Method and system for protecting three-dimensional mesh model based on hybrid encryption and geometric projection

Abstract

A three-dimensional mesh model protection method and system based on hybrid encryption and geometric projection, the method comprising: determining reference vertices and embeddable vertices including isolated vertices and connected vertices according to the topological structure of the three-dimensional mesh model; performing geometric projection prediction on the embeddable vertices to obtain isolated vertex prediction values and connected vertex prediction values; performing a most significant bit replacement operation on the coordinates of the embeddable vertices to release the data embedding space and generate a compressed three-dimensional model and indication information; rearranging the compressed three-dimensional model; symmetrically encrypting the rearranged three-dimensional mesh model to generate an encrypted three-dimensional model; embedding the session key in the encrypted three-dimensional model after encapsulation; encrypting the management information and embedding it in the data embedding space of the encrypted three-dimensional model to obtain a three-dimensional model with encryption; and a model receiver selects to extract and decrypt the management information or extracts the encapsulated session key and decrypts the model data to reversibly restore the three-dimensional mesh model according to the access permission.

Description

Technical Field

[0001] This invention relates to the field of data information security technology, and in particular to a method and system for protecting three-dimensional mesh models based on hybrid encryption and geometric projection. Background Technology

[0002] Three-dimensional mesh models typically contain a large amount of high-precision geometric information. Their construction involves complex modeling processes and significant computational resources, thus gradually becoming digital assets with high economic value and intellectual property attributes. In practical applications, three-dimensional mesh models often need to be stored, transmitted, and distributed across different users, platforms, or cloud environments, which places higher demands on the security, access control capabilities, and copyright protection of model data.

[0003] Existing 3D mesh model protection schemes mainly include overall model encryption, digital watermarking, and reversible data hiding. While overall encryption can prevent unauthorized access to some extent, it typically lacks fine-grained access control. Once the key is leaked, the model data is completely exposed, making it difficult to support personalized authorization or tiered service requirements. Digital watermarking technology embeds identification information into the model to mark copyright, but most methods prioritize robustness while neglecting reversibility, often causing irreversible damage to model accuracy or geometry, limiting its application in high-precision modeling scenarios. Furthermore, most existing reversible data hiding methods follow the grouping strategy from 2D image processing, dividing vertices into fixed groups and processing them independently. This type of method generally suffers from limited vertex utilization in 3D models; some vertices cannot participate in embedding due to grouping constraints, resulting in limited overall embedding capacity. Simultaneously, grouping strategies often ignore the topological relationships and geometric correlations between vertices, making it difficult to accurately characterize vertex variation patterns, thus affecting prediction accuracy and embedding efficiency. Existing solutions typically employ a single key or centralized decryption method for access control, lacking flexible support for different users or service levels. This makes it difficult to meet the granular access control requirements of application scenarios such as cloud-based model distribution and customized services. In terms of security mechanism design, most 3D model protection methods are still limited to a single encryption form, rarely combining symmetric and asymmetric encryption mechanisms organically, and failing to fully consider multiple requirements such as encryption efficiency, key management flexibility, and security.

[0004] In summary, existing 3D mesh model protection technologies still have shortcomings in terms of access control flexibility, vertex utilization, embedding capacity, processing efficiency, and prediction accuracy, and have not fully integrated the topological characteristics of 3D models with hybrid encryption mechanisms in modern cryptography. Summary of the Invention

[0005] In view of the above-mentioned deficiencies of the prior art, the present invention provides a method and system for protecting three-dimensional mesh models based on hybrid encryption and geometric projection. While ensuring the reversible recovery of the model and high embedding capacity, it achieves more refined access control and a more efficient and secure model protection mechanism to meet the actual needs of complex scenarios such as personalized services and cloud applications.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] The first aspect is a method for protecting 3D mesh models based on hybrid encryption and geometric projection, which includes the following steps:

[0008] S1. The key management center generates public and private keys for the model provider and model receiver respectively on the elliptic curve group;

[0009] S2. Determine the reference vertices and the embeddable vertices, including isolated vertices and connected vertices, based on the topology of the 3D mesh model;

[0010] S3. Perform geometric projection prediction on isolated vertices and connected vertices respectively to obtain the predicted values ​​of isolated vertices and connected vertices.

[0011] S4. Based on the predicted values ​​of isolated vertices and connected vertices, perform a multiple most significant bit replacement operation on the coordinates of embeddable vertices to release the data embedding space and generate a compressed 3D model and indication information for restoring the 3D mesh model; rearrange the compressed 3D model.

[0012] S5. Perform symmetric encryption on the rearranged 3D mesh model to generate an encrypted 3D model; encapsulate the session key and embed it into the encrypted 3D model;

[0013] S6. Encrypt the management information and embed it into the data embedding space of the encrypted 3D model to obtain the encrypted 3D model; the model receiver can choose to extract and decrypt the management information or extract the encapsulated session key and decrypt the model data to reversibly recover the 3D mesh model according to the access permissions.

[0014] Preferably, S2 includes:

[0015] S21. Represent the 3D mesh model as a set of vertices and a set of faces;

[0016] S22. Integerize the coordinates of any vertex according to a preset scaling factor to obtain the integer coordinates of the vertex;

[0017] S23. Construct the adjacency set of each vertex from the face set to obtain the adjacency set sequence; sort the vertices from high to low according to the number of elements in the adjacency set to obtain the sorted adjacency set sequence and select the first vertex of the sorted sequence as the reference vertex; set all other vertices except the reference vertex as embeddable vertices.

[0018] Preferably, in S3, performing geometric projection prediction on isolated vertices includes:

[0019] Identify isolated vertex sets with empty adjacency sets; for any isolated vertex, gradually expand the search radius centered on its index to find the first vertex with a non-empty adjacency set; use the coordinates of the first vertex with a non-empty adjacency set as the predicted value of the isolated vertex and record it in the prediction set.

[0020] Preferably, in S3, performing geometric projection prediction on connected vertices includes:

[0021] Establish a set of processed vertices to mark the processed vertices; establish a queue set Q to store the vertices to be processed;

[0022] Mark the reference vertex as a processed vertex and add all adjacent vertices of the reference vertex to the queue set Q;

[0023] For queue sets The first vertex to be processed in the order it was added. Select a candidate set of vertices that have been marked as processed from its adjacency set. According to the candidate set Retrieving and processing the number of vertices in the middle The predicted value.

[0024] As a preferred option, based on the candidate set The number of vertices in the middle is used to obtain the vertices to be processed. The predicted values ​​include the following two prediction methods:

[0025] When candidate set When the number of vertices in the middle is less than 3, the average coordinates of the candidate set are used as the vertices to be processed. Predicted value; when the candidate set When the number of vertices in the middle set is greater than or equal to 3, calculate the pairwise distances between vertices in the candidate set and select the two vertices with the greatest distance. Using the midpoint of the two points as the geometric center, perform mirror projection on the remaining candidate vertices and calculate the mean. Compare the prediction error of the projection mean with the prediction error of the global mean of the candidate set, and select the vertex with the smaller prediction error as the vertex to be processed. The predicted value.

[0026] Preferably, performing geometric projection prediction on connected vertices further includes:

[0027] Use a position mapping table to record the prediction method and list the vertices to be processed. Mark vertices as processed; mark vertices to be processed. From queue collection Remove it from the list and add its adjacent vertices that have not yet been marked as processed vertices to the queue set. Then, a breadth-first order based on adjacency expansion is adopted to process embeddable vertices adjacent to already processed vertices layer by layer, ensuring that each vertex is processed sequentially provided its predicted reference is determined; for the queue set The prediction steps described above are repeated for the vertices to be processed in the queue until the set is complete. Empty, to complete the prediction processing for all connected embeddable vertices.

[0028] Preferably, S4 includes:

[0029] An XOR operation is performed on the binary representation of the embeddable vertex coordinates and its predicted binary representation to obtain the predicted difference bit string; the number of consecutive identical bits starting from the most significant bit is counted and recorded as a tag, and the tag represents the number of most significant bits that can be replaced or reused; the entire tag sequence is used to form tag information, and entropy coding is used to compress the indication information to obtain the encoding table and encoding result; the compressed 3D model is rearranged in the order of entropy coding table, embeddable vertex tags, reference pixels, embeddable vertex residual bits, position mapping table, and redundancy space.

[0030] As a preferred embodiment, S5 includes:

[0031] The model provider generates a random session key for each model and uses a symmetric encryption algorithm to encrypt the rearranged 3D mesh model to obtain an encrypted 3D model;

[0032] The model provider calculates the shared amount based on elliptic curve key negotiation and generates a derived key through a key derivation function, and encapsulates the session key into an elliptic curve encapsulated session key.

[0033] Write the elliptic curve encapsulation session key into the predetermined end bit region of the encrypted 3D model;

[0034] Location tags are written into the encrypted 3D model to record the length of the compressed 3D model data and indicate the location boundaries of the available space for data hiding;

[0035] The model provider sends the encrypted 3D model to the cloud server, and at the same time sends the public key pair to the cloud server to bind the model.

[0036] As a preferred embodiment, S6 includes:

[0037] The cloud server reads the embeddable space length from the location tags without decrypting the encrypted 3D model;

[0038] The cloud server uses a data hiding key to encrypt the management information, and writes the encrypted management information into an embeddable space to obtain a encrypted 3D model.

[0039] The model recipient provides a public key pair to the cloud server to obtain a encrypted 3D model;

[0040] When the model receiver only extracts management information, it obtains the data hiding key, extracts the encrypted management information from the encrypted 3D model based on the location tag, and decrypts it to obtain the plaintext management information.

[0041] When the model receiver reconstructs the 3D mesh model, it extracts the elliptic curve encapsulation session key from the end of the encrypted 3D model and recovers the session key. The model receiver uses the session key to decrypt the compressed 3D model data, decodes the indication information and position mapping table according to the encoding table, and reconstructs the reference vertex coordinates, residual bits, and the most significant bit that has been replaced. The model receiver reproduces the geometric projection prediction and mean prediction process in the same prediction order as the model owner, and recovers the coordinates vertex by vertex by combining the indication information and residual bits, thus realizing the reversible reconstruction of the 3D mesh model.

[0042] Secondly, a 3D mesh model protection system based on hybrid encryption and geometric projection includes:

[0043] The key management center is used to generate public and private keys for the model provider and model receiver respectively on the elliptic curve group;

[0044] The vertex classification module is used to determine reference vertices and embeddable vertices, including isolated vertices and connected vertices, based on the topology of the 3D mesh model.

[0045] The geometric projection prediction module is used to perform geometric projection prediction on isolated vertices and connected vertices respectively, and obtain the prediction values ​​of isolated vertices and connected vertices.

[0046] The compression module performs a most significant bit substitution operation on the coordinates of embeddable vertices based on the predicted values ​​of isolated vertices and connected vertices, releases the data embedding space, and generates a compressed 3D model and indication information for restoring the 3D mesh model; it then rearranges the compressed 3D model.

[0047] The encryption module performs symmetric encryption on the rearranged 3D mesh model to generate an encrypted 3D model; it encapsulates the session key and embeds it into the encrypted 3D model; it encrypts the management information and embeds it into the data embedding space of the encrypted 3D model to obtain a encrypted 3D model.

[0048] The decryption module allows the model receiver to choose, based on access permissions, to extract and decrypt management information, or to extract the encapsulated session key and decrypt model data to reversibly recover the 3D mesh model.

[0049] The three-dimensional mesh model protection system based on hybrid encryption and geometric projection is used to implement the three-dimensional mesh model protection method based on hybrid encryption and geometric projection as described in the first aspect.

[0050] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0051] 1. A geometric prediction mechanism based on vertex topological relationships is proposed. This invention no longer adopts traditional grouping processing or fixed neighborhood strategies, but dynamically determines the prediction order and reference set of vertices based on the topological connectivity of a 3D mesh model. By characterizing the geometric correlation and change relationships between vertices, higher accuracy vertex prediction is achieved, providing a more reliable prediction basis for subsequent data embedding.

[0052] 2. This paper proposes for the first time to use geometric projection prediction for reversible data hiding of 3D mesh models. By performing geometric projection prediction on connected vertices and fast prediction on isolated vertices, the paper fully utilizes the spatial structural characteristics of 3D models, avoids the problems of strong dependence on model shape and insufficient generalization ability of traditional prediction methods, and improves prediction stability and embedding ability.

[0053] 3. This paper proposes a vertex-level data embedding method that breaks through the limitations of traditional grouping processing strategies. Unlike existing methods that divide vertices into fixed groups for processing, this invention uses vertices as the basic processing unit, enabling more vertices to participate in data embedding, thereby significantly improving vertex utilization, overall embedding capacity, and algorithm time efficiency.

[0054] 4. This invention is the first to introduce a hybrid encryption mechanism for access control and customized services in the protection of 3D mesh models. It combines symmetric encryption with elliptic curve-based asymmetric key encapsulation, ensuring efficient encryption of model data while addressing the flexibility issues of key distribution and management, thus providing a cryptographic foundation for multi-user access control and customized services. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0056] Figure 2 The original three-dimensional mesh model of Embodiment 1 of this invention;

[0057] Figure 3 The hybrid encryption model of Embodiment 1 of the present invention;

[0058] Figure 4The encrypted 3D model with embedded additional information in Embodiment 1 of the present invention;

[0059] Figure 5 The original model after reversible recovery in Embodiment 1 of the present invention. Detailed Implementation

[0060] To make the technical means, inventive features, objectives, and effects of the invention readily understandable, the invention is further described below with reference to specific illustrations. However, the invention is not limited to the embodiments described below.

[0061] It should be noted that the structures, proportions, sizes, etc., illustrated in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0062] This invention discloses a method for protecting 3D mesh models based on hybrid encryption and geometric projection, aiming to ensure the security of 3D model data while achieving controllable access, reversible recovery, and secure embedding of privacy information. The method first preprocesses the 3D mesh model, representing vertex coordinates as integers and determining the processing order of reference vertices and embeddable vertices based on the model's topology. Subsequently, geometric prediction is performed on embeddable vertices, including geometric projection prediction for connected vertices and fast prediction for isolated vertices. Based on the prediction results, a multiple most significant bit (LN) substitution operation is performed on the vertex coordinates to release the data embedding space and generate indication information for model recovery. On this basis, a hybrid encryption mechanism is used to protect the model data. A symmetric encryption algorithm is used to encrypt the processed model data, and an elliptic curve key negotiation mechanism is used to encapsulate the session key and embed it into the encrypted 3D model. Without decrypting the model data, the encrypted management information is embedded into the data embedding space, resulting in a encrypted 3D mesh model. In the recovery phase, the management information or the recovery session key is extracted according to access permissions, and the reversible reconstruction of the 3D mesh model is achieved by combining the indication information and prediction rules. This invention achieves secure encryption of model data, separable embedding of information, and lossless recovery of the model without affecting the normal use of the 3D model. It has the advantages of high security, fast speed, strong embedding capability and wide applicability, and is suitable for application scenarios such as 3D model distribution, cloud storage and access control.

[0063] Example 1:

[0064] like Figure 1The method for protecting 3D mesh models based on hybrid encryption and geometric projection aims to achieve secure protection, controllable access, and reversible recovery of 3D mesh models during storage, transmission, and distribution by combining a data embedding mechanism based on geometric prediction with a key management method based on hybrid encryption. It is applicable to cloud-based model management, 3D model copyright protection, and secure data sharing, and includes the following steps:

[0065] S1. The key management center generates and distributes key information for the model provider and the model receiver respectively on the elliptic curve group;

[0066] The key management entity generates elliptic curve public and private keys for the model provider and model receiver respectively, and completes key distribution; in step S1 of this embodiment, the key generation and distribution method is as follows:

[0067] S11. The key management center generates a private key for the model provider on the elliptic curve group. With public key Generate a private key for the model receiver. With public key G represents a predefined and publicly disclosed base point on the elliptic curve.

[0068] S12. The key management center distributes key information to the model provider. Distribute key information to model receivers And enable the cloud server to store the public key pair used for accessing the binding. .

[0069] S2. Determine the reference vertices and embeddable vertices based on the topology of the 3D mesh model;

[0070] The 3D mesh model is preprocessed by representing the vertex coordinates as integers and determining the processing order of reference vertices and other embeddable vertices based on the model's topology.

[0071] In step S2 of this embodiment, the vertex coordinates are represented as integers, and the processing order of the reference vertex and other embeddable vertices is determined according to the topology of the model as follows:

[0072] S21. Represent the 3D mesh model as a set of vertices. With face set Each vertex contains three coordinate axes;

[0073] S22, for any vertex coordinates By scaling factor Integerize to obtain vertex integer coordinates ,in According to the scaling factor Choose binary representation of bit length and with Bit-bit binary representation of vertex integer coordinates ;

[0074] S23, From surface set Construct the adjacency set for each vertex And obtain the adjacency set sequence. Sort the vertices in descending order of the number of elements in their adjacency sets to obtain the sorted sequence of adjacency sets. The first vertex after sorting is selected as the reference vertex. If a model contains multiple independent sub-models, the first vertex of each sub-model after sorting is used as the reference vertex and processed in the same way.

[0075] All vertices except the reference vertex are set as embeddable vertices, which include isolated vertices and connected vertices.

[0076] S3. Perform geometric projection prediction on isolated vertices and connected vertices respectively to obtain the predicted values ​​of isolated vertices and connected vertices.

[0077] S31. Perform geometric projection prediction on isolated vertices to obtain predicted values ​​for isolated vertices; in this embodiment, the fast prediction method for isolated vertices is as follows:

[0078] Identify isolated vertex sets whose adjacency sets are empty. ,in Represents isolated vertices The number of adjacent vertices; for any isolated vertex Using its index as the center, gradually expand the search radius to find the first vertex with a non-empty adjacency set. Set the first non-empty set of vertices. The coordinates of the isolated vertex The prediction results, i.e., the predicted values ​​of isolated vertices, are recorded in the prediction set. .

[0079] S32. Perform geometric projection prediction on connected vertices to obtain the predicted values ​​of connected vertices; the geometric projection prediction method for connected vertices is as follows:

[0080] Establish the set of processed vertices Used to mark processed vertices and establish a queue set. Store the vertices to be processed, mark the reference vertex as a processed vertex, and add all its adjacent vertices. In the set, the index of the processed vertex is in the middle. The middle part will be marked as 1; for the queue set The first vertex to be processed in the order it was added. Select a candidate set of vertices that have been marked as processed from its adjacency set. , express The candidate set, Indicates both belonging to The adjacent vertex, and at the same time, the index is in the set. The vertex in the middle is marked as 1 (representing a processed vertex);

[0081] when When the coordinates of the candidate set are used as the predicted value, |.| represents the count of vertices in the set;

[0082] when When calculating the pairwise distances within the candidate set, select the two vertices with the greatest distance. Using the midpoint of the two points as the geometric center, perform mirror projection on the remaining candidate vertices and calculate the mean. Compare the prediction error of the projection mean with the global mean of the candidate set, and select the one with the smaller error as the candidate vertex. The final predicted value is obtained, where the prediction error is defined as the sum of the absolute differences between the predicted vertex coordinates and the corresponding original vertex coordinates along the three-dimensional coordinate axes. Because a position mapping table records which prediction method was used, it can be directly restored during reconstruction.

[0083] Record the selected prediction method in the location mapping table, and These vertices are marked as processed for subsequent vertex prediction. Simultaneously, From queue collection Remove the vertex from the set and add it to the queue set if it is not yet marked as processed in the adjacent set. Then, a breadth-first order based on adjacency expansion is used to process embeddable vertices adjacent to already processed vertices layer by layer, thus ensuring that each vertex is processed sequentially given its predicted reference is determined. The above steps apply to the queue set. The pending vertices in the queue are processed repeatedly until the queue is complete. If empty, then the prediction process for all connected embeddable vertices is completed.

[0084] S4. Based on the predicted values ​​of isolated vertices and connected vertices, perform a most significant bit replacement operation on the coordinates of embeddable vertices to release the data embedding space, generate indication information for restoring the original model, and rearrange the model.

[0085] In this embodiment, the method for replacing the most significant bit and generating the indication information is as follows:

[0086] Perform an XOR operation on the binary representation of each embeddable vertex coordinate and its predicted binary representation to obtain the predicted difference bit string; count the number of consecutive identical bits starting from the most significant bit and record it as the tag. ,by This indicates the number of the most significant bits that can be replaced or reused, thereby freeing up embeddable space;

[0087] All label sequences are used to form label information, and entropy coding is used to compress the indication information to obtain the coding table and coding results. The compressed model is rearranged according to the entropy coding table, the labels of embeddable vertices, reference pixels, residual bits of embeddable vertices, position mapping table, and the order of redundancy space.

[0088] S5. Perform symmetric encryption on the rearranged model data to generate an encrypted 3D model, and embed the session key into the encrypted 3D model after encapsulating it based on the elliptic curve key negotiation mechanism.

[0089] In this embodiment, the symmetric encryption and session key encapsulation embedding method is as follows:

[0090] The model provider generates a random session key for each model. The rearranged model data was then encrypted using a symmetric encryption algorithm to obtain an encrypted 3D model. ;

[0091] The model provider calculates the shared quantity based on elliptic curve key negotiation and generates a derived key using a key derivation function, then encapsulates the session key into an elliptic curve encapsulated session key. ;

[0092] Encapsulate the session key with the encapsulated elliptic curve. Write the predetermined end bit region into the encrypted 3D model;

[0093] Write location tags into the encrypted 3D model. The location tags are used to record the length of the compressed model data and indicate the location boundaries of the available space for data hiding.

[0094] The model provider sends the encrypted 3D model to the cloud server, along with the public key pair. Send it to the cloud server for model binding.

[0095] S6. Without decrypting the encrypted 3D model, the cloud encrypts the management information and embeds it into the data embedding space to obtain a encrypted 3D model. The receiver can choose to extract and decrypt the management information or extract the encapsulation key and restore the session key to decrypt the model data according to the access permissions. Then, the 3D mesh model can be reversibly restored according to the instruction information and prediction rules.

[0096] In this embodiment, the cloud data hiding, permission-based extraction, and model reversible recovery methods are as follows:

[0097] S61. The cloud server reads the embeddable space length from the location tag without decrypting the encrypted 3D model.

[0098] S62, cloud server uses data hiding key The management information is encrypted, and the management information includes at least one of user identifiers, access control parameters, index information, and tracking information.

[0099] S63. Write the encrypted management information into the embeddable space to obtain the encrypted 3D model.

[0100] S64. The recipient provides the public key pair to the cloud server. To obtain a dense model.

[0101] S65. When the receiver only extracts management information, the receiver obtains the data hiding key. Based on the location tags, the encrypted management information is extracted from the encrypted 3D model and then decrypted to obtain the plaintext management information;

[0102] S66. When the receiver recovers the 3D mesh model, the receiver extracts the encapsulation key from the end of the encrypted 3D model. and calculate Restore session key;

[0103] S67. The receiver uses the session key to decrypt the compressed model data, and reconstructs the reference vertex coordinates, residual bits and the most significant bit that has been replaced according to the encoding table decoding instruction information and the position mapping table.

[0104] S68. The receiver reproduces the geometric projection prediction and mean prediction process in the same prediction order as the model owner, and recovers the coordinates vertex by vertex by combining the indication information and residual bits to achieve the reversible reconstruction of the original three-dimensional mesh model.

[0105] i. Performance Analysis

[0106] Figures 2-5 Taking a typical 3D mesh model, Bunny, as an example, the processing results after embedding a certain amount of additional information are shown. Figure 2 The original 3D mesh model, Figure 3 The model after hybrid encryption. Figure 4 For encrypted 3D models with embedded additional information, Figure 5 This is the original model after reversible recovery. (From...) Figure 2 It can be seen that the encrypted 3D model does not retain any recognizable original structural features in terms of geometric shape, and the model after embedding additional information does not expose the visual features of the embedded information, thus effectively preventing unauthorized users from obtaining sensitive information by directly observing or analyzing model data.

[0107] Tables 1-3 present the comparison results of the embedding capacity of the present invention and several existing methods under different scale parameters. Experimental results show that, under all test conditions, the average embedding capacity of the present invention on three public databases (dataset 1: Princeton Segmentation Benchmark, dataset 2: Princeton Shape Benchmark, dataset 3: ModelNet-40) is significantly higher than that of the comparison methods (100 models were randomly selected for testing in each database), indicating that the geometric prediction strategy based on topological relationships can significantly improve the embeddability of the model.

[0108] Table 1. Comparison of embedding capacity in dataset 1:

[0109]

[0110] Table 2 Comparison of embedding capacity in dataset 2:

[0111]

[0112] Table 3. Comparison of embedding capacity in dataset 3:

[0113]

[0114] Furthermore, Table 4 compares and analyzes the performance of the method of this invention with existing methods in terms of runtime and vertex utilization. The results show that the method of this invention, by avoiding the traditional grouping processing strategy and using vertices as the basic processing unit, allows more vertices to participate in data embedding, thereby improving vertex utilization while reducing overall processing complexity. Its runtime on multiple test models is superior to the comparative methods.

[0115] Table 4 Characteristic Analysis:

[0116]

[0117] The experimental results above show that the method of the present invention exhibits the best performance in key performance indicators such as embedding capacity, operating efficiency, and vertex utilization. It can achieve efficient data embedding and flexible access control while ensuring the reversible recovery of the 3D mesh model and data security, and has high practical application value.

[0118] Example 2:

[0119] A 3D mesh model protection system based on hybrid encryption and geometric projection includes:

[0120] The key management center is used to generate public and private keys for the model provider and model receiver respectively on the elliptic curve group;

[0121] The vertex classification module is used to determine reference vertices and embeddable vertices, including isolated vertices and connected vertices, based on the topology of the 3D mesh model.

[0122] The geometric projection prediction module is used to perform geometric projection prediction on isolated vertices and connected vertices respectively, and obtain the prediction values ​​of isolated vertices and connected vertices.

[0123] The compression module performs a most significant bit substitution operation on the coordinates of embeddable vertices based on the predicted values ​​of isolated vertices and connected vertices, releases the data embedding space, and generates a compressed 3D model and indication information for restoring the 3D mesh model; it then rearranges the compressed 3D model.

[0124] The encryption module performs symmetric encryption on the rearranged 3D mesh model to generate an encrypted 3D model; it encapsulates the session key and embeds it into the encrypted 3D model; it encrypts the management information and embeds it into the data embedding space of the encrypted 3D model to obtain a encrypted 3D model.

[0125] The decryption module allows the model receiver to choose, based on access permissions, to extract and decrypt management information, or to extract the encapsulated session key and decrypt model data for reversible recovery of the 3D mesh model.

Claims

1. A method for protecting three-dimensional mesh models based on hybrid encryption and geometric projection, characterized in that, Includes the following steps: S1. The key management center generates public and private keys for the model provider and model receiver respectively on the elliptic curve group; S2. Determine the reference vertices and the embeddable vertices, including isolated vertices and connected vertices, based on the topology of the 3D mesh model; S3. Perform geometric projection prediction on isolated vertices and connected vertices respectively to obtain the predicted values ​​of isolated vertices and connected vertices. Performing geometric projection prediction on connected vertices includes: Establish a set of processed vertices to mark the processed vertices; establish a queue set Q to store the vertices to be processed; Mark the reference vertex as a processed vertex and add all adjacent vertices of the reference vertex to the queue set Q; For queue sets The first vertex to be processed in the order it was added. Select a candidate set of vertices that have been marked as processed from its adjacency set. According to the candidate set Retrieving and processing the number of vertices in the middle The predicted value; Based on the candidate set The number of vertices in the middle is used to obtain the vertices to be processed. The predicted values ​​include the following two prediction methods: When candidate set When the number of vertices in the middle is less than 3, the average coordinates of the candidate set are used as the vertices to be processed. Predicted value; when the candidate set When the number of vertices in the middle set is greater than or equal to 3, calculate the pairwise distances between vertices in the candidate set and select the two vertices with the greatest distance. Using the midpoint of the two points as the geometric center, perform mirror projection on the remaining candidate vertices and calculate the mean. Compare the prediction error of the projection mean with the prediction error of the global mean of the candidate set, and select the vertex with the smaller prediction error as the vertex to be processed. The predicted value; S4. Based on the predicted values ​​of isolated vertices and connected vertices, perform a multiple most significant bit replacement operation on the coordinates of embeddable vertices to release the data embedding space and generate a compressed 3D model and indication information for restoring the 3D mesh model; rearrange the compressed 3D model. S5. Perform symmetric encryption on the rearranged 3D mesh model to generate an encrypted 3D model; encapsulate the session key and embed it into the encrypted 3D model; S6. Encrypt the management information and embed it into the data embedding space of the encrypted 3D model to obtain the encrypted 3D model; the model receiver can choose to extract and decrypt the management information or extract the encapsulated session key and decrypt the model data to reversibly recover the 3D mesh model according to the access permissions.

2. The method for protecting three-dimensional mesh models based on hybrid encryption and geometric projection according to claim 1, characterized in that, S2 include: S21. Represent the 3D mesh model as a set of vertices and a set of faces; S22. Integerize the coordinates of any vertex according to a preset scaling factor to obtain the integer coordinates of the vertex; S23. Construct the adjacency set of each vertex from the face set to obtain the adjacency set sequence; sort the vertices from high to low according to the number of elements in the adjacency set to obtain the sorted adjacency set sequence and select the first vertex of the sorted sequence as the reference vertex; set all other vertices except the reference vertex as embeddable vertices.

3. The method for protecting three-dimensional mesh models based on hybrid encryption and geometric projection according to claim 1, characterized in that, In S3, performing geometric projection prediction on isolated vertices includes: Identify isolated vertex sets with empty adjacency sets; for any isolated vertex, gradually expand the search radius centered on its index to find the first vertex with a non-empty adjacency set; use the coordinates of the first vertex with a non-empty adjacency set as the predicted value of the isolated vertex and record it in the prediction set.

4. The method for protecting three-dimensional mesh models based on hybrid encryption and geometric projection according to claim 1, characterized in that, Performing geometric projection prediction on connected vertices also includes: Use a position mapping table to record the prediction method and list the vertices to be processed. Mark vertices as processed; mark vertices to be processed. From queue collection Remove it from the list and add its adjacent vertices that have not yet been marked as processed vertices to the queue set. Then, a breadth-first order based on adjacency expansion is adopted to process embeddable vertices adjacent to already processed vertices layer by layer, ensuring that each vertex is processed sequentially provided its predicted reference is determined; for the queue set The prediction steps described above are repeated for the vertices to be processed in the queue until the set is complete. Empty, to complete the prediction processing for all connected embeddable vertices.

5. The method for protecting three-dimensional mesh models based on hybrid encryption and geometric projection according to claim 1, characterized in that, S4 include: An XOR operation is performed on the binary representation of the embeddable vertex coordinates and its predicted binary representation to obtain the predicted difference bit string; the number of consecutive identical bits starting from the most significant bit is counted and recorded as a tag, and the tag represents the number of most significant bits that can be replaced or reused; the entire tag sequence is used to form tag information, and entropy coding is used to compress the indication information to obtain the encoding table and encoding result; the compressed 3D model is rearranged in the order of entropy coding table, embeddable vertex tags, reference pixels, embeddable vertex residual bits, position mapping table, and redundancy space.

6. The method for protecting three-dimensional mesh models based on hybrid encryption and geometric projection according to claim 1, characterized in that, S5 include: The model provider generates a random session key for each model and uses a symmetric encryption algorithm to encrypt the rearranged 3D mesh model to obtain an encrypted 3D model; The model provider calculates the shared amount based on elliptic curve key negotiation and generates a derived key through a key derivation function, and encapsulates the session key into an elliptic curve encapsulated session key. Write the elliptic curve encapsulation session key into the predetermined end bit region of the encrypted 3D model; Location tags are written into the encrypted 3D model to record the length of the compressed 3D model data and indicate the location boundaries of the available space for data hiding; The model provider sends the encrypted 3D model to the cloud server, and at the same time sends the public key pair to the cloud server to bind the model.

7. The method for protecting three-dimensional mesh models based on hybrid encryption and geometric projection according to claim 6, characterized in that, S6 include: The cloud server reads the embeddable space length from the location tags without decrypting the encrypted 3D model; The cloud server uses a data hiding key to encrypt the management information, and writes the encrypted management information into an embeddable space to obtain a encrypted 3D model. The model recipient provides a public key pair to the cloud server to obtain a encrypted 3D model; When the model receiver only extracts management information, it obtains the data hiding key, extracts the encrypted management information from the encrypted 3D model based on the location tag, and decrypts it to obtain the plaintext management information. When the model receiver reconstructs the 3D mesh model, it extracts the elliptic curve encapsulation session key from the end of the encrypted 3D model and recovers the session key. The model receiver uses the session key to decrypt the compressed 3D model data, decodes the indication information and position mapping table according to the encoding table, and reconstructs the reference vertex coordinates, residual bits, and the most significant bit that has been replaced. The model receiver reproduces the geometric projection prediction and mean prediction process in the same prediction order as the model owner, and recovers the coordinates vertex by vertex by combining the indication information and residual bits, thus realizing the reversible reconstruction of the 3D mesh model.

8. A 3D mesh model protection system based on hybrid encryption and geometric projection, characterized in that, include: The key management center is used to generate public and private keys for the model provider and model receiver respectively on the elliptic curve group; The vertex classification module is used to determine reference vertices and embeddable vertices, including isolated vertices and connected vertices, based on the topology of the 3D mesh model. The geometric projection prediction module is used to perform geometric projection prediction on isolated vertices and connected vertices respectively, and obtain the prediction values ​​of isolated vertices and connected vertices. The compression module performs a most significant bit substitution operation on the coordinates of embeddable vertices based on the predicted values ​​of isolated vertices and connected vertices, releasing the data embedding space and generating a compressed 3D model and indication information for recovering the 3D mesh model. Rearrange the compressed 3D model; The encryption module performs symmetric encryption on the rearranged 3D mesh model to generate an encrypted 3D model; the session key is then encapsulated and embedded into the encrypted 3D model. The management information is encrypted and embedded into the data embedding space of the encrypted 3D model to obtain the encrypted 3D model; The decryption module allows the model receiver to choose, based on access permissions, to extract and decrypt management information, or to extract the encapsulated session key and decrypt model data to reversibly recover the 3D mesh model. The three-dimensional mesh model protection system based on hybrid encryption and geometric projection is used to implement the three-dimensional mesh model protection method based on hybrid encryption and geometric projection as described in claim 1.

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