Three-dimensional image encryption method and system based on four-dimensional hyper-chaotic system, and medium

Abstract

The invention relates to a three-dimensional image encryption method and system based on a four-dimensional hyper-chaotic system and a medium in the technical field of information security. The three-dimensional image encryption method comprises the following steps: mapping all vertexes in V into bytes to obtain an original byte matrix; a four-dimensional hyper-chaotic system is constructed, and a row and column key Kperm and a diffusion key Kdpff are generated. Firstly, scrambling is carried out through the Kperm pair, and then diffusion is carried out through the Kdpff. According to the method, grid vertex coordinates of a three-dimensional image are equivalently mapped into a two-dimensional unsigned integer matrix, on the basis, a designed four-dimensional hyperchaotic system is introduced to respectively generate a row scrambling sequence, a column scrambling sequence and a diffusion mask matrix, and scrambling and XOR diffusion processing is performed on vertex data on a byte level, so that a three-dimensional image is obtained. Therefore, while the encryption security is ensured, the encryption and decryption reversibility is high, and the method can be flexibly expanded under different file formats, different chaotic parameters and different projection strategies, and is suitable for engineering implementation and subsequent optimization.

Description

Technical Field

[0001] This invention relates to the field of information security technology, and in particular to a three-dimensional image encryption method, system and medium based on a four-dimensional hyperchaotic system. Background Technology

[0002] With the rapid development of applications such as virtual reality, 3D printing, digital cultural heritage, medical imaging, and industrial CAD, a large number of 3D images (such as mesh models and point cloud objects) are frequently stored and transmitted in network environments, highlighting the growing demand for privacy and copyright protection of 3D data. A typical 3D mesh model consists of a set of vertices and a set of faces. Vertex coordinates are continuous real numbers, and faces record vertex indices. Therefore, the underlying data structure of a 3D image contains both continuous geometric data and discrete topological information. Existing 3D object encryption methods can be broadly classified into two categories: one category involves simple geometric transformations or random scrambling of node coordinates, such as translation, scaling, or symmetry transformations, or rearrangement of vertex indices. These methods have low computational complexity and are easy to implement, but lack diffusion capabilities and are difficult to resist statistical analysis and differential attacks. The other category attempts to map floating-point coordinates to binary or integer space, such as encrypting coordinates bit-by-bit based on the PEEE754 floating-point format, or dividing the 3D object into several blocks for separate encryption. These methods offer higher security but are complex to design and often lack a unified mathematical framework. Summary of the Invention

[0003] To address the technical problems of existing 3D image encryption methods being either insecure or having complex encryption processes, this invention provides a 3D image encryption method, system, and medium based on a four-dimensional hyperchaotic system.

[0004] Firstly, this invention proposes a three-dimensional image encryption method based on a four-dimensional hyperchaotic system, which only encrypts the vertex matrix of the three-dimensional image. V Encryption is performed on the V Encryption methods include: Will V The Middle p vertices v p The three-dimensional coordinates are converted to floating-point numbers and expanded into A-bit binary representations. Then, each B-bit is packed into one byte, resulting in... v p A / B bytes s p,1 … s p,A / B Traversing all vertices yields the original byte matrix. Construct a four-dimensional hyperchaotic system and fix the parameter vector. l : ; ; ; x h,k For the first h Each dimension k The state vector at time t, Q ( X k ) is an orthogonal rotation matrix. R It is a diagonal matrix. Based on a four-dimensional hyperchaotic system, two initial value sets containing four dimensions are set. , and 2 iterations of discard steps L p , L d .pass l , , L p Constructing row and column keys K perm .pass l , , L d Constructing a diffusion key K dpff . use K perm generate Row scrambling index vector Pr And column scrambled index vector PC . use K dpff generate diffusion mask matrix .

[0005] First pass Pr right The rows are rearranged, and then... PC right Rearrange the columns to obtain the row and column permutation matrix. Then through right Perform bitwise XOR diffusion to obtain the ciphertext byte matrix Then Restore to floating-point numbers and reconstruct the encrypted vertex matrix V (c) Finally, V (c) and F The encrypted 3D image is obtained by combining the data.

[0006] Secondly, this invention also proposes a three-dimensional image encryption system based on a four-dimensional hyperchaotic system, which uses the three-dimensional image encryption method based on a four-dimensional hyperchaotic system from the first aspect. The three-dimensional image encryption system includes: a coordinate mapping module, a key generation module, and an encryption module. The coordinate mapping module is used to map the vertex matrix of the three-dimensional image... V The Middle p vertices v p The three-dimensional coordinates are converted to floating-point numbers and expanded into A-bit binary representations. Then, each B-bit number is packed into one byte, resulting in... v p A / B bytes s p,1 … s p,A / B Traversing all vertices yields the original byte matrix. The key generation module is used to construct a four-dimensional hyperchaotic system and fix the parameter vector. l : .

[0007] .

[0008] .

[0009] x h,k For the first h Each dimension k The state vector at time t, Q ( X k ) is an orthogonal rotation matrix. R It is a diagonal matrix. Two initial value sets, each containing four dimensions, are set based on the four-dimensional hyperchaotic system. , and 2 iterations of discard steps L p , L d .pass l , , L p Constructing row and column keys K perm .pass l , , L d Constructing a diffusion key K dpff The encryption module is used to exploit... K perm generate Row scrambling index vector PrAnd column scrambled index vector PC . use K dpff generate diffusion mask matrix First pass Pr right The rows are rearranged, and then... PC right Rearrange the columns to obtain the row and column permutation matrix. .pass right Perform bitwise XOR diffusion to obtain the ciphertext byte matrix .Will Restore to floating-point numbers and reconstruct the encrypted vertex matrix V (c) .Will V (c) and F The encrypted 3D image is obtained by combining the data.

[0010] Thirdly, this year's invention proposes a cloud storage encryption method for medical 3D models, which includes: storing the medical 3D model in a standard mesh format and uploading it to cloud storage. Before uploading to cloud storage, the model is encrypted using the 3D image encryption method based on a four-dimensional hyperchaotic system described in the first aspect.

[0011] Fourthly, the present invention also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the three-dimensional image encryption method based on a four-dimensional hyperchaotic system in the first aspect.

[0012] The beneficial effects of this invention are as follows: 1. This invention maps the grid vertex coordinates of a 3D image to an equivalent 2D unsigned integer matrix. Based on this, a designed 4D hyperchaotic system is introduced to generate row scrambling sequences, column scrambling sequences, and a diffusion mask matrix. Scrambling and XOR diffusion processing are performed on vertex data at the byte level, thereby ensuring encryption security while maintaining strong encryption and decryption reversibility. It can be flexibly extended under different file formats, different chaos parameters, and different projection strategies, making it suitable for engineering implementation and subsequent optimization.

[0013] 2. This invention constructs a four-dimensional chaotic system with a controllable Lyapunov exponent and selects a four-dimensional instance to operate under specific parameters. It uses four coupled state components to generate the key streams required for scrambling and diffusion, respectively. Compared with traditional one-dimensional or two-dimensional chaotic mapping, this invention increases the dimensionality of the key stream and the sequence complexity, and enhances the resistance to statistical analysis and differential attacks.

[0014] 3. This invention is based on the PEEE754 single-precision floating-point format, which maps the vertices of a three-dimensional mesh to a two-dimensional byte matrix. It constructs a scrambling-diffusion structure under a unified integer matrix framework, which not only maintains the compatibility of three-dimensional object file formats, but also enables the algorithm to directly reuse mature security analysis tools in the field of two-dimensional image encryption.

[0015] 4. This invention utilizes the original vertex coordinates and face set to project a 3D model from a selected viewpoint, generating a 2D grayscale thumbnail to represent the overall geometric contour and structural features of the model. The projected thumbnail can serve as a visual entry point for users with low privileges, while the complete 3D geometric information is only accessible to users holding the correct key, achieving the "perceptible" characteristic of 3D image encryption and balancing security and usability. Attached Figure Description

[0016] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of a three-dimensional image encryption method based on a four-dimensional hyperchaotic system; Figure 2 , Figure 3 , Figure 4 It is a phase diagram of a four-dimensional hyperchaotic system in different dimensions; Figure 5 It is the Lyapunov exponent spectrum and l 1. Relationship diagram; Figure 6 It is a bifurcation diagram and l 1. Relationship diagram; Figure 7 It is a bifurcation diagram and l 2. Relationship diagram; Figure 8 It is a bifurcation diagram and l 3. Relationship diagram; Figure 9 It is a bifurcation diagram and l 4. Relationship diagram; Figure 10 This is a schematic diagram of the key scrambling and diffusion process; Figure 11 This is a correlation analysis chart of the encryption and decryption results; Figure 12 This is a graph showing the results of a robustness test on the encryption and decryption results; Figure 13It is a comparison image of the original image, encrypted image, decrypted image, and projection image. Detailed Implementation

[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below. 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.

[0019] It should be noted that when a component is said to be "installed on" another component, it can be directly on the other component or it may be in a component that is centered on it. When a component is said to be "set on" another component, it can be directly set on the other component or it may also be in a component that is centered on it. When a component is said to be "fixed to" another component, it can be directly fixed to the other component or it may also be in a component that is centered on it.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "or / and" as used herein includes any and all combinations of one or more of the associated listed items.

[0021] This invention constructs an equivalent mapping from 3D mesh vertices to byte matrices, utilizing the initial value sensitivity, parameter sensitivity, and pseudo-randomness of chaotic systems. It combines this with a specially designed 4D hyperchaotic system that generates multi-component chaotic sequences under specific parameters to drive scrambling and diffusion, thereby achieving strong encryption of the geometric information of 3D images. Specifically, as... Figure 1 As shown, this embodiment proposes a three-dimensional image encryption method based on a four-dimensional hyperchaotic system. Taking an OFF (or OBJ or other mesh formats containing vertex and face information) mesh file as an example, it illustrates the specific implementation steps of the invention in the most basic scenario: First, the 3D mesh model file is read from the storage device, and then the file is represented as a vertex matrix by a parsing program. V ∈ R P×3 . V The Middle p vertices v p The coordinates are represented as: v p = ( x p , y p , zp ). P for V The total number of mid-vertex, p ∈[1, P Patch matrix F Record the vertices corresponding to each triangular facet. v p Index triples. This embodiment only applies to vertex matrices. V Encryption is performed on the patch matrix. F Keep it unchanged to ensure file structure compatibility.

[0022] Next, the mapping from vertex coordinates to byte matrices is performed. Specifically, first... V Each coordinate in the array is converted to a PEEE754 single-precision floating-point number and expanded into 32-bit binary bits. For v p Its three-dimensional coordinates contain a total of 3 × 32 = 96 bits, which can be represented in sequence as follows: ; Then pack each 8 bits into one unsigned byte: ; Thus, a description can be obtained. v p 12 bytes s p,1 … s p,12 Traverse all vertices to construct the original byte matrix. : ; After the above mapping, Structurally, it resembles a two-dimensional image with 12 channels, providing a unified representation for the subsequent construction of scrambling-diffusion algorithms based on image encryption.

[0023] This embodiment requires a specially designed four-dimensional hyperchaotic system to generate row and column keys. K perm diffusion key K dpff The methods for constructing four-dimensional hyperchaotic systems include: First, we design an n-dimensional chaotic system with Lyapunov exponential control (ER-nCHS), whose iterative equation is: .

[0024] .

[0025] .

[0026] in, X k+1 For four-dimensional hyperchaotic systems in k The state vector at time +1. X k for k The state vector at time t. Q Let be an n×n orthogonal rotation matrix used to perform globally coupled linear transformations on each dimension of the state vector in each iteration. This is the matrix acting on the . i peacekeeping j The Givens rotation matrix in dimension 1 is essentially an identity matrix, except that it is in the 1st dimension. i , j Replace the corresponding 2×2 sub-blocks in rows and columns with rotation matrices: .

[0027] The other rows and columns retain their identity matrix form. This is achieved by applying the matrix to all rows and columns where 1 ≤ ... i < j Dimensional pairs ≤ n i , j Multiply by each other in sequence to obtain Q Mathematically, this involves a rotational coupling for each pair of coordinate components, thereby achieving a full blending of the n-dimensional states. is the rotation angle corresponding to the rotation matrix, where x i,k and x j,k These are the current iterations. k Time-state vector X k The i The and the first j Each component. α , β These are the control parameters (constants) of the chaotic system, used to adjust the maximum amplitude of the rotation angle and the nonlinear intensity.

[0028] Based on the chaotic system framework designed above, a specific four-dimensional hyperchaotic system is constructed, allowing... α =1.55, β =2.50.

[0029] .

[0030] .

[0031] ; ; ; ; ; ; according to , Then we can obtain: .

[0032] x h,k+1 For the four-dimensional hyperchaotic system h Each dimension is mapped to k The state vector at time +1 x h,k For the first h Each dimension k The state vector at each moment. After constructing this four-dimensional hyperchaotic system, this embodiment will use the parameter vector. l Fixed as: .

[0033] This four-dimensional hyperchaotic system possesses at least three positive Lyapunov exponents over a relatively wide parameter range, with the fourth Lyapunov exponent being positive in most regions and only slightly less than zero in narrow intervals. Further phase diagram analysis of this four-dimensional hyperchaotic system yielded three different three-dimensional projections of the state variables, as shown below. Figure 2 , Figure 3 , Figure 4 As shown, the trajectory forms a densely distributed point cloud within the bounded region, and no obvious periodic trajectory was observed, indicating that the system is bounded and exhibits good chaotic behavior and ergodicity. Figure 5 It shows information about control parameters l The Lyapunov exponent spectrum of 1. (The entire interval is missing from the original text.) l Within the range [0.6, 1.6], the first three Lyapunov exponents are always strictly positive, while LE4 is... l The value is slightly negative and very close to zero when 1∈[0.6, 0.8], and then as... l The value of 1 gradually becomes positive. This indicates that the system has at least three positive Lyapunov exponents across the entire parameter range, and four positive exponents in most intervals, thus exhibiting robust high-dimensional hyperchaotic behavior. Figure 6 , Figure 7 , Figure 8 , Figure 9 The state variables were described respectively. x 1,k , x 2,k , x 3,k , x 4,k (corresponding to the image) x , y , z ,w (Dimension) About l 1. l 2. l 3. l The bifurcation diagram of Figure 4 shows that for each parameter scan, the values ​​of the four variables form a high-density, noise-like band of dots; only a slight contraction is observed in the narrow parameter region where LE4 is slightly close to zero, while no obvious periodic windows or period-doubling cascades appear in the rest of the range. Furthermore, the trajectories of the four components are completely intertwined on the vertical axis, further confirming the strong coupling between the state variables and the persistent presence of high-dimensional strong chaos almost throughout the entire parameter region, providing a solid dynamic foundation for generating high-quality pseudo-random sequences in subsequent 3D image encryption schemes. This demonstrates that the proposed four-dimensional hyperchaotic system exhibits stable high-dimensional strong chaotic behavior overall.

[0034] After obtaining the four-dimensional hyperchaotic system, based on encryption requirements, two initial value sets containing four dimensions are set for scrambling and diffusion, respectively. , and 2 iterations of discard steps L p , L d To form two subsets of keys: row keys and column keys. K perm diffusion key K dpff It can be represented as: K perm =( l , , L p ); .

[0035] K dpff =( l , , L d , c ); .

[0036] in, , These are all the initial states of a four-dimensional hyperchaotic system. c This is the scaling factor for the diffusion stage.

[0037] Then you can use K perm generate Row scrambling index vector Pr And column scrambled index vector PC ,useK dpff generate diffusion mask matrix Specifically, utilizing K perm Generate row scrambled index vector Pr , PC The method includes the following steps: S1, with Starting with the four-dimensional hyperchaotic system, iteratively... L p + P +12 times.

[0038] S2, discard the previous one first L p The next iteration generated L p Each iteration value. (The following will be...) P The next iteration generated P The iteration values ​​form a row scrambled sequence. After sorting the iteration values ​​in the row scrambled sequence in ascending order, we obtain... Pr .

[0039] S3. Take the 12 iteration values ​​generated from the last 12 iterations and form a scrambled sequence. Then, sort the iteration values ​​in the scrambled sequence in ascending order to obtain... PC .

[0040] The result obtained through the above process Pr and PC Byte matrix The rows and columns are uniformly scrambled to achieve a combined disruption of the vertex order and the internal byte order of each vertex.

[0041] use K dpff Generate ciphertext byte matrix The method includes the following steps: S1, with Starting with the four-dimensional hyperchaotic system, iteratively... L d +12 P Second-rate.

[0042] S2, discard the previous one first. L d The next iteration generated L d Each iteration value is then retrieved sequentially. P The 12 generated in the next iteration P The iteration values ​​constitute a length of 12. P A chaotic sequence of real numbers.

[0043] S3. Rearrange the chaotic real number sequence into a matrix, first by row from left to right, then by column from top to bottom. M ∈ R P ×12 And map it to the byte space to obtain the diffusion mask matrix. ∈{0, …, 255} P×12 The mapping process can be expressed as: .

[0044] s The row number in the matrix. t This represents the column index in the matrix. (The result is...) Pr , PC , Later Perform scrambling-diffusion encryption. First, according to... Pr right Rearrange the rows, then by PC right Rearrange the columns to obtain the row and column permutation matrix. : .

[0045] Then through right Perform bitwise XOR diffusion to obtain the ciphertext byte matrix : .

[0046] ⊕ represents a bitwise XOR operation at the byte level. (This is followed by a seemingly unrelated sentence about obtaining...) Then, perform the reverse byte-to-bit-to-floating-point conversion, and... V (c) Each line of 12 bytes is restored to 3 single-precision floating-point numbers to reconstruct the encrypted vertex matrix. V (c) The entire process of its disorderly spread is as follows Figure 10 As shown. Finally, V (c) With patch matrix F Combine and output encrypted 3D images and their 3D model files.

[0047] For encrypted 3D models, the decryption process is the reverse of the encryption process described above, and includes the following steps: First, read the encrypted vertex matrix from the encrypted 3D model file. V (c) and the matrix of dough pieces F And remapped into a ciphertext byte matrix Then use the same diffusion key. Kdpff Generate diffusion mask matrix And thus remove diffusion: Using the same row and column keys. K perm generate Pr , PC Construct its inverse sequence Pr -1 , PC -1 and to Reverse row and column rearrangement to obtain the original byte matrix. Finally, Inverse conversion to vertex matrix V , and patch matrix F Combine the data to reconstruct the original 3D model. Within the PEEE754 single-precision floating-point precision limit, the maximum absolute error between the decrypted vertex coordinates and the original vertex coordinates can be controlled within 10. −8 The geometric information is recovered with virtually no loss. Correlation analysis of the encryption and decryption results is as follows: Figure 11 As shown. Further robustness tests were conducted on this 3D image encryption method, and the results are as follows. Figure 12 As shown: a1-a4 represent encryption after randomly losing 5%, 10%, 15%, and 20% of the vertex data. b1-b4 are the decrypted images corresponding to a1-a4. c1-c4 represent encryption after adding 0.2%, 0.4%, 0.8%, and 1% salt-and-pepper noise. d1-d4 are the decrypted images corresponding to c1-c4.

[0048] In summary, this invention can maintain high security and a large key space while ensuring compatibility with 3D model file formats, and supports encryption, decryption, and projection thumbnail generation under a unified chaotic framework. It is suitable for widespread application in scenarios such as 3D asset management, digital rights protection, cloud storage and transmission.

[0049] In another embodiment, while encrypting the 3D image as described in the above embodiment, a 2D projection thumbnail of the original 3D image is also generated and output together. Specifically, in practical applications, the viewing angle of the original 3D image is first selected according to the needs of retrieval and preview. For example, when the 3D model mainly extends along the Z-axis, a top-down projection along the +Z direction can be selected onto the XY plane to display the overall outer contour and local concave and convex structures of the object. In this embodiment, orthogonal projection is fixed, and the +Z direction is used as the viewing direction.

[0050] Then v p The three-dimensional coordinates are projected onto a two-dimensional plane to obtain two-dimensional coordinates and a projected view. For more complex viewpoints, rotation matrices can be superimposed. Based on the projected vertex two-dimensional coordinates and... FA two-dimensional pixel network is constructed and rasterized on a grid of specified resolution. Based on patch depth, normal vector, or curvature information, each pixel is assigned a grayscale or pseudo-color value, resulting in a grayscale thumbnail. This grayscale thumbnail is saved in a common image format (such as PNG or JPEG) and named model_thumbnapl.png. Subsequently, model_thumbnapl.png is stored or packaged and transmitted together with the encrypted 3D model model_encrypted.off. This is associated with the model in the file system or database using a unified model PD or filename, providing users with a visual preview of the object's shape without revealing precise geometric data.

[0051] like Figure 13 As shown, ordinary users or users with low privileges can only access the projected thumbnail model_thumbnapl.png, and understand the approximate shape, orientation, and complexity of the 3D object through a 2D view, but cannot recover the specific geometric coordinates. For authorized users or users with high privileges, the decryption process of this invention performs a complete decryption process on model_encrypted.off, recovering the 3D geometric information, enabling the viewing, editing, and further processing of the 3D model. Thus, while achieving strong encryption, it also retains the ability to retain the projected thumbnail, achieving a balance between security and usability.

[0052] In another embodiment, a cloud storage encryption method for medical 3D models is proposed, which is applied in medical imaging and remote diagnosis scenarios, such as the secure storage and transmission of 3D organ mesh models after CT / MRP data reconstruction. This cloud storage encryption method stores the medical 3D model in a standard mesh format and uploads it to cloud storage. Before uploading to cloud storage, encryption is performed using the 3D image encryption method based on a four-dimensional hyperchaotic system as described in the above embodiment. Specifically, the cloud storage encryption method for medical 3D models includes the following steps: In hospitals or medical imaging centers, tomographic data obtained from CT or MRP scans are used to generate corresponding 3D mesh models (such as those of the heart, liver, and brain blood vessels) through reconstruction algorithms, and stored in a standard mesh format (such as OBJ, PLY, or OFF). Before uploading the model to cloud storage, the following steps are performed: Parse OBJ / PLY files into vertex matrices V and the matrix of dough pieces F and will V Mapped to raw byte matrix A unified representation is constructed. Then, based on the hospital's or platform's security policies, a unique set of keys is assigned to each patient model. K perm , Kdpff (Initial values ​​can be generated using information such as medical record number and timestamp) , ; parameter vector l Different small perturbations can be selected within a safe range to increase the key difference between different patient models. Then, row and column scrambling and diffusion are performed to obtain the ciphertext byte matrix. An encrypted model file is generated. A grayscale thumbnail is also created and saved for retrieval and preview. During decryption, the corresponding parameter scheme and key subset are found based on the metadata of the encrypted model file, and the original 3D geometric information is recovered by performing the reverse process.

[0053] This cloud server only stores encrypted model files and their corresponding projection thumbnails; it does not store plaintext vertex coordinates. The access control policy can be set as follows: Doctors, holding the decryption key or having it distributed on demand by a key management server, can perform full decryption and reproduce 3D organ models for diagnosis or surgical planning. Researchers or users with lower privileges can only view projected thumbnails or partially simplified models, unable to reconstruct the precise structure, thus protecting patient privacy. If a key is leaked, it can be resolved through updates. , , l The model is re-encrypted with parameters such as [parameter name], without affecting the cloud storage structure.

[0054] In medical scenarios, the four-dimensional hyperchaotic keystream proposed in this invention guarantees high randomness and key space, and only performs byte-level encryption on vertices, adding almost no additional storage overhead to slices and file structures. Its encryption / decryption process mainly involves floating-point to byte type conversion and simple XOR operations, keeping computational overhead within the acceptable range for doctor workstations and cloud servers. The medical platform can build feature indexes based on grayscale thumbnails, such as extracting edges, shape descriptors, or depth features for content retrieval. Since the encryption process only affects the 3D vertex data and does not affect the generation of grayscale thumbnails, the medical platform can complete most retrieval operations without decrypting the model. The decryption module is only invoked to restore geometric data when the user actually needs to download or view the 3D model.

[0055] In another embodiment, a three-dimensional image encryption system based on a four-dimensional hyperchaotic system is proposed, which uses the three-dimensional image encryption method based on a four-dimensional hyperchaotic system as described in the above embodiment. The three-dimensional image encryption system includes: a coordinate mapping module, a key generation module, and an encryption module. The coordinate mapping module is used to map the vertex matrix of the three-dimensional image... V The Middle p vertices v pThe three-dimensional coordinates are converted to floating-point numbers and expanded into A-bit binary representations. Then, each B-bit number is packed into one byte, resulting in... v p A / B bytes s p,1 … s p,A / B Traversing all vertices yields the original byte matrix. The key generation module is used to construct a four-dimensional hyperchaotic system and fix the parameter vector. l : .

[0056] .

[0057] .

[0058] x h,k For the first h Each dimension k The state vector at time t, Q ( X k ) is an orthogonal rotation matrix. R It is a diagonal matrix. Two initial value sets, each containing four dimensions, are set based on the four-dimensional hyperchaotic system. , and 2 iterations of discard steps L p , L d .pass l , , L p Constructing row and column keys K perm .pass l , , L d Constructing a diffusion key K dpff The encryption module is used to exploit... K perm generate Row scrambling index vector Pr And column scrambled index vector PC . use K dpff generate diffusion mask matrix First pass Pr right The rows are rearranged, and then... PC right Rearrange the columns to obtain the row and column permutation matrix. .pass right Perform bitwise XOR diffusion to obtain the ciphertext byte matrix .Will Restore to floating-point numbers and reconstruct the encrypted vertex matrix V (c) .Will V (c) and F The encrypted 3D image is obtained by combining the data.

[0059] In another embodiment, a computer-readable storage medium is also proposed, which stores a computer program that, when executed by a processor, implements the steps of the three-dimensional image encryption method based on a four-dimensional hyperchaotic system as described in the above embodiment. This computer-readable storage medium may include, but is not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0060] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0061] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A three-dimensional image encryption method based on a four-dimensional hyperchaotic system, characterized in that, It only applies to the vertex matrix of a 3D image. V Encryption is performed on the V Encryption methods include: Will V The Middle p vertices v p The three-dimensional coordinates are converted to floating-point numbers and expanded into A-bit binary representations; then, each B-bit is packed into one byte, resulting in... v p A / B bytes σ p,1 … σ p,A / B Traversing all vertices yields the original byte matrix. ; Construct a four-dimensional hyperchaotic system and fix the parameter vector λ : ； ； ； x h,k For the first h Each dimension k The state vector at time t, Q ( X k ) is an orthogonal rotation matrix. R It is a diagonal matrix; Based on a four-dimensional hyperchaotic system, two initial value sets containing four dimensions are set. , and 2 iterations of discard steps L p , L d ; pass λ , , L p Constructing row and column keys K perm ;pass λ , , L d Constructing a diffusion key K dpff ; use K perm generate Row scrambling index vector Pr And column scrambled index vector Pc ;use K dpff generate diffusion mask matrix ; First pass Pr right The rows are rearranged, and then... Pc right Rearrange the columns to obtain the row and column permutation matrix. ; Through the Perform bitwise XOR diffusion to obtain the ciphertext byte matrix ; Will Restore to floating-point numbers and reconstruct the encrypted vertex matrix V (c) ;Will V (c) and F The encrypted 3D image is obtained by combining the data.

2. v p The three-dimensional coordinate transformation floating-point number is expanded into a 96-bit binary representation, and then packed into 8 bits per byte to obtain 12 bytes. σ p,1 … σ p,12 ; And / or, The expression is: 。 3. The three-dimensional image encryption method based on a four-dimensional hyperchaotic system according to claim 1, characterized in that, In a four-dimensional hyperchaotic system, the initial value set , Each includes initial values ​​for four dimensions, and its expression is: ； ； K perm , K dpff The expression is: K perm =( λ , , L p )； K dpff =( λ , , L d , γ )； In the formula, γ This is the scaling factor for the diffusion stage.

4. The three-dimensional image encryption method based on a four-dimensional hyperchaotic system according to claim 1, characterized in that, Generate row scrambled index vector Pr , Pc The methods include: by Starting with the four-dimensional hyperchaotic system, iteratively... L p + P +12 times; P for V The total number of mid-vertices; Before discarding L p Each iteration value will be followed by P The iterative values ​​form a row scrambling sequence. After sorting the row scrambling sequence in ascending order, we obtain... Pr ; The last 12 iteration values ​​are arranged into a column scrambled sequence, and then sorted in ascending order to obtain... Pc .

5. The three-dimensional image encryption method based on a four-dimensional hyperchaotic system according to claim 1, characterized in that, Generate ciphertext byte matrix The methods include: by Starting with the four-dimensional hyperchaotic system, iteratively... L d +A / B× P Second-rate; P for V The total number of mid-vertices; Before discarding L d Each iteration value is used to sequentially extract the subsequent A / B× values. P Each iteration value constitutes a length of A / B× P A chaotic sequence of real numbers; The chaotic real number sequence is first rearranged row by row from left to right, and then column by column from top to bottom into a matrix. M And map it to the byte space to obtain the diffusion mask matrix. .

6. The three-dimensional image encryption method based on a four-dimensional hyperchaotic system according to claim 5, characterized in that, M The process expression for mapping to byte space is: ； In the formula, s The row number in the matrix. t is the column index in the matrix.

7. The three-dimensional image encryption method based on a four-dimensional hyperchaotic system according to claim 1, characterized in that, The three-dimensional image encryption method also includes: generating a two-dimensional projection thumbnail of the original three-dimensional image, which includes: Select the viewing angle of the original 3D image and project the 3D image onto a 2D plane to obtain a projected view; A two-dimensional pixel network is constructed on the projected view and rasterized to obtain a grayscale thumbnail. The grayscale thumbnails are output as image files and packaged with the encrypted 3D image.

8. A three-dimensional image encryption system based on a four-dimensional hyperchaotic system, characterized in that, It uses the three-dimensional image encryption method based on a four-dimensional hyperchaotic system as described in any one of claims 1 to 7; the three-dimensional image encryption system includes: The coordinate mapping module is used to map the vertex matrix of a 3D image. V The Middle p vertices v p The three-dimensional coordinates are converted to floating-point numbers and expanded into A-bit binary representations; then, each B-bit is packed into one byte to obtain... v p A / B bytes σ p,1 … σ p,A / B Traversing all vertices yields the original byte matrix. ; The key generation module is used to construct a four-dimensional hyperchaotic system and fix the parameter vector. λ : ； ； ； x h,k For the first h Each dimension k The state vector at time t, Q ( X k ) is an orthogonal rotation matrix. R It is a diagonal matrix; and based on the four-dimensional hyperchaotic system, two initial value sets containing four dimensions are set. , and 2 iterations of discard steps L p , L d ;pass λ , , L p Constructing row and column keys K perm ;pass λ , , L d Constructing a diffusion key K dpff ; Encryption module, which is used to exploit K perm generate Row scrambling index vector Pr And column scrambled index vector Pc ;use K dpff generate diffusion mask matrix First pass Pr right The rows are rearranged, and then... Pc right Rearrange the columns to obtain the row and column permutation matrix. ;pass right Perform bitwise XOR diffusion to obtain the ciphertext byte matrix ;Will Restore to floating-point numbers and reconstruct the encrypted vertex matrix V (c) ;Will V (c) and F The encrypted 3D image is obtained by combining the data.

9. A cloud storage encryption method for medical 3D models, characterized in that, It includes: The medical 3D model is stored in a standard mesh format and uploaded to the cloud for storage. Before uploading to cloud storage, the image is encrypted using the three-dimensional image encryption method based on a four-dimensional hyperchaotic system as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the three-dimensional image encryption method based on a four-dimensional hyperchaotic system as described in any one of claims 1 to 7.

Images