Encryption method for alignment plane image of grid multi-scroll conservative chaotic system

Abstract

The invention discloses image encryption based on combination of a grid multi-scroll conservative chaotic system and bit plane decomposition, and relates to the technical field of image encryption. According to the method, bit plane encryption is carried out on the image by constructing the multi-scroll conservative chaotic system, so that higher-level information security guarantee is realized through a complex phase space structure and rich dynamic behaviors of the multi-scroll conservative chaotic system, the complexity of the system is increased by the multi-scroll characteristic, a more flexible parameter adjustment space is also provided, and the image security is improved. And a solid foundation is laid for designing an efficient and safe encryption algorithm.

Description

Technical Field

[0001] The invention relates to the technical field of image encryption, and in particular to an encryption method for a plane image using a grid multi-scroll conservative chaotic system. Background Art

[0002] In recent years, with the improvement of computing power and the development of mathematical models, the application research of chaotic systems in image encryption has made significant progress. Hu et al. proposed a new image coding scheme under the framework of parallel compressed sensing; Hanis et al. designed an image encryption system based on integer key generation algorithm and improved logical mapping; Niu et al. proposed an image encryption scheme by integrating evolutionary operators. However, the encryption algorithms in these studies have not been strictly verified by cryptanalysis. It can be seen from the information entropy and correlation data that these algorithms have poor anti-attack and robustness. In order to improve the defects of these algorithms, this study combines a highly complex and random conservative chaotic system with medical images to design a highly robust medical image encryption algorithm. In this process, cryptographic analysis, algorithm optimization, hardware acceleration and other technical means can be used to enhance anti-attack capabilities, optimize key management, improve implementation efficiency, and enhance numerical stability to improve the security and practicality of the algorithm.

[0003] Conservative chaotic systems are a type of nonlinear systems with conservative dynamic characteristics. Compared with traditional chaotic systems, the trajectory of conservative chaotic systems in phase space does not shrink to the attractor, but spreads throughout the entire phase space. This characteristic makes conservative chaotic systems more complex and unpredictable in the key space, and is suitable for use in encryption technology to enhance security. In addition, the initial value sensitivity and pseudo-randomness of the multi-scroll conservative chaotic system with multi-piecewise functions are more conducive to generating complex encryption sequences, thereby increasing the difficulty of cracking. Studies have shown that the image encryption algorithm based on the multi-scroll conservative chaotic system can achieve high encryption efficiency and low computational complexity while ensuring security, meeting the real-time requirements in practical medical applications. Summary of the invention

[0004] The purpose of the present invention is to solve the above-mentioned problem and to provide a method for encrypting the bit plane of an image using a grid multi-scroll conservative chaotic system.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: using a grid multi-scroll conservative chaotic system to perform bit plane encryption on an image, and the specific content of the grid multi-scroll conservative chaotic system is as follows:

[0006] The equation of the 1D grid multi-scroll conservative chaotic system is shown in formula (3):

[0007] (3)

[0008] The equation of the 2D grid multi-scroll conservative chaotic system is shown in equation (4):

[0009] (4)

[0010] The equation of the 3D grid multi-scroll conservative chaotic system is shown in equation (5):

[0011] (5)

[0012] The equation of the 4D grid multi-scroll conservative chaotic system is shown in equation (6):

[0013] (6)

[0014] Among them, a=10, b=9, c=6 are parameters, x, y, z, w are state variables, initial values ​​(x0, y0, z0, w0)=(0.9, 0.9, 0.9, 0.9), g(x), g(y), g(z), g(w) are four multi-piece functions;

[0015] Then, Matlab is used to numerically simulate the multi-scroll conservative chaotic system and conduct dynamic analysis on it;

[0016] Secondly, the circuit simulation software is used to conduct circuit simulation on the multi-scroll conservative chaotic system;

[0017] Finally, the image is encrypted by combining the bit plane image and the multi-scroll conservative chaotic system. The specific steps are as follows:

[0018] Step 1. Input image: Substitute an 8-bit grayscale plaintext image P with a size of M×N and randomly select 5000 pixels;

[0019] Step 2, bit plane decomposition: decompose each pixel value of the plaintext image P into a high four-bit matrix H and a low four-bit matrix L;

[0020] Step 3, generate chaotic sequence: input the key parameters of the chaotic system, and obtain 4 chaotic sequences (x, y, z, w) of length M×N through iterative operation;

[0021] Step 4: Sort the chaotic sequence x to generate a new sequence x' and a position sequence T. Use T to scramble the columns and rows of the high four-bit matrix H to obtain H'; use the chaotic sequence z to obtain the matrix H T , and then use H T Perform diffusion operation on H' to obtain the final encrypted high four-bit matrix H"; the scrambling and diffusion equations are shown in equations (7) and (8):

[0022] (7)

[0023] (8)

[0024] Step 5: Sort the chaotic sequence y to generate the position sequence K, use K to scramble the columns and rows of the lower four-bit matrix L to obtain L', and use the chaotic sequence w to diffuse L' to obtain the final encrypted lower four-bit matrix L";

[0025] Step 6: Merge the encrypted high four-bit matrix H" and low four-bit matrix L" to generate the final 8-bit ciphertext image P';

[0026] The above method is used to encrypt the grayscale image of chest X-ray film with a standard size of 512×512;

[0027] During the encryption process, the Arnold algorithm is used to perform a scrambling operation on the binary matrix. The scrambling operation is defined as:

[0028] (9)

[0029] The Arnold algorithm converts the i row and j column in the matrix to p row and q column, sets the parameters a and b to 3 and 5, and the number of iterations to 20.

[0030] Furthermore, the circuit simulation steps are as follows:

[0031] (1) Standardize the required chaotic system equations;

[0032] (2) Draw the circuit according to the standardized equation and select the required components from the component library of Multisim software;

[0033] (3) Set the parameters of each component according to the parameters of the chaotic system equation;

[0034] (4) Add measurement tools such as oscilloscopes and multimeters to the circuit to observe the dynamic behavior of the system.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) The chaotic sequence generated by the conservative chaotic system has good randomness and unpredictability, and has strong encryption and anti-attack capabilities when applied to image encryption.

[0037] (2) The bit plane decomposition and reorganization process can ensure the integrity of the image and prevent information loss. The encryption process of different bit planes increases the difficulty of attack.

[0038] (3) The scrambling process is complex enough that even if the attacker obtains partial information, it is still difficult to infer the original image. The diffusion process fully mixes each pixel of the image to enhance resistance to differential attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a multi-segmented function diagram of different M values ​​of the present invention;

[0040] Figure 2 A schematic diagram of constructing a multi-scroll conservative chaotic system according to the present invention;

[0041] Figure 3 It is a circuit simulation diagram of the 4D multi-scroll conservative chaotic system of the present invention;

[0042] Figure 4 It is a block diagram of the encryption principle of the present invention;

[0043] Figure 5 The encrypted images of the present invention when the number of iterations n is different;

[0044] Figure 6 A schematic diagram showing the comparison of the original image and the encrypted image histogram of the present invention;

[0045] Figure 7 It is a schematic diagram of correlation comparison between the original image and the encrypted image of the present invention;

[0046] Figure 8 This is the eight-bit encrypted phase diagram of the present invention. DETAILED DESCRIPTION

[0047] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0048] A method for encrypting a plane image using a grid multi-scroll conservative chaotic system. The invention first constructs a multi-scroll conservative chaotic system, so that it can achieve a higher level of information security through a complex phase space structure and rich dynamic behavior. The multi-scroll characteristic not only increases the complexity of the system, but also provides a more flexible parameter adjustment space, laying a solid foundation for designing an efficient and secure encryption algorithm.

[0049] The chaotic system proposed by the present invention is:

[0050] (1)

[0051] The multi-piecewise function is:

[0052] (2)

[0053] Among them, a=10, b=9, c=6 are parameters, x, y, z, w are state variables, and the initial values ​​are (x0, y0, z0, w0)=(0.9, 0.9, 0.9, 0.9). σ is a state variable, M is an adjustable parameter, and when M takes different values, the graph of function g(σ) is shown in Figure (1). It can be seen that function g(σ) is a sawtooth function symmetrical based on the origin, and the number of segments of function g(σ) also changes due to different values ​​of M. In addition, it is observed that the scroll structure usually appears in the positive slope region of the function g(σ) broken line, while the bond band structure is concentrated in the negative slope region.

[0054] Figure 1 (a) M=1; (b) M=2; (c) M=3.

[0055] The construction method of multi-scroll conservative chaotic system is as follows Figure 2 shown.

[0056] The equation of the 1D grid multi-scroll conservative chaotic system is shown in formula (3):

[0057] (3)

[0058] The equation of the 2D grid multi-scroll conservative chaotic system is shown in formula (4):

[0059] (4)

[0060] The equation of the 3D grid multi-scroll conservative chaotic system is shown in equation (5):

[0061] (5)

[0062] The equation of the 4D grid multi-scroll conservative chaotic system is shown in equation (6):

[0063] (6)

[0064] Matlab is used to perform numerical simulation on the chaotic system and to perform dynamic analysis on it to verify the chaotic characteristics of the system. For example, the Lyapunov index analysis of the system found that the four indexes are completely symmetrical based on the horizontal axis; by calculating the equilibrium point of the system, it is found that its type is central type and saddle type, which conforms to the characteristics of conservative chaotic systems; secondly, the circuit simulation software is used to perform circuit simulation on the chaotic system. The circuit simulation steps are as follows:

[0065] (1) Standardize the required chaotic system equations.

[0066] (2) Draw the circuit according to the standardized equation. Select the required components in the component library of Multisim software, such as operational amplifiers, resistors, capacitors, etc.

[0067] (3) Set the parameters of each component (such as resistance value, capacitance value) according to the parameters of the chaotic system equation.

[0068] (4) Add measurement tools such as oscilloscopes and multimeters to the circuit to observe the dynamic behavior of the system.

[0069] The circuit simulation diagram of the multi-scroll conservative chaotic system is shown in Figure 3 shown.

[0070] Finally, the image is encrypted by combining bit plane image and multi-scroll conservative chaotic system.

[0071] The core principle of bit-plane image encryption is to use the internal structural characteristics of pixel values ​​in digital images. Each pixel value can be represented as a binary number consisting of 8 binary bits, which can be divided into different bit planes. Taking chest X-ray images as an example, the detailed description of the principle is as follows Figure 4 As shown;

[0072] The steps of image encryption combining bit plane image and multi-scroll conservative chaotic system are as follows:

[0073] Step 1: Input image. Substitute into an 8-bit grayscale plaintext image P, whose size is M×N, and randomly select 5000 pixels.

[0074] Step 2: Bit plane decomposition: Decompose each pixel value of the plaintext image P into a high four-bit matrix H and a low four-bit matrix L.

[0075] Step 3: Generate chaotic sequences. Input the key parameters of the chaotic system and obtain four chaotic sequences (x, y, z, w) of length M×N through iterative operations.

[0076] Step 4: Sort the chaotic sequence x to generate a new sequence x' and position sequence T. Use T to scramble the columns and rows of the high four-bit matrix H to get H'. Use the chaotic sequence z to get the matrix H T , and then use H T Perform diffusion operation on H' to obtain the final encrypted high four-bit matrix H". The scrambling and diffusion equations are shown in equations (7) and (8):

[0077] (7)

[0078] (8)

[0079] Step 5: Sort the chaotic sequence y to generate the position sequence K. Use K to scramble the columns and rows of the lower four-bit matrix L to obtain L'. Use the chaotic sequence w to diffuse L' to obtain the final encrypted lower four-bit matrix L".

[0080] Step 6: Combine the encrypted high four-bit matrix H" and low four-bit matrix L" to generate the final 8-bit ciphertext image P'.

[0081] The above method is used to encrypt a chest X-ray grayscale image with a standard size of 512×512. The encryption results of different iteration times are as follows:

[0082] During the encryption process, the Arnold algorithm is used to scramble the binary matrix. Its characteristic is that after multiple iterations, the image will gradually return to its initial state, forming a periodic cycle. Therefore, the Arnold transform is reversible, which allows the encryption process to be decrypted through an inverse transform. This scrambling method is derived from the Arnold-Cat mapping, which is a transformation method that repeatedly stretches and folds pixel coordinates in a limited space and is defined as:

[0083] (9)

[0084] The Arnold algorithm converts the i row and j column in the matrix to p row and q column, sets the parameters a and b to 3 and 5, and the number of iterations to 20. Figure 5 It can be seen that when the number of iterations is very low, the image has not been completely encrypted. When the number of iterations increases to 10, the image has been completely encrypted. When the number of iterations reaches 18, some details of the image gradually appear.

[0085] Figure 5 In the figure, (a) n=0; (b) n=2; (c) n=10; (d) n=18, where n is the number of iterations.

[0086] Example:

[0087] (1) Grayscale histogram

[0088] like Figure 6 As shown, the histogram of the original chest X-ray image shows an uneven distribution and there is obvious pixel correlation. This makes the image vulnerable to attacks based on statistical analysis. However, the histogram encrypted by the algorithm proposed in the present invention shows a highly uniform distribution feature. This fully demonstrates that the encryption method can effectively conceal the gray value distribution of the plaintext image and greatly reduce the correlation between pixels. It shows that the encryption algorithm based on the bit plane can effectively change the statistical characteristics of the original image, which not only hides the effective information of the image, but also greatly increases the difficulty of decryption for attackers, providing a strong guarantee for image security protection.

[0089] Figure 6 (a) is the original image histogram; (b) is the encrypted image histogram.

[0090] (2) Correlation analysis of adjacent pixels

[0091] It can be clearly seen from the experimental data in Table 1 that this algorithm does significantly reduce the correlation between adjacent pixels in the image during the encryption process. The correlation coefficients of the plaintext image in the horizontal, vertical and diagonal directions are all large, indicating that there is a strong correlation between adjacent pixels. After encryption, the correlation coefficients of the ciphertext image in all directions are significantly reduced and approach 0, indicating that the correlation between adjacent pixels has been well destroyed. The pixel distribution of the original and encrypted images of the chest X-ray in different directions is shown in Figure 1. Figure 7 As shown in the figure. It can be clearly seen that the adjacent pixels of the plaintext image show obvious linear distribution in the horizontal, vertical and diagonal directions, reflecting strong correlation. The distribution of adjacent pixels of the encrypted ciphertext image in these three directions becomes uniform and irregular, indicating that the correlation is greatly reduced. This significant disturbance of the correlation of adjacent pixels effectively destroys the statistical characteristics of the original image and greatly improves the image's ability to resist statistical analysis attacks. This not only improves the security of the algorithm, but also enhances its feasibility and practicality in practical applications.

[0092]

[0093] Figure 7 (a), (b), (c) are the horizontal, vertical and diagonal directions of the original image; (d), (e), (f) are the horizontal, vertical and diagonal directions of the encrypted image.

[0094] (3) Information entropy

[0095] Information entropy is an important indicator for measuring the information content of image pixels and plays a key role in evaluating the performance of encryption algorithms. The calculation method is shown in formula (10):

[0096] (10)

[0097] L is the gray level, p(x i ) represents the gray value x i The probability of occurrence. For an 8-bit grayscale image, the theoretical maximum value of information entropy is 8. The information entropy of the algorithm calculated by formula (10) is 7.9994. It can be found that the information entropy after encryption is closer to the theoretical value. The encryption algorithm can effectively disturb the statistical characteristics of the original image, so that the encrypted image information tends to be randomly distributed, which not only enhances the algorithm's ability to resist statistical analysis attacks, but also improves the security and privacy protection level of image data. From the perspective of information entropy, the encryption algorithm has achieved remarkable results in improving the randomness of image data.

[0098] In the field of digital image processing, bit plane decomposition is a widely used technique. Each pixel value of a grayscale image with a size of M×N and a grayscale level of 256 is represented as an 8-bit binary number. The bit value distribution of the 8 different bit planes constituting the image can be calculated by equation (11).

[0099] (11)

[0100] Wherein, P(i, j) represents the pixel value at the coordinate (i, j), and k∈{1, 2, ..., 8} represents the kth bit plane.

[0101] Figure 8 It is the original image of the grayscale image and the eight bit planes it is decomposed into, which are the original image, the first bit, the second bit... the eighth bit. From the figure, we can clearly observe that there are significant differences in the plaintext image information contained in different bit planes. Although the clarity of the planes located in the high bit positions, such as the eighth to the fifth bit, gradually decreases, the general outline of the image can still be outlined. However, as the level of the bit plane decreases, the image details gradually disappear. Starting from the fourth bit, the image is difficult to identify, and at the first bit plane, almost no valid information can be seen. This shows that a large amount of plaintext information contained in the low-bit bit planes has been hidden.

[0102] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0103] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for encrypting an image bit plane using a grid multi-scroll conservative chaotic system, comprising constructing a grid multi-scroll conservative chaotic system by introducing a multi-segment function, characterized in that: The image is bit-plane encrypted using a grid multi-scroll conservative chaotic system, and the specific content of the grid multi-scroll conservative chaotic system is as follows: The equation of the 1D grid multi-scroll conservative chaotic system is shown in formula (3): (3) The equation of the 2D grid multi-scroll conservative chaotic system is shown in formula (4): (4) The equation of the 3D grid multi-scroll conservative chaotic system is shown in equation (5): (5) The equation of the 4D grid multi-scroll conservative chaotic system is shown in formula (4): (6) Among them, a=10, b=9, c=6 are parameters, x, y, z, w are state variables, g(x), g(y), g(z), g(w) are four multi-piece functions, and the initial values ​​(x0, y0, z0, w0)=(0.9, 0.9, 0.9, 0.9); Then, Matlab is used to numerically simulate the grid multi-scroll conservative chaotic system, and dynamic analysis is performed to verify the chaotic characteristics of the system. Secondly, the circuit simulation software is used to conduct circuit simulation on the multi-scroll conservative chaotic system; Finally, the image is encrypted by combining the bit plane image and the multi-scroll conservative chaotic system. The specific steps are as follows: Step 1. Input image: Substitute an 8-bit grayscale plaintext image P with a size of M×N and randomly select 5000 pixels; Step 2, bit plane decomposition: decompose each pixel value of the plaintext image P into a high four-bit matrix H and a low four-bit matrix L; Step 3, generate chaotic sequence: input the key parameters of the chaotic system, and obtain 4 chaotic sequences (x, y, z, w) of length M×N through iterative operation; Step 4: Sort the chaotic sequence x to generate a new sequence x' and position sequence T. Use T to scramble the columns and rows of the high four-bit matrix H to obtain H'; use the chaotic sequence z to process the matrix H T , and then use H T Perform diffusion operation on H' to obtain the final encrypted high four-bit matrix H"; the scrambling and diffusion equations are shown in equations (7) and (8): (7) (8) Step 5: Sort the chaotic sequence y to generate the position sequence K, use K to scramble the columns and rows of the lower four-bit matrix L to obtain L', and use the chaotic sequence w to diffuse L' to obtain the final encrypted lower four-bit matrix L"; Step 6: Merge the encrypted high four-bit matrix H" and low four-bit matrix L" to generate the final 8-bit ciphertext image P'; The above method is used to encrypt the grayscale image of chest X-ray film with a standard size of 512×512; During the encryption process, the Arnold algorithm is used to perform a scrambling operation on the binary matrix. The scrambling operation is defined as: (9) The Arnold algorithm converts the i row and j column in the matrix to p row and q column, sets the parameters a and b to 3 and 5, and the number of iterations to 20.

2. The method for encrypting a bit plane image using a grid multi-scroll conservative chaotic system according to claim 1, characterized in that: The circuit simulation steps are as follows: (1) Standardize the required chaotic system equations; (2) Draw the circuit according to the standardized equation and select the required components from the component library of Multisim software; (3) Set the parameters of each component according to the parameters of the chaotic system equation; (4) Add measurement tools such as oscilloscopes and multimeters to the circuit to observe the dynamic behavior of the system.

Images