Data privacy protection method based on gaussian process regression and related device

Abstract

This invention discloses a data privacy protection method and related equipment based on Gaussian process regression, including: acquiring training data and test data; calculating the covariance matrix and training Gaussian process regression based on the training data; generating exponential random numbers and performing exponential calculation on a Gaussian integer ring using a secret sharing technique; decomposing the positive definite matrix in the Gaussian process regression according to the Joliski decomposition method, and inverting the decomposed positive definite matrix on a Gaussian integer ring using a secret sharing technique to construct a Gaussian process regression model; and predicting test data based on the Gaussian process regression model. This method can improve the efficiency of exponential calculation and achieve secure inversion without revealing the privacy of the input matrix.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a data privacy protection method, apparatus, smart terminal, and computer storage medium based on Gaussian process regression. Background Technology

[0002] Gaussian process regression (GPR) is widely used in various fields, such as disease detection and traffic prediction, to help improve the quality and efficiency of work in these areas. However, in practical applications, especially in key application areas such as finance and healthcare, the data used for GPR model building or prediction is often held by multiple parties. For reasons such as protecting personal privacy, data owners need to implement data privacy protection for multiple parties during the GPR model building and prediction stages.

[0003] In existing technologies, homomorphic encryption (HE) algorithms are typically used to encrypt prediction data, and the GPR algorithm achieves efficient privacy-preserving prediction through interactive computation between the server and the user. However, existing technologies usually employ polynomial approximation to implement nonlinear operations in GPR, such as exponentiation and division, which leads to low efficiency in protecting data privacy.

[0004] Therefore, existing technologies still need improvement and development. Summary of the Invention

[0005] The main objective of this invention is to provide a data privacy protection method, device, smart terminal, and computer storage medium based on Gaussian process regression. This invention aims to solve the problem that existing technologies typically employ polynomial approximation calculations to perform nonlinear operations such as exponentiation and division in Gaussian process regression, resulting in low efficiency in protecting data privacy.

[0006] To achieve the above objectives, a first aspect of the present invention provides a data privacy protection method based on Gaussian process regression, the data privacy protection method based on Gaussian process regression comprising:

[0007] Obtain training and test data;

[0008] Calculate the covariance matrix and train Gaussian process regression based on the training data;

[0009] Generate an exponential random number, and perform exponential calculation on a Gaussian integer ring based on the exponential random number using a secret sharing technique;

[0010] The positive definite matrix in Gaussian process regression is decomposed according to the Jolisky decomposition method. The inverse of the decomposed positive definite matrix is ​​then obtained on the Gaussian integer ring through the secret sharing technique, and a Gaussian process regression model is constructed.

[0011] The test data are predicted based on the Gaussian process regression model.

[0012] Optionally, the generation of exponential random numbers specifically includes:

[0013] The control assistance server generates exponential random numbers from the Gaussian integer ring. These exponential random numbers include a first random number, a second random number, a third random number, and a fourth random number, which satisfy the following expression:

[0014] ([r]0+[r]1)modL=r,

[0015] ([e r ]0+[e r 1) mod L = e r ,

[0016] Where [r]0 represents the first random number, [r]1 represents the second random number, r represents the modulus of L taken from ([r]0+[r]1), and [e r ]0 represents the third random number, [e r ]1 represents the fourth random number, e r Let r represent the natural constant raised to the power of r, and modL represents the modulo operation L;

[0017] The control assistance server sends the first random number and the third random number to the first computing server, and sends the second random number and the fourth random number to the second computing server.

[0018] Optionally, the step of calculating the exponent on a Gaussian integer ring based on the random number using a secret sharing technique specifically includes:

[0019] The input data is split into a first input data and a second input data using secret sharing technology;

[0020] Control the first computing server to input the first input data, and control the second computing server to input the second input data.

[0021] Optionally, the step of calculating the exponent on a Gaussian integer ring based on the random number using a secret sharing technique further includes:

[0022] The first computing server is controlled to calculate the first difference between the first input data and the first random number, and then send the first difference to the second computing server.

[0023] The second computing server is controlled to calculate the second difference between the second input data and the second random number, and then send the second difference to the first computing server.

[0024] The third difference is calculated based on the first difference and the second difference;

[0025] The first computing server is controlled to calculate and output the first output data based on the third difference and the third random number;

[0026] The second computing server is controlled to calculate and output the second output data based on the third difference and the fourth random number.

[0027] Optionally, the step of decomposing the positive definite matrix in Gaussian process regression according to the Jolisky decomposition method specifically includes:

[0028] The positive definite matrix in Gaussian process regression is decomposed according to the first expression, which is:

[0029] U = LDL T ,

[0030] Among them, U=(u h,k h,k=1,2,...,n, represents a symmetric positive definite matrix; u h,k Let h and k represent the elements of matrix U, and let L = (l h,k h,k=1,2,...,n, represents a unit lower triangular matrix, l h,k Denotes the elements of matrix L, D = (d k ), k = 1, 2, ..., n, representing a diagonal matrix, d k Represents the elements of matrix D.

[0031] Optionally, the step of inverting the decomposed positive definite matrix on a Gaussian integer ring using a secret-sharing technique specifically includes:

[0032] The input positive definite matrix is ​​split into a first positive definite matrix and a second positive definite matrix using a secret sharing technique.

[0033] The first computing server is controlled to input the first positive definite matrix, and the second computing server is controlled to input the second positive definite matrix.

[0034] Optionally, the step of inverting the decomposed positive definite matrix on the Gaussian integer ring using the secret sharing technique further includes:

[0035] The process of finding the inversion of the positive definite matrix in Gaussian process regression is transformed into a combination of addition, multiplication, and division operations;

[0036] The first computing server is controlled to call addition, multiplication, and division algorithms to invert the first positive definite matrix and output the result;

[0037] The second computing server is controlled to call addition, multiplication, and division algorithms to invert the second positive definite matrix and output the results.

[0038] A second aspect of the present invention provides a data privacy protection device based on Gaussian process regression, characterized in that the data privacy protection device based on Gaussian process regression comprises:

[0039] The acquisition module is used to acquire training and test data.

[0040] The training module is used to calculate the covariance matrix and train Gaussian process regression based on the training data.

[0041] The calculation module is used to generate exponential random numbers and perform exponential calculations on a Gaussian integer ring based on the exponential random numbers using a secret sharing technique.

[0042] The inversion module is used to decompose the positive definite matrix in Gaussian process regression according to the Choliski decomposition method. Through the secret sharing technique, the inversion of the decomposed positive definite matrix is ​​carried out on the Gaussian integer ring to construct the Gaussian process regression model.

[0043] The prediction module is used to predict the test data based on the Gaussian process regression model.

[0044] A third aspect of the present invention provides a smart terminal, the smart terminal including a memory, a processor, and a data privacy protection program based on Gaussian process regression stored in the memory and executable on the processor, wherein the data privacy protection program based on Gaussian process regression, when executed by the processor, implements the steps of the data privacy protection method based on Gaussian process regression as described above.

[0045] A fourth aspect of the present invention provides a computer storage medium storing a data privacy protection program based on Gaussian process regression, wherein the data privacy protection program based on Gaussian process regression, when executed by a processor, implements the steps of the data privacy protection method based on Gaussian process regression as described above.

[0046] As can be seen from the above, the present invention discloses a data privacy protection method based on Gaussian process regression. The method includes: acquiring training data and test data; calculating the covariance matrix and training Gaussian process regression based on the training data; generating exponential random numbers and performing exponential calculations on a Gaussian integer ring using a secret sharing technique; decomposing the positive definite matrix in the Gaussian process regression using the Choliski decomposition method and inverting the decomposed positive definite matrix on a Gaussian integer ring using the secret sharing technique to construct a Gaussian process regression model; and predicting the test data based on the Gaussian process regression model. Compared with existing technologies, the present invention improves the efficiency of exponential calculation by performing exponential operations on a Gaussian integer ring using the secret sharing technique, and the decomposition of the positive definite matrix in the Gaussian process regression using the Choliski decomposition method and the inversion of the decomposed positive definite matrix can achieve secure inversion without leaking the privacy of the input matrix. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a flowchart illustrating a data privacy protection method based on Gaussian process regression provided in an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram of the process of constructing and predicting the Gaussian process regression algorithm model provided in the embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of a data privacy protection device based on Gaussian process regression provided in an embodiment of the present invention;

[0051] Figure 4 This is a block diagram illustrating the internal structure of a smart terminal provided in an embodiment of the present invention.

[0052] Figure 5 This is a schematic diagram comparing the accuracy of the exponential algorithm provided in the embodiments of the present invention;

[0053] Figure 6 This is a schematic diagram comparing the accuracy of positive definite matrix inversion provided in an embodiment of the present invention;

[0054] Figure 7 This is a schematic diagram comparing the efficiency of positive definite matrix inversion provided in an embodiment of the present invention. Detailed Implementation

[0055] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0056] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0057] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0058] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0059] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrases "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0062] In existing technologies, the following methods are commonly used to protect the privacy of multi-party data during the GPR model building and prediction stages:

[0063] By using the HE algorithm to encrypt prediction data and performing interactive calculations between the server and the user, the GPR algorithm achieves efficient privacy-preserving prediction. The drawbacks of the above method are: on the one hand, it can only protect the privacy of the prediction data of the model user, but cannot protect the data privacy during the GPR model construction process; on the other hand, due to the use of polynomial approximation calculation to implement nonlinear operations in GPR, such as exponentiation and division, the algorithm is inefficient in protecting data privacy.

[0064] Differential privacy (DP) is used to protect the privacy of training data label information by adding noise that meets certain conditions. However, the drawback of this method is that it can only protect the privacy information of the GPR algorithm label data, but cannot protect other privacy information of GPR in the process of model building and prediction, such as training data and prediction data. In addition, the above method requires the injection of noise to achieve privacy protection during the GPR model building process, which makes the algorithm perform poorly in protecting data privacy.

[0065] Federated learning (FL) is used to build a privacy-preserving model of GPR by exchanging GPR-related parameter information, thus avoiding the direct transmission of raw privacy data. The disadvantage of the above method is that it is only applicable to the construction of GPR model in the scenario of horizontal partitioning of privacy data, and the parameter information exchanged during the model construction process may leak users' privacy data.

[0066] To address the problems existing in the prior art, this embodiment proposes a data privacy protection method, device, smart terminal, and computer storage medium based on Gaussian process regression, which can improve the efficiency of exponential operations and achieve secure inversion without leaking the privacy of the input matrix.

[0067] Exemplary methods

[0068] In this embodiment, χ is a d-dimensional input domain, for each The corresponding output is Let the noise variance be... function Noise observations. Function Modeling is done using Gaussian process regression, meaning that for each finite subset... Both follow a multivariate Gaussian distribution, and their Gaussian process regression is entirely determined by their prior mean. Covariance Specify, where

[0069]

[0070] Assumption Covariance is defined by a kernel function. Specifically, the kernel function can be a squared exponential (SE) kernel, as shown in expression (1):

[0071]

[0072] Where l represents the length range, σ s This represents the sign variance.

[0073] Suppose we have a set containing n samples. in The GPR model can be tested with any test input. Provide prediction distribution To perform probabilistic regression, let Given an n×d input matrix, Given a column vector of n noise outputs, predict the distribution. The posterior mean can be calculated using expression (2) to predict the distribution. The variance can be calculated using expression (3).

[0074]

[0075]

[0076] in, It is a 1×n matrix. It is an n×n matrix.

[0077] Assumption It has been trained and is publicly available on the computing server. At this point, the main operations involved in the model construction and prediction process of the Gaussian process regression algorithm are: addition, multiplication, exponentiation, and inversion of positive definite matrices. Among them, secure addition and secure multiplication operations based on secret sharing technology have been implemented in existing technologies.

[0078] To address the issues of security indices and positive definite matrix inversion, this embodiment provides a data privacy protection method based on Gaussian process regression. This embodiment employs a three-party semi-honest security model, where the Gaussian process regression algorithm runs on three mutually non-colluding servers. These three servers include two computation servers and one assistant server. Specifically, as follows... Figure 1 As shown, the method includes the following steps:

[0079] Step S100: Obtain training data and test data.

[0080] Step S200: Calculate the covariance matrix and train Gaussian process regression based on the training data.

[0081] The training data includes first training data and second training data. The first computing server is controlled to calculate the covariance matrix based on the first training data, and the second computing server is controlled to calculate the covariance matrix based on the second training data.

[0082] Step S300: Generate an exponential random number, and perform exponential calculation on a Gaussian integer ring based on the exponential random number using a secret sharing technique.

[0083] In some embodiments, generating exponential random numbers specifically includes: controlling an assistance server to generate exponential random numbers from the Gaussian integer ring, wherein the exponential random numbers include a first random number, a second random number, a third random number, and a fourth random number, and the first random number, the second random number, the third random number, and the fourth random number satisfy the following expression:

[0084] ([r]0+[r]1)modL=r,

[0085] ([e r ]0+[e r 1) mod L = e r ,

[0086] Where [r]0 represents the first random number, [r]1 represents the second random number, r represents the modulus of L taken from ([r]0+[r]1), and [e r ]0 represents the third random number, [e r ]1 represents the fourth random number, e r The natural constant r is raised to the power of r, and modL represents the modulo operation L; that is, the generated random numbers must satisfy the above expression.

[0087] The control assistance server sends the first random number and the third random number to the first computing server, and sends the second random number and the fourth random number to the second computing server.

[0088] In some embodiments, the step of performing exponential calculation on a Gaussian integer ring based on the random number using a secret sharing technique specifically includes: splitting the input data into first input data and second input data using a secret sharing technique; controlling the first computing server to input the first input data; and controlling the second computing server to input the second input data.

[0089] In some embodiments, the step of performing exponential calculation on a Gaussian integer ring based on the random number using the secret sharing technique further includes: controlling the first computing server to calculate a first difference between the first input data and the first random number, and sending the first difference to the second computing server; controlling the second computing server to calculate a second difference between the second input data and the second random number, and sending the second difference to the first computing server; calculating a third difference based on the first difference and the second difference; controlling the first computing server to calculate and output first output data based on the third difference and the third random number; and controlling the second computing server to calculate and output second output data based on the third difference and the fourth random number.

[0090] In another embodiment, an exponential random number is generated, and an exponential calculation is performed on a Gaussian integer ring based on the exponential random number using a secret sharing technique. This is called a secure exponential algorithm. In the secure exponential algorithm, the shares[u]0,[u]1 of the server input u are calculated, and e is obtained with the help of the assisting server. u shares[e u ]0,[e u 1. Includes the following methods:

[0091] The first computing server is controlled to input [u]0, and the second computing server is controlled to input [u]1;

[0092] The offline phase includes:

[0093] Control assistance server from integer ring Z L Randomly generate [r]0, [r]1, [e] r ]0,[e r ]1,[r]0,[r]1,[e r ]0,[e r ]1 satisfies ([r]0+[r]1)modL=r and ([e r ]0+[e r 1) mod L = e r ;

[0094] The control and assistance server will [r]0, [e r ]0 is sent to the first computing server; [r]1, [e r]1 is sent to the second computing server.

[0095] The online phase includes:

[0096] For j∈{0,1}:

[0097] Control computing server S j Calculate d respectively j =[u] j -[r] j =[ur] j And send it to the other party;

[0098] Control computing server S j Reconstruct d = ([d]0 + [d]1) mod L = ur;

[0099] Control computing server S j Local computing [e u ] j =e d ·[e r ] j modL;

[0100] Control computing server S j Output [e u ] j ;

[0101] Control the output of the first computing server [e u ]0, the second computing server outputs [e u ]1.

[0102] The security index algorithm in this embodiment only requires the control computing server to spend one round of communication to reconstruct d = ur, with a total communication volume of 2^l. Utilizing parallel computing, the security index algorithm in this embodiment of the patent can complete the security index calculation for n data points through one round of 2^nl bit communication, improving computational efficiency.

[0103] Step S400: Decompose the positive definite matrix in Gaussian process regression according to the Jolisky decomposition method. Then, through the secret sharing technique, invert the decomposed positive definite matrix on the Gaussian integer ring to construct the Gaussian process regression model.

[0104] In some embodiments, the step of decomposing the positive definite matrix in Gaussian process regression according to the Joliski decomposition method specifically includes: decomposing the positive definite matrix in Gaussian process regression according to a first expression, wherein the first expression is:

[0105] U = LDL T ,

[0106] Among them, U=(u h,kh,k=1,2,...,n, represents a symmetric positive definite matrix; u h,k Let h and k represent the elements of matrix U, and let L = (l h,k h,k=1,2,...,n, represents a unit lower triangular matrix, l h,k Denotes the elements of matrix L, D = (d k ), k = 1, 2, ..., n, representing a diagonal matrix, d k Represents the elements of matrix D.

[0107] For a symmetric positive definite matrix U = (u h,k h,k=1,2,...,n, can be decomposed into U=LDL using the Choliski decomposition method. T Specifically, L and D can be calculated using the following expressions:

[0108]

[0109]

[0110] Let V = DL T U -1 Then LV = LDL T U -1 =UU -1 =I, where I is the identity matrix. V = L is calculated using the following expression. -1 :

[0111]

[0112] At this point, U can be calculated. -1 =(LDL) T ) -1 =(L -1 ) T D -1 L -1

[0113] In some embodiments, the step of inverting the decomposed positive definite matrix on the Gaussian integer ring using a secret sharing technique specifically includes: splitting the input positive definite matrix into a first positive definite matrix and a second positive definite matrix using a secret sharing technique; controlling the first computing server to input the first positive definite matrix; and controlling the second computing server to input the second positive definite matrix.

[0114] In some embodiments, the step of inverting the decomposed positive definite matrix on the Gaussian integer ring using the secret sharing technique further includes: converting the inversion process of the positive definite matrix in Gaussian process regression into a combination of addition, multiplication, and division operations; controlling the first computing server to call the addition, multiplication, and division algorithms to invert the first positive definite matrix and output the result; and controlling the second computing server to call the addition, multiplication, and division algorithms to invert the second positive definite matrix and output the result.

[0115] In another embodiment, the positive definite matrix in Gaussian process regression is decomposed according to the Joliski decomposition method. The inversion of the decomposed positive definite matrix on the Gaussian integer ring is performed using a secret sharing technique, known as the secure positive definite matrix inversion algorithm. In this algorithm, shares[U]0,[U]1 of the server input positive definite matrix U are calculated. With the assistance of the assisting server, U is obtained. -1 shares[U -1 ]0,[U -1 1. Includes the following methods:

[0116] The first computing server is controlled to input [U]0, and the second computing server is controlled to input [U]1;

[0117] The offline phase includes:

[0118] Control assistance server from integer ring Z L Generate a sufficient number of random numbers a, b, c, such that a, b, c satisfy a·b=c;

[0119] The control assistance server will [a] j [b] j [c] j Send to S j .

[0120] The online phase includes:

[0121] For j∈{0,1}; control computing server S j Let [d1] be respectively. j =[u 1,1 ] j Control computing server S j By calling the safe division algorithm, [l] is calculated. 1:n,1 ] j =[u 1:n,1 ] j / [u 1,1 ] j ;

[0122] For k∈{2,3,...,n}: Control computing server S jBy invoking the safe multiplication algorithm, the calculation is performed. Control computing server S j By invoking the safe multiplication algorithm, the calculation is performed. Control computing server S j By invoking the safe multiplication algorithm, the calculation is performed.

[0123] Control computing server S j [L] j [D] j .

[0124] Let v 1,1 ←1, For j∈{0,1}: For k∈{2,3,...,n}: Control computation server S j By invoking the safe multiplication algorithm, the calculation is performed.

[0125] Control computing server S j Get [V] j ;

[0126] Control computing server S j [U] is calculated by calling the safe multiplication algorithm. -1 ] j =[V T D -1 V] j ;

[0127] Control computing server S j Output [U -1 ] j ;

[0128] Control the output of the first computing server [e u ]0, the second computing server outputs [e u ]1.

[0129] Step S500: Predict the test data based on the Gaussian process regression model.

[0130] It should be noted that the meanings of the above symbols are shown in Table 1:

[0131] Table 1

[0132] symbol meaning <![CDATA[Z L ,L=2 32 (2 64 )]]> Integer ring <![CDATA[[x]0,[x]1∈Z L The condition [x]0 + [x]1 = x is satisfied. <![CDATA[Additive shares over ring Z L > [l:n] From l to n

[0133] This embodiment employs a three-way semi-honest security model. The Gaussian process regression algorithm runs on three servers that do not collude with each other in any pair. These three servers include two computation servers and one assistant server. The computation servers handle data input and output, while the assistant server generates and sends random numbers that meet preset conditions during the computation process, assisting the computation servers in completing the privacy-preserving training and prediction process. Specifically, as... Figure 2 As shown, the training data (training data X and label y) includes first training data ([X]0,[y]0) and second training data ([X]1,[y]1). The first computing server is controlled to input the first input data, and the second computing server is controlled to input the second input data. The first computing server and the second computing server calculate the covariance matrix according to the first input data and the second input data respectively. Then, a Gaussian process regression model is constructed according to the safety index algorithm and the safety positive definite matrix inversion algorithm provided in this embodiment, and the training data is predicted according to the Gaussian regression model.

[0134] It should be noted that in the Gaussian process regression algorithm model construction and prediction process, it is assumed that one of the computing servers is controlled by a semi-honest adversary A. The adversary can obtain the internal state of this computing server during protocol execution. Adversary A will not violate the rules of the protocol during execution, but will attempt to obtain more advantageous information based on the obtained internal state. In this embodiment, a probabilistic multinomial time simulator is set up. During the Gaussian process regression algorithm model construction and prediction process, the simulator can obtain more information by analyzing the input and output information of the computing server and the publicly available parameters (already trained). Simulating the internal state of the computing server in a way that makes it indistinguishable from the real state indicates that the process is secure under a semi-honest model.

[0135] It should also be noted that, for If b is a random uniform distribution on Z and is independent of a, then a+b is also on Z. L The elements are randomly and uniformly distributed and are independent of each other.

[0136] In the security index algorithm, the input information is [u]0, [u]1, and the output information is [e]. u ]0,[e u ]1. Its correctness can be verified by the following equation:

[0137] [e u ]0+[e u ]1=e d ·[e r ]0+e d ·[e r ]1

[0138] =e d ·([e r ]0+[e r ]1)

[0139] =e d ·e r =e u-r ·e r

[0140] =e u

[0141] Therefore, in this embodiment, the security index algorithm, under the semi-honest model, calculates [e] by inputting [u]0 and [u]1. u ]0,[e u ]1, satisfying ([e u ]0+[e u 1) mod L = e u .

[0142] In terms of security, during the execution of the security index algorithm, the assisting server only generates random numbers that meet the public conditions in the offline stage. Therefore, there exists a polynomial time simulator S that can simulate the view of the assisting server, making it impossible for the semi-honest adversary A to distinguish it from the real computational view.

[0143] The view of the first computing server is {[u]0,[r]0,[e]0,[r ... r ]0,d}, where [u]0 is the input information, and {[r]1,[e]1,d} r ]1} For opponent A, it is in Z L The random uniform distribution is on Z, where d = ur is in Z. L The data are randomly and uniformly distributed on the plane and are independent of each other with u. Therefore, there exists a polynomial time simulator that can simulate the view of the first server and make it impossible for the semi-honest adversary A to distinguish it from the real view.

[0144] Similarly, it can be proven that a polynomial-time simulator exists that can simulate the view of the second computing server, making it impossible for the semi-honest adversary A to distinguish it from the real view. Therefore, the exponential function is safe in this embodiment under the semi-honest model.

[0145] As can be seen from the above, the present invention discloses a data privacy protection method based on Gaussian process regression. The method includes: acquiring training data and test data; calculating the covariance matrix and training Gaussian process regression based on the training data; generating exponential random numbers and performing exponential calculations on a Gaussian integer ring using a secret sharing technique; decomposing the positive definite matrix in the Gaussian process regression using the Choliski decomposition method and inverting the decomposed positive definite matrix on a Gaussian integer ring using the secret sharing technique to construct a Gaussian process regression model; and predicting the test data based on the Gaussian process regression model. Compared with existing technologies, the present invention improves the efficiency of exponential calculation by performing exponential operations on a Gaussian integer ring using the secret sharing technique, and the decomposition of the positive definite matrix in the Gaussian process regression using the Choliski decomposition method and the inversion of the decomposed positive definite matrix can achieve secure inversion without leaking the privacy of the input matrix.

[0146] Exemplary device

[0147] like Figure 3 As shown, corresponding to the data privacy protection method based on Gaussian process regression, this embodiment of the invention also provides a data privacy protection device based on Gaussian process regression, the data privacy protection device based on Gaussian process regression comprising:

[0148] Module 301 is used to acquire training data and test data;

[0149] Training module 302 is used to calculate the covariance matrix and train Gaussian process regression based on the training data;

[0150] Calculation module 303 is used to generate exponential random numbers and perform exponential calculation on a Gaussian integer ring based on the exponential random numbers using a secret sharing technique;

[0151] The inversion module 304 is used to decompose the positive definite matrix in Gaussian process regression according to the Choliski decomposition method, and to invert the decomposed positive definite matrix on the Gaussian integer ring through the secret sharing technique to construct the Gaussian process regression model.

[0152] The prediction module 305 is used to predict the test data based on the Gaussian process regression model.

[0153] Specifically, in this embodiment, the specific functions of the data privacy protection device based on Gaussian process regression and its various modules can be referred to the corresponding description in the data privacy protection method based on Gaussian process regression, and will not be repeated here.

[0154] Based on the above embodiments, the present invention also provides a smart terminal, the principle block diagram of which can be as follows: Figure 4 As shown. The smart terminal includes a processor and a memory. The memory of the smart terminal includes a data privacy protection program based on Gaussian process regression, and the memory provides an environment for the operation of the data privacy protection program based on Gaussian process regression. When the Gaussian process regression-based data privacy protection program is executed by the processor, it refers to the steps for implementing any of the above-described data privacy protection methods based on Gaussian process regression.

[0155] Those skilled in the art will understand that Figure 4 The block diagram shown is merely a partial structural diagram related to the present invention and does not constitute a limitation on the smart terminal to which the present invention is applied. Specifically, the smart terminal may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0156] In one embodiment, when the aforementioned data privacy protection program based on Gaussian process regression is executed by the aforementioned processor, it performs the following operation instructions:

[0157] Obtain training and test data;

[0158] Calculate the covariance matrix and train Gaussian process regression based on the training data;

[0159] Generate an exponential random number, and perform exponential calculation on a Gaussian integer ring based on the exponential random number using a secret sharing technique;

[0160] The positive definite matrix in Gaussian process regression is decomposed according to the Jolisky decomposition method. The inverse of the decomposed positive definite matrix is ​​then obtained on the Gaussian integer ring through the secret sharing technique, and a Gaussian process regression model is constructed.

[0161] The test data are predicted based on the Gaussian process regression model.

[0162] This invention also provides a computer storage medium storing a data privacy protection program based on Gaussian process regression. When the Gaussian process regression-based data privacy protection program is executed by a processor, it implements the steps of any of the data privacy protection methods based on Gaussian process regression provided in this invention.

[0163] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0164] Model simulation analysis:

[0165] To verify the effectiveness of this embodiment, the accuracy and computational efficiency of the security index algorithm and security matrix inversion algorithm proposed in this patent were tested.

[0166] The specific testing process is as follows:

[0167] Security Index Algorithm: The security index algorithm (PP-Exp) in this embodiment is compared with the calculation results of the plaintext index algorithm, the Crypton security index algorithm, and the algorithm using a sixth-order polynomial approximation (Poly). The results are as follows: Figure 5 As shown, by Figure 5 It can be seen that the calculation results of the security index algorithm proposed in this embodiment are better than those of other security index algorithms.

[0168] Safe matrix inversion algorithm: By randomly generating covariance matrices of different dimensions Where X∈[-10,10] n,2 The computational accuracy and computation time of the secure matrix inversion algorithm (PP-MI) proposed in this patent were tested and compared with those of plaintext decomposition and inversion (Plaintext-Cholesky) and the plaintext inversion algorithm built into PyTorch (Plaintext-inv). Figure 6 This diagram illustrates a comparison of the computational accuracy of the positive definite matrix inversion algorithm in this embodiment. Figure 7 This diagram illustrates the comparison of computation time between the positive definite matrix inversion algorithm and the computation time of the matrix inversion algorithm in this embodiment. Dimonsion of matrix represents the matrix size, and Λ is the computation result of the matrix inversion algorithm. ||UΛ-I|| 2 This measures the computational error of the inversion algorithm. Figure 6 and Figure 7 It can be seen that the algorithm for inverting a safe positive definite matrix in this embodiment is superior to other algorithms in terms of accuracy and efficiency.

[0169] In a specific implementation, the training data can be a traffic dataset or a diabetes dataset. In this embodiment, when the training data is a traffic dataset, the SE kernel is used, and the parameter σ is set on the traffic dataset. s =0.7969, l = 0.6276; When the training data is a diabetes dataset, the SE kernel is used, and its parameter σ is set on the diabetes dataset. s =1.0, l = 0.06.

[0170] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the above device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this invention. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0171] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0172] In the embodiments provided by this invention, it should be understood that the disclosed apparatus / terminal devices and methods can be implemented in other ways. For example, the apparatus / terminal device embodiments described above are merely illustrative. For instance, the division of the above modules or units is merely a logical functional division, and in actual implementation, it can be divided in other ways. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0173] If the integrated modules / units described above are implemented as software functional units and sold or used as independent products, they can be stored in a computer storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer-readable medium described above may include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the above computer storage medium may be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction.

[0174] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not mean that the essence of the corresponding technical solutions deviates from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A data privacy protection method based on Gaussian process regression, characterized in that, The data privacy protection method based on Gaussian process regression includes: Obtain training and test data; Calculate the covariance matrix and train Gaussian process regression based on the training data; Generate an exponential random number, and perform exponential calculation on a Gaussian integer ring based on the exponential random number using a secret sharing technique; The positive definite matrix in Gaussian process regression is decomposed according to the Choliski decomposition method. The inverse of the decomposed positive definite matrix is ​​then obtained on the Gaussian integer ring through the secret sharing technique, and a Gaussian process regression model is constructed. The test data are predicted based on the Gaussian process regression model. The control assistance server generates exponential random numbers from the Gaussian integer ring, the exponential random numbers including a first random number, a second random number, a third random number, and a fourth random number; The method of calculating the exponent on a Gaussian integer ring based on the random number using a secret sharing technique specifically includes: The input data is split into a first input data and a second input data using secret sharing technology; Control the first computing server to input the first input data, and control the second computing server to input the second input data; The method of performing exponential calculation on a Gaussian integer ring based on the random number using a secret sharing technique specifically includes: The first computing server is controlled to calculate the first difference between the first input data and the first random number, and then send the first difference to the second computing server. The second computing server is controlled to calculate the second difference between the second input data and the second random number, and then send the second difference to the first computing server. The third difference is calculated based on the first difference and the second difference; The first computing server is controlled to calculate and output the first output data based on the third difference and the third random number; The second computing server is controlled to calculate and output the second output data based on the third difference and the fourth random number.

2. The data privacy protection method based on Gaussian process regression according to claim 1, characterized in that, The generation of exponential random numbers specifically includes: The first random number, the second random number, the third random number, and the fourth random number satisfy the following expression: ， ， in, Represents the first random number. Represents the second random number. Indicates to Pick The model, Represents the third random number. Represents the fourth random number. Representing the natural constant to the power of, Indicates modulo Operations; The control assistance server sends the first random number and the third random number to the first computing server, and sends the second random number and the fourth random number to the second computing server.

3. The data privacy protection method based on Gaussian process regression according to claim 1, characterized in that, The decomposition of the positive definite matrix in Gaussian process regression according to the Jolisky decomposition method specifically includes: The positive definite matrix in Gaussian process regression is decomposed according to the first expression, which is: ， in, , represents a symmetric positive definite matrix; Representation matrix elements, and Indicates the index of an element. , represents a unit lower triangular matrix. Representation matrix elements, , represents a diagonal matrix. Representation matrix Element.

4. The data privacy protection method based on Gaussian process regression according to claim 1, characterized in that, The method of inverting the decomposed positive definite matrix on a Gaussian integer ring using a secret sharing technique specifically includes: The input positive definite matrix is ​​split into a first positive definite matrix and a second positive definite matrix using a secret sharing technique. The first computing server is controlled to input the first positive definite matrix, and the second computing server is controlled to input the second positive definite matrix.

5. The data privacy protection method based on Gaussian process regression according to claim 4, characterized in that, The method of inverting the decomposed positive definite matrix on the Gaussian integer ring using the secret sharing technique specifically includes: The process of finding the inversion of the positive definite matrix in Gaussian process regression is transformed into a combination of addition, multiplication, and division operations; The first computing server is controlled to call addition, multiplication, and division algorithms to invert the first positive definite matrix and output the result; The second computing server is controlled to call addition, multiplication, and division algorithms to invert the second positive definite matrix and output the results.

6. A data privacy protection device based on Gaussian process regression, characterized in that, The data privacy protection device based on Gaussian process regression is used to implement the data privacy protection method based on Gaussian process regression according to any one of claims 1-5, and the data privacy protection device based on Gaussian process regression includes: The acquisition module is used to acquire training and test data. The training module is used to calculate the covariance matrix and train Gaussian process regression based on the training data. The calculation module is used to generate exponential random numbers and perform exponential calculations on a Gaussian integer ring based on the exponential random numbers using a secret sharing technique. The inversion module is used to decompose the positive definite matrix in Gaussian process regression according to the Choliski decomposition method. Through the secret sharing technique, the inversion of the decomposed positive definite matrix is ​​carried out on the Gaussian integer ring to construct the Gaussian process regression model. The prediction module is used to predict the test data based on the Gaussian process regression model.

7. A smart terminal, characterized in that, The smart terminal includes a memory, a processor, and a data privacy protection program based on Gaussian process regression stored in the memory and executable on the processor. When the Gaussian process regression-based data privacy protection program is executed by the processor, it implements the steps of the data privacy protection method based on Gaussian process regression as described in any one of claims 1-5.

8. A computer storage medium, characterized in that, The computer storage medium stores a data privacy protection program based on Gaussian process regression, which, when executed by a processor, implements the steps of the data privacy protection method based on Gaussian process regression as described in any one of claims 1-5.

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