An image encryption method based on AERZN-SD

Abstract

This invention discloses an AERZN-SD-based image encryption method, belonging to the field of image encryption technology. The method comprises the following steps: S1, obtaining an image to be encrypted and calculating the pixel values of its three RGB channels; S2, substituting the calculated pixel values into a constructed secondary chaotic system and generating a chaotic sequence under the action of a controller; wherein the controller in the secondary chaotic system is an AERZN image encryption controller constructed based on the AERZN-PS evolution model and the image encryption chaotic sequence generation dynamics model; S3, performing diffuse XOR processing on the image to be encrypted using the generated chaotic sequence to generate an encrypted image. The method has the characteristics of high security and stability, a strong correlation between the key and the image content, and a fast convergence of the chaotic sequence generation process. Furthermore, the method is adaptable and flexible, and can achieve real-time dynamic encryption of large-scale images.

Description

Technical Field

[0001] The present invention belongs to the field of image encryption technology, and specifically relates to an image encryption method based on AERZN-SD; wherein AERZN refers to Adaptive Error Correlated Zeroing Neural Dynamics, and SD (Scrambling-Diffusion) refers to Scrambling-Diffusion. Background Art

[0002] Image encryption is a secure method for protecting image data by transforming and manipulating image content to render it incomprehensible and prevent unauthorized access. Its core purpose is to ensure the confidentiality and integrity of images during transmission, storage, or processing. Typical image encryption algorithms incorporate cryptographic techniques, transforming the original image into ciphertext through transformation, obfuscation, diffusion, and scrambling. Only those holding the correct key can recover the original information.

[0003] Among existing image encryption methods, the implementation of image scrambling encryption based on the Arnold transform involves periodically mapping image pixel coordinates using the Arnold transform matrix, iteratively scrambling pixel positions (conventional scrambling). This method has the following drawbacks: the Arnold transform has a fixed period, allowing attackers to crack it by exhaustively counting the number of iterations; the pixel values remain unchanged, and the encrypted image retains the original pixel statistical characteristics (such as the histogram), making it vulnerable to statistical attacks; and noise interference can cause scrambling to fail or decrypt errors.

[0004] The implementation process of a chaotic encryption method based on the logistic map involves generating a pseudo-random sequence using the logistic map formula, quantizing the chaotic sequence into index values, scrambling the pixel positions, and modifying the pixel values through an exclusive-or operation. This method has the following drawbacks: under certain parameters, the logistic map exhibits periodicity rather than chaos, resulting in insufficient randomness; in noisy environments, chaotic sequence synchronization is difficult, and the encryption and decryption processes are prone to mismatch; and generating high-quality chaotic sequences requires a high computational load, making it difficult to process large images in real time. Summary of the Invention

[0005] In view of the above-mentioned deficiencies in the prior art, the image encryption method based on AERZN-SD provided by the present invention solves the problem that the existing image encryption method has insufficient security and stability and is difficult to support the requirements of size image encryption.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: an image encryption method based on AERZN-SD, comprising the following steps:

[0007] S1. Obtain the image to be encrypted and calculate the pixel values of its RGB channels respectively;

[0008] S2, substituting the calculated pixel values into the constructed secondary chaotic system and generating a chaotic sequence under the action of the controller;

[0009] The controller in the secondary chaotic system is an AERZN image encryption controller constructed based on the AERZN-PS evolution model and the image encryption chaotic sequence generation dynamics model; the AERZN image encryption controller is constructed by substituting the first-order derivative of the error in the AERZN-PS evolution model into the image encryption chaotic sequence generation dynamics model;

[0010] S3. Use the generated chaotic sequence to perform diffusion XOR processing on the image to be encrypted to generate an encrypted image.

[0011] Furthermore, in step S2, the secondary chaotic system is expressed as:

[0012] ;

[0013] Where, 、 、 and Represent the four state variables in the secondary chaotic system, 、 、 and Respectively 、 、 and The first derivative of 、 、 and Respectively 、 、 and The corresponding four controllers, , , , .

[0014] Furthermore, in step S2, the method for constructing the AERZN image encryption controller is specifically as follows:

[0015] S21. Define the error function in the synchronization process of the hyperchaotic Lorenz system and derive it;

[0016] S22, bringing the primary chaotic system and the secondary chaotic system into the derived error function to obtain a dynamic model for chaotic sequence generation for image encryption;

[0017] S23, constructing the AERZN evolution formula, and performing nonlinear activation based on it to obtain the AERZN-PS evolution model;

[0018] S24. Based on the image encryption chaotic sequence generation dynamic model and AERZN-PS evolution model, an AERZN image encryption controller is constructed.

[0019] Furthermore, in step S21, the error function is:

[0020] ;

[0021] Where, , , , Indicates error, They represent the errors corresponding to the four state variables in the hyperchaotic Lorenz system, represents the state variables in the main chaotic system, Represent the four state variables in the main chaotic system, represents the state variables in the secondary chaotic system, Represent the four state variables in the secondary chaotic system, Represents the transpose operator.

[0022] Furthermore, in step S22, the image encryption chaotic sequence generation dynamics model is expressed as:

[0023] ;

[0024] Where, 、 、 and They represent the first-order derivatives of the errors of the four state variables in the synchronization process of the hyperchaotic Lorenz system, 、 、 and Represent the four state variables in the secondary chaotic system, Represent the four state variables in the main chaotic system, 、 、 and They represent the four controllers corresponding to the four state variables in the synchronization process of the hyperchaotic Lorenz system, , , , .

[0025] Furthermore, in step S23, the AERZN-PS evolution model is expressed as:

[0026] ;

[0027] Where, Representation error The first derivative of Representation and Error The related positive increasing scalar function is expressed as , represents the parameter used to control the convergence speed, Represents a vector-valued activation function.

[0028] Furthermore, in step S24, the AERZN image encryption controller is represented as:

[0029] ;

[0030] Where, 、 、 and Represent the four state variables in the secondary chaotic system, 、 、 and Respectively 、 、 and The corresponding four controllers, 、 、 and Represent the four state variables in the main chaotic system, 、 、 and Represent the activation functions corresponding to the four state vectors, 、 、 and They represent the errors corresponding to the four state variables in the hyperchaotic Lorenz system, Representation and Error The associated positive increasing scalar function, , , , .

[0031] Furthermore, in step S2, the chaotic sequence generated Expressed as:

[0032] ;

[0033] Where, They represent the four state variables in the chaotic sequence formed after continuous adjustment by the controller in the secondary chaotic system.

[0034] The beneficial effects of the present invention are:

[0035] (1) High-security encryption mechanism:

[0036] The method of the present invention is based on the hyperchaotic Lorenz system, generates a complex pseudo-random sequence, has a huge key space, and resists exhaustive attacks; the present invention adopts a scrambling-diffusion joint operation to further improve encryption security, wherein scrambling refers to disrupting pixel positions through a chaotic sequence to destroy image spatial correlation, and diffusion refers to modifying pixel values through an exclusive-or operation to uniformize the histogram.

[0037] (2) The key is strongly associated with the image content:

[0038] In the method of the present invention, the hash sum of the three-channel pixel values of the original image is used as the initial value of the chaotic system to achieve "one Figure 1 Key", to avoid the vulnerability of fixed keys.

[0039] (3) Strong noise resistance and stability:

[0040] The method of the present invention introduces a nonlinear activation function into the AERZN-PS evolution formula to effectively suppress high-frequency noise interference; in a noisy environment, According to the dynamic adjustment of the error, the error adaptive suppression is achieved to ensure the robustness of the chaotic system synchronization.

[0041] (4) Rapid convergence:

[0042] The AERZN model in the method of the present invention is adaptive error related parameters The convergence speed is adjusted in real time. The larger the error, the higher the k(t) value, which accelerates the synchronization process. Simulation results show that the synchronization error convergence time of the AERZN controller is only 0.016 seconds, which is much faster than the 0.142 seconds of the PTNIZNN controller.

[0043] (5) Adaptability and flexibility:

[0044] The method of the present invention adjusts the parameters of the control convergence speed The value of can be adjusted according to the user's needs to balance the convergence speed and computational overhead. The AERZN model used in this invention has low computational complexity and can support real-time processing of large-size images (such as 512×512), realizing real-time dynamic encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1This is a flow chart of the image encryption method based on AERZN-SD provided by the present invention.

[0046] Figure 2 Schematic diagram of the three-dimensional trajectory of the hyperchaotic Lorzen system synchronization provided by the present invention.

[0047] Figure 3 Schematic diagram of the synchronization error norm of the hyperchaotic Lorenz system under the action of different controllers provided by the present invention.

[0048] Figure 4 This is a schematic diagram of the image to be encrypted provided by the present invention.

[0049] Figure 5 This is a schematic diagram of the encryption effect of the encrypted image after processing using the AERZN-SD algorithm provided by the present invention.

[0050] Figure 6 The pixel distribution histograms of the three channels provided by the present invention. DETAILED DESCRIPTION

[0051] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0052] The embodiment of the present invention provides an image encryption method based on AERZN-SD, such as Figure 1 As shown, the following steps are included:

[0053] S1. Obtain the image to be encrypted and calculate the pixel values of its RGB channels respectively;

[0054] S2, substituting the calculated pixel values into the constructed secondary chaotic system and generating a chaotic sequence under the action of the controller;

[0055] The controller in the secondary chaotic system is an AERZN image encryption controller constructed based on the AERZN-PS evolution model and the image encryption chaotic sequence generation dynamics model; the AERZN image encryption controller is constructed by substituting the first-order derivative of the error in the AERZN-PS evolution model into the image encryption chaotic sequence generation dynamics model;

[0056] S3. Use the generated chaotic sequence to perform diffusion XOR processing on the image to be encrypted to generate an encrypted image.

[0057] In step S1 of the embodiment of the present invention, for the three-way color image to be encrypted, the size is , whose three channel pixel matrices are 、 and , calculate the pixel values of the three RGB channels of the image to be encrypted respectively, which are expressed as follows:

[0058] ;

[0059] The pixel value of the image to be encrypted after processing is used as the initial value of the secondary chaotic system to enhance the correlation between the image and the key, which is expressed as follows:

[0060] ;

[0061] In step S2 of this embodiment, the chaotic system becomes an ideal tool for image encryption due to its extreme sensitivity to initial conditions and pseudo-random characteristics. The main chaotic system is described as follows:

[0062] ;

[0063] Where, 、 、 and Represent the four state variables in the main chaotic system, 、 、 and Respectively 、 、 and The first-order derivative of , , , .

[0064] The secondary chaotic system is expressed as:

[0065] ;

[0066] Where, 、 、 and Represent the four state variables in the secondary chaotic system, 、 、 and Respectively 、 、 and The first derivative of 、 、 and Respectively 、 、 and The corresponding four controllers, , , , .

[0067] In step S2 of the embodiment of the present invention, the method for constructing the AERZN image encryption controller is specifically as follows:

[0068] S21. Define the error function in the synchronization process of the hyperchaotic Lorenz system and derive it;

[0069] S22, bringing the primary chaotic system and the secondary chaotic system into the derived error function to obtain a dynamic model for chaotic sequence generation for image encryption;

[0070] S23, constructing the AERZN evolution formula, and performing nonlinear activation based on it to obtain the AERZN-PS evolution model;

[0071] S24. Based on the image encryption chaotic sequence generation dynamic model and AERZN-PS evolution model, an AERZN image encryption controller is constructed.

[0072] In step S21 of this embodiment, the error function is defined as:

[0073] ;

[0074] Where, , , , Indicates error, They represent the errors corresponding to the four state variables in the hyperchaotic Lorenz system, represents the state variables in the main chaotic system, Represent the four state variables of the main chaotic system, represents the state variables in the secondary chaotic system, Represent the four state variables in the secondary chaotic system, represents the transpose operator;

[0075] Taking the derivative of the above error function, we get:

[0076] ;

[0077] Substituting the primary chaotic system and the secondary chaotic system into the above derivation formula, the dynamic model of image encryption chaotic sequence generation is obtained as follows:

[0078] ;

[0079] Where, 、 、 and They represent the first-order derivatives of the errors of the four state variables in the synchronization process of the hyperchaotic Lorenz system, 、 、 and Represent the four state variables in the secondary chaotic system, 、 、 and Represent the four state variables in the main chaotic system, 、 、 and They represent the four controllers corresponding to the four state variables in the synchronization process of the hyperchaotic Lorenz system, , , , .

[0080] In step S23 of this embodiment, the new AERZN evolution formula constructed is:

[0081] ;

[0082] in, Representation and Error The related positive increasing scalar function is expressed as:

[0083] ;

[0084] Where, represents the parameter used to control the convergence speed, specifically, The larger the value of , the faster the convergence speed. Therefore, in practical applications, we should choose a larger or appropriately larger value as much as possible according to the needs. value.

[0085] In order to further improve the convergence speed, this embodiment provides an AERZN evolution formula activated by a nonlinear function, which is called the AERZN-PS evolution model, which is expressed as:

[0086] ;

[0087] Where, Representation error The derivative of Representation and Error The related positive increasing scalar function is expressed as , represents the parameter used to control the convergence speed, Represents a vector-valued activation function.

[0088] In this embodiment, the robustness of the system to high-frequency interference is enhanced by performing nonlinear activation on the AERZN evolution formula; at the same time, Coefficients according to state Dynamic adjustment is performed to achieve noise suppression, where .

[0089] In step S24 of this embodiment, based on the synchronization of the AERZN model and the chaotic system, the AERZN image encryption controller constructed in this embodiment is expressed as:

[0090] ;

[0091] Where, 、 、 and Represent the four state variables in the secondary chaotic system, 、 、 and Respectively 、 、 and The corresponding four controllers, 、 、 and Represent the four state variables in the main chaotic system, 、 、 and Represent the activation functions corresponding to the four state vectors, 、 、 and They represent the errors corresponding to the four state variables in the hyperchaotic Lorenz system, Representation and Error The associated positive increasing scalar function, , , , .

[0092] Based on the above controller, in step S2 of the embodiment of the present invention, the chaotic sequence generated Expressed as:

[0093] ;

[0094] Where, They represent the four state variables in the chaotic sequence formed after continuous adjustment by the controller in the secondary chaotic system.

[0095] Where, Represent the four state variables in the secondary chaotic system respectively.

[0096] In step S3 of the embodiment of the present invention, the process of performing diffusion XOR processing on the encrypted image using the chaotic sequence is as follows:

[0097] Quantize the chaotic sequence, including normalizing the floating point values of the chaotic sequence to the range of 0 to 255 and merging the four-dimensional sequence into a one-dimensional sequence;

[0098] Perform diffusion XOR operation on the R, G, and B channels of the encrypted image respectively;

[0099] The chaotic sequence is XORed with the image pixel value bit by bit in sequence, and the encryption result of the current pixel in the encrypted image depends not only on the current chaotic sequence value, but also on the previous encrypted pixel value.

[0100] The embodiment of the present invention provides a simulation verification example of the above-mentioned image encryption method.

[0101] In this embodiment, numerical and simulation experiments are used to verify the AERZN model in terms of time-varying parameters. The effectiveness of image encryption under the effect of MATLAB R2023b software platform is simulated, and the simulation results are as follows: Figure 2 As shown, in Figure 2 In the figure, the red and blue solid lines represent the synchronization trajectories of the master and slave systems, respectively. The three-dimensional projections from four different perspectives clearly demonstrate that the proposed AERZN image encryption controller (hereafter referred to as the AERZN controller) can accurately synchronize the master and slave systems.

[0102] To verify the fast convergence of the AERZN controller and the stability of the AERZN-PS controller, the PTTIZNN (predefined-time noise immunity ZNN) controller was selected as a comparison benchmark. Figure 3 Show the synchronization error norm of the hyperchaotic Lorenz system under different controllers. Figure 2The solid red, blue, and green lines represent the synchronization error norms for the PTTIZNN, AERZN, and AERZN-PS controllers, respectively. Under the same conditions, the AERZN controller (blue curve) converges to zero in approximately 0.016 seconds, significantly faster than the PTTIZNN controller (red curve, 0.142 seconds). Furthermore, the AERZN-PS controller (green curve) exhibits excellent stability and achieves superior synchronization accuracy.

[0103] In this embodiment, the AERZN-SD method of the present invention is used to process a 512×512 fruit image ( Figure 4 ) is encrypted, and the encryption result is as follows Figure 5 As shown, it can be seen that the information in the original image is completely scrambled and no valuable information can be obtained from the encrypted image.

[0104] The distribution of pixels in an image is often described as a histogram, which shows the number of pixels at a certain gray level in the image. Figure 6 The histograms of different channels of the original image and the encrypted image are shown. From the results, it can be seen that the pixel distribution of the encrypted image is very different from that of the original image and is evenly distributed. Figure 6 In the figure, the top three images are the R, G, and B component channels of the original image, and the bottom three images are the R, G, and B component channels of the encrypted image.

[0105] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0106] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. An image encryption method based on AERZN-SD, characterized in that: The following steps are involved: S1. Obtain the image to be encrypted and calculate the pixel values of its RGB channels respectively; S2, substituting the calculated pixel values into the constructed secondary chaotic system and generating a chaotic sequence under the action of the controller; The controller in the secondary chaotic system is an AERZN image encryption controller constructed based on the AERZN-PS evolution model and the image encryption chaotic sequence generation dynamics model; the AERZN image encryption controller is constructed by substituting the first-order derivative of the error in the AERZN-PS evolution model into the image encryption chaotic sequence generation dynamics model; S3. Use the generated chaotic sequence to perform diffusion XOR processing on the image to be encrypted to generate an encrypted image.

2. The image encryption method based on AERZN-SD according to claim 1, characterized in that: In step S2, the secondary chaotic system is expressed as: ； Where, 、 、 and Represent the four state variables in the secondary chaotic system, 、 、 and Respectively 、 、 and The first derivative of 、 、 and Respectively 、 、 and The corresponding four controllers, , , , .

3. The image encryption method based on AERZN-SD according to claim 1, characterized in that: In step S2, the method for constructing the AERZN image encryption controller is specifically as follows: S21. Define the error function in the synchronization process of the hyperchaotic Lorenz system and derive it; S22, bringing the primary chaotic system and the secondary chaotic system into the derived error function to obtain a dynamic model for chaotic sequence generation for image encryption; S23, constructing the AERZN evolution formula, and performing nonlinear activation based on it to obtain the AERZN-PS evolution model; S24. Based on the image encryption chaotic sequence generation dynamic model and AERZN-PS evolution model, an AERZN image encryption controller is constructed.

4. The image encryption method based on AERZN-SD according to claim 3, characterized in that: In step S21, the error function is: ； Where, , , , Indicates error, They represent the errors corresponding to the four state variables in the hyperchaotic Lorenz system, represents the state variables in the main chaotic system, Represent the four state variables in the main chaotic system, represents the state variables in the secondary chaotic system, Represent the four state variables in the secondary chaotic system, Represents the transpose operator.

5. The image encryption method based on AERZN-SD according to claim 3, characterized in that: In step S22, the image encryption chaotic sequence generation dynamics model is expressed as: ； Where, 、 、 and They represent the first-order derivatives of the errors of the four state variables in the synchronization process of the hyperchaotic Lorenz system, 、 、 and Represent the four state variables in the secondary chaotic system, Represent the four state variables in the main chaotic system, 、 、 and They represent the four controllers corresponding to the four state variables in the synchronization process of the hyperchaotic Lorenz system, , , , .

6. The image encryption method based on AERZN-SD according to claim 3, characterized in that: In step S23, the AERZN-PS evolution model is expressed as: ； Where, Representation error The first derivative of Representation and Error The related positive increasing scalar function is expressed as , represents the parameter used to control the convergence speed, Represents a vector-valued activation function.

7. The image encryption method based on AERZN-SD according to claim 3, characterized in that: In step S24, the AERZN image encryption controller is represented as: ； Where, 、 、 and Represent the four state variables in the secondary chaotic system, 、 、 and Respectively 、 、 and The corresponding four controllers, 、 、 and Represent the four state variables in the main chaotic system, 、 、 and Represent the activation functions corresponding to the four state vectors, 、 、 and They represent the errors corresponding to the four state variables in the hyperchaotic Lorenz system, Representation and Error The associated positive increasing scalar function, , , , .

8. The image encryption method based on AERZN-SD according to claim 3, characterized in that: In step S2, the chaotic sequence generated Expressed as: ； Where, They represent the four state variables in the chaotic sequence formed after continuous adjustment by the controller in the secondary chaotic system.

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