from the system as follows:

[0026] ;

[0027] in, and These are switching the chaotic time-delay neural network from the system's state and output. yes The derivative; It is a known constant matrix; For disturbance compensation controller;

[0028] An unknown disturbance generated by an external system is represented as:

[0029] ;

[0030] in, It refers to the external system status. express The derivative of and It is a known constant matrix.

[0031] Furthermore, in S21, the specific content of establishing a switching synchronization error system that includes external disturbances and can transform the synchronization problem between the master system and slave system of the switching chaotic time-delay neural network into a stability problem for analysis, and designing the corresponding combined switching strategy of the switching synchronization error system, includes:

[0032] Based on the aforementioned switching chaotic time-delay neural network master and slave systems, the following is defined:

[0033] ,

[0034] ,

[0035] ,

[0036] ,

[0037] Furthermore, a switching synchronization error system is established, represented as:

[0038] ;

[0039] in, express The derivative;

[0040] The combined switching strategy for the switching synchronization error system is designed as follows:

[0041] ;

[0042] Among them, switching signal express A subsystem that is always active. This refers to the period of stay.

[0043] This represents the set of candidate subsystems that can be switched after excluding the current subsystem. ,Right now Sets represented by intervals , Less than Positive integers;

[0044] , express The state vector at time step contains accumulated information about the current system state and historical states. When, it indicates the current subsystem Its performance is no worse than that of the candidate subsystem The performance remains unchanged. , and This represents the positive definite matrix function for different subsystems corresponding to different time periods.

[0045] Furthermore, the disturbance observer designed for estimating external disturbances in the switching synchronization error system is expressed as follows:

[0046]

[0047] in, , , Indicates the gain of the perturbation observer; express The derivative;

[0048] Define symbols The augmented synchronization error system is then represented as:

[0049] .

[0050] Furthermore, a disturbance compensation controller is established based on the disturbance observer, expressed as follows:

[0051] ,

[0052] in, The gain of the disturbance compensation controller to be determined; Indicates unknown disturbance The estimated value.

[0053] Further, in S3, the specific steps of generating an encryption key for the preprocessed image to be encrypted based on the synchronous switching chaotic time-delay neural network master system, and encrypting the preprocessed image to be encrypted using the encryption key to obtain the encrypted image include:

[0054] S31. Based on the pixel size of each single-channel pixel value matrix, a random number algorithm is used to randomly generate the row scrambling index perm_row and the column scrambling index perm_col.

[0055] S32. Perform two-dimensional row and column scrambling on each single-channel pixel value matrix based on the row scrambling index perm_row and the column scrambling index perm_col. The processing formula includes:

[0056] ,

[0057] ,

[0058] in, This represents the pixel value after scrambling. This represents the pixel value after row and column scrambling.

[0059] S33. Construct three sets of key matrices for single-channel pixel value matrix encryption using the state of the synchronous switching time-delay neural network master system, and encrypt the three single-channel pixel value matrices respectively based on the encryption keys;

[0060] S34. Merge the three encrypted single-channel pixel value matrices to obtain the encrypted image.

[0061] Furthermore, in S33, the specific steps of constructing three sets of key matrices for encrypting single-channel pixel value matrices using the state of the synchronously switching time-delay neural network master system, and encrypting the three single-channel pixel value matrices based on the encryption keys respectively, include:

[0062] S331. Select the state sample of the switching time-delay neural network master system after the synchronization time.

[0063] S332. Establish a one-to-one correspondence between state samples and pixel positions based on the pixel order in the single-channel pixel value matrix;

[0064] S333. Generate an encryption key according to the following key generation rules, and encrypt the three single-channel pixel value matrices based on the encryption key, wherein:

[0065] The encryption key is represented as:

[0066] ;

[0067] The encrypted single-channel pixel value matrix is ​​represented as follows:

[0068] ;

[0069] in, This indicates that the switching time-delay neural network master system is in time. The state; Represents a nonlinear mapping function; This represents the magnification factor of the corresponding single-channel pixel value matrix; This is an XOR operation; The size of the corresponding pixel position generated by the main system state is The key matrix.

[0070] Beneficial Effects: This invention fully utilizes the nonlinear dynamic characteristics of switched-delay chaotic neural networks, the high complexity brought by the switching mechanism, and the robust advantages of anti-interference synchronization control technology. Through the collaborative design of a disturbance observer and a disturbance compensation controller, it achieves precise synchronization of the master-slave system under complex external disturbance environments. Simultaneously, it fully leverages the chaotic characteristics and switching mechanism of switched-delay chaotic neural networks to achieve high-security image encryption. This invention not only theoretically expands switched-delay neural network synchronization technology and enriches the design ideas for anti-interference synchronization control, but also provides a simple, easy-to-implement, highly anti-interference, and secure image encryption solution in engineering practice, ensuring the reliability of encryption and decryption in complex application scenarios and providing efficient technical support for the secure storage and transmission of image data. Attached Figure Description

[0071] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] Figure 1 This is a flowchart of an image encryption / decryption method based on switching chaotic neural network anti-interference synchronization in this invention;

[0073] Figure 2 This is a diagram of the encryption and decryption framework based on the switching time-delay chaotic neural network anti-interference synchronization technology in this invention.

[0074] Figure 3 This is the phase diagram of the switched chaotic time-delay neural network in an embodiment of the present invention;

[0075] Figure 4 This is a schematic diagram of the switching signal generated by the combined switching strategy in an embodiment of the present invention;

[0076] Figure 5 This is a diagram showing the result of image encryption in an embodiment of the present invention;

[0077] Figure 6 This is a diagram showing the successful image decryption result under interference conditions in an embodiment of the present invention;

[0078] Figure 7 This is a comparison chart showing the image decryption failure when the disturbance compensation controller fails to estimate the interference in an embodiment of the present invention.

[0079] Figure 8 This is a histogram of the RGB channels before and after encryption in an embodiment of the present invention. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] This embodiment provides an image encryption / decryption method based on switching chaotic neural network anti-interference synchronization, such as... Figure 1 and Figure 2 As shown, the specific steps include:

[0082] S1. Obtain the image to be encrypted and preprocess the image to be encrypted to obtain the preprocessed image to be encrypted;

[0083] S2. Construct a pair of structurally matched switching chaotic time-delay neural network master and slave systems. The phase diagram of the switching chaotic time-delay neural network is as follows: Figure 3 As shown, in the presence of external disturbances in the channel, anti-interference synchronization control technology is used to enable the state of the slave system to asymptotically synchronize with the state of the master system, specifically including:

[0084] S21. Establish a switching synchronization error system that includes external disturbances and can transform the synchronization problem between the master system and slave system of the switching chaotic time-delay neural network into a stability problem for analysis, and design a combined switching strategy for the switching synchronization error system accordingly, thereby laying the foundation for the design of the disturbance observer and the derivation of the synchronization conditions.

[0085] S22. Design a disturbance observer for estimating external disturbances in the switching synchronization error system, thereby forming an augmented synchronization error system;

[0086] S23. Based on the disturbance observer, a disturbance compensation controller is established. The disturbance compensation controller can ensure that the augmented synchronization error system asymptotically converges to zero, thereby realizing anti-interference synchronization of the switching chaotic time-delay neural network master system and slave system.

[0087] S3. Based on the synchronous switching chaotic time-delay neural network master system, an encryption key for the preprocessed image to be encrypted is generated, and the encryption key is used to encrypt the preprocessed image to be encrypted to obtain an encrypted image.

[0088] S4. A synchronous switching chaotic time-delay neural network generates a decryption key from the system and uses the decryption key to perform the inverse operation on the encrypted image to achieve image decryption.

[0089] Specifically, in this embodiment, the decryption process is the inverse of the encryption process. Therefore, after obtaining the decryption key matrix, an XOR operation can be performed, followed by reverse column scrambling and reverse row scrambling to recover the original image.

[0090] Specifically, this embodiment uses the chaotic state sequence of the switching chaotic time-delay neural network master system (sender) to construct the encryption key, uses the state synchronized from the system (receiver) by the switching chaotic time-delay neural network to construct the decryption key, and combines a two-dimensional pixel scrambling and diffusion mechanism to achieve high-security encryption of color images.

[0091] Specifically, this embodiment constructs a master-switching time-delay neural network (master system) model integrating time-varying delays, switching signals, and external system disturbance terms. The resulting chaotic state is directly used as a highly sensitive key source for image encryption, laying a core foundation for encryption security. Addressing key issues such as synchronization performance degradation and inconsistent key generation easily caused by external disturbances, this embodiment further constructs a slave-switching time-delay neural network (slave system) affected by external disturbances and introduces an external system to construct a disturbance observer, achieving accurate estimation and dynamic compensation of external disturbances. A synchronization error system is constructed based on the master-slave system, and a disturbance compensation controller is specifically designed to ensure that the slave system can stably approximate the state trajectory of the master system under the dual influence of time-varying delays and external disturbances, achieving a highly reliable synchronization effect and ensuring consistency for subsequent encryption and decryption. Simultaneously, based on the master-slave system synchronization, this embodiment utilizes the synchronization state of the master system to construct three independent key matrices, corresponding to the R, G, and B channels of the color image for encryption processing. On the decryption end, thanks to the anti-interference synchronization characteristics of the slave system and the master system, the slave system can generate a key matrix and key sequence that are completely consistent with the encryption end; by performing reverse diffusion and reverse scrambling operations, lossless reconstruction of the encrypted image can be achieved.

[0092] Specifically, this embodiment overcomes the limitations of traditional non-switching neural network encryption schemes in terms of key space complexity and anti-interference capability. It innovatively designs a combined switching method and combines it with efficient anti-interference synchronization control technology to construct an encryption and decryption system based on switching chaotic time-delay neural network anti-interference synchronization control technology. This design not only overcomes the single key space of traditional non-switching time-delay neural networks, but also enhances the sensitivity of the encryption system to initial values, switching signals, and control parameters, thereby increasing the key space complexity. Furthermore, it effectively achieves accurate compensation for external uncertain disturbances through a disturbance observer, significantly improving the synchronization stability and anti-interference performance of the switching time-delay neural network. In addition, it expands the key space dimension by relying on the switching mechanism and chaotic characteristics, providing a more secure and robust technical solution for image encryption.

[0093] In a specific embodiment, S1 involves acquiring the image to be encrypted and preprocessing it to obtain the preprocessed image to be encrypted. The specific steps include:

[0094] S11. Read the image to be encrypted and separate its R, G, and B channels to obtain three independent single-channel pixel value matrices.

[0095] S12. Obtain the pixel dimensions of each single-channel pixel value matrix, with height m and width n, thereby determining the total number of pixels in the image and laying the foundation for subsequent pixel encryption operations.

[0096] S13. Convert each single-channel pixel value matrix into a numeric type suitable for cryptographic operations, such as double (double).

[0097] Specifically, the preprocessed image to be encrypted generated by the above steps lays the foundation for subsequent key generation and pixel operations.

[0098] In a specific embodiment, the established switching chaotic neural network master system is represented as follows:

[0099] ;

[0100] in, and These represent the switching states and outputs of the time-delay neural network master system, respectively. for The derivative; It is an external input vector; Indicates a switching signal. Represents a set , It is a positive integer; and It is a known constant matrix. Is affected Indicates the subsystem index; Represents the initialization function; This represents the activation function of a continuously bounded neuron. ,and , s =1,2,…, n , n This indicates the number of neurons in a neural network;

[0101] It is time-varying and time-delayed, and satisfies the following constraints:

[0102] ;

[0103] in, Given constants, for The derivative;

[0104] at the same time, Must meet:

[0105] ;

[0106] in, and It is a known constant.

[0107] In a specific embodiment, the established switching chaotic time-delay neural network is represented from the system as follows:

[0108] ;

[0109] in, and These are switching the chaotic time-delay neural network from the system's state and output. yes The derivative; It is a known constant matrix; For disturbance compensation controller;

[0110] An unknown disturbance generated by an external system is represented as:

[0111] ;

[0112] in, It refers to the external system status. express The derivative of and It is a known constant matrix.

[0113] In a specific embodiment, S21 involves establishing a switching synchronization error system that includes external disturbances and can transform the synchronization problem between the master system and slave system of the switching chaotic time-delay neural network into a stability problem for analysis. The specific content of designing the combined switching strategy for the switching synchronization error system includes:

[0114] Based on the aforementioned switching chaotic time-delay neural network master and slave systems, the following is defined:

[0115] ,

[0116] ,

[0117] ,

[0118] ,

[0119] Furthermore, a switching synchronization error system is established, represented as:

[0120] ;

[0121] in, express The derivative;

[0122] Design a combined switching strategy for the switching synchronization error system. A schematic diagram of the switching signal generated by the combined switching strategy is shown below. Figure 4 As shown, it is represented as:

[0123] ;

[0124] Among them, switching signal express A subsystem that is always active. This refers to the period of stay. This represents the set of candidate subsystems that can be switched after excluding the current subsystem. ,Right now Sets represented by intervals , Less than Positive integers;

[0125] , express The state vector at time step contains accumulated information about the current system state and historical states. When, it indicates the current subsystem Its performance is no worse than that of the candidate subsystem The performance remains unchanged. .

[0126] In a specific embodiment, the disturbance observer designed to estimate external disturbances in the switching synchronization error system is represented as follows:

[0127]

[0128] in, , , Indicates the gain of the perturbation observer; express The derivative;

[0129] Define symbols The augmented synchronization error system is then represented as:

[0130] .

[0131] Specifically, this embodiment takes a switched chaotic time-delay neural network as the research background. In view of the unavoidable external disturbance problem in practical applications, it achieves accurate estimation and dynamic compensation of external disturbances through the collaborative design of a combination of switching strategy and disturbance observer technology, which significantly improves the robustness of the synchronization performance of the switched time-delay neural network.

[0132] In a specific embodiment, to overcome unknown disturbances The impact on expected synchronization performance, based on the disturbance observer, is established by a disturbance compensation controller, expressed as follows:

[0133] ,

[0134] in, The gain of the disturbance compensation controller to be determined; Indicates unknown disturbance The estimated value.

[0135] Specifically, the disturbance compensation controller can integrate the disturbance estimate output by the disturbance observer to achieve disturbance compensation, making the disturbance estimation error asymptotically approach zero and ensuring the stability of the closed-loop switching synchronization error system.

[0136] In a specific embodiment, S3 involves generating an encryption key for the preprocessed image to be encrypted based on the synchronized switching chaotic time-delay neural network master system, and using the encryption key to encrypt the preprocessed image to obtain an encrypted image. The specific steps include:

[0137] S31. To break the inherent spatial arrangement structure of the image, the row scrambling index perm_row and the column scrambling index perm_col are randomly generated based on the pixel size of each single-channel pixel value matrix and using a random number algorithm.

[0138] S32. Based on the row scrambling index perm_row and the column scrambling index perm_col, perform two-dimensional row and column scrambling on each single-channel pixel value matrix to achieve double scrambling of pixel positions in two-dimensional space. The processing formula includes:

[0139] ,

[0140] ,

[0141] in, This represents the pixel value after scrambling. This represents the pixel value after row and column scrambling.

[0142] S33. Construct three sets of key matrices for single-channel pixel value matrix encryption using the state of the synchronous switching time-delay neural network master system, and encrypt the three single-channel pixel value matrices respectively based on the encryption keys;

[0143] In a specific embodiment, S33, the specific steps of constructing three sets of key matrices for encrypting single-channel pixel value matrices using the state of the synchronously switching time-delay neural network master system, and encrypting the three single-channel pixel value matrices based on the encryption keys respectively, include:

[0144] S331. Select the state sample of the switching time-delay neural network master system after the synchronization time.

[0145] S332. Establish a one-to-one correspondence between state samples and pixel positions based on the pixel order in the single-channel pixel value matrix;

[0146] S333. Generate an encryption key according to the following key generation rules, and encrypt the three single-channel pixel value matrices based on the encryption key, wherein:

[0147] The encryption key is represented as:

[0148] ;

[0149] The encrypted single-channel pixel value matrix is ​​represented as follows:

[0150] ;

[0151] in, This indicates that the switching time-delay neural network master system is in time. The state; Represents a nonlinear mapping function; This represents the magnification factor of the corresponding single-channel pixel value matrix, used to enhance the dynamic range of the key; This is an XOR operation; The size of the corresponding pixel position generated by the main system state is The key matrix;

[0152] S34. Merge the three encrypted single-channel pixel value matrices to obtain the encrypted image.

[0153] Specifically, the key calculation rules for the R, G, and B channels, using the encryption key generated in the synchronization state, include:

[0154] R-channel key: ,

[0155] G-channel key: ,

[0156] Channel B key: ,

[0157] in, , and These are the magnification factors for the R, G, and B single-channel pixel value matrices, respectively; and To switch the state of the time-delay neural network master system.

[0158] Specifically, this embodiment, based on the synchronization state vector of the main system and combined with a preset sampling step size and synchronization starting point, accurately samples and reassembles the system state to generate a chaotic key sequence with complex distribution, strong randomness, and excellent anti-predictability. A row-column scrambling index is constructed based on this chaotic key sequence to spatially rearrange the pixel matrix of the original image, completely destroying the inherent spatial structure and inter-pixel correlation of the image, achieving preliminary encryption. Subsequently, using the dedicated key matrix corresponding to each channel, a bitwise XOR pixel diffusion operation is performed on the scrambled image to further enhance the encryption effect.

[0159] Specifically, such as Figure 5 The image shown is the result of image encryption, displaying a color image after scrambling, diffusion, and XOR operation with a chaotic key. The encrypted image exhibits overall random noise characteristics, making it visually indistinguishable from the original image content, reflecting the effectiveness of the encryption algorithm against statistical analysis attacks. Figure 6 The image shown is the result after successful image decryption. By employing the same chaotic sequence and inverse scrambling strategy as the encryption end, the original image was successfully recovered, and the visual quality is identical to the original. Figure 1 The consistency indicates that the synchronization mechanism proposed in this embodiment can guarantee the complete consistency of the chaotic state of the master and slave systems, thereby achieving correct and reliable image decryption.

[0160] This embodiment derives sufficient conditions for the asymptotic stability of the augmented synchronization error system by constructing a time-varying Lyapunov-Krasovskii functional, including:

[0161] Lemma 1: For a vector sum matrix For an n-order positive definite matrix, the following inequality holds:

[0162] ,

[0163] ;

[0164] Lemma 2: For differentiable vectors ,matrix For an N-dimensional positive definite matrix, and The following conclusion holds true:

[0165] ,

[0166] in, ,and

[0167] ,

[0168] ,

[0169] ,

[0170] Lemma 3: For differentiable vectors , ,and For a scalar, the following inequalities hold:

[0171] ,

[0172] in,

[0173] ;

[0174] ;

[0175] ;

[0176] ;

[0177] ;

[0178] Construct the following time-varying Lyapunov–Krasovskii functional, expressed as:

[0179] ,

[0180] ,

[0181] ,

[0182] ,

[0183] ,

[0184] ,

[0185] ,

[0186] ,

[0187] in, , Indicates the transition time between adjacent times and The determined number A switching interval, express The derivative; All are positive definite matrix functions whose dimensions are known and change with the switching mode, and satisfy the following conditions:

[0188] ;

[0189] in,

[0190] , , Or 2;

[0191] ;

[0192] To ensure the stability of the augmented synchronization error system, the following inequality must hold:

[0193] , ,

[0194] , ,

[0195] in, for The derivative;

[0196] To facilitate a unified solution to the above inequalities, the derivative of the Lyapunov–Krasovskii functional is expressed in a form that can be verified using linear matrix inequalities. Therefore, this embodiment makes the following unified stipulations regarding the matrices and symbols used in the derivation: All are symmetric positive definite matrices consistent with the system state dimension; Represented by matrix and The combined block structure matrix, ;

[0197] , ,

[0198] , ,

[0199] ,

[0200] ,

[0201] ,

[0202] ,

[0203] ,

[0204] in, These are known constants;

[0205] After unifying the notation as described above, we can further derive the following theorem to make the augmented synchronization error system asymptotically stable:

[0206] ,

[0207] ,

[0208] ,

[0209] ,

[0210] ,

[0211] ,

[0212] ,

[0213] ,

[0214] ,

[0215] ,

[0216] in, and Represents a positive definite diagonal matrix;

[0217] ,

[0218] , , ,

[0219] , ,

[0220] ,

[0221] ,

[0222] Based on the above theorems, we can conclude that:

[0223] ,

[0224] ,

[0225] In the formula, Given a constant, and A positive definite matrix function representing the time periods corresponding to different subsystems;

[0226] The above analysis shows that, in the presence of external disturbances, the augmented synchronization error system is asymptotically stable, and the slave system state can accurately track the master system state. On the one hand, it maintains the inherent chaotic characteristics and sensitivity to initial values ​​of the master system, and can generate high-dimensional, high-complexity key sequences; on the other hand, through master-slave system synchronization, the sending and receiving ends can still obtain consistent keys without directly transmitting keys, providing a consistent and reliable key foundation for image encryption and decryption.

[0227] Specifically, such as Figure 7 As shown, a set of comparative experiments demonstrates that when the disturbance-free controller suppresses disturbances, the slave system struggles to maintain synchronization with the master system, leading to a significant deviation between the chaotic key sequence generated at the decryption end and that at the encryption end. This key discrepancy directly causes decryption failure, making it impossible to recover the original image. This comparative experimental phenomenon fully demonstrates that the anti-interference synchronization control technology proposed in this embodiment can effectively cope with the damage to the system's synchronization performance caused by unknown external disturbances, significantly improving the stability and robustness of the encryption and decryption system, and verifying the effectiveness and practical application value of this technical solution.

[0228] Specifically, such as Figure 8 The image shows a comparison of the RGB channel histograms before and after encryption. As can be seen from the image, the grayscale value distribution in the three channel histograms of the original image exhibits a clear concentration, with each channel displaying statistical distribution characteristics consistent with the image content. In contrast, the encrypted histogram shows a nearly uniform distribution, with pixel grayscale values ​​scattered within the 0-255 range, making it difficult to observe any statistical characteristics related to the original image.

[0229] The present invention has the following beneficial effects:

[0230] The method proposed in this embodiment fully leverages the nonlinear dynamics of switching time-delay chaotic neural networks, the high complexity brought about by the switching mechanism, and the robustness of anti-interference synchronization control technology. By designing a combined switching strategy and a disturbance compensation control coordination mechanism, it achieves accurate synchronization of the master-slave system under complex external disturbance environments. This method not only enhances the sensitivity of the encryption system to initial values, switching signals, and control parameters, and improves the key space complexity and anti-attack capability, but also effectively resists the impact of external disturbances on synchronization performance, ensuring the reliability of encryption and decryption in complex application scenarios, and providing efficient technical support for the secure storage and transmission of image data.

[0231] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An image encryption and decryption method based on anti-jamming synchronization of switching chaotic neural network, characterized in that, The specific steps include: S1. Obtain the image to be encrypted and preprocess the image to be encrypted to obtain the preprocessed image to be encrypted; S2. Construct a pair of structurally matched switching chaotic time-delay neural network master and slave systems, and in the presence of external disturbances in the channel, use anti-interference synchronization control technology to enable the state of the slave system to asymptotically synchronize with the state of the master system, specifically including: S21. Establish a switching synchronization error system that includes external disturbances and can transform the synchronization problem between the master system and slave system of the switching chaotic time-delay neural network into a stability problem for analysis, and design a combined switching strategy for the switching synchronization error system accordingly. S22. Design a disturbance observer for estimating external disturbances in the switching synchronization error system, thereby forming an augmented synchronization error system; S23. Based on the disturbance observer, a disturbance compensation controller is established. The disturbance compensation controller can ensure that the augmented synchronization error system asymptotically converges to zero, thereby realizing anti-interference synchronization of the switching chaotic time-delay neural network master system and slave system. S3. Based on the synchronous switching chaotic time-delay neural network master system, an encryption key for the preprocessed image to be encrypted is generated, and the encryption key is used to encrypt the preprocessed image to be encrypted to obtain an encrypted image. S4. A synchronous switching chaotic time-delay neural network generates a decryption key from the system and uses the decryption key to perform the inverse operation on the encrypted image to achieve image decryption.

2. The image encryption / decryption method according to claim 1, characterized in that, The established switching chaotic neural network master system is represented as follows: ； where and denote the state and output of the switched time-delay neural network master system, respectively, is the derivative of ; is the external input vector; denotes the switching signal, denotes the set , is a positive integer; and are known constant matrices, is subject to the subsystem index indicated by denotes the initial function; denotes a continuous bounded neuron activation function, , and , s = 1, 2, …, n , n denotes the number of neurons in the neural network; It is time-varying and time-delayed, and satisfies the following constraints: ； in, Given constants, for The derivative; at the same time, Must meet: ； in, and It is a known constant.

3. The image encryption / decryption method according to claim 2, characterized in that, The established switching chaotic time-delay neural network is represented from the system as follows: ； in, and These are switching the chaotic time-delay neural network from the system's state and output. yes The derivative; It is a known constant matrix; For disturbance compensation controller; An unknown disturbance generated by an external system is represented as: ； in, It refers to the external system status. express The derivative of and It is a known constant matrix.

4. The image encryption / decryption method according to claim 3, characterized in that, In S21, the specific content of establishing a switching synchronization error system that includes external disturbances and can transform the synchronization problem between the master system and slave system of the switching chaotic time-delay neural network into a stability problem for analysis, and designing the combined switching strategy of the switching synchronization error system accordingly, includes: Based on the aforementioned switching chaotic time-delay neural network master and slave systems, the following is defined: ， ， ， ， Furthermore, a switching synchronization error system is established, represented as: ； in, express The derivative; The combined switching strategy for the switching synchronization error system is designed as follows: ； Among them, switching signal express A subsystem that is always active. This refers to the period of stay. This represents the set of candidate subsystems that can be switched after excluding the current subsystem. ,Right now Sets represented by intervals , Less than Positive integers; , express The state vector at time step contains accumulated information about the current system state and historical states. When, it indicates the current subsystem Its performance is no worse than that of the candidate subsystem The performance remains unchanged. , and This represents the positive definite matrix function for different subsystems corresponding to different time periods.

5. The image encryption / decryption method according to claim 4, characterized in that, The disturbance observer designed for estimating external disturbances in the switching synchronization error system is denoted as: in, , , Indicates the gain of the perturbation observer; express The derivative; Define symbols The augmented synchronization error system is then represented as: 。 6. The image encryption / decryption method according to claim 5, characterized in that, A disturbance compensation controller is established based on the disturbance observer, expressed as follows: ， in, The gain of the disturbance compensation controller to be determined; Indicates unknown disturbance The estimated value.

7. The image encryption / decryption method according to claim 6, characterized in that, In S3, the specific steps of generating an encryption key for the preprocessed image to be encrypted based on the synchronous switching chaotic time-delay neural network master system, and encrypting the preprocessed image to be encrypted using the encryption key to obtain the encrypted image include: S31. Based on the pixel size of each single-channel pixel value matrix, a random number algorithm is used to randomly generate the row scrambling index perm_row and the column scrambling index perm_col. S32. Perform two-dimensional row and column scrambling on each single-channel pixel value matrix based on the row scrambling index perm_row and the column scrambling index perm_col. The processing formula includes: ， ， in, This represents the pixel value after scrambling. This represents the pixel value after row and column scrambling. S33. Construct three sets of key matrices for single-channel pixel value matrix encryption using the state of the synchronous switching time-delay neural network master system, and encrypt the three single-channel pixel value matrices respectively based on the encryption keys; S34. Merge the three encrypted single-channel pixel value matrices to obtain the encrypted image.

8. The image encryption / decryption method according to claim 7, characterized in that, In S33, the specific steps of constructing three sets of key matrices for encrypting single-channel pixel value matrices using the state of the synchronously switching time-delay neural network master system, and encrypting the three single-channel pixel value matrices based on the encryption keys, include: S331. Select the state sample of the switching time-delay neural network master system after the synchronization time. S332. Establish a one-to-one correspondence between state samples and pixel positions based on the pixel order in the single-channel pixel value matrix; S333. Generate an encryption key according to the following key generation rules, and encrypt the three single-channel pixel value matrices based on the encryption key, wherein: The encryption key is represented as: ； The encrypted single-channel pixel value matrix is ​​represented as follows: ； in, This indicates that the switching time-delay neural network master system is in time. The state; Represents a nonlinear mapping function; This represents the magnification factor of the corresponding single-channel pixel value matrix; This is an XOR operation; The size of the corresponding pixel position generated by the main system state is The key matrix.

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