Image encryption method, device and equipment based on unknown parameter inertial memristor neural network synchronization and storage medium

Abstract

The invention discloses an image encryption method and device based on unknown parameter inertial memristor neural network synchronization, equipment and a storage medium, and relates to the technical field of neural network encryption. The image encryption method based on unknown parameter inertial memristor neural network synchronization comprises the following steps: acquiring driving state data of a driving system and response state data of a response system, and constructing a driving and response error model based on the driving state data and the response state data; determining a synchronous control strategy for the error model; the synchronous control strategy is applied to enable the driving system and the response system to be synchronous and generate a chaotic signal; and performing encryption processing on an image by using the chaotic signal. According to the invention, the anti-attack capability of the image encryption system can be improved.

Description

Technical Field

[0001] This application relates to the field of neural network encryption technology, and in particular to an image encryption method, apparatus, device, and storage medium based on unknown parameter inertial memristor neural network synchronization. Background Technology

[0002] In current image encryption technologies, chaotic encryption methods based on memristor neural networks have attracted attention due to their near-random characteristics. However, most existing schemes assume that the network parameters are known, and when dealing with high-order networks with inertial terms, they generally employ dimensionality-increasing reduction methods, which not only increase computational complexity but also limit the strength of chaotic signals. Parameter uncertainty and dimensionality reduction weaken the security of encryption systems. Therefore, how to improve the anti-attack capability of image encryption systems remains a problem to be solved.

[0003] The above content is only used to help understand the technical solution of this application and does not represent an admission that the above content is prior art. Summary of the Invention

[0004] The main objective of this application is to provide an image encryption method, apparatus, device, and storage medium based on unknown parameter inertial memristor neural network synchronization, aiming to solve the technical problem of how to improve the anti-attack capability of image encryption systems.

[0005] To achieve the above objectives, this application proposes an image encryption method based on synchronization of an inertial memristor neural network with unknown parameters. The method includes: Obtain the drive status data of the drive system and the response status data of the response system, and construct an error model of drive and response based on the drive status data and the response status data; A synchronization control strategy is determined for the error model; The synchronous control strategy is applied to synchronize the drive system and the response system and generate chaotic signals. The chaotic signal is used to encrypt the image.

[0006] In one embodiment, the step of constructing an error model of drive and response based on the drive state data and the response state data includes: Define the state error between the drive state data and the response state data; Based on the non-order reduction method and differential inclusion theory, the driving model and the response model are processed to obtain the error dynamic equation; Based on the error dynamic equation, the error model is established.

[0007] In one embodiment, the step of determining a synchronization control strategy for the error model includes: Design a state feedback controller that includes a gain parameter for the error model; Design adaptive weight update rules for the unknown parameters in the driving model and the response model; The synchronization control strategy is formed by combining the state feedback controller and the adaptive weight update rule.

[0008] In one embodiment, the step of designing an adaptive weight update rule for the unknown parameters in the driving model and the response model includes: Based on the state error, calculate the estimation error of the unknown parameters in the response model; Derive the adaptive update law for the unknown parameters; The adaptive update law is applied to adjust the weights of the unknown parameters in real time, so that the estimation error asymptotically converges, thus obtaining the adaptive weight update law.

[0009] In one embodiment, the step of applying the synchronization control strategy to synchronize the drive system and the response system and generate a chaotic signal includes: Construct a Lyapunov functional for analyzing the stability of the error model; Based on the Lyapunov functional, the stability of the error model is analyzed and a synchronization control criterion is generated; According to the synchronization control criterion, the synchronization control strategy is applied to make the state error asymptotically converge to zero; When synchronization is achieved, chaotic signals are extracted from the driving model or the response model.

[0010] In one embodiment, the step of constructing a Lyapunov functional for analyzing the stability of the error model includes: The positive definite function of the state error is selected as the basis of the Lyapunov functional; The Lyapunov functional is extended by introducing the integral term and time delay term of the state error; Verify that the Lyapunov functional satisfies the stability condition.

[0011] In one embodiment, the step of encrypting the image using the chaotic signal includes: The chaotic signal is converted into an encrypted key stream; The encrypted key stream is used to obfuscate and diffuse the image pixel values ​​to obtain encrypted image data.

[0012] Furthermore, to achieve the above objectives, this application also proposes an image encryption device based on unknown parameter inertial memristor neural network synchronization, the image encryption device based on unknown parameter inertial memristor neural network synchronization comprising: A construction module is used to acquire the drive status data of the drive system and the response status data of the response system, and to construct an error model of drive and response based on the drive status data and the response status data. The determination module is used to determine the synchronization control strategy for the error model; A generation module is used to apply the synchronization control strategy to synchronize the drive system and the response system and generate chaotic signals. An encryption module is used to encrypt the image using the chaotic signal.

[0013] Furthermore, to achieve the above objectives, this application also proposes an image encryption device based on unknown parameter inertial memristor neural network synchronization. The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor. The computer program is configured to implement the steps of the image encryption method based on unknown parameter inertial memristor neural network synchronization as described above.

[0014] In addition, to achieve the above objectives, this application also proposes a storage medium, which is a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the image encryption method based on unknown parameter inertial memristor neural network synchronization as described above.

[0015] In addition, to achieve the above objectives, this application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the image encryption method based on unknown parameter inertial memristor neural network synchronization as described above.

[0016] This application provides an image encryption method based on synchronization using an inertial memristor neural network with unknown parameters. The method involves acquiring drive state data of a driving system and response state data of a response system, constructing an error model of the driving and response systems based on these data, determining a synchronization control strategy for the error model, applying the synchronization control strategy to synchronize the driving system and the response system and generate a chaotic signal, and using the chaotic signal to encrypt the image. This application improves the anti-attack capability of the image encryption system by solving the synchronization control problem of the inertial memristor neural network with uncertain parameters and employing a non-order reduction method. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating an embodiment of the image encryption method based on unknown parameter inertial memristor neural network synchronization provided in this application. Figure 2 This is a flowchart illustrating Embodiment 2 of the image encryption method based on unknown parameter inertial memristor neural network synchronization provided in this application; Figure 3 This is a schematic diagram of the module structure of an image encryption device based on unknown parameter inertial memristor neural network synchronization according to an embodiment of this application; Figure 4 This is a schematic diagram of the device structure of the hardware operating environment involved in the image encryption method based on unknown parameter inertial memristor neural network synchronization in the embodiments of this application.

[0020] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0021] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0022] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0023] This application obtains the driving state data of the driving system and the response state data of the response system, constructs an error model of driving and response based on the driving state data and the response state data, determines a synchronization control strategy for the error model, applies the synchronization control strategy to synchronize the driving system and the response system and generate a chaotic signal, and uses the chaotic signal to encrypt the image.

[0024] In current image encryption technologies, chaotic encryption methods based on memristor neural networks have attracted attention due to their near-random characteristics. However, most existing schemes assume that the network parameters are known, and when dealing with high-order networks with inertial terms, they generally employ dimensionality-increasing reduction methods, which not only increase computational complexity but also limit the strength of chaotic signals. Parameter uncertainty and dimensionality reduction weaken the security of encryption systems. Therefore, how to improve the anti-attack capability of image encryption systems remains a problem to be solved.

[0025] This application improves the anti-attack capability of image encryption systems by solving the synchronization control problem of parameter-delayed inertial memristor neural networks and adopting a non-decrease-order method.

[0026] Based on this, the embodiments of this application provide an image encryption method based on unknown parameter inertial memristor neural network synchronization, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the image encryption method based on unknown parameter inertial memristor neural network synchronization according to this application.

[0027] In this embodiment, the image encryption method based on unknown parameter inertial memristor neural network synchronization includes steps S10~S40: Step S10: Obtain the drive status data of the drive system and the response status data of the response system, and construct an error model of drive and response based on the drive status data and the response status data; It should be noted that the executing entity in this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or an electronic device capable of performing the above functions, such as an image encryption device based on unknown parameter inertial memristor neural network synchronization. The following description uses an image encryption device based on unknown parameter inertial memristor neural network synchronization as an example to illustrate this embodiment and the subsequent embodiments.

[0028] It should be noted that memristors are the fourth fundamental circuit element, in addition to resistors, capacitors, and inductors. Because memristors can simulate the function of brain synapses, memristive neural networks (MNNs) have been developed and successfully applied in signal processing, image processing, associative memory, pattern recognition, robotics and control, and other engineering and scientific fields. Currently, there are two types of MNN models in terms of differential order: first-order MNNs and second-order MNNs with inertial terms. Compared to first-order MNNs, MNNs with inertial terms have significant advantages such as larger storage capacity and stronger fault tolerance. There are two common research methods for MNNs: one is to transform the second-order MNN system into a first-order system for study through order reduction methods, but this method leads to an increase in system dimensionality and computational burden. The other is the non-order reduction method, which preserves the higher-order dynamic information of the system and avoids the problem of increased computational burden due to increased system dimensionality, but it is more difficult to study. The synchronization control problem of memristive neural networks (IMNNs) with inertial terms can not only improve the stability of the network but also enhance its performance in practical applications. In particular, in the digital age, images carry a large amount of sensitive information. Image encryption ensures the confidentiality and integrity of visual content during storage and transmission by transforming it into unrecognizable gibberish. Memristive neural networks generate chaotic signals, which possess unique dynamic characteristics such as extreme sensitivity to initial conditions, aperiodicity, wide spectrum, and quasi-randomness. Applying them to encryption systems can greatly enhance the complexity and unpredictability of the algorithm, effectively resisting statistical analysis and other cracking methods, and significantly improving the anti-attack capability and overall security of the encryption system. This application studies the synchronization control problem of time-delay IMNNs with uncertain parameters. First, IMNNs are analyzed based on set-valued mapping and differential inclusion theory, and a non-reduction-order method is used to establish a driver-response error system. Second, a state feedback controller and a weight update rule for unknown parameters are designed for the error system. Finally, Lyapunov stability theory is applied to analyze the error system and a synchronization control criterion for time-delay IMNNs with unknown parameters is given.

[0029] In one feasible approach, the step of constructing an error model of drive and response based on the drive state data and the response state data includes: defining the state error between the drive state data and the response state data; processing the drive model and the response model based on a non-order reduction method and differential inclusion theory to obtain an error dynamic equation; and establishing the error model according to the error dynamic equation.

[0030] It should be noted that the time-delay IMNNs considered are: (Formula 1) in, Indicates the first in the network i At time 1 neuron t state, For the first i The capacitance correlation coefficient of each neuron. It is the first i One neuron in t Damping coefficient at time t, For the first i The first neuron to the second j The connection weights of each neuron It is the first i The first neuron to the second j The dynamic connection weights of each neuron with time delay, and It is unknown. and The activation functions representing neurons with and without time delay. It is time-varying and time-delayed, satisfying and ( (These are positive numbers) It is an external disturbance.

[0031] Based on the simplification of the memristor, the weighting of the memristor is considered as follows: (Formula 2) make ,in All are constants, switch switching It is a positive number.

[0032] To arrive at the main conclusions, we present commonly used assumptions for time-delay MNNs. For example, the neural activation function... and yes Lipschitz Continuous, which means for any constant and All of the following conditions must be met: (Formula 3) in, and It is a positive constant. Another example is the neural activation function. and It is bounded and satisfies the following conditions: (Formula 4) Where, constant , .

[0033] Considering that MNNs is a right-hand discontinuous differential equation, we consider the solution in the Filippov sense. Based on differential inclusion and set-valued mapping theory, Equation 1 above can be expressed in the following form: (Formula 5) in, (Formula 6) in, .

[0034] Equivalent land exists , so that: (Formula 7) Considering driver-response synchronization, and taking the time-delay IMNNs model (Equation 1) as the driving system, the response system with unknown parameters is described as follows: (Formula 8) For response systems, and This represents the activation function of neurons with and without time delay. , , , For unknown parameters, Control input for drive-response synchronization.

[0035] Based on differential inclusion and set-valued mapping theory, the response system can be represented in the following form: (Formula 9) Equivalent land exists , so that: (Formula 10) definition For the error of the drive-response system, the synchronization error system can be obtained. (Formula 11) in: (Formula 12) Step S20: Determine a synchronization control strategy for the error model; It should be noted that a state feedback controller can be designed, in which the controller gain can be adjusted according to the error magnitude, and an adaptive update rule can be designed for unknown parameters (such as damping coefficient and connection weight). The combination of the two forms a complete control strategy.

[0036] In one feasible approach, the step of determining the synchronization control strategy for the error model includes: designing a state feedback controller containing gain parameters for the error model; designing an adaptive weight update rule for the unknown parameters in the driving model and the response model; and combining the state feedback controller and the adaptive weight update rule to form the synchronization control strategy. The step of designing the adaptive weight update rule for the unknown parameters in the driving model and the response model includes: calculating the estimation error of the unknown parameters in the response model based on the state error; deriving the adaptive update rule for the unknown parameters; and applying the adaptive update rule to adjust the weights of the unknown parameters in real time, causing the estimation error to asymptotically converge, thereby obtaining the adaptive weight update rule.

[0037] It should be noted that a controller was designed to implement time-delayed IMNNs with unknown parameters, i.e., to synchronize Equations 1 and 12 above. The controller form is as follows: (Formula 13) in, , , Let be the gain of the controller, and satisfy: (Formula 14) There are positive numbers The model parameter update law satisfies (Formula 15) Then, the IMNNs driving system and response system with uncertain parameters can be synchronized under the action of the controller.

[0038] Step S30: Apply the synchronization control strategy to synchronize the drive system and the response system and generate a chaotic signal; It should be noted that by applying the controller output and updating the parameter estimates in real time, the state error is asymptotically converged to zero, thus achieving synchronization. After synchronization, a chaotic time series with quasi-random characteristics is extracted from the output of the driving neural network as a chaotic signal.

[0039] Step S40: Encrypt the image using the chaotic signal.

[0040] It should be noted that the chaotic signal is quantized into an encryption key stream, and then the image pixel matrix is ​​permuted (obfuscated) and XORed (diffused) to generate unrecognizable encrypted image data.

[0041] In one feasible approach, the step of encrypting the image using the chaotic signal includes: converting the chaotic signal into an encryption key stream; and using the encryption key stream to perform obfuscation and diffusion operations on the image pixel values ​​to obtain encrypted image data.

[0042] It should be noted that the chaotic time series is quantized, for example, by mapping it to the integer range [0, 255] through modulo operation, to generate a keystream matrix that matches the image pixel size. First, obfuscation is performed: pixel positions are permuted according to the keystream; then, diffusion is performed: the pixel values ​​are XORed bit by bit with the keystream to change the statistical distribution of pixel values, and finally, the encrypted image is output.

[0043] This embodiment acquires the drive state data of the drive system and the response state data of the response system, constructs an error model of drive and response based on the drive state data and the response state data, determines a synchronization control strategy for the error model, applies the synchronization control strategy to synchronize the drive system and the response system and generate a chaotic signal, and uses the chaotic signal to encrypt the image. This embodiment improves the anti-attack capability of the image encryption system by solving the synchronization control problem of parameter uncertain time-delay inertial memristor neural networks and adopting a non-order reduction method.

[0044] Based on the first embodiment of this application, in the second embodiment of this application, the content that is the same as or similar to that in the first embodiment described above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 2 Step S30 also includes steps S301 to S304: Step S301: Construct a Lyapunov functional for analyzing the stability of the error model; It should be noted that the Lyapunov functional is a special kind of "energy function" used to prove whether a dynamic system can automatically stabilize.

[0045] In one feasible approach, the steps of constructing a Lyapunov functional for analyzing the stability of the error model include: selecting a positive definite function of the state error as the basic part of the Lyapunov functional; introducing an integral term and a time delay term of the state error to extend the Lyapunov functional; and verifying that the Lyapunov functional satisfies the stability condition.

[0046] It should be noted that the Lyapunov functional is constructed as follows: (Formula 16) in, (Formula 17) Differentiating the Lyapunov functional along the trajectory of the error system, we obtain: (Formula 18) (Formula 19) (Formula 20) Based on formulas 18, 19, and 20 above, the derivatives of the Lyapunov functional can be obtained from these three derivative functions: (Formula 21)

[0047] According to the theory of the mean inequality, we can obtain: (Formula 22) Therefore, the derivative of the Lyapunov functional, i.e., Formula 21, can be rewritten as: (Formula 23) And set the following conditions: (Formula 24) (Formula 25) (Formula 26) We can obtain: (Formula 27) Therefore, the drive system and the response system can achieve synchronization even when parameters are uncertain.

[0048] Step S302: Based on the Lyapunov functional, analyze the stability of the error model and generate a synchronization control criterion; It should be noted that by calculating the derivative of V(t), substituting it into the error equation and control law, and proving the negative definiteness of the derivative through inequality scaling, sufficient conditions for synchronization (such as the gain parameter needing to be greater than a certain threshold) are obtained, thus forming the synchronization control criterion.

[0049] Step S303: According to the synchronization control criterion, apply the synchronization control strategy to make the state error asymptotically converge to zero; It should be noted that the controller gain is set according to the criteria, and control signals and parameter updates are applied in real time to bring the state error index to converge.

[0050] Step S304: When synchronization is achieved, extract chaotic signals from the driving model or the response model.

[0051] It should be noted that after synchronization, the time series output by the driving neural network is collected. This series exhibits non-periodic randomness due to its chaotic characteristics, and serves as the chaotic signal required for encryption.

[0052] This embodiment constructs a Lyapunov functional for analyzing the stability of the error model; based on the Lyapunov functional, the stability of the error model is analyzed and a synchronization control criterion is generated; according to the synchronization control criterion, the synchronization control strategy is applied to make the state error asymptotically converge to zero; when synchronization is achieved, chaotic signals are extracted from the driving model or the response model. This application, through rigorous stability proof and a closed-loop control mechanism, ensures that the driving response system can still achieve accurate synchronization even when parameters are unknown. The resulting chaotic signals have higher unpredictability and initial value sensitivity, thereby directly improving the anti-attack capability of subsequent image encryption.

[0053] This application also provides an image encryption device based on unknown parameter inertial memristor neural network synchronization. Please refer to [link / reference]. Figure 3 The image encryption device based on unknown parameter inertial memristor neural network synchronization includes: Module 10 is used to acquire drive status data of the drive system and response status data of the response system, and to construct an error model of drive and response based on the drive status data and the response status data. The determination module 20 is used to determine a synchronization control strategy for the error model; The generation module 30 is used to apply the synchronization control strategy to synchronize the drive system and the response system and generate chaotic signals. The encryption module 40 is used to encrypt the image using the chaotic signal.

[0054] This embodiment acquires the drive state data of the drive system and the response state data of the response system, constructs an error model of drive and response based on the drive state data and the response state data, determines a synchronization control strategy for the error model, applies the synchronization control strategy to synchronize the drive system and the response system and generate a chaotic signal, and uses the chaotic signal to encrypt the image. This embodiment improves the anti-attack capability of the image encryption system by solving the synchronization control problem of parameter uncertain time-delay inertial memristor neural networks and adopting a non-order reduction method.

[0055] In one embodiment, the construction module 10 is further configured to define the state error between the driving state data and the response state data; process the driving model and the response model based on the non-reduction method and differential inclusion theory to obtain the error dynamic equation; and establish the error model according to the error dynamic equation.

[0056] In one embodiment, the determining module 20 is further configured to design a state feedback controller including gain parameters for the error model; design an adaptive weight update rule for the unknown parameters in the driving model and the response model; and combine the state feedback controller and the adaptive weight update rule to form the synchronization control strategy.

[0057] In one embodiment, the determining module 20 is further configured to calculate the estimation error of the unknown parameters in the response model based on the state error; derive the adaptive update law of the unknown parameters; apply the adaptive update law to adjust the weights of the unknown parameters in real time, so that the estimation error asymptotically converges, thereby obtaining the adaptive weight update rule.

[0058] In one embodiment, the generation module 30 is further configured to construct a Lyapunov functional for analyzing the stability of the error model; based on the Lyapunov functional, analyze the stability of the error model and generate a synchronization control criterion; according to the synchronization control criterion, apply the synchronization control strategy to make the state error asymptotically converge to zero; when synchronization is achieved, extract chaotic signals from the driving model or the response model.

[0059] In one embodiment, the generation module 30 is further configured to select a positive definite function of the state error as the basic part of the Lyapunov functional; introduce an integral term and a time delay term of the state error to extend the Lyapunov functional; and verify that the Lyapunov functional satisfies the stability condition.

[0060] In one embodiment, the encryption module 40 is further configured to convert the chaotic signal into an encryption key stream; and use the encryption key stream to perform obfuscation and diffusion operations on the image pixel values ​​to obtain encrypted image data.

[0061] The image encryption device based on unknown parameter inertial memristor neural network synchronization provided in this application, employing the image encryption method based on unknown parameter inertial memristor neural network synchronization in the above embodiments, can solve the technical problem of how to improve the anti-attack capability of the image encryption system. Compared with the prior art, the beneficial effects of the image encryption device based on unknown parameter inertial memristor neural network synchronization provided in this application are the same as the beneficial effects of the image encryption method based on unknown parameter inertial memristor neural network synchronization provided in the above embodiments, and other technical features in the image encryption device based on unknown parameter inertial memristor neural network synchronization are the same as the features disclosed in the methods of the above embodiments, and will not be repeated here.

[0062] This application provides an image encryption device based on unknown parameter inertial memristor neural network synchronization. The image encryption device based on unknown parameter inertial memristor neural network synchronization includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the image encryption method based on unknown parameter inertial memristor neural network synchronization in the above embodiment 1.

[0063] The following is for reference. Figure 4 This document illustrates a structural schematic diagram of an image encryption device suitable for implementing the unknown parameter inertial memristor neural network synchronization in the embodiments of this application. The image encryption device based on unknown parameter inertial memristor neural network synchronization in the embodiments of this application may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 4 The image encryption device shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0064] like Figure 4As shown, an image encryption device based on unknown parameter inertial memristor neural network synchronization may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in ROM (Read Only Memory) 1002 or a program loaded from storage device 1003 into RAM (Random Access Memory) 1004. RAM 1004 also stores various programs and data required for the operation of the image encryption device based on unknown parameter inertial memristor neural network synchronization. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via bus 1005. Input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to I / O interface 1006: input devices 1007 including, for example, touchscreens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. Communication device 1009 allows the image encryption device based on unknown parameter inertial memristor neural network synchronization to communicate wirelessly or wiredly with other devices to exchange data. Although the figure shows image encryption devices based on unknown parameter inertial memristor neural network synchronization with various systems, it should be understood that it is not required to implement or possess all the systems shown. More or fewer systems can be implemented alternatively.

[0065] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from ROM 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0066] The image encryption device based on unknown parameter inertial memristor neural network synchronization provided in this application, employing the image encryption method based on unknown parameter inertial memristor neural network synchronization in the above embodiments, can solve the technical problem of how to improve the anti-attack capability of the image encryption system. Compared with the prior art, the beneficial effects of the image encryption device based on unknown parameter inertial memristor neural network synchronization provided in this application are the same as the beneficial effects of the image encryption method based on unknown parameter inertial memristor neural network synchronization provided in the above embodiments, and other technical features in the image encryption device based on unknown parameter inertial memristor neural network synchronization are the same as the features disclosed in the previous embodiment method, and will not be repeated here.

[0067] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0068] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0069] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, which are used to execute the image encryption method based on unknown parameter inertial memristor neural network synchronization in the above embodiments.

[0070] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0071] The aforementioned computer-readable storage medium may be included in an image encryption device based on an unknown parameter inertial memristor neural network synchronization; or it may exist independently and not assembled into an image encryption device based on an unknown parameter inertial memristor neural network synchronization.

[0072] The aforementioned computer-readable storage medium carries one or more programs. When these programs are executed by an image encryption device synchronized based on an unknown parameter inertial memristor neural network, the image encryption device synchronized based on the unknown parameter inertial memristor neural network performs the following: acquiring drive state data of the drive system and response state data of the response system; constructing an error model of drive and response based on the drive state data and the response state data; determining a synchronization control strategy for the error model; applying the synchronization control strategy to synchronize the drive system and the response system and generate a chaotic signal; and using the chaotic signal to encrypt the image.

[0073] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0074] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0075] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0076] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described image encryption method based on unknown parameter inertial memristor neural network synchronization. This addresses the technical problem of improving the anti-attack capability of image encryption systems. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the image encryption method based on unknown parameter inertial memristor neural network synchronization provided in the above embodiments, and will not be elaborated upon here.

[0077] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the image encryption method based on unknown parameter inertial memristor neural network synchronization as described above.

[0078] The computer program product provided in this application can solve the technical problem of how to improve the anti-attack capability of image encryption systems. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the image encryption method based on unknown parameter inertial memristor neural network synchronization provided in the above embodiments, and will not be repeated here.

[0079] The above description is only a part of the embodiments of this application and does not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. An image encryption method based on synchronization of an inertial memristor neural network with unknown parameters, characterized in that, The method includes: Obtain the drive status data of the drive system and the response status data of the response system, and construct an error model of drive and response based on the drive status data and the response status data; A synchronization control strategy is determined for the error model; The synchronous control strategy is applied to synchronize the drive system and the response system and generate chaotic signals. The chaotic signal is used to encrypt the image.

2. The method as described in claim 1, characterized in that, The step of constructing an error model of drive and response based on the drive state data and the response state data includes: Define the state error between the drive state data and the response state data; Based on the non-order reduction method and differential inclusion theory, the driving model and the response model are processed to obtain the error dynamic equation; Based on the error dynamic equation, the error model is established.

3. The method as described in claim 1, characterized in that, The steps for determining the synchronization control strategy for the error model include: Design a state feedback controller that includes a gain parameter for the error model; Design adaptive weight update rules for the unknown parameters in the driving model and the response model; The synchronization control strategy is formed by combining the state feedback controller and the adaptive weight update rule.

4. The method as described in claim 3, characterized in that, The steps for designing adaptive weight update rules for the unknown parameters in the driving model and the response model include: Based on the state error, calculate the estimation error of the unknown parameters in the response model; Derive the adaptive update law for the unknown parameters; The adaptive update law is applied to adjust the weights of the unknown parameters in real time, so that the estimation error asymptotically converges, thus obtaining the adaptive weight update law.

5. The method as described in claim 1, characterized in that, The step of applying the synchronization control strategy to synchronize the drive system and the response system and generate a chaotic signal includes: Construct a Lyapunov functional for analyzing the stability of the error model; Based on the Lyapunov functional, the stability of the error model is analyzed and a synchronization control criterion is generated; According to the synchronization control criterion, the synchronization control strategy is applied to make the state error asymptotically converge to zero; When synchronization is achieved, chaotic signals are extracted from the driving model or the response model.

6. The method as described in claim 5, characterized in that, The steps for constructing a Lyapunov functional for analyzing the stability of the error model include: The positive definite function of the state error is selected as the basis of the Lyapunov functional; The Lyapunov functional is extended by introducing the integral term and time delay term of the state error; Verify that the Lyapunov functional satisfies the stability condition.

7. The method as described in claim 1, characterized in that, The step of encrypting the image using the chaotic signal includes: The chaotic signal is converted into an encrypted key stream; The encrypted key stream is used to obfuscate and diffuse the image pixel values ​​to obtain encrypted image data.

8. An image encryption device based on unknown parameter inertial memristor neural network synchronization, characterized in that, The device includes: Obtain the drive status data of the drive system and the response status data of the response system, and construct an error model of drive and response based on the drive status data and the response status data; A synchronization control strategy is determined for the error model; The synchronous control strategy is applied to synchronize the drive system and the response system and generate chaotic signals. The chaotic signal is used to encrypt the image.

9. An image encryption device based on unknown parameter inertial memristor neural network synchronization, characterized in that, The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the image encryption method based on unknown parameter inertial memristor neural network synchronization as described in any one of claims 1 to 7.

10. A storage medium, characterized in that, The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, it implements the image encryption method based on unknown parameter inertial memristor neural network synchronization as described in any one of claims 1 to 7.

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