Image encryption method and image decryption method based on heterogeneous neural network synchronization with uncertainty

Abstract

The invention provides an image encryption method and an image decryption method based on heterogeneous neural network synchronization with uncertainty, and relates to the technical field of image processing. The method comprises the following steps: under the condition that a driving system and a response system realize synchronization, acquiring at least two groups of chaotic sequences generated by the driving system in a synchronization state; fusing the at least two groups of chaotic sequences to generate a composite chaotic sequence; and based on the composite chaotic sequence, performing encryption processing on the original image to generate an encrypted image. And at least two groups of response chaos sequences generated by the response system in a synchronous state are obtained, the at least two groups of chaos response sequences are fused to generate a composite response sequence, and then the encrypted image is decrypted by using an encryption reverse process. According to the embodiment of the invention, the multiple groups of chaotic sequences generated by the heterogeneous neural network with uncertainty in the synchronous state are fused, the composite key with more complex dynamic characteristics and higher randomness is generated, and the security strength of an image encryption system is improved.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to an image encryption method and an image decryption method based on the synchronization of heterogeneous neural networks with uncertainty. Background Technology

[0002] Neural network synchronization techniques can generate highly complex and unpredictable chaotic sequences, making them an ideal source for constructing dynamic keys in image encryption. Current mainstream methods involve building a driver-response system based on homogeneous neural networks with identical structures. Once synchronized, the generated chaotic sequence is used to encrypt the image. This approach introduces dynamic characteristics into the encryption process, enhancing the security of traditional static encryption schemes.

[0003] However, existing technologies suffer from two major drawbacks at the source of key generation. First, most studies are based on "homogeneous" scenarios where the driving and response systems have the same model structure and idealized deterministic parameters. Real-world systems often exhibit inherent differences due to manufacturing tolerances, environmental disturbances, or modeling errors. The uncertainty and structural heterogeneity of these systems are ignored by existing solutions, limiting their applicability in complex real-world environments. Second, in constructing key materials, existing methods typically extract a single chaotic sequence from a synchronization state (such as asymptotic synchronization) to generate the key. This key generation mechanism is relatively simple, and the complexity and randomness of the generated keys are limited. Faced with increasingly sophisticated cryptanalysis techniques, its potential security strength may be insufficient.

[0004] Therefore, how to utilize the uncertainty of system parameters, how to overcome the theoretical limitations of homogeneous systems, how to effectively utilize neural networks with uncertain and dissimilar structures to achieve synchronization, and on this basis, how to design a method that can integrate more dimensional and richer dynamic characteristics of the system to generate a high-strength composite key, has become a key technical issue for improving the security, robustness and practicality of neural network-based image encryption schemes. Summary of the Invention

[0005] This invention provides an image encryption method and an image decryption method based on the synchronization of heterogeneous neural networks with uncertainty. By fusing multiple chaotic sequences generated by heterogeneous neural networks with uncertainty in a synchronized state, a composite key with more complex dynamic characteristics and stronger randomness is generated, which fundamentally improves the security strength of the image encryption system.

[0006] In a first aspect, the present invention provides an image encryption method based on heterogeneous neural network synchronization with uncertainty, comprising the following steps: When the driving system and the response system are synchronized, at least two sets of chaotic sequences generated by the driving system in the synchronized state are obtained; The at least two sets of chaotic sequences are fused to generate a composite chaotic sequence; Based on the aforementioned complex chaotic sequence, the original image is encrypted to generate an encrypted image; The driving system is a first neural network with proportional time delay and uncertainty parameters, and the response system is a second neural network without time delay and uncertainty parameters. The internal structures of the first neural network and the second neural network are different, and the first neural network and the second neural network constitute a heterogeneous neural network with uncertainty.

[0007] Secondly, the present invention also provides an image decryption method based on heterogeneous neural network synchronization with uncertainty, applied to the image encryption method based on heterogeneous neural network synchronization with uncertainty described in the first aspect, comprising: When using the same adaptive controller as during encryption to achieve synchronization between the driving system and the response system, obtain at least two sets of chaotic response sequences generated by the response system during synchronization; The at least two sets of response chaotic sequences are fused to generate a composite response chaotic sequence; Based on the composite response chaotic sequence, the received encrypted image is decrypted to obtain a decrypted image; The driving system is a first neural network with proportional time delay and uncertainty parameters, and the response system is a second neural network without time delay and uncertainty parameters. The internal structures of the first neural network and the second neural network are different, and the first neural network and the second neural network constitute a heterogeneous neural network with uncertainty.

[0008] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the image encryption method based on heterogeneous neural network synchronization with uncertainty as described above.

[0009] Fourthly, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the image encryption method based on heterogeneous neural network synchronization with uncertainty as described above.

[0010] Fifthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the image encryption method based on heterogeneous neural network synchronization with uncertainty as described above.

[0011] This invention provides an image encryption and decryption method based on heterogeneous neural network synchronization with uncertainty. By fusing multiple chaotic sequences generated by heterogeneous neural networks with uncertainty in a synchronized state, a composite key with more complex dynamic characteristics and stronger randomness is generated, which fundamentally improves the security strength of the image encryption system. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in this 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 this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0013] Figure 1 This is one of the flowcharts illustrating the image encryption and decryption methods based on heterogeneous neural network synchronization with uncertainty provided by the present invention.

[0014] Figure 2 This is the second flowchart of the image encryption and decryption method based on heterogeneous neural network synchronization with uncertainty provided by the present invention.

[0015] Figure 3 This is a schematic diagram illustrating the application of image encryption and image decryption provided by the present invention.

[0016] Figure 4 This is a schematic diagram of synchronous control achieved by a heterogeneous neural network with uncertainty, as provided by the present invention.

[0017] Figure 5 This is a schematic diagram of the drive system provided by the present invention.

[0018] Figure 6 This is a schematic diagram of the structure of the response system provided by the present invention.

[0019] Figure 7 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0021] The following is combined with Figures 1-7This invention describes an image encryption and decryption method based on the synchronization of a heterogeneous neural network with uncertainty. By fusing multiple chaotic sequences generated by the heterogeneous neural network with uncertainty in the synchronization state, a composite key with more complex dynamic characteristics and stronger randomness is generated, which fundamentally improves the security strength of the image encryption system.

[0022] Figure 1 This is one of the flowcharts illustrating an image encryption method based on heterogeneous neural network synchronization with uncertainty provided by the present invention, such as... Figure 1 As shown, the method may include, but is not limited to, steps S100 to S300: S100, when the driving system and the response system are synchronized, acquire at least two sets of chaotic sequences generated by the driving system in the synchronized state; S200, the at least two sets of chaotic sequences are fused to generate a composite chaotic sequence; S300, Based on the composite chaotic sequence, the original image is encrypted to generate an encrypted image; The driving system is a first neural network with proportional time delay and uncertainty parameters, and the response system is a second neural network without time delay and uncertainty parameters. The internal structures of the first neural network and the second neural network are different, and the first neural network and the second neural network constitute a heterogeneous neural network with uncertainty.

[0023] The following is combined with Figure 1 and Figure 2 This invention describes an image encryption method and an image decryption method based on heterogeneous neural network synchronization with uncertainty, provided by the present invention.

[0024] In steps S100 and S200 of some embodiments, it is understood that, when the driving system and the response system are synchronized, at least two sets of chaotic sequences generated by the driving system in the synchronized state are obtained, and the at least two sets of chaotic sequences are fused to generate a composite chaotic sequence, including: Based on the global polynomial synchronization result, the first chaotic sequence of the driving system is obtained; Based on the global exponential synchronization result, the second chaotic sequence of the driving system is obtained; The first chaotic sequence and the second chaotic sequence are fused to generate the composite chaotic sequence used for encryption.

[0025] Select an image of size RGB images, such as Figure 3 As shown in (a).

[0026] a) Pixel Extraction: Pixel intensity is defined on a discrete integer range [0, 255]. Figure 3 (a) Decomposed into three channel matrices: red channel Green Channel and the blue channel Each matrix has a dimension of 1. ,in and These represent the row index and column index of the image matrix, respectively.

[0027] b) Image perturbation: Based on the parameters and initial values ​​of the driving system (1) and the response system (2), two sets of chaotic driving sequences corresponding to the driving system are selected, namely the first chaotic sequence. (When global polynomial synchronization is achieved) and the second chaotic sequence (When global exponential synchronization is achieved, since the drive system does not have a controller and the initial value does not change, they are actually completely identical at this time.)

[0028] For the first chaotic sequence Second chaotic sequence The mixture is fused to form a composite driving sequence. The advantage of this approach is that it increases the elements of the chaotic sequence, and subsequent perturbations generate a more complex chaotic perturbation sequence, resulting in better image encryption.

[0029] In step S300 of some embodiments, the original image is encrypted based on the composite chaotic sequence to generate an encrypted image; The driving system is a first neural network with proportional time delay and uncertainty parameters, and the response system is a second neural network without time delay and uncertainty parameters. The internal structures of the first neural network and the second neural network are different, and the first neural network and the second neural network constitute a heterogeneous neural network with uncertainty.

[0030] It is understandable that we can derive the complex chaotic sequence from X_comp.

[0031] Design a nonlinear driven sequence generation algorithm using this composite chaotic sequence X_comp Using algorithms Generate pseudo-random sequences for scrambling pixel positions. And generate another random sequence. .

[0032] Using pseudo-random sequences The pixel positions of the R, G, and B channel matrices of the original image are rearranged (scrambled). The scrambled three channels are then recombined to obtain an intermediate image with disordered positions.

[0033] Using the random sequence The composite driving sequence X_comp is perturbed to obtain a chaotic perturbation driving sequence.

[0034] Then use the predetermined position parameters Loc The stable portion of the chaotic perturbation driving sequence is extracted. Finally, based on the extracted stable chaotic perturbation driving sequence, three encryption key matrices K_R, K_G, and K_B are generated.

[0035] The perturbed channel matrices R_s, G_s, and B_s are XORed with the corresponding encryption key matrices K_R, K_G, and K_B to obtain the encrypted channel matrices E_R, E_G, and E_B, which are then combined to form the final encrypted image.

[0036] In some embodiments of the present invention, the step of encrypting the original image based on a complex chaotic sequence to generate an encrypted image includes: The original image is decomposed into multiple initial color channel matrices; Based on the composite chaotic sequence and the multiple initial color channel matrices, the image pixel positions of the original image are perturbed to obtain the perturbed color channel matrix. Based on the composite chaotic sequence and the perturbed color channel matrix, the image pixel values ​​of the original image are encrypted to obtain the encrypted image.

[0037] Understandably, selecting an image of size... RGB images, such as Figure 3 As shown in (a).

[0038] a) Pixel Extraction: Pixel intensity is defined on a discrete integer range [0, 255]. Figure 3 (a) Decomposed into three channel matrices: red channel Green Channel and the blue channel Each matrix has a dimension of 1. ,in and These represent the row index and column index of the image matrix, respectively.

[0039] In some embodiments of the present invention, the step of perturbing the image pixel positions of the original image based on the composite chaotic sequence and the plurality of initial color channel matrices to obtain a perturbed color channel matrix includes: A nonlinear driven sequence generation algorithm is designed based on the aforementioned composite chaotic sequence, and a pseudo-random sequence is generated according to the nonlinear driven sequence generation algorithm. By using a pseudo-random sequence, the pixel positions of each initial color channel matrix are rearranged to obtain a scrambled color channel matrix.

[0040] It is understandable that generating a length of random sequence A nonlinear driven sequence generation algorithm was designed based on composite chaotic sequences. To generate a sequence based on a nonlinear driving algorithm Generate pseudo-random sequences The algorithm The calculation formula is: Using pseudo-random sequences Scramble the pixel positions of the three color channels: specifically the red channel. Green Channel and the blue channel The pixel positions are rearranged, and the three channels are recombined to form an intermediate image with disordered positions, that is, the disordered color channel matrix.

[0041] Pseudo-random sequences Used to scramble pixel positions, random sequences This is used to scramble the complex chaotic sequence, resulting in a chaotic perturbation-driven sequence.

[0042] It should be noted that, The generated pseudo-random sequence rearranges the pixel positions of the three RGB channels by establishing an index mapping relationship (most commonly using a sorting and scrambling method). Each channel can independently use different sequences or different transformations of the same sequence to enhance the degree of scrambling. Scrambling only changes the pixel position, not the pixel value, therefore it is the position scrambling stage.

[0043] This formula is a deterministic calculation process, but it is designed to generate a pseudo-random sequence. It is a step in a pseudo-random number generator. The formula itself does not generate a sequence; it is merely an output function that maps chaotic states to random integers. Generating a sequence requires the chaotic system to iteratively update its state. At each step, the new state is substituted into the formula to obtain a number, and this process is repeated multiple times to obtain the sequence. Only the entire system (chaotic mapping + output function) constitutes a pseudo-random sequence generation algorithm.

[0044] In some embodiments of the present invention This formula essentially maps the state variables of a chaotic system to an output function that represents the desired range of random integers. Generating pseudo-random sequences requires incorporating a chaotic iterative process. The complete pseudo-random sequence generation process is as follows: Step 1: Definition and initialization steps include: 1. System parameters: Target interval size (e.g., total number of pixels in the image): Modulus .

[0045] 2. Choosing a Chaotic System: This involves four state variables. , , , Choosing a chaotic sequence and 3. Initialization steps: Initial values , , , .

[0046] Step 2: Sequence Generation Main Loop Steps include: Assuming the desired sequence length is... pseudo-random integer sequence , recorded as : Steps to substitute into the output function: Polynomial Combinations The states of two chaotic systems are coupled, enhancing the mixing effect.

[0047] Add 1 to the absolute value to avoid logarithmic singularities.

[0048] Logarithmic functions compress the dynamic range, resulting in a more uniform output. Multiply by Extract the most significant digits of the logarithmic fractional part as the "random source".

[0049] : Rounding down and then taking the modulo to map to the target interval get The purpose of this design is to produce a pseudo-random sequence in the output. exist It has an approximately uniform distribution and low autocorrelation, thus passing the randomness test.

[0050] In some embodiments of the present invention, the step of encrypting the image pixel values ​​of the original image based on the composite chaotic sequence and the perturbed color channel matrix to obtain the encrypted image includes: The random sequence is used to perturb the complex chaotic sequence to obtain a chaotic perturbation driving sequence. The stable portion of the chaotic perturbation driving sequence is extracted according to preset position parameters to obtain the target chaotic perturbation driving sequence; Based on the target chaotic perturbation driving sequence, an encryption key matrix corresponding to each color channel is generated; The perturbed color channel matrix is ​​XORed with the corresponding encryption key matrix of the color channel to obtain the target encryption channel matrix corresponding to each color channel. The target encryption channel matrix corresponding to each color channel is then combined to generate the encrypted image.

[0051] Understandably, using random sequences chaotic driving sequences Perturbation is performed to obtain a more chaotic perturbation-driven sequence. Therefore, three encryption keys were designed: Next, to ensure the stability of the sequence driven by the aforementioned chaotic perturbation, position parameters are used. Loc Cut off, in sequence For example: This truncation operation skips the transient process of the chaotic perturbation-driven sequence, using the sequence from the first... A stable chaotic sequence segment starting from a point enhances the security of the encryption system. The encrypted image is thus obtained. .

[0052] In other embodiments of the present invention, predetermined position parameters are used. Loc The stable portion of the chaotic perturbation driving sequence is extracted. Finally, based on the extracted stable chaotic perturbation driving sequence, three encryption key matrices K_R, K_G, and K_B are generated.

[0053] The perturbed channel matrices R_s, G_s, and B_s are XORed with their corresponding encryption key matrices K_R, K_G, and K_B to obtain the encrypted channel matrices E_R, E_G, and E_B, which are then combined to form the final encrypted image. .

[0054] In some embodiments of the present invention, prior to the step of fusing the at least two sets of chaotic sequences to generate a composite chaotic sequence, the method includes: An adaptive controller is applied to the response system to drive the state of the response system to synchronize with the state of the driving system, thereby obtaining a synchronization result of a heterogeneous neural network with uncertainty; The adaptive controller includes at least a global polynomial synchronization controller, a global exponential synchronization controller, and a global asymptotic synchronization controller; the synchronization result of the heterogeneous neural network with uncertainty includes at least a global polynomial synchronization result, a global exponential synchronization result, and a global asymptotic synchronization result.

[0055] In the relevant technologies, at least the following technical problems exist: Neural network synchronization refers to the asymptotic tracking of the state of the driving system by the response system to the state of the driving system when two dynamic systems, namely the driving system and the response system, have different initial states, through a specific control strategy. Existing research on time-delay neural network synchronization and its application in image encryption mostly deals with bounded time delays and ideal cases where the driving and response systems have the same parameters and structure, such as deterministic parameters. For example, the driving and response systems may be of the following forms: and They are typically parameter-defined and homogeneous structures, but this is a very idealized situation.

[0056] In practical applications, external disturbances, modeling errors, and other factors significantly affect the accuracy of the model in reflecting the true state of the network. Common parameter uncertainties profoundly impact the overall system model performance; therefore, constructing neural networks with uncertainties is essential to better characterize the true state of the neural network. Furthermore, the aforementioned factors often lead to fundamental structural differences in the dynamic models of two systems. This heterogeneity is a more prevalent real-world scenario and constitutes a more challenging core problem in system synchronization. Most current synchronization control methods focus on the synchronization problem between homogeneous systems, while this invention achieves synchronization control under uncertain heterogeneous structural conditions by synchronizing a type of proportional-delay neural network with uncertainty to a type of time-delay-free neural network with uncertainty. Therefore, it overcomes the limitations of homogeneous neural network synchronization. In-depth research into the synchronization control of heterogeneous neural networks with uncertainties enables image encryption and decryption.

[0057] Furthermore, existing research mainly focuses on bounded time-varying time delays. Or a time-delay-free neural network framework. In contrast, proportional delay is an unbounded time delay, which can be mathematically expressed as: ,in The proportional time delay factor makes the dynamic behavior of the system heavily dependent on the entire historical state, thus greatly increasing the complexity of theoretical analysis. The analysis process is far more complex than that for bounded time-varying time delays or time-free cases. However, precisely because of this characteristic, the proportional time delay can more realistically reflect the long-range historical dependencies existing in many real-world systems, and therefore has a wider range of applications than the former.

[0058] The approximately consistent chaotic sequence generated after system synchronization can be used as an encryption / decryption key in the field of image encryption, providing a new security mechanism for this field. This invention designs an adaptive controller to achieve various synchronization types, including global polynomial synchronization, global exponential synchronization, and global asymptotic synchronization, for uncertain heterogeneous neural networks with proportional and non-delay time delays. Furthermore, it proposes a novel key generation mechanism that integrates the results of global polynomial and exponential synchronization.

[0059] The following combination Figure 4 This paper describes an embodiment of synchronization control using a heterogeneous neural network with uncertainty. First, the operators used in this embodiment are explained, and will not be repeated hereafter.

[0060] set up It is a mapping The Banach space constitutes , . ( yes dimensional vector, yes (Veuve space) (Represents the 1-norm of a vector). (Bundle Abbreviated as ). express The symbolic function.

[0061] In step S100 of some embodiments, a heterogeneous neural network is constructed; wherein the heterogeneous neural network includes at least a driving system and a response system, the driving system is a first neural network with proportional time delay and uncertainty parameters, the response system is a second neural network without time delay with uncertainty parameters, and the internal structure of the first neural network and the second neural network are different.

[0062] It should be noted that the following type of neural network model with proportional time delay uncertainty is constructed: (1) System (1) is a driving system that contains proportional time delay terms. This also serves as a subsequent encryption system. Represents state variables; Indicates the neuron's self-inhibition coefficient; and Indicates the connection weights; , and Let represent an uncertain parameter that satisfies: , , , The uncertain parameters are bounded; Indicates the proportional time delay factor; Represents an unbounded proportional time delay function; and Let represent the activation function, and let the activation function satisfy: Lipschitz conditions. The activation function value at the origin is 0. The Lipschitz constant is greater than 0; Lipschitz conditions. The activation function value at the origin is 0. The Lipschitz constant is greater than 0; and These represent the external input and the initial function, respectively.

[0063] Using system (1) as the driving system, the following time-delay-free neural network model with uncertainty is constructed as the response system. (2) System (2) is a response system, which does not contain a time delay term and is structurally heterogeneous with the driving system (1). The response system (2) serves as the subsequent decryption system. Indicates controller; This represents the initial function.

[0064] The structural diagrams of the drive system (1) and the response system (2) are as follows: Figure 5 and Figure 6 As shown, the two exhibit significant heterogeneity in terms of structure and dynamic properties.

[0065] In other embodiments of the invention, particularly, if and Then the driving system (1) and the response system (2) are simplified to the following deterministic system: (3) and (4) In step S200 of some embodiments, an adaptive controller is applied to the second neural network, and the state of the second neural network is driven by the adaptive controller to approximate the state of the first neural network with a preset synchronization type, so as to realize the synchronization of the state of the second neural network with the state of the first neural network and generate a heterogeneous neural network synchronization result with uncertainty.

[0066] It is understandable that, in order to synchronize the driving system (1) and the response system (2), the following adaptive controller is constructed: the adaptive controller includes at least a global polynomial synchronization controller, a global exponential synchronization controller, and a global asymptotic synchronization controller.

[0067] a) Global polynomial synchronization controller applied to global polynomial synchronization control: (5) in , , . and For adaptive control of gain, For adaptive control parameters, .

[0068] To achieve global polynomial synchronization between the drive system (1) and the response system (2), the gain derivative of the global polynomial synchronization controller (5) is specifically designed to contain a polynomial function. The absolute value of the state term of the state error system All of these designs are intended to enable the construction of Lyapunov functionals that satisfy polynomial synchronization conditions in subsequent embodiments, thereby strictly guaranteeing the implementation of global polynomial synchronization.

[0069] The Lyapunov functional is differentiated along the system (3) and (4), and then scaled using the Lipschitz condition, etc. Substituting this into the controller (5), we finally obtain that the derivative of the Lyapunov functional is less than or equal to 0. This implies that the Lyapunov functional is monotonically decreasing, and therefore the Lyapunov functional is less than or equal to its initial time step. The value of, i.e. Re-estimate Combining the expression of the Lyapunov functional with the known conditions, if the norm of the state error of the driving and response systems satisfies an estimate of an exponential polynomial decay... This demonstrates that heterogeneous drive and response systems achieve global polynomial synchronization.

[0070] b) Global exponential synchronization controller applied to global exponential synchronization control: (6) in , , , .

[0071] In some embodiments, the design concept of the global exponential synchronization controller (6) is similar to that of the global polynomial synchronization controller (5). However, the global exponential synchronization controller (6) is constructed to ensure the global exponential synchronization of the system. Therefore, the design of its controller and the controller's gain derivative both include exponential functions. Similarly, Lyapunov functionals It also contains exponential functions, and then, using a calculation method similar to that used in proving global polynomial synchronization, it is proved... ,thereby Re-estimate Then, combining the expression of the Lyapunov functional with the known conditions, we obtain an estimate of the norm of the state error of the driving and response systems that satisfies an exponential decay. Therefore, it can be seen that global polynomial synchronization and global exponential synchronization are consistent in their core methodology. Their essential difference lies in the fact that, in order to achieve a faster exponential convergence rate, the global exponential synchronization controller (6) has made targeted adjustments to the specific structure of the controller and the Lyapunov functional.

[0072] c) Global asymptotic synchronization controller applied to global asymptotic synchronization control: (7) in , , , .

[0073] The function of the global asymptotic synchronization controller (7) is to achieve global asymptotic synchronization between the driving system (1) and the response system (2). Global polynomial synchronization and global exponential synchronization both fall under the category of global asymptotic synchronization, but they have fixed convergence rates and convergence orders. Therefore, global asymptotic synchronization can be regarded as a degenerate form of global polynomial synchronization and global exponential synchronization. Based on this understanding, the design concept of the global asymptotic synchronization controller (7) is consistent with that of the global polynomial synchronization controller (5) and the global exponential synchronization controller (6). In terms of form, it is when At that time, a special form of the global polynomial synchronization controller (5) and the global exponential synchronization controller (6) is required in the subsequent proof to design a Lyapunov functional that contains neither polynomial functions nor exponential functions. We prove that its derivative is negative definite, thus ensuring global asymptotic synchronization of the system.

[0074] In some other embodiments of the present invention, the structural design of the global polynomial synchronization controller (5) is simpler than that of the global exponential synchronization controller (6). This is because the core inequality is used in the derivation of the global polynomial synchronization. The scaling is explained in detail in the proof section of Example 1 below.

[0075] This invention employs an adaptive controller, the core difference of which lies in the design of the controller gain compared to a traditional feedback controller: the gain of a traditional feedback controller is typically a fixed constant, while the gain of an adaptive controller is time-varying, possessing the ability to adjust parameters online in real time. Due to this characteristic, adaptive control typically only needs to satisfy relatively few theorem conditions to achieve system synchronization; in contrast, feedback control schemes often require more stringent and complex conditions, making them more difficult to implement in practical applications.

[0076] In some embodiments, both global exponential synchronization and global polynomial synchronization are time-dependent. Global asymptotic synchronization is an asymptotic behavior in which the state variables of a state-error system tend towards an equilibrium point, falling under the category of global asymptotic synchronization. The essential difference between the three lies in the mathematical description of their convergence performance: global exponential synchronization and global polynomial synchronization have explicit convergence rates and orders, while global asymptotic synchronization only ensures that the states of the driving and response systems eventually converge, without imposing specific constraints on the convergence speed. The mathematical definitions of global polynomial synchronization, global exponential synchronization, and global asymptotic synchronization are as follows: Definition 1: If there exists a constant and a suitable controller Make Then the driving system (1) and the response system (2) can achieve global polynomial synchronization, where : Represents the summation of the supremum components of the initial function of system (1) : Represents the summation of the supremum components of the initial function of the state error. : indicates the maximum value of the two. , : These represent the state vectors of the driver-response system.

[0077] The definition of global polynomial synchronization uses the L2 norm of the error. This definition method is more compact in form, and and It is a special definition. The initial time... Setting it to a non-zero value makes the definition more widely applicable.

[0078] Definition 2: If there exists a constant and a suitable controller Make Then the driving system (1) and the response system (2) can achieve global exponential synchronization. The definition of global exponent synchronization is the same as that of global polynomial synchronization, and will not be repeated here.

[0079] Definition 3: If a suitable controller exists For any Make Then the driving system (1) and the response system (2) can achieve global asymptotic synchronization.

[0080] In some embodiments of the present invention, the heterogeneous neural network synchronization result includes at least a global polynomial synchronization result, a global exponential synchronization result, and a global asymptotic synchronization result, specifically: By using a global polynomial synchronization controller, the state of the second neural network is driven to approximate the state of the first neural network with a preset synchronization type, thereby synchronizing the state of the second neural network with the state of the first neural network and generating a global polynomial synchronization result.

[0081] By using a global exponential synchronization controller, the state of the second neural network is driven to approximate the state of the first neural network with a preset synchronization type, thereby synchronizing the state of the second neural network with the state of the first neural network and generating a global exponential synchronization result.

[0082] By using a global asymptotic synchronization controller, the state of the second neural network is driven to approximate the state of the first neural network with a preset synchronization type, thereby synchronizing the state of the second neural network with the state of the first neural network and generating a global asymptotic synchronization result.

[0083] In step S300 of some embodiments, a chaotic sequence for image encryption is determined from the heterogeneous neural network based on the synchronization results of the heterogeneous neural network.

[0084] Based on the synchronization results of the heterogeneous neural network, a chaotic sequence for image encryption is determined from the heterogeneous neural network. The original image is then encrypted using the chaotic sequence of the driving system to obtain a complex encrypted image. The encrypted image is then decrypted using the chaotic sequence of the response system to obtain a decrypted image. The response system during decryption is synchronized with the driving system through an adaptive controller.

[0085] In some embodiments of the present invention, the adaptive controller drives the state of the second neural network to approximate the state of the first neural network with a preset synchronization type, thereby synchronizing the state of the second neural network with the state of the first neural network, including: Based on the second neural network and the first neural network, a state error system is constructed, and a Lyapunov functional is constructed for the state error system. Based on the Lyapunov functional and the adaptive controller of the corresponding synchronization type, the state of the second neural network is synchronized with the state of the first neural network.

[0086] Understandably, to prove that the driving system and the response system achieve synchronization, it is only necessary to construct the state error system between the second neural network corresponding to the response system and the first neural network of the driving system. When the error system in this state is close to 0, it can be determined that the drive system and the response system are synchronized.

[0087] In some embodiments of the present invention, the Lyapunov functional includes at least a first functional term and a second functional term; The adaptive controller, based on the Lyapunov functional and the corresponding synchronization type, synchronizes the state of the second neural network with the state of the first neural network. This includes: differentiating the first functional term to obtain a first derivative, where the first derivative includes a proportional delay term; differentiating the second functional term to obtain a second derivative, where the second derivative includes an integral term used to eliminate the proportional delay term; and calculating the first and second derivatives to obtain the target derivative of the Lyapunov functional. Based on the adaptive controller, it is determined that the target derivative of the Lyapunov functional is less than or equal to a preset threshold, thereby determining the estimation formula satisfied by the state error norm.

[0088] It is understandable that, after substituting the adaptive controller into the derivative of the Lyapunov functional, the parameters in the second functional of Lyapunov are... and satisfy Therefore, the derivative of the Lyapunov functional is less than or equal to 0 (i.e., a preset threshold), indicating that the Lyapunov functional is monotonically decreasing. Re-estimate By combining the expression of the Lyapunov functional and the known conditions, an estimate of the state error norm is obtained, thereby determining whether the driving system and the response system are in global polynomial synchronization or global exponential synchronization. Global asymptotic synchronization is also one of the two synchronization methods mentioned above. Special circumstances.

[0089] Based on the norm estimation of the state error, it is determined that the state of the second neural network is synchronized with the state of the first neural network.

[0090] Specifically, That is, the norm of the state error of the driving and response systems satisfies a polynomial-form estimate of decay, which shows that the heterogeneous driving and response systems achieve global polynomial synchronization.

[0091] If the norm of the state error of the driving and response systems satisfies an exponentially decaying estimate... This demonstrates that heterogeneous drive and response systems achieve global exponential synchronization.

[0092] If the norm of the state error of the driving and response systems is equal to the time... The limit approaches infinity and becomes 0, that is... This is what the global polynomial synchronization and global exponent synchronization mentioned above mean. This is a special case, which shows that heterogeneous driving and response systems achieve global asymptotic synchronization.

[0093] Understandably, in the Lyapunov method, the global asymptotic stability criterion (i.e., the criterion for synchronizing the state of the second neural network with the state of the first neural network) is as follows: If there exists a Lyapunov functional Simultaneously satisfying: Positive definiteness: The equals sign "=" here only applies when... Established at that time; Negative definiteness of derivative: The derivative is negative definite, that is The equals sign "=" only applies when... If it holds true, it holds true throughout the entire state space; Radial unboundedness: .

[0094] Therefore, the equilibrium point is globally asymptotically stable, which proves that the driving system and the response system achieve global asymptotic synchronization.

[0095] In the synchronization analysis of drive-response systems, the synchronization problem is transformed into a stability problem of an error system. We define the synchronization error as... The state difference between the driving system and the response system is used to construct a new state error system. Then, a Lyapunov functional satisfying the above theorem is constructed for this state error system. If it can be proven that it is globally asymptotically stable, it means that the error will asymptotically converge to zero, thus rigorously proving that the two systems have achieved global asymptotic synchronization.

[0096] To address the synchronization control problem between the driving system (1) and the response system (2), this invention, based on the Lyapunov method and combined with the designed adaptive controller, utilizes basic inequalities and scaling methods to derive several criteria for ensuring system synchronization. The following will describe in detail the three cases of global polynomial synchronization, global exponential synchronization, and global asymptotic synchronization: Firstly, in the embodiments of the present invention in, It is represented as a Lyapunov functional. Represented as the first functional term, It is represented as the second functional term. and These are represented as the first derivative and the second derivative, respectively. This is expressed as the objective derivative. The differentiation process utilizes the Lipschitz condition and inequalities. After scaling, substitute the adaptive controller into the Lyapunov derivative, and let the parameters in the Lyapunov functional... and satisfy Therefore, the derivative of the Lyapunov functional is less than or equal to 0, thus... Re-estimate Then estimate the Lyapunov functional at the initial time. value , ,in Combining the expression of the Lyapunov functional with the given conditions, we obtain... This allows for the determination that the state of the second neural network is globally synchronized with the state of the first neural network.

[0097] Example 1: When the activation function and uncertain parameters of the driving system satisfy the assumptions, the driving system (1) and the response system (2) can achieve global polynomial synchronization under the action of the global polynomial synchronization controller (5).

[0098] First, construct a Lyapunov functional of the following form: in, It is represented as a Lyapunov functional. Represented as the first functional term, It is represented as the second functional term.

[0099] It is an essential component of Lyapunov functionals, and its construction form is usually adopted. and However, proving the global polynomial synchronization of the system will introduce an additional polynomial function. Furthermore, a key aspect of the derivation process lies in handling the challenges posed by the time delay term. To address this, a parameter term from the Lyapunov functional is specifically introduced (to eliminate...). (Time delay term generated during differentiation) Its specific form will vary depending on the type of target synchronization. Furthermore, (Used to eliminate adaptive control parameters in adaptive controllers) This step is designed for adaptive controller analysis; if a feedback controller is used, this step can be omitted. The core idea of ​​the proof will be outlined below. The entire proof will revolve around the following key steps: Step 1: Define the function: Such a function is defined for the sake of simplicity in the subsequent proof. For the first functional term... Taking the derivative, we obtain the first derivative: Step 2: Combine the equations for the driving system (1) and the response system (2), and substitute them into... (The difference between the response system (1) and the driving system (2)) is taken to the first derivative, and scaling is performed using the absolute value property and the boundedness of the uncertain parameters: We obtain an expression related to the driving system (1) and the response system (2), the first derivative after scaling: Step 3: For the part of the algebraic expression in Step 2 that contains the activation function, we use the Lipschitz condition for scaling: Substituting the scaling result into step 2, we obtain the following analysis results: Step 4: Analysis results from Step 3 Includes time delay term , The designed integral term This is to eliminate the time delay term after differentiation. The influence of the first functional term is discussed below. Taking the derivative yields the second derivative: Step 5: Merge and It can be observed that the time delay term has been eliminated. Simultaneously, according to the inequality... It can be proved that the final expression of the derivative of a Lyapunov functional is always derived from a polynomial. It is dominant, so there is no need to introduce additional calculation terms.

[0100] Step 6: Substitute the expression of the global polynomial synchronization controller (5) into the objective derivative of the Lyapunov functional obtained in Step 5, select appropriate parameters for the Lyapunov functional, and finally achieve... This demonstrates that Lyapunov functionals It is a monotonically decreasing function, therefore the Lyapunov functional is less than or equal to its initial time step. The value of, i.e. Then estimate the Lyapunov functional at the initial time. value , ,in Combining the expression of the Lyapunov functional with the given conditions, we obtain... Finally, based on Lyapunov stability theory and definition 1, it can be determined that the driving system (1) and the response system (2) are globally polynomial synchronized.

[0101] In some embodiments of the present invention, the following description utilizes a global exponential synchronization controller to determine the global exponential synchronization result, as follows: Example 2: Under the assumptions of the activation function and the uncertain parameters, and satisfying... Then, the drive system (1) and the response system (2) can achieve global exponential synchronization under the action of the global exponential synchronization controller (6).

[0102] First, construct a Lyapunov functional of the following form: in, It is represented as a Lyapunov functional. Represented as the first functional term, It is represented as the second functional term.

[0103] The design method and overall proof process of the global exponential synchronization controller in Example 2 refer to the basic architecture of Example 1, with corresponding modifications made to meet the requirements of exponential synchronization. A significant difference in the proof process occurs in step five: because the exponential function does not possess... The simplified scaling property of the form will result in an additional mathematical processing step. This makes it impossible for it to directly connect with mainstream forms. The terms are merged. This mathematical difference directly leads to the requirement that the global exponential synchronization controller (6) must adopt a more complex structure than the global polynomial synchronization controller (5) to compensate for the effect of this term. In step 6, the expression of the global exponential synchronization controller (6) is substituted into the objective derivative of the Lyapunov functional obtained in step 5, and appropriate parameters of the Lyapunov functional are selected to ultimately make thereby Re-estimate , ,in Combining the expression of the Lyapunov functional with the given conditions, we obtain... Finally, based on Lyapunov stability theory and definition 2, it can be determined that the driving system (1) and the response system (2) are globally exponentially synchronized.

[0104] Example 3: When the assumptions of activation function and uncertain parameters are met, the driving system (1) and the response system (2) can achieve global asymptotic synchronization under the action of global asymptotic synchronization controller (7).

[0105] Specifically, construct a Lyapunov functional of the following form: in, It is represented as a Lyapunov functional. Represented as the first functional term, It is represented as the second functional term.

[0106] Example 3 is a continuation of Examples 1 and 2. In special cases, the process of synchronizing the state of the second neural network with the state of the first neural network is similar to that in Embodiments 1 and 2, and will not be repeated here.

[0107] Overall, the analytical approaches for the three cases are basically the same, all relying on mathematical methods such as differential processing and inequality scaling to prove that the derivative of the Lyapunov functional satisfies... This demonstrates that Lyapunov functionals It is a monotonically decreasing function, therefore the Lyapunov functional is less than or equal to its initial time step. The value of, i.e. Re-estimate Then, based on the expression of the Lyapunov functional and the corresponding known conditions, the error state norm is given. The corresponding estimation formula is obtained, and then the corresponding synchronization criterion is obtained according to Definition 1, Definition 2 and Definition 3.

[0108] Finally, based on the above stability conclusions and the definition of synchronization, it can be rigorously proven that the driving system and the response system (a heterogeneous neural network with uncertainty) achieve the required global polynomial synchronization, global exponential synchronization, or global asymptotic synchronization.

[0109] In some embodiments of the present invention, numerical simulations using MATLAB were performed to verify the synchronization results of heterogeneous neural networks with uncertainties. The simulation results, including phase diagrams of the system state and time response curves, effectively confirmed the correctness of the synchronization results of the neural networks with uncertainties. Through the above embodiments, synchronization of the driving system and the response system can be achieved.

[0110] In some embodiments of the present invention, the present invention also provides an image decryption method based on heterogeneous neural network synchronization with uncertainty, applicable to an image encryption method based on heterogeneous neural network synchronization with uncertainty, comprising: When using the same adaptive controller as during encryption to achieve synchronization between the driving system and the response system, obtain at least two sets of chaotic response sequences generated by the response system during synchronization; The at least two sets of response chaotic sequences are fused to generate a composite response chaotic sequence; Based on the composite response chaotic sequence, the received encrypted image is decrypted to obtain a decrypted image; The driving system is a first neural network with proportional time delay and uncertainty parameters, and the response system is a second neural network with uncertainty and no time delay. The internal structures of the first neural network and the second neural network are different, and the first neural network and the second neural network constitute a heterogeneous neural network with uncertainty.

[0111] In some embodiments of the present invention, prior to the step of fusing the at least two sets of response chaotic sequences to generate a composite response chaotic sequence, the method includes: An adaptive controller is applied to the response system to drive the state of the response system to synchronize with the state of the driving system, thereby obtaining a synchronization result of a heterogeneous neural network with uncertainty; The adaptive controller includes at least a global polynomial synchronization controller, a global exponential synchronization controller, and a global asymptotic synchronization controller; the synchronization result of the heterogeneous neural network with uncertainty includes at least a global polynomial synchronization result, a global exponential synchronization result, and a global asymptotic synchronization result.

[0112] In some embodiments of the present invention, fusing the at least two sets of response chaotic sequences to generate a composite response chaotic sequence includes: Based on the global polynomial synchronization result, the first response chaotic sequence of the response system is obtained; Based on the global exponential synchronization result, the second response chaotic sequence of the response system is obtained; The first response chaotic sequence and the second response chaotic sequence are fused to generate the composite response chaotic sequence for decryption.

[0113] In some embodiments of the present invention, the step of decrypting the received encrypted image based on the composite response chaotic sequence to obtain a decrypted image includes: The received encrypted image is subjected to channel decomposition processing to obtain multiple target encrypted channel matrices; The stable portion of the composite response chaotic sequence is extracted based on the position parameters used during encryption to obtain the target composite response chaotic sequence. A pseudo-random sequence is generated using a nonlinear driven sequence generation algorithm and the target composite response chaotic sequence; Based on the pseudo-random sequence, the multiple target encrypted channel matrices are reversed and rearranged in terms of pixel position to obtain the color channel matrix after restoring the pixel position. The decryption process is performed based on the color channel matrix after restoring the pixel positions and the composite response chaotic sequence to obtain the decrypted image.

[0114] In some embodiments of the present invention, generating a pseudo-random sequence using a nonlinear driven sequence generation algorithm and the target composite response chaotic sequence includes: Based on the aforementioned composite response chaotic sequence, a nonlinear driven sequence generation algorithm (consistent with encryption) is designed. A nonlinear driven sequence generation algorithm is used to process the chaotic sequence of the target composite response to generate a pseudo-random sequence. The pseudo-random sequence is used to inversely perturb the pixel position and restore the pixel position.

[0115] In some embodiments of the present invention, the step of decrypting the image based on the color channel matrix after restoring pixel positions and the composite response chaotic sequence includes: perturbing the composite response chaotic sequence using the random sequence to obtain a perturbed composite response chaotic sequence; generating a decryption key matrix corresponding to each color channel based on the perturbed composite response chaotic sequence; performing a bitwise XOR operation on the decryption key matrix corresponding to each color channel and the color channel matrix after restoring pixel positions to recover multiple initial color channel matrices, and combining the initial color channel matrices to obtain the decrypted image.

[0116] The following example illustrates the decryption process: d) Image decryption: ① Generate response sequence: Take the response system sequence generated by the response system (2) under the action of the global polynomial synchronous controller (5). The response sequence generated under the action of the global exponential synchronization controller (6) To form a composite response sequence .

[0117] ② Sequence truncation processing steps: using the same positional parameters Loc = 20000 truncation sequence, skipping transient processes: For other sequences Perform the same interception operation.

[0118] ③ Generate pseudo-random sequences: Use the same formula as during encryption to generate nonlinear response sequences using an algorithm. .

[0119] By synchronizing the response system and the driving system, a nonlinear response sequence generation algorithm consistent with the encryption process is designed. (This refers to the consistency of coefficient signs, etc.), and then by the algorithm Generate pseudo-random sequences .

[0120] ④ Position perturbation recovery: using pseudo-random sequences Reverse the order of the three color channels of the encrypted image: Encrypt images Decomposed into three channels: : Encrypted red channel; : An encrypted green channel; The encrypted blue channel uses a pseudo-random sequence. Reverse mapping to restore the original pixel position: ⑤ Generate decryption key: Use the exact same random sequence as the encryption process. For composite response sequences Perturbation is performed to generate more complex chaotic perturbation response sequences. And construct three decryption keys: ⑥ Reverse XOR operation: Apply the inverse XOR operation to each of the three channels after position recovery: ⑦ Reconstruct and decrypt the image: The three decrypted color channel matrices are recombined to obtain the final decrypted image. .

[0121] Note: Symbols This represents a bitwise XOR operation. The decryption process is based on the reflexivity of the XOR operation: ,in, These are the original pixel values. It is the key.

[0122] In image encryption systems based on neural network synchronization control, the fundamental reason why the decrypted image sometimes cannot completely restore the original image is that synchronization can only achieve approximate rather than absolute consistency within a finite time. The resulting small synchronization error, after being amplified by the chaotic system and nonlinear transformation, leads to a non-negligible divergence between the key streams at the encryption and decryption ends, thus making it impossible to completely restore the decrypted image.

[0123] The chaotic sequences generated by the above synchronization control have the following characteristics: (i) For the same driving and response systems (1) and (2), the chaotic driving sequences that can achieve the three synchronizations (global polynomial synchronization, global exponential synchronization, and global asymptotic synchronization) are the same. The driving system (1) and the response system (2) are themselves chaotic (non-chaotic systems cannot be used for image encryption). The chaotic sequence used for encryption is generated by the driving system neural network (1) (which is the sequence corresponding to the driving system after the driving and response systems have achieved synchronization). Then, artificial perturbation is added to generate a perturbed chaotic sequence (the purpose of perturbation is to make the chaotic sequence more chaotic so that the confidentiality effect is better) for image encryption.

[0124] (ii) The response system under different controllers is the key to decryption. The response system (2) can be used for image decryption under three types of synchronization (global polynomial synchronization, global exponential synchronization, and global asymptotic synchronization). The reason is that under the three types of controllers, the response system can be synchronized with the driving system after a certain period of time (synchronization means that the driving and response systems are basically the same after a certain period of time). Therefore, the response system (2) with added controller can be used to decrypt the encrypted image.

[0125] In some embodiments of the present invention, the following embodiments can also be used for image decryption: M1. Image pixel decomposition: The received encrypted image is decomposed into an encrypted red channel matrix E_R, an encrypted green channel matrix E_G, and an encrypted blue channel matrix E_B; M2. Synchronization sequence generation and processing: M21. Two sets of chaotic response sequences generated by the response chaotic system under the action of different synchronization controllers are obtained and combined into a composite response sequence Y_comp; the response chaotic system and the driving chaotic system have been synchronized. M22. Using the same position parameter Loc as in the encryption step, the stable part of the composite response sequence Y_comp is extracted. M23. Using the stable part of the composite response sequence Y_comp, a nonlinear generation algorithm identical to that in the encryption step is designed to generate a pseudo-random sequence. .

[0126] M3. Image pixel position recovery: M31. Calculating pseudo-random sequences The inverse mapping. M32. Using pseudo-random sequences. The reverse mapping is used to rearrange the pixel positions of the encrypted channel matrices E_R, E_G, and E_B respectively, to obtain the channel matrices D_R, D_G, and D_B with the positions restored.

[0127] M4. Image Pixel Value Decryption: M41. Using the exact same random sequence as the encryption process. The composite response sequence Y_comp is perturbed to obtain a chaotic perturbed response sequence, and three decryption key matrices DK_R, DK_G, and DK_B are generated based on it. M42. The recovered channel matrices D_R, D_G, and D_B are XORed with their corresponding decryption key matrices DK_R, DK_G, and DK_B to decrypt the red channel matrix R, green channel matrix G, and blue channel matrix B. M5. Image reconstruction: The recovered R, G, and B channel matrices are reconstructed to obtain the decrypted image.

[0128] Figure 7 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 7 As shown, the electronic device may include a processor 710, a communications interface 720, a memory 730, and a communication bus 740. The processor 710, communications interface 720, and memory 730 communicate with each other via the communication bus 740. The processor 710 can call logical instructions from the memory 730 to execute an image encryption method based on heterogeneous neural network synchronization with uncertainty, or to execute an image decryption method based on heterogeneous neural network synchronization with uncertainty.

[0129] Furthermore, the logical instructions in the aforementioned memory 730 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0130] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the image encryption method based on heterogeneous neural network synchronization with uncertainty provided by the above methods, or to perform the image decryption method based on heterogeneous neural network synchronization with uncertainty.

[0131] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0132] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0133] 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 of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An image encryption method based on heterogeneous neural network synchronization with uncertainty, characterized in that, include: When the driving system and the response system are synchronized, at least two sets of chaotic sequences generated by the driving system in the synchronized state are obtained; The at least two sets of chaotic sequences are fused to generate a composite chaotic sequence; Based on the aforementioned complex chaotic sequence, the original image is encrypted to generate an encrypted image; The driving system is a first neural network with proportional time delay and uncertainty parameters, and the response system is a second neural network without time delay and uncertainty parameters. The internal structures of the first neural network and the second neural network are different, and the first neural network and the second neural network constitute a heterogeneous neural network with uncertainty.

2. The image encryption method based on heterogeneous neural network synchronization with uncertainty according to claim 1, characterized in that, Before the step of fusing the at least two sets of chaotic sequences to generate a composite chaotic sequence, the method includes: An adaptive controller is applied to the response system to drive the state of the response system to synchronize with the state of the driving system, thereby obtaining the synchronization result of the heterogeneous neural network. The adaptive controller includes at least a global polynomial synchronization controller, a global exponential synchronization controller, and a global asymptotic synchronization controller; the heterogeneous neural network synchronization result includes at least a global polynomial synchronization result, a global exponential synchronization result, and a global asymptotic synchronization result.

3. The image encryption method based on heterogeneous neural network synchronization with uncertainty according to claim 2, characterized in that, The step of fusing the at least two sets of chaotic sequences to generate a composite chaotic sequence includes: Based on the global polynomial synchronization result, the first chaotic sequence of the driving system is obtained; Based on the global exponential synchronization result, the second chaotic sequence of the driving system is obtained; The first chaotic sequence and the second chaotic sequence are fused to generate the composite chaotic sequence used for encryption.

4. The image encryption method based on heterogeneous neural network synchronization with uncertainty according to claim 2, characterized in that, The step of encrypting the original image based on the composite chaotic sequence to generate an encrypted image includes: The original image is decomposed into multiple initial color channel matrices; Based on the composite chaotic sequence and the multiple initial color channel matrices, the image pixel positions of the original image are perturbed to obtain the perturbed color channel matrix. Based on the composite chaotic sequence and the perturbed color channel matrix, the image pixel values ​​of the original image are encrypted to obtain the encrypted image.

5. The image encryption method based on heterogeneous neural network synchronization with uncertainty according to claim 4, characterized in that, The step of perturbing the image pixel positions of the original image based on the composite chaotic sequence and the plurality of initial color channel matrices to obtain a perturbed color channel matrix includes: A nonlinear driven sequence generation algorithm is designed based on the aforementioned composite chaotic sequence, and a pseudo-random sequence is generated according to the nonlinear driven sequence generation algorithm. The pixel positions of each initial color channel matrix are rearranged using the pseudo-random sequence to obtain a scrambled color channel matrix.

6. The image encryption method based on heterogeneous neural network synchronization with uncertainty according to claim 5, characterized in that, The step of encrypting the image pixel values ​​of the original image based on the composite chaotic sequence and the perturbed color channel matrix to obtain the encrypted image includes: A random sequence is generated, and the random sequence is used to perturb the composite chaotic sequence to obtain a chaotic perturbation driving sequence. The stable portion of the chaotic perturbation driving sequence is extracted according to preset position parameters to obtain the target chaotic perturbation driving sequence; Based on the target chaotic perturbation driving sequence, an encryption key matrix corresponding to each color channel is generated; The perturbed color channel matrix is ​​XORed with the corresponding encryption key matrix of the color channel to obtain the target encryption channel matrix corresponding to each color channel. The target encryption channel matrix corresponding to each color channel is then combined to generate the encrypted image.

7. An image decryption method based on heterogeneous neural network synchronization with uncertainty, applied to the image encryption method based on heterogeneous neural network synchronization with uncertainty as described in any one of claims 1 to 6, characterized in that, include: When using the same adaptive controller as during encryption to achieve synchronization between the driving system and the response system, obtain at least two sets of chaotic response sequences generated by the response system during synchronization; The at least two sets of response chaotic sequences are fused to generate a composite response chaotic sequence; Based on the composite response chaotic sequence, the received encrypted image is decrypted to obtain a decrypted image; The driving system is a first neural network with proportional time delay and uncertainty parameters, and the response system is a second neural network without time delay and uncertainty parameters. The internal structures of the first neural network and the second neural network are different, and the first neural network and the second neural network constitute a heterogeneous neural network with uncertainty.

8. The image decryption method based on heterogeneous neural network synchronization with uncertainty according to claim 7, characterized in that, Prior to the step of fusing the at least two sets of response chaotic sequences to generate a composite response chaotic sequence, the method includes: An adaptive controller is applied to the response system to drive the state of the response system to synchronize with the state of the driving system, thereby obtaining the synchronization result of the heterogeneous neural network. The adaptive controller includes at least a global polynomial synchronization controller, a global exponential synchronization controller, and a global asymptotic synchronization controller; the heterogeneous neural network synchronization result includes at least a global polynomial synchronization result, a global exponential synchronization result, and a global asymptotic synchronization result.

9. The image decryption method based on heterogeneous neural network synchronization with uncertainty according to claim 8, characterized in that, The step of fusing the at least two sets of response chaotic sequences to generate a composite response chaotic sequence includes: Based on the global polynomial synchronization result, the first response chaotic sequence of the response system is obtained; Based on the global exponential synchronization result, the second response chaotic sequence of the response system is obtained; The first response chaotic sequence and the second response chaotic sequence are fused to generate the composite response chaotic sequence for decryption.

10. The image decryption method based on heterogeneous neural network synchronization with uncertainty according to claim 9, characterized in that, The process of decrypting the received encrypted image based on the composite response chaotic sequence to obtain a decrypted image includes: The received encrypted image is subjected to channel decomposition processing to obtain multiple target encrypted channel matrices; The stable portion of the composite response chaotic sequence is extracted based on the position parameters used during encryption to obtain the target composite response chaotic sequence. A pseudo-random sequence is generated using a nonlinear driven sequence generation algorithm and the target composite response chaotic sequence; Based on the pseudo-random sequence, the multiple target encrypted channel matrices are reversed and rearranged in terms of pixel position to obtain the color channel matrix after restoring the pixel position. The decryption process is performed based on the color channel matrix after restoring the pixel positions and the composite response chaotic sequence to obtain the decrypted image.

11. The image decryption method based on heterogeneous neural network synchronization with uncertainty according to claim 10, characterized in that, The process of generating a pseudo-random sequence using a nonlinear driven sequence generation algorithm and the target composite response chaotic sequence includes: A nonlinear driven sequence generation algorithm is designed based on the aforementioned composite response chaotic sequence. The nonlinear driven sequence generation algorithm is used to process the target composite response chaotic sequence to generate a pseudo-random sequence identical to that used during encryption.

12. The image decryption method based on heterogeneous neural network synchronization with uncertainty according to claim 11, characterized in that, The decryption process, based on the color channel matrix after recovering pixel positions and the composite response chaotic sequence, yields a decrypted image, including: The composite response chaotic sequence is perturbed using the same random sequence as that used during encryption to obtain the perturbed composite response chaotic sequence. Based on the perturbed composite response chaotic sequence, a solution key matrix corresponding to each color channel is generated; Perform a bitwise XOR operation on the key matrix corresponding to each color channel and the color channel matrix after restoring the pixel positions to recover multiple initial color channel matrices. Then, combine the initial color channel matrices to obtain the decrypted image.

Images