Three-dimensional point cloud encryption method based on Logistic mapping

Abstract

The invention discloses a three-dimensional point cloud model encryption method based on Logistic mapping, and belongs to the field of information security cryptography. The three-dimensional point cloud data encryption method is constructed based on the chaos theory, and the calculation efficiency is optimized while the encryption complexity and reliability are improved by means of the extreme sensitivity of a chaos system and the mass characteristic of the point cloud data. According to the method, based on preset control parameters and initial values, iterative updating is carried out through an alternating mapping function, then a high-randomness sequence is generated through Logistic mapping, a random unit vector is constructed in combination with a spherical coordinate method, an orthogonal matrix is generated through a vector projection subtraction method, and finally a transformation matrix is dynamically constructed according to the scale of point cloud data to achieve encryption. Experimental results show that the scheme can effectively defend multiple attack modes, has the characteristics of high security and rapid encryption and decryption, and shows excellent protection capability and application value in secure storage and transmission of three-dimensional point cloud data.

Description

Technical Field

[0001] The present invention belongs to the field of information security cryptography, and particularly relates to a three-dimensional point cloud encryption method based on the Logistic map. Background Art

[0002] In recent years, with the rapid development of new generation information technologies such as artificial intelligence, big data, and cloud computing, the three-dimensional point cloud model technology has made breakthrough progress. As an important carrier of digital three-dimensional space information, the point cloud model has made remarkable breakthroughs in aspects such as algorithm optimization, hardware upgrade, and application innovation. Especially under the joint promotion of multiple factors such as the continuous optimization of deep learning algorithms, the iterative upgrade of high-precision sensor technology, and the substantial improvement of computing power, the three-dimensional point cloud technology has achieved a leapfrog development from laboratory research to industrial application. At present, this technology is deeply penetrating into many important fields such as industrial manufacturing, medical and health, national defense and military, consumer electronics, biometrics, and smart cities, showing broad application prospects and huge commercial value. However, with the in-depth application of three-dimensional point cloud technology in multiple fields, while providing convenience, it has also raised concerns about personal privacy and data security. Traditional three-dimensional point cloud data storage and processing methods often involve recording the precise geometric information of the environment, which may inadvertently disclose sensitive information. For example, the internal layout of a personal residence, the placement of furniture, and even living habits may be snooped by outsiders through high-precision three-dimensional point cloud data; the three-dimensional human face structure, as an important part of biometric information, once leaked, will seriously threaten personal identity security; in addition, the detailed structure of public spaces, such as the three-dimensional models of key facilities such as transportation hubs and government agencies, if obtained by criminals, may be used for malicious analysis or planning criminal activities.

[0003] The emergence of chaotic systems has promoted the development of image encryption technology. As a nonlinear dynamic system, chaos has key characteristics that make it an ideal cryptographic tool. First, chaotic systems are extremely sensitive to initial conditions. Small differences in initial values can lead to completely different evolutionary trajectories, which provides encryption systems with extremely high key sensitivity. Second, chaotic sequences are easy to generate through simple mathematical equations, with low computational complexity but strong randomness. Most importantly, chaotic systems are unpredictable over long time scales. Even if the system equations and partial sequences are known, the subsequent states cannot be accurately predicted, which perfectly meets the strict requirements of cryptography for pseudo-randomness. These characteristics make chaos-based image encryption algorithms significantly superior to traditional encryption methods in terms of security, computational efficiency, and anti-attack capabilities. They have been successfully applied to security-sensitive fields such as medical image protection, military communications, and digital copyright management. The application of chaotic systems in the field of cryptography shows significant advantages. Its simplicity of implementation and computational efficiency make it an ideal choice for big data encryption. Compared with traditional cryptographic algorithms, chaotic encryption has a low computational complexity for chaotic sequence generation algorithms based on simple nonlinear equations, and chaotic systems have low hardware resource requirements. In recent years, with the growing demand for three-dimensional data security, the application of chaotic encryption has expanded from two-dimensional images to the field of three-dimensional model protection, providing a new solution for three-dimensional data security that balances efficiency and strength.

[0004] The present invention combines chaos theory to study and design a three-dimensional point cloud encryption method based on Logistic mapping to ensure the data security of the three-dimensional point cloud model. Summary of the invention

[0005] In view of the rapid development of multimedia technology, the popularization of technologies such as 3D printing, 3D scanning and 3D face recognition, which in turn brings about point cloud data security challenges, this solution innovatively combines Logistic chaotic mapping with spherical coordinate transformation to construct an encryption system with dynamic characteristics.

[0006] At the technical implementation level, based on the extreme sensitivity of chaotic systems to initial conditions, the initial key is iteratively updated through an alternating mapping function, and the initial key includes a control parameter μ and an initial value x0; the updated new key is used as the key for processing the current point in the three-dimensional point cloud encryption scheme for encryption; then the updated new key is used as the initial key for processing the next point for iterative update, and the updated new key is used as the encryption key for the next point for encryption; then the iteratively updated key uses Logistic mapping to generate a pseudo-random sequence of length 9 as an encryption primitive; then the spherical coordinate transformation algorithm is used to construct a three-dimensional random vector space, and the orthogonal matrix is generated through a vector projection subtraction process, and finally the transformation matrix is dynamically constructed according to the scale of the point cloud data to achieve encryption.

[0007] Based on the defects and deficiencies of the current three-dimensional point cloud model encryption scheme, some existing technical defects in designing an encryption algorithm based on chaotic mapping can be summarized as follows: 1) Traditional methods usually fixedly use a single chaotic mapping to update parameters, which is prone to falling into periodic or short-orbit attractors; 2) When the traditional Logistic mapping directly generates a sequence, numerical instability is likely to occur when the control parameter μ approaches 4 or the initial value x0 approaches the boundary; 3) Some use high-dimensional chaotic systems (such as hyperchaotic Lorenz). Although they have strong chaos, their computational complexity is high and it is difficult to apply in real time.

[0008] 4) The traditional three-dimensional point cloud model encryption and decryption mechanism is limited by low computational efficiency. In particular, it is difficult to adapt to the real-time processing requirements of high-density point cloud files and also difficult to meet the processing efficiency requirements of large-scale point cloud data.

[0009] 5) The traditional three-dimensional point cloud encryption scheme is limited by technical characteristics and its actual application scenarios are relatively limited.

[0010] The technical solution adopted by the present invention to solve the above-mentioned existing technical defects is as follows: Step 1, use a three-dimensional point cloud model encryption method to generate an initial key. The initial key includes the initial value x0 and the control parameter μ of the Logistic chaotic mapping; Step 2, read the three-dimensional point cloud model file, parse the coordinates (x, y, z) of the points from the file, and expand them into a 4D homogeneous coordinate form (x, y, z, w) by adding a w component. Specifically, add a component with w value of 1 for expansion, and the expanded 4D homogeneous coordinate form is (x, y, z, 1); Step 3, use the initial key as a parameter to perform iterative update using an alternating mapping. Each iteration generates a new initial value x0 and control parameter μ of the Logistic chaotic mapping. The specific implementation is as follows: 1) Initialization, use the initial key as the initialization parameter of the alternating mapping. Set the control parameter μ in the range (3.5699, 4], and the initial value x0 in the range (0, 1). At this time, the Logistic chaotic mapping enters the chaotic state; 2) Normalization processing, linearly scale the control parameter μ to the interval (0, 1] using formula (1). Formula (1) is as follows: (1) 3) Control parameter μ update, select the update rule according to the parity of the current iteration step. For odd steps, select non-linear coupling to update the control parameter μ, and for even steps, use the Tent mapping to update the control parameter μ; for odd steps, use formula (2) for non-linear coupling update. Formula (2) is as follows: (2) In the even steps, the Tent mapping is updated using formula (3) and the perturbation parameter β is added. Formula (3) is as follows: (3) 4) Anti-normalization processing is performed to linearly map the obtained μ new_scaled to the set range using formula (4) to obtain the updated control parameter μ new , and formula (4) is as follows: (4) 5) Update the state value x0. The initial value x0 is processed using the Logistic chaotic mapping, and then updated using the boundary clipping function clip. The boundary clipping function clip is defined as follows:

[0011] The initial value x0 is processed using the Logistic chaotic mapping formula (5). Formula (5) is as follows: (5) Then, boundary clipping is performed using formula (6) to obtain the updated initial value x0. Formula (6) is as follows: (6) At this point, the update of the initial value x0 and the control parameter μ is completed.

[0012] Step 4: Use the iteratively updated initial value x0 and control parameter μ as keys, and generate a pseudo-random sequence x of length 9 through the Logistic chaotic mapping n = {x1, x2, x3, x4, x5, x6, x7, x8, x9}. Generate a 3rd-order random orthogonal matrix R from the first 6 bits of the pseudo-random sequence x n and a random 3rd-order column vector T from the last 3 bits. The specific implementation is as follows: 1) Use the iteratively updated initial value and control parameter of the Logistic mapping to generate a pseudo-random sequence x of length 9 bits n ; 2) Take x1 and x2 in the pseudo-random sequence as the polar angle and azimuth angle respectively, and then convert them to Cartesian coordinates through spherical coordinates to generate the first random unit vector v1; 3) Take x3 and x4 in the pseudo-random sequence as the polar angle and azimuth angle respectively, and then convert them to Cartesian coordinates through spherical coordinates to generate a random unit vector v2. Subtract its projection on v1 using vector projection subtraction, and then unitize it; 4) Take x5 and x6 in the pseudo-random sequence as the polar angle and azimuth angle respectively, then convert them to Cartesian coordinates through spherical coordinates to generate a random unit vector v3. Use vector projection subtraction to subtract its projections on v1 and v2, and then normalize it; 5) Combine the three generated orthogonal units as column vectors to form a 3-order random orthogonal matrix R = (v1, v2, v3); 6) Arrange x7, x8, and x9 in the pseudo-random sequence into a 3-order column vector T = (x7, x8, x9)T by columns.

[0013] Step Five, use the 3-order random orthogonal matrix and the random 3-order column vector generated in Step Four to combine them into a 4-order random transformation matrix according to formula (). Formula (7) is as follows: (7) Step Six, perform matrix multiplication on the 4-order random transformation matrix generated in Step Five and the 4D homogeneous coordinate points to obtain a 4-order row vector, and restore this row vector to 3D coordinates through normalization to form the encrypted new coordinates (x, y, z).

[0014] Iteratively execute Step Two to Step Six. After traversing all the data points in the point cloud file, write the updated coordinates (x, y, z) back to the original file to generate an encrypted model file.

[0015] The present invention proposes a chaotic dynamic encryption algorithm for three-dimensional point cloud model encryption. By optimizing the initial value sensitivity and iteration parameters of the Logistic mapping, it realizes the efficient non-linear confusion of the spatial coordinates of the point cloud. While ensuring the encryption and decryption efficiency, this method can resist known plaintext attacks and statistical analysis. Compared with the prior art, the advantages of the present invention are as follows: 1) The present invention uses alternating mapping to iteratively update the initial key, significantly enhancing the chaos and security of the pseudo-random sequence. Alternating mapping can break some inherent periods of a single mapping, combine dynamic perturbation and strict boundary clipping to enhance complexity and anti-prediction ability, and at the same time avoid numerical overflow to ensure that the key parameter iteration is always effective.

[0016] 2) The present invention uses the random numbers generated by the Logistic chaotic mapping with the iteratively updated key to generate random polar angles and azimuth angles, convert them to Cartesian coordinates to generate random unit vectors, and then use vector projection subtraction to construct an orthogonal matrix; the process of constructing the orthogonal matrix optimizes the cumbersome calculation of Schmidt orthogonalization, further reducing the computational overhead of encryption, and the inverse matrix of the orthogonal matrix is its transpose. When the point cloud scale is particularly large, it will greatly save the overhead of calculating the inverse matrix of the transformation matrix and optimize its decryption efficiency.

[0017] 3) The present invention realizes efficient point cloud encryption through the construction of a lightweight transformation matrix. Single-point encryption requires 9 chaotic iterations and 1 matrix multiplication, and supports GPU parallel computing, perfectly adapting to the real-time encryption requirements of large-scale point clouds.

[0018] 4) The present invention has broad application adaptability and excellent engineering practicability, and can meet the encryption requirements in various scenarios. For example, real-time point cloud data processing, 3D model copyright protection, medical image protection, and cloud computing environments, etc.

[0019] In summary, the present invention designs a method for encrypting 3D point cloud models using the Logistic map. The initial key is iterated through alternating mappings, and the generated pseudo-random sequence is more unpredictable. Then, a random unit vector is generated using the spherical coordinate method, and an orthogonal matrix is constructed using vector projection subtraction, and then a 4th-order transformation matrix is constructed. Finally, single-point encryption is performed using matrix multiplication. This method has proven to achieve good encryption effects through experiments, saving computational overhead during encryption and optimizing the efficiency during decryption. The present invention not only solves the special challenges of point cloud data encryption but also expands the application boundaries through technological innovation, providing a new solution for the 3D data security of various industries. This multi-scenario applicability gives it significant advantages in industrial applications and can meet the diverse needs of different fields for data security and processing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is the encryption flow chart of the present invention; Figure 2 is the iterative update diagram of the key alternating mapping of the present invention; Figure 3 is the encryption and decryption simulation experiment diagram, a) is the plaintext 3D point cloud model, b) is the ciphertext 3D point cloud model, c) is the decrypted 3D point cloud model DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] To better understand the technical solution of the present invention, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0022] The initial key includes the initial value x0 of the Logistic map and the control parameter μ, and it is ensured that the control parameter μ is within the range (3.5699, 4], and the initial value x0 is within the range (0, 1). At this time, the Logistic map enters the chaotic state, is very sensitive to the initial conditions, and generates an unpredictable random sequence. The Logistic map equation is shown in formula (8): (8) According to Figure 1 the encryption flow chart, the implementation steps of the present invention are described as follows: Step 1: Input the 3D point cloud file, extract the coordinate values (x, y, z) of all points in the point cloud file, and then expand them into 4D homogeneous coordinates in the form of (x, y, z, w), where the value of w is 1.

[0023] Step 2: According to Figure 2 perform key alternating iterative updates. First, update the control parameter μ and then update the initial value x0. When updating the control parameter μ, perform normalization first to facilitate unifying the range and calculation. Determine the parity based on the current iteration step number. For each point processed in the point cloud, the iteration step number increases by one. In odd steps, select non-linear coupling update, and in even steps, use Tent mapping for update. Such alternating updates can further increase the complexity of the system, break the periodicity of a single mapping, and perform anti-normalization after the update to map to the control parameter range where the set Logistic mapping enters the chaotic state. Then, update the initial value x0 using the Logistic mapping, and clip the updated value to the set Logistic mapping initial value range. Thus, the key alternating update is completed.

[0024] Step 3: According to the iteratively updated key, use the Logistic mapping equation to generate a pseudo-random sequence x of length 9 n = {x1, x2, x3, x4, x5, x6, x7, x8, x9}. x1 to x6 are used to generate a 3rd-order orthogonal matrix. First, use x1 and x2 as the polar angle and azimuth angle respectively, and then convert to Cartesian coordinates through the spherical coordinate transformation formula (9) to generate the first random unit vector v1. The formula (9) is as follows: (9) Then, use x3 and x4 as the polar angle and azimuth angle respectively, and convert to Cartesian coordinates through the spherical coordinate transformation to generate a random unit vector v2. Subtract its projection on v1 using the vector projection subtraction formula (10), and then unitize it. The formula (10) is as follows: (10) Next, use x5 and x6 as the polar angle and azimuth angle respectively, and convert to Cartesian coordinates through the spherical coordinate transformation to generate a random unit vector v3. Subtract its projections on v1 and v2 using the vector projection subtraction formula (11), and then unitize it. The formula (11) is as follows: (11) Finally, combine the three 3D column vectors v1, v2, and v3 into an orthogonal matrix R = (v1, v2, v3), and arrange x7, x8, and x9 in columns to form a 3rd-order column vector T = (x7, x8, x9)T.

[0025] Step 4: Combine them into a 4th-order transformation matrix according to formula (12), and formula (12) is as follows: 12) Step 5: Perform matrix multiplication on the point cloud coordinates in the extended point cloud and the random transformation matrix to obtain a 4th-order row vector, and then use normalization to restore it to the new three-dimensional coordinate values after transformation.

[0026] Write the newly obtained three-dimensional coordinate values into the three-dimensional point cloud model file, and the encryption process of the point cloud model is completed.

[0027] The decryption process is the inverse process of the three-dimensional point cloud encryption process, and a brief description is given here: First, according to the initial key, use alternating mapping for iterative update, and use the updated key to generate a pseudo-random number sequence through the Logistic mapping equation; Second, generate a 3rd-order unit column vector using the spherical coordinate method according to the pseudo-random sequence, then construct a 3rd-order orthogonal matrix using vector projection subtraction, and then construct a 3rd-order column vector; Third, combine the 3rd-order orthogonal matrix and the 3rd-order column vector into a 4D transformation matrix. Since the orthogonal matrix is invertible, the 4D transformation matrix is an invertible matrix.

[0028] Fourth, use formula (13) to find the inverse matrix of the 4D transformation matrix. Since the transpose of the orthogonal matrix is its inverse matrix, the calculation cost of the inverse matrix of the 4D transformation matrix is greatly optimized. Formula (13) is as follows: (13) Fifth, perform matrix multiplication on the homogeneous form of the encrypted three-dimensional point cloud model coordinates and the inverse transformation matrix of this point, and then use normalization to restore it to the three-dimensional coordinate values after transformation, which is the decrypted three-dimensional point cloud model.

[0029] It should be noted that in this application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device.

[0030] The above are only specific embodiments of the present application, enabling those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but rather will be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A three-dimensional point cloud encryption method based on the Logistic map, characterized in that It is implemented through the following six steps: Step 1: Generate an initial key using a three-dimensional point cloud model encryption method. The initial key includes the initial value x0 and the control parameter μ of the Logistic chaotic map; Step 2: Read the three-dimensional point cloud model file, parse the coordinates (x, y, z) of the points from the file, and expand them into the 4D homogeneous coordinate form (x, y, z, w) by adding a w component; Step 3: Use the initial key as a parameter and perform iterative updates using an alternating map. Each iteration generates a new initial value x0 and control parameter μ of the Logistic chaotic map; Step 4: Input the iteratively updated initial value \(x_0\) and the control parameter \(\mu\) as the key, and generate a pseudo-random sequence \(x\) of length 9 through the Logistic chaotic map n = \(\{x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9\}\). Generate a 3rd-order random orthogonal matrix \(R\) from the first 6 bits of the pseudo-random sequence \(x\), and generate a random 3rd-order column vector \(T\) from the last 3 bits; n ​ Step 5: Combine the 3rd-order random orthogonal matrix and the random 3rd-order column vector generated in Step 4 to form a 4th-order random transformation matrix; Step 6: Perform matrix multiplication on the 4th-order random transformation matrix generated in Step 5 and the 4D homogeneous coordinate points to obtain a 4th-order row vector, and restore the row vector to 3D coordinates through normalization to form the encrypted new coordinates (x, y, z); Iteratively execute Steps 2 to 6. After traversing all the data points in the point cloud file, write the updated coordinates (x, y, z) back to the original file to generate an encrypted model file.

2. The 3D point cloud encryption method based on Logistic mapping according to claim 1, characterized in that It is implemented through the following six steps: In Step 2, expand by adding a component with w value of 1, and the expanded 4D homogeneous coordinate form is (x, y, z, 1).

3. A three-dimensional point cloud encryption method based on the Logistic mapping according to claim 1, characterized in that It is implemented through the following six steps: In Step 3, use the initial key as a parameter to perform alternating mapping to gradually update the key. The iterative update can be achieved through the following steps: The first step: Initialization. Use the initial key (the initial value x0 and the control parameter μ of the Logistic chaotic map) as the initialization parameter of the alternating map. The set control parameter μ is in the range (3.5699, 4], and the initial value x0 is in the range (0, 1). At this time, the Logistic chaotic map enters the chaotic state; The second step: Normalization processing. Linearly scale the control parameter μ to the interval (0, 1] using formula (1). Formula (1) is as follows: (1) The third step: Update of the control parameter μ. Select the update rule according to the parity of the current iteration step. For odd steps, select non-linear coupling to update the control parameter μ, and for even steps, use the Tent map to update the control parameter μ; For odd steps, use formula (2) for non-linear coupling update. Formula (2) is as follows: (2) For even steps, use formula (3) for Tent map update and add a perturbation parameter β. Formula (3) is as follows: (3) Step 4: Anti-normalization processing, and linearly map the obtained μ new_scaled to the set range using formula (4) to obtain the updated control parameter μ new , and formula (4) is as follows: (4) The fifth step: Update the state value x0. Process the initial value x0 using the Logistic chaotic map, and then update it using the boundary clipping function clip. The boundary clipping function clip is defined as follows: Process the initial value x0 using the Logistic chaotic mapping formula (5), and formula (5) is as follows: (5) Then use formula (6) for boundary clipping to obtain the updated initial value x0. Formula (6) is as follows: (6)。 4. A three-dimensional point cloud encryption method based on the Logistic mapping according to claim 1, characterized in that It is implemented through the following six steps: In step four, according to the pseudo-random sequence x n Generate a 3rd-order random orthogonal matrix R and a random 3rd-order column vector T, which can be achieved through the following steps: Step 1: Use the initial value and control parameters of the iteratively updated Logistic map to generate a pseudo-random sequence x of length 9 bits n ; The second step: Take x1 and x2 in the pseudo-random sequence as the polar angle and azimuth angle respectively, and then convert them to Cartesian coordinates through spherical coordinates to generate the first random unit vector v1; Step 3: Take x3 and x4 in the pseudo-random sequence as the polar angle and azimuth angle respectively, and then convert them into Cartesian coordinates through spherical coordinates to generate a random unit vector v2. Subtract its projection on v1 using vector projection subtraction, and then normalize it; Step 4: Take x5 and x6 in the pseudo-random sequence as the polar angle and azimuth angle respectively, and then convert them into Cartesian coordinates through spherical coordinates to generate a random unit vector v3. Subtract its projections on v1 and v2 using vector projection subtraction, and then normalize it; Step 5: Combine the three generated orthogonal units as column vectors to form a 3-order random orthogonal matrix R = (v1, v2, v3); Step 6: Take x7, x8, and x9 in the pseudo-random sequence and arrange them into a 3-order column vector T = (x7, x8, x9)T by column.

5. A three-dimensional point cloud encryption method based on Logistic mapping according to claim 1, characterized in that It is implemented through the following six steps: The 4-order random transformation matrix in Step 5 can be arranged according to formula (7) for implementation (7)。

Images