3D ciphertext domain reversible information hiding method and system based on spatial clustering

Abstract

The invention provides a 3D ciphertext domain reversible information hiding method and system based on spatial clustering, and belongs to the field of information security. Firstly, neighbor vertexes are classified into the same cluster space through a multistage spatial clustering algorithm, and the neighbor of the vertexes in the cluster space is ensured; then identifying the optimal reference vertex of each cluster space by using an optimal reference vertex search algorithm, so that the embedding space reaches the maximum; then, in each cluster space, multi-MSB prediction is carried out on the reference vertex and the embedded vertex, and the embeddable length of the embedded vertex is calculated; in addition, the basic embedding length of the reference vertex is used as an additional embedding space, so that the embedding capacity is further improved. And finally, embedding the data into the reserved embedding space through a bit replacement strategy. According to the scheme of the invention, a robust, high-capacity and extensible solution is provided for security data embedding of the encrypted three-dimensional model, and the method can be widely applied to live-action three-dimensional, computer graphics, digital twinning and other application scenes.

Description

Technical Field

[0001] The present invention belongs to the field of information security, and specifically relates to a 3D ciphertext domain reversible information hiding method combining spatial clustering technology with prediction error detection technology, which can be used for reversible information hiding of encrypted 3D models. Background Art

[0002] With the development of computer graphics and the improvement of computing performance in the era of big data, human beings' digital perception and description of the physical world have gradually entered the three-dimensional era, and 3D data has been widely used in various fields. For example, 3D mesh models are used in the medical industry to make human organ models; 3D data is used in the field of geographic information to build three-dimensional geological models and real-life three-dimensional models, etc. Considering the complex structure and large amount of data of three-dimensional models, it has become a trend to outsource 3D models to cloud servers for storage.

[0003] Although cloud service providers have improved the convenience of users storing and obtaining 3D data resources, the data stored in cloud servers also face serious security issues. The confidentiality, authentication and integrity of the data are constantly threatened by illegal activities such as hacker attacks, theft or malicious use. Therefore, in order to protect the security of 3D model data in the cloud, the 3D model will be encrypted during the transmission process to the cloud server to reduce the risk of 3D data privacy leakage. At the same time, data administrators need to embed data labels and annotation information into ciphertext data, and extract the embedded information to achieve effective ciphertext management, access control and security protection of massive encrypted data in the cloud. However, the process of data embedding and extraction may cause distortion of the carrier data, resulting in the inability to meet application scenarios such as medicine, justice, and artworks that emphasize the accuracy of the carrier content.

[0004] Reversible data hiding technology in encrypted domain has emerged in this context. It is a technology that embeds additional secret messages in encrypted carriers without affecting the decryption of encrypted carriers. It has potential application value in cloud encrypted storage, confidential communication, etc. Compared with the information hiding process in the plaintext domain, the encryption operation masks the redundancy in the data, resulting in a low payload of the carrier in the ciphertext domain; and the complex and redundant spatial relationship and structural information of the 3D model make it difficult to reserve embedding space in the encrypted domain. To solve the above problems, most of the current 3D ciphertext domain reversible information hiding schemes reserve embedding space by mining the correlation or local spatial correlation of adjacent vertices. This type of method fails to consider the global spatial correlation of the 3D model and the spatial distribution characteristics of the model vertices, and cannot ensure that the nearest neighbor vertices are included in the same space, resulting in limited spatial redundancy between the embedded vertices and the reference vertices, resulting in limited embedding capacity of the existing schemes. Therefore, how to achieve high-capacity reversible information hiding has become a major technical challenge for reversible information hiding in 3D ciphertext domain. Summary of the invention

[0005] The present invention aims to propose a reversible information hiding method in 3D encrypted domain based on spatial clustering. Combining multi-level spatial clustering technology with prediction error detection technology, the present invention proposes a reversible information hiding method in 3D encrypted domain based on spatial clustering. The multi-level spatial partitioning model based on spatial clustering is studied to mine the global spatial correlation and distribution characteristics of the model, and the neighboring vertices are divided into the same subspace to ensure the proximity of the subspace vertices. An adaptive optimal reference vertex search algorithm is designed to mine the local spatial correlation of the model, identify the best reference vertex in each cluster space, and maximize the embedding space of the cluster space. In addition, the basic embedding length of the reference vertex is used as an additional embedding space to further improve the embedding capacity. Finally, in each cluster space, multiple most significant bits (multi-MSB) predictions are performed on the reference vertex and the embedded vertex to calculate the embeddable length of the embedded vertex, and then the total embedding space embedding information is obtained. This scheme does not depend on the topological relationship of the model, so it can also be applied to geometric models with vertex information (such as point clouds, etc.). The present invention breaks through the bottlenecks of high computational overhead and limited embedding capacity in the field of reversible information hiding in 3D ciphertext domain by constructing a 3D ciphertext domain reversible information hiding computational framework based on multi-level spatial clustering and multiple most important bit predictions, and creates a separable, reversible, high embedding capacity, low computational overhead, and scalable 3D ciphertext domain reversible information hiding technical path, providing technical support and innovative path for reversible information hiding in encrypted 3D.

[0006] The solution for this program is:

[0007] The participants of this scheme include the model owner, the data hider, and the model receiver. The model owner applies spatial clustering and prediction error detection to reserve embedding space, encrypts the original model, and embeds the label graph into the encrypted model, generating an encrypted model with a label graph and sending it to the data hider. The data hider embeds the secret message into the embedding space reserved by the encrypted model. The model receiver can extract the secret message or restore the model according to the provided key. Specifically, the model owner first normalizes and compresses the coordinate values ​​of the model vertices through coordinate transformation, converts them into integer coordinates, and applies a multi-level spatial clustering model to divide the vertices in the model into mutually exclusive cluster spaces. In each cluster space, an adaptive optimal reference vertex search algorithm is applied to identify the best reference vertex, and prediction error detection is performed on the best reference vertex and the embedded vertex to determine the embedding length of each embeddable vertex, and the embedding length and the number of vertices in each cluster are represented in the label graph. Then the model owner encrypts the model, embeds the label graph into the reserved embedding space through a bit replacement strategy, generates an encrypted model with a label graph and sends it to the data hider. After receiving the encrypted model with the label graph, the data hider extracts the label graph to identify the reserved embedding space, and uses the data hiding key to embed the secret message into the remaining embeddable space, thereby generating a labeled encrypted model and sending it to the model receiver. The model receiver can use the corresponding key to extract the secret message or restore the model, and the operation is separable. In addition, the scheme does not depend on the topological relationship of the model, so it can also be applied to geometric models with vertex information (such as point clouds, etc.).

[0008] The present invention provides a 3D ciphertext domain reversible information hiding method based on spatial clustering, comprising the following steps:

[0009] Step 1: The model owner (both the owner of the 3D model data and the owner of the encrypted model) performs coordinate transformation on the vertex coordinate values ​​of the 3D model, compresses the model, and converts the floating-point coordinate values ​​into integer coordinate values;

[0010] Step 2: The model owner applies a multi-level spatial clustering algorithm to divide the vertices of the 3D model into mutually exclusive cluster spaces. In each cluster space, an adaptive optimal reference vertex search algorithm is applied to identify the best reference vertex, and the 3D model is re-meshed. Then, a prediction error test is performed between the best reference vertex and the embedded vertex to determine the embedding length of each embeddable vertex.

[0011] Step 3: The model owner encrypts the model using the encryption key to obtain the encrypted model;

[0012] Step 4: The model owner represents the compression threshold, vertex embeddable length, and the number of vertices in each cluster in the label graph, compresses it using compression coding technology, and embeds it into the encrypted model through a bit replacement strategy to obtain an encrypted model with a label graph.

[0013] Step 5: The data hider extracts the label graph from the encrypted model containing the label graph to identify the reserved embedding space, and uses the data hiding key to embed the secret message into the remaining embeddable space, and generates a labeled encrypted model and sends it to the model receiver;

[0014] In step 6, after the model recipient obtains the encrypted model with the tag, he or she can perform model decryption or data extraction based on the key he or she has.

[0015] Furthermore, the specific implementation of step 1 is as follows:

[0016] Step 1.1, normalization: The 3D model is represented as M = {V, F}, where the vertex set V = {v1, v2, …, v N} and the face set F = {f(v i ,v j ,v k )|v i ,v j ,,v k ∈V}, where N is the number of model vertices, f(v i ,v j ,v k ) is the vertex v i ,v j ,v k Determine the minimum boundary B of the model in three coordinate dimensions min The values ​​are:

[0017]

[0018] Among them, [x m ,y m ,z m ] are the minimum values ​​of the model in the three coordinate dimensions respectively. The coordinate transformation is performed on each vertex so that the vertex coordinates of the 3D model are transformed into coordinate values ​​in the range of 0-1. The calculation formula of the coordinate transformation process is as follows:

[0019]

[0020] Among them, R i is the ratio scaled to the range of 0-1, k is the number of integer digits of the maximum vertex coordinate value after the 3D model is translated, such as the maximum integer digit of 12.345 is 2.

[0021] Step 1.2, compression model: Under the control of the compression threshold m, the floating point coordinate values ​​in the above 0-1 interval are converted into integer coordinate value tuples J i , calculate the compressed vertex integer coordinate value J i The formula is as follows, where is a floor rounding function. For example, when the compression threshold m = 4, R i =0.123456, compressed integer coordinate value J i is 1234;

[0022]

[0023] Step 1.3, coordinate transformation: transform the integer coordinate value J of the compressed model according to the compression threshold m i The coordinate value j converted into a binary representation of fixed length L i,p To store the compressed 3D model, J i refers to the compressed vertex integer coordinate value, j i,p refers to the coordinate value j in binary representation i,p The conversion process and the calculation formula of the length L of the binary representation are as follows, for example, J i The integer 1234 converted to binary is 0000010011010010.

[0024]

[0025] Furthermore, the specific implementation of step 2 is as follows:

[0026] Step 2.1, multi-level spatial clustering: Use a multi-level spatial clustering algorithm to divide the vertices in the 3D model space into non-overlapping subspaces. For example, perform initial clustering on the model vertices, with the number of clusters being k1, to obtain a relatively compact subspace Then cluster each subspace again, with the number of clusters being k2, to obtain the final compact subspace The calculation formula is as follows:

[0027] S=Clustering(J,k1)(6)

[0028]

[0029] Where J is the transformed integer coordinate value, Clustering represents the existing clustering algorithm, which is not limited to a specific clustering algorithm, and can be adapted to clustering methods such as k-means, k-medoids, spectral clustering, and density-based clustering based on partitioning. S refers to the set of k1 clusters obtained after clustering. i represents the i-th cluster in the set S. j Represents cluster si The cluster set obtained after clustering again.

[0030] Step 2.2, search for the best reference point: treat each cluster as an independent subunit, take each vertex in the cluster as the reference vertex in turn, take other vertices in the cluster as embedded vertices, perform multi-MSB prediction on the reference vertex r and the embedded vertex e to calculate the embeddable length I of the embedded vertex r,e , and then identify the reference vertex that makes the sum of the embeddable lengths of the subspace reach the maximum value as the optimal reference vertex:

[0031]

[0032] Step 2.3, re-meshing: group the vertices according to their cluster indices, and place the best reference point of each cluster at the first position of the group. Update the index of the vertices in the face set according to the position index after the vertex indices are re-sorted.

[0033] Step 2.4, prediction error detection: The basic embedding length of the reference vertex is used as the reserved embedding space to embed the data. For the embedded vertex, multiple most significant bits (multi-MSB) prediction is performed on the reference vertex and the embedded vertex to calculate the embeddable length of the embedded vertex.

[0034] Furthermore, the specific implementation of step 3 is as follows:

[0035] Step 3.1, generate a random sequence: use the encryption key k E Generate a binary random sequence n;

[0036] Step 3.2, encryption model: continuously sample L bits of the binary random sequence b, and then perform an XOR operation with the binary representation of the vertex coordinates to obtain the encryption model. The calculation formula is as follows:

[0037]

[0038] where j i,k is the kth bit of the binary representation of the coordinate value of vertex i after transformation, b i,k It is the k-th bit message after continuous sampling of the binary random sequence b. Represents XOR operation. Its encryption method is not limited to stream encryption, and can be adapted to symmetric encryption algorithms such as RC4, DES, AES, SM1 and SM4.

[0039] Furthermore, the specific implementation of step 4 is as follows:

[0040] Step 4.1, characterize the label graph: consider the compression threshold m, the embeddable length I of each embedded vertex, and the number of vertices Num of each cluster as labels:

[0041] label={m,I,Num}(10)

[0042] Step 4.2, compression coding: The compression threshold uses fixed-length coding, and for the embeddable length of the embedded vertex and the number of vertices in each cluster, the embeddable length symbol frequency of each embedded vertex and the number of vertices in each cluster are counted, and the Huffman coding tree is constructed according to the frequency. By traversing the constructed Huffman coding tree, the coding results of each embedding length and number of vertices are obtained. The final label graph is represented as a binary sequence of length HL, which is determined by the compression threshold, the Huffman coding tree structure and the coding result;

[0043] Step 4.3, embedding label graph: embed the label graph into the basic embedding length EL of each vertex (including the reference vertex) through the bit replacement strategy B If the length HL exceeds 3×EL B × N, where N is the number of vertices in the input model, then the predicted embedding length EL of the embedded vertex P The encrypted model E′(M) with the embedded label graph is generated from the binary bits of

[0044] Furthermore, the specific implementation of step 5 is as follows:

[0045] Step 5.1, encrypt the secret message: use the data hiding key k D Generate a binary random sequence s, and then perform an XOR operation with the secret message AD to obtain the encrypted secret message ED. The calculation formula is as follows:

[0046]

[0047] Step 5.2, embedding data: The data hider extracts the label graph from the encryption model E′(M) with the embedded label graph, extracts the Huffman coding tree sequence from the label graph, reconstructs the Huffman coding tree and retrieves the encoding of each symbol, decodes the Huffman coding result, and thus determines the reserved embedding space. Finally, the encrypted secret message is embedded into the remaining available embedding space through the bit replacement strategy to generate a labeled encryption model. The calculation formula is as follows:

[0048]

[0049] Among them ED i is the i-th bit of the encrypted secret message, I i is the embeddable length of the i-th vertex, and j represents the x, y, and z coordinate axes.

[0050] Furthermore, the specific implementation of step 6 is as follows:

[0051] Step 6.1, Secret message extraction: The model receiver can obtain the embedding length of each embedded vertex by extracting the label graph, extract the encrypted secret message from the embedding space containing the labeled encrypted model vertex coordinate values, and then D Generate a binary random sequence and XOR it to get the decrypted message.

[0052] Step 6.2, restore the model: The model recipient can obtain the embedding space of each embedded vertex by extracting the label graph, and compare the coordinate values ​​of the encrypted model vertices with the encryption key k E The generated binary random sequence is XORed to obtain a preliminary decryption model. The basic embedding length of the reference vertex coordinate value is then set to 0 to recover the coordinates of the reference point, while the embedded vertex coordinates can be recovered from their corresponding reference vertices by using prediction error detection.

[0053] Step 6.3, Secret Message Extraction and Recovery Model: The model receiver also has the encryption key k E and data hiding key k D , the model can be restored and the secret message can be extracted respectively through the above steps. The secret message extraction and model restoration operations can be performed in any order and are separable.

[0054] The present invention also provides a 3D ciphertext domain reversible information hiding system based on spatial clustering, comprising:

[0055] A processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a 3D ciphertext domain reversible information hiding method based on spatial clustering as described in the above technical solution.

[0056] Compared with other methods, the present invention has the following advantages: the 3D ciphertext domain reversible information hiding method based on multi-level spatial clustering and multiple most important bit prediction proposed by the present invention systematically mines and utilizes the spatial correlation of the 3D model, ensures the proximity between the embedded vertices and the reference vertices, thereby improving the prediction efficiency of the embedded vertices, greatly improving the embedding capacity of the 3D model, and overcoming the problem of insufficient embedding capacity of 3D ciphertext domain reversible information hiding. The method uses multi-level spatial clustering to divide the model vertices, which can greatly reduce the computational overhead while ensuring the proximity of the vertices in the cluster space, so that the method can be applied to 3D models with a large number of vertices. In addition, by using the optimal reference point search algorithm and using the basic embedding length of the reference vertex as an additional embedding space and other strategies, the embedding rate and embedding capacity of the scheme are further improved, so that the scheme has the advantages of reversibility, separability, scalability, high embedding rate, high embedding capacity and low computational overhead, breaking through the bottlenecks of high computational overhead and limited embedding capacity in the field of 3D ciphertext domain reversible information hiding, and providing technical support and innovative paths for 3D ciphertext domain reversible information hiding. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is an overall schematic diagram of the 3D ciphertext domain reversible information hiding method according to an embodiment of the present invention.

[0058] Figure 2 It is a specific processing flow chart of prediction error detection in an embodiment of the present invention.

[0059] Figure 3 It is a specific processing flow chart of the data embedding process of an embodiment of the present invention.

[0060] Figure 4 Graph showing experimental results of an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0062] The embodiment of the present invention provides a 3D ciphertext domain reversible information hiding method based on spatial clustering. Taking the Princeton segmentation benchmark (PSB) 3D dataset as an example, combined with the attached Figure 1 , 2, 3, detailed description of the implementation steps of the present invention:

[0063] 1. Processing on the Model Owner Side

[0064] Step 1a: First, normalize the vertex coordinates and represent the 3D model as M = {V, F}, where the vertex set V = {v1, v2, …, v N} and the face set F = {f(v i ,vj ,v k )|v i ,v j ,,v k ∈V}. Where N is the number of model vertices, f(v i ,v j ,v k ) is the vertex v i ,v j ,v k The triangular surface composed of the model determines the minimum boundary B in the three coordinate dimensions min The values ​​are:

[0065]

[0066] Among them, [x m ,y m ,z m ] are the minimum values ​​of the model in the three coordinate dimensions respectively. The coordinate transformation is performed on each vertex so that the vertex coordinates of the 3D model are transformed into coordinate values ​​in the range of 0-1. The calculation formula of the coordinate transformation process is as follows:

[0067]

[0068] Among them, R i is the ratio scaled to the range of 0-1, and k is the integer number of the maximum vertex coordinate value after the 3D model is translated.

[0069] Step 1b: Compression model, under the control of compression threshold m, converts the floating point coordinate values ​​in the 0-1 interval into integer coordinate value tuple J i , calculate the compressed vertex integer coordinate value J i The formula is as follows, where is the floor function.

[0070]

[0071] Step 1c: Perform coordinate transformation and convert the integer coordinate value J of the compressed model into i The coordinate value j converted into a binary representation of fixed length L i,p To store the compressed 3D model, J i refers to the compressed vertex integer coordinate value, j i,p refers to the coordinate value j in binary representation i,p The conversion process and the calculation formula of the length L of the binary representation are as follows:

[0072]

[0073] Step 1d: Multi-level spatial clustering to divide the 3D model space. Use a multi-level spatial clustering algorithm to divide the vertices in the 3D model space into non-overlapping subspaces. For example, perform initial clustering on the model vertices, with the number of clusters being k1, to obtain a relatively compact subspace. Then cluster each subspace again, with the number of clusters being k2, to obtain the final compact subspace The calculation formula is as follows:

[0074] S=Clustering(J,k1)(6)

[0075]

[0076] Where J is the transformed integer coordinate value, Clustering represents the existing clustering algorithm; S refers to the set of k1 clusters obtained after clustering, s i represents the i-th cluster in set S, c j Represents cluster s i The cluster set obtained after clustering again;

[0077] Step 1e: Search for the best reference point, treat each cluster as an independent subunit, take each vertex in the cluster as a reference vertex in turn, take other vertices in the cluster as embedded vertices, perform multi-MSB prediction on the reference vertex r and the embedded vertex e to calculate the embeddable length I of the embedded vertex r,e , and then identify the reference vertex that makes the sum of the embeddable lengths of the subspace reach the maximum value as the optimal reference vertex:

[0078]

[0079] Step 1f: Re-mesh the 3D model, group the vertices according to their cluster indices, and place the best reference point of each cluster at the first position of the group, and update the index of the vertices in the face set according to the position index after the vertex indices are reordered;

[0080] Step 1g: Perform prediction error detection, use the basic embedding length of the reference vertex as the reserved embedding space to embed data, and for the embedded vertex, perform multi-MSB prediction on the reference vertex and the embedded vertex to calculate the embeddable length of the embedded vertex;

[0081] Step 1h: Generate a random sequence and use the encryption key k E Generate a binary random sequence b;

[0082] Step 1i: Encryption model, continuously sample L bits of the binary random sequence b, and then perform an XOR operation with the binary representation of the vertex coordinates to obtain the encryption model. The calculation formula is as follows:

[0083]

[0084] where j i,p is the kth bit of the binary representation of the coordinate value of vertex i after transformation, b i,k It is the k-th bit message after continuous sampling of the binary random sequence b; its encryption method is not limited to stream encryption, and can be adapted to symmetric encryption algorithms such as RC4, DES, AES, SM1 and SM4.

[0085] Step 1j: Characterize the label graph, and regard the compression threshold m, the embeddable length I of each embedded vertex, and the number of vertices Num of each cluster as labels:

[0086] label={m,I,Num}(10)

[0087] Step 1k: Compression coding, the compression threshold uses fixed-length coding, and for the embeddable length of the embedded vertex and the number of vertices in each cluster, the embeddable length symbol frequency of each embedded vertex and the number of vertices in each cluster are counted, and the Huffman coding tree is constructed according to the frequency. By traversing the constructed Huffman coding tree, the coding results of each embedding length and number of vertices are obtained. The final label graph is represented as a binary sequence of length HL, which is determined by the compression threshold, the Huffman coding tree structure and the coding result;

[0088] Step 1l: Embed the label graph by embedding the label graph into the basic embedding length EL of each vertex (including the reference vertex) through a bit replacement strategy B If the length HL exceeds 3×EL N × N, where N is the number of vertices in the input model, then the predicted embedding length EL of the embedded vertex P The encrypted model E′(M) with the embedded label graph is generated from the binary bits of

[0089] 2. Processing on the Data Hider Side

[0090] Step 2a: Use data to hide key k D Generate a binary random sequence s, and then perform an XOR operation with the secret message AD to obtain the encrypted secret message ED. The calculation formula is as follows:

[0091]

[0092] Step 2b: Embed data. The data hider extracts the label graph from the encryption model E′(M) with the embedded label graph, extracts the Huffman coding tree sequence from the label graph, reconstructs the Huffman coding tree and retrieves the encoding of each symbol, decodes the Huffman coding result, and thus determines the reserved embedding space. Finally, the encrypted secret message is embedded into the remaining available embedding space through the bit replacement strategy to generate a labeled encryption model. The calculation formula is as follows:

[0093]

[0094] Among them ED i is the i-th bit of the encrypted secret message, I i is the embeddable length of the i-th vertex, and j represents the x, y, and z coordinate axes.

[0095] 2. Processing on the Model Receiver

[0096] Step 3a: Extract the secret message. The model receiver can obtain the embedding length of each embedded vertex by extracting the label graph, extract the encrypted secret message from the embedding space containing the labeled encrypted model vertex coordinate values, and then add it to the data hiding key k. D Generate a binary random sequence and XOR it to get the decrypted message.

[0097] Step 3b: Recover the model. The model recipient can obtain the embedding space of each embedded vertex by extracting the label graph and compare the coordinate values ​​of the encrypted model vertices with the encryption key k. E The generated binary random sequence is XORed to obtain a preliminary decryption model. The basic embedding length of the reference vertex coordinate value is then set to 0 to recover the coordinates of the reference point, while the embedded vertex coordinates can be recovered from their corresponding reference vertices by using prediction error detection.

[0098] Step 3c: Secret message extraction and recovery model: The model receiver also has the encryption key k E and data hiding key k D , the model can be restored and the secret message can be extracted respectively through the above steps. The secret message extraction and model restoration operations can be performed in any order and are separable.

[0099] In summary, the present invention combines a multi-level clustering algorithm and a multi-most significant bit (multi-MSB) prediction technology to propose a reversible information hiding method for 3D encrypted domain based on spatial clustering. First, the neighboring vertices are divided into the same cluster space by a multi-level spatial clustering algorithm to ensure the proximity of the vertices in the cluster space; then, the optimal reference vertex search algorithm is used for each cluster space to identify the best reference vertex in the cluster space, so that the embedding space is maximized; then, in each cluster space, multi-MSB prediction is performed on the reference vertex and the embedded vertex to calculate the embeddable length of the embedded vertex. In addition, the basic embedding length of the reference vertex is used as an additional embedding space to further improve the embedding capacity. Finally, the data is embedded into the reserved embedding space through a bit replacement strategy. The scheme uses a multi-level spatial clustering algorithm and an optimal reference vertex search algorithm to ensure the proximity of the vertices in the cluster space, fully utilizes the spatial coordinate redundancy between vertices, achieves higher embedding capacity and lower computational overhead, and supports reversibility and separability. The proposed scheme provides a robust, high-capacity, and scalable solution for secure data embedding of encrypted 3D models, which can be widely used in application scenarios such as real-life 3D, computer graphics, and digital twins.

[0100] The above contents are further detailed descriptions of the present invention in combination with the best implementation scheme, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. It should be understood by those skilled in the art that various modifications can be made to the details without departing from the scope of the appended claims, and all should be deemed to belong to the protection scope of the present invention.

[0101] To evaluate the embedding capacity of our method, we compared the average net embedding capacity of our method with other related methods [1-7] on 380 models provided by the Princeton ShapeSegmentationBenchmark model database [8]. The comparison results are shown in Figure 2. Figure 4 As shown. By comparison, it can be seen that the average embedding capacity of the method proposed in the present invention on the PSB model database is the highest compared with other methods, and is nearly 9.7 bits per vertex higher than the most advanced method currently. This fully demonstrates the superior performance of the reversible information hiding method for encrypted 3D models based on spatial clustering proposed in the present invention.

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[0109] [8]

[0110] On the other hand, an embodiment of the present invention further provides a 3D ciphertext domain reversible information hiding system based on spatial clustering, comprising:

[0111] A processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a 3D ciphertext domain reversible information hiding method based on spatial clustering as described in the above technical solution.

[0112] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A reversible information hiding method in 3D ciphertext domain based on spatial clustering, characterized in that: The steps include: Step S1, the model owner performs coordinate transformation processing on the vertex coordinate values ​​of the 3D model, compresses the model, and converts the floating-point coordinate values ​​into integer coordinate values; Step S2, the model owner applies a multi-level spatial clustering algorithm to divide the vertices of the 3D model into mutually exclusive cluster spaces, and in each cluster space, an adaptive optimal reference vertex search algorithm is applied to identify the best reference vertex, and the 3D model is re-meshed, and then a prediction error test is performed between the best reference vertex and the embedded vertex to determine the embedding length of each embeddable vertex; Step S3, the model owner encrypts the 3D model using the encryption key to obtain an encrypted model; Step S4, the model owner represents the compression threshold, vertex embeddable length, and the number of vertices of each cluster in the label graph, compresses it using compression coding technology, and embeds it into the encryption model through a bit replacement strategy to obtain an encrypted model with a label graph; Step S5, the data hider extracts the label graph from the encrypted model containing the label graph to identify the reserved embedding space, and uses the data hiding key to embed the secret message into the remaining embeddable space, and generates a labeled encrypted model and sends it to the model receiver; Step S6: After the model receiver obtains the encrypted model with the mark, he / she performs model decryption or data extraction according to the key he / she has.

2. The method for reversible information hiding in 3D ciphertext domain based on spatial clustering as claimed in claim 1, characterized in that: The specific implementation of step S1 is as follows: S11, normalization: The 3D model is represented as M = {V, F}, where the vertex set V = {v1, v2, ..., v N } and the face set F = {f(v i ,v j ,v k )|v i ,v j ,,v k ∈V}, where N is the number of vertices in the 3D model, f(v i ,v j ,v k ) is the vertex v i ,v j ,v k The triangular surface composed of the model determines the minimum boundary B in the three coordinate dimensions min The values ​​are: Among them, [x m ,y m ,z m ] are the minimum values ​​of all vertices of the model in the three coordinate dimensions, [x i ,y i ,z i ] are the coordinate values ​​of the i-th vertex in the three coordinate dimensions, and min means taking the minimum value; coordinate transformation is performed on each vertex so that the vertex coordinates of the 3D model are transformed into coordinate values ​​in the range of 0-1; S12, compression model: under the control of the compression threshold m, the floating point coordinate values ​​in the range of 0-1 are converted into integer coordinate value tuples J i , calculate the compressed vertex integer coordinate value J i The formula is as follows, where is the floor function; Among them, R i is a ratio scaled to the 0-1 interval; S13, coordinate conversion: according to the compression threshold m, the integer coordinate value J of the compression model is converted to i The coordinate value j converted into a binary representation of fixed length L i,p To store the compressed 3D model, J i refers to the compressed vertex integer coordinate value, j i,p refers to the coordinate value j in binary representation i,p .

3. The method for reversible information hiding in 3D ciphertext domain based on spatial clustering as claimed in claim 2, characterized in that: In S11, the calculation formula for converting the vertex coordinates of the 3D model to coordinate values ​​in the range of 0-1 is as follows: Among them, R i is the ratio scaled to the range of 0-1, and k is the integer number of the maximum vertex coordinate value after the 3D model is translated.

4. The method for reversible information hiding in 3D ciphertext domain based on spatial clustering as claimed in claim 2, characterized in that: In S13, J i The length L of the binary representation is calculated as follows:

5. The method for reversible information hiding in 3D ciphertext domain based on spatial clustering as claimed in claim 1, characterized in that: The specific implementation of step S2 is as follows: S21, multi-level spatial clustering: Use a multi-level spatial clustering algorithm to divide the vertices in the 3D model space into non-overlapping subspaces; first perform initial clustering on the model vertices, with the number of clusters being k1, to obtain a relatively compact subspace Then cluster each subspace again, with the number of clusters being k2, to obtain the final compact subspace The calculation formula is as follows: S=Clustering(J,k1)(6) Where J is the transformed integer coordinate value; Clustering represents the existing clustering algorithm; S refers to the set of k1 clusters obtained after clustering, s i represents the i-th cluster in set S, c j Represents cluster s i The cluster set obtained after clustering again; S22, search for the best reference point: treat each cluster as an independent subunit, take each vertex in the cluster as a reference vertex in turn, take other vertices in the cluster as embedded vertices, perform multiple most important bit predictions on the reference vertex r and the embedded vertex e to calculate the embeddable length I of the embedded vertex r,e , and then identify the reference vertex that makes the sum of the embeddable lengths of the subspace reach the maximum value as the optimal reference vertex: S23, re-meshing the 3D model, grouping the vertices according to the cluster index of the vertices, placing the best reference point of each cluster at the first position of the group, and updating the index of the vertex in the face set according to the position index after the vertex index is reordered; S24, performing prediction error detection, using the basic embedding length of the reference vertex as the reserved embedding space to embed data, and for the embedded vertex, performing Multi-MSB prediction on the reference vertex and the embedded vertex to calculate the embeddable length of the embedded vertex.

6. The method for reversible information hiding in 3D ciphertext domain based on spatial clustering as claimed in claim 1, characterized in that: The specific implementation of step S3 is as follows: S31, generate a random sequence, using the encryption key k E Generate a binary random sequence b; S32, encryption model, continuously samples L bits of the binary random sequence b, and then performs an XOR operation with the binary representation of the vertex coordinates to obtain the encryption model; the calculation formula is as follows: where j i,p is the kth bit of the binary representation of the coordinate value of vertex i after transformation, b i,k is the k-th bit message after continuous sampling of the binary random sequence b, and L is the bit length of the coordinate value in binary representation.

7. The method for reversible information hiding in 3D ciphertext domain based on spatial clustering as claimed in claim 1, characterized in that: The specific implementation of step S4 is as follows: S41, characterize the label graph: consider the compression threshold m, the embeddable length I of each embedded vertex, and the number of vertices Num of each cluster as labels: label={m,I,Num}(10) S42, compression coding: The compression threshold uses fixed-length coding, and for the embeddable length of the embedded vertex and the number of vertices in each cluster, the symbol frequency of the embeddable length of each embedded vertex and the symbol frequency of the number of vertices in each cluster are counted, and a Huffman coding tree is constructed according to the frequency. By traversing the constructed Huffman coding tree, the coding result of each embedding length and number of vertices is obtained. The final label graph is represented as a binary sequence of length HL, and the length is jointly determined by the compression threshold, the Huffman coding tree structure and the coding result; S43, Embedding Label Graph: Embed the label graph to the basic embedding length EL of each vertex through a bit replacement strategy B If the length HL exceeds 3×EL B × N, where N is the number of vertices in the input model, then the predicted embedding length EL of the embedded vertex P The encrypted model E′(M) with the embedded label graph is generated from the binary bits of 8. The method for reversible information hiding in 3D ciphertext domain based on spatial clustering as claimed in claim 1, characterized in that: The specific implementation of step S5 is as follows: S51, Encrypting a secret message: Using the data hiding key k D Generate a binary random sequence s, and then perform an XOR operation with the secret message AD to obtain the encrypted secret message ED. The calculation formula is as follows: S52, Embedding Data: Data Hider from Encrypted Model E with Embedded Label Graph ′ (M) extracts the label graph, extracts the Huffman coding tree sequence from the label graph, reconstructs the Huffman coding tree and retrieves the encoding of each symbol, decodes the Huffman coding result, and thus determines the reserved embedding space; finally, the encrypted secret message is embedded into the remaining available embedding space through the bit replacement strategy to generate a labeled encryption model. The calculation formula is as follows: Among them ED i is the i-th bit of the encrypted secret message, I i is the embeddable length of the i-th vertex, j represents the x, y, z coordinate axes, N is the number of vertices in the 3D model, mod represents the remainder, and L is the bit length of the coordinate value in binary representation.

9. The method for reversible information hiding in 3D ciphertext domain based on spatial clustering as claimed in claim 1, characterized in that: The specific implementation of step S6 is as follows: S61, extract secret message: The model receiver obtains the embedding length of each embedded vertex by extracting the label graph, extracts the encrypted secret message from the embedding space containing the marked encrypted model vertex coordinate values, and then D Generate a binary random sequence and perform XOR operation to obtain the decrypted message; S62, restore the model: The model receiver obtains the embedding space of each embedded vertex by extracting the label graph, and compares the coordinate value of the encrypted model vertex with the encryption key k E The generated binary random sequence is XORed to obtain a preliminary decryption model; the coordinates of the reference point are then restored by setting the basic embedding length of the reference vertex coordinate value to 0, while the embedded vertex coordinates are restored from their corresponding reference vertices by using prediction error detection; S63, extract secret message and restore model: the model receiver also has the encryption key k E and data hiding key k D , the model is restored and the secret message is extracted respectively through steps S62 and S61; the secret message extraction and model restoration operations are performed in any order and are separable.

10. A 3D ciphertext domain reversible information hiding system based on spatial clustering, characterized in that: include: A processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a 3D ciphertext domain reversible information hiding method based on spatial clustering as described in any one of claims 1 to 9.

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