Image encryption and restoration method of bimodal isomorphic dynamics system

Abstract

The invention discloses an image encryption and restoration method for a bimodal isomorphic dynamics system in a scene with high real-time requirements. The method comprises the following steps: firstly, constructing a nonlinear system, adjusting parameters under the same structure to obtain a four-dimensional chaotic system for encryption and decryption and a stochastic resonance system for noise reduction, and carrying out characteristic analysis on the two systems; and then, a chaotic encryption and decryption algorithm is researched, the algorithm firstly uses a high-randomness chaotic sequence to perform random point scrambling on an original image, then performs diffusion encryption in combination with a Latin matrix, and decryption is an inverse process of encryption, so that high-security encryption and decryption of the image are realized. And finally, a repair algorithm after large-area damage of the image is researched, the algorithm firstly utilizes a stochastic resonance system to carry out noise reduction processing on the damaged image, and then feature information is clearer through integral repair. Experiments verify that the encryption algorithm has good communication confidentiality, and the restoration algorithm can effectively restore the feature information of the image under the condition that the image is seriously damaged.

Description

Technical Field

[0001] This invention relates to the fields of communication security and image restoration, and more specifically to an image encryption and restoration method for a bimodal isomorphic dynamic system. Background Technology

[0002] Digital images, as a crucial carrier of the information age, are vital for secure transmission and integrity assurance in fields such as military, medical, financial, and personal privacy. However, image data faces a dual challenge when transmitted over public network channels: on the one hand, unauthorized access and malicious attacks continuously threaten the confidentiality and integrity of images; on the other hand, the inherent instability of the channels and packet loss can easily lead to large-scale image damage, severely impacting the availability of information.

[0003] Traditional secure transmission schemes suffer from structural flaws in addressing channel unreliability. Current mainstream image secure transmission methods generally employ a "encrypt first, transmit later, retransmit if packet loss occurs" approach. In conventional communication environments, this approach can ensure complete data delivery through the retransmission mechanism of the transport layer protocol. However, in extreme scenarios involving high-intensity warfare, high real-time demands, or limited resources—such as electronic warfare in military communications, unstable channels in emergency command, transmission delays of tens of minutes in deep space exploration, and extremely limited bandwidth in underwater sensor networks—retransmission mechanisms often fail due to excessive latency, resource consumption, or link unavailability. In such cases, even with strong encryption, widespread packet loss or corruption leaves the receiver with only incomplete, undecipherable ciphertext, resulting in the complete loss of critical information. Regarding encryption technology, chaotic systems, due to their initial value sensitivity, ergodicity, and quasi-random characteristics, have become a crucial foundation for constructing high-strength image encryption algorithms. Meanwhile, stochastic resonance, a nonlinear phenomenon that utilizes noise to enhance weak signals, offers a new approach to extracting feature information from strong noise backgrounds.

[0004] In summary, an integrated solution that organically combines high-strength chaotic encryption with a repair algorithm for large-scale ciphertext damage is crucial in communication conditions with high real-time requirements, extremely limited communication resources, unreliable links, or those under attack. This invention aims to solve this technical problem. Summary of the Invention

[0005] This invention provides an image encryption and restoration method for a dual-modal isomorphic dynamic system to address the issues of protecting the privacy of image information and restoring image information in scenarios with high real-time requirements, extremely limited communication resources, unreliable links, or under attack, where data retransmission has failed. The method utilizes the initial value sensitivity, ergodicity, and pseudo-randomness of chaotic systems to encrypt image information, increasing the difficulty of decryption during communication. Furthermore, it leverages the noise reduction function and integral algorithm of stochastic resonance systems to make the image's feature information clearer.

[0006] A method for image encryption and restoration of a bimodal isomorphic dynamical system includes the following steps: S1. Construct a nonlinear system, and under the same construction, adjust the parameters to obtain a four-dimensional chaotic system for encryption and decryption, and a stochastic resonance system for noise reduction. The chaotic sequence generated by the chaotic system can be used for image encryption and decryption, and the stochastic resonance system can be used for signal noise reduction. S2. A chaotic encryption and decryption algorithm is proposed. The algorithm first uses a highly random chaotic sequence to randomly scramble the points of the original image, and then combines it with a Latin matrix for diffusion encryption. Decryption is the reverse process of encryption, thereby achieving high-security encryption and decryption of the image. S3. Research on restoration algorithms for large-area image damage. The algorithm first uses a stochastic resonance system to denoise the damaged image, and then uses integral restoration to make the feature information clearer.

[0007] 1. A method for image encryption and restoration of a bimodal isomorphic dynamic system, characterized in that step S1 of claim 1 specifically includes the following steps: S11. A four-dimensional chaotic system was constructed, where x, y, z, and w are the system's state variables, and a, b, c, d, e, f, g, k, m, and n are adjustable parameters. Its mathematical expression is as follows: , Let a=50, b=15, c=15, d=10, e=11, f=26, g=6, k=30, m=1, n=10, with an initial value of [1 1 1 1]. Use the chaotic sequence under these parameter conditions for subsequent encryption and decryption operations.

[0008] S12. Select the first dimension as the signal input and adjust the parameters to transform the differential equation into a stochastic resonance system with noise reduction function. , As shown in the following formula, express y, z, and w using a relation containing x. , Substituting the relational expression shown above into -ax-by+czw+S(t)=0, we obtain the equilibrium equation of the stochastic resonance system as shown below. , make Then -F(x) + S(t) = 0, that is, the intersection of the equilibrium curves F(x) and S(t) is the equilibrium point of the stochastic resonance system.

[0009] Let a=1, b=-8, c=-12, d=10, e=40, f=-90, g=-15, k=10, m=20, n=60. Using this parameter condition, a stochastic resonance system is subjected to subsequent noise reduction. Substituting the parameters, the equilibrium point curve is shown in the following equation. , When a noisy signal is input into this stochastic resonance system, the particles can convert the noise energy into the driving force for the signal to cross the potential barrier, thereby extracting the weak signal component in the nonlinear response and amplifying it to achieve effective signal noise reduction.

[0010] 2. A method for image encryption and restoration of a bimodal isomorphic dynamic system, characterized in that step S2 of claim 1 specifically includes the following steps: Chaotic sequences have high randomness, which can be used to scramble and spread image matrices.

[0011] S21. The steps for randomizing points are as follows: 1) Input an image matrix A of size r*c, and perform the following preprocessing on a chaotic sequence x, y, z, w of a certain length. , Where i can be 1, 2, 3, or 4, N can be x, y, z, or w, and M can be r or c. Randomly paired to form a set of unique coordinate points that conform to the image size. ;; 2) After decomposing the RGB layers of the original image, first fold the three layer matrices horizontally, then perform row transformations according to the row and column transformation rules based on the random number of points Ir. Next, fold the transformed layer matrices vertically, and then perform column transformations based on the random number of points Ic. , Row and column transformation rules: When the value of I is 0, no row or column transformation occurs; when the value of I is 1, the row transformation is a left rotation and the column transformation is an upward rotation; when the value of I is 2, the row transformation is a right rotation and the column transformation is a downward transformation. 3) Extract the data at the corresponding row and column positions of R1 in sequence and store them in a one-dimensional matrix B. Then, put B into matrix C in sequence according to R2 to obtain a scrambled matrix C of size r*c.

[0012] S22. Combine the scrambled matrix data C with a Latin matrix and perform diffusion encryption. The Latin matrix diffusion encryption steps are as follows: 1) Input matrix C, and perform the following preprocessing on chaotic sequences x and y of length r*c*4 to obtain I5 and I6 with numerical range [0,3]. 2) Traverse matrix I5 sequentially until a one-dimensional matrix D of size 1*4 containing only different values ​​is stored. Then, perform plane addition and solid addition operations on matrix D to obtain a 4*4*4 Latin matrix E with a value range of [0,3]. This results in a three-dimensional solid matrix, and x, y, and z coordinate axes are constructed. Taking a one-dimensional matrix D=[0 2 3 1] as an example, perform a planar increment operation (i.e. ), resulting in a 4x4x4 Latin matrix. ; 3) Convert matrix C into a one-dimensional matrix F, and convert the values ​​from decimal to quaternary to obtain a one-dimensional matrix G of size 1*(4*r*c); 4) By mapping the values ​​of I5 to the x-axis of the 3D coordinate system, the values ​​of I6 to the y-axis, and the values ​​of matrix G to the z-axis, we can obtain the corresponding new values ​​Hh, thus achieving data diffusion. ; 5) Convert the diffused data from quaternary to decimal, and finally reassemble it into an r*c encryption matrix J to obtain the encryption graph.

[0013] S23. Decrypt the encrypted graph. The decryption process is the reverse of the encryption process.

[0014] 3. A method for image encryption and restoration of a bimodal isomorphic dynamic system, characterized in that step S3 of claim 1 specifically includes the following steps: Image restoration first uses a stochastic resonance system to denoise the encrypted image after interpolation by 100 times, and then uses the equilibrium point curve to restore the values. Finally, the feature information of the denoised image is restored using an integral algorithm.

[0015] S31. The random resonance noise reduction steps are as follows: 1) Set the interpolation factor to 100, extend the signal of the original image using linear interpolation, and then perform encryption and decryption operations. If a large-scale attack occurs during transmission, process the data information of the decrypted image that has not been interpolated and restored into a row matrix data, then normalize the data to the range of [-1,1], and input the data into the x dimension of the system for noise reduction processing. 2) Match the output data to the curve Restoring the numerical value to its original value before numerical gain by the stochastic resonance system, while retaining only the noise reduction effect of the stochastic resonance system; 3) Normalize the values ​​restored according to the curve to the range of [0,255], perform interpolation restoration, and finally reassemble them into the required denoised image.

[0016] The steps of the S32 integral repair algorithm are as follows: 1) Obtain the corresponding histogram from the image, connect the vertices of the histogram, and smooth it into a curve; 2) Divide the curve evenly into 8 sub-intervals, and fit a cubic polynomial curve to each interval using least squares to accurately describe the histogram distribution characteristics. Then, integrate each piecewise polynomial and adjust the integration constant to ensure the continuity of adjacent segments at the boundaries, forming a smooth integral curve; 3) Globally normalize the integral curves to map them to the range [0, 255] that meets the requirements of image pixel values. Then, according to the piecewise continuous transformation function, transform each pixel value of the image to the corresponding value according to the mapping relationship, and finally reconstruct the output image.

[0017] The beneficial effects of this invention are as follows: In response to the problem of retransmission mechanism failure in high real-time, high-confrontation, and resource-constrained scenarios such as military confrontation, emergency command, deep space exploration, and underwater communication, this invention can directly recover decryptable image information from damaged ciphertext without data retransmission, effectively ensuring the continuity of critical services and the ultimate accessibility of information.

[0018] By organically combining the security of chaotic encryption systems with the signal recovery capabilities of stochastic resonance systems, a complete integrated technical solution of "encryption-transmission-damage repair" has been constructed. This solution overcomes the limitation of traditional methods where encryption and fault tolerance mechanisms are independent, enabling the system to autonomously repair large-scale damage to encrypted data while ensuring data confidentiality. Attached Figure Description

[0019] Figure 1 This is a time series diagram of a chaotic system for an image encryption and restoration method for a bimodal isomorphic dynamic system.

[0020] Figure 2 This paper presents a chaotic system attractor phase diagram of different dimensions for an image encryption and repair method for a bimodal isomorphic dynamic system.

[0021] Figure 3 The chaotic system complexity diagrams for an image encryption and repair method for a bimodal isomorphic dynamic system are shown in (a) and (b) respectively.

[0022] Figure 4 This is a schematic diagram of the equilibrium point of a stochastic resonance system and the input and output of an x-dimensional noisy signal, which is used for image encryption and restoration of a dual-modal isomorphic dynamic system.

[0023] Figure 5 The potential function curve of a stochastic resonance system is presented as an image encryption and restoration method for a dual-modal isomorphic dynamic system.

[0024] Figure 6 This is a flowchart illustrating the image encryption and decryption process for an image encryption and restoration method for a bimodal isomorphic dynamic system.

[0025] Figure 7 This is an example of a random point scrambling row and column transformation for an image encryption and restoration method of a bimodal isomorphic dynamic system.

[0026] Figure 8 This is an example of random coordinate scrambling for random point scrambling in an image encryption and restoration method for a bimodal isomorphic dynamic system.

[0027] Figure 9 The image encryption and restoration method for a bimodal isomorphic dynamic system is represented by the Latin matrix E-cubic coordinate diagram.

[0028] Figure 10 The image encryption and decryption algorithm is shown as an experimental result of an image encryption and restoration method for a bimodal isomorphic dynamic system.

[0029] Figure 11 This is a basic flowchart of the noise reduction and restoration method for image encryption and restoration of a dual-modal isomorphic dynamic system.

[0030] Figure 12 This is a flowchart of a noise reduction method for image encryption and restoration of a bimodal isomorphic dynamic system.

[0031] Figure 13 This is an integral restoration flowchart for an image encryption and restoration method for a bimodal isomorphic dynamic system.

[0032] Figure 14 This is an encrypted image of different attacked regions for an image encryption and repair method of a bimodal isomorphic dynamic system.

[0033] Figure 15 This image shows the restoration effect of different attacked regions in a method for image encryption and restoration of a bimodal isomorphic dynamic system. Detailed Implementation

[0034] The invention will now be further described with reference to the accompanying drawings.

[0035] like Figure 1 As shown, an image encryption and restoration method for a bimodal isomorphic dynamic system includes the following steps: S1. Construct a nonlinear system, and under the same construction, adjust the parameters to obtain a four-dimensional chaotic system for encryption and decryption, and a stochastic resonance system for noise reduction. The chaotic sequence generated by the chaotic system can be used for image encryption and decryption, and the stochastic resonance system can be used for signal noise reduction. S2. A chaotic encryption and decryption algorithm is proposed. The algorithm first uses a highly random chaotic sequence to randomly scramble the points of the original image, and then combines it with a Latin matrix for diffusion encryption. Decryption is the reverse process of encryption, thereby achieving high-security encryption and decryption of the image. S3. Research on restoration algorithms for large-area image damage. The algorithm first uses a stochastic resonance system to denoise the damaged image, and then uses integral restoration to make the feature information clearer.

[0036] 1. A method for image encryption and restoration of a bimodal isomorphic dynamic system, characterized in that step S1 of claim 1 specifically includes the following steps: S11. A four-dimensional chaotic system was constructed, where x, y, z, and w are the system's state variables, and a, b, c, d, e, f, g, k, m, and n are adjustable parameters. Its mathematical expression is as follows: , Let a=50, b=15, c=15, d=10, e=11, f=26, g=6, k=30, m=1, n=10, with an initial value of [1 1 1 1]. Use the chaotic sequence under these parameter conditions for subsequent encryption and decryption operations. (1) When c=15, the timing diagram and attractor phase diagram are as follows: Figure 1 and Figure 2 As shown, from Figure 1 and Figure 2 It can be seen that the time-series trajectory exhibits a continuous broadband spectrum, noise-like and non-repeating non-periodic oscillations, indicating that the motion has inherent randomness; the attractor forms a strange attractor with a complex and fine structure in the phase space, and its trajectory is stretched, folded and densely entangled in a finite region, revealing the nonlinearity of the system, its sensitive dependence on initial conditions and its long-term unpredictability. (2) Select The SE complexity plot and CO complexity plot at parameter c are as follows: Figure 3 As shown, from Figure 3 It can be seen that the maximum SE complexity of x, y, z, and w dimensions is above 0.6, and the maximum CO complexity is above 0.2. Among them, the maximum CO complexity of x dimension is above 0.7. This indicates that the chaotic sequence of the chaotic system has high complexity and can be used as a random sequence in the process of image encryption and decryption to improve the confidentiality of image encryption and decryption.

[0037] S12. Select the first dimension as the signal input and adjust the parameters to transform the differential equation into a stochastic resonance system with noise reduction function. , As shown in the following formula, express y, z, and w using a relation containing x. , Substituting the relational expression shown above into -ax-by+czw+S(t)=0, we obtain the equilibrium equation of the stochastic resonance system as shown below. , make Then -F(x) + S(t) = 0, that is, the intersection of the equilibrium curves F(x) and S(t) is the equilibrium point of the stochastic resonance system.

[0038] Let a=1, b=-8, c=-12, d=10, e=40, f=-90, g=-15, k=10, m=20, n=60. Using this parameter condition, a stochastic resonance system is subjected to subsequent noise reduction operations. A schematic diagram showing the input and output of the x-dimensional noisy signal with the parameter equilibrium point is shown below. Figure 4 As shown, the equilibrium point curve at this point is given by the following formula. , Calculation yields Figure 4 Central origin O(0,0), zero point Zero point Maximum point Minimum point .

[0039] And by Figure 4 It can be known that when and When S(t) intersects the curve F(x) at only one point, When S(t) intersects the curve F(x) at points C and N, when At time t, S(t) intersects the curve F(x) at points D and M. S(t) intersects the curve F(x) at three points.

[0040] like Figure 4 As shown, when a noisy signal is input into the x-dimensional stochastic resonance system, the value of F(x) on the equilibrium point curve corresponds to the value of x, thus achieving signal gain processing. However, this invention only needs to apply the noise reduction effect of stochastic resonance. To improve the image restoration effect, the value of x of the noise-reduced gain signal is substituted into the formula F(x) to obtain the corresponding F(x) value, thereby restoring the signal gain effect.

[0041] Integrating F(x) yields the potential function ,like Figure 5 As shown, the potential function curve exhibits a symmetrical double-potential-well characteristic, and calculations show that... When, the two minimum points are respectively , At this point, the system is in a stable equilibrium state, and the corresponding potential energy value is The potential barrier vertex between these two potential wells is located at the origin O(0,0), and the barrier height is... .

[0042] When a noisy signal is input into this stochastic resonance system, the particles can convert the noise energy into the driving force for the signal to cross the potential barrier, thereby extracting the weak signal component in the nonlinear response and amplifying it to achieve effective signal noise reduction.

[0043] 2. A method for image encryption and restoration of a bimodal isomorphic dynamic system, characterized in that step S2 of claim 1 specifically includes the following steps: like Figure 6 As shown, chaotic sequences have high randomness, which can be used to scramble and diffuse image matrices.

[0044] S21. The steps for randomizing points are as follows: 1) Input an image matrix A of size r*c, and perform the following preprocessing on a chaotic sequence x, y, z, w of a certain length. , Where i can be 1, 2, 3, or 4, N can be x, y, z, or w, and M can be r or c. Randomly paired to form a set of unique coordinate points that conform to the image size. ; 2) After decomposing the RGB layers of the original image, first fold the three layer matrices horizontally, then perform row transformations according to the row and column transformation rules based on the random number of points Ir. Next, fold the transformed layer matrices vertically, and then perform column transformations based on the random number of points Ic. , Row and column transformation rules: When the value of I is 0, no row or column transformation occurs; when the value of I is 1, the row transformation is a leftward rotation, and the column transformation is an upward rotation; when the value of I is 2, the row transformation is a rightward rotation, and the column transformation is a downward transformation. For example... Figure 7 As shown, matrix transformations are performed using I=[0 1 2 0 1 2] as an example; 3) Extract the data at the corresponding row and column positions of R1 sequentially and store them in a one-dimensional matrix B. Then, sequentially insert B into matrix C according to R2 to obtain a scrambled matrix C of size r*c; for example... Figure 8 As shown, taking R1=[1,2;2,2;2,1;1,1] and R2=[2,1;1,2;1,1;2,2] as examples, random number scrambling is performed.

[0045] S22. Combine the scrambled matrix data C with a Latin matrix and perform diffusion encryption. The Latin matrix diffusion encryption steps are as follows: 1) Input matrix C, and perform the following preprocessing on chaotic sequences x and y of length r*c*4 to obtain I5 and I6 with values ​​in the range [0,3]. ; 2) Traverse matrix I5 sequentially until a one-dimensional matrix D of size 1*4 containing only different values ​​is stored. Then, perform plane addition and solid addition operations on matrix D to obtain a 4*4*4 Latin matrix E with a value range of [0,3]. This results in a three-dimensional solid matrix, and x, y, and z coordinate axes are constructed. Taking a one-dimensional matrix D=[0 2 3 1] as an example, perform a planar increment operation (i.e. ), resulting in a 4x4x4 Latin matrix. , can be represented as Figure 9 The cube diagram shown; 3) Convert matrix C into a one-dimensional matrix F, and convert the values ​​from decimal to quaternary to obtain a one-dimensional matrix G of size 1*(4*r*c); 4) By mapping the values ​​of I5 to the x-axis of the 3D coordinate system, the values ​​of I6 to the y-axis, and the values ​​of matrix G to the z-axis, we can obtain the corresponding new values ​​Hh, thus achieving data diffusion. ; 5) Convert the diffused data from quaternary to decimal, and finally reassemble it into an r*c encryption matrix J to obtain the encryption graph.

[0046] S23. Decrypt the encrypted image; the decryption process is the reverse of the encryption process. An experimental result of encrypting and decrypting an image is shown below. Figure 10 As shown.

[0047] 3. A method for image encryption and restoration of a bimodal isomorphic dynamic system, characterized in that step S3 of claim 1 specifically includes the following steps: like Figure 11 As shown, the image restoration first uses a stochastic resonance system to denoise the encrypted image after interpolation by 100 times, and then uses the equilibrium point curve to restore the values. Finally, the feature information of the denoised image is restored using an integral algorithm.

[0048] S31. For example Figure 12 As shown, the random resonance noise reduction steps are as follows: 1) Set the interpolation factor to 100, extend the signal of the original image using linear interpolation, and then perform encryption and decryption operations. If a large-scale attack occurs during transmission, process the data information of the decrypted image that has not been interpolated and restored into a row matrix data, then normalize the data to the range of [-1,1], and input the data into the x dimension of the system for noise reduction processing. 2) Match the output data to the curve Restoring the numerical value to its original value before numerical gain by the stochastic resonance system, while retaining only the noise reduction effect of the stochastic resonance system; 3) Normalize the values ​​restored according to the curve to the range of [0,255], perform interpolation restoration, and finally reassemble them into the required denoised image.

[0049] S32. For example Figure 13 As shown, the steps of the integral repair algorithm are as follows: 1) Obtain the corresponding histogram from the image, connect the vertices of the histogram, and smooth it into a curve; 2) Divide the curve evenly into 8 sub-intervals, and fit a cubic polynomial curve to each interval using least squares to accurately describe the histogram distribution characteristics. Then, integrate each piecewise polynomial and adjust the integration constant to ensure the continuity of adjacent segments at the boundaries, forming a smooth integral curve; 3) Globally normalize the integral curves to map them to the range [0, 255] that meets the requirements of image pixel values. Then, according to the piecewise continuous transformation function, transform each pixel value of the image to the corresponding value according to the mapping relationship, and finally reconstruct the output image.

[0050] To verify the effectiveness of this noise reduction and restoration algorithm in restoring images subjected to different large-area attacks during chaotic encryption and decryption processes, comparative experiments were conducted, such as... Figure 14 The images shown are encrypted images with 70%, 75%, and 80% of their data area affected by the attack. The experimental results of image denoising and restoration after decryption of these encrypted images with data loss in different areas are shown below. Figure 15 As shown.

[0051] In the figure, (a1), (a2), and (a3) ​​are the original images; (b1), (b2), and (b3) are the images directly interpolated and restored after decryption of the encrypted images in different attacked areas; (c1), (c2), and (c3) are the images restored after decryption of the encrypted images in different attacked areas by noise reduction and interpolation using a random resonance system; (d1), (d2), and (d3) are the integral restoration images of (c1), (c2), and (c3), respectively; Figures (a1), (b1), (c1), and (d1) show the experimental results when the attacked area is 70%; Figures (a1), (b1), (c1), and (d1) show the experimental results when the attacked area is 75%; and Figures (a1), (b1), (c1), and (d1) show the experimental results when the attacked area is 80%.

[0052] It can be observed that Figure 15 Figures (b1), (b2), and (b3) obscure most of the image's feature information, and as the attacked area increases, more and more information is obscured. Consequently, the amount of normal pixel values ​​available for recovery decreases in steps (c1), (c2), (c3), and (d1), (d2), and (d3). However, comparing figures (b1), (b2), and (b3) with figures (d1), (d2), and (d3), figures (d1), (d2), and (d3) show more of the feature information from figures (a1), (a2), and (a3), while figures (b1), (b2), and (b3) show less or no of the feature information from figures (a1), (a2), and (a3). This demonstrates that when subjected to large-scale attacks during chaotic encryption and decryption, this noise reduction and repair algorithm can effectively recover the feature information interfered with by noise.

[0053] The scope of protection of this invention is not limited to the embodiments described above. Those skilled in the art can make obvious adjustments, modifications, or equivalent substitutions to the technical solutions without departing from the concept of this invention. Any modifications, equivalent substitutions, and improvements to these embodiments should be included within the scope of protection of the claims of this invention.

Claims

1. A method for image encryption and restoration of a dual-modal isomorphic dynamic system, characterized in that, Includes the following steps: S1. Construct a nonlinear system, and under the same construction, adjust the parameters to obtain a four-dimensional chaotic system for encryption and decryption, and a stochastic resonance system for noise reduction. The chaotic sequence generated by the chaotic system can be used for image encryption and decryption, and the stochastic resonance system can be used for signal noise reduction. S2. A chaotic encryption and decryption algorithm is proposed. The algorithm first uses a highly random chaotic sequence to randomly scramble the points of the original image, and then combines it with a Latin matrix for diffusion encryption. Decryption is the reverse process of encryption, thereby achieving high-security encryption and decryption of the image. S3. Research on restoration algorithms for large-area image damage. The algorithm first uses a stochastic resonance system to denoise the damaged image, and then uses integral restoration to make the feature information clearer.

2. A method for image encryption and restoration of a dual-modal isomorphic dynamic system, characterized in that, Step S1 as described in claim 1 specifically includes the following steps: S11. A four-dimensional chaotic system was constructed, where x, y, z, and w are the system's state variables, and a, b, c, d, e, f, g, k, m, and n are adjustable parameters. Its mathematical expression is as follows: ， Let a=50, b=15, c=15, d=10, e=11, f=26, g=6, k=30, m=1, n=10, with an initial value of [1 1 1 1]. Use the chaotic sequence under these parameter conditions for subsequent encryption and decryption operations. S12. Select the first dimension as the signal input and adjust the parameters to transform the differential equation into a stochastic resonance system with noise reduction function. ， Let a=1, b=-8, c=-12, d=10, e=40, f=-90, g=-15, k=10, m=20, n=60, and perform subsequent noise reduction operations on the stochastic resonance system under these parameter conditions.

3. A method for image encryption and restoration of a dual-modal isomorphic dynamic system, characterized in that, Step S2 as described in claim 1 specifically includes the following steps: Chaotic sequences possess high randomness, a property that can be used to scramble and diffuse image matrices. S21. The steps for randomizing points are as follows: 1) Input an image matrix A of size r*c, and perform the following preprocessing on a chaotic sequence x, y, z, w of a certain length. ， Where i can be 1, 2, 3, or 4, N can be x, y, z, or w, and M can be r or c. Randomly paired to form a set of unique coordinate points that conform to the image size. ; 2) After decomposing the RGB layers of the original image, first fold the three layer matrices horizontally, then perform row transformations according to the row and column transformation rules based on the random number of points Ir. Next, fold the transformed layer matrices vertically, and then perform column transformations based on the random number of points Ic. ， Row and column transformation rules: When the value of I is 0, no row or column transformation occurs; when the value of I is 1, the row transformation is a left rotation and the column transformation is an upward rotation; when the value of I is 2, the row transformation is a right rotation and the column transformation is a downward transformation. 3) Extract the data at the corresponding row and column positions of R1 in sequence and store them in a one-dimensional matrix B. Then put B into matrix C in sequence according to R2 to obtain a scrambled matrix C of size r*c. S22. Combine the scrambled matrix data C with a Latin matrix and perform diffusion encryption. The Latin matrix diffusion encryption steps are as follows: 1) Input matrix C, and perform the following preprocessing on chaotic sequences x and y of length r*c*4 to obtain I5 and I6 with numerical range [0,3]. ， 2) Traverse matrix I5 sequentially until a one-dimensional matrix D of size 1*4 containing only different values ​​is stored. Then, perform plane addition and solid addition operations on matrix D to obtain a 4*4*4 Latin matrix E with a value range of [0,3]. This results in a three-dimensional solid matrix, and x, y, and z coordinate axes are constructed. 3) Convert matrix C into a one-dimensional matrix F, and convert the values ​​from decimal to quaternary to obtain a one-dimensional matrix G of size 1*(4*r*c); 4) By mapping the values ​​of I5 to the x-axis of the three-dimensional coordinate system, the values ​​of I6 to the y-axis, and the values ​​of matrix G to the z-axis, we can obtain the corresponding new values ​​Hh, thereby achieving data diffusion. ， 5) Convert the diffused data from quaternary to decimal, and finally reassemble it into an r*c encryption matrix J to obtain the encryption diagram; S23. Decrypt the encrypted graph. The decryption process is the reverse of the encryption process.

4. A method for image encryption and restoration of a dual-modal isomorphic dynamic system, characterized in that, Step S3 as described in claim 1 specifically includes the following steps: Image restoration first uses a stochastic resonance system to denoise the original image (after interpolation by a factor of 100) and then recovers the numerical values ​​using an equilibrium point curve. Finally, an integral algorithm is used to restore the feature information of the denoised image. S31. The random resonance noise reduction steps are as follows: 1) Set the interpolation factor to 100, extend the signal of the original image using linear interpolation, and then perform encryption and decryption operations. If a large-scale attack occurs during transmission, process the data information of the decrypted image that has not been interpolated and restored into a row matrix data, then normalize the data to the range of [-1,1], and input the data into the x dimension of the system for noise reduction processing. 2) Match the output data to the curve Restoring the numerical value to its original value before numerical gain by the stochastic resonance system, while retaining only the noise reduction effect of the stochastic resonance system; 3) Normalize the values ​​restored according to the curve to the range of [0,255], perform interpolation restoration, and finally reassemble them into the required denoised image; The steps of the S32 integral repair algorithm are as follows: 1) Obtain the corresponding histogram from the image, connect the vertices of the histogram, and smooth it into a curve; 2) Divide the curve evenly into 8 sub-intervals, and fit a cubic polynomial curve to each interval using least squares to accurately describe the histogram distribution characteristics. Then, integrate each piecewise polynomial and adjust the integration constant to ensure the continuity of adjacent segments at the boundaries, forming a smooth integral curve; 3) Globally normalize the integral curves to map them to the range [0, 255] that meets the requirements of image pixel values. Then, according to the piecewise continuous transformation function, transform each pixel value of the image to the corresponding value according to the mapping relationship, and finally reconstruct the output image.

Images