Three-dimensional point cloud encryption method based on lorentz chaotic system

Abstract

The application discloses a three-dimensional point cloud encryption method based on a Lorenz chaotic system and belongs to the technical field of multimedia information security. The application aims at the security problem of three-dimensional point cloud data, combines the theory of chaotic encryption, and designs a novel point cloud coordinate encryption method. The method selects the Lorenz chaotic system, and the generated chaotic sequence is improved so that the value is more random. An efficient encryption method is designed based on the chaotic sequence, and the traditional two-dimensional encryption structure of "scrambling-diffusion-diffusion" is extended to three-dimensional data. A random mask matrix is defined to generate the encryption method, so that the security of the encryption method is higher, and the information security of the point cloud coordinate data is ensured. The experimental results show that the method has high security and wide application prospect and practical value in the protection of three-dimensional data information.

Description

Technical Field

[0001] This invention belongs to the field of multimedia information security technology, specifically relating to a three-dimensional point cloud encryption method based on the Lorentz chaotic system. Background Technology

[0002] In recent years, multimedia technology has developed rapidly, and the emergence of technologies such as 3D printing and 3D modeling has led to a diversification of information carriers used by people. These carriers are no longer limited to two-dimensional images; 3D models are increasingly appearing in daily life, becoming an important information carrier in the modern communication field. 3D models have significant applications in industrial production, cultural relic preservation, daily life, and media entertainment, thus placing higher demands on their storage, transmission, and security. Point clouds are a typical data type of 3D models. They are massive sets of points representing the spatial distribution and surface characteristics of a target object within the same spatial reference frame, formed by obtaining the spatial coordinates of each sampled point on the object's surface. While watermarking can be used to prevent point cloud information leakage, encryption technology provides a more effective and direct protection mechanism.

[0003] Encryption schemes typically require an external random sequence as the basis for encryption operations; therefore, chaos theory is one of the most studied techniques. A chaotic system is a mathematical model or equation describing chaotic behavior, possessing properties such as randomness, unpredictability, nonlinearity, and sensitivity to initial conditions, which can satisfy encryption requirements. These properties mean that adjacent iterations of a chaotic system yield completely different sequences after a finite number of iterations, and small changes lead to different computational results. Furthermore, methods applying chaos to cryptography are easy to implement, with computational costs far lower than those of other traditional cryptographic methods, making them highly suitable for encrypting large amounts of data. Due to the favorable properties of chaos, many chaos-based encryption algorithms have been proposed.

[0004] This invention, based on chaos theory, studies and designs a 3D point cloud encryption method based on the Lorentz chaotic system. By studying and analyzing the Lorentz chaotic system, pseudo-random sequences are generated, and a novel encryption scheme is designed to ensure the security of the 3D point cloud data. Summary of the Invention

[0005] This invention addresses the security issues of 3D point cloud data by designing a novel encryption method for point cloud data. This method uses the Lorentz chaotic system to generate pseudo-random sequences, resulting in fast encryption and decryption speeds, strong key sensitivity, resistance to various attacks, and extremely wide application areas.

[0006] This invention extends the method of chaotic image encryption to point cloud data, and designs a data conversion module specifically for the unique characteristics of 3D point cloud data. In terms of method design, a pseudo-random sequence with sufficient randomness and security is generated using the Lorentz chaotic system to perform scrambling and diffusion operations on the point cloud coordinate data. Furthermore, scrambling and diffusion can be performed simultaneously, improving encryption and decryption speed and achieving higher encryption efficiency. This invention can visually encrypt point cloud data using an efficient encryption method, transforming the encrypted point cloud data into a uniformly randomly distributed 3D point set, thus protecting the security of the original model.

[0007] Current encryption methods for point cloud data still have some shortcomings, such as improper data format conversion, simple encryption methods, and slow encryption speed.

[0008] The technical solution adopted by the present invention to solve the above problems is: designing a three-dimensional point cloud encryption method based on the Lorentz chaotic system.

[0009] This invention relates to two main modules: a pseudo-random sequence generation module and a data encryption module.

[0010] 1. Lorentz chaotic systems and pseudo-random sequence generation

[0011] The Lorentz system is a well-known three-dimensional chaotic system with complex dynamic behavior, and its equations are as follows: (1) In the formula For real number variables; when The system is in a chaotic state. The phase space diagram of the chaotic system used in this invention is as follows: Figure 1 As shown.

[0012] Given initial system values, two sets of chaotic sequences are obtained using the Lorentz chaotic equation (1). .

[0013] right Real-valued chaotic sequences require the following preprocessing: (1) Since the data at the beginning time are all relatively small, the data at the beginning time are removed; (2) Remove the integer part of each real value and unify the value range; (3) In order to enhance the irregularity of the sequence values ​​and the uniformity of the overall distribution, the decimal point is moved to the right after rounding, as shown in equation (2).

[0014] (2) In the formula, To perform operations that take the closest integer.

[0015] The preprocessed chaotic sequence has good uniform distribution characteristics, random statistical characteristics, and correlation characteristics.

[0016] Normalization The chaotic sequence is sorted, and the sorting index is saved for coordinate scrambling. Chaotic sequences are used to perform diffusion operations, changing coordinate values ​​and altering the statistical properties of the coordinates.

[0017] 2. Encryption Method Design This invention presents an efficient 3D encryption method for 3D point cloud data.

[0018] 2.1 Point Cloud Data Conversion To achieve efficient encryption of 3D point cloud models, the first step is to transform the point cloud data based on its characteristics. This invention extracts the 3D coordinate data of the point cloud into a 2D matrix for processing, thus planarizing the 3D data.

[0019] 2.2 Point Cloud Data Encryption The scrambling-diffusion encryption method is often used in traditional image encryption. This invention innovatively extends this method to 3D point cloud data, using a "scrambling-diffusion-diffusion" encryption method to encrypt the converted point cloud data. The first round of scrambling and diffusion is performed simultaneously, which can achieve higher encryption efficiency.

[0020] 1. Scrambling methods There is a significant adjacency correlation between coordinates in 3D point clouds, and scrambling can break this correlation. First, the random matrix generated by the Lorentz chaotic mapping is sorted. Then, data from different positions in the matrix are randomly selected according to the sorting index, and the selected coordinate data are arranged into a circular shape for scrambling.

[0021] Assume the chaotic sequence is The transformed point cloud coordinate matrix is The data after scrambling is The specific scrambling steps are as follows: (1) The generated chaotic sequence form random matrix Sort each column to obtain the sorted matrix. ; (2) Save the sorted indices as a matrix ; (3) Using the index matrix For each row, coordinate data points are randomly selected. For example, the first row... In the second iteration, the selected coordinate data points are: They form a ring; (4) Shift the adjacent data points in the ring. ; (5) Obtain the scrambled point cloud coordinate matrix .

[0022] 2. Diffusion methods Scrambling operations can only disrupt the order of data, while diffusion operations can alter the statistical properties of the original data, change the coordinate values, and improve encryption security. Furthermore, it propagates minute changes throughout the entire data matrix, effectively creating a cascading effect.

[0023] (1) First round of diffusion: the first random sequence generated based on the Lorentz chaotic system This forms a random matrix. The specific diffusion mechanism is shown in equation (3): (3) The first round of diffusion and scrambling processes are carried out simultaneously, directly targeting the randomly selected data points in the scrambling method for diffusion operations, which improves the efficiency of the encryption process.

[0024] (2) Generation of the random mask matrix: based on the second random sequence generated by the Lorentz chaotic system. The resulting random matrix ,based on and the converted point cloud coordinate plaintext data A method for generating a random mask matrix is ​​defined, and the specific formula is shown in equation (4).

[0025] (4) (3) Second round of diffusion: based on the generated random mask matrix H(i,j) A second diffusion is carried out, and the diffusion formula is shown in equation (5).

[0026] (5) 3. Overall encryption process The encryption process of this invention involves inputting a pre-processed size of... Data matrix and key Based on a series of encryption steps, ciphertext data is output. The encryption process is as follows: Figure 2 As shown.

[0027] Input: Size is Plain text point cloud coordinate data key

[0028] Output: Ciphertext data C (1) Using the key As the initial value for the chaotic system, two sets of chaotic sequences are iteratively generated, and quantized to form two sequences of size . random matrix ; (2) Sort each column and save the sorted index, forming a sorted index of size . index matrix ; (3) Using the index matrix Random selection The coordinate data points are scrambled, and the diffusion operation of equation (3) is performed on these data points. (4) Based on and the converted point cloud coordinate plaintext data A random matrix is ​​generated according to equation (4).

[0029] (5) Perform a second round of diffusion according to equation (5) to obtain the ciphertext data C.

[0030] 4. Encryption Flowchart The encryption flowchart of this invention is as follows: Figure 2 As shown, the point cloud data is first transformed to reduce the dimensionality of the 3D data. Encryption is then performed, consisting of a first round of diffusion scrambling, generation of a random matrix, and a second round of diffusion, ultimately yielding the encrypted data.

[0031] 5. Decryption process The decryption process is the reverse of the encryption process. First, the key is substituted into the chaotic equation to obtain a chaotic sequence, which is then quantized and converted into a random matrix. A second round of reverse diffusion is performed, followed by the reverse process of the first diffusion and scrambling. The resulting plaintext coordinate data matrix is ​​then rewritten into the point cloud file.

[0032] 3. Experimental Simulation and Analysis The experimental simulations in this section demonstrate the actual effectiveness of this invention. Through these simulations, the encryption and decryption effects of the invention can be visually observed, verifying its validity. Furthermore, the security of the encryption method used is analyzed through key space, key sensitivity, encryption / decryption speed, and information entropy.

[0033] 3.1 Encryption / Decryption Effects A simulation experiment was conducted on the classic 3D model, the Stanford Rabbit. The original model, encryption effect, and decryption effect are as follows: Figure 3 As shown, the coordinate distribution of the encrypted 3D point cloud model is random and uniform, and the shape features of the original model are no longer discernible, thus ensuring the model's security.

[0034] 3.2 Key Space The Lorentz chaotic system key used in this invention is The parameters and initial values ​​of the chaotic system are obtained. According to the IEEE 754-2008 standard, double-precision (binary64) data is used for storage, with eight bytes representing a double-precision number. Therefore, the key space of this encryption method is... With current computing power, this key space is large enough to resist brute-force attacks.

[0035] 3.3 Key Sensitivity Due to the initial value sensitivity of chaos, even a slight change in the key will result in a different chaotic sequence. Therefore, even a slight key change in this invention cannot produce the correct decryption result.

[0036] 3.4 Encryption / Decryption Speed This paper tests the encryption and decryption time of the Stanford Rabbit model. The encryption time is 0.0091s and the decryption time is 0.0080s, which can complete fast encryption and decryption and has high encryption efficiency.

[0037] 3.5 Information Entropy Analysis Information entropy reflects the degree of randomness in ciphertext; the higher the information entropy, the higher the security. Information entropy, also known as average self-information, characterizes the average uncertainty of events occurring in a source. Information entropy is calculated as follows: (6) The ideal value of information entropy is 8. The closer the result is to 8, the better the randomness of the ciphertext. In this invention, the encrypted point cloud data was tested and the information entropy value was 7.9915, which is close to the ideal value, indicating that the encryption effect is good.

[0038] This invention designs a novel chaotic encryption method for 3D point cloud models, which can achieve efficient encryption of 3D point clouds and ensure the security of 3D point cloud data.

[0039] (1) Based on the Lorentz chaotic system, the present invention improves the preprocessing of the generated chaotic sequence before encryption. The improved Lorentz chaotic sequence x, y, z has more irregular values ​​and good uniform distribution and random statistical properties.

[0040] (2) The present invention transforms the three-dimensional point cloud data so that its coordinate data is stored in the form of a two-dimensional matrix, thereby realizing the dimensionality reduction operation of the three-dimensional data.

[0041] (3) In the encryption design process of this invention, the traditional image encryption structure is extended to three-dimensional point cloud data for the first time. The scrambling diffusion structure is adopted, which achieves a better encryption effect.

[0042] (4) The present invention defines a random mask matrix, which is generated based on plaintext data and a chaotic matrix and participates in the second diffusion, making the encryption structure more secure.

[0043] (5) In the encryption structure of the present invention, the first round of scrambling and diffusion are carried out simultaneously, resulting in faster encryption speed and higher encryption efficiency.

[0044] In summary, this invention designs a chaotic encryption method for 3D point cloud models. For the chaotic system, an improved Lorentz chaotic system is selected, which generates chaotic sequences with better randomness, making it more suitable for encryption. In terms of encryption method design, this invention extends traditional image encryption structures to 3D data, achieving better encryption and decryption results. The highly efficient encryption structure is of great significance for the information security of 3D point cloud models. Attached Figure Description

[0045] Figure 1 is a phase space diagram of the Lorentz chaotic system used in this invention; Figure 2 is a flowchart of the encryption process of this invention; Figure 3 shows the encryption / decryption simulation experiment diagram, where a) is the original model, b) is the ciphertext model, and c) is the decryption model. Detailed Implementation

[0046] To better understand the technical solution of the present invention, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0047] The first step is to input a 3D point cloud file and visualize it.

[0048] The second step is extraction. The coordinate data of all points in the three dimensions are rearranged into a new... The matrix is ​​quantized into values ​​between 0 and 255.

[0049] The third step is to input the initial values ​​for the Lorentz chaotic equation. As the key, two pseudo-random sequences are generated. Then it is quantized, with the quantized value between 0 and 255, resulting in two values. random matrix This is used for subsequent disruption and spread.

[0050] The fourth step is to process the first random matrix. Sort each column of data and save the index of the sorting process.

[0051] The fifth step is to determine the position of the selected coordinate points according to the index, arrange the selected coordinate points in a circular pattern, and move them one position clockwise to achieve a scrambling effect. After each shift, the coordinate points are directly subjected to the first round of diffusion operation of equation (3).

[0052] Step 6: Repeat step 5 in a loop until all coordinate points have been traversed, completing the first round of scrambling and diffusion.

[0053] Step 7, based on the second random matrix and the converted point cloud coordinate plaintext data Generate a random mask matrix according to equation (4). H ( i,j ).

[0054] Step 8: Based on the generated random mask matrix, perform the second round of diffusion of equation (5).

[0055] The ninth step yields encrypted point cloud data, achieving a good encryption effect.

[0056] Step 10: Perform security testing on the encrypted ciphertext point cloud data.

[0057] Following the steps above, the experimental test platform was MATLAB 2021R running on Windows 10 operating system. The hardware platform was an Intel Core i5, 2.90GHz, with 16GB of memory.

Claims

1. A 3D point cloud encryption method based on the Lorentz chaotic system, which is implemented in the following six steps: The first step is to input a 3D point cloud file and extract... The coordinate data of all points in the three dimensions are rearranged into a new... A matrix, quantized into values ​​between 0 and 255; The second step is to input the initial values ​​of the Lorentz chaotic system. Using the Lorentz chaotic equation as the initial key, two pseudo-random sequences are generated, and then normalized to a value between 0 and 255, resulting in two pseudo-random sequences. Quantization conversion random matrix This is used for subsequent disruption and spread; The Lorentz chaotic equation is shown below: （1） The third step is to process the first random matrix. Sort each column of data and save the index of the sorting process; determine the position of the selected point cloud coordinate data points based on the index, arrange the selected data points in a circular arrangement, and shift them one position clockwise to achieve a scrambling effect; use the first random matrix The data points after each shift are directly subjected to the first round of diffusion operation. The diffusion formula is as follows: （2） Repeat step 3 repeatedly until all point cloud coordinate data points have been traversed, completing the first round of scrambling and diffusion; Fourth step, based on and the converted point cloud coordinate plaintext data Generate a random mask matrix according to the following formula. H ( i,j ): （3） Fifth, based on the generated random mask matrix, perform a second round of diffusion, as detailed below: （4） The sixth step yields encrypted point cloud data, which achieves a good encryption effect.

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