CN114417414A - Privacy protection method based on edge calculation - Google Patents

Privacy protection method based on edge calculation Download PDF

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CN114417414A
CN114417414A CN202210067677.1A CN202210067677A CN114417414A CN 114417414 A CN114417414 A CN 114417414A CN 202210067677 A CN202210067677 A CN 202210067677A CN 114417414 A CN114417414 A CN 114417414A
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杨国强
孙晨昊
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Sanwei Xin'an Technology Co ltd
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    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract

The invention discloses a privacy protection method based on edge calculation, which is applied to a system consisting of a user client and an edge server; the method comprises the following steps: a user client generates a key and encrypts an original input; the user client sends a computing task and the encrypted original input to an edge server; the edge server calculates the encrypted original input according to the calculation task and returns a calculation result to the user client; the user client receives a calculation result returned by the edge server and verifies the correctness of the calculation result; and when the calculation result passes the verification, the user client decrypts the calculation result by using the key to obtain the original output corresponding to the original input. The method designs a safe algorithm for outsourcing the optimization problem with the equality constraint condition for the resource-limited Internet of things equipment, and is beneficial to improving the working efficiency of the Internet of things equipment and reducing the consumption of computing resources.

Description

Privacy protection method based on edge calculation
Technical Field
The invention relates to the field of information security, in particular to a privacy protection method based on edge calculation, and relates to a convex optimization problem of equality constraint.
Background
The convex optimization problem with equality constraints is one of the most common mathematical problems in the field of machine learning and in the field of smart grids. The convex optimization problem with equality constraints can be defined in the form:
Figure BDA0003480825990000011
here f (x):
Figure BDA0003480825990000012
is a non-linear and convex objective function; x ═ x1,x2,...,xn)TIs an n-dimensional optimization vector; a is an n x m dimensional matrix and is a column full rank matrix; b ═ b1,b2,...,bm)TIs an m-dimensional boundary vector.
For a convex optimization problem with equality constraints, define μ (A) as
Figure BDA00034808259900000112
Is generated from each column in matrix a. a isiRepresenting the columns in matrix a.
Figure BDA0003480825990000013
Figure BDA0003480825990000014
Can be decomposed into μ (A) and μ (A) orthogonal complement spaces. The mu (A) orthogonal complement space is defined as mu (A)⊥。
Figure BDA0003480825990000015
Therefore, the first and second electrodes are formed on the substrate,
Figure BDA0003480825990000016
can be expressed in the following form:
Figure BDA0003480825990000017
the matrix a has a QR decomposition as follows:
Figure BDA0003480825990000018
wherein
Figure BDA0003480825990000019
And
Figure BDA00034808259900000110
q is an orthogonal matrix and R is a lower triangular matrix. The substrate of μ (A) can be easily found to be Q1Each column in (1) constitutes, mu (A)⊥Is composed of a substrate of2Each column of (1). The vector x can be expressed as:
Figure BDA00034808259900000111
then, the user can use the device to perform the operation,
Figure BDA0003480825990000021
can be calculated by
Figure BDA0003480825990000022
And obtaining u. Therefore, the first and second electrodes are formed on the substrate,
Figure BDA0003480825990000023
solving unconstrained optimization problems by applying some existing algorithms
Figure BDA0003480825990000024
Figure BDA0003480825990000025
The original solution to the convex optimization problem with the equality constraints can be obtained.
The scale of a convex optimization problem is often large because in real life there are many variables and constraints to be taken into account. For example, the SVM algorithm is a classical machine learning algorithm, and is actually a convex optimization problem. The user can use the lagrangian method to train the model and adjust the parameters. When the training data set is large in scale, the training process is complex and time consuming. In the smart grid system, engineers need to consider many influencing factors, such as the number of users and the topology of the grid system, in order to make a reasonable power supply strategy. A user can convert the convex optimization problem with equality constraint conditions into the optimization problem without constraint conditions by a simplified constraint method. In this process, the involved complex operation is QR decomposition, which is also a mathematical tool commonly used in data analysis. For example, in a smart grid, engineers may utilize QR decomposition to estimate the state of the system. For an n × m dimensional matrix, the temporal complexity of QR decomposition is O (mn)2). This makes it difficult for some resource-constrained internet-of-things devices to perform this computational task.
Therefore, how to design a safe algorithm for outsourcing an optimization problem with equality constraint conditions for the resource-limited internet-of-things equipment, improve the working efficiency of the internet-of-things equipment, reduce the consumption of computing resources and become a key problem which needs to be solved urgently.
Disclosure of Invention
The invention mainly aims to provide a privacy protection method based on edge computing, which is based on edge server auxiliary computing and encryption matrix technology, designs a privacy protection method based on edge computing and with an equality constraint convex optimization problem, and can solve the problem that resource-limited Internet of things equipment is difficult to execute a computing task. The method can help to improve the working efficiency of the Internet of things equipment and reduce the consumption of computing resources.
In order to achieve the purpose, the invention adopts the technical scheme that:
the embodiment of the invention provides a privacy protection method based on edge calculation, which is applied to a system consisting of a user client and an edge server; the method comprises the following steps:
s10, generating a key by the user client, and encrypting the original input by using the key;
s20, the user client sends a calculation task and the encrypted original input to an edge server;
s30, the edge server calculates the encrypted original input according to the calculation task and returns the calculation result to the user client;
s40, the user client receives the calculation result returned by the edge server and verifies the correctness of the calculation result;
and S50, when the calculation result is verified, the user client decrypts the calculation result by using the key to obtain the original output corresponding to the original input.
Further, in step S10, the user client generating the key includes: user client generates a series of orthogonal key matrix GiAnd a series of upper triangular key matrices Pi。
Further, the original input is set as matrix A, the row number of matrix A is used as input, and orthogonal key matrix G is usedi1,2, n, as an expected output;
the series of orthogonal key matrices GiThe generation process is as follows:
1) setting a set Ω ═ 1, ·., n };
2) sequentially traversing the elements in the set Ω ═ { 1.·.., n }, and performing steps 3) -6);
3) setting GiIs an identity matrix, wherein the index i is an index value and represents the ith matrix; randomly selecting an angle theta from (0 deg., 360 deg.)i(ii) a Setting ci＝cosθiAnd si＝sinθi；
4) Setting alphaiI and deleting i from the set Ω { 1.
5) Randomly selecting a number j from a set Ω ═ 1...., n };matrix GiThe element in (1) is set to gi,i＝ci,gj,j＝ci,gi,j＝-si,gj,i＝si；
6) If α isiDeletion in step 4), the element α is removediAdding the obtained product into a set omega;
and the user client generates n orthogonal key matrixes according to the steps 3) -6), wherein n is the row number of the matrix A.
Further, let the original input be matrix A, take the number of columns of matrix A as input, and go up triangular key matrix Pi1,2, m. as an expected output;
the series of upper triangular key matrices PiThe generation process comprises the following steps:
1) setting a set Ω ═ 1, ·.
2) Sequentially traversing the elements in the set Ω ═ { 1.·.., m }, and performing steps 3) -4);
3) setting PiIs an identity matrix, wherein the index i is an index value and represents the ith matrix; random slave (i, m)]Selecting an integer j;
4) when i is equal to 1 or equal to m, the m is the column number of the matrix A; random from (-2)λ,2λ) Selecting a real number ηiThe matrix PiIs set to pi,i＝ηi；
Else from (-2)λ,2λ) Two real numbers η iniAnd ki(ii) a Matrix PiIs set to pi,i＝ηi,pi,j＝ki；
And the user client generates m upper triangular key matrixes according to the steps 3) -4).
Further, in step S10, encrypting the original input by using the key includes:
encrypting the original matrix a to a' as follows:
A′＝Gn...G1AP1...Pm
g represents an orthogonal key matrix, and n represents the row number of the matrix A; p denotes the upper triangular key matrix and m denotes the number of columns of matrix a.
Further, in step S20, the calculation task is QR decomposition.
Further, step S30 includes:
the edge server performs QR decomposition operation on the encrypted original input A': a ' ═ Q ' R ';
the first m rows of the edge server selection matrix R' form a new upper triangular matrix R1' and calculate its inverse matrix:
Figure BDA0003480825990000051
and the edge server returns the calculation results Q ', R' and B to the user client.
Further, step S40 includes:
s41, the user client firstly verifies whether R' and B are upper triangular matrixes;
s42, selecting 0/1 vector r of (n x 1) dimension by user client1And calculate Q '(Q')Tr1-Ir1(ii) a The user client selects 0/1 vector r with one (m × 1) dimension2And calculating A' r2-Q′R′r2(ii) a The user client selects the first m rows of matrix R' as new matrix R1', the user client then selects an 0/1 vector r of dimension (m × 1)3And calculating R1′Br3-Ir3；
If Q '(Q')Tr1-Ir1＝(0,...,0)T，A′r2-Q′R′r2＝(0,...,0)TAnd R1′Br3-Ir3＝(0,...,0)TIf the result is verified, the calculation result is correct.
Further, step S50 includes:
when the calculation result passes the verification, the user client recovers the original calculation results Q, R and R in the following mode1 -1：
Figure BDA0003480825990000052
Figure BDA0003480825990000053
Figure BDA0003480825990000054
Wherein G represents an orthogonal key matrix, and n represents the number of rows of the matrix A; p denotes the upper triangular key matrix and m denotes the number of columns of matrix a.
The invention has the beneficial effects that:
the invention provides a privacy protection method based on edge calculation, which is applied to a system consisting of a user client and an edge server; the method comprises the following steps: a user client generates a key, and the original input is encrypted by using the key; the user client sends a computing task and the encrypted original input to an edge server; the edge server calculates the encrypted original input according to the calculation task and returns a calculation result to the user client; the user client receives a calculation result returned by the edge server and verifies the correctness of the calculation result; and when the calculation result passes the verification, the user client decrypts the calculation result by using the key to obtain the original output corresponding to the original input. The method designs a safe algorithm for outsourcing the optimization problem with the equality constraint condition for the resource-limited Internet of things equipment, and is beneficial to improving the working efficiency of the Internet of things equipment and reducing the consumption of computing resources.
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Fig. 1 is a flowchart of a privacy protection method based on edge calculation according to an embodiment of the present invention;
fig. 2 is an interaction scene diagram of a user client and an edge server according to an embodiment of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "front", "rear", "both ends", "one end", "the other end", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it is to be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "disposed," "connected," and the like are to be construed broadly, such as "connected," which may be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The privacy protection method based on edge calculation is applied to a system consisting of a user client and an edge server; referring to fig. 1, the method includes:
s10, generating a key by the user client, and encrypting the original input by using the key;
s20, the user client sends a calculation task and the encrypted original input to an edge server;
s30, the edge server calculates the encrypted original input according to the calculation task and returns the calculation result to the user client;
s40, the user client receives the calculation result returned by the edge server and verifies the correctness of the calculation result;
and S50, when the calculation result is verified, the user client decrypts the calculation result by using the key to obtain the original output corresponding to the original input.
In the embodiment of the invention, in order to design an optimal power supply strategy, many influencing factors, such as cost, the number of electric equipment, a system topology structure and the like, need to be considered, and the factors and the optimal power supply strategy jointly form a convex optimization problem with an equation, wherein the influencing factors are equivalent to limiting conditions in the optimization problem, and the power supply strategy is equivalent to an objective function. The method designs a safe algorithm for outsourcing the optimization problem with the equality constraint condition for the resource-limited Internet of things equipment, and is beneficial to improving the working efficiency of the Internet of things equipment and reducing the consumption of computing resources.
A system model composed of a user client and an edge server is shown in fig. 2, and system members include: a user and an edge server. The method is realized by interaction between users (data owners and data users) and an edge server.
An honest but resource-constrained user wants to outsource the computationally complex part of the simplified constraint algorithm to a server. However the server is not fully trusted by the outsourcing user. The user does not want the server to know any private information about the input and output. The user first generates a key SK (a series of orthogonal key matrices G)iAnd an upper triangular key matrix Pi) The original input x (original matrix a) is de-encrypted. The user then sends a calculation task F (QR decomposition) and the encrypted input σx(encrypted matrix a') to the server. Calculating F (sigma) at the serverx) After (QR decomposition of matrix A'), the server returns σy(matrices Q ', R', and B encrypted after matrix decomposition) to the user. User authentication sigmay(matrices Q ', R', and B encrypted after matrix decomposition). If the authentication is passed, the user uses the key SK (a series of orthogonal key matrices G)iAnd an upper triangular key matrix Pi) De-decryption of sigmay(encrypted moments after matrix decompositionArrays Q ', R' and B) and obtain the original output y (original computation Q, R and R)1 -1) (ii) a Otherwise, the user outputs "error".
To protect input and output privacy, the outsourcing user first selects a series of orthogonal key matrices GiAnd an upper triangular key matrix PiThe matrix a is de-encrypted. The matrix a is the original matrix to be QR decomposed, i.e., the matrix in the constraint equation of the optimization problem. The generation of the orthogonal key matrix is performed according to algorithm 1, and the generation of the upper triangular key matrix is performed according to algorithm 2.
Algorithm 1 the orthogonal key matrix is generated as follows: first, set GiIs an identity matrix (subscript i represents the ith matrix); randomly selecting an angle theta from (0 deg., 360 deg.)i(ii) a Setting ci＝cosθiAnd si＝sinθi(ii) a Setting alphaiI and deleting i from the set Ω { 1. Randomly selecting a number j from a set Ω ═ 1...., n }; matrix GiThe element in (1) is set to gi,i＝ci,gj,j＝ci,gi,j＝-si,gj,i＝si(ii) a If α isiBefore deletion, the element alpha is deletediAdd to the set omega. The outsourcing user may generate n orthogonal key matrices in the manner described above, where n is the number of rows in matrix a.
Orthogonal key matrix generation algorithm
Figure BDA0003480825990000091
The triangular key matrix on algorithm 2 is generated as follows: setting PiIs an identity matrix (subscript i stands for ith matrix) randomly selected from (i, m)]To select an integer j. If i ═ 1 or i ═ m, random from (-2)λ,2λ) Selecting a real number ηi(ii) a Matrix PiIs set to pi,i＝ηi(ii) a Else from (-2)λ,2λ) Selecting two real numbers ηiAnd, (-2)λ,2λ) Represents the power of lambda from-2 to the power of lambda of 2, and represents exponential operation; matrix PiIs set to pi,i＝ηi,pi,j＝ki. The outsourcing user may generate m orthogonal key matrices in the manner described above, where m is the number of columns of matrix a.
Upper triangular key matrix generation algorithm
Figure BDA0003480825990000092
Figure BDA0003480825990000101
The orthogonal key matrix and the upper triangular key matrix are sparse matrices, and the complexity of the dense matrix multiplied by the dense matrix is O (n)2). The outsourcing user may encrypt the original matrix a to a' in the following way:
A′＝Gn...G1AP1...Pm
Gn...G1represents n orthogonal key matrixes; a is the original matrix; p1...PmRepresents m upper triangular key matrixes; a' represents the matrix after blinding.
Then, the outsourcing user sends the matrix A 'to the server, and the outsourcing user performs QR decomposition operation on the matrix A':
A′＝Q′R′
two matrices are obtained after QR decomposition is performed on the encrypted original input a'. Where Q 'is an orthogonal matrix and R' is an upper triangular matrix.
Then, the first m rows of the server selection matrix R' form a new upper triangular matrix R1' and calculate its inverse B:
Figure BDA0003480825990000102
the server returns the calculation results Q ', R' and B to the outsourcing user. And the outsourcing user runs a verification algorithm to verify the correctness of the returned result.
The verification algorithm is as follows: firstly, an outsourcing user firstly verifies whether R' and B are upper triangular matrixes; second, the outsourcing user selects an 0/1 vector r of dimension (n × 1)1And calculate Q '(Q')Tr1-Ir1I represents an identity matrix; the outsourcing user selects an 0/1 vector r with (m x 1) dimension2And calculating A' r2-Q′R′r2(ii) a Outsourcing the first m rows of the user selection matrix R' as a new matrix R1', then the outsourcing user selects an 0/1 vector r of dimension (m x 1)3And calculating R1′Br3-Ir3. If Q '(Q')Tr1-Ir1＝(0,...,0)T，A′r2-Q′R′r2＝(0,...,0)TAnd R1′Br3-Ir3＝(0,...,0)TThe result is verified, and the result is proved to be correct. The outsourcing user needs to run step 2/times repeatedly (l is an integer defined by the user) to improve the validation probability of the result.
Verification algorithm
Figure BDA0003480825990000111
If the verification is passed, the outsourcing user recovers the original calculation results Q, R and R in the following way1 -1：
Figure BDA0003480825990000121
Figure BDA0003480825990000122
Figure BDA0003480825990000123
After successful decryption, the outsourcing user divides the orthogonal matrix Q into [ Q1,Q2]And calculate new optimization variables in the following way:
Figure BDA0003480825990000124
by means of the transformation, the optimization problem with equality constraint conditions in the machine learning field and the smart grid field can be converted into the optimization problem without constraint conditions.
The original input x is the original matrix a and the orthogonal matrix Q is one of the matrices after QR decomposition of the matrix a.
According to the privacy protection method based on the edge calculation, the privacy protection method based on the convex optimization problem with equality constraint of the edge calculation is designed based on the encryption matrix technology by utilizing the edge server to assist calculation, and the problem that the computing task is difficult to execute by the equipment of the Internet of things with limited resources can be solved. The method can help to improve the working efficiency of the Internet of things equipment and reduce the consumption of computing resources.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (9)

1. A privacy protection method based on edge calculation is characterized in that the method is applied to a system consisting of a user client and an edge server; the method comprises the following steps:
s10, generating a key by the user client, and encrypting the original input by using the key;
s20, the user client sends a calculation task and the encrypted original input to an edge server;
s30, the edge server calculates the encrypted original input according to the calculation task and returns the calculation result to the user client;
s40, the user client receives the calculation result returned by the edge server and verifies the correctness of the calculation result;
and S50, when the calculation result is verified, the user client decrypts the calculation result by using the key to obtain the original output corresponding to the original input.
2. The method according to claim 1, wherein in step S10, the user client generating the key comprises: user client generates a series of orthogonal key matrix GiAnd a series of upper triangular key matrices Pi。
3. The method of claim 2, wherein the original input is set to matrix a, the number of rows of matrix a is used as input, and the orthogonal key matrix G is used as inputi1,2, n, as an expected output;
the series of orthogonal key matrices GiThe generation process is as follows:
1) setting a set Ω ═ 1, ·., n };
2) sequentially traversing the elements in the set Ω ═ { 1.·.., n }, and performing steps 3) -6);
3) setting GiIs an identity matrix, wherein the index i is an index value and represents the ith matrix; randomly selecting an angle theta from (0 deg., 360 deg.)i(ii) a Setting ci＝cosθiAnd si＝sinθi；
4) Setting alphaiI and deleting i from the set Ω { 1.
5) Randomly selecting a number j from a set Ω ═ 1...., n }; matrix GiThe element in (1) is set to gi,i＝ci,gj,j＝ci,gi,j＝-si,gj,i＝si；
6) If α isiDeletion in step 4), the element α is removediAdding the obtained product into a set omega;
and the user client generates n orthogonal key matrixes according to the steps 3) -6), wherein n is the row number of the matrix A.
4. The method of claim 3, wherein the original input is set to matrix A, the number of columns of matrix A is used as input, and the upper triangular key matrix P is used as inputi1,2, m. as an expected output;
the series of upper triangular key matrices PiThe generation process comprises the following steps:
1) setting a set Ω ═ 1, ·.
2) Sequentially traversing the elements in the set Ω ═ { 1.·.., m }, and performing steps 3) -4);
3) setting PiIs an identity matrix, wherein the index i is an index value and represents the ith matrix; random slave (i, m)]Selecting an integer j;
4) when i is equal to 1 or equal to m, the m is the column number of the matrix A; random from (-2)λ,2λ) Selecting a real number ηiThe matrix PiIs set to pi,i＝ηi；
Else from (-2)λ,2λ) Two real numbers η iniAnd ki(ii) a Matrix PiIs set to pi,i＝ηi,pi,j＝ki；
And the user client generates m upper triangular key matrixes according to the steps 3) -4).
5. The method according to claim 4, wherein in step S10, encrypting the original input with the key comprises:
encrypting the original matrix a to a' as follows:
A′＝Gn...G1AP1...Pm
g represents an orthogonal key matrix, and n represents the row number of the matrix A; p denotes the upper triangular key matrix and m denotes the number of columns of matrix a.
6. The method according to claim 5, wherein in step S20, the computing task is QR decomposition.
7. The method according to claim 6, wherein step S30 includes:
the edge server performs QR decomposition operation on the encrypted original input A': a ' ═ Q ' R ';
the first m rows of the edge server selection matrix R' form a new upper triangular matrix R1'and calculates its inverse matrix of B ═ R'1 -1；
And the edge server returns the calculation results Q ', R' and B to the user client.
8. The method according to claim 7, wherein step S40 includes:
s41, the user client firstly verifies whether R' and B are upper triangular matrixes;
s42, selecting 0/1 vector r of (n x 1) dimension by user client1And calculate Q '(Q')Tr1-Ir1(ii) a The user client selects 0/1 vector r with one (m × 1) dimension2And calculating A' r2-Q′R′r2(ii) a User client selects the first m rows of matrix R 'as new matrix R'1Then the user client selects 0/1 vector r of one (m x 1) dimension3And calculating R'1Br3-Ir3；
If Q '(Q')Tr1-Ir1＝(0,...,0)T，A′r2-Q′R′r2＝(0,...,0)TAnd R'1Br3-Ir3＝(0,...,0)TIf the result is verified, the calculation result is correct.
9. The method according to claim 8, wherein step S50 includes:
when the calculation result passes the verification, the user client recovers the original calculation results Q, R and R in the following mode1 -1：
Figure FDA0003480825980000041
Figure FDA0003480825980000042
Figure FDA0003480825980000043
Wherein G represents an orthogonal key matrix, and n represents the number of rows of the matrix A; p denotes the upper triangular key matrix and m denotes the number of columns of matrix a.
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Publication number Priority date Publication date Assignee Title
EP4318846A1 (en) * 2022-08-02 2024-02-07 Hitachi Energy Ltd State estimation for a power system using parameterized potential functions for inequality constraints
EP4318845A1 (en) * 2022-08-02 2024-02-07 Hitachi Energy Ltd State estimation for a power system using parameterized potential functions for equality constraints
WO2024028348A1 (en) * 2022-08-02 2024-02-08 Hitachi Energy Ltd State estimation for a power system using parameterized potential functions for inequality constraints
WO2024028345A1 (en) * 2022-08-02 2024-02-08 Hitachi Energy Ltd State estimation for a power system using parameterized potential functions for equality constraints
CN116318690A (en) * 2023-05-25 2023-06-23 山东大学 Safe outsourcing calculation method and system based on matrix singular value decomposition
CN116318690B (en) * 2023-05-25 2023-08-15 山东大学 Safe outsourcing calculation method and system based on matrix singular value decomposition
CN116841750A (en) * 2023-08-29 2023-10-03 恒辉信达技术有限公司 Edge computing device integrating encryption algorithm
CN116841750B (en) * 2023-08-29 2023-12-12 恒辉信达技术有限公司 Edge computing device integrating encryption algorithm
CN117857040A (en) * 2024-03-05 2024-04-09 建投物联股份有限公司 Internet of things equipment security auxiliary method, device, equipment and storage medium
CN117857040B (en) * 2024-03-05 2024-06-04 建投物联股份有限公司 Internet of things equipment security auxiliary method, device, equipment and storage medium

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