A method for differentially private secure multi-party data publishing of horizontally partitioned datasets

Abstract

This invention discloses a differential privacy-preserving secure multi-party data publishing method for horizontally partitioned datasets, belonging to the field of data security and privacy protection. The method first involves each data owner obtaining and preprocessing the distribution of noisy individual attributes with the help of a server. Then, the server and each data owner jointly calculate the correlation strength of all attribute pairs, and the server selects the attribute pairs with strong correlations. Next, each data owner merges the selected attribute pairs to obtain several multi-attribute combinations, and together with the server, calculates the noisy multi-attribute marginal distributions. Finally, the noisy multi-attribute marginal distributions are post-processed, and the processed marginal distributions are used to update a random initial composite dataset, thereby obtaining a synthesized composite dataset. This invention extends the existing unilateral data synthesis scheme PrivSyn to multi-party data publishing, enabling secure multi-party data publishing with a wider range of applications.

Description

Technical Field

[0001] This invention belongs to the field of data security and privacy protection, and relates to a differential privacy-preserving and secure multi-party data publishing method for horizontally partitioned datasets. Background Technology

[0002] With the rapid development of big data technology, high-dimensional data, such as healthcare data or user behavior data, are being collected and used for various purposes. Typically, this data is owned by different companies or institutions, and aggregating it can better support decision-making or provide services. However, datasets held by various parties may contain sensitive individual information. If parties simply integrate and share their local datasets, it poses a serious threat to the privacy of individuals within the dataset. Therefore, privacy protection requirements must be met when aggregating datasets from various parties.

[0003] In recent years, the issue of privacy-preserving data publication has attracted the attention of scholars. After several attempts to define privacy requirements in data publication, differential privacy has become a widely accepted privacy model. Unlike traditional privacy models (such as k-anonymity and l-diversity), differential privacy provides strong theoretical guarantees for data publication, which are not affected by the attacker's background knowledge.

[0004] The problem of differential privacy-preserving data distribution has been extensively studied, with both unilateral and multilateral distribution methods. Unilateral distribution methods include PrivBayes, JTree, and PivSyn. PrivBayes uses a Bayesian network to define a set of noisy low-dimensional distributions to approximate the joint distribution of the input data; JTree identifies a set of marginal distributions from the dependency graph and approximates the joint distribution using inference based on a tree-based algorithm; PivSyn updates an initial dataset with a large number of low-dimensional marginal distributions, ultimately obtaining a synthetic dataset that closely approximates the low-dimensional marginal distributions. All three methods estimate the low-dimensional marginal distributions to obtain an approximate overall joint distribution, with PivSyn showing the best performance. This method was proposed in the "NIST.2018 Differential Privacy Synthetic Data Challenge". Multilateral distribution methods include later proposed methods such as DP-SUBN and DPLT. DP-SUBN is used for horizontally partitioning datasets. With the help of a third party, all participants jointly initialize a Bayesian network structure and update it serially, then learn the parameters of the Bayesian network. Finally, the third party samples the dataset from the Bayesian network. DPLT, on the other hand, is used for vertically partitioning datasets. With the help of a third party, any two parties generate a hidden tree model (a special Bayesian network structure), and merge the two index trees (i.e., only hidden attribute nodes) into one tree. Then, the third party samples this tree to obtain the dataset. Among the aforementioned methods, PrivBayes, JTree, DP-SUBN, and DPLT all put low-dimensional marginal distributions into graph models and use sampling methods to generate synthetic datasets. When the graph is dense, the algorithm efficiency is not high. For multi-party scenarios that require secure multi-party computation, the complexity is even greater. PivSyn, however, does not use a graph model but updates the initial synthetic dataset with a large number of low-dimensional marginal distributions, which seems much simpler and more efficient.

[0005] Therefore, inspired by PivSyn, this invention extends it to multi-party scenarios. Unlike DP-SUBN and DPLT, which use cumbersome graph models to represent datasets, this invention selects some highly correlated attribute combinations and updates the randomly initialized synthetic dataset with their low-dimensional marginal distributions, so that the distribution of the final synthetic dataset is close to all the low-dimensional marginal distributions. Summary of the Invention

[0006] Purpose of the invention: This invention provides a method for differential privacy protection and secure multi-party data publishing of horizontally partitioned data. It extends the existing unilateral data synthesis scheme PivSyn to multi-party data publishing, and can be used for secure multi-party data publishing with a wider range of applications.

[0007] To achieve the above-mentioned objectives, the technical solution provided by this invention is as follows:

[0008] A method for differential privacy-preserving and secure multi-party data publishing with horizontally partitioned data includes the following steps:

[0009] S1. With the help of the server, each data owner obtains the distribution of the noisy individual attributes and performs preprocessing.

[0010] The added noise is Laplace noise, consisting of four Gaussian variables Y that follow a normal distribution. i ~N(0,λ / 2), i∈{1,2,3,4} are generated: The probability distribution function of Lap(λ) is: Furthermore, each data owner has four Gaussian variables;

[0011] S2. The server and each data owner jointly calculate the association strength of all attribute pairs, and the server selects the attribute pairs with the strongest association.

[0012] Suppose there are d attributes X1, ..., Xd. d Then all The association strength of attribute pairs, expressed in InDif. a,b =|M a,b -M a ×M b |2 2 Measure, where M a,b M is the true joint distribution of attribute pairs a and b. a ×M b It assumes that attributes a and b are independent, and the outer product of their distributions is M, where M is the distribution table and |·|2 denotes the L2 norm.

[0013] The attribute pair selection problem can be transformed into an optimization problem:

[0014]

[0015] Each attribute pair corresponds to a label i (i∈{1,…,m}); the indicator variable x i =1 indicates that the attribute pair is selected, otherwise it is not selected; Ψ i This is the noise error introduced by Laplace noise, taking the l1 error as Ψ. i =c i *λ i , where c i It is the size of the i-th attribute pair, i.e., c i =2 (i∈{1,...,m}), and λ i Φ is the scale of the added Laplace noise for the i-th attribute pair; i This represents the dependency error caused by attribute pairs that should have been selected but were not, and Φi and InDif i Positive correlation, therefore for Φ i Approximation: Φ i ≈InDif i +noise (noise is Laplace noise generated using Gaussian variables, just like in step (S1), but with a different privacy budget);

[0016] S3. Each data owner merges the selected attribute pairs to obtain some multi-attribute distributions, and works with the server to calculate the noisy multi-attribute marginal distribution (i.e., the joint distribution of multiple attributes).

[0017] S4. Post-process the noisy multi-attribute edge distribution, and use the processed edge distribution to update a random initial comprehensive dataset to obtain the synthesized comprehensive dataset.

[0018] Furthermore, step (S1) includes the following process:

[0019] With the help of the server, each data owner obtains the distribution of a noisy individual attribute;

[0020] Data owners preprocess the distribution of the noisy individual attributes by filtering and merging low-frequency values.

[0021] Furthermore, step (S2) includes the following process:

[0022] Each data owner assigns labels to all attribute pairs and the two attributes involved in each attribute pair (the server will not know this), and encrypts the distribution of attribute pairs and the distribution of the two attributes involved in their respective datasets using the threshold Paillier algorithm before sending them to the server.

[0023] The server uses InDif a,b =|M a,b -M a ×M b |2 2 Calculate the InDif for each attribute pair;

[0024] The server selects the option that minimizes the overall error. The smallest set of attribute pairs, returns the labels of the selected attribute pairs.

[0025] Furthermore, step (S3) includes the following process:

[0026] The server sends the labels of the attribute pairs selected in step (S2) (the server does not know which label corresponds to which attribute pair) to each data owner. Each data owner performs the same attribute pair merging operation to obtain some attribute combinations.

[0027] Each data owner then assigns a label to the multi-attribute combination obtained after the merging operation, and together with the server, calculates the noisy multi-attribute edge distribution. The noise is generated in the same way as in step (S1). The noisy multi-attribute edge distribution is obtained by the server, and the server still does not know which label corresponds to which multi-attribute combination.

[0028] Furthermore, step (S4) includes the following process:

[0029] The server sends the noisy multi-attribute edge distribution obtained in step (S3) to a data owner, who then performs post-processing on the noisy multi-attribute edge distribution to ensure that the noisy edge distribution is consistent.

[0030] The data owner initializes a comprehensive dataset;

[0031] The data owner updated the initial composite dataset using the noisy edge distribution obtained from post-processing, ultimately resulting in the synthetic dataset.

[0032] Beneficial effects: This invention extends the existing efficient synthetic dataset scheme PivSyn to multi-party scenarios. On the one hand, it avoids the use of graph models in previous multi-party data publishing, which is more efficient. On the other hand, it expands the application scenarios of PivSyn to multi-party scenarios, while using secure multi-party computation technology to protect the data privacy of all parties, making its application more widespread. Attached Figure Description

[0033] Figure 1 This is the overall flowchart of the present invention;

[0034] Figure 2 This is an example of horizontally partitioned data in an embodiment of the present invention;

[0035] Figure 3 This is an example of horizontally partitioned data publishing that satisfies differential privacy according to an embodiment of the present invention;

[0036] Figure 4 This refers to the information structure held by the data owner in the DLPA method used in the embodiments of the present invention;

[0037] Figure 5(a) is a schematic diagram of the process of aggregating the secret information of each data owner in the DLPA method used in the embodiment of the present invention;

[0038] Figure 5(b) is a schematic diagram of the process of obtaining the square of the sum of Gaussian variables of each data owner in the DLPA method used in the embodiment of the present invention;

[0039] Figure 5(c) is a schematic diagram of the process of aggregating the encrypted value of secret information with added Laplace noise in the DLPA method used in the embodiment of the present invention;

[0040] Figure 6 This is an example of a data structure defined in the problem definition of this invention;

[0041] Figure 7 This is an example of a graph constructed when merging attributes in an embodiment of the present invention;

[0042] Figure 8 The symbol g in step 4.1 is used to explain the meaning of the symbol g in this embodiment of the invention. i A schematic diagram;

[0043] Figure 9 This is an example of updating the initial dataset in an embodiment of the present invention. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0045] Example

[0046] This embodiment involves two key elements: horizontally partitioned data publication that satisfies differential privacy, and the noisy composite distribution of the dataset attribute subset obtained through secure multi-party computation, i.e., the noisy marginal distribution. The two key elements are first introduced below; then, a formal definition of the differential privacy-preserving secure multi-party computation problem for horizontally partitioned data is given.

[0047] (1) Horizontal partitioning of data release that satisfies differential privacy

[0048] A horizontally partitioned dataset can be viewed as a whole dataset divided into multiple groups based on records. Each group is a local dataset, belonging to different data owners, just like a dataset being horizontally partitioned among multiple data owners.

[0049] For example, in a certain area there are three hospitals, H1, H2, and H3, which possess medical information about some local residents (such as gender, age, occupation, and illnesses). Figure 2 As shown, the three hospitals want to combine their datasets to facilitate more effective clinical research.

[0050] Directly aggregating multiple local datasets poses a threat to personal privacy; therefore, differential privacy techniques can be used to protect published composite datasets. For example... Figure 3 As shown, the horizontal partitioning of data publication that satisfies differential privacy means that, given the privacy parameter ε, P1, P2, and P3 jointly publish a set of data. The overall dataset D' has a similar joint distribution, and the published algorithm is guaranteed to meet the requirements of ε-differential privacy protection. Achieving differential privacy generally requires adding noise through a Laplace or Gaussian mechanism. This invention uses the Laplace mechanism, which is defined as follows:

[0051] Laplace mechanism: Given a function f and an input dataset D, a Laplace mechanism that satisfies ∈-differential privacy can be represented as:

[0052]

[0053] in The global L1 sensitivity of f determines the magnitude of the noise; L(λ) represents a random variable sampled from a Laplace distribution, with a scale parameter of λ, i.e.

[0054] To better constrain the cumulative privacy loss caused by combining multiple differential privacy mechanisms, this invention employs a zero-concentrated differential privacy (zCDP) mechanism, which is more suitable for algorithms consisting of a large number of tasks. The Laplace mechanism can also implement the zCDP mechanism, as detailed below:

[0055] The Laplace mechanism satisfies zCDP: the added noise is L(Δ) f The Laplace mechanism of x) satisfies

[0056] Based on the aforementioned properties of zCDP, a scale of can be added. The ρ-zCDP is achieved using Laplace noise.

[0057] (2) The composite edge distribution with added noise is obtained by secure multi-party computation.

[0058] Implementing differential privacy mechanisms generally requires adding noise. However, the horizontal partitioning data publishing problem that this invention aims to solve involves multiple data owners. Therefore, it is necessary to have multiple data owners jointly add noise. At the same time, secure multi-party computation technology must be used to protect the original data that needs to be noisy and the noise contributed by each party.

[0059] To achieve the above objectives, this invention utilizes the existing distributed Laplace perturbation algorithm (DLPA). This method employs threshold Paillier encryption, where each data owner possesses a portion of the decryption key. Only by aggregating the decryption results from all data owners can the correct decryption result be obtained. Furthermore, threshold Paillier encryption also exhibits homomorphism, meaning that the encryption of ciphertext multiplication equals the sum of plaintext (Enc(a)*Enc(b)=Enc(a+b),Enc(a)…) b =Enc(a*b)), using this property, the data of each data owner can be aggregated together in ciphertext form.

[0060] Suppose there are three data owners, P1, P2, and P3, who own data s1, s2, and s3 respectively. They need the help of a semi-trusted third-party server S to jointly... Noise is added. The added noise is Laplace noise, consisting of four Gaussian variables Y. i ~N(0,λ / 2), i∈{1,2,3,4} are generated: Each data owner has four Gaussian variables.

[0061] In addition to the four Gaussian variables, each data owner also needs to generate five random numbers, as well as randomly generated private keys a and b, and Σb i =0, such as Figure 4 As shown. All parties need S's help to obtain...

[0062] The specific implementation of DLPA is as follows:

[0063] ①Seek

[0064] As shown in Figure 5(a), P i Use the threshold Paillier to... Encryption is performed and sent to S. S then aggregates the ciphertexts sent by all parties by multiplying them together to obtain...

[0065] ②Seek

[0066] As shown in Figure 5(b), P i Use the threshold Paillier to... Encryption is performed, and the ciphertext is sent to S. S then aggregates the ciphertexts sent by all parties to obtain... Then S sends c back to all parties P. i P i calculate Concurrently sent to S, S aggregates and multiplies by Enc(a) 2 ) get

[0067] Following the steps outlined above, the parties and S can cooperate to obtain...

[0068] (The random number can be eliminated during decryption);

[0069] ③ Decrypt and eliminate the random number:

[0070] As shown in Figure 5(c), S is calculated. And send it back to all parties, then each party calculates. (where λ) i It is part of the Paillier private key held by all parties. The information is sent to S, which then aggregates the information from each party by multiplying them to obtain the result. Then calculate get That is, the sum of the secret values ​​of the parties that added noise.

[0071] (3) Problem Definition

[0072] Based on the above two factors, a formal description of the comprehensive data publishing problem that satisfies differential privacy in a horizontal partitioning scenario is given:

[0073] There are K data owners P1,…,P K Each data owner P i (1≤i≤K) has a local dataset D i ,D1,…,D K Containing the same attribute χ={X1,…,X d}, the information of an individual is contained in only a local dataset, namely D i ∩ Given the aforementioned K local datasets and a privacy parameter ε, the K data owners, with the help of a third-party server S, jointly publish a comprehensive dataset D', such that D' and They have similar joint distributions and can guarantee that the published algorithm meets the ε-differential privacy protection requirements.

[0074] On the other hand, it is assumed that the data owner and the third-party server are semi-trusted, meaning they will diligently enforce the agreement but may use background knowledge, intermediate results, and final calculation results to infer sensitive individual information in other local datasets.

[0075] Based on the problem definition above, there are K data owners P1,…,P K They each possess datasets D1, ..., D K These K datasets each have d attributes χ = {X1, ..., X...} d}, assuming their dataset is as follows Figure 6 As shown, where X1={x 11 ,x 12}, X2={x 21 ,x 22 ,x 23 ,x 24 ,x 25}, X3={x 31 ,x 32 ,x 33 ,x 34},…,Xd ={x d1 ,x d2 ,x d3}, that is, X1, X2, X3, ..., X d There are 2, 5, 4, ..., 3 possible values.

[0076] Specifically, combining Figure 1 A differential privacy-preserving and secure multi-party data publishing method for horizontally partitioned datasets, comprising the following steps:

[0077] S1: With the help of the server, each data owner obtains the distribution of the noisy individual attributes and performs preprocessing, specifically including the following sub-steps:

[0078] Step 1.1: Each data owner, with the help of the server, obtains the distribution of the noisy individual attribute. For each attribute, each data owner counts the number of each value of that attribute in their respective local dataset (the count is used because Paillier encryption is used to handle integers; the probability can be obtained by aggregating the data and then using the homomorphism of Paillier). Where [*] represents the encrypted form, M represents the count distribution table obtained by aggregating K datasets, and N represents the total number of records in the K datasets), then using the DLPA method shown in (2) above, the noisy distribution of this attribute is obtained with the help of the server. For example, for Figure 6 The attribute X1 = {x 11 ,x 12}, referring to Figures 5(a), (b), and (c), for the value x 11 P1, P2, ..., P K The secret values ​​are: s1 = 3, s2 = 0, ..., s K =3, and each data owner and server jointly obtain N(X1=x) using the DLPA method described in (2). 11 )+noise, where N(·) represents the number, and similarly, we can obtain N(X1=x 12 )+noise, thus obtaining the noisy distribution of attribute X1.

[0079] Step 1.2: The data owners preprocess the distribution of the noisy individual attributes obtained in Step 1.2, i.e., they filter and merge low-frequency values. Specifically, they retain values ​​with a frequency (which should be calculated here) higher than a threshold θ, where θ = 3σ, and σ is the standard deviation of the added noise. For the Laplace mechanism Lap(λ), For values ​​with frequencies less than θ, sum their frequencies. If the total frequency is still less than θ, set the count of these values ​​to 0. Otherwise, create a new value to represent those low-frequency values. For example, if the sum of the frequencies of "myopia," "color blindness," and "hyperopia" is greater than θ, replace them with a new value "eye disease." After synthesizing the dataset, replace the newly created value back. This operation allows the server to send the distribution of the noisy individual attributes obtained in step 1.1 to a data owner, who then performs preprocessing. Other data owners then preprocess their own datasets based on the data owner's preprocessing results (discarding or replacing certain values).

[0080] S2: The server and each data owner jointly calculate the association strength of all attribute pairs, and the server selects the attribute pairs with strong associations. This includes the following sub-steps:

[0081] Step 2.1: Each data owner assigns labels to all attribute pairs and the two attributes involved in each attribute pair (the server will not know which label corresponds to which attribute pair), and encrypts the distribution of attribute pairs and the two attributes involved in each attribute pair in their respective dataset using the Paillier thresholding algorithm, before sending them to the server. For example, for attribute pair X1X... d , there is {x 11 x d1 ,x 11 x d2 ,x 11 x d3 ,x 12 x d1 ,x 12 x d2 ,x 12 x d3 There are six possible values, which can be numbered as: X1X d →8;x 11 →8.1, x 12 →8.2, x d1 →-8.1, x d2 →-8.2, x d3 →-8.3; x 11 x d1 →8.11, x 11 x d2 →8.12, x 11 x d3 →8.13, x 12 x d1 →8.21, x 12 x d2 →8.22, x 12 x d3→8.23. Each data owner sends a ciphertext containing the label and a count of the corresponding attribute values ​​(pairs) to the server.

[0082] Step 2.2: The server uses InDif a,b =|M a,b -M a ×M b |2 2 Calculate the InDif for each attribute pair, where M a M b M a,b This is obtained by the server according to the encrypted data of each data owner in step 2.1, summarized by label. To calculate the InDif of two attributes, we subtract the corresponding values ​​from the two distribution tables, square the results, and then sum them. For example... Where N * This represents the sum of counts of attribute values ​​(pairs) labeled * in each dataset. Furthermore, the above InDif calculation process involves multiplication of Paillier ciphertexts, with N... 8.1 ×N -8.1 For example, let [*] represent the ciphertext format, specifically implemented as: server aggregation Get [N] 8.1 ], sent back to each data owner, each data owner P i Then The data is sent to the server, which multiplies the ciphertext sent by each data owner. Based on the homomorphism of Paillier encryption, [N] is obtained. 8.1 ×N -8.1 ].

[0083] Step 2.3: The server selects the option that minimizes the overall error. The smallest set of attribute pairs is selected, and the labels of the selected attribute pairs are returned. As described in claim S2, the attribute pair selection problem can be transformed into an optimization problem:

[0084]

[0085] Each attribute pair corresponds to a label i (i∈{1,…,m}), and the indicator variable x i =1 indicates that the attribute pair is selected, otherwise it is not selected; Φ i This represents the dependency error caused by attribute pairs that should have been selected but were not, and Φ i and InDif i Positive correlation, therefore for Φ i Approximation: Φ i ≈InDif i+noise (noise is Laplace noise generated using Gaussian variables, just like in step (S1), but with a different privacy budget).

[0086] Ψ i This is the noise error introduced by Laplace noise, taking the l1 error as Ψ. i =c i *λ i , where c i The size c of the i-th attribute pair i =2(i∈{1,…,m}), and λ i It is the scale of the Laplace noise added to the i-th attribute pair. As mentioned above (1), given the original attribute pair M i Add scale as The noise can be reduced to ensure that each attribute pair satisfies ρ. i -zCDP, then and Since this is a constant, it can be extracted. Therefore, transforming the aforementioned optimization problem yields the optimal privacy budget allocation, specifically:

[0087]

[0088]

[0089] Constructing the Lagrange function achievable From ∑ i ρ i =ρ, we can get therefore

[0090] S3: Each data owner merges the selected attribute pairs to obtain several multi-attribute combinations, and works with the server to calculate the noisy multi-attribute marginal distribution (i.e., the joint distribution of multiple attributes). This includes the following sub-steps:

[0091] Step 3.1: The server sends the labels of the attribute pairs selected in Step 2.3 to each data owner. Each data owner then performs the same attribute pair merging operation, as detailed below:

[0092] Step 3.1.1: Each data owner converts the labels into attribute pairs;

[0093] Step 3.1.2: Let the attributes be nodes. If an attribute pair is selected, draw an edge between the two attributes to construct a graph G. For example, assuming the selected attribute pair is X1X2, X1X3, X2X3, X3X4, X3X5, X4X5, the graph G drawn would look like this. Figure 7 As shown;

[0094] Step 3.1.3: Find all cliques in graph G whose size (i.e., number of attributes) is greater than 2, such as... Figure 7 In the set X1X2X3, X3X4X5, if the size of the attribute domain of the clique is no greater than the threshold γ = 5000, and the intersection with the set of already selected attributes is no greater than 2, then the attribute pairs contained in the clique are merged into some multi-attribute combinations. Figure 7 For example, suppose X1X2, X1X3, X2X3 have been merged into a multi-attribute combination X1X2X3, and attributes X3, X4, and X5 have 4, 10, and 20 values ​​respectively. Then, for the group X3X4X5, its domain size is 4 × 10 × 20 = 800 < γ, and |{X1,}2,X3}∩{X3,X4,X5}| = |{X3}| = 1 < 2. Therefore, X3X4, X3X5, and X4X5 are merged into a multi-attribute combination X3X4X5.

[0095] Step 3.2: Each data owner again labels the merged multi-attribute combination (e.g., X1X2X3, which has 2×5×4=40 possible values, so these 40 values ​​are numbered), and then works with the server to calculate the noisy multi-attribute edge distribution. The noise is still generated using the DLPA method described in (2). This step is related to finding M. a,b The process is the same.

[0096] S4. Post-process the noisy multi-attribute edge distribution, and update an initial composite dataset with the processed edge distribution to obtain the synthesized dataset. This includes the following sub-steps:

[0097] Step 4.1: The server sends the noisy multi-attribute edge distribution obtained in Step 3.2 to a data owner. The data owner performs post-processing operations on the noisy multi-attribute edge distribution to ensure the consistency of the noisy edge distribution. For example, an attribute set A consists of s multi-attribute combinations M1,…,M… s Sharing, i.e., A = M1 ∩ … ∩ M s Therefore, it is necessary to process A in these s multi-attribute combinations to ensure that the distribution of attribute set A is consistent across them. Specifically:

[0098] Assign weights w to these s multi-attribute combinations i We perform a weighted average on them to minimize the variance of the distribution of A among these multi-attribute combinations, i.e., in ∑ i w i Under the condition that = 1, make the variance Minimum. Where g i It is the number of cells in multi-attribute combination i that make up a single cell in A, such as Figure 8As shown, multi-attribute combination 1 = {gender, age}, multi-attribute combination 2 = {gender, disease}, then A = {gender}. In multi-attribute combination 1, the sum of the three cells results in one cell in A, i.e., g1 = 3. Similarly, g2 = 2; 2λ i 2 From the random variable Lap(λ) in the Laplace distribution i The variance of zCDP, according to the properties of zCDP described above (1), is obtained as follows: but Therefore, the following optimization problem arises:

[0099]

[0100]

[0101] The optimal weight allocation can be obtained using the Lagrange optimization method:

[0102] Step 4.2: The data owner mentioned in Step 4.1 initializes a random composite dataset D. s .

[0103] Step 4.3: The data owner mentioned in Step 4.1 uses the noisy edge distribution obtained from this post-processing step to process the initial composite dataset D. s The dataset is updated in a manner similar to multiplicative updates to obtain the final synthetic dataset. Specifically, a parameter α∈(0,1) is set, and n is denoted as the number of records in the multi-attribute marginal distribution. t The number of records in D0 is n 0 For cells in D0 whose frequency is higher than the expected frequency in the post-processed noisy marginal distribution, reduce the number of records by a maximum of α times, i.e., min{n 0 -n t ,αn 0}; For cells in D0 whose frequency is lower than the expected frequency in the post-processed noisy edge distribution, add a maximum of β times the number of records, i.e., min{n t -n 0 ,βn 0 Since the total number of records is fixed, given α, β can be calculated to... Figure 9 For example, to make <tall, male, *> and <tall, female, *> in (a) closer to the target, i.e., the 1 and 4 obtained after post-processing, taking α = 0.5, the maximum reduction in the number of records is 0.5 * 4 = 2. Therefore, the two <tall, male, *> can be modified to <tall, female, *>, becoming (c). Then, for β, n 0 =1 (1 <tall, female, *> in (a)), n t =3((c) contains 3 <tall, female, *>), On the other hand, to change the two <tall, male, *> to <tall, female, *>, you can directly replace them, that is, change "male" to "female", such as... Figure 9 Replace "male" with "female" in v4 of (a); alternatively, you can copy, i.e., delete a row <high, male, *> and copy the record of the row <high, female, *> to the row where you just deleted the record, such as Figure 9 Delete v3 from (a) and copy v5 over. When updating D0, you can use either a replacement operation or a copy operation. When D0 is close to the desired distribution, you should prefer the copy operation because replacement will disrupt the joint distribution of attributes in the marginal distribution and attributes not in the marginal distribution.

[0104] In the further integration step (S2), it should be noted that the server's computation of InDif requires calculating the joint distribution of attribute pairs in the aggregated dataset of multiple datasets. These datasets are held by different data owners, and the InDif must be obtained while ensuring the data privacy of each data owner. The current approach is for each data owner to compute the InDif of each attribute pair in their own dataset separately, add noise locally, and then combine their results to obtain the InDif of each attribute pair in the aggregated dataset. However, this results in excessive noise in the InDif, hindering the selection of highly correlated attribute pairs and thus reducing the data utility of the generated synthetic dataset. Therefore, a secure multi-party computation technique is needed to allow data owners to collaborate on computing the InDif of each attribute pair in the aggregated dataset without compromising their privacy, while simultaneously generating and adding distributed noise. This approach ensures the data security of each data owner while introducing less noise during the generation of the synthetic dataset, resulting in a synthetic dataset with higher data utility.

[0105] Based on the above specific implementation process, the following are the experimental results of the present invention.

[0106] The experiment used three datasets: Adult, accidential_drug_deaths, and drug_deaths. Details of these datasets are shown in Table 1. The experiment evaluated the statistical performance of the synthetic dataset on a data analysis task involving the distribution of marginal distributions. Marginal distributions for all attribute pairs were calculated using the synthetic dataset, resulting in a frequency distribution table. The average L1 error between the marginal distributions of the synthetic and original datasets was used to measure performance.

[0107] Table 1. Detailed information on the datasets used in the experiment.

[0108]

[0109] In the experiments of this invention, two types of data synthesis were performed: one was to divide the Adult dataset into four parts, and then have the four participants synthesize them into an Adult dataset. * One approach involves distributing the accidential_drug_deaths and drug_deaths datasets to two participants, who then generate a combined dataset, drug_all, based on their respective datasets. The experimental results are shown in Table 2-4.

[0110] Table 2 Calculation Costs

[0111] Dataset Running time (s) Adult 72.2 accidental_drug_deaths+drug_deaths 66.0

[0112] Table 3 Communication Overhead

[0113] Dataset Communication overhead (MB) Adult 0.24 accidental_drug_deaths+drug_deaths 0.16

[0114] Table 4 shows the average l1 error between the marginal distribution of the original dataset and the original dataset.

[0115]

[0116] The results show that the present invention can generate multi-party synthetic datasets with high data utility with relatively small computational and communication overhead. When the privacy budget takes values ​​within a small range, the change of ε will not have a significant impact on the data utility of the synthetic dataset.

[0117] In summary, this invention addresses the problem of multi-party data publishing by proposing a multi-party horizontal partitioning data synthesis mechanism under differential privacy protection, including a detailed implementation process. Experimental results demonstrate that this invention can generate highly effective synthetic datasets with relatively low overhead while ensuring the security of all participating parties.

[0118] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for secure multi-party data publishing with differential privacy protection for horizontally partitioned datasets, characterized in that, Includes the following steps: S1. With the help of the server, each data owner obtains the distribution of the noisy individual attributes and performs preprocessing. The added noise is Laplacian noise, with 4 Gaussian variables obeying normal distribution , Generation: where the probability distribution function of is , and each data owner has 4 Gaussian variables; S2. The server and each data owner jointly calculate the association strength of all attribute pairs, and the server selects the attribute pairs with the strongest association. Assume there is Attributes Then all The association strength of attribute pairs, the association strength is expressed as... Measurement, among which It is an attribute pair The true joint distribution, It is a hypothetical attribute and Independent, the outer product of their distributions, It is a distribution table. Represents the L2 norm; The attribute selection problem is transformed into an optimization problem: ， Each attribute corresponds to a label. Indicator variables This indicates that the attribute pair is selected, or conversely, it is not selected. This is the noise error introduced by Laplace noise. Error, i.e. ,in It is the first The size of each attribute pair, i.e. ,and It is the first Each attribute corresponds to a scale of the added Laplace noise; This represents the dependency error caused by an attribute pair that should have been selected but was not. and Positive correlation, therefore for Approximation: ; It uses Laplace noise generated by Gaussian variables, just like in step S1, but with a different privacy budget; S3. Each data owner merges the selected attribute pairs to obtain a combination of multiple attributes, and works with the server to calculate the noisy multi-attribute edge distribution. S4. Process the noisy multi-attribute edge distribution and update a random initial comprehensive dataset with the processed edge distribution to obtain the synthesized comprehensive dataset.

2. The differential privacy-preserving secure multi-party data publishing method for horizontally partitioned datasets according to claim 1, characterized in that, Step S1 includes the following process: With the help of the server, each data owner obtains the distribution of a noisy individual attribute; Data owners preprocess the distribution of the noisy individual attributes by filtering and merging low-frequency values.

3. The differential privacy-preserving secure multi-party data publishing method for horizontally partitioned datasets according to claim 1, characterized in that, Step S2 includes the following process: Each data owner assigns labels to all attribute pairs and the two attributes involved in each attribute pair, and encrypts the distribution of attribute pairs and the distribution of the two attributes involved in their respective datasets using the threshold Paillier algorithm, and then sends them to the server. At this time, the server will not know the aforementioned two attribute assignment numbers. server Calculate each attribute pair ; The server selects the option that minimizes the overall error. The smallest set of attribute pairs, returns the labels of the selected attribute pairs.

4. The differential privacy-preserving secure multi-party data publishing method for horizontally partitioned datasets according to claim 1, characterized in that, Step S3 includes the following process: The server sends the labels of the attribute pairs selected in step S2 to each data owner. Each data owner performs the same attribute pair merging operation. At this time, the server does not know which label corresponds to which attribute pair. Each data owner then assigns a label to the multi-attribute combination obtained after the merging operation, and together with the server, calculates the noisy multi-attribute edge distribution. The noise is generated in the same way as in step S1. The noisy multi-attribute edge distribution is obtained by the server aggregation, and the server still does not know which label corresponds to which multi-attribute combination.

5. The differential privacy-preserving secure multi-party data publishing method for horizontally partitioned datasets according to claim 1, characterized in that, Step S4 includes the following process: The server sends the noisy multi-attribute edge distribution obtained in step S3 to a data owner, who then performs post-processing on the noisy multi-attribute edge distribution to ensure that the noisy edge distribution is consistent. The data owner initializes a comprehensive dataset; The data owner updated the initial composite dataset using the noisy edge distribution obtained from post-processing, ultimately resulting in the synthetic dataset.

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