Privacy protection spatial data set connectable query method based on sample

Abstract

The invention belongs to the field of data retrieval, and discloses an example-based privacy protection spatial data set connectable query method, which comprises the following steps of: in a data preprocessing stage, firstly, processing a spatial data set in a data warehouse, vectorizing the spatial data set, and constructing a key to code and encrypt the key; storing the encrypted spatial data set into a hierarchical vector index and sending the hierarchical vector index to a cloud server; in a data query stage, a given sample space data set is subjected to vectorization processing and encryption to form a search trap door, and the search trap door is used as a search instruction to be sent to a cloud server; and the cloud server executes connectable query operation of the privacy protection spatial data set on the encrypted data index by using the trap door, so that the data privacy of the spatial data set is ensured, the search of connectable query is realized, and the first k data sets are searched as final result sets to be returned. According to the method, the latest index and the new query method are utilized, and the search efficiency is high.

Description

Technical Field

[0001] The present invention belongs to the field of data retrieval, and more particularly, relates to a method for join query of privacy-preserving spatial data sets based on examples. Background Art

[0002] Nowadays, we are in the era of data explosion. With the development of technology, more and more data is currently collected for serving society. As an important part of data sets in the real world, spatial data sets are increasingly widely used. The spatial data set search technology for meeting user needs has become an important research direction, and the research on spatial data set search methods is urgent. The join query of spatial data sets based on examples is a new query method, different from the density-based spatial data set query method. It finds spatial data sets that are spatially joined and have a relatively high spatial difference degree from a data warehouse according to a given example data set. This technology has great application value in fields such as geographical systems, transportation rail systems, urban management systems, and municipal planning.

[0003] The join query of spatial data sets requires similarity calculation between data sets. To achieve the similarity calculation and search of data sets, many methods have been proposed in existing literature. For example, the difference degree calculation method in the join search of tabular data is to compare the number of different columns while ensuring that one or several columns are joined to determine the difference degree; the similarity calculation method in spatial data search is to normalize Jaccard similarity, cosine similarity, or distance similarity, etc. as the total similarity for comparison; in trajectory data search, density is mostly used as a measure of similarity. In the research on data set search, grid-based overlap (GBO) filtering is used to perform coarse-grained filtering through the overlap degree of grid indexes; intersection distance (IA) filtering is used to perform coarse-grained filtering through the overlap or intersection relationship of MBRs between two data sets; Hausdorff distance (Haus) is used to judge the maximum and minimum distances between two data sets, and finer-grained filtering is performed through this distance. Therefore, as a new query method, the join query of spatial data sets can analogize new similarity judgment methods from the search of other data sets and utilize the filtering and pruning strategies in data set search to achieve efficient join query of spatial data sets.

[0004] However, the process of performing join query of spatial data sets may lead to the leakage of spatial data. The privacy-preserving join query of spatial data sets can query the data sets required by users on the premise of ensuring the privacy of data sets is not leaked. Summary of the Invention

[0005] To address the gaps in the existing technology and solve the privacy protection problem in the process of join queries on spatial data sets, the present invention provides a new and efficient example-based privacy protection method for join queries on spatial data sets. This query method vectorizes the spatial data set and, after encryption, converts the spatial data set into a form of ciphertext vector, which supports join queries on spatial data sets with privacy protection capabilities without revealing the plaintext data of the spatial data set. A method for calculating the spatial difference degree of spatial data sets under ciphertext is proposed, and the search efficiency is improved by using vector hierarchical indexing.

[0006] To achieve the above object, the present invention is implemented through the following technical solutions:

[0007] The present invention is an example-based privacy protection method for join queries on spatial data sets, applicable to an application scenario consisting of a data owner, a cloud server, and a query user. This query method includes a data preprocessing stage and a data query stage.

[0008] The first stage: In the data preprocessing stage, it specifically includes the following steps:

[0009] Step 1-1: According to the set join parameter threshold ξ, perform global grid division on the spatial data warehouse Let the join parameter threshold Divide the spatial data warehouse into θ×θ grids of the same size to form a grid set And assign a unique cell ID to each grid cell (such as the ID of g 0 is ID 0 ), with a range of [0, θ 2 -1];

[0010] Step 1-2: The data owner generates a key K = {s, M 1 , M 2}, where s is a randomly generated θ 2 -dimensional vector, and M 1 , M 2 are (θ 2 )×(θ 2 )-dimensional invertible matrices. The key K is shared by the data owner and the query user;

[0011] Step 1-3: For each spatial data set D in the spatial data warehouse, map each spatial data point in the spatial data set D i into the grid. Each said spatial data set D i forms a grid data set i And the grid data set And the grid data set Mapped to the Bloom filter, according to each grid data set Form a vector BF i , and for the vector BF i After vectorization, encryption is performed to form an encrypted vector Let the decision vector The decision vector v is vectorized and encrypted to form an encrypted decision vector Finally, the encrypted vector and the encrypted decision vector Store in high-dimensional vector index;

[0012] The second stage: In the data query stage, the following steps are included:

[0013] Step 2-1: For the sample spatial dataset D given by the user e , the sample spatial dataset D e Mapped to the spatial grid of the spatial data warehouse, the sample spatial dataset D e Corresponding grid data set Each ID in is mapped to a Bloom filter to form a vector set Then for the vector set After vectorization and encryption, it is transmitted to the cloud server as the search trapdoor Tr;

[0014] Step 2-2: After receiving the search trap Tr, the cloud server performs a connectable dataset query on the high-dimensional vector index to obtain the candidate set Candidate Set The corresponding encryption vector set is

[0015] Step 2-3: By calculating the candidate set The corresponding encryption vector set The encryption vector in and encryption decision vector The vector dot product of is used to find the top k spatial datasets with the largest spatial difference from the sample spatial dataset as the query result R, and finally the query result R is returned to the user.

[0016] A further improvement of the present invention is that: the step 1-1 is based on the connectable parameter threshold ξ to the spatial data warehouse Perform global mesh division to form a mesh set The specific process is as follows: define the connectivity threshold ξ, that is, When represents the sample spatial dataset D e and spatial dataset D i Connectivity, at this stage, this problem is converted into a grid problem, and the connectivity threshold is Using θ as the partitioning strength, the data space of the entire data warehouse is partitioned into θ×θ grids to form a grid set And a unique cell ID is assigned to each grid cell.

[0017] A further improvement of the present invention is that: in the above steps 1-3, for the spatial data set D in the spatial data warehouse i The specific process of vectorized encryption processing is as follows:

[0018] Step 1-3-1: For each spatial data set D in the spatial data warehouse i The formed grid data set Is subjected to Bloom filter mapping to form a vector BF i ;

[0019] Step 1-3-2: For the vector BF of each spatial data set i , using the random vector s in the secret key K, the vector BF i Is split into BF i ′ and BF i ″, denoted as BF i =(BF i ′, BF i ″), and the splitting rule is as follows:

[0020]

[0021] Using the invertible matrices M 1 and M 2 in the secret key K to encrypt the vector BF i To generate the corresponding encrypted vector Let the θ×θ dimensional all-1 vector be the judgment vector Using the random vector s and the invertible matrices M 1 and M 2 To split and encrypt the judgment vector v to generate an encrypted judgment vector

[0022] Step 1-3-3: Use a high-dimensional vector index (such as Faiss, etc.) to store the encrypted vector And the encrypted judgment vector This index is a multi-layer structure and can meet the fast query of multi-dimensional vectors.

[0023] A further improvement of the present invention is that: in the above step 2-1, the specific process of constructing the trapdoor according to the sample spatial data set D e is as follows:

[0024] Step 2-1-1: The sample spatial data set D eForm a grid data set by mapping into the spatial grid of the spatial data warehouse For the grid data set Map each ID in it into a Bloom filter to form a vector set

[0025] Step 2-1-2: Use the random vector s and invertible matrix M in the key K 1 and M 2 For each vector in the vector set Perform segmentation and encryption to form an encrypted vector set Specifically for each item in the set Take the encrypted vector set As the search trapdoor Tr, and send the search trapdoor Tr to the cloud server to perform a search operation

[0026] A further improvement of the present invention is that in step 2-2, the cloud server performs a search operation through the search trapdoor as follows: After receiving the search trapdoor Tr, the cloud server judges the sample space data set D in the high-dimensional vector index through the vector inner product e and the spatial data set D i Whether they are connectable. When the number of overlapping grids of the sample space data set D e and the spatial data set D i is greater than the connection threshold τ, it is connectable. If it is connectable, add the spatial data set D i to the candidate set The calculation and judgment method is as follows

[0027] In the high-dimensional vector index, use each item in the encrypted vector set in the set to perform a dot product operation with the encrypted vector If the dot product calculation result is 0, it indicates that there is no connectable area between the sample space data set D e and the spatial data set D i Otherwise, it indicates that there is a connectable area between the sample space data set D e and the spatial data set D i Record the number of overlapping grids Sum. Given the connection threshold τ, when Sum>τ, it indicates that the sample space data set D e and the spatial data set D i are connectable, and add the spatial data set D i to the candidate set

[0028] A further improvement of the present invention is that in step 2-3, the cloud server calculates the spatial difference degree between the sample space data set D e and the spatial data set D i The operation is as follows: Use the candidate set The set of encrypted vectors and the encrypted decision vector for each item in Calculate the spatial difference degree through the dot product of vectors, and return the first k spatial data sets as the final result set R. The specific calculation and judgment method are as follows:

[0029] In the candidate data set use the encrypted decision vector and the candidate set Calculate the dot product of each item in the set of encrypted vectors in and subtract the number of connectable regions Sum of each spatial data set as the spatial difference degree. Specifically, calculate The result shows the spatial difference degree between the sample spatial data set D e and the spatial data set D i Sort the calculation results and return the first k spatial data sets as the result set R to the user.

[0030] The beneficial effects of the present invention are:

[0031] By using the grid inverted index to judge the connectability of the spatial data set, the present invention can effectively reduce the calculation amount and complexity of the query and shorten the query time.

[0032] The present invention converts the calculation of the spatial difference degree of the non-overlapping region of the candidate set connected to the sample data set into the calculation of the number of non-connected grids, greatly reducing the calculation amount of the spatial difference degree.

[0033] The present invention can specify the specific connectability accuracy problem by adjusting the parameter ξ to achieve a finer-grained data set connectability query.

[0034] During the whole query process, the present invention adopts the dot product operation of vectors, which perfectly fits the above design and takes into account both security and query efficiency. Description of the Drawings

[0035] Figure 1 is the flow chart of the present invention.

[0036] Figure 2 is the description diagram of the connectable region of the spatial data set of the present invention.

[0037] Figure 3 is the description diagram of the spatial difference of the spatial data set of the present invention.

[0038] Figure 4 is the system architecture diagram of the present invention.

[0039] Figure 5 is the comparison diagram of the encryption method without index and the encryption of the present application in terms of search time.

[0040] Figure 6 It is a schematic diagram comparing the encryption method without indexing and the search time when the encryption method of the present application has a fixed grid division intensity. Specific embodiments

[0041] The following will disclose the embodiments of the present invention with illustrations. For the sake of clarity, many practical details will also be described in the following narrative. However, it should be understood that these practical details should not be used to limit the present invention. That is to say, in some embodiments of the present invention, some practical details are unnecessary.

[0042] For the convenience of description, the following symbols are defined as follows:

[0043] Spatial data warehouse which contains m spatial data sets, is a spatial data set containing n two-dimensional spatial position points, D i ={p i,1 , p i,2 , …, p i,n}, the sample spatial data set is D e , and the grid set of the entire data space is

[0044] Figure 1 As shown, the present invention is a method for connectable query of privacy-protected spatial data sets based on examples, and the method includes the following two stages: the first stage is the data preprocessing stage; the second stage is the data query stage.

[0045] The first stage: In the data preprocessing stage, it specifically includes the following steps:

[0046] Step 1-1, according to the set connectable parameter threshold ξ, perform global grid division on the spatial data warehouse , and let the connectable parameter threshold divide the spatial data warehouse into grids of the same size of θ×θ to form a grid set and assign a unique cell ID to each grid cell (such as the ID of f 0 is ID 0 ), and the range is [0, θ 2 -1].

[0047] The specific process is as follows: Define the connectability threshold ξ, that is, when it means that the sample spatial data set D e and the spatial data set D i are connectable. In this stage, this problem is converted into a grid problem, and let the connectability threshold Divide the data space of the entire data warehouse into θ×θ grids with θ as the partitioning strength, forming a grid set. And assign a unique cell ID to each grid cell.

[0048] Step 1-2: The data owner generates the key K = {s, M 1 , M 2}, where s is a randomly generated θ 2 -dimensional vector, and M 1 , M 2 are (θ 2 )×(θ 2 )-dimensional invertible matrices. The key K is shared by the data owner and the query user.

[0049] Step 1-3: For each spatial data set D in the spatial data warehouse i , map each spatial data point in the spatial data set D i into the grid. Each said spatial data set D i forms a grid data set And map the grid data set onto a Bloom filter. According to each grid data set , form a vector BF i , and after vectorizing the vector BF i , encrypt it to form an encrypted vector Let the decision vector And after vectorizing and encrypting the decision vector v, form an encrypted decision vector Finally, store the encrypted vector and the encrypted decision vector into the high-dimensional vector index. The specific steps are as follows:

[0050] The specific process is as follows:

[0051] Step 1-3-1: For each grid data set formed by each spatial data set D i in the spatial data warehouse , perform Bloom filter mapping to form a vector BF i ;

[0052] Step 1-3-2: For the vector BF i of each spatial data set, use the random vector s in the key K to split the vector BF i into BF i ′ and BF i ″, denoted as BF i =(BF i ′, BF i″), the splitting rules are as follows:

[0053]

[0054] Use the invertible matrix M in the secret key K 1 and M 2 to encrypt the vector BF i to generate the corresponding encrypted vector Let the θ×θ dimensional all-1 vector be the judgment vector Use the random vector s and the invertible matrix M 1 and M 2 to split and encrypt the judgment vector v to generate the encrypted judgment vector

[0055] Step 1-3-3: Use a high-dimensional vector index such as Faiss to store the encrypted vector and the encrypted judgment vector This index is a multi-layer structure and can meet the fast query of multi-dimensional vectors.

[0056] The data query phase includes the following steps:

[0057] Step 2-1: For the sample space data set D given by the user e , map the sample space data set D e to the space grid of the space data warehouse, and map the grid data set e corresponding to the sample space data set D each ID in to the Bloom filter to form a vector set After that, perform vectorization processing and encryption on the vector set and use it as the search trapdoor Tr to be transmitted to the cloud server.

[0058] The specific process of constructing the trapdoor according to the sample space data set D e is as follows:

[0059] Step 2-1-1: Map the sample space data set D e to the space grid of the space data warehouse to form a grid data set Map each ID corresponding to the grid data set to the Bloom filter to form a vector set

[0060] Step 2-1-2: Use the random vector s and the invertible matrix M in the secret key k 1 and M 2 to split and encrypt each vector in the vector set to form an encrypted vector set For each item in the set, specifically Take the encrypted vector set as the search trapdoor Tr, and send the search trapdoor Tr to the cloud server to perform a search operation.

[0061] Step 2-2: After receiving the search trapdoor Tr, the cloud server performs a query on the connectable data set in the high-dimensional vector index to obtain a candidate set Candidate set The corresponding encrypted vector set is The cloud server performs a search operation through the search trapdoor as follows: After receiving the search trapdoor Tr, the cloud server determines the sample space data set D in the high-dimensional vector index through the vector inner product e and the space data set D i Whether they are connectable. When the number of overlapping grids of the sample space data set D e and the space data set D i is greater than the connectable threshold τ, they are connectable. If they are connectable, the space data set D i is added to the candidate set The calculation and judgment method is as follows:

[0062] In the high-dimensional vector index, use each item in the encrypted vector set in the set to perform a dot product operation with the encrypted vector If the dot product calculation result is 0, it indicates that there is no connectable area between the sample space data set D e and the space data set D i Otherwise, it indicates that there is a connectable area between the sample space data set D e and the space data set D i Record the number of overlapping grids Sum. Given the connectable threshold τ, when Sum>τ, it indicates that the sample space data set D e and the space data set D i are connectable, and the space data set D i is added to the candidate set

[0063] Step 2-3: By calculating the dot product of the encrypted vector corresponding to the candidate set in the encrypted vector set with the encrypted decision vector Find the top k space data sets with the largest spatial difference degree from the sample space data set as the query result R, and finally return the query result R to the user.

[0064] The cloud server calculates the spatial difference degree between the sample space data set D e and the space data set D i The operation is as follows: Using the candidate set The set of encrypted vectors and the encrypted decision vector for each item in Calculate the spatial difference degree through vector dot product, and return the top k spatial data sets as the final result set R. The specific calculation and judgment method is as follows:

[0065] In the candidate data set using the encrypted decision vector and the candidate set the encrypted vector set in After performing dot product operations on each item and subtracting the number of connectable regions Sum of each spatial data set as the spatial difference degree, specifically calculate The result shows the sample spatial data set D e and the spatial data set D i The spatial difference degree. After sorting the calculation results, return the top k spatial data sets as the result set R to the user.

[0066] Figure 2 The following shows the description diagram of the connectable region of the spatial data set of the present invention, where the shaded area is the sample spatial data set D e and the spatial data set D i The spatial connectable region, from Figure 2 it can be seen that the sample spatial data set is D e and the spatial data set D i There are two connectable regions.

[0067] Figure 3 The following shows the description diagram of the spatial difference of the spatial data set of the present invention, where the yellow area is the spatial difference degree area of the query data set for the sample spatial data set. It can be seen from the figure that the spatial data set D i and the sample spatial data set is D e The spatial difference degree is 5.

[0068] Figure 4 The following is the system framework diagram of the present invention, including the data owner, the cloud server, and the query user. The data owner has the plaintext data warehouse data and is responsible for vectorizing and encrypting the spatial data sets in the data warehouse, then outsourcing and storing the encrypted data to the cloud server, and sharing the key with the query user; when the query user performs a sample query of the spatial data set, constructs a search trapdoor according to the spatial distribution characteristics of the sample data set and sends it to the cloud server; the cloud server uses the search trapdoor and the encrypted spatial data set to execute the privacy-preserving spatial data set connectable query and returns the query result to the query user.

[0069] To verify this application, when the vector dimension of the fixed Bloom filter is 1000, a search time comparison is made between the encryption method without an index and the encryption of this application, as Figure 5 shown. The search times of both vary around a certain value as the grid division strength changes, but the query method of this application is two orders of magnitude faster than the ordinary query method.

[0070] Meanwhile, as Figure 6 shown, when the grid division strength is fixed, a search time comparison is made between the encryption method without an index and the method of this application. As the vector dimension increases, the query times of both increase. However, the query time of the method without an index increases by a larger margin as the vector dimension increases, while the encryption method of this application increases by a smaller margin as the vector dimension increases. The search time of the encryption method of this application is three orders of magnitude faster than that of the method without an index, with a large gap. Therefore Figure 6 the time data is represented in logarithmic scale data with log 2 .

[0071] The above are only embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, various changes and modifications can be made to the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A sample-based privacy-preserving spatial dataset connectable query method, applicable to an application scenario consisting of a data owner, a cloud server, and a query user, characterized by: Assume that the spatial data warehouse is The number of data sets in the spatial data warehouse is m, and a spatial data set D i ={p i,1 ,p i,2 ,…,p i,n }, which contains n spatial data points. The sample spatial data set is D e , the privacy-preserving spatial dataset based on the sample can be connected and queried, that is, in the spatial data warehouse in the encrypted state Get the sample spatial dataset D e Candidate datasets that can be connected, and find the original sample spatial dataset D in the candidate dataset e The top k spatial datasets with the largest spatial differences are queried in two stages: The first stage: In the data preprocessing stage, the following steps are included: Step 1-1: According to the set connectable parameter threshold ξ, the spatial data warehouse Perform global meshing and set the connectable parameter threshold Divide the spatial data warehouse into grids of the same size θ×θ to form a grid set Each grid cell is assigned a unique cell ID in the range of [0,θ 2 -1]; Step 1-2: The data owner generates a key K = {s, M1, M2}, where s is a randomly generated θ 2 dimensional vector, M1, M2 is (θ 2 )×(θ 2 )-dimensional reversible matrix, the key K is shared by the data owner and the query user; Steps 1-3: For spatial data warehouse Each spatial dataset D i , the spatial dataset D i Each spatial data point in is mapped into a grid, and each of the spatial data sets D i Form a grid data set And the grid data set Mapped to the Bloom filter, according to each grid data set Form a vector BF i , and for the vector BF i After vectorization, encryption is performed to form an encrypted vector Let the decision vector The decision vector v is vectorized and encrypted to form an encrypted decision vector Finally, the encrypted vector and the encrypted decision vector Store in high-dimensional vector index; The second stage: In the data query stage, the following steps are included: Step 2-1: For the sample spatial dataset D given by the user e , the sample spatial dataset D e Mapped to the spatial grid of the spatial data warehouse, the sample spatial dataset D e Corresponding grid data set Each ID in is mapped to a Bloom filter to form a vector set Then for the vector set After vectorization and encryption, it is transmitted to the cloud server as the search trapdoor Tr; Step 2-2: After receiving the search trap Tr, the cloud server performs a connectable dataset query on the high-dimensional vector index to obtain the candidate set Candidate Set The corresponding encryption vector set is Step 2-3: By calculating the candidate set The corresponding encryption vector set The encryption vector in and encryption decision vector The vector dot product of is used to find the top k spatial datasets with the largest spatial difference from the sample spatial dataset as the query result R, and finally the query result R is returned to the user.

2. The example-based privacy-preserving spatial dataset connectable query method according to claim 1, characterized in that: The step 1-1 is based on the connectable parameter threshold ξ to calculate the spatial data warehouse Perform global mesh division to form a mesh set The specific process is as follows: define the connectivity threshold ξ, that is, When represents the sample spatial dataset D e and spatial dataset D i Connectivity, at this stage, this problem is converted into a grid problem, and the connectivity threshold is 3. The example-based privacy-preserving spatial dataset connectable query method according to claim 1, characterized in that: Steps 1-3 are performed on the spatial data set D in the spatial data warehouse. i The specific process of vectorized encryption is as follows: Step 1-3-1: For spatial data warehouse Each spatial dataset D i The grid data set formed Perform Bloom filter mapping to form a vector BF i ; Step 1-3-2: Vector BF for each spatial data set i , using the random vector s in the key K to transform the vector BF i Split into BF i ′ and BF i ″, denoted as BF i =(BF i ′,BF i ″), using the reversible matrices M1 and M2 in the key K to vector BF i Encrypt and generate the corresponding encryption vector Let the θ×θ-dimensional all-1 vector be the decision vector Use random vector s and reversible matrices M1 and M2 to split and encrypt the decision vector v to generate an encrypted decision vector Step 1-3-3: Use high-dimensional vector index to store encrypted vector and encryption decision vector 4. The example-based privacy-preserving spatial dataset connectable query method according to claim 1, characterized in that: The step 2-1 is based on the sample space dataset D e The specific process of constructing a trapdoor is as follows: Step 2-1-1: Set the sample spatial dataset D e Mapped to the spatial grid of the spatial data warehouse to form a grid data set Grid data collection Each ID in the map is mapped to the Bloom filter to form a vector set Step 2-1-2: Use the random vector s in the key K and the reversible matrices M1 and M2 to calculate the vector set Each vector in is split and encrypted to form an encrypted vector set For each item in the collection, Encrypt the vector set As the search trapdoor Tr, the search trapdoor Tr is sent to the cloud server to perform the search operation.

5. The example-based privacy-preserving spatial dataset connectable query method according to claim 4, characterized in that: In step 2-2, the cloud server performs a search operation through a search trap as follows: after receiving the search trap Tr, the cloud server determines the sample space data set D through the vector inner product in the high-dimensional vector index. e and spatial dataset D i Whether it is connectable, when the sample spatial dataset D e and spatial dataset D i When the number of overlapping grids is greater than the connectable threshold τ, it is connectable. If it is connectable, the spatial dataset D i Add to candidate set The calculation and judgment method is as follows: In high-dimensional vector indexing, use encrypted vector collections Each item in the set is associated with the encrypted vector Perform a dot product operation. If the dot product calculation result is 0, it indicates that the sample space dataset D e and spatial dataset D i There is no connectable area; otherwise, it indicates that the sample spatial dataset D e and spatial dataset D i There is a connectable area, record the number of overlapping grids Sum, given a connectable threshold τ, when Sum>τ, it indicates that the sample space dataset D e and spatial dataset D i To be connectable, the spatial dataset D i Add to candidate set 6. According to the example-based privacy protection spatial dataset connectable query method of claim 1: in the step 2-3, the cloud server calculates the sample spatial dataset D e and spatial dataset D i The spatial difference operation is: using the candidate set The set of encrypted vectors in Each item in and the encrypted decision vector The spatial difference is calculated by vector dot product, and the first k spatial data sets are returned as the final result set R. The specific calculation and judgment method is as follows: In the candidate dataset In the encryption decision vector and candidate set Encrypted vector collection After performing dot product operations on each item of , the number of connectable areas of each spatial data set Sum is subtracted as the spatial difference. Specifically, the calculation The results show that the sample spatial dataset D e and spatial dataset D i The spatial difference of the calculation results is sorted and the top k spatial data sets are returned as the result set R to the user.

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