Privacy protection data mining method and system based on secure multi-party computing

Abstract

The invention discloses a privacy protection data mining method and system based on secure multi-party computing, and the method comprises the steps: 1, dividing a private data set of each participant into a plurality of secret shares through a secret sharing mechanism, and distributing the plurality of secret shares to other participants; 2, each participant preliminarily calculates the secret share to obtain the secret share of an intermediate result; 3, all the participants jointly calculate the secret share of the intermediate result through secure multi-party calculation to obtain the intermediate result, and the intermediate result is calculated according to the secure multi-party calculation to obtain a final result; 4, all the participants calculate the final result through result restoration, and a data mining result is obtained. According to the method, security protection is carried out on data privacy in the multi-source joint data mining process through security multi-party computing, users are helped to share sensitive but valuable data, and multiple users are enabled to jointly mine data of multiple data sets.

Description

Technical Field

[0001] The present invention relates to the technical field of cryptography, and in particular to a privacy-preserving data mining method and system based on secure multi-party computing. Background Art

[0002] With the booming development of artificial intelligence, data mining, as the basic technology of artificial intelligence, has attracted widespread attention from academia and industry in recent years. Data mining technology is widely used to discover potential valuable patterns from large amounts of data for various applications such as medical diagnosis, speech recognition, and personalized recommendation systems. In massive data scenarios, the massive data to be mined is often distributed in multiple institutions. In massive data scenarios, the data to be mined is often distributed in multiple organizations. Multi-source data mining can aggregate these massive data collected from multiple sources to produce more accurate and reliable patterns for various decisions. For example, multiple medical institutions aggregate patients' medical records to collaboratively analyze diseases so that better clinical diagnoses can be made for patients. Therefore, multi-source data mining plays an important role in various massive data applications. However, data security in multi-database data mining has attracted serious attention. Especially in multi-data scenarios, multiple institutions are reluctant to share their sensitive but valuable data due to corporate competitive advantages, user privacy issues, legal compliance, and other reasons. On the other hand, institutions also want to aggregate their private datasets with other datasets so that they can provide more accurate and reliable mining results for business decisions. Therefore, how to jointly conduct multi-dataset data mining among multiple participants without leaking private datasets is a challenging problem. Summary of the invention

[0003] In order to solve the problem of how to enable multiple participants to jointly conduct data mining on multiple data sets without leaking private data sets, the present invention provides a privacy-preserving data mining method and system based on secure multi-party computing. By constructing a secure multi-party computing model and combining it with a data mining algorithm, multiple participants can jointly conduct data mining without leaking private data sets.

[0004] In order to achieve the above object, the technical solution of the present invention is:

[0005] The first aspect of the present invention proposes a privacy-preserving data mining method based on secure multi-party computing, comprising:

[0006] Step 1: Each participant divides his private data set into multiple secret shares through a secret sharing mechanism, and distributes the multiple secret shares to other participants to facilitate multi-party computing;

[0007] Step 2: Each participant performs a preliminary calculation on the secret share to obtain the secret share of the intermediate result, which is convenient for data mining;

[0008] Step 3: All participants jointly calculate the secret share of the intermediate result through secure multi-party computing to obtain the intermediate result, and calculate the intermediate result according to secure multi-party computing to obtain the final result, so as to facilitate data mining without leaking the private data set;

[0009] Step 4: All participants calculate the final result through result restoration to obtain the data mining result.

[0010] Furthermore, the step 1 specifically includes:

[0011] Determine the number of participants and the minimum number of participants, and assign a unique identifier to each participant to ensure the fairness, effectiveness, and reliability of secure multi-party computing;

[0012] Split the private data set into multiple secret shares based on unique identifiers to facilitate calculations by participants;

[0013] Send multiple secret shares to corresponding participants.

[0014] Furthermore, the splitting of the private data set into multiple secret shares according to the unique identifier specifically includes:

[0015]

[0016] Among them, f x (a i ) secret share, x is the private data set, t is the minimum number of participants, a i is the unique identifier corresponding to the i-th participant, a l is a random number, x i is the secret share corresponding to the unique identifier of the i-th participant in the private data set x, mod p is the modulus operation, and p is a large prime number.

[0017] Furthermore, the preliminary calculation in step 2 includes distance calculation or similarity calculation.

[0018] Furthermore, in the secure multi-party computation, the addition operation is performed according to the following formula:

[0019]

[0020] Among them, z i is the result of addition calculation, z is the sum of the private data sets of x and y, b l is the random number corresponding to the sum of the private data sets, and x and y are different private data sets.

[0021] Furthermore, in the secure multi-party computation, the multiplication operation is performed according to the following process:

[0022] Construct multiplication triples [a] t , [b] t and [c] t , so that [c] t =[a·b] t , set the participant P king , each participant computes [u] locally t =[x] t +[a] t and [v] t =[y] t +[b] t , where [u] t and [v] t are different reconstructed secret share subsets, x and y are different private data sets, a, b and c are the data in the multiplication triplet;

[0023] Participant P king Collect all reconstructed secret share subsets [u] t and [v] t , obtain the reconstructed secret share u and the reconstructed secret share v, calculate u·v, and send u, v and u·v to all participants;

[0024] Participants compute locally Among them, b i is the data in b, a i is the data in a;

[0025] The multiplication result is expressed as follows: [z] t =(z1, z2, ..., z n ), where [z] t The result of the multiplication.

[0026] Furthermore, the step 4 specifically includes:

[0027] Each participant calculates the verification result based on all local final results through the verification algorithm, and exchanges the verification result with other participants to ensure the correctness of the final result;

[0028] If the verification results of all participants are consistent, all participants use the Lagrange interpolation method to restore the final results to obtain the data mining results.

[0029] Furthermore, each participant obtains a verification result by calculating the verification algorithm based on all local final results, including:

[0030] z check :=z 1* +z 2* ·r+…+z n* ·r n-1

[0031] Among them, z check To verify the results, r is the parameter, z n* is the final result of the nth participant.

[0032] Furthermore, all the participants use the Lagrange interpolation method to restore the final result to obtain the data mining result, which specifically includes:

[0033]

[0034] Among them, f x (0) is the data mining result, M(0) is the interpolation basis function, x j is the jth secret share corresponding to the private dataset, x i is the i-th secret share corresponding to the private data set, and x is the private data set.

[0035] The second aspect of the present invention proposes a privacy-preserving data mining system based on secure multi-party computing, comprising:

[0036] The data sharing module is used for each participant to divide his private data set into multiple secret shares through a secret sharing mechanism, and distribute the multiple secret shares to other participants to facilitate multi-party computing;

[0037] The initial calculation module is used for each participant to perform preliminary calculations on the secret share and obtain the secret share of the intermediate result to facilitate data mining;

[0038] A secure multi-party computing module is used for all participants to jointly calculate the secret share of the intermediate result through secure multi-party computing to obtain the intermediate result, and to calculate the intermediate result according to the secure multi-party computing to obtain the final result, so as to facilitate data mining without leaking the private data set;

[0039] The result restoration module is used by all participants to calculate the final result through result restoration to obtain the data mining result.

[0040] Beneficial effects of the present invention:

[0041] (1) The present invention improves the addition and multiplication operations in secure multi-party computing to facilitate data mining for participants. It can also provide security protection for data privacy during multi-source joint data mining for participants, helping participants share their sensitive but valuable data.

[0042] (2) The present invention first exchanges the final results held by the participants with each other, verifies all the final results according to the verification algorithm to ensure the correctness of the final results, and then restores the final results to obtain the data mining results, thereby realizing the separation of data ownership and use rights, thereby protecting data privacy, and realizing that multiple participants can jointly participate in data mining of multiple data sets without leaking private data sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A flowchart of a privacy-preserving data mining method based on secure multi-party computing is provided in an embodiment of the present invention.

[0044] Figure 2 A flowchart of a multiplication operation provided by an embodiment of the present invention.

[0045] Figure 3 A schematic diagram of the specific process of a privacy-preserving data mining method based on secure multi-party computing provided in an embodiment of the present invention.

[0046] Figure 4 An architecture diagram of a privacy-preserving data mining system based on secure multi-party computing provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution in the embodiment of the present invention will be clearly described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] Secure Multi-Party Computation (SMPC or MPC) involves multiple participants who want to jointly compute the output of a function but are unwilling to expose their private input information to each other. Its goal is to ensure that the computation is performed correctly without revealing their own private data sets, and that even during the computation, no participant can obtain additional information about other parties' inputs except the final computation result. Secure Multi-Party Computation (SMPC) can provide strong privacy protection for multi-source data mining, allowing multiple participants to collaborate on common data analysis and data mining tasks without sharing the original data.

[0049] Example 1

[0050] like Figure 1As shown, a privacy-preserving data mining method based on secure multi-party computing includes:

[0051] S101: Each participant divides his private data set into multiple secret shares through a secret sharing mechanism, and distributes the multiple secret shares to other participants.

[0052] S102: Each participant performs a preliminary calculation on the secret share to obtain the secret share of the intermediate result.

[0053] S103: All participants jointly calculate the secret share of the intermediate result through secure multi-party computing to obtain the intermediate result, and calculate the intermediate result according to secure multi-party computing to obtain the final result.

[0054] S104: All participants calculate the final result through result restoration to obtain data mining results.

[0055] The present invention performs data mining by combining a data mining algorithm with a secure multi-party computing model, divides a private data set through a secret sharing mechanism to obtain secret shares, and then uses secure multi-party computing to calculate the secret shares, so that multiple participants can collaborate to complete common data analysis and data mining tasks without sharing the original data, thereby achieving the separation of data ownership and usage rights, thereby protecting data privacy.

[0056] Example 2

[0057] On the basis of the above embodiments, the embodiment of the present invention provides a specific process of a privacy-preserving data mining method based on secure multi-party computing, which specifically includes:

[0058] S201: Each participant divides his private data set into multiple secret shares through a secret sharing mechanism, and distributes the multiple secret shares to other participants.

[0059] Specifically, the public parameters and computing tasks required by the data mining algorithm are first determined, such as the radius of the cluster, the threshold, etc. Then all participants first determine the number of participants n and the minimum number of participants t in the process of restoring the secret through public dialogue or a set protocol. After determining these two initial parameters, each participant P i A unique identifier will be assigned to it, which is denoted as α, which represents its role and identity in this computing activity. i This identifier can be regarded as the fixed identity of the participant in the entire computing process, and can also be used to verify its legitimacy during data exchange to ensure the security of the computing. This method of presetting parameters ensures the fairness, effectiveness and reliability of secure multi-party computing.

[0060] The setting of common parameters is represented by the following formula:

[0061] ParamGen(1 k ,n,t) → pp

[0062] where k is the security parameter, n is the number of participants, t is the minimum number of participants, t < n, pp is the common parameter, and ParamGen is the common parameter function.

[0063] The private data set is segmented using the secret sharing operation, which is represented by the following formula:

[0064] Share(x) → [x] t

[0065] where Share is the secret sharing operation and x is the private data set.

[0066] For the private data set x, select t - 1 random integers (a1, a2,..., a t-1 ), and generate a random polynomial:

[0067]

[0068] where f x (a i ) is the sub - key, x is the private data set, a i is the unique identifier corresponding to the i - th participant, and a l is a random number.

[0069] Next, for all security parameters k ∈ [1, n], substitute them into the generated random polynomial for calculation:

[0070]

[0071] where α k is the random number corresponding to the security parameter, mod p is the modulo operation, p is a large prime number, [x] t is the secret share vector, [x] t = (x1,..., x n ), x n is the n - th secret share, and f x (α k ) is the secret share.

[0072] For a single calculation operation, the private data sets x and y participating in the calculation are subjected to the secret sharing operation to generate corresponding n secret shares x i , y i and send them to the corresponding participants P iSpecifically, the private data sets x and y are brought into the generated random polynomial for calculation. The specific calculation process is expressed as follows:

[0073]

[0074] Among them, x i is the secret share corresponding to the unique identifier of the i-th participant in the private dataset x, y i is the secret share corresponding to the unique identifier in the private dataset y, where x and y are different private datasets.

[0075] S202: Each participant performs a preliminary calculation on the secret share to obtain the secret share of the intermediate result.

[0076] Specifically, each participant performs basic computing operations (such as distance calculation, similarity calculation, etc.) in the data mining algorithm according to the allocated secret share to generate a secret share of the intermediate result.

[0077] S203: All participants jointly calculate the secret share of the intermediate result through secure multi-party computing to obtain the intermediate result, and calculate the intermediate result according to secure multi-party computing to obtain the final result.

[0078] Specifically, secure multi-party computing includes two types of operations. When performing secure multi-party computing, it is necessary to determine the operation type and two private data sets [x] t and [y] t , [y] t =(y1,...,y n ), y n is the nth secret share of the private dataset y.

[0079] For addition, [x+y] t =[x] t +[y] t , each participant P i Addition result z i It is expressed as follows:

[0080]

[0081] Among them, z i is the result of addition calculation, z is the sum of the private data sets of x and y, b l is the random number corresponding to the sum of the private data set.

[0082] For multiplication operations, such as Figure 2 As shown, each participant P i The multiplication result z iAs follows: For the multiplication gate, assume that the two private data sets of the input are represented as [x] t ,[y] t In order to calculate [z] t =[x·y] t , we need to use Beaver triples [a] t ,[b] t ,[c] t , so that [c] t =[a·b] t , where a, b and c are the data in the multiplication triplet. The calculation result is expressed as follows:

[0083] z=x·y=(x+aa)·(y+bb)=(x+a)·(y+b)-(x+a)·b-(y+b)·a+a·b

[0084] Among them, x and y are different private data sets, and z is the multiplication result.

[0085] Specifically, each participant first agrees on a special participant P king , and then each participant performs the following steps:

[0086] S2031: Each participant computes [u] locally t =[x] t +[a] t and [v] t =[y] t +[b] t .

[0087] Among them, [u] t and [v] t Subsets of secret shares for different reconstructions.

[0088] S2032: Special Participant P king Collect the reconstructed secret share subset [u] t and [v] t All shares of , get the reconstructed secret share u and the reconstructed secret share v, then the special participant P king Calculate u·v. Special participant P king Send u, v, and u·v to all participants.

[0089] S2033: All participants compute [z] locally t =u·vu·[b] t -v · [a] t +[c] t

[0090] Specifically,

[0091] S2034: The calculation result is used to form a multiplication calculation result [z] t =(z1, z2, ..., z n ).

[0092] Participants collaborate through secure multi-party computation and obtain intermediate results (such as updating cluster centers, generating distance matrices, etc.) for the secret shares of the intermediate results. After that, all participants collaborate to perform secure multi-party computation on the final steps of the data mining algorithm (such as merging cluster results, reaching classification decisions, etc.) and generate the final results in the form of secret shares.

[0093] S204: All participants calculate the final result through result restoration to obtain data mining results.

[0094] Specifically, the privacy calculation of the secret share is completed through secure multi-party computing to obtain the final result. The final result held by each participant is the calculation result of the secret share rather than the data mining result. Then each participant sends the secret share they hold to each other, and the data mining result is restored based on the final result.

[0095] Each participant communicates with each other to exchange their own secret shares, and all participants obtain the same final result vector [z] = (z 1* , z 2* , ..., z n* ), z n* is the final result of the nth participant.

[0096] Each participant calculates the verification result based on all local final results through the verification algorithm and exchanges the verification result with other participants.

[0097] The verification method proposed in the present invention satisfies the property of result consistency. More precisely, under the semi-honest adversary model, the adversary does not engage in active destructive behavior, but there may be non-malicious errors in the calculation process. Specifically, if the nodes have error detection capabilities, they will produce consistent calculation results when the number of nodes that terminate normally exceeds or equals t+1. Faulty nodes are able to automatically stop operating when errors occur, preventing such errors from propagating to other normal nodes. This means that these errors will not affect the subsequent calculation process of other normal nodes, and the consistency of the calculation results is guaranteed by the following method.

[0098] Specifically, all participants generate a random element r∈F, where F is a finite field. Each participant computes locally

[0099] z check :=z 1* +z 2*·r+…+z n* ·r n-1

[0100] Among them, z check To verify the results, r is a parameter.

[0101] All participants exchange verification results z with other participants check and check if they are the same.

[0102] If a participant P i Received a different verification result z check , participant P i Abort the calculation. Assume P i and P j There are two honest participants, and they each received the final result z 1* ,...,z n* and Assume that there exists i∈[n] where Consider the following calculation

[0103] f(r)=z 1* +z 2* ·r+…+z n* ·r N-1

[0104]

[0105] Among them, f(r) and For different validation values.

[0106] if Means P i and P j Will receive different verification results from each other, and the party that receives different verification results from others will abort the computation.

[0107] For the final result vector [z] = (z 1* , z 2* , ..., z n* ), for any n or more final results, construct the same t-1 polynomial using Lagrange interpolation.

[0108]

[0109] Among them, f x (z) is the result of polynomial calculation, M(z) is the interpolation basis function, x j is the jth secret share corresponding to the private dataset, x i is the i-th secret share corresponding to the private data set, f x (x i) is an intermediate function.

[0110] The data mining results can be calculated using the following formula:

[0111]

[0112] Among them, f x (0) is the data mining result, M(0) is the interpolation basis function when the input is 0, L(i) is the polynomial, and x. is the data mining result.

[0113] Example 3

[0114] On the basis of the above embodiments, the embodiments of the present invention provide a specific example of a privacy-preserving data mining method based on secure multi-party computing, which specifically includes:

[0115] like Figure 3 As shown, different private data sets are input into the local client, and then the private data sets are divided through data sharing to obtain secret shares, and the secret shares are shared. The secret shares are then calculated on the server to obtain the final result, and the final result is restored and reconstructed to obtain the data mining result.

[0116] Specifically, the data mining algorithm to be used is determined according to the type of data mining to be performed. Taking the classic clustering (DBSCAN) algorithm as an example, the DBSCAN process with privacy protection is implemented in combination with secure multi-party computing.

[0117] Secure multi-party computing is applied to the DBSCAN algorithm to achieve privacy-preserving data mining. First, we determine that there are n participants, P1, ..., P n , each participant P i Contains m i The private dataset S of a data object i ,Right now, where i∈[1,n]. Let S={S i |1≤i≤n} is the union of data objects from n participants. Let m be the total number of data objects in S, where m = m1+m2+...+m n All participants want to jointly cluster the union of their data objects without revealing their private datasets.

[0118] Initialize the cluster set C to be empty, and all data points in the cluster set have not been visited. Randomly select an unvisited data point s from the union of data objects S i , mark it as visited, and use secret sharing (Share(s i )) Generate secret share [s i ], then [s j] is distributed to n participants. Next, n participants jointly determine whether each data object in S is in s i in the neighborhood of .

[0119] Assume [s i ] and [s j ] are two r-dimensional integer vectors. n participants jointly compute the data object s i and j The distance between them, that is: d ij =(s i,1 -s j,1 ) 2 +(s i,2 -s j,2 ) 2 +…+(s i,l -s j,l ) 2

[0120] Among them, s i,l and j,l are integer vectors [s i ] and [s j ] the lth element, d ij For i,l and j,l The distance between.

[0121] The square of the Euclidean distance is used to measure the distance between data objects. Obviously, the above expression only involves addition, subtraction and square operations, which can be considered as the multiplication of two identical data. Therefore, n participants can jointly call the Evaluate algorithm to [s i ] and [s j ] to obtain d ij , and call the Reconstruct algorithm to reconstruct s i and j The distance between ij Then, d ij Compare with the specified sample point radiation radius (radius Eps) to determine the data object s j Is it in s i If so, include it in s i The adjacent points of .

[0122] Perform the above operation on all data points in the union of data objects S and calculate the secret share s iThe size of the neighboring point set N is judged. If it is less than the density MinPts, it is marked as a noise point; otherwise, a new cluster C is established with it as the core point. For point p in the neighboring point set N, a radius check is performed on all points in the neighborhood of N to obtain their neighboring point set N′. If the size of N′ is greater than or equal to MinPts, the number of N is expanded. If p does not belong to any cluster, it is added to cluster C. Repeat this process until no new core point is found.

[0123] The classification results C1, C2, ... are returned as output to all participants, and the classification results are verified by result restoration to ensure the consistency of the results and obtain the final classification results. All participants can achieve joint data mining without exposing private data sets and obtain the same data mining results.

[0124] Example 4

[0125] Corresponding to the above method, such as Figure 4 As shown, an embodiment of the present invention provides a privacy protection data mining system based on secure multi-party computing, including:

[0126] The data sharing module is used for each participant to divide his or her private data set into multiple secret shares through a secret sharing mechanism, and distribute the multiple secret shares to other participants.

[0127] The initial calculation module is used for each participant to perform preliminary calculations on the secret share to obtain the secret share of the intermediate result.

[0128] The secure multi-party computing module is used for all participants to jointly calculate the secret share of the intermediate result through secure multi-party computing to obtain the intermediate result, and calculate the intermediate result according to the secure multi-party computing to obtain the final result.

[0129] The result restoration module is used by all participants to calculate the final result through result restoration to obtain the data mining result.

[0130] It should be noted that the privacy-preserving data mining system based on secure multi-party computing provided in an embodiment of the present invention is for realizing the above-mentioned privacy-preserving data mining method based on secure multi-party computing. Its specific functions can be referred to the above-mentioned method embodiments and will not be repeated here.

[0131] In summary, the present invention improves the addition and multiplication operations in secure multi-party computing to facilitate data mining for participants, and can protect data privacy during multi-source joint data mining, helping participants share their sensitive but valuable data. The present invention first exchanges the final results held by the participants with each other, verifies all the final results according to the verification algorithm to ensure the correctness of the final results, and then restores the final results to obtain the data mining results, thereby realizing the separation of data ownership and use rights, thereby protecting data privacy, and realizing that multiple participants can jointly participate in data mining of multiple data sets without leaking private data sets.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A privacy-preserving data mining method based on secure multi-party computing, characterized in that: include: Step 1: Each participant divides his private data set into multiple secret shares through a secret sharing mechanism, and distributes the multiple secret shares to other participants; Step 2: Each participant performs a preliminary calculation on the secret share to obtain the secret share of the intermediate result; Step 3: All participants jointly calculate the secret share of the intermediate result through secure multi-party computing to obtain the intermediate result, and calculate the intermediate result according to secure multi-party computing to obtain the final result; Step 4: All participants calculate the final result through result restoration to obtain the data mining result.

2. A privacy-preserving data mining method based on secure multi-party computing according to claim 1, characterized in that: The step 1 specifically includes: Determine the number of participants and the minimum number of participants, and assign a unique identifier to each participant; Split the private dataset into multiple secret shares based on the unique identifier; Send multiple secret shares to corresponding participants.

3. A privacy-preserving data mining method based on secure multi-party computing according to claim 2, characterized in that: The step of splitting the private data set into multiple secret shares according to the unique identifier specifically includes: Among them, f x (a i ) secret share, x is the private data set, t is the minimum number of participants, a i is the unique identifier corresponding to the i-th participant, a l is a random number, x i is the secret share corresponding to the unique identifier of the i-th participant in the private data set x, mod p is the modulus operation, and p is a large prime number.

4. The privacy-preserving data mining method based on secure multi-party computing according to claim 1, characterized in that: The preliminary calculation in step 2 includes distance calculation or similarity calculation.

5. The privacy-preserving data mining method based on secure multi-party computing according to claim 1, characterized in that: In the secure multi-party computation, the addition operation is performed according to the following formula: Among them, z i is the result of addition calculation, z is the sum of the private data sets of x and y, b l is the random number corresponding to the sum of the private data sets, and x and y are different private data sets.

6. A privacy-preserving data mining method based on secure multi-party computing according to claim 5, characterized in that: In the secure multi-party computation, the multiplication operation is performed according to the following process: Construct multiplication triples [a] t , [b] t and [c] t , so that [c] t =[a·b] t , set the participant P king , each participant computes [u] locally t =[x] t +[a] t and [v] t =[y] t +[b] t , where [u] t and [v] t are different reconstructed secret share subsets, x and y are different private data sets, a, b and c are the data in the multiplication triplet; Participant P king Collect all reconstructed secret share subsets [u] t and [v] t , obtain the reconstructed secret share u and the reconstructed secret share v, calculate u·v, and send u, v and u·v to all participants; Participants compute locally Among them, b i is the data in b, a i is the data in a; The multiplication result is expressed as follows: [z] t =(z1, z2, ..., z n ), where [z] t The result of the multiplication.

7. The privacy-preserving data mining method based on secure multi-party computing according to claim 4, characterized in that: The step 4 specifically includes: Each participant exchanges the final result held by others; Each participant calculates the verification result based on all local final results through the verification algorithm and exchanges the verification result with other participants; If the verification results of all participants are consistent, all participants use the Lagrange interpolation method to restore the final results to obtain the data mining results.

8. The privacy-preserving data mining method based on secure multi-party computing according to claim 7, characterized in that: Each participant obtains the verification result by calculating the verification algorithm based on all local final results, including: z check :=z 1* +z 2* ·r+…+z n* ·r n-1 Among them, z check To verify the results, r is the parameter, z n* is the final result of the nth participant.

9. The privacy-preserving data mining method based on secure multi-party computing according to claim 7, characterized in that: All the participants use the Lagrange interpolation method to restore the final results to obtain data mining results, including: Among them, f x (0) is the data mining result, M(0) is the interpolation basis function, x j is the jth secret share corresponding to the private dataset, x i is the i-th secret share corresponding to the private data set, and x is the private data set.

10. A privacy-preserving data mining system based on secure multi-party computing, characterized in that: include: A data sharing module, which is used for each participant to divide his private data set into multiple secret shares through a secret sharing mechanism, and distribute the multiple secret shares to other participants; The initial calculation module is used for each participant to perform a preliminary calculation on the secret share and obtain the secret share of the intermediate result; A secure multi-party computing module, used for all participants to jointly calculate the secret share of the intermediate result through secure multi-party computing to obtain the intermediate result, and to calculate the intermediate result according to the secure multi-party computing to obtain the final result; The result restoration module is used by all participants to calculate the final result through result restoration to obtain the data mining result.

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