Secure multi-party computation method and system based on decision tree and privacy protection

Abstract

The present invention relates to the field of privacy computation. Disclosed are a secure multi-party computation method and system based on a decision tree and privacy protection. In a data processing stage, the method uses a gradient-based one-sided sampling algorithm, so as to exclude most small-gradient samples, thus ensuring balance in accuracy while reducing the data volume; then, the method uses a histogram algorithm to construct a decision tree, thus reducing the memory consumption and increasing the computational speed; and in addition, the method also uses a differential privacy technology to perform encryption and perturbation processing on parameters of local models, so as to ensure that individual privacy information is not leaked. The secure multi-party computation method based on a decision tree and privacy protection of the prevent invention can implement prediction tasks such as classification efficiently and reliably while protecting privacy.

Description

Multi-party secure computing method and system based on decision tree and privacy protection TECHNICAL FIELD

[0001] The present application belongs to the technical field of privacy computing, and specifically relates to a multi-party secure computing method and system based on a decision tree and privacy protection. BACKGROUND

[0002] In today's information age, data security and privacy protection have become important social issues. With the rapid development of cloud computing and big data, more and more sensitive data is stored and processed in the cloud, and the computing problems between multiple participants are increasing. For example, financial institutions need to analyze customer data while protecting customer privacy; medical institutions need to cooperatively process medical data but do not want to disclose patients' personal information. Traditional data sharing and analysis methods have limitations, so a new multi-party secure computing method is needed to protect data privacy while achieving efficient and accurate computation.

[0003] A decision tree is an efficient data analysis and decision algorithm that can generate results in a short time. By combining the decision tree algorithm with a privacy protection method, efficient computation can be achieved while protecting data privacy. Compared with traditional secure computing methods, the decision tree-based method can provide faster computation results and improve computation efficiency.

[0004] SUMMARY

[0005] Based on the above background and problems existing in the prior art, the present application adopts the following technical solutions: In a first aspect, a multi-party secure computing method based on a decision tree and privacy protection is provided, which can utilize multi-party data and efficiently and accurately complete machine learning computation tasks under the premise of protecting privacy through a secure differential privacy gradient descent algorithm.

[0006] A multi-party secure computing method based on a decision tree and privacy protection includes the following steps:

[0007] A gradient-based one-sided sampling algorithm is used to preprocess local data to obtain preprocessed data, wherein the local data comes from each participant.

[0008] The preprocessed data is input into a decision tree model for training to obtain a local model for each participant, wherein the decision tree model is optimized by a histogram algorithm to find the optimal split point.

[0009] The parameters of the local model are encrypted based on a differential privacy algorithm to obtain an encrypted local model.

[0010] The encrypted local models of each participant are aggregated to obtain a global model.

[0011] Classifying and predicting the local data to be processed by the global model to obtain an output result.

[0012] As an implementable manner, the gradient-based one-sided sampling algorithm performs data preprocessing on the local data, including the following steps:

[0013] Calculating the gradient of the data sample, wherein the data sample is the local data;

[0014] Arranging the data sample in descending order according to the absolute value of the gradient to obtain a sorted data sample;

[0015] Retaining the first a x 100% of the sorted data sample to obtain first gradient data, wherein a is a preset proportion threshold;

[0016] Randomly sampling the (1-a) x 100% of the sorted sample to obtain a random sampling result, and the sampling proportion is b x 100%, b ∈ [0, 1];

[0017] Multiplying the random sampling result by the balance coefficient to maintain the original distribution of the data sample to obtain second gradient data;

[0018] Summarizing the first gradient data and the second gradient data to obtain preprocessed data.

[0019] As an implementable manner, the preprocessed data is input into a decision tree model for training to obtain a local model of each participant, including the following steps:

[0020] Bucketing and normalizing the preprocessed data to obtain a normalized result;

[0021] Calculating the initial gradient value of the normalized result by a loss function, wherein the bgistic loss function is used as the loss function;

[0022] Constructing a decision tree model based on the initial gradient value and updating the initial gradient value of the decision tree model;

[0023] Repeating the process of constructing the decision tree model and updating the initial gradient value of the decision tree model until the preset condition of the decision tree model is met, thereby obtaining a local model of each participant.

[0024] As an implementable manner, the decision tree model is constructed, including the following steps:

[0025] Constructing a corresponding segmented function for each normalized result, and dividing the value of all preprocessed data on the corresponding feature into a box;

[0026] constructing a histogram for each normalized result, and further transforming the normalized result to find an optimal split point;

[0027] obtaining the optimal split point from the histogram, and selecting a best split feature and a best split feature value based on the optimal split point;

[0028] establishing a root node of the decision tree by the best split feature and the best split feature value;

[0029] splitting the samples according to the best split feature and the best split feature value, and judging based on a pair-wise algorithm until all leaf nodes of the decision tree cannot be split or reach a maximum limit of splitting, thereby obtaining a decision tree model.

[0030] As an implementable manner, the step of constructing a histogram for each normalized result, and further transforming the normalized result to find an optimal split point, comprises the following steps:

[0031] discretizing the normalized result into an integer, and constructing a histogram using a binning operation;

[0032] traversing all normalized results, and accumulating statistical values in the histogram according to the discretized integer as an index;

[0033] traversing to find an optimal split point according to the statistical values of the histogram.

[0034] As an implementable manner, the step of judging based on a pair-wise algorithm until all leaf nodes of the decision tree cannot be split or reach a maximum limit of splitting, thereby obtaining a decision tree model, comprises the following steps:

[0035] traversing the entire decision tree to obtain a position, a split feature and a feature value of each point;

[0036] obtaining a two-by-two combination of the position, the split feature and the feature value of each point from top to bottom;

[0037] traversing each leaf node to determine whether the two-by-two combination has appeared in each leaf node, and if so, deleting it, otherwise, saving it;

[0038] repeatedly executing the above steps to arrange all leaf nodes in the order of nodes of the original decision tree, thereby forming a decision tree model.

[0039] As an implementable manner, the step of encrypting the parameters of the local model based on a differential privacy algorithm, thereby obtaining an encrypted local model, comprises the following steps:

[0040] mapping the local model parameters of each participant, and calculating a global sensitivity;

[0041] generate noise conforming to a Laplace distribution based on the global sensitivity;

[0042] encrypt local model parameters based on the noise conforming to the Laplace distribution to obtain encrypted local models.

[0043] A multi-party secure computing system based on a decision tree and privacy protection includes a data processing module, a decision tree construction module, a privacy protection module, and an aggregation output module.

[0044] The data processing module performs data preprocessing on local data based on a gradient-based one-sided sampling algorithm to obtain preprocessed data, wherein the local data is from each participant.

[0045] The decision tree construction module inputs the preprocessed data into a decision tree model for training to obtain local models of each participant, wherein the decision tree model is optimized by a histogram algorithm to find optimal split points.

[0046] The privacy protection module encrypts parameters of the local models based on a differential privacy algorithm to obtain encrypted local models.

[0047] The aggregation output module aggregates the encrypted local models of each participant to obtain a global model, and classifies and predicts local data to be processed based on the global model to obtain an output result.

[0048] A computer-readable storage medium stores a computer program, and the computer program is executed by a processor to implement the following method:

[0049] The data preprocessing module performs data preprocessing on local data based on a gradient-based one-sided sampling algorithm to obtain preprocessed data, wherein the local data is from each participant.

[0050] The decision tree construction module inputs the preprocessed data into a decision tree model for training to obtain local models of each participant, wherein the decision tree model is optimized by a histogram algorithm to find optimal split points.

[0051] The privacy protection module encrypts parameters of the local models based on a differential privacy algorithm to obtain encrypted local models.

[0052] The aggregation output module aggregates the encrypted local models of each participant to obtain a global model.

[0053] The aggregation output module aggregates the encrypted local models of each participant to obtain a global model.

[0054] A multi-party secure computing device based on a decision tree and privacy protection comprises a memory, a processor, and a computer program stored in the memory and running on the processor, and the processor implements the method as follows when executing the computer program:

[0055] The gradient-based one-sided sampling algorithm is used for data preprocessing of local data to obtain preprocessed data, wherein the local data is from each participant;

[0056] The preprocessed data is input into a decision tree model for training to obtain a local model of each participant, wherein the decision tree model is optimized by a histogram algorithm to find an optimal split point;

[0057] The parameters of the local model are encrypted based on a differential privacy algorithm to obtain an encrypted local model;

[0058] The encrypted local models of each participant are aggregated to obtain a global model;

[0059] The global model is used for classification and prediction of to-be-processed local data to obtain an output result.

[0060] The present application has the following technical effects:

[0061] (1) A multi-party secure computing method and system based on a decision tree and privacy protection are proposed, a gradient-based one-sided sampling method is used for data preprocessing, most of the small gradient samples are excluded from the perspective of reducing samples, and the balance between reducing data volume and ensuring accuracy is ensured;

[0062] (2) A multi-party secure computing method and system based on a decision tree and privacy protection are proposed, a histogram algorithm is used to construct a decision tree, a discretization operation is used to reduce memory consumption, and the number of times of calculating split point gain is greatly reduced, thereby improving the operation speed.

[0063] (3) A multi-party secure computing method and system based on a decision tree and privacy protection are proposed, a pair-wise algorithm is used, the node splitting is reduced in the process of establishing a decision tree, the depth is reduced, and overfitting is prevented.

[0064] Other advantages, objects and features of the present application will be embodied in part by the following description, and will be understood by those skilled in the art through research and practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0065] Fig. 1 is a flowchart of the multi-party secure computing method based on a decision tree and privacy protection of the present application;

[0066] Figure 2 is a schematic diagram of the structure of the system of the present application. DETAILED DESCRIPTION

[0067] In order to clearly illustrate the present application, the purposes, technical solutions and advantages of the embodiments of the present application are made more apparent, the technical solutions of the embodiments of the present application are clearly and completely described below with reference to the accompanying drawings of the embodiments of the present application, so that those skilled in the art can implement the present application according to the description in the specification.

[0068] In the context of the present application, a trusted execution environment provides an isolated running environment from the perspective of underlying hardware and operating system, which can protect the code and data running therein from external attacks, including attacks from operating system, hardware and other application programs. This technology has been used in some fields to achieve the purposes described above, and some basic principles of this technology are known to those skilled in the art, but those skilled in the art will know how to use this technology in the present context after reading the present application, and will clearly know that the technology has novelty in combination with other features in the specific context.

[0069] The technical solutions of the present application will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0070] Embodiment 1

[0071] A multi-party secure computing method based on decision tree and privacy protection, as shown in Figure 1, includes the following steps:

[0072] S100, a gradient-based one-sided sampling algorithm is used to pre-process local data to obtain pre-processed data, wherein the local data is from each participant;

[0073] S200, the pre-processed data is input into a decision tree model for training to obtain a local model of each participant, wherein the decision tree model is optimized by a histogram algorithm to find the optimal split point;

[0074] S300, the parameters of the local model are encrypted based on a differential privacy algorithm to obtain an encrypted local model;

[0075] S400, the encrypted local models of each participant are aggregated to obtain a global model;

[0076] S500, the global model is used to classify and predict the to-be-processed local data to obtain an output result.

[0077] The application is based on a multi-party secure computing method combining efficient learning algorithm and privacy protection technology based on decision tree and differential privacy technology. As an efficient and high-precision machine learning algorithm, the decision tree has fast speed and good performance in the model training process; the differential privacy technology can effectively protect local private data. By combining the two, it can realize sharing data between institutions and model training, monitoring and prediction, and ensure that individual privacy is fully protected.

[0078] An innovative multi-party secure computing method and system based on decision tree and differential privacy technology are proposed. The method makes full use of the advantages of decision tree model in classification and prediction tasks, and combines differential privacy technology to realize safe and efficient sharing of sensitive data between multiple parties for computing and analysis. In the data processing stage, a one-sided sampling algorithm based on gradient is used to exclude most small gradient samples, reducing the amount of data while ensuring the balance of accuracy. Secondly, a histogram algorithm is used to construct a decision tree, reducing memory consumption and improving operation speed. In addition, differential privacy technology is used to encrypt and perturb local model parameters to ensure that individual privacy information is not leaked.

[0079] (1) The one-sided sampling algorithm based on gradient is used for data preprocessing of local data, wherein the local data is obtained from each participant.

[0080] The one-sided sampling algorithm based on gradient includes the following steps:

[0081] Calculate the gradient of the data sample.

[0082] The samples are arranged in descending order according to the absolute value of the gradient to obtain sorted samples.

[0083] The first a*100% of the sorted samples are retained to obtain large gradient data, where a is a proportion threshold.

[0084] Randomly sample the samples that are (1-a)*100% of the sorted samples, and the sampling ratio is b*100%, b [0,1].

[0085] The sampled samples are multiplied by a balance coefficient to maintain the original distribution of the data to obtain small gradient data.

[0086] The large gradient data and the small gradient data are combined to obtain preprocessed data.

[0087] (2) The preprocessed feature data is input into the decision tree model for training to obtain a local model for each participant, including the following steps:

[0088] The features obtained after feature preprocessing are represented as:

[0089] After all the features obtained after feature preprocessing are binned and normalized:

[0090] The features b 11 to b nm are taken as the target vector y i .

[0091] The initial gradient value is calculated;

[0092] The bgistic loss function is used as the loss function of the features, and the formula is as follows:

[0093] L(y i ,F(x i ))=y i log(p i )+(1-y i )log(1-p i )

[0094] Where F(x i ) is the gradient value, p i is the loss probability, and y i is the predicted value.

[0095] Then the initial gradient value is:

[0096] Where η is the learning rate, and F m-1 (x i ) is set to 0 or a random value. The original feature value is converted to:

[0097] A decision tree is established, including the following steps:

[0098] A segmentation function is performed on each feature, and all sample values on the feature are divided into a bin; a histogram is constructed for each feature to further convert the original feature;

[0099] Where e ij =(s ij ,n ij ), s ij is the sum of the sample gradients in the bin, and n ij is the number of samples in the bin.

[0100] The optimal split point is selected from the histogram to obtain the best split feature G and the best split feature value H; the calculation formula is as follows:

[0101] The best split feature and the best split feature value are used to establish the root node of the decision tree;

[0102] T i = argmax(G i ) 1≤i≤m

[0103] That is, the root node is (T i , G i , H i ).

[0104] According to the optimal split feature G i and the optimal split feature value H i , the sample is cut, and the pair-wise algorithm is used for judgment until all leaf nodes of the decision tree cannot be split or reach the maximum limit of splitting.

[0105] The pair-wise algorithm comprises the following steps:

[0106] First step: traverse the entire decision tree to obtain each point position, split feature and feature value, that is, (T i , G i , H i ) ;

[0107] Second step: obtain two-by-two combinations of the three factors of each point position, split feature and feature value from top to bottom of the decision tree;

[0108] Third step: traverse each node to determine whether the two-by-two combination of the three factors in each node has appeared above, if yes, delete it, otherwise save it;

[0109] Fourth step: repeat the second step and the third step above;

[0110] Fifth step: arrange the points according to the node order of the original tree to form a new tree.

[0111] Update the gradient value F m (x i ) of the decision tree;

[0112] Repeat the above process of establishing a decision tree and updating the gradient value until all decision trees are built to obtain local models of each participant.

[0113] (3) Based on the differential privacy algorithm, the parameters of the local model are encrypted to obtain an encrypted local model, comprising the following steps:

[0114] Calculate the global sensitivity;

[0115] Given a function f that maps local model parameters to real numbers, the global sensitivity of f is defined as the global sensitivity of f​ is defined as follows:

[0116] where d(x, x') denotes the distance between two parameters.

[0117] generate noise conforming to a Laplace distribution based on the global sensitivity;

[0118] encrypt the local model parameters based on the noise conforming to the Laplace distribution to obtain encrypted local models.

[0119] According to the Laplace mechanism, for a function that can output a numerical result Φ(x) defined as follows satisfies ∈-differential privacy:

[0120] where θ is the sensitivity of , ∈ is a privacy parameter, denotes Laplace distribution sampling. The sensitivity of the function is the change in the output of when the input changes from x to the adjacent x'.

[0121] (4) aggregating the encrypted local models of each participant to obtain a global model;

[0122] (5) performing classification and prediction tasks through the global model to obtain an output result.

[0123] In summary, the multi-party secure computing method and system based on a decision tree and privacy protection provided by the present application can exclude most small gradient samples in the data processing stage by using a gradient-based one-sided sampling algorithm, thereby reducing the data volume while ensuring the balance in accuracy. Then, a decision tree is constructed through a histogram algorithm, thereby reducing memory consumption and improving operation speed. In addition, differential privacy technology is used to encrypt and perturb the local model parameters, so as to ensure that individual privacy information is not leaked. The multi-party secure computing method based on a decision tree and privacy protection can efficiently and reliably implement classification and other prediction tasks while protecting privacy.

[0124] Embodiment 2:

[0125] A multi-party secure computing system based on a decision tree and privacy protection, as shown in FIG. 2, includes a data processing module 100, a decision tree construction module 200, a privacy protection module 300, and an aggregation output module 400.

[0126] The data processing module 100 performs data preprocessing on local data based on a gradient-based one-sided sampling algorithm to obtain preprocessed data, wherein the local data is from each participant.

[0127] The decision tree construction module 200 inputs the preprocessed data into a decision tree model for training to obtain a local model of each participant, wherein the decision tree model is optimized by a histogram algorithm to find an optimal split point;

[0128] The privacy protection module 300 encrypts parameters of the local model based on a differential privacy algorithm to obtain an encrypted local model;

[0129] The aggregation output module 400 aggregates the encrypted local models of the participants to obtain a global model, and classifies and predicts the to-be-processed local data through the global model to obtain an output result.

[0130] Various changes and modifications can be made to the application without departing from the spirit and scope of the application. All equivalent technical solutions belong to the scope of the application.

[0131] Each embodiment in the specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same and similar parts between the embodiments can be referred to each other.

[0132] Those skilled in the art should understand that the embodiments of the application can be provided as a method, device, or computer program product. Therefore, the application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the application can be in the form of a computer program product implemented on one or more computer usable storage media containing computer usable program code (including but not limited to disk storage, CD-ROM, optical storage, etc.).

[0133] The application is described with reference to flowcharts and / or block diagrams according to the method, terminal device (system), and computer program product of the application. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of the flows and / or blocks in the flowchart and / or block diagram can be realized by computer program instructions. These computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to produce a machine, so that the instructions executed by the computer or other programmable data processing terminal device produce a device for realizing the functions specified in one or more flows in the flowchart and / or one or more blocks in the block diagram.

[0134] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart or flowsheets and / or block or blocks of the block diagrams.

[0135] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart or flowsheets and / or block or blocks of the block diagrams.

[0136] It is to be understood that:

[0137] Reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the application. Thus, appearances of the phrases "one embodiment" or "an embodiment" throughout this specification are not necessarily all referring to the same embodiment.

[0138] The above description of the embodiments is given for clearness of understanding only. No unnecessary limitations are intended to be part of the application. It will be apparent to those skilled in the art that various modifications can be practiced within the scope of the application claimed and that the general principles applied can be employed to analogous embodiments. Such modifications and variations are intended to come within the scope of the application.

Claims

1. A method for multi-party secure computation based on decision tree and privacy protection, characterized in that, The method comprises the following steps: Data preprocessing is performed on local data based on a gradient-based one-sided sampling algorithm to obtain preprocessed data, wherein the local data is from each participant; The preprocessed data is input into a decision tree model for training to obtain a local model of each participant, wherein the decision tree model is optimized by a histogram algorithm to find an optimal split point; Parameters of the local model are encrypted based on a differential privacy algorithm to obtain an encrypted local model; The encrypted local model of each participant is aggregated to obtain a global model; The global model is used to classify and predict the to-be-processed local data to obtain an output result. 2.The method of claim 1, wherein, The data preprocessing on the local data based on the gradient-based one-sided sampling algorithm comprises the following steps: The gradient of a data sample is calculated, wherein the data sample is the local data; The data sample is arranged in descending order of the absolute value of the gradient to obtain an ordered data sample; The first gradient data is obtained by retaining the first a×100% of the ordered data sample, wherein a is a preset proportion threshold; Random sampling processing is performed on the (1-a)×100% of the ordered sample to obtain a random sampling result, and the sampling proportion is b×100%, b∈[0,1]; The random sampling result is multiplied by a balance coefficient to maintain the original distribution of the data sample to obtain second gradient data; The first gradient data and the second gradient data are summarized to obtain the preprocessed data. 3.The method of claim 1, wherein, The preprocessed data is input into the decision tree model for training to obtain the local model of each participant, comprising the following steps: The preprocessed data is subjected to bucketing processing and normalization processing to obtain a normalization result; The initial gradient value of the normalization result is calculated by a loss function, wherein a bgistic loss function is used as the loss function; A decision tree model is constructed based on the initial gradient value, and the initial gradient value of the decision tree model is updated; The process of constructing the decision tree model and the process of updating the initial gradient value of the decision tree model are repeated until the preset condition of the decision tree model is met, and then the local model of each participant is obtained.

4. The method of claim 3, wherein, The decision tree model is constructed, comprising the following steps: A corresponding segmentation function is constructed for each normalization result, and the values of all preprocessed data on the corresponding feature are divided into a box; A histogram is constructed for each normalization result to further convert the normalization result to find an optimal split point; The optimal split point is obtained from the histogram, and the best split feature and the best split feature value are selected based on the optimal split point; The root node of the decision tree is established by the best split feature and the best split feature value; The samples are split according to the best split feature and the best split feature value, and a pair-wise algorithm is used for judgment until all leaf nodes of the decision tree cannot be split or the maximum limit of splitting is reached, and then the decision tree model is obtained.

5. The method of claim 4, wherein, The histogram is constructed for each normalization result to further convert the normalization result to find an optimal split point, comprising the following steps: The normalization result is discretized into an integer, and a binning operation is used to construct a histogram; All normalization results are traversed, and the statistical value is accumulated in the histogram according to the discretized integer as an index; According to the statistical value of the histogram, the optimal split point is found by traversal.

6. The decision tree and privacy protection based multi-party secure computing method of claim 5, wherein the pair-wise algorithm is used for judgment until all leaf nodes of the decision tree cannot be split or the maximum limit of splitting is reached, and a decision tree model is obtained, including the following steps: Traverse the whole decision tree to obtain the position of each point, the split feature, and the feature value; Obtain the two-by-two combination of the position of each point, the split feature, and the feature value from top to bottom; Traverse each leaf node to determine whether the two-by-two combination has appeared in each leaf node, and if it has appeared, delete it, otherwise save it; Repeat the above steps to arrange all leaf nodes in the order of the nodes of the original decision tree, and then form a decision tree model.

7. The method of claim 1, wherein, The parameter of the local model is encrypted based on the differential privacy algorithm, and then an encrypted local model is obtained, including the following steps: Map the local model parameters of each participant, and calculate the global sensitivity; Generate noise conforming to the Laplace distribution based on the global sensitivity; Encrypt the local model parameters based on the noise conforming to the Laplace distribution to obtain an encrypted local model.

8. A multi-party secure computing system based on decision tree and privacy protection, characterized in that, The system comprises a data processing module, a decision tree construction module, a privacy protection module, and an aggregation output module. The data processing module performs data preprocessing on the local data based on the gradient one-sided sampling algorithm to obtain preprocessed data, wherein the local data is from each participant. The decision tree construction module inputs the preprocessed data into the decision tree model for training to obtain a local model of each participant, wherein the decision tree model is optimized by a histogram algorithm to find the optimal split point. The privacy protection module encrypts the parameters of the local model based on the differential privacy algorithm to obtain an encrypted local model. The aggregation output module aggregates the encrypted local models of each participant to obtain a global model. The global model is used to classify and predict the to-be-processed local data to obtain an output result.

9. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 8. The computer program is executed by the processor to implement the method of any one of claims 1 to 7.

10. A privacy-preserving multi-party secure computing apparatus based on decision tree, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, The processor executes the computer program to implement the method of any one of claims 1 to 7.

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