Point cloud encryption method based on logistic perturbed chen chaotic system

Abstract

A point cloud encryption method based on Logistic perturbed Chen chaotic system is proposed. In the primary encryption, the point cloud data is scrambled and diffused by Chebyshev chaotic mapping. In the secondary encryption, the RK4 method is used to discretize the Chen system, and a complex sequence is generated by Logistic perturbation, which is used for spatial coordinate perturbation and RGB attribute XOR operation. The experiment on the Semantic3D dataset and security analysis show that the encrypted point cloud histogram is uniform, the neighborhood correlation is low, and the NPCR and UACI values are ideal and the key space is large. The method can resist common attacks, alleviate the degradation of chaotic dynamics, achieve high security and efficiency in point cloud storage and transmission, and enrich the chaotic cryptography research of three-dimensional data encryption, which has theoretical and practical value.

Description

Technical Field

[0001] This invention relates to the field of point cloud encryption technology, and in particular to a point cloud encryption method based on a Logistic perturbation Chen chaotic system. Background Technology

[0002] The 21st century is an era of information explosion. With the rapid development of computer technology, point clouds, as a high-precision, high-density three-dimensional spatial data carrier, are widely used. Consequently, the need for secure point cloud data is becoming increasingly urgent. In traditional cryptography research, encryption algorithms suitable for 3D remote sensing point clouds have not been fully studied. Classic, universally applicable encryption algorithms such as DES (Data Encryption Standard), AES (Advanced Encryption Standard), or RSA (Rivest Shamir Adleman) are prone to problems such as low encryption efficiency, complex key management, and compromised data usability after encryption. Therefore, designing a new encryption method adapted to the characteristics of 3D remote sensing point clouds to ensure their secure transmission and storage has significant practical application value.

[0003] Since the early 1990s, chaotic systems have been applied to research on secure communication. Currently, three-dimensional data encryption schemes based on chaos are gradually becoming a research hotspot and an important branch of chaotic cryptography. Given the complex characteristics of 3D remote sensing point clouds, the limitations of traditional encryption algorithms are becoming increasingly apparent, while multidimensional chaotic systems show broad application prospects in this area. Compared to traditional encryption algorithms, multidimensional chaotic systems can further expand the encryption dimension, enhance sequence randomness, improve the anti-attack capability of encryption schemes, and are more suitable for the high security requirements of 3D remote sensing point clouds. Therefore, applying multidimensional chaotic systems to 3D remote sensing point cloud encryption and constructing encryption schemes adapted to its characteristics has become an effective new path to solve the security problems of 3D remote sensing point clouds.

[0004] Conducting research on 3D remote sensing point cloud encryption has significant theoretical and practical value. On one hand, it can overcome the limitations of traditional encryption algorithms in adapting to 3D remote sensing point cloud data, enrich the research results of chaotic cryptography in the field of three-dimensional spatial data encryption, and broaden the engineering application scope of multidimensional chaotic systems. On the other hand, related encryption schemes can effectively solve security risks in the transmission and storage of 3D remote sensing point cloud data, meeting the high-efficiency encryption requirements in practical engineering applications.

[0005] Chaotic systems, due to their characteristics such as sensitivity to initial conditions, pseudo-randomness, uncertainty, and ergodicity, are widely used in image encryption. They not only significantly improve image security but also possess high practical engineering feasibility. Therefore, chaotic systems have found widespread application in the field of image encryption. For example, Shi Pengfei et al. proposed a novel image encryption algorithm combining chaotic systems and DNA encoding technology. This algorithm effectively solves the problem of the degradation of chaotic dynamic properties in practical applications of chaotic systems used in traditional chaotic image encryption algorithms by applying DNA encoding technology. Furthermore, Zhao Mingjie constructed three chaotic structures with complex characteristics of different dimensions by introducing mathematical tools such as trigonometric functions, absolute values, and inverse trigonometric functions. Then, by substituting the traditional one-dimensional chaotic mapping as a seed mapping into the proposed chaotic structure, new chaotic mappings were generated. Based on this, several novel chaotic systems were designed, effectively solving the problems of small parameter ranges, high difference uniformity of chaotic S-boxes, and low encryption / decryption efficiency in traditional image encryption. Jiang Defeng et al., based on fractional calculus theory and memristor models, constructed a novel fractional-order five-dimensional memristor hyperchaotic system. They further proposed an encryption scheme for color images based on a Rubik's Cube scrambling algorithm, a double diffusion algorithm, and an optimized Arnold scrambling algorithm. For complex application scenarios, this encryption scheme demonstrates significant security advantages. Lu Xu proposed a novel bit-level image encryption algorithm based on piecewise linear chaotic mapping (PWLCM). Simulation experiments and performance analysis show that this algorithm is secure and reliable for image encryption. Xiuli Chai proposed an image encryption algorithm based on chaotic systems and DNA sequence operations. Experimental results and security analysis confirm that this algorithm not only has excellent encryption performance but also resists various typical attacks. Xing-Yuan Wang proposed a novel image encryption scheme based on DNA sequence operations and chaotic systems. Experimental and theoretical analysis show that this scheme can resist various attacks and has extremely high security. Jiang Tianjiao et al. designed a novel image encryption algorithm based on hyperchaotic Lorenz systems and Mandelbrot fractal sets. Experimental simulation results and multiple security tests verify that it can effectively encrypt plaintext images. Chaotic systems have been widely used in the field of image encryption and provide important reference value for encryption in the field of point clouds.

[0006] However, it's important to note that compared to traditional 2D images, 3D point clouds lack a fixed topological structure; that is, there are no strict row and column relationships between points. While concepts such as strictly regular rows and columns, and semi-regular rows and columns do exist for point clouds, these essentially describe the orderliness of the point cloud—the index sequence of points in storage—rather than the spatial structure of the point cloud. Furthermore, point clouds possess multi-dimensional attributes. In addition to the basic 3D coordinates (x, y, z), point clouds acquired by modern LiDAR and depth cameras typically include rich additional attributes such as intensity, normal vectors, reflectivity, and RGB color. Point clouds also generally have massive data volumes; a medium-sized scene point cloud can contain millions or even hundreds of millions of points. Therefore, traditional 2D image encryption algorithms are insufficient for the encryption requirements of point clouds.

[0007] In 1999, OA Gonzalez et al. designed a successful stream cipher scheme based on a three-Lorentz chaotic system, marking a significant step in the engineering application research of chaotic cryptography from one-dimensional discrete mappings to high-dimensional continuous chaotic systems. Wenhao Liu et al. proposed a novel two-dimensional sinusoidal ICMIC modulation mapping (2D-SIMM) based on the closed-loop modulation coupling (CMC) model, and presented a fast image encryption algorithm. Simulation and analysis results show that the algorithm has high security. Yang Liu et al. designed a multidimensional chaotic image encryption algorithm based on DNA encoding. First, the original image is converted into DNA encoding. Then, using a four-dimensional hyperchaotic Lorentz system improved from the traditional three-dimensional Lorentz system, a series of operations are performed on the DNA encoding sequence, finally decoding to obtain the encrypted image. This algorithm has good encryption performance. This method is suitable for secure transmission of image data; however, its time complexity is not ideal. Mahmoud I. Moussa used a trilinear chaotic system for color image encryption. By combining a multidimensional chaotic system with the encryption algorithm, this method significantly improves security. Zhu Congxu et al. proposed a novel algorithm for simultaneously scrambling image pixel positions and encrypting pixel values ​​based on a multidimensional chaotic system. This method uses a generalized Arnold mapping to scramble image pixel positions and obtains an integer key sequence from the chaotic sequence generated by a three-dimensional Liu chaotic system to encrypt the scrambled image pixel values ​​one by one. Based on a complex nonlinear high-dimensional chaotic system, this method successfully overcomes the weakness of one-dimensional chaotic systems in resisting phase space reconstruction attacks. Wang Jiayin designed an image encryption scheme based on a four-dimensional Chen chaotic system, achieving streaming encryption for video. This scheme broadens the application scope of multidimensional chaotic systems in encryption. As mentioned above, multidimensional chaotic systems have been widely applied in the field of image encryption, providing important insights for research in point cloud encryption. The unique multidimensional properties of multidimensional chaotic systems are perfectly suited to the multidimensional properties of point clouds, thereby reducing the computational load when dealing with large amounts of point cloud data.

[0008] Although multidimensional chaotic systems have shown great promise in point cloud encryption, their potential has not been fully explored, and relevant research data is still scarce. Pengfei Yan et al. proposed an asymmetric encryption and compression method for 3D remote sensing point clouds based on 3D Tent-CubicICMIC mapping (3D-TCICM) and elliptic curve cryptography (ECC). First, the point cloud is divided into blocks, then compressed using an octree through a point cloud library (PCL), and finally the generated data stream is encrypted. During the encryption process, a chaotic system with excellent chaotic behavior, 3D-TCICM, is proposed, whose initial values ​​are generated from the point cloud data and the ECC algorithm. This scheme outperforms existing algorithms in terms of security, randomness, and plaintext correlation, while maintaining low computational complexity. However, due to limitations in computer precision, this scheme inevitably suffers from the problem of degraded chaotic mechanical behavior. In general image encryption, the length of the chaotic sequence does not need to reach a very long level, so this problem is not particularly prominent. However, in point cloud encryption, the large volume of point cloud data (generally in the millions to tens of millions) makes this issue a risk that needs to be considered. Summary of the Invention

[0009] The purpose of this invention is to solve the problems in the prior art and propose a point cloud encryption method based on the Logistic perturbation Chen chaotic system.

[0010] This invention is achieved through the following technical solution: A point cloud encryption method based on a Logistic perturbation Chen chaotic system is proposed. The method employs a two-stage encryption process: primary encryption and secondary encryption. In the primary encryption stage, a pseudo-random scrambling sequence is generated using the Chebyshev chaotic mapping to scramble and diffuse the point cloud data. In the secondary encryption stage, the Chen chaotic system is solved using the fourth-order Runge-Kutta RK4 discretization method, and combined with Logistic sequence perturbation, a complex chaotic sequence is generated. This sequence is then used to perturb the coordinates of the primary encrypted point cloud data and perform XOR operations on the RGB components. Subsequently, XOR operations are performed on adjacent RGB components to further enhance the encryption effect.

[0011] Furthermore, the Chen chaotic system is coupled with the Logistic perturbation, and the coupling process is as follows: Generate three initial values ​​for the Logistic mapping, calculate three Logistic chaotic sequences, discard the first 200 steps, and name them respectively. , , The Chen chaotic system was then discretized using the Runge-Kutta method (RK4) with a time step of Δt = dt = 0.01. The RK4 iterative formula is as follows: (4) (5) (6) (8) The final result for solving RK4; then, based on the Logistic sequence, the... , , The perturbation is performed to achieve the perturbation of the Chen system. The perturbation formula is: (9) , , For the calculated iterative results, The perturbation intensity coefficients of the Logistic sequence for the Chen chaotic system are given. Given a Logistic sequence, three scrambled sequences were calculated. .

[0012] Furthermore, a Chebyshev chaotic sequence is generated, and an index sequence and an index guidance sequence are constructed to achieve primary encryption of the point cloud. The specific process is as follows: Step 1: Generate pseudo-random sequences using a second-order Chebyshev chaotic map. The iterative formula is as follows:

[0013] The sequence obtained by the iteration is chaotic and ergodic, and 1000 transient iterations are required before the iteration to eliminate the influence of the initial value disturbance. Step 2: Randomly generate 7 independent initial values ​​for scrambling and diffusion. Seven Chebyshev chaotic sequences of length N+1000 were calculated. The first 1000 values ​​were removed to eliminate the initial perturbation, resulting in... Among them, will The index sequence is obtained by sorting all elements in non-increasing order. , For indexing the sequence; Step 3, based on index pairs in To achieve reordering in a single dimension, i.e., using Shuffle them one by one Dimension; Step 4 For Space and The choice of arrangement pattern within two spaces, for any point in the point cloud, whether or not... Space or Each space has only three dimensions, therefore, for any given space, there are only 6 possible rearrangements. ; Using the interval mapping method, let ,set up One of the elements is ,pass Will from Mapped to Calculate the index value , ; Indicates rounding down;

[0014]

[0015] in, This represents integer division, i.e., taking the quotient. This indicates the modulo operation, i.e., taking the remainder; Spatial Rearrangement Index ,correspond Methods of scrambling forms; Spatial Rearrangement Index ,correspond Diffusion methods in various forms.

[0016] Furthermore, the specific process of the secondary encryption is as follows: Step 5: Calculate the relevant initial values ; The initial values ​​for the Chen chaotic system are... For the generation of equation (8) , , The initial values ​​of the perturbed Logistic sequence are shown in Equation (9); Step 6: Set the initial value Substituting the logistic perturbation-based Chen chaotic system into the calculation, we obtain 6 lines of length. chaotic sequence ; Step 7: First, determine the position disturbance amplitude based on the numerical scale of the original coordinates. As an amplitude scaling factor for chaotic perturbation of point cloud coordinates, it is used to dynamically adjust the overall magnitude of the coordinate perturbation term; Step 8: Calculate the Logistic sequence Normalized to RGB value range Then, a bitwise XOR operation is performed with the original RGB values; based on the spatial order of the point cloud, an associated XOR operation is constructed for adjacent RGB values; finally, the RGB components of the encrypted point cloud are obtained. , , The final encrypted point cloud is... .

[0017] Further, in Step 5, the SHA256 of the initially encrypted point cloud is first calculated to obtain a 64-bit hexadecimal string. The SHA-256 of the 64-bit hexadecimal string is then calculated again to obtain a new 64-bit hexadecimal string. Based on the correspondence between hexadecimal and binary, the new 64-bit hexadecimal string is converted into a 256-bit binary string. The first 128 bits and the last 128 bits are XORed sequentially to obtain a 128-bit binary string. The above XOR operation is repeated to obtain a 64-bit binary string. The 64-bit binary string is divided into three consecutive binary substrings: the first 22 bits, bits 23 to 44, and bits 45 to 64. For each binary substring, it is converted into decimal integers D1, D2, and D3, and a normalized division operation is performed.

[0018] Map the results to Within the range, the final three target values ​​are obtained. .

[0019] Furthermore, in Step 7,

[0020] The maximum absolute value in the XYZ coordinates of the PLY point cloud. Round down; Using dynamic calculation The Chen sequence is magnified and superimposed onto the original XYZ coordinates to achieve perturbation encryption. Assume the spatial coordinates of the point are... ;

[0021] Obtain the encrypted point cloud spatial coordinates .

[0022] Furthermore, in Step 8, let the RGB dimension components of the point be (R, G, B), and the XOR formula is:

[0023] Indicates the color components after XOR. Round down. This indicates bitwise XOR.

[0024] Furthermore, in the correlation XOR process, the iterative formula is: .

[0025] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the point cloud encryption method based on the Logistic perturbation Chen chaotic system.

[0026] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the point cloud encryption method based on the Logistic perturbation Chen chaotic system.

[0027] The beneficial effects of this invention are: As a carrier of high-precision three-dimensional spatial data, the security requirements for point clouds are becoming increasingly urgent. Traditional general-purpose encryption algorithms are inefficient and incompatible with the unstructured topology and massive data of point clouds, while two-dimensional image encryption methods cannot adapt to their multi-dimensional properties. Meanwhile, single chaotic systems suffer from dynamic degradation due to limited computational precision, restricting their application. To address these issues, this invention proposes a two-stage point cloud encryption method based on a Logistic perturbation Chen chaotic system. In the primary encryption stage, Chebyshev chaotic mapping is used to scramble and diffuse the point cloud data. In the secondary encryption stage, the Chen system is discretized using the RK4 method, and a complex sequence is generated through Logistic perturbation for spatial coordinate perturbation and RGB attribute XOR operations. Experiments and security analysis on the Semantic3D dataset show that the encrypted point cloud histogram is uniform, has low neighborhood correlation, and possesses ideal NPCR (≈99.61%) and UACI (≈33.46%) values, as well as a large key space (2... 754 This method can resist common attacks, alleviate chaotic dynamics degradation, achieve high security and high efficiency in point cloud storage and transmission, and enrich the research on chaotic cryptography for three-dimensional data encryption, thus possessing both theoretical and practical value. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0029] Figure 1 This is a schematic diagram of the Chen's chaotic sequence xn.

[0030] Figure 2 This is a schematic diagram of the Chen's chaotic sequence yn.

[0031] Figure 3 This is a schematic diagram of the Chen's chaotic sequence zn.

[0032] Figure 4 The flowchart shows the point cloud encryption method based on the Logistic perturbation Chen chaotic system.

[0033] Figure 5 This is a schematic diagram of the point cloud of Birmingham_block_13; where a is the plaintext point cloud, b is the ciphertext point cloud, and c is the decrypted point cloud.

[0034] Figure 6 This is a schematic diagram of the point cloud of Birmingham_block_11; where a is the plaintext point cloud, b is the ciphertext point cloud, and c is the decrypted point cloud.

[0035] Figure 7 This is a schematic diagram of Cambridge_Block32 point clouds; where a is the plaintext point cloud, b is the ciphertext point cloud, and c is the decrypted point cloud.

[0036] Figure 8 Here are the plaintext and encrypted histograms of the Birmingham_block_13 point cloud, where a is the plaintext red channel histogram, b is the plaintext green channel histogram, c is the plaintext blue channel histogram, d is the encrypted red channel histogram, e is the encrypted green channel histogram, and f is the encrypted blue channel histogram.

[0037] Figure 9 Here are the plaintext and encrypted histograms of the Birmingham_block_11 point cloud, where a is the plaintext red channel histogram, b is the plaintext green channel histogram, c is the plaintext blue channel histogram, d is the encrypted red channel histogram, e is the encrypted green channel histogram, and f is the encrypted blue channel histogram.

[0038] Figure 10The plaintext and encrypted histograms are shown for the Cambridge_Block32 point cloud, where a is the plaintext red channel histogram, b is the plaintext green channel histogram, c is the plaintext blue channel histogram, d is the encrypted red channel histogram, e is the encrypted green channel histogram, and f is the encrypted blue channel histogram.

[0039] Figure 11 The diagrams show the ciphertext point cloud before and after modification; where a is the ciphertext point cloud before modification and b is the ciphertext point cloud after modification.

[0040] Figure 12 This is a schematic diagram of the decryption point cloud obtained after modifying the decryption key. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] Coupling multiple chaotic systems can effectively improve the degradation of chaotic mechanical behavior caused by the impact of accuracy on chaotic systems. This invention constructs a Chen chaotic system based on Logistic perturbation. Based on this, a 3D remote sensing point cloud encryption method is designed. This method consists of primary encryption and secondary encryption. First, considering the large data volume of point clouds, the Chebyshev chaotic mapping is selected to perform scrambling and diffusion operations, i.e., primary encryption. Then, the Chen chaotic system based on Logistic perturbation is used to encrypt the point cloud after primary encryption, thereby achieving secondary encryption.

[0043] Specifically, in combination Figures 1-12 This invention proposes a point cloud encryption method based on a Logistic perturbation Chen chaotic system. The method employs a two-stage encryption process: primary encryption and secondary encryption. In the primary encryption stage, a pseudo-random scrambling sequence is generated using the Chebyshev chaotic mapping to scramble and diffuse the point cloud data. In the secondary encryption stage, the Chen chaotic system is solved using the fourth-order Runge-Kutta RK4 discretization method, and combined with Logistic sequence perturbation to generate a complex chaotic sequence. This sequence is then used to perturb the coordinates of the primary encrypted point cloud data and perform XOR operations on the RGB components. Subsequently, XOR operations are performed on adjacent RGB components to further enhance the encryption effect.

[0044] A chaotic system refers to a seemingly random and irregular motion within a deterministic system. Its behavior is characterized by uncertainty, non-repeatability, and unpredictability; this is the phenomenon of chaos. Chaos is an inherent characteristic of nonlinear dynamical systems and a ubiquitous phenomenon in nonlinear systems. In 1854, the Russian mathematician Pafnuty Lvovich Chebyshev proposed Chebyshev polynomials and subsequently developed Chebyshev chaotic systems. The mathematical expression of this chaotic system is shown below.

[0045] (1) Chebyshev chaotic systems exhibit excellent traversal within their value range, covering the entire range in a nearly uniform manner. Therefore, they can achieve relatively uniform encryption for point clouds.

[0046] In 1999, Professor Chen proposed a new type of chaotic system—the Chen system, also known as the Chen chaotic system. This system is similar to the Lorenz system, but topologically inequivalent and exhibits more complex dynamic behavior. The mathematical expression of this chaotic system is shown below.

[0047] (2) When a=35, b=3, and c=28, the system exhibits a chaotic state.

[0048] The Logistic mapping, also known as the insect population model, is a simple mathematical model used to statistically analyze changes in insect or human population numbers. It is the most typical one-dimensional mapping, and its difference equation was proposed by Furhust in 1845. Logistic chaotic sequences are a classic model of nonlinear dynamic systems, widely used in chaos theory research, random number generation, and image encryption.

[0049] (3) when and At that time, the system exhibits a chaotic state.

[0050] Furthermore, the Chen chaotic system is coupled with Logistic perturbation to ensure high security of large-scale remote sensing point clouds under low computational load. The coupling process is as follows: Generate three initial values ​​for the Logistic mapping, calculate three Logistic chaotic sequences, discard the first 200 steps, and name them respectively. , , The Chen chaotic system was then discretized using the Runge-Kutta method (RK4) with a time step of Δt = dt = 0.01. The RK4 iterative formula is as follows: (4) (5) (6) (8) The final result for solving RK4; then, based on the Logistic sequence, the... , , The perturbation is performed to achieve the perturbation of the Chen system. The perturbation formula is: (9) , , For the calculated iterative results, The perturbation strength coefficient of the Logistic sequence for the Chen chaotic system is set to 5 here. Given a Logistic sequence, three scrambled sequences were calculated. .

[0051] exist The time series diagram of the chaotic system is as follows, with the values ​​0.598270416259766, 0.347802400588989, 0.871992111206055, 7.805792687192500, -4.545638800443761, and 2.051435049712038. Figure 1 , Figure 2 , Figure 3 As shown.

[0052] Three-dimensional point clouds, as a discretized form of spatial geometric data representation, possess multi-dimensional attributes. However, generally speaking, three-dimensional point clouds consist only of spatial coordinate attributes (X, Y, Z) and color attributes (R, G, B). Therefore, a point cloud can be expressed by the following formula.

[0053] That is, the points in the point cloud. The coordinate attributes of the point cloud. For the color attributes of point clouds, This represents the total number of point clouds.

[0054] Overall, the encryption process consists of two parts: primary encryption and secondary encryption. The encryption flowchart is as follows: Figure 4 As shown.

[0055] Primary encryption: Generate a Chebyshev chaotic sequence, construct an index sequence and an index guidance sequence to achieve primary encryption of the point cloud. The specific process is as follows: Step 1: Generate pseudo-random sequences using a second-order Chebyshev chaotic map. The iterative formula is as follows:

[0056] The sequence obtained through iteration is chaotic and traversal; here we take... =2. Before the initial iteration, 1000 transient iterations are required to eliminate the influence of initial value disturbances; Step 2: Randomly generate 7 independent initial values ​​for scrambling and diffusion. Seven Chebyshev chaotic sequences of length N+1000 were calculated. The first 1000 values ​​were removed to eliminate the initial perturbation, resulting in... Among them, will The index sequence is obtained by sorting all elements in non-increasing order. , For indexing the sequence; Step 3, based on index pairs in To achieve reordering in a single dimension, i.e., using Shuffle them one by one Dimension; Step 4 For Space and The choice of arrangement pattern within two spaces, for any point in the point cloud, whether or not... Space or Each space has only three dimensions, therefore, for any given space, there are only 6 possible rearrangements. ; Using the interval mapping method, let ,set up One of the elements is ,pass Will from Mapped to Calculate the index value , ; Indicates rounding down;

[0057]

[0058] in, This represents integer division, i.e., taking the quotient. This indicates the modulo operation, i.e., taking the remainder; Spatial Rearrangement Index ,correspond Methods of scrambling forms; Spatial Rearrangement Index ,correspond Diffusion methods in various forms.

[0059] Secondary encryption: Point cloud encryption is achieved through a Chen chaotic sequence with Logistic perturbation, thereby improving encryption security. The specific process of secondary encryption is as follows: Step 5: Calculate the relevant initial values ; The initial value is set to (-30, 30). The initial value of the Chen chaotic system does not have a strict range requirement and is usually set to (-30, 30). For the generation of equation (8) , , The initial values ​​of the perturbed Logistic sequence are shown in Equation (9); In Step 5, the SHA256 hash of the initially encrypted point cloud is first calculated to obtain a 64-bit hexadecimal string. The SHA-256 hash of this 64-bit hexadecimal string is then calculated again to obtain a new 64-bit hexadecimal string. Based on the correspondence between hexadecimal and binary, the new 64-bit hexadecimal string is converted to a 256-bit binary string. The first 128 bits and the last 128 bits are XORed sequentially to obtain a 128-bit binary string. This XOR operation is repeated to obtain a 64-bit binary string. The 64-bit binary string is divided into three consecutive binary substrings: the first 22 bits, bits 23 to 44, and bits 45 to 64. For each binary substring, it is converted to decimal integers D1, D2, and D3, and a normalized division operation is performed.

[0060] Map the results to Within the range, the final three target values ​​are obtained. .

[0061] Step 6: Set the initial value Substituting the logistic perturbation-based Chen chaotic system into the calculation, we obtain 6 lines of length. chaotic sequence ; Step 7: First, determine the position disturbance amplitude based on the numerical scale of the original coordinates. As an amplitude scaling factor for chaotic perturbation of point cloud coordinates, it is used to dynamically adjust the overall magnitude of the coordinate perturbation term; In Step 7,

[0062] The maximum absolute value in the XYZ coordinates of the PLY point cloud. Round down; Using dynamic calculation The Chen sequence is magnified and superimposed onto the original XYZ coordinates to achieve perturbation encryption. Assume the spatial coordinates of the point are... ;

[0063] Obtain the encrypted point cloud spatial coordinates .

[0064] Step 8: Calculate the Logistic sequence Normalized to RGB value range Then, a bitwise XOR operation is performed with the original RGB values; based on the spatial order of the point cloud, an associated XOR operation is constructed for adjacent RGB values; finally, the RGB components of the encrypted point cloud are obtained. , , The final encrypted point cloud is... .

[0065] In Step 8, let the RGB dimension components of the point be (R, G, B), and the XOR formula is:

[0066] Indicates the color components after XOR. Round down. This indicates bitwise XOR.

[0067] Furthermore, in the correlation XOR process, the iterative formula is: .

[0068] The decryption process is the inverse operation of encryption. First, a chaotic sequence is calculated based on the key, and then decryption is performed by reversing the order.

[0069] Experimental results and their analysis: To test the performance of the proposed point cloud encryption method, this invention uses point clouds from the SensatUrban dataset for experiments. The plaintext point clouds used in the experiments include: birmingham_block_13, birmingham_block_11, and cambridge_block_32 point clouds. Figure 5 shows the plaintext, encrypted, and decrypted point clouds of birmingham_block_13. Figure 6 shows the plaintext, encrypted, and decrypted point clouds of birmingham_block_11. Figure 7 shows the plaintext, encrypted, and decrypted point clouds of cambridge_block_32.

[0070] Histogram analysis: To resist statistical attacks, the histogram of the ciphertext point cloud should be sufficiently balanced. Figure 8 , Figure 9 and Figure 10 Histograms of the red, green, and blue components of the plaintext point clouds and corresponding ciphertext point clouds for the point clouds of birmingham_block_13, birmingham_block_11, and cambridge_block_32 are presented respectively. It can be seen from the figures that the frequency of each component in the histogram of the ciphertext point cloud is quite uniform. Therefore, the pixel distribution information of the plaintext point cloud cannot be seen from the histogram of the ciphertext point cloud.

[0071] Correlation Analysis of Neighboring Pixels: Compared to traditional two-dimensional images with raster geometry, three-dimensional point clouds do not have a strict geometric structure; they are spatially discrete. Therefore, traditional correlation analysis methods for neighboring pixels, such as those based on horizontal proximity, vertical proximity, and diagonal proximity, are not suitable for point clouds. For example, in a point cloud, the neighboring points of a point on the horizontal plane (XOY plane) may be significantly distant on the vertical plane (Z-axis), failing to effectively reflect the correlation between neighboring pixels. Therefore, for point clouds, neighboring pixels should be selected based on their spatial geometric distance. Three point clouds were selected, and 10,000 pairs of neighboring pixels with the closest spatial geometric distance were randomly chosen from both plaintext and ciphertext point clouds. The correlation coefficients of the Red, Green, and Blue components were calculated, and the correlation distribution of the plaintext point cloud is shown in Table 1, while the correlation distribution of the ciphertext point cloud is shown in Table 2.

[0072] Table 1. Correlation Distribution of Plaintext Point Clouds

[0073] Table 2. Correlation Distribution of Ciphertext Point Clouds

[0074] The correlation analysis table shows that, compared to plaintext point clouds, the correlation coefficients of the Red, Green, and Blue components in ciphertext point clouds are significantly lower. This indicates that adjacent pixels in plaintext point clouds are highly correlated, while the correlation between adjacent pixels in ciphertext point clouds is greatly reduced.

[0075] Differential Analysis: To defend against differential attacks, encryption systems must be highly sensitive to minute changes in plaintext. Here, NPCR (Non-Pixel Rate of Change) and UACI (Uniform Average Change Intensity) are used to measure this sensitivity, with the relevant formulas as follows:

[0076]

[0077] The total number of points in the point cloud. Represents the RGB channel. : Indicator function, returns 1 if the condition is true, otherwise returns 0. These represent the corresponding values ​​of the i-th point in the first and second point clouds under the same RGB channel.

[0078] A point (1211.031250 1223.968750 16.029999 101 13262) is randomly selected from the plaintext point cloud. If the value of B is changed from 62 to 61, the calculation results of NPCR and UACI of the ciphertext point cloud obtained by encrypting the plaintext point cloud before modification and the ciphertext point cloud obtained by encrypting the plaintext point cloud after modification are shown in Table 3.

[0079] Table 3. NPCR and UACI of the ciphertext point cloud before and after modification

[0080] As can be seen, both NPCR and UACI are quite close to the ideal values, indicating that the algorithm is very sensitive to changes in the plaintext point cloud. Therefore, the method has excellent resistance to differential attacks.

[0081] Key Sensitivity Analysis: First, when the key at the encryption end is changed, the algorithm's sensitivity to the key is verified. The SHA256 in the key is changed from 5b006c00484a5a00000000563100000000000000000006e00007f0a326d3500 to 3f004b05b006c00484a5a000000005631000000000000000000006e00007f0a326d3501. Table 4 shows the NPCR and UACI of the two point clouds obtained by encrypting the plaintext point cloud before and after the modification.

[0082] Table 4. NPCR and UACI of the ciphertext point cloud before and after modification

[0083] The above analysis shows that the changes in the modified ciphertext point cloud are extremely different from those before the modification, indicating that the algorithm is very sensitive to changes in the key.

[0084] Next, we verify the algorithm's sensitivity to the key when the decryption key is changed. This is done when the initial value of the Chen chaotic system is changed. When the value was changed from 5.024656087853553 to 5.024656087853552, the point cloud was as follows: Figure 12 As shown in the figure. It can be seen that when the key changes very little (approximately...), Since plaintext point clouds cannot be deciphered, the algorithm is extremely sensitive to the key.

[0085] Key space analysis: Overall, the key consists of the SHA-256 hash of the initial encrypted point cloud and the initial value of the Chebyshev chaotic sequence. Using the initial values ​​of Chen's chaotic sequence Together they form a 64-bit hexadecimal key. and All are 64-bit double-precision floating-point numbers conforming to the IEEE floating-point standard, with a calculation precision of approximately As verified above, the key precision can reach... Therefore, it can be estimated that the system key space is at least [size missing]. Much greater than 2 100 This fully demonstrates that the system has a sufficiently large key space.

[0086] To address the security protection needs of point cloud data, this invention conducts research on encryption algorithms based on chaos theory. The aim is to solve the unique characteristics of point cloud data, such as its massive volume, unstructured nature, and three-dimensional spatial correlation, as well as the various shortcomings of traditional encryption algorithms in encrypting this type of data. This invention completes the design of a Chen chaotic sequence encryption algorithm based on Logistic perturbation: the algorithm adopts a two-stage encryption process of primary encryption and secondary encryption. In the primary encryption stage, a pseudo-random scrambling sequence is generated using Chebyshev chaotic mapping to scramble and diffuse the point cloud data. In the secondary encryption stage, the Chen chaotic system is solved using the fourth-order Runge-Kutta (RK4) discretization method, and combined with Logistic sequence perturbation, a complex chaotic sequence is generated. This sequence is then used to perturb the coordinates of the primary encrypted point cloud data and perform XOR operations on the RGB components. Subsequently, XOR operations are performed on adjacent RGB components to further enhance the encryption effect. Through tests and verifications including histogram analysis, adjacent pixel correlation analysis, differential attack analysis, key sensitivity analysis, and key space analysis, the results show that the proposed algorithm can resist various attacks and has excellent encryption performance.

[0087] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the point cloud encryption method based on the Logistic perturbation Chen chaotic system.

[0088] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the point cloud encryption method based on the Logistic perturbation Chen chaotic system.

[0089] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0090] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0091] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0092] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0093] The point cloud encryption method based on the Logistic perturbation Chen chaotic system proposed in this invention has been described in detail above. Specific examples have been used to illustrate the principle and implementation of this invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A point cloud encryption method based on a Logistic perturbation Chen chaotic system, characterized in that, The method employs a two-stage encryption process: primary encryption and secondary encryption. In the primary encryption stage, a pseudo-random scrambling sequence is generated using the Chebyshev chaotic mapping to scramble and diffuse the point cloud data. In the secondary encryption stage, the Chen chaotic system is solved using the fourth-order Runge-Kutta RK4 discretization method, and combined with Logistic sequence perturbation to generate a complex chaotic sequence. This sequence is then used to perturb the coordinates of the primary encrypted point cloud data and perform XOR operations on the RGB components. Subsequently, XOR operations are performed on adjacent RGB components to further enhance the encryption effect.

2. The method according to claim 1, characterized in that, The Chen chaotic system is coupled with the Logistic perturbation, and the coupling process is as follows: Generate three initial values ​​for the Logistic mapping, calculate three Logistic chaotic sequences, discard the first 200 steps, and name them respectively. , , ; The Chen chaotic system was then discretized using the Runge-Kutta method (RK4) with a time step of Δt = dt = 0.

01. The RK4 iterative formula is as follows: (4) (5) (6) (8) The final result for solving RK4; then, based on the Logistic sequence, the... , , The perturbation is performed to achieve the perturbation of the Chen system. The perturbation formula is: (9) , , For the calculated iterative results, The perturbation intensity coefficients of the Logistic sequence for the Chen chaotic system are given. Given a Logistic sequence, three scrambled sequences were calculated. .

3. The method according to claim 2, characterized in that, Generate a Chebyshev chaotic sequence, construct an index sequence and an index guidance sequence, and implement basic encryption of the point cloud. The specific process is as follows: Step 1: Generate pseudo-random sequences using a second-order Chebyshev chaotic map. The iterative formula is as follows: The sequence obtained by the iteration is chaotic and ergodic, and 1000 transient iterations are required before the iteration to eliminate the influence of the initial value disturbance. Step 2: Randomly generate 7 independent initial values ​​for scrambling and diffusion. Seven Chebyshev chaotic sequences of length N+1000 were calculated. The first 1000 values ​​were removed to eliminate the initial perturbation, resulting in... Among them, will The index sequence is obtained by sorting all elements in non-increasing order. , For indexing the sequence; Step 3, based on index pairs in To achieve reordering in a single dimension, i.e., using Shuffle them one by one Dimension; Step 4 For Space and The choice of arrangement pattern within two spaces, for any point in the point cloud, whether or not... Space or Each space has only three dimensions, therefore, for any given space, there are only 6 possible rearrangements. ; Using the interval mapping method, let ,set up One of the elements is ,pass Will from Mapped to Calculate the index value , ; Indicates rounding down; in, This represents integer division, i.e., taking the quotient. This indicates the modulo operation, i.e., taking the remainder; Spatial Rearrangement Index ,correspond Methods of scrambling forms; Spatial Rearrangement Index ,correspond Diffusion methods in various forms.

4. The method according to claim 3, characterized in that, The specific process of the secondary encryption is as follows: Step 5: Calculate the relevant initial values ; The initial values ​​for the Chen chaotic system are... For the generation of equation (8) , , The initial values ​​of the perturbed Logistic sequence are shown in Equation (9); Step 6: Set the initial value Substituting the logistic perturbation-based Chen chaotic system into the calculation, we obtain 6 lines of length. chaotic sequence ; Step 7: First, determine the position disturbance amplitude based on the numerical scale of the original coordinates. As an amplitude scaling factor for chaotic perturbation of point cloud coordinates, it is used to dynamically adjust the overall magnitude of the coordinate perturbation term; Step 8: Calculate the Logistic sequence Normalized to RGB value range Then, a bitwise XOR operation is performed with the original RGB values; based on the spatial order of the point cloud, an associated XOR operation is constructed for adjacent RGB values; finally, the RGB components of the encrypted point cloud are obtained. , , The final encrypted point cloud is... .

5. The method according to claim 4, characterized in that, In Step 5, the SHA256 hash of the initially encrypted point cloud is first calculated to obtain a 64-bit hexadecimal string. The SHA-256 hash of this 64-bit hexadecimal string is then calculated again to obtain a new 64-bit hexadecimal string. Based on the correspondence between hexadecimal and binary, the new 64-bit hexadecimal string is converted to a 256-bit binary string. The first 128 bits and the last 128 bits are XORed sequentially to obtain a 128-bit binary string. This XOR operation is repeated to obtain a 64-bit binary string. This 64-bit binary string is then divided into three consecutive binary substrings: the first 22 bits, bits 23 to 44, and bits 45 to 64. Each binary substring is then converted to a decimal integer. D 1, D 2, D 3. Perform normalized division; Map the results to Within the range, the final three target values ​​are obtained. .

6. The method according to claim 4, characterized in that, In Step 7, The maximum absolute value in the XYZ coordinates of the PLY point cloud. Round down; Using dynamic calculation The Chen sequence is magnified and superimposed onto the original XYZ coordinates to achieve perturbation encryption. Assume the spatial coordinates of the point are... ; Obtain the encrypted point cloud spatial coordinates .

7. The method according to claim 4, characterized in that, In Step 8, let the RGB dimension components of the point be (R, G, B), and the XOR formula is: Indicates the color components after XOR. Round down. This indicates bitwise XOR.

8. The method according to claim 4, characterized in that, In the associated XOR process, the iterative formula is: 。 9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-8.

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