Inertial neural network encryption method based on class proportion-differential event protocol

Abstract

The invention provides an inertial neural network encryption method based on a class proportion-differential event protocol, and belongs to the technical field of chaotic system encryption. The method comprises the following steps: constructing an inertial neural network model with system parameter modal jump as a drive-response system model; designing a self-adaptive proportional-differential event triggering safety synchronization mechanism and a synchronization controller based on the drive-response system model; the driving system generates a chaotic sequence; combining the chaotic sequence with the original data to generate a ciphertext; the response system triggers a safety synchronization mechanism through a self-adaptive proportional-differential event to be synchronized with the driving system, and a chaotic sequence is obtained; and original data is restored by combining the chaotic sequence and the ciphertext, so that encryption and decryption of the data are realized. According to the method, the influence of external attack interference on inertial neural network synchronization is considered in the chaotic synchronization process, interference factors in an actual system are modeled by establishing the generalized uncertain semi-Markov parameter hopping model, and the encryption security of the chaotic system is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of chaotic system encryption, and particularly to an encryption method for inertial neural networks based on a proportional-derivative-like event protocol. Background Art

[0002] At present, with the rapid development of Internet technology, personal privacy protection has become particularly important. The spread of a large amount of personal information on the network is extremely likely to lead to the leakage of privacy information; therefore, it is particularly necessary to take encryption measures to protect personal information data.

[0003] Currently, the encryption methods for information on the network include: chaos-based encryption, optical encryption, compression encryption, frequency-domain encryption, etc. Among them, the chaotic system is extremely sensitive to the initial conditions, and a tiny error in the initial conditions may lead to completely different motion trajectories. Without knowing the initial conditions, it is almost impossible to predict the long-term trajectory of chaotic encryption. Its chaotic characteristics show good security, so it is widely used. For example, the Chinese patent "CN117857716A Image Encryption Method and System Based on Inertial Neural Network Event-Triggered Synchronization" uses a chaotic map to generate keys to achieve image encryption. However, although this method provides high security, it does not fully consider the influence of multiple factors such as external perturbations to system parameters and network attacks. The event-triggered mechanism it adopts cannot effectively reduce the burden on the communication channel, and lacks a feasible security synchronization strategy in the face of network attacks and system parameter perturbations, affecting the security and stability of the encryption system.

[0004] Therefore, there is a need for an inertial neural network data encryption and decryption method that considers network attacks and system parameter perturbations. Summary of the Invention

[0005] In view of this, the present invention proposes an encryption method for inertial neural networks based on a proportional-derivative-like event protocol, which models factors such as external environmental changes and internal system disturbances by constructing a generalized uncertain semi-Markov parameter jump inertial neural network model; and combines a synchronization controller applicable to hybrid network attack scenarios to solve the problem of insufficient security and stability of the encryption system in the prior art when chaotic encryption faces network attacks or system parameter perturbations.

[0006] To this end, the present invention provides the following technical solutions: An encryption method for inertial neural networks based on a proportional-derivative-like event protocol, comprising: Constructing an inertial neural network model considering internal system parameter perturbations as a drive-response system model; Designing an adaptive proportional-derivative-like event-triggered security synchronization mechanism and a synchronization controller based on the drive-response system model; The drive system generates a chaotic sequence, and combines the chaotic sequence with the original data to generate ciphertext; The response system is synchronized with the drive system through an adaptive proportional-derivative event-triggered synchronization mechanism to obtain the chaotic sequence; the original data is restored by combining the chaotic sequence and the ciphertext.

[0007] Furthermore, the internal parameter perturbation of the system is described by a generalized uncertain semi-Markov parameter jump mechanism.

[0008] Furthermore, the drive-response system model includes: S1. Establish the drive and response neural dynamic equations of a time-delay inertial neural network with a Markov jump structure:

[0009] Where: represents the state of the -th neuron at time ; and are known scalar values; and are the weights connecting the neurons; is the activation function of the -th neuron, satisfying the Lipschitz condition, where , is a natural number; is the external input applied to the -th neuron; the time-varying delay is in the interval , and its derivative is in the interval , where , and are all real numbers; the initial conditions specify that for , there is and , and and both belong to the function space; S2. Introduce the variable substitution formula , and reconstruct the drive and response neural dynamic equations of the time-delay inertial neural network with a Markov jump structure into a first-order dynamic equation:

[0010] Where: ; The initial condition is , where ; S3. Use the Markov jump state transition matrix to describe the system parameter jump model:

[0011] Where: And ; is the transition rate from mode at time to mode at time and satisfies is a right - continuous Markov process with its value range being the finite state space ; S4. Combine the parameter jump model to obtain the state equation of the drive system:

[0012] Where: is represented by ; ; , , , , , , , , ; S5. According to the state equation of the drive system, obtain the corresponding state equation of the response system:

[0013] Where: , is the state response of the controlled system; is the control; ; .

[0014] Furthermore, the adaptive proportional - derivative event - triggered safety synchronization mechanism includes: Update the trigger controller and transmit information if and only if the trigger event reaches the adaptive event - trigger threshold; The adaptive event - trigger threshold satisfies:

[0015] Where, , , , where ; is an adaptive threshold parameter related to sensitivity; adaptively adjust the trigger frequency according to the change trend of the drive system state:

[0016] Among them, is the sampling period, is an adaptive event-triggering threshold restricted within ; is an event-triggering parameter used to adjust the derivative of the error system state term; represents at the th trigger moment before the th denial-of-service attack interval, ; represents the current sampling moment; represents the th error state between the state received at the last event-triggering moment and the current sampling moment; represents the event-triggering weighting matrix.

[0017] Further, the secure synchronization controller describes the spoofing attack signal through a non-linear function and describes the randomness of the spoofing attack signal through a Bernoulli variable.

[0018] Further, the synchronization controller includes: S1. Define the synchronization controller received signal considering the denial-of-service attack:

[0019] The initial moment is represented by . After the th denial-of-service attack, the communication channel is detected to be accessible; the time period during which the communication channel remains accessible is represented by ; represents the spoofing attack signal; is a Bernoulli variable; S2. Determine the transmitted data of the denial-of-service attack according to the synchronization controller received signal:

[0020] S3. Design the synchronization controller considering the denial-of-service attack and the spoofing attack:

[0021] Among them, represents the attack-free interval before the th denial-of-service attack; Represent the active interval of the th denial-of-service attack; ; .

[0022] 7. A method for encrypting an inertial neural network based on a proportional-integral-derivative event protocol according to claim 6, characterized in that the design of the synchronization controller further includes: By establishing a Lyapunov functional, the gain matrix of the synchronization controller is obtained.

[0023] Furthermore, the original data includes: image data.

[0024] Furthermore, the driving system generates a chaotic sequence, and combines the chaotic sequence with the original image data to generate ciphertext, including: Obtain the two-dimensional pixel matrix of the red, green, and blue channels of the original image; Convert the two-dimensional pixel matrix of each channel into a one-dimensional time series; Merge the one-dimensional time series of all channels to obtain a fusion sequence; Normalize the fusion sequence and decompose it into an integer part and a fractional part; Set the parameters of the driving system and calculate through a hash 256 key to obtain a 256-bit key; Divide the 256-bit key into 8 groups for exclusive OR operation to obtain the initial value of the driving system; Generate a chaotic sequence based on the initial value of the driving system; Use the chaotic sequence to scramble and diffuse the fusion sequence to obtain ciphertext.

[0025] Advantages and positive effects of the present invention: In the present invention, through an adaptive proportional-integral-derivative event-triggered synchronization mechanism, the consideration of the system state change rate is emphasized, the distribution of event trigger times is optimized, an adaptive term is introduced to reduce the number of times communication data is exposed at the attack moment, reduce the impact of network attacks and improve communication efficiency, and improve the system synchronization performance. At the same time, in the process of chaotic synchronization, the influence of external interference on the inertial neural network is considered, and a generalized uncertain semi-Markov parameter jump model is established to model and quantify the interference factors in the actual system, improving the encryption security of the chaotic system. Description of the Drawings

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0027] Figure 1 Schematic diagram of constructing an inertial neural network model in an embodiment of the present invention; Figure 2 Flowchart of disassembling the image encryption steps based on an inertial neural network in an embodiment of the present invention; Figure 3 Flowchart of the image encryption and decryption algorithms based on an inertial neural network in an embodiment of the present invention. Detailed implementation manners

[0028] In order to enable those skilled in the art of the present technology to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0029] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0030] The present invention provides an encryption method for inertial neural networks based on a proportional-derivative event protocol. Considering factors such as changes in the external environment and internal system interference, the parameters may be time-varying, jumping rather than fixed. A generalized semi-Markov parameter jumping mechanism is designed to model and describe the parameter changes of the chaotic system. To save communication resources and reduce the energy consumption of wireless device signal transmission, a proportional-derivative event triggering mechanism is used to optimize and reduce the occupancy of network communication channel resources by continuous communication, reducing the communication burden and cost. By establishing a piecewise Lyapunov functional, the system stability is analyzed in different cases, and the controller gain matrix is obtained to control the chaotic error system to achieve convergence.

[0031] Combined with Figure 1 , the method of the present invention is further described as follows: S1. Establish a Markov jump inertial neural network model; In chaotic encryption technology, a chaotic system can generate dynamically changing chaotic sequences. The complexity of the chaotic system makes it difficult to crack information encryption. The present invention considers the influence of changes in the external environment and internal system interference, and introduces a generalized uncertain semi-Markov parameter jumping structure into the chaotic system, making the establishment of the chaotic model more in line with the real system.

[0032] S11. The driving and response neural dynamics equations of the time-delay inertial neural network with a Markov jump structure:

[0033] Where: represents the state of the -th neuron at time . and are known scalar values. and are the weights connected to the neurons. is the activation function of the -th neuron that satisfies the Lipschitz condition, where , is a natural number. is the external input applied to the -th neuron. The time-varying delay is located in the interval , and its derivative is located in the interval , where , and are all real numbers. The initial conditions are specified as follows: for , there is and , and and both belong to function spaces, that is, the space of real-valued functions continuous on the interval .

[0034] S12. To simplify subsequent mathematical derivations and analyses, the drive system equations are processed by a reduction method. The variable substitution formula is introduced to reconstruct the obtained neural dynamics equations into two first-order dynamics equations for analysis:

[0035] where: ; The initial condition is , where ; S13. The Markov jump state transition matrix is used to describe the system parameter jump model and introduced into the drive system equations. is a right-continuous Markov process with its range being the finite state space . The transition rate matrix can be expressed as:

[0036] where: and . is the transition rate from mode at time to mode at time , satisfying . The transition rate matrix (TransitionRate Matrix, TRM) is as follows:

[0037] where: ; "?" represents a completely unknown transition rate; the time-varying estimated transition rate is expressed as , where the estimated value is described as and the estimation error is described as . and represent 's lower and upper bounds respectively. The upper bound of the estimation error is expressed as . The set of known elements is and the set of unknown elements is .

[0038] S14. Convert the inertial neural network-driven system with Markov parameter jumps into a vector-form equation. The driven system is represented in matrix-vector form, where is represented by ( ), and the system is expressed as follows:

[0039] where: , , , , , , , , .

[0040] S15. According to the state equation of the driven system, obtain the corresponding state equation of the response system:

[0041] where: , is the state response of the controlled system; is the control; , .

[0042] S2. Design an adaptive proportional-derivative event-triggered safety synchronization mechanism; Based on the dynamic model designed in S1, in order to save precious communication resources and reduce the energy consumption of signal transmission of wireless devices, the event-triggered mechanism is used to reduce the occupancy of the network communication channel resources by continuous communication, and reduce the communication burden and cost. Considering that the static event-triggered mechanism only utilizes the state information of the system and does not consider the change trend of the system state, therefore, the adaptive proportional-derivative event-triggered synchronization mechanism proposed in the present invention takes into account the change rate of the system state, increases the trigger frequency in advance when the state changes violently, and reduces the trigger times after the state changes smoothly, improving the communication efficiency and the system control performance.

[0043] To save communication resources and reduce redundant information, the controller is updated and information is transmitted if and only if the trigger event trigger condition is met:

[0044] where is the sampling period, is an adaptive event-triggering threshold restricted within the range. is the event-triggering parameter used to adjust the derivative of the error system state term. denotes at the th triggering moment before the th denial-of-service attack interval, where and . denotes the current sampling moment. denotes the th error state between the state received at the last event-triggering moment and the current sampling moment. denotes the event-triggering weighting matrix. The adaptive event-triggering threshold satisfies the following conditions:

[0045] where: , , ; where .

[0046] is the adaptive threshold parameter related to sensitivity.

[0047] S3. Design a secure synchronization controller under a hybrid network attack scenario; The spoofing attack signal is modeled as a nonlinear function that satisfies the Lipschitz condition. To describe its randomness, a Bernoulli variable is introduced and satisfies the expectation . For , the signal actually received by the controller affected by the denial-of-service attack is described as follows:

[0048] The initial moment is denoted by . At the th denial-of-service attack, it is detected that the communication channel is accessible. The time period during which the communication channel remains accessible is denoted by . Specifically, denotes the attack-free interval before the th denial-of-service attack, while represents the active interval of the th denial-of-service attack. Therefore, the following relationship holds: .

[0049] The transmitted data under a denial-of-service attack is represented as follows:

[0050] The communication is affected by spoofing attacks, making the entire attack-free interval unable to be covered by the event-triggered intervals. To analyze the stability of the system, define ; Then . If no event occurs during this interval, then at the end time of the th spoofing attack, only one virtual trigger occurs. By considering the situation with denial-of-service attacks and spoofing attacks in the event-triggered scheme, for , construct the following controller for control:

[0051] S4. Obtain the controller gain matrix; According to the established closed-loop system, through the Lyapunov functional, obtain linear matrix inequalities, and use Matlab to solve for the controller matrix to achieve event-triggered secure synchronization control of inertial neural networks.

[0052] In view of network attack behaviors such as communication channel congestion or communication data tampering existing in the chaos synchronization process, the present invention solves the problem that the chaos encryption system cannot be synchronized under limited network attacks through an adaptive proportional-derivative event-triggered secure synchronization mechanism, and improves the efficiency of synchronous communication. Considering factors such as changes in the external environment and internal interference of the system, a generalized uncertain semi-Markov parameter jump mechanism is proposed to model and describe the parameter changes of the chaos system, solving the problem that it is difficult for the chaos encryption system to be synchronized due to parameter perturbations.

[0053] Combined with Figures 2-3 shown as the specific application example of chaos synchronization encryption of picture information, the method of the present invention is further described: Using the chaos synchronization method constructed by S1~4, construct a drive-response inertial neural network, and use the chaos characteristics of the inertial neural network to complete the encryption of image information.

[0054] Step 1: The original image , with a size of , respectively extract the matrix information of the red, green, and blue three channels. The pixel matrix of each channel can be expressed as: .

[0055] Step 2: Convert the two-dimensional pixel matrix of each channel into a one-dimensional time series. Using the row-major order, expand the matrix row by row from left to right and from top to bottom into a one-dimensional vector.

[0056] Sequence of the red channel

[0057] Sequence of the green channel

[0058] Sequence of the blue channel

[0059] The merged one - dimensional sequence can be expressed as: .

[0060] Step 3: Normalize the one - dimensional sequence obtained above The value range of is , and the new normalized is obtained through the following formula:

[0061] After processing the value range of . Subsequently, is split into an integer part and a fractional part .

[0062] Step 4: Select the parameters of the inertial neural network system, calculate through the Hash256 key, and obtain a 256 - bit key , and divide the key into 8 groups for XOR operation in the following way.

[0063]

[0064] Step 5: Substitute the initial value of the calculated chaotic system into the inertial neural network system for operation:

[0065] Four groups of chaotic sequences are obtained: ; The chaotic sequences are divided into two groups according to the following formula:

[0066] Step 6: Use the disordered characteristics of the chaotic sequence to perform the following scrambling operation on the one - dimensional sequence , define the sorting vector , which satisfies , and , .

[0067] Step 7: Perform a diffusion operation on the chaotic sequence and the original signal through the following formula. First, determine the initial situation of the recursive diffusion formula through the following formula:

[0068]

[0069] The diffusion of the sequence can be determined by the following recurrence formula:

[0070]

[0071] Step 8: The finally obtained scrambled and diffused sequence and the fractional part are recombined to obtain the encrypted ciphertext .

[0072] This embodiment also includes constructing a drive-response inertial neural network simulation platform to perform numerical simulation on the drive-response system to verify the role of the controller, and building an image encryption software platform to complete the encryption of image information by using the chaotic characteristics of the inertial neural network.

[0073] The present invention establishes an inertial neural network model with generalized uncertain semi-Markov jump parameters to consider the model parameter changes of the chaotic model under external disturbances and system parameter perturbations; proposes a new type of adaptive proportional-derivative event-triggered mechanism to reduce redundant sampling data by introducing proportional and derivative terms while maintaining system performance; designs an event-triggered output feedback controller to cope with denial-of-service attacks and spoofing attacks, and realizes the secure synchronization of the drive-response system in a mixed attack environment; establishes stability constraint conditions for the inertial neural network system based on the Lyapunov functional and obtains the system controller gain; uses the chaotic sequence generated by the synchronization of the inertial neural network, applies the event-triggered synchronization condition to image encryption, and improves the security of encryption. The present invention solves the drive-response synchronization problem of the time-delay inertial neural network with generalized uncertain semi-Markov in the scenario of complex network attacks, can improve the security of image encryption while ensuring the encryption performance of the chaotic system, and is applicable to various secure communication scenarios.

[0074] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An inertial neural network encryption method based on a proportional-differential event protocol, characterized in that: include: An inertial neural network model considering the internal parameter disturbance of the system is constructed as a drive-response system model; Design an adaptive proportional-derivative event-triggered safety synchronization mechanism and a synchronization controller based on the drive-response system model; The driving system generates a chaotic sequence, and combines the chaotic sequence with original data to generate ciphertext; The response system and the drive system are synchronized through an adaptive proportional-differential event-triggered synchronization mechanism to obtain the chaotic sequence; the chaotic sequence and the ciphertext are combined to restore the original data.

2. According to claim 1, an inertial neural network encryption method based on a proportional-differential event protocol is characterized in that: The internal parameter disturbance of the system is described by a generalized uncertain semi-Markov parameter jump mechanism.

3. According to claim 2, an inertial neural network encryption method based on a proportional-differential event protocol is characterized in that: The drive-response system model comprises: S1. Establish the driving and response neural dynamic equations of the time-delay inertial neural network with Markov jump structure: in: Indicates Neurons at time Status; and is a known scalar value; and are the weights of the connections between neurons; It is The activation function of neurons satisfies the Lipschitz condition, where , is a natural number; is applied to the External input to each neuron; time-varying delays Located in the interval Inside, and its derivative Located in the interval In which , and are all real numbers; the initial conditions stipulate that: ,have and ,and and All belong to Function space; S2. Introduce variable substitution formula , the driving and response neural dynamics equations of the time-delay inertial neural network with Markov jump structure are reconstructed into first-order dynamics equations: in: ; The initial condition is ,in ; S3. Use the Markov jump state transfer matrix to describe the system parameter jump model: in: and ; From mode In time To Mode In time The transfer rate satisfies is a right-continuous Markov process whose value range is a finite state space ; S4. Combining the parameter jump model to obtain the state equation of the drive system: in: Depend on express, ; ， ， ， ， ， ， ， ， ； S5. According to the state equation of the driving system, the corresponding state equation of the response system is obtained: in: , is the state response of the controlled system; For control; ; .

4. According to claim 1, an inertial neural network encryption method based on a proportional-differential event protocol is characterized in that: The adaptive proportional-derivative event triggers a safety synchronization mechanism, including: When and only when the trigger event reaches the adaptive event trigger threshold, the trigger controller is updated and information is transmitted; The adaptive event triggering threshold satisfies: in, , , ,in ; is the adaptive threshold parameter related to sensitivity; Adaptively adjust the trigger frequency according to the changing trend of the drive system status: in, is the sampling period, is a Adaptive event triggering thresholds within range; is the event trigger parameter, which is used to adjust the derivative of the error system state term; Indicated in The first time before the denial of service attack interval The triggering moment, ; Indicates the current sampling time; Indicates the state received between the last event triggering time and the current sampling time. error state; Represents the event trigger weighting matrix.

5. According to claim 1, an inertial neural network encryption method based on a proportional-differential event protocol is characterized in that: The safety synchronization controller describes the deception attack signal through a nonlinear function, and describes the randomness of the deception attack signal through a Bernoulli variable.

6. According to claim 5, an inertial neural network encryption method based on a proportional-differential event protocol is characterized in that: The synchronization controller comprises: S1. Define the synchronization controller receiving signal considered to be subject to denial of service attack: Initial time Indicates that in After a denial of service attack, the communication channel is detected to be accessible; the period of time during which the communication channel remains accessible is express; Indicates a deception attack signal; is a Bernoulli variable; S2. Determine the transmission data of the denial of service attack according to the signal received by the synchronization controller: S3. Design synchronization controller considering denial of service attacks and spoofing attacks: in, Indicated in The attack-free interval before the next denial of service attack; Representative The active interval of the denial of service attack; ; ; 。 7. According to claim 6, an inertial neural network encryption method based on a proportional-differential event protocol is characterized in that: The design synchronization controller also includes: By establishing the Lyapunov functional, the gain matrix of the synchronous controller is obtained.

8. According to claim 1, an inertial neural network encryption method based on a proportional-differential event protocol is characterized in that: The original data includes: image data.

9. According to claim 8, an inertial neural network encryption method based on a proportional-differential event protocol is characterized in that: The driving system generates a chaotic sequence, and combines the chaotic sequence with original image data to generate ciphertext, including: Get the two-dimensional pixel matrix of the red, green and blue channels of the original image; Convert the two-dimensional pixel matrix of each channel into a one-dimensional time series; Merge the one-dimensional time series of all channels to obtain the fused sequence; Normalize the fused sequence and split it into integer and decimal parts; Set the drive system parameters and calculate through the hash 256 key to obtain a 256-bit key; Divide the 256-bit key into 8 groups and perform XOR operations to obtain the initial value of the drive system; Generate a chaotic sequence based on the initial value of the driving system; The chaotic sequence is used to scramble and diffuse the fusion sequence to obtain the ciphertext.

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