Encrypted 3D model reversible data hiding method based on dual high significant bit prediction

Abstract

The invention relates to an encrypted 3D model reversible data hiding method based on dual high significant bit prediction. The method comprises the following steps: converting floating point vertex coordinate data of a 3D model into binary coordinate data through integer mapping and system; generating redundant data based on high significant bit self-prediction, creating a data embedding space, and performing secondary prediction on a target vertex by using another group of vertexes to further generate more data embedding spaces; performing XOR operation by using the random binary sequence and the vertex data to realize encryption, recombining the vertex data and embedding auxiliary data to generate an encryption model containing an embedding space; respectively encrypting the additional data and then placing the encrypted additional data into the reserved space; and positioning the position of the additional data by decrypting the auxiliary data, and correctly extracting, decrypting and recovering the original 3D model and vertex coordinates thereof. According to the method, through integer mapping and integration of an enhanced dual multi-bit high significant bit prediction strategy, 3D model data security is guaranteed, and meanwhile 3D model ciphertext domain large-capacity data embedding is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of reversible data hiding, and in particular to a reversible data hiding method for an encrypted 3D model based on double high-order significant bit prediction. Background Art

[0002] In the digital age, three-dimensional (3D) models are the cornerstone of building the virtual world, and they play a vital role in fields such as virtual reality and game development. They provide new solutions to real-world problems by providing intuitive industrial design displays, improving manufacturing efficiency and quality, improving the accuracy of medical diagnosis, or promoting the development of scientific research. With the rapid advancement of technology and the continuous expansion of application fields, the amount of data in three-dimensional (3D) models has increased dramatically, making the issues of data security and privacy protection particularly prominent and urgent.

[0003] With the development of cloud technology, encryption ensures the confidentiality and integrity of data in cloud environments, and reversible data hiding (RDH) technology further embeds additional data on encrypted data, providing additional security for sensitive information in cloud storage. RDH technology provides an effective solution for privacy protection and secure storage of 3D models, becoming a new hotspot in the research field. However, the embedding capacity of reversible data hiding of encrypted 3D models is relatively low.

[0004] Due to the relatively low embedding capacity, the widespread application of 3D models in actual scenarios is greatly limited. Funded, supported and promoted by the "Xiamen Natural Science Foundation Project" (No.: 3502Z20227192), it is urgently needed to design a reversible data hiding method that can significantly increase the capacity of embedded data in encrypted 3D models while maintaining data integrity and recoverability, so as to better meet the growing data security needs and provide a more effective solution for the secure storage and transmission of 3D models. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a reversible data hiding method for encrypted 3D models based on dual high-order significant bit prediction. By utilizing the correlation between vertices of the 3D model, a larger data embedding space is generated before the 3D model is encrypted through dual high-order significant bit prediction, thereby improving the data embedding capacity of the 3D model encryption domain.

[0006] The specific plan is as follows:

[0007] On the one hand, a reversible data hiding method for an encrypted 3D model based on double high-order significant bit prediction includes:

[0008] S1, converting each floating-point vertex coordinate data of the 3D model into vertex binary coordinate data through integer mapping and base conversion;

[0009] S2, performing self-prediction of the high-order significant bits of the binary coordinate data of each vertex in turn, obtaining the number of consecutive equal bits of the high-order significant bits of the binary coordinate data of each vertex, determining the redundant data on the high-order significant bits corresponding to the binary coordinate data of all vertices based on the number of consecutive equal bits, and generating a data embedding space based on the redundant data;

[0010] S3, shielding the redundant data on the high-order significant bits corresponding to the binary coordinate data of each vertex, and dividing all the binary coordinate data of the vertices into V E and V R Two groups, use V R The binary coordinate data pairs of the vertices in V E The binary coordinate data of the vertices in the binary coordinate data are predicted twice for the high-order significant bits to obtain the accurately predicted tag value; the accurately predicted tag value is used as auxiliary data to obtain V E The data of the vertices in the embedding space;

[0011] S4, using the first secret key to generate a random binary sequence of the same length as the binary coordinate data of each vertex, performing a bitwise XOR operation between the binary coordinate data of each vertex and the random binary sequence to obtain the encrypted binary coordinate data of each vertex; for the encrypted binary coordinate data of each vertex, combining the high-significant bit data containing the data embedding space with the low-significant bit data, and then rearranging the data to obtain the rearranged binary coordinate data of each vertex; replacing the high-significant bit data encrypted by the first secret key with the auxiliary data encrypted by the second secret key and embedding it into the data space, and obtaining the encrypted 3D model data containing the embedding space based on the rearranged binary coordinate data of each vertex;

[0012] S5, based on V E The data embedding space of the vertices in the encrypted 3D model is re-divided into V E and V R Two groups; Arrange the vertex indices in ascending order, and connect the binary values ​​of the x, y, and z coordinates of each vertex in sequence to form a binary sequence From the binary sequence Extract the auxiliary data and decrypt it with the second key to locate the auxiliary data and the reserved data embedding space; encrypt the additional data to be embedded with the third key, embed the encrypted additional data into the reserved data embedding space by direct replacement, and obtain the modified binary sequence The modified binary sequence Reconstruction, obtain the encrypted 3D model with embedded additional data.

[0013] Furthermore, in S1, all floating point vertex coordinate data V = {v i |v i ∈R 3 ,1≤i≤N}; where v i is the coordinate of the ith vertex, N is the number of vertices, R represents the set of real numbers, R 3 Represents a three-dimensional coordinate set; through integer mapping and base conversion, each floating-point vertex coordinate data is converted into binary coordinate data of a specified length.

[0014] Furthermore, in S2, the size of the generated data embedding space is 3·N·(l-1) bits, where N is the number of vertices and l is the number of bits whose high-order significant bits of the binary coordinate data of all vertices are consecutively equal.

[0015] Furthermore, the S3 specifically includes:

[0016] After masking the redundant high-order significant bits of the binary coordinate data (l-1) of each vertex, the vertex V is divided into V E and V R Two groups; use V R The vertex pair V E The vertex v in j Perform a second prediction of the high-order significant bits and get v j The predicted accurate high-order significant bit mark values ​​of the three coordinates of x, y and z are recorded as k (j|x) ,k (j|y) ,k (j|z) ; v j The three coordinates share a label value k (j) =min(k (j|x) ,k (j|y) ,k (j|z) ), get V E The data embedding space of the vertices is Bit.

[0017] Furthermore, after S5, the method further includes: extracting data from the encrypted 3D model after the additional data is embedded and restoring the model, as follows:

[0018] Re-divide the encrypted 3D model vertices after embedding the additional data into V E and V R Two groups, arranged in ascending order of vertex index, concatenate the binary values ​​of the x, y, and z coordinates of each vertex in sequence to form a binary sequence From the binary sequence The auxiliary data is extracted from the auxiliary data and decrypted with the second key, and the additional data embedding position is located based on the decrypted auxiliary data; the encrypted additional data is extracted from the additional data embedding position; the additional data obtained is decrypted with the third key to obtain the content of the additional data; the original 3D model is restored with the first key; based on the auxiliary data, a binary coordinate data sequence composed of the least significant bits of the encryption is extracted, and the additional data embedding position is identified in each coordinate of each vertex; the encrypted least significant bit sequence is reorganized to obtain the reorganized vertex data; a random binary sequence of the same length as the binary coordinate data of each vertex is generated with the first key, and a bitwise XOR operation is performed between the reorganized vertex data and the random binary sequence to obtain the decrypted vertex coordinate data output; according to the vertex grouping and belonging to V E The mark value information of the group is used to restore part of the high-order significant bits through secondary multi-bit high-order significant bit prediction to obtain the vertex coordinate data restored by the first part of the high-order significant bits; the high-order significant bits of the second part are restored through sign bit extension to obtain the restored coordinate data of each vertex.

[0019] Furthermore, after extracting the encrypted additional data from the additional data embedding position, if the third key is not possessed, the extraction of data from the encrypted 3D model after the additional data is embedded is immediately terminated, and if the first key is not possessed, the recovery of the encrypted 3D model is immediately terminated.

[0020] The present invention adopts the above technical solution and has the following beneficial effects:

[0021] (1) The method of the present invention achieves higher data embedding capacity in the 3D model encryption domain through an enhanced dual multiple most significant bit (multi-MSB) prediction strategy;

[0022] (2) The present invention accurately locates the embedding position and correctly extracts the embedded data, so that the encrypted model can be decrypted and restored to the original model without distortion;

[0023] (3) The present invention realizes lossless data extraction and distortion-free model restoration by reverse operation on the encrypted 3D model after embedding the additional data, and the two operations are separable. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a flow chart of a reversible data hiding method for an encrypted 3D model based on double high-order significant bit prediction according to an embodiment of the present invention;

[0025] Figure 2 A schematic diagram of self-prediction of high-order significant bits of a 3D model according to an embodiment of the present invention;

[0026] Figure 3 A schematic diagram of model vertex encryption and auxiliary data embedding according to an embodiment of the present invention;

[0027] Figure 4 A schematic diagram of embedding data in the model encryption domain according to an embodiment of the present invention;

[0028] Figure 5 Schematic diagram of data extraction and original model restoration according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The present invention is further described in detail below in conjunction with the embodiments and drawings, but the embodiments of the present invention are not limited thereto. Figure 1 As shown, the reversible data hiding method of encrypted 3D model based on double high-order significant bit prediction of the present invention comprises:

[0030] S1, converting each floating-point vertex coordinate data of the 3D model into each vertex binary coordinate data through integer mapping and base conversion.

[0031] Specifically, all floating point vertex coordinate data V = {v i |v i ∈R 3 ,1≤i≤N}; where v i is the coordinate of the ith vertex, N is the number of vertices, R represents the set of real numbers, R 3 Represents a three-dimensional coordinate set; through integer mapping and base conversion, each floating-point vertex coordinate data is converted into binary coordinate data of a specified length.

[0032] For the convenience of discussion, in this embodiment, the vertex data is V={v i |v i =(v i|x ,v i|y ,v i|z )∈R 3 ,1≤i≤N}, the surface data is F={f 1 ,f 2 ,…,f j ,…,f M The 3D model of} (M is the number of faces) is encrypted and data is embedded, and arithmetic coding is used as the implementation method of lossless compression coding of tag values.

[0033] Specifically, the floating-point vertex coordinates v of the 3D model are i|c (c∈{x,y,z} is the coordinate axis) converted into an integer formula as follows:

[0034]

[0035] in, For the rounding operation, m (m∈[1,33]) represents the conversion precision, and n is the maximum number of integer digits of each vertex coordinate. Different m values ​​correspond to different numbers of L-bit binary coordinate data, and the corresponding relationship is:

[0036]

[0037] S2, self-predict the high-order significant bits of the binary coordinate data of each vertex in turn, obtain the number of consecutive equal bits of the high-order significant bits of the binary coordinate data of each vertex, determine the redundant data on the high-order significant bits corresponding to the binary coordinate data of all vertices based on the number of consecutive equal bits, and generate a data embedding space based on the redundant data.

[0038] Specifically, the size of the generated data embedding space is 3·N·(l-1) bits, where N is the number of vertices and l is the number of bits whose high-order significant bits of the binary coordinate data of all vertices are consecutively equal.

[0039] Specifically, the binary coordinate data of each vertex is self-predicted in turn for the most significant bit, and the number of consecutive and identical high-order significant bits of each vertex coordinate is determined, from which the number of consecutive and identical high-order significant bits of all vertex coordinates is obtained, thereby determining the redundant data on the high-order significant bits corresponding to all vertices, and generating a data embedding space of 3·N·(l-1) bits. The l value requires A 1 =log 2 L data storage; when m = 5, the schematic diagram of the 3D model high-order significant bit self-prediction data embedding space is as follows Figure 2 shown.

[0040] S3, shielding the redundant data on the high-order significant bits corresponding to the binary coordinate data of each vertex, and dividing all the binary coordinate data of the vertices into V E and V R Two groups, use V R The binary coordinate data pairs of the vertices in V E The binary coordinate data of the vertices in the binary coordinate data are predicted twice for the high-order significant bits to obtain the accurately predicted tag value; the accurately predicted tag value is used as auxiliary data to obtain V E The data of the vertices in the embedding space.

[0041] Specifically, after masking the redundant high-order significant bits of the binary coordinate data (l-1) of each vertex, all vertices are divided into V E and V R Two groups; use V R The vertex pair V E The vertex v in j Perform a second prediction of the high-order significant bits and get v j The predicted accurate high-order significant bit mark values ​​of the three coordinates of x, y and z are recorded as k (j|x) ,k (j|y) ,k (j|z) ; v j The three coordinates share a label value k (j) =min(k(j|x) ,k (j|y) ,k (j|z) ), get V E The data embedding space of the vertices is Bit.

[0042] Specifically, in this embodiment, after masking the (l-1)-bit redundant high-order significant bits of the binary coordinate data of each vertex, all vertices are divided into V and E and V R Two groups, first, set V E and V R All are empty sets Traverse each f in ascending order of index value j ∈F, get the component face f j All vertices of like None of them belong to V E ①If None of them belong to V R ,Will Classified as V E , and the rest are classified as V R ;②If only one vertex belongs to V R , and the remaining two are classified as V E 、V R ;③If there are two vertices belonging to V R , the remaining one is classified as V E ④If All belong to V R , the grouping remains unchanged. At least one vertex in V E , then it will not belong to V E The other vertices of R . Traverse all V R The vertex of the face is counted as belonging to the set V E 、V R The number of E 、N P , if N E ≤2×N P And N P ≥1, change the current vertex from V R Move to V E . Traverse all V W A vertex is a vertex if all its adjacent vertices on the same face do not belong to V R , then move the current vertex from V E Move to V R . Divide all vertices into V E and V R Then, traverse all theE The vertex v j , find the value with v j On the same side and belonging to V R All adjacent vertices of V, starting from the highest bit plane, for a specific bit plane of a coordinate, count the number of vertices belonging to V R The number of 0s and 1s that appear in the bit plane for all adjacent vertices of v. If the number of 0s is not less than the number of 1s, the predicted value is 0, otherwise the predicted value is 1. j The predicted value of each plane is compared with the original value to obtain the number of correct bit planes k predicted continuously from the most significant bit of the x, y, and z coordinates. (j|x) ,k (j|y) ,k (j|z) In order to reduce the amount of auxiliary data, v j The three coordinates share a common tag value, namely

[0043] k (j) =min(k (j|x) ,k (j|y) ,k (j|z) );

[0044] Determine V E The data embedding space of the vertices is Bit.

[0045] S4, using the first secret key to generate a random binary sequence of the same length as the binary coordinate data of each vertex, performing a bitwise XOR operation between the binary coordinate data of each vertex and the random binary sequence to obtain the encrypted binary coordinate data of each vertex; for the encrypted binary coordinate data of each vertex, combining the high-significant bit data containing the data embedding space with the low-significant bit data and then rearranging the data to obtain the rearranged binary coordinate data of each vertex; replacing the high-order data encrypted by the first secret key with the auxiliary data encrypted by the second secret key and embedding it into the data space, and based on the rearranged binary coordinate data of each vertex, obtaining the encrypted 3D model data containing the embedding space.

[0046] Specifically, vertex coordinates are preprocessed to obtain integer values, and then encoded into binary sequences in the following way:

[0047]

[0048] The model owner uses the first key to generate a pseudo-random binary sequence, denoted as p i|c,u , which is the same as the original binary sequence Perform an XOR operation to obtain the encrypted binary sequence, marked as

[0049]

[0050] in, The encrypted binary sequence is then converted back to the encrypted coordinates of the integer value:

[0051]

[0052] Get the encrypted vertex coordinate data

[0053] Specifically, Figure 3 As shown, the encrypted high-order data is embedded in the spatial data and the low-order valid data is combined together to rearrange the data to obtain a binary sequence The auxiliary data such as l value and mark value after lossless compression of arithmetic coding are encrypted with the second secret key and then directly replace the encrypted high-order data and embed it into the spatial data to obtain Then The rearranged data is reorganized into vertex coordinate data to obtain encrypted 3D model data containing embedded space

[0054] S5, based on V E The data embedding space of the vertices in the encrypted 3D model is re-divided into V E and V R Two groups; Arrange the vertex indices in ascending order, and connect the binary values ​​of the x, y, and z coordinates of each vertex in sequence to form a binary sequence From the binary sequence Extract the auxiliary data and decrypt it with the second key to locate the auxiliary data and the reserved data embedding space; encrypt the additional data to be embedded with the third key, embed the encrypted additional data into the reserved data embedding space by direct replacement, and obtain the modified binary sequence The modified binary sequence Reconstruction, obtain the encrypted 3D model with embedded additional data.

[0055] Specifically, Figure 4 As shown, the specific implementation steps of embedding the above embedding space generation and the model encryption domain data corresponding to the model encryption are as follows:

[0056] According to the surface data F, the vertices of the encrypted 3D model containing the embedded space are re-divided into V E and V R Two groups: First, let V E and V R All are empty sets Traverse all f in ascending order of index value j ∈F, get the component face f j All vertices of like None of them belong to VE ①If None of them belong to V R ,Will Classified as V E , and the rest are classified as V R ;②If only one vertex belongs to V R , and the remaining two are classified as V E 、V R ;③If there are two vertices belonging to V R , the remaining one is classified as V E ④If All belong to V R , the grouping remains unchanged. At least one vertex in V E , then it will not belong to V E The other vertices of R . Traverse all V R The vertex of the face is counted as belonging to the set V E 、V R The number of E 、N P , if N E ≤2×N P And N P ≥1, change the current vertex from V R Move to V E . Traverse all V E A vertex is a vertex if all its adjacent vertices on the same face do not belong to V R , then move the current vertex from V E Move to V R . Divide the vertices of the encrypted 3D model containing the embedded space into V E and V R Then, the L-bit binary values ​​of the x, y, and z axes of each vertex are connected in ascending order to form a binary sequence. Use the second key to encrypt the binary sequence Decrypt, extract the embedded auxiliary data, locate the auxiliary data and the reserved data embedding space; encrypt the additional data to be embedded with the third key, and embed it into the reserved data embedding space by direct replacement to obtain a binary sequence The modified binary sequence Recombination to obtain encrypted 3D model data with additional data embedded

[0057] Specifically, extracting data and restoring the model from the encrypted 3D model after embedding the additional data includes:

[0058] Re-divide the encrypted 3D model vertices after embedding the additional data into V E and V R Two groups, arranged in ascending order of vertex index, concatenate the binary values ​​of the x, y, and z coordinates of each vertex in sequence to form a binary sequence From the binary sequence The auxiliary data is extracted from the auxiliary data and decrypted with the second key, and the additional data embedding position is located based on the decrypted auxiliary data; the encrypted additional data is extracted from the additional data embedding position; the additional data obtained is decrypted with the third key to obtain the content of the additional data; the original 3D model is restored with the first key; based on the auxiliary data, a binary coordinate data sequence composed of the least significant bits of the encryption is extracted, and the additional data embedding position is identified in each coordinate of each vertex; the encrypted least significant bit sequence is reorganized to obtain the reorganized vertex data; a random binary sequence of the same length as the binary coordinate data of each vertex is generated with the first key, and a bitwise XOR operation is performed between the reorganized vertex data and the random binary sequence to obtain the decrypted vertex coordinate data output; according to the vertex grouping and belonging to V E The mark value information of the group is used to restore part of the high-order significant bits through secondary multi-bit high-order significant bit prediction to obtain the vertex coordinate data restored by the first part of the high-order significant bits; the high-order significant bits of the second part are restored through sign bit extension to obtain the restored coordinate data of each vertex.

[0059] Specifically, after extracting the encrypted additional data from the additional data embedding position, if the third key is not possessed, the extraction of data from the encrypted 3D model after the additional data is embedded is immediately terminated, and if the first key is not possessed, the recovery of the encrypted 3D model is immediately terminated.

[0060] Specifically, Figure 5 As shown, according to the surface data F, the vertices of the encrypted 3D model after embedding the additional data are re-divided into V E and V R Two groups; first, let V E and V R All are empty sets Traverse all f in ascending order of index value j ∈F, get the component face f j All vertices of like None of them belong to V E ①If None of them belong to V R ,Will Classified as V E , and the rest are classified as V R ;②If only one vertex belongs to V R , and the remaining two are classified as V E 、V R;③If there are two vertices belonging to V R , the remaining one is classified as V E ④If All belong to V R , the grouping remains unchanged. At least one vertex in V E , then it will not belong to V E The other vertices of R . Traverse all V R The vertex of the face is counted as belonging to the set V E 、V R The number of E 、N P , if N E ≤2×N P And N P ≥1, change the current vertex from V R Move to V E . Traverse all V E A vertex is a vertex if all its adjacent vertices on the same face do not belong to V R , then move the current vertex from V E Move to V R The encrypted 3D model vertices after embedding the additional data are divided into V E and V R Then, the L-bit binary values ​​of the x, y, and z axes of each vertex are connected in ascending order to form a binary sequence. Use the second key to encrypt the binary sequence Decryption, extracting the embedded auxiliary data; locating the additional data embedding position based on the auxiliary data; extracting the encrypted additional data from the additional data embedding position; if the third key is possessed, the additional data can be decrypted; otherwise, the content of the additional data cannot be obtained; if the first key is not possessed, the original model cannot be further restored; based on the auxiliary data, extracting the binary coordinate data sequence composed of the least significant bits of the encryption, and identifying the additional data embedding position in each coordinate of each vertex; reorganizing the encrypted least significant bit sequence to obtain the reorganized vertex data

[0061] Specifically, reorganized vertex data Encoded into a binary sequence as follows:

[0062]

[0063] The model owner uses the first key to generate a pseudo-random binary sequence, denoted as p i|c,u This sequence is similar to the binary sequence Perform an XOR operation to obtain the decrypted binary sequence, marked as

[0064]

[0065] The decrypted binary sequence is then converted back to the encrypted coordinates with integer values:

[0066]

[0067] Get the decrypted vertex coordinate data Output. According to the vertex grouping, traverse all the E Vertex Find with On the same side and belonging to V R All adjacent vertices of V, starting from the highest bit plane, for a specific bit plane of a coordinate, count the number of vertices belonging to V R The number of 0s and 1s that appear in the bit plane for all adjacent vertices of . If the number of 0s is not less than the number of 1s, the predicted value is 0, otherwise the predicted value is 1. (j) Values, respectively, are restored using the predicted values The x, y, and z axis height k (j) bit is valid, that is Get the vertex coordinate data restored by the high-order significant bits For each coordinate x, y, and z of each vertex, the remaining (l-1) most significant bits are restored by sign bit extension to obtain the restored vertex coordinate data

[0068] Although the present invention has been specifically shown and described in conjunction with the preferred embodiments, it should be understood by those skilled in the art that various changes may be made to the present invention in form and details without departing from the spirit and scope of the present invention as defined by the appended claims, all of which are within the scope of protection of the present invention.

Claims

1. A reversible data hiding method for encrypted 3D models based on double high-order significant bit prediction, characterized in that: include: S1, converting each floating-point vertex coordinate data of the 3D model into vertex binary coordinate data through integer mapping and base conversion; S2, performing self-prediction of the high-order significant bits of the binary coordinate data of each vertex in turn, obtaining the number of consecutive equal bits of the high-order significant bits of the binary coordinate data of each vertex, determining the redundant data on the high-order significant bits corresponding to the binary coordinate data of all vertices based on the number of consecutive equal bits, and generating a data embedding space based on the redundant data; S3, shielding the redundant data on the high-order significant bits corresponding to the binary coordinate data of each vertex, and dividing all the binary coordinate data of the vertices into V E and V R Two groups, use V R The vertex binary coordinate data pairs V E The binary coordinate data of the vertices in the binary coordinate data are predicted twice for the high-order significant bits to obtain the accurately predicted tag value; the accurately predicted tag value is used as auxiliary data to obtain V E The data of the vertices in the embedding space; S4, using the first secret key to generate a random binary sequence of the same length as the binary coordinate data of each vertex, performing a bitwise exclusive OR operation between the binary coordinate data of each vertex and the random binary sequence, and obtaining the encrypted binary coordinate data of each vertex; for the encrypted binary coordinate data of each vertex, combining the high-significant bit data containing the data embedding space with the low-significant bit data, and then rearranging the data to obtain the rearranged binary coordinate data of each vertex; The auxiliary data encrypted by the second secret key replaces the high-order data encrypted by the first secret key and is embedded into the data space, and the encrypted 3D model data containing the embedded space is obtained based on the rearranged binary coordinate data of each vertex; S5, based on V E The data embedding space of the vertices in the encrypted 3D model is re-divided into V E and V R Two groups; Arrange the vertex indices in ascending order, and connect the binary values ​​of the x, y, and z coordinates of each vertex in sequence to form a binary sequence From the binary sequence extracting the auxiliary data and decrypting it with a second key to locate the auxiliary data and the reserved data embedding space; The additional data to be embedded is encrypted with the third key, and the encrypted additional data is embedded into the reserved data embedding space by direct replacement to obtain a modified binary sequence. The modified binary sequence Reconstruction, obtain the encrypted 3D model with embedded additional data.

2. The reversible data hiding method for encrypted 3D models based on double high-order significant bit prediction according to claim 1 is characterized in that: In S1, all floating point vertex coordinate data V = {v i |v i ∈R 3 ,1≤i≤N}; Among them, v i is the coordinate of the ith vertex, N is the number of vertices, R represents the set of real numbers, R 3 Represents a three-dimensional coordinate set; through integer mapping and base conversion, each floating-point vertex coordinate data is converted into binary coordinate data of a specified length.

3. The reversible data hiding method for encrypted 3D models based on double high-order significant bit prediction according to claim 1 is characterized in that: In S2, the size of the generated data embedding space is 3·N·(l-1) bits, where N is the number of vertices and l is the number of bits whose high-order significant bits of the binary coordinate data of all vertices are consecutive and equal.

4. The reversible data hiding method for encrypted 3D models based on double high-order significant bit prediction according to claim 3 is characterized in that: The S3 specifically includes: After masking the redundant high-order significant bits of the binary coordinate data (l-1) of each vertex, the vertex V is divided into V E and V R Two groups; use V R The vertex pair V E The vertex v in j Perform a second prediction of the high-order significant bits and get v j The predicted accurate high-order significant bit mark values ​​of the three coordinates of x, y and z are recorded as k (j|x) ,k (j|y) ,k (j|z) ; v j The three coordinates share a label value k (j) =min(k (j|x) ,k (j|y) ,k (j|z) ), get V E The data embedding space of the vertices is Bit.

5. The reversible data hiding method for encrypted 3D models based on double high-order significant bit prediction according to claim 1 is characterized in that: After S5, the method further includes: extracting data from the encrypted 3D model after the additional data is embedded and restoring the model, which is specifically as follows: Re-divide the encrypted 3D model vertices after embedding the additional data into V E and V R Two groups, arranged in ascending order of vertex index, concatenate the binary values ​​of the x, y, and z coordinates of each vertex in sequence to form a binary sequence From the binary sequence The auxiliary data is extracted from the auxiliary data and decrypted with the second key, and the additional data embedding position is located based on the decrypted auxiliary data; the encrypted additional data is extracted from the additional data embedding position; the additional data obtained is decrypted with the third key to obtain the content of the additional data; the original 3D model is restored with the first key; based on the auxiliary data, a binary coordinate data sequence composed of the least significant bits of the encryption is extracted, and the additional data embedding position is identified in each coordinate of each vertex; the encrypted least significant bit sequence is reorganized to obtain the reorganized vertex data; a random binary sequence of the same length as the binary coordinate data of each vertex is generated with the first key, and a bitwise XOR operation is performed between the reorganized vertex data and the random binary sequence to obtain the decrypted vertex coordinate data output; according to the vertex grouping and belonging to V E The mark value information of the group is used to restore part of the high-order significant bits through secondary multi-bit high-order significant bit prediction to obtain the vertex coordinate data restored by the first part of the high-order significant bits; the high-order significant bits of the second part are restored through sign bit extension to obtain the restored coordinate data of each vertex.

6. The reversible data hiding method for encrypted 3D models based on double high-order significant bit prediction according to claim 5 is characterized in that: After extracting the encrypted additional data from the additional data embedding position, if the third key is not possessed, the extraction of data from the encrypted 3D model after the additional data is embedded is immediately terminated, and if the first key is not possessed, the recovery of the encrypted 3D model is immediately terminated.

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