Distributed secure outsourcing computation processing method based on sparse matrix transformation

Abstract

The application provides a distributed security outsourcing computing processing method based on sparse matrix transformation, and relates to the technical field of computers, and the method comprises the following steps: acquiring a first matrix and a second matrix; randomly generating a key set comprising a binary permutation matrix, a sparse triangular matrix and a random vector; performing primary encryption on the first matrix and the second matrix based on the binary permutation matrix; performing secondary encryption on the primary encrypted matrix based on the sparse triangular matrix; distributing the secondary encrypted first secondary encrypted matrix to each edge end in an integrated manner, distributing the second secondary encrypted matrix to each edge end in an even manner after dividing the second secondary encrypted matrix into column vectors according to columns, and enabling the edge end to perform a subtask calculation operation by using the received matrix and return the result to the user end; receiving the calculation results of the edge ends, and aggregating the results; verifying the reliability of the aggregated results by using the random vector, and decrypting the final calculation result. The scheme can improve the security and timeliness of outsourcing computing.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a distributed secure outsourced computing processing method based on sparse matrix transformation. Background Technology

[0002] In recent years, the amount of data generated at the network edge has surged exponentially. According to IDC (Internet Data Center), by 2025, over 75% of global data processing tasks will have migrated to the network edge. To efficiently utilize edge data and unlock its potential value, edge intelligence, as an emerging computing paradigm, has been widely adopted. This paradigm aims to meet the stringent requirements of intelligent services for ultra-low latency and high bandwidth by deploying artificial intelligence models to network edge nodes.

[0003] In the edge computing paradigm, large-scale matrix multiplication is a crucial and computationally intensive core operation in deep learning inference and signal processing. However, edge devices are typically resource-constrained, limited by energy budgets, computing power, and storage space, making it difficult to efficiently execute such high-load computational tasks locally. To overcome this computing bottleneck, outsourcing computationally intensive tasks to resource-rich cloud servers or edge servers has become an inevitable choice. While this outsourcing model significantly improves processing efficiency, it also introduces serious security and privacy challenges. Cloud or edge service providers may be honest but curious, attempting to snoop on users' raw private data while performing computational tasks. On the other hand, cloud or edge servers may even be malicious, deliberately returning incorrect or falsified computation results to save computing resources or for commercial sabotage purposes.

[0004] Therefore, the existing outsourced computing model has serious security and privacy risks. Summary of the Invention

[0005] In view of this, and to address the above shortcomings, it is necessary to propose a distributed secure outsourced computing processing method based on sparse matrix transformation to improve the privacy and security of outsourced computing.

[0006] In a first aspect, the present invention provides a distributed secure outsourced computation processing method based on sparse matrix transformation. This method is applied at the user end to implement large-scale matrix multiplication. Specifically, the method includes:

[0007] Obtain the first and second matrices in the large-scale matrix multiplication to be calculated;

[0008] Generate random binary permutation matrices, random sparse triangular matrices, and random vectors, and construct a key set;

[0009] Based on the random binary permutation matrix, the first matrix and the second matrix are subjected to primary encryption to obtain a first primary encryption matrix and a second primary encryption matrix;

[0010] Based on the random sparse triangular matrix, the first primary encryption matrix and the second primary encryption matrix are subjected to secondary encryption to obtain the first-level encryption matrix and the second-level encryption matrix.

[0011] The first-level encryption matrix is ​​completely distributed to each edge terminal, and the second-level encryption matrix is ​​divided into column vectors and evenly distributed to each edge terminal. Each edge terminal uses the received column vectors of the first-level encryption matrix and the second-level encryption matrix to perform sub-task calculation operations and returns the sub-task calculation results to the user terminal.

[0012] Receive the subtask calculation results from each edge end, and aggregate the calculation results of each subtask to obtain the subtask aggregation result;

[0013] The reliability of the subtask aggregation result is verified using the random vector, and the calculation result of the final large-scale matrix multiplication is obtained by decryption.

[0014] Preferably, the step of generating a random binary permutation matrix, a random sparse triangular matrix, and a random vector, and constructing a key set, includes:

[0015] Call the random permutation generator to construct three random 0-1 permutation matrices. , , This is used to eliminate spatial structural correlations in the data;

[0016] Generate a series of random upper triangular sparse triangular matrices with all diagonal elements being 1. , , To leverage its single-mode property to ensure numerical accuracy of the inverse matrix;

[0017] Randomly generate an n-dimensional row vector This is for use in subsequent reliability verification;

[0018] Construct the output key set ;in, , , These are subsets of Q, V, and R, respectively.

[0019] Preferably, the initial encryption of the first matrix and the second matrix based on the random binary permutation matrix is ​​achieved in the following manner:

[0020]

[0021] Where X and Y are the first matrix and the second matrix, respectively. and These are the first primary encryption matrix and the second primary encryption matrix, respectively.

[0022] Preferably, when performing secondary encryption on the first primary encryption matrix and the second primary encryption matrix based on the random sparse triangular matrix, it is implemented in the following way:

[0023]

[0024] in, and These are the first-level encryption matrix and the second-level encryption matrix, respectively.

[0025] Preferably, assuming the total number of edge terminals is p and the number of column vectors in the second-level encryption matrix is ​​m, the rules for distributing the column vectors of the second-level encryption matrix to the edge terminals include:

[0026] like Then the m column vectors are randomly assigned to any m of the p edge ends, and any edge end is assigned no more than 1 column vector;

[0027] like , ,and Then the m column vectors are evenly distributed to the p edge ends, and each edge end is assigned m / p column vectors;

[0028] like , ,and Then, the (mh) column vectors are evenly distributed to p edge ends, and each edge end is assigned (mh) / p column vectors. The remaining h column vectors are randomly assigned to any h of the p edge ends, and any edge end is assigned no more than (mh) / p+1 column vectors.

[0029] Preferably, the reliability verification of the subtask aggregation result using the random vector includes:

[0030] use Calculate the verification vector; where, For verification vector, A matrix representing the aggregated results of subtasks;

[0031] Determine whether the verification vector W is a zero vector;

[0032] If the verification vector W is a zero vector, the subtask aggregation result is reliable; if the verification vector W is a non-zero vector, the subtask aggregation result is unreliable, and the edge corresponding to the non-zero element in the verification vector W is unreliable.

[0033] Preferably, obtaining the calculation result of the final large-scale matrix multiplication through decryption includes:

[0034] The aggregation results of subtasks are decrypted using the following calculation formula:

[0035]

[0036] Where Z represents the final calculation result.

[0037] Secondly, this invention provides a distributed secure outsourced computing processing method based on sparse matrix transformation. This method is applied to any edge endpoint and is used to implement large-scale matrix multiplication. Specifically, the method includes:

[0038] Receive column vectors of the first-level encryption matrix and the second-level encryption matrix sent by the user terminal, which are obtained by two-level encryption processing of the first and second matrices in the large-scale matrix multiplication to be calculated using a key set;

[0039] The computational task is performed using the column vectors of the first-level encryption matrix and the second-level encryption matrix to obtain the subtask computation results;

[0040] The calculation results of the subtasks are sent to the user terminal, which then performs aggregation, verification, and decryption to obtain the final calculation result.

[0041] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform any of the methods described in the first aspect.

[0042] Fourthly, the present invention provides a computing device including a memory and a processor, wherein the memory stores executable code, and when the processor executes the executable code, it implements any of the methods described in the first aspect.

[0043] As can be seen from the above technical solution, in the distributed secure outsourced computing processing method based on sparse matrix transformation provided by the embodiments of the present invention, the user end first obtains the first and second matrices in the large-scale matrix multiplication to be calculated, then generates a random binary permutation matrix, a random sparse triangular matrix, and a random vector, and constructs a key set. Further, the first and second matrices are initially encrypted based on the random binary permutation matrix, and the initially encrypted matrices are then further encrypted using the random sparse triangular matrix, resulting in a first-level encryption matrix and a second-level encryption matrix. Then, the first-level encryption matrix is ​​completely distributed to each edge end, and the second-level encryption matrix is ​​divided into column vectors and evenly distributed to each edge end. Each edge end, upon receiving the column vectors of the first-level and second-level encryption matrices, performs subtask computation operations and returns the computation results to the user end. The user end, upon receiving the subtask computation results returned by each edge end, aggregates the subtask computation results to obtain a subtask aggregation result. Further, the reliability of the subtask aggregation result is verified using the random vector in the key set, and the final computation result can be obtained by decryption. Therefore, this scheme, through a hybrid encryption mechanism of sparse single-modulus matrices and random permutations, significantly reduces the preprocessing complexity on the user end while leveraging the inverse transformation property of single-modulus matrices to achieve lossless reconstruction in a high-precision environment, ensuring data security and computational reliability. Furthermore, this scheme also verifies the results after aggregating the subtask computation results, effectively defending against malicious computational laziness and data tampering attacks with extremely low computational overhead. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of a secure outsourcing computing model framework provided in an embodiment of the present invention.

[0045] Figure 2 This is a flowchart of a distributed secure outsourcing computation processing method based on sparse matrix transformation, provided as an embodiment of the present invention.

[0046] Figure 3 This is a comparison chart of the execution time of existing outsourced calculation methods and this solution. Detailed Implementation

[0047] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are 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] Matrix multiplication, as a fundamental linear algebra operation, has wide applications in many fields of computer science, such as artificial intelligence and image processing. Matrix multiplication typically has high complexity; to improve the computational efficiency of matrix multiplication, researchers have proposed several improved algorithms. Generally, the complexity of matrix multiplication is O(n log n). 3 However, due to limited local computing resources, large-scale matrix multiplication tasks cannot be completed. To address this issue, many secure outsourcing algorithms for matrix multiplication have emerged. However, previous secure outsourcing algorithms were all based on cloud computing. Unlike cloud computing, edge nodes are closer to the data source, making computation more real-time and efficient. Therefore, this application proposes a distributed secure outsourcing computation method based on sparse matrix transformations to improve data privacy and computational efficiency.

[0049] like Figure 1 The diagram illustrates the secure outsourced computing model framework provided in this application. The framework involves two types of participants: powerful but untrusted edge nodes and users with limited resources. Users with insufficient computing resources outsource heavy computing tasks to edge nodes with powerful computing capabilities. However, edge nodes cannot be fully trusted by users. Assuming each edge node has the same computing power, to ensure data is not leaked to the edge nodes, the original input can first be encrypted. Then, the encrypted input is split and distributed to each edge node, while the computing task is also sent to the edge. For each edge node, after executing the corresponding computing task, the computing result is returned to the user. The user can then obtain the final computing result by verifying and decrypting the computing results returned by each edge node. Specifically, for the user side, such as... Figure 2 As shown, the distributed secure outsourcing computing processing method based on sparse matrix transformation provided by the present invention may include the following steps:

[0050] Step 101: Obtain the first and second matrices in the large-scale matrix multiplication to be calculated;

[0051] Step 102: Generate a random binary permutation matrix, a random sparse triangular matrix, and a random vector, and construct a key set;

[0052] Step 103: Perform primary encryption on the first matrix and the second matrix based on the random binary permutation matrix to obtain the first primary encryption matrix and the second primary encryption matrix;

[0053] Step 104: Perform secondary encryption on the first primary encryption matrix and the second primary encryption matrix based on the random sparse triangular matrix to obtain the first secondary encryption matrix and the second secondary encryption matrix;

[0054] Step 105: Distribute the first-level encryption matrix completely to each edge terminal, and divide the second-level encryption matrix into column vectors and distribute them evenly to each edge terminal, so that each edge terminal can use the column vectors of the received first-level encryption matrix and second-level encryption matrix to perform sub-task calculation operations, and return the sub-task calculation results to the user terminal;

[0055] Step 106: Receive the subtask calculation results from each edge end, and aggregate the subtask calculation results to obtain the subtask aggregation result;

[0056] Step 107: Use the random vector to verify the reliability of the subtask aggregation result, and obtain the calculation result of the final large-scale matrix multiplication to be calculated by decryption.

[0057] Suppose that the specific computational task is formally defined as follows: given two large-scale matrices , The user intends to obtain the result of problem Z=XY by delegating the computation task to p edge nodes. The following section provides a more detailed explanation of each step based on this assumption.

[0058] For step 101, obtain the first and second matrices in the large-scale matrix multiplication to be calculated;

[0059] In this step, two large-scale matrices are used. , As input.

[0060] Step 102: Generate a random binary permutation matrix, a random sparse triangular matrix, and a random vector, and construct a key set;

[0061] In this step, when constructing the key set, the random permutation generator is first called to construct three random 0-1 permutation matrices. , , This is used to shuffle the positional order of the original matrix, eliminating spatial structural correlations in the data; then, a series of random upper triangular sparse triangular matrices with all diagonal elements being 1 are generated. , , This utilizes its single-modality to ensure the numerical accuracy of the inverse matrix, achieving the goal of blinding the data information of the original matrix during subsequent encryption; furthermore, an n-dimensional row vector is randomly generated. This is used for subsequent reliability verification; thus, the output key set can be constructed. ;in, , , These are subsets of Q, V, and R, respectively.

[0062] Step 103: Perform primary encryption on the first matrix and the second matrix based on the random binary permutation matrix to obtain the first primary encryption matrix and the second primary encryption matrix;

[0063] In this step, we consider performing basic encryption on the first and second matrices. Specifically, this can be achieved as follows:

[0064]

[0065] Where X and Y are the first matrix and the second matrix, respectively. and These are the first primary encryption matrix and the second primary encryption matrix, respectively.

[0066] Step 104: Perform secondary encryption on the first primary encryption matrix and the second primary encryption matrix based on the random sparse triangular matrix to obtain the first secondary encryption matrix and the second secondary encryption matrix;

[0067] In this step, we consider further encryption of the first and second primary encryption matrices using a second level of encryption. Specifically, this can be achieved as follows:

[0068]

[0069] in, and These are the first-level encryption matrix and the second-level encryption matrix, respectively.

[0070] In this embodiment, the original feature matrices X and Y and the key set SK are used as input, and a matrix composite transformation strategy is employed for encryption. The algorithm first performs structural permutation, randomly shuffling the spatial positions of the original data matrix using the permutation matrix to eliminate structural correlations. Next, data obfuscation is performed, using a sparse single-modulus matrix to perform a linear transformation on the intermediate results, achieving deep obfuscation of the data. This ensures computational feasibility while protecting the privacy of the original data.

[0071] Step 105: Distribute the first-level encryption matrix completely to each edge terminal, and divide the second-level encryption matrix into column vectors and distribute them evenly to each edge terminal, so that each edge terminal can use the column vectors of the received first-level encryption matrix and second-level encryption matrix to perform sub-task calculation operations, and return the sub-task calculation results to the user terminal;

[0072] In this step, we consider the total number of edge nodes and the matrix. The task distribution is performed based on the number of column vectors. To ensure resource optimization in edge computing environments and the construction of a public computing infrastructure, a dual distribution strategy is considered. Specifically, a full broadcast is performed first, which involves the first-level encryption matrix. The entire distribution is completed to each edge. Further load balancing is performed, involving the second-level encryption matrix. The m column vectors are evenly distributed among the p nodes. Specifically, the distribution rules for the column vectors may include:

[0073] like Then the m column vectors are randomly assigned to any m of the p edge ends, and any edge end is assigned no more than 1 column vector;

[0074] like , ,and Then the m column vectors are evenly distributed to the p edge ends, and each edge end is assigned m / p column vectors;

[0075] like , ,and Then, the (mh) column vectors are evenly distributed to p edge ends, and each edge end is assigned (mh) / p column vectors. The remaining h column vectors are randomly assigned to any h of the p edge ends, and any edge end is assigned no more than (mh) / p+1 column vectors.

[0076] In this way, each edge end obtains a complete Replicas, and those partitioned by load balancing A partial column vector.

[0077] Step 106: Receive the subtask calculation results from each edge end, and aggregate the subtask calculation results to obtain the subtask aggregation result;

[0078] In this step, the edge device receives column vectors of the first-level encryption matrix and the second-level encryption matrix, which are obtained by two-level encryption of the first and second matrices in the large-scale matrix multiplication to be calculated using a key set, sent by the user terminal. Then, it performs a calculation task using the column vectors of the first-level encryption matrix and the second-level encryption matrix to obtain the subtask calculation result. Further, the calculated subtask calculation result is sent to the user terminal, so that the user terminal can obtain the final calculation result through aggregation, verification and decryption.

[0079] It is important to note that when the user terminal aggregates the subtask calculation results from each edge terminal, it should merge the original data according to the distributed column vectors to obtain the subtask aggregation result. .

[0080] Step 107: Use the random vector to verify the reliability of the subtask aggregation result, and obtain the calculation result of the final large-scale matrix multiplication to be calculated by decryption.

[0081] To mitigate computational biases caused by potential malicious behavior or hardware / software malfunctions at edge nodes, a probabilistic verification mechanism is introduced. The verification process begins with dimensionality reduction verification, i.e., constructing a verification vector W using a pre-defined verification random vector r. This reduces the computational complexity of verification from O(n) matrix multiplication. 3 Reduced to O(n) for vector-matrix multiplication 2 This significantly improves the system's verification efficiency. Specifically, verification can be performed in the following ways:

[0082] use Calculate the verification vector; where, For verification vector, A matrix representing the aggregated results of subtasks;

[0083] Determine whether the verification vector W is a zero vector;

[0084] If the verification vector W is a zero vector, the subtask aggregation result is reliable; for example, if P=(0,0,...,0), it means that the result returned by each edge is correct. If the verification vector W is a non-zero vector, the subtask aggregation result is unreliable, and the edge corresponding to the non-zero element in the verification vector W is unreliable. In this case, the calculation result is rejected.

[0085] If the verification passes, further decryption is performed to reconstruct the true result. The decryption process first considers numerical demasking, i.e., using the inverse of the sparse matrix to eliminate numerical confusion and generate an intermediate matrix, and then performing structure restoration, using the inverse of the permutation matrix to restore the original spatial order of the data and obtain the accurate calculation result. Specifically, the true result can be reconstructed in the following way:

[0086]

[0087] Where Z represents the final calculation result.

[0088] The effectiveness of this scheme will be further explained below with specific verification experiments.

[0089] To comprehensively evaluate the overall performance of this solution, we compare it with current mainstream computing methods from key dimensions such as client-side computational complexity, edge-side computational complexity, communication overhead, result accuracy, and verifiability. A comprehensive comparison of this method with current mainstream outsourced computing methods is shown in Table 1 below.

[0090] As shown in Table 1 above, although existing solutions such as HE-CKKS, CodedComp, and LightSecAgg can all reduce client-side computational complexity from O(n) as presented in this paper, 3 Optimized to O(n) 2 However, these solutions still have limitations in terms of communication efficiency and security features. Specifically, the HE-CKKS scheme is limited by high communication costs and the accuracy loss caused by approximate calculations. While CodedComp and LightSecAgg guarantee lossless accuracy in computation, they come with moderate communication overhead and lack a mechanism to verify the computation results. In contrast, this scheme not only achieves the lowest communication overhead and lossless computational accuracy, but is also the only scheme among all compared schemes that is verifiable. This key feature ensures that the client can effectively verify the correctness of the results returned by the edge nodes, filling the gap in the field of trusted verification in existing efficient outsourced computing schemes.

[0091] It should be noted that the HE-CKKS scheme was mentioned in the 2017 paper "Homomorphic encryption for arithmetic of approximate numbers". The CodedComp scheme was mentioned in the 2021 paper "Coded Computation for Multistage Data flows". The LightSecAgg scheme was mentioned in the 2022 paper "LightSecAgg: A Lightweight and Versatile Design for SecureAggregation in Federated Learning".

[0092] Furthermore, to systematically evaluate the performance advantages of this solution in real-world edge intelligence scenarios, the algorithm mechanism underwent end-to-end latency testing on various computational models on a physical hardware platform, covering key aspects such as encryption, data transmission, core computation, and decryption. The tests show that the existing HE-CKKS solution exhibits extremely high computational latency due to its complex homomorphic encryption operations, while local computation faces severe device computing power bottlenecks in large-scale matrix tasks. This solution, by introducing an algebraic coefficient transformation mechanism, significantly improves computational efficiency, fully validating the necessity of the outsourcing computation strategy. Compared to lightweight solutions such as CodedComputing, which introduces coding redundancy, and LightSecAgg, which involves dense masking operations, the core advantage of this solution lies in its ability to greatly reduce preprocessing complexity through sparse single-modulus matrix transformation and its perfect compatibility with the GPU's TensorCore hardware architecture, achieving efficient computation without redundancy.

[0093] Therefore, while ensuring security, this solution not only solves the algorithmic constraints at the edge, but also achieves the lowest latency compared to other security outsourcing solutions across all test dimensions, demonstrating near-bare-metal performance and excellent scalability. Its test results are as follows: Figure 3 As shown in the figure, the X-axis represents the matrix dimension N, and the Y-axis represents the average computation time (seconds). The data curves intuitively reflect the significant performance advantages of this solution compared to HE-CKKS, CodedComputing, and LightSecAgg when handling large-scale matrix operations.

[0094] This specification also provides a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the methods in any of the embodiments of the specification.

[0095] This specification also provides a computing device, including a memory and a processor, wherein the memory stores executable code, and when the processor executes the executable code, it implements the method in any of the embodiments of the specification.

[0096] The device embodiments provided by the present invention are based on the same inventive concept as the method embodiments in this specification. For details, please refer to the description in the method embodiments of this specification, which will not be repeated here.

[0097] The modules or units in the device of this invention can be merged, divided, and deleted according to actual needs. The above-disclosed embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of the invention. Those skilled in the art will understand that implementing all or part of the processes of the above embodiments and making equivalent changes according to the claims of this invention still fall within the scope of the invention.

Claims

1. A distributed secure outsourced computing processing method based on sparse matrix transformation, characterized in that, This method is applied on the user end to implement large-scale matrix multiplication; the method specifically includes: Obtain the first and second matrices in the large-scale matrix multiplication to be calculated; Generate random binary permutation matrices, random sparse triangular matrices, and random vectors, and construct a key set; Based on the random binary permutation matrix, the first matrix and the second matrix are subjected to primary encryption to obtain a first primary encryption matrix and a second primary encryption matrix; Based on the random sparse triangular matrix, the first primary encryption matrix and the second primary encryption matrix are subjected to secondary encryption to obtain the first-level encryption matrix and the second-level encryption matrix. The first-level encryption matrix is ​​completely distributed to each edge terminal, and the second-level encryption matrix is ​​divided into column vectors and evenly distributed to each edge terminal. Each edge terminal uses the received column vectors of the first-level encryption matrix and the second-level encryption matrix to perform sub-task calculation operations and returns the sub-task calculation results to the user terminal. Receive the subtask calculation results from each edge end, and aggregate the calculation results of each subtask to obtain the subtask aggregation result; The reliability of the subtask aggregation result is verified using the random vector, and the calculation result of the final large-scale matrix multiplication is obtained by decryption.

2. The distributed secure outsourcing computing processing method based on sparse matrix transformation according to claim 1, characterized in that, The process of generating random binary permutation matrices, random sparse triangular matrices, and random vectors, and constructing a key set, includes: Call the random permutation generator to construct three random 0-1 permutation matrices. , , This is used to eliminate spatial structural correlations in the data; Generate a series of random upper triangular sparse triangular matrices with all diagonal elements being 1. , , To leverage its single-mode property to ensure numerical accuracy of the inverse matrix; Randomly generate an n-dimensional row vector This is for use in subsequent reliability verification; Construct the output key set ;in, , , These are subsets of Q, V, and R, respectively.

3. The distributed secure outsourcing computing processing method based on sparse matrix transformation according to claim 2, characterized in that, When performing primary encryption on the first and second matrices based on the random binary permutation matrix, it is achieved in the following way: ； Where X and Y are the first matrix and the second matrix, respectively. and These are the first primary encryption matrix and the second primary encryption matrix, respectively.

4. The distributed secure outsourcing computing processing method based on sparse matrix transformation according to claim 3, characterized in that, When performing secondary encryption on the first primary encryption matrix and the second primary encryption matrix based on the random sparse triangular matrix, it is achieved in the following way: ； in, and These are the first-level encryption matrix and the second-level encryption matrix, respectively.

5. The distributed secure outsourcing computing processing method based on sparse matrix transformation according to claim 1, characterized in that, Let the total number of edge devices be p, and the number of column vectors in the second-level encryption matrix be m. The rules for distributing the column vectors of the second-level encryption matrix to the edge devices include: like Then the m column vectors are randomly assigned to any m of the p edge ends, and any edge end is assigned no more than 1 column vector; like , ,and Then the m column vectors are evenly distributed to the p edge ends, and each edge end is assigned m / p column vectors; like , ,and Then, the (mh) column vectors are evenly distributed to p edge ends, and each edge end is assigned (mh) / p column vectors. The remaining h column vectors are randomly assigned to any h of the p edge ends, and any edge end is assigned no more than (mh) / p+1 column vectors.

6. The distributed secure outsourcing computing processing method based on sparse matrix transformation according to claim 4, characterized in that, The reliability verification of the subtask aggregation result using the random vector includes: use Calculate the verification vector; where, For verification vector, A matrix representing the aggregated results of subtasks; Determine whether the verification vector W is a zero vector; If the verification vector W is a zero vector, the subtask aggregation result is reliable; if the verification vector W is a non-zero vector, the subtask aggregation result is unreliable, and the edge corresponding to the non-zero element in the verification vector W is unreliable.

7. The distributed secure outsourcing computing processing method based on sparse matrix transformation according to claim 6, characterized in that, The calculation result of the final large-scale matrix multiplication to be calculated by decryption includes: The aggregation results of subtasks are decrypted using the following calculation formula: ； Where Z represents the final calculation result.

8. A distributed secure outsourced computing processing method based on sparse matrix transformation, characterized in that, This method is applicable to arbitrary edge points and is used to implement large-scale matrix multiplication; the method specifically includes: Receive column vectors of the first-level encryption matrix and the second-level encryption matrix sent by the user terminal, which are obtained by two-level encryption processing of the first and second matrices in the large-scale matrix multiplication to be calculated using a key set; The computational task is performed using the column vectors of the first-level encryption matrix and the second-level encryption matrix to obtain the subtask computation results; The calculation results of the subtasks are sent to the user terminal, where the user terminal performs aggregation, verification, and decryption to obtain the final calculation result.

9. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method described in any one of claims 1-8.

10. A computing device, comprising a memory and a processor, wherein the memory stores executable code, and the processor, when executing the executable code, implements the method of any one of claims 1-8.

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