Parallel collaborative privacy computing method under non-uniform edge network computing power condition

Abstract

The invention relates to the technical field of homomorphic encryption and distributed computing, and discloses a parallel collaborative privacy computing method under the condition of non-uniform computing power of an edge network, which is applied to a star network topology structure consisting of a main node and K edge nodes, and aims to solve the problems of minimum absolute shrinkage and operator selection. And solving and constructing a minimum absolute shrinkage and selection operator problem based on an alternating direction multiplier method by adopting the alternating direction multiplier method, segmenting the compression matrix to obtain a plurality of sub-problems, solving each sub-problem by utilizing edge nodes, and obtaining a minimum absolute shrinkage and selection operator problem based on the minimum absolute shrinkage and selection operator problem. The solution process is as follows: a main node generates encryption and decryption parameters, Euler function values corresponding to the encryption and decryption parameters, encrypted plaintext parameters and quantized plaintext parameters and shares the parameters to an edge node, homomorphic iterative calculation is performed, and three times of communication with the main node is performed, so that parallel collaborative privacy calculation is realized; according to the method, the calculation overhead is reduced while the encryption and decryption precision is not influenced, and meanwhile, the overall calculation speed is increased.

Description

Technical Field

[0001] The present invention relates to the field of homomorphic encryption and distributed computing technology, and specifically to a parallel collaborative privacy computing method under conditions of uneven computing power in an edge network. Background Art

[0002] With the development of big data, data privacy and security have become key global concerns. When processing and computing large datasets, a single computing node can incur high overhead and even run out of memory. However, collaborative computing across multiple nodes can significantly reduce computational overhead by processing and computing datasets in parallel. In border areas of Tibet, computing power is uneven across nodes due to the aging and replacement of collaborative node equipment. This situation requires the adoption of appropriate computing and communication methods to maximize parallel computing across nodes. Furthermore, data in border areas contains a large amount of sensitive information, raising the question of how to protect data privacy and security during collaborative computing.

[0003] Currently, there are differentially private ADMM methods for distributed alternating direction multiplication method (ADMM) privacy computation. These methods combine the optimization strategies of ADMM with the privacy protection of differential privacy, solving optimization problems while ensuring data privacy. However, achieving differential privacy requires introducing noise that disrupts the learning process, necessitating careful consideration of parameter settings. Improper settings can lead to insufficient privacy protection or degraded algorithm performance. Furthermore, the introduction of differential privacy can affect the algorithm's convergence speed, especially when noise is introduced at each iteration, making it more difficult for the algorithm to converge to a stable solution. There are also homomorphic encryption ADMM methods. This combination of homomorphic encryption and ADMM results in minimal loss of accuracy, but to meet privacy protection requirements, the key length must be increased, significantly increasing computational overhead. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present invention provides a parallel collaborative privacy computing method under the condition of uneven computing power in the edge network, which is used to solve the problems of high computational overhead or low computational accuracy in existing homomorphic encryption and distributed computing methods under the condition of uneven computing power of edge nodes.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A parallel collaborative privacy computing method under the condition of uneven edge network computing power is applied to a star network topology consisting of 1 main node and K edge nodes. The alternating direction multiplier method is used to solve the minimum absolute contraction and selection operator problem. The minimum absolute contraction and selection operator problem based on the alternating direction multiplier method is constructed, and then the compression matrix is partitioned to obtain several sub-problems to utilize the edge nodes. Solve each sub-problem. The solution process includes: S1. The master node generates several private keys, public keys, encryption and decryption parameters, and the corresponding Euler function values. Then, the master node uses the Paillier homomorphic encryption scheme combined with the quantization method to quantize and encrypt the first plaintext parameter in the subproblem to generate the encrypted plaintext parameter. At the same time, the master node quantizes the second plaintext parameter in the subproblem to generate the quantized plaintext parameter. S2. The master node shares the encryption and decryption parameters, the Euler function values corresponding to the encryption and decryption parameters, the encrypted plaintext parameters, and the quantized plaintext parameters with the edge nodes. S3. After the edge node receives the encryption and decryption parameters, the Euler function values corresponding to the encryption and decryption parameters, the encrypted plaintext parameters, and the quantized plaintext parameters and shares them with the edge node, it performs homomorphic iterative calculations and communicates with the master node three times after each homomorphic iterative calculation is completed to achieve parallel collaborative privacy computing.

[0006] The present invention has the following beneficial effects: The present invention proposes a parallel collaborative privacy computing method under the condition of uneven edge network computing power. Based on the Paillier homomorphic encryption scheme and combined with a quantization method, it improves the accuracy of the encryption scheme in the distributed computing process without affecting its convergence process; at the same time, in the encryption and decryption process, the modular exponent calculation is optimized, which significantly reduces the computational overhead of the Paillier homomorphic encryption scheme; in addition, the introduction of a parallel encryption and decryption calculation method with GPU accelerated computing not only realizes parallel encryption and decryption calculations, but also speeds up the calculation speed of the entire method. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 This is a flow chart of a parallel collaborative privacy computing method proposed by the present invention under the condition of uneven edge network computing power; Figure 2 Schematic diagram of the three-stage process of edge nodes solving each sub-problem in the embodiment; Figure 3 Schematic diagram of three communication processes in iterative calculation in the embodiment; Figure 4 Schematic diagram of the GPU computing process of each node in the embodiment; Figure 5For example, in a network topology with a laptop computer with 16GB RAM as the main node and three Raspberry Pi computers with 8GB RAM as the edge nodes, when , , Schematic diagram of the accuracy of inverse quantization when ; Figure 6 For example, in a network topology with one laptop with 16GB of RAM as the master node and three Raspberry Pis with 8GB of RAM as the edge nodes, , , Schematic diagram of the accuracy of inverse quantization when ; Figure 7 For example, in a network topology with one laptop with 16GB of RAM as the master node and three Raspberry Pis with 8GB of RAM as the edge nodes, , , Schematic diagram of the accuracy of inverse quantization when ; Figure 8 The figure is a schematic diagram comparing the mean square error calculated by the method proposed in the present invention and other methods in a network topology with one laptop with 16GB of RAM as the main node and three Raspberry Pis with 8GB of RAM as the edge nodes. DETAILED DESCRIPTION

[0008] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0009] like Figure 1 As shown in the figure, a parallel collaborative privacy computing method under the condition of uneven edge network computing power is applied to a star network topology consisting of 1 main node and K edge nodes. The alternating direction multiplier method is used to solve the minimum absolute contraction and selection operator problem. The minimum absolute contraction and selection operator problem based on the alternating direction multiplier method is constructed, and then the compression matrix is partitioned to obtain several sub-problems to utilize the edge nodes. Solve each subproblem.

[0010] Specifically, the alternating direction multiplier method is used to solve the least absolute contraction and selection operator problem. The specific process of constructing the least absolute contraction and selection operator problem based on the alternating direction multiplier method is as follows: First, construct the expression of the least absolute contraction and selection operator problem, namely:

[0011]

[0012]

[0013] in, Indicates data to be restored, and , represents auxiliary variables, express dimensional real number set, represents the observation vector, and , represents the compressed matrix, and ( ), 、 Both represent the dimensions of the compressed matrix, represents the L2 norm, represents the regularization parameter, and , represents the L1 norm, To satisfy it, represents the noise vector.

[0014] Secondly, the expression of the least absolute contraction and selection operator problem is expressed using the Lagrangian function, that is:

[0015] in, represents the Lagrangian function, represents the Lagrange multiplier vector, and , represents transpose, represents the penalty parameter, and .

[0016] Then, based on the Lagrangian function, the expression of the least absolute contraction and selection operator problem based on the alternating direction multiplier method is constructed as follows:

[0017]

[0018]

[0019] in, Indicates the The data to be recovered for the iteration, express -dimensional identity matrix, Indicates the Auxiliary variables at the iteration, Indicates the The Lagrange multiplier vector for the iteration, Indicates the Auxiliary variables at the iteration, represents the soft threshold function, Indicates the The Lagrange multiplier vector for the iteration.

[0020] Finally, the least absolute contraction and selection operator problem based on the alternating direction multiplier method is transformed to construct the transformation formula of the least absolute contraction and selection operator problem based on the alternating direction multiplier method, namely:

[0021]

[0022]

[0023] in, Indicates the The data to be recovered for the iteration.

[0024] In this embodiment, the formula middle Transformed into 、Jiang Shi middle Transformed into The purpose is to facilitate the synchronous calculation of subsequent steps; in addition, for the iterative calculation of the LASSO problem (least absolute shrinkage and selection operator problem), when the dimension of the compression matrix is large, there is The inverse operation has a high computational overhead, so it is divided into multiple sub-problems, and each sub-problem is solved by the edge nodes to achieve parallel collaborative privacy computing under the condition of uneven computing power of the edge network. The specific operation is as follows: Specifically, the least absolute contraction and selection operator problem based on the alternating direction multiplier method is constructed, and then several sub-problems are obtained by partitioning the contraction matrix to utilize the edge nodes. The expression for solving each subproblem is:

[0025]

[0026] in, Represents an edge node The observation vector required to solve each subproblem, Represents an edge node The compressed matrix required to solve each subproblem, and , Represents an edge node The data to be recovered is needed to solve each sub-problem, and , Represents an edge node The auxiliary variables needed to solve each subproblem, and .

[0027] In this embodiment, the compressed matrix is divided into several sub-problems by using the number of edge nodes, thereby speeding up the calculation. Figure 2 As shown, Figure 2 Demonstrated the use of edge nodes The solution process for each sub-problem includes steps S1-S3: S1 and the master node generate several private keys, public keys, encryption and decryption parameters, and the Euler function values corresponding to the encryption and decryption parameters, respectively. Then, the Paillier homomorphic encryption scheme is used in combination with the quantization method to quantize and encrypt the first plaintext parameter in the subproblem to generate the encrypted plaintext parameter. At the same time, the second plaintext parameter in the subproblem is quantized to generate the quantized plaintext parameter.

[0028] In this embodiment, step S1 is the initialization stage, and its specific operation process is as follows: Specifically, the master node generates several private keys, public keys, encryption and decryption parameters, and the Euler function values corresponding to the encryption and decryption parameters as follows: First, the master node generates the first private key With the second private key ,in, 、 are all Blum integers; then according to the first private key With the second private key , generate the first encryption and decryption parameters , Second encryption and decryption parameters , the Euler function value corresponding to the first encryption and decryption parameter , the Euler function value corresponding to the second encryption and decryption parameter .

[0029] In this embodiment, the parameters 、 For large prime numbers with additional requirements 、 , and satisfies ,and , such prime numbers are called Blum integers, where express and The greatest common factor of . Among them, the method of generating Blum integers is: randomly select two large numbers of length L-bit ,calculate , detection and Is it a prime number? If so, calculate , detection Furthermore, while the master node is looking for the Blum integer and When the encryption algorithm is executed multiple times, the time required is relatively long, but the key is not frequently changed, and the encryption algorithm needs to be executed multiple times, which is ultimately beneficial to speed up the encryption algorithm, and the master node can also calculate and store and Finally, the generated Blum integer 、 As the first private key and second private key of the master node.

[0030] Secondly, the master node uses the first private key With the second private key , calculate the first public key in sequence , second public key and the third public key , and its corresponding formula is:

[0031]

[0032]

[0033]

[0034] in, represents a random number, and , represents the set of positive integers, represents the intermediate variable, Represents the modulo operation.

[0035] Specifically, the master node generates several private keys, public keys, encryption and decryption parameters, and the Euler function values corresponding to the encryption and decryption parameters, and defines all parameters that need to be encrypted as plain text. , and in plain text The corresponding ciphertext is , so for all The modular exponent calculation of the structural form is accelerated by introducing the Chinese remainder theorem and Pei Shu theorem. The process is as follows: First, The structure is converted to Structural form, then let Structural form or The structural form is Structural form.

[0036] Secondly, The structural form is optimized by first performing parallel calculations in two small spaces, and then using the Chinese remainder theorem to linearly aggregate the calculation results in the small spaces back to the large space to generate an expression for the aggregated results. This includes the following steps: Step 1-Step 3: Step 1: Make a large space Decomposed into two small spaces multiplied, namely:

[0037] in, Indicates the first small space, Indicates the second smallest space.

[0038] Step 2: The structural form is mapped in the first small space Calculate the first and second variables, and then calculate the third variable based on the first and second variables, that is:

[0039]

[0040]

[0041] in, 、 represent the first variable and the second variable respectively, Represents the third variable.

[0042] At the same time, The structural form is mapped in the second small space Calculate the fourth and fifth variables, and then calculate the sixth variable based on the fourth and fifth variables, that is:

[0043]

[0044]

[0045] in, 、 represent the fourth and fifth variables respectively, Represents the sixth variable.

[0046] In this embodiment, the calculation of the third variable and the sixth variable is a parallel process, which introduces a GPU parallel method to reduce computational overhead.

[0047] Step 3: Use the Chinese remainder theorem to convert the first small space The third variable and the second smallest space calculated above The sixth variable calculated above is linearly aggregated to restore to the large space Above, we get the expression of the aggregation result, namely:

[0048] in, Represents the aggregation result.

[0049] Then, according to Pei Shu's theorem and the principle that the first and second private keys are mutually prime, the modular exponential calculation expressions of the first and second private keys are generated, namely: .

[0050] Finally, substitute the modular exponential calculation expressions of the first private key and the second private key into the expression of the aggregation result to obtain a simplified aggregation result expression, namely: .

[0051] In this embodiment, all parameters that need to be encrypted can be defined as plain text, and their corresponding cipher texts are calculated based on the public key, that is, In order to reduce the amount of calculation for modular exponential operations in this structure, it is necessary to use the Chinese remainder theorem and Pei Shu theorem to optimize the modular exponential calculation. The condition for using the Chinese remainder theorem is to know Decomposition factor and , so that we can create the two small spaces mentioned above 、 In the minimum absolute contraction and selection operator problems based on the alternating direction multiplier method, the encryption and decryption processes are all performed on the master node, and the master node must know and Therefore, modular exponential optimization can be used for calculation, that is, by performing calculations in two small spaces in parallel, and then using the Chinese remainder theorem to linearly aggregate the small spaces back to the large space, the optimized solution is finally achieved. In addition, the decryption calculation is consistent with the unoptimized decryption calculation and does not change, but the modular exponential calculation in the decryption calculation is consistent with the modular exponential calculation in the encryption calculation. If it involves The modular exponent calculations of the structural forms are all performed using the above optimization methods, thereby speeding up the calculation speed and reducing the calculation overhead.

[0052] Specifically, the Paillier homomorphic encryption scheme is used in combination with the quantization method to quantize and encrypt the first plaintext parameter in the subproblem to generate the encrypted plaintext parameter. At the same time, the second plaintext parameter in the subproblem is quantized. The specific process of generating the quantized plaintext parameter is as follows: According to the use of edge nodes Solve the expression for each subproblem , so in each iteration, the edge nodes are used The expression for solving the subproblem is:

[0053]

[0054]

[0055] in, Indicates the Edge nodes at iteration Solve the required data to be recovered, express dimensional identity matrix, Indicates the Edge nodes at iteration Solve for the auxiliary variables needed, Indicates the Edge nodes at iteration Solve for the required Lagrange multiplier vector, Indicates the Edge nodes at iteration Solve for the auxiliary variables needed, Indicates the Edge nodes at iteration Solve the required data to be recovered, Indicates the Edge nodes at iteration Find the Lagrange multiplier vector required for the solution.

[0056] Since the data in each iteration 、 is known, so the expression The data to be calculated is the first plaintext parameter And the second plaintext parameter .

[0057] Therefore, the Paillier homomorphic encryption scheme is used in combination with the quantization method to encrypt the first plaintext parameter in the sub-problem Quantify and encrypt to generate encrypted plaintext parameters ,in, represents the encryption function, Represents the quantization function.

[0058] At the same time, the second plaintext parameter in the subproblem Quantize and generate quantized plaintext parameters .

[0059] In this embodiment, since Paillier homomorphic encryption can only encrypt unsigned integers, the present invention proposes a quantization method that can quantize real numbers to the positive integer domain, and this quantization method does not destroy the homomorphism of the Paillier encryption scheme, and the precision loss of inverse quantization can reach 10 -16 , can be ignored.

[0060] Specifically, the quantification process is: Assume the parameter to be quantized is ,and , then the quantization formula of the parameter to be quantized is:

[0061]

[0062] in, represents the quantization parameter, Indicates the parameter to be quantized No. elements, 、 Represent the parameters to be quantized The minimum and maximum values of represents the center rounding operation, Indicates the magnification factor.

[0063] In addition, the inverse quantization formula is: , and the accuracy of inverse quantization is The selection is related to .

[0064] S2. The master node shares the encryption and decryption parameters, the Euler function values corresponding to the encryption and decryption parameters, the encrypted plaintext parameters, and the quantized plaintext parameters with the edge nodes. In this embodiment, step S2 is the data security sharing stage, and its specific operation process is as follows: The master node will encrypt the plaintext parameters , quantized plaintext parameters , the first encryption and decryption parameters The Euler function value corresponding to the first encryption and decryption parameter Distribute to the corresponding edge nodes.

[0065] S3. After the edge node receives the encryption and decryption parameters, the Euler function values corresponding to the encryption and decryption parameters, the encrypted plaintext parameters, and the quantized plaintext parameters and shares them with the edge node, it performs homomorphic iterative calculations and communicates with the master node three times after each homomorphic iterative calculation is completed to achieve parallel collaborative privacy computing.

[0066] In this embodiment, step S3 is the parallel privacy calculation stage, and its specific operation process is as follows: Specifically, step S3 includes S31-S32: S31. After receiving the encryption and decryption parameters, the Euler function values corresponding to the encryption and decryption parameters, the encrypted plaintext parameters, and the quantized plaintext parameters, the edge node performs the corresponding homomorphic iterative calculation, which includes the edge node calculating the current task and the master node coordinating decryption, specifically: First, calculate the current task of the edge node ,Right now: .

[0067] At the same time, the current task of computing edge nodes in space Modulo exponential parameter on ,Right now: .

[0068] Then, the master node modulus index parameter Perform collaborative decryption, specifically: Determine whether the master node is performing the first iteration. If so, calculate the current task of the master node. Otherwise, the master node first sends the edge node Decrypt and inverse quantize, then concatenate and calculate auxiliary variables and the Lagrange multiplier vector ,Right now:

[0069]

[0070] in, Represents the decryption function.

[0071] For auxiliary variables and the Lagrange multiplier vector Perform modular exponential calculation to obtain the first intermediate parameter and the second intermediate parameter ,Right now: .

[0072] .

[0073] Then, the first intermediate parameter and the second intermediate parameter Collaborative decryption is achieved through modular exponential calculation.

[0074] S32. After each homomorphic iterative calculation is completed, the edge node communicates with the master node three times, as follows: Figure 3 As shown, it specifically includes steps S321-S326: S321, perform the first communication and send the current task of the edge node to , modular exponential parameters Send to the master node, and the master node sends the auxiliary variable and the negative of the Lagrange multiplier vector After quantization and confusion, segmentation is performed to generate the first segmentation parameters and the second segmentation parameter , and send it to the edge node, where represents the confusion function.

[0075] S322. After the first communication is completed, the master node calculates the current task of the edge node in space Modulo exponential parameter on ,Right now: .

[0076] Then, the master node modulus index parameter Perform collaborative decryption, inverse quantize and splice the data to be recovered At the same time, the edge nodes have the first segmentation parameter and the second segmentation parameter Perform modular exponential calculation to generate the third intermediate parameter , the fourth intermediate parameter ,Right now: .

[0077] .

[0078] In this embodiment, the GPU performs parallel calculations, thereby reducing computational overhead.

[0079] S323, the second communication is carried out, and the edge node sends the three intermediate parameters , the fourth intermediate parameter Sent to the master node.

[0080] S324. After the second communication is completed, the master node and the negative of the Lagrange multiplier vector Perform deobfuscation, encryption, and segmentation to generate segmentation auxiliary variables and the negative of the Lagrange multiplier vector of the partition .

[0081] S325, the third communication is carried out, the master node divides the auxiliary variables and the negative of the Lagrange multiplier vector of the partition Sent to edge nodes.

[0082] S326. Determine whether the maximum number of iterations has been reached or the mean square error has reached the convergence threshold. If so, terminate the iteration; otherwise, proceed to the next homomorphic iterative calculation.

[0083] In this embodiment, if the mean square error between the final calculated data and the original data reaches the convergence threshold or the current number of iterations reaches the maximum number of iterations, the iteration is terminated. Otherwise, based on the data sent by the master node to the edge node after the third communication, the next iteration is continued.

[0084] Specifically, GPU parallel methods are introduced to accelerate and optimize the encryption and decryption calculation process, specifically: First, the plaintext data is converted into a set base vector. If multiplication operation of two converted base vectors is involved, the fast Fourier transform method is introduced for calculation. At the same time, multiplication and shift operations are used to replace the division operation in the modular exponential calculation.

[0085] In this embodiment, when encrypting and decrypting data, the master node and the edge node can use the GPU to encrypt and decrypt the elements in the vector data in parallel; however, the GPU has a word length limit for the data that needs to be operated. The maximum length of data that can be operated by each CUDA core is 32 bits or 64 bits, but the data length in the initialization phase and the parallel privacy calculation phase is much larger than this limit; therefore, the present invention proposes a parallel encryption and decryption calculation framework for GPU accelerated computing, which first converts the plaintext data into a base, such as converting decimal to 100. Base ( ), and then process a large decimal integer in the form of a vector. When multiplying two large integers, the fast Fourier transform is used to accelerate the calculation. When performing large integer modular exponential operations in encryption and decryption calculations, the division operation is replaced by multiplication and shift operations, and the stream multiprocessor is used to coordinate and schedule multiple CUDA cores, allowing multiple CUDA cores to collaboratively calculate a task. Among them, the calculation process of each node GPU is as follows Figure 4 shown.

[0086] In order to verify the effectiveness of the proposed parallel collaborative privacy computing method under the condition of uneven edge network computing power, the following experiments were conducted: like Figure 5-Figure 7 As shown in the figure, in a network topology with a laptop computer with 16GB RAM as the main node and three Raspberry Pis with 8GB RAM as the edge nodes, different 、 as well as value to obtain the accuracy of inverse quantization, where Figure 5 in the middle , , When the absolute value of the difference between the unencrypted data and the encrypted data is taken, the inverse quantization loss is approximately ; Figure 6 In, when , , When the absolute value of the difference between the unencrypted data and the encrypted data is taken, the inverse quantization loss is approximately ; Figure 7 In, when , , When the absolute value of the difference between the unencrypted data and the encrypted data is taken, the inverse quantization loss is approximately Therefore, the combination Figure 5-Figure 7 It can be seen that the precision loss of inverse quantization using the quantization method proposed in the present invention is approximately .

[0087] Secondly, the proposed method was used to conduct experiments with centralized ADMM, distributed ADMM, and differentially private ADMM. In the same network topology with a laptop with 16GB of RAM as the master node and three Raspberry Pis with 8GB of RAM as the edge nodes, the mean square error produced by the proposed method was compared with that of the other methods, and the results were obtained from the experiments. Figure 8 As can be seen in the results, the mean squared error between our proposed method and the centralized ADMM differs by approximately 0.07, while the mean squared error between the differentially private ADMM and the centralized ADMM differs by approximately 0.2. The mean squared errors of our proposed method and the distributed ADMM coincide at convergence, indicating that the accuracy loss of our proposed quantization method is negligible.

[0088] In summary, the present invention proposes a parallel collaborative privacy computing method under the condition of uneven edge network computing power. It combines the quantization method with the Paillier homomorphic encryption scheme, allowing the encryption scheme to maintain high accuracy during distributed computing without affecting the algorithm's convergence process. At the same time, it introduces an optimization scheme for the Paillier encryption and decryption process, significantly reducing the computational overhead of the Paillier homomorphic encryption scheme. In addition, the optimized encryption and decryption scheme is combined with the distributed computing method to propose a parallel encryption and decryption computing framework for GPU-accelerated computing. This not only realizes parallel encryption and decryption of elements in the vector, but also speeds up the calculation speed of the overall algorithm.

[0089] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0090] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A parallel collaborative privacy computing method under the condition of uneven edge network computing power, characterized by: It is applied to a star network topology consisting of 1 main node and K edge nodes. The alternating direction multiplier method is used to solve the least absolute contraction and selection operator problem. The least absolute contraction and selection operator problem based on the alternating direction multiplier method is constructed, and then the compression matrix is partitioned to obtain several sub-problems to utilize the edge nodes. Solve each sub-problem. The solution process includes: S1. The master node generates several private keys, public keys, encryption and decryption parameters, and the corresponding Euler function values. Then, the master node uses the Paillier homomorphic encryption scheme combined with the quantization method to quantize and encrypt the first plaintext parameter in the subproblem to generate the encrypted plaintext parameter. At the same time, the master node quantizes the second plaintext parameter in the subproblem to generate the quantized plaintext parameter. S2. The master node shares the encryption and decryption parameters, the Euler function values corresponding to the encryption and decryption parameters, the encrypted plaintext parameters, and the quantized plaintext parameters with the edge nodes. S3. After the edge node receives the encryption and decryption parameters, the Euler function values corresponding to the encryption and decryption parameters, the encrypted plaintext parameters, and the quantized plaintext parameters and shares them with the edge node, it performs homomorphic iterative calculations and communicates with the master node three times after each homomorphic iterative calculation is completed to achieve parallel collaborative privacy computing.

2. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 1 is characterized in that: For the least absolute shrinkage and selection operator problem, the alternating direction multiplier method is used to solve it. The specific process of constructing the least absolute shrinkage and selection operator problem based on the alternating direction multiplier method is as follows: First, construct the expression of the least absolute contraction and selection operator problem, namely: in, Indicates data to be restored. represents auxiliary variables, express dimensional real number set, represents the observation vector, represents the compressed matrix, represents the L2 norm, represents the regularization parameter, represents the L1 norm, To satisfy it, represents the noise vector; Secondly, the expression of the least absolute contraction and selection operator problem is expressed using the Lagrangian function, that is: in, represents the Lagrangian function, represents the Lagrange multiplier vector, represents transpose, represents the penalty parameter; Then, based on the Lagrangian function, the expression of the least absolute shrinkage and selection operator problem based on the alternating direction multiplier method is constructed as follows: in, Indicates the The data to be recovered for the iteration, express -dimensional identity matrix, Indicates the Auxiliary variables at the iteration, Indicates the The Lagrange multiplier vector for the iteration, Indicates the Auxiliary variables at the iteration, represents the soft threshold function, Indicates the The Lagrange multiplier vector for the iteration; Finally, the least absolute contraction and selection operator problem based on the alternating direction multiplier method is transformed to construct the transformation formula of the least absolute contraction and selection operator problem based on the alternating direction multiplier method, namely: in, Indicates the The data to be recovered for the iteration.

3. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 2 is characterized in that: Construct the least absolute contraction and selection operator problem based on the alternating direction multiplier method, and then obtain several sub-problems by partitioning the contraction matrix to utilize the edge nodes The expression for solving each subproblem is: in, Represents an edge node The observation vector required to solve each subproblem, Represents an edge node The compressed matrix required to solve each subproblem, Represents an edge node The data to be recovered required to solve each sub-problem, Represents an edge node Auxiliary variables needed to solve each subproblem.

4. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 3 is characterized in that: The specific process of the master node generating several private keys, public keys, encryption and decryption parameters, and the Euler function values corresponding to the encryption and decryption parameters is as follows: First, the master node generates the first private key With the second private key ,in, 、 are all Blum integers; then according to the first private key With the second private key , generate the first encryption and decryption parameters , Second encryption and decryption parameters , the Euler function value corresponding to the first encryption and decryption parameter , the Euler function value corresponding to the second encryption and decryption parameter ; Secondly, the master node uses the first private key With the second private key , calculate the first public key in sequence , second public key and the third public key , and its corresponding formula is: in, represents a random number, and , represents the set of positive integers, represents the intermediate variable, Represents the modulo operation.

5. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 4 is characterized in that: After the master node generates several private keys, public keys, encryption and decryption parameters, and the Euler function values corresponding to the encryption and decryption parameters, it defines all parameters that need to be encrypted as plain text. , and in plain text The corresponding ciphertext is , so for all The modular exponent calculation of the structural form is accelerated by introducing the Chinese remainder theorem and Pei Shu theorem. The process is as follows: First, The structure is converted to Structural form, then let Structural form or The structural form is Structural form; Secondly, The structural form is optimized by first performing parallel calculations in two small spaces, and then using the Chinese remainder theorem to linearly aggregate the calculation results in the small spaces back to the large space to generate an expression for the aggregated results. The steps include: Step 1: Make a large space Decomposed into two small spaces multiplied, namely: in, Indicates the first small space, Indicates the second smallest space; Step 2: The structural form is mapped in the first small space Calculate the first and second variables, and then calculate the third variable based on the first and second variables, that is: in, 、 represent the first variable and the second variable respectively, represents the third variable; At the same time, The structural form is mapped in the second small space Calculate the fourth and fifth variables, and then calculate the sixth variable based on the fourth and fifth variables, that is: in, 、 represent the fourth and fifth variables respectively, represents the sixth variable; Step 3: Use the Chinese remainder theorem to convert the first small space The third variable and the second smallest space calculated above The sixth variable calculated above is linearly aggregated to restore to the large space Above, we get the expression of the aggregation result, namely: in, Represents the aggregation result; Then, according to Pei Shu's theorem and the principle that the first and second private keys are mutually prime, the modular exponential calculation expressions of the first and second private keys are generated, namely: ； Finally, substitute the modular exponential calculation expressions of the first private key and the second private key into the expression of the aggregation result to obtain a simplified aggregation result expression, namely: 。 6. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 5 is characterized in that: The Paillier homomorphic encryption scheme is used in combination with the quantization method to quantize and encrypt the first plaintext parameter in the subproblem to generate the encrypted plaintext parameter. At the same time, the second plaintext parameter in the subproblem is quantized. The specific process of generating the quantized plaintext parameter is as follows: According to the use of edge nodes Solve the expression for each subproblem , so in each iteration, the edge nodes are used The expression for solving the subproblem is: in, Indicates the Edge nodes at iteration Solve the required data to be recovered, express dimensional identity matrix, Indicates the Edge nodes at iteration Solve for the auxiliary variables needed, Indicates the Edge nodes at iteration Solve for the required Lagrange multiplier vector, Indicates the Edge nodes at iteration Solve for the auxiliary variables needed, Indicates the Edge nodes at iteration Solve the required data to be recovered, Indicates the Edge nodes at iteration Solve for the required Lagrange multiplier vector; Since the data in each iteration 、 is known, so the expression The data to be calculated is the first plaintext parameter And the second plaintext parameter ; Therefore, the Paillier homomorphic encryption scheme is used in combination with the quantization method to encrypt the first plaintext parameter in the sub-problem Quantify and encrypt to generate encrypted plaintext parameters ,in, represents the encryption function, represents the quantization function; At the same time, the second plaintext parameter in the subproblem Quantize and generate quantized plaintext parameters .

7. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 6 is characterized in that: The quantification process is: Assume the parameter to be quantized is ,and , then the quantization formula of the parameter to be quantized is: in, represents the quantization parameter, Indicates the parameter to be quantized No. elements, 、 Represent the parameters to be quantized The minimum and maximum values of represents the center rounding operation, Indicates the magnification factor.

8. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 7 is characterized in that: Step S3 specifically includes: S31. After receiving the encryption and decryption parameters, the Euler function values corresponding to the encryption and decryption parameters, the encrypted plaintext parameters, and the quantized plaintext parameters, the edge node performs the corresponding homomorphic iterative calculation, which includes the edge node calculating the current task and the master node coordinating decryption, specifically: First, calculate the current task of the edge node ,Right now: ； At the same time, the current task of computing edge nodes in space Modulo exponential parameter on ,Right now: ； Then, the master node modulus index parameter Perform collaborative decryption, specifically: Determine whether the master node is performing the first iteration. If so, calculate the current task of the master node. Otherwise, the master node first sends the edge node Decrypt and inverse quantize, then concatenate and calculate auxiliary variables and the Lagrange multiplier vector ,Right now: in, Represents the decryption function; For auxiliary variables and the Lagrange multiplier vector Perform modular exponential calculation to obtain the first intermediate parameter and the second intermediate parameter ,Right now: ； ； Then, the first intermediate parameter and the second intermediate parameter Collaborative decryption is achieved through modular exponential calculation. S32. After each homomorphic iterative calculation is completed, the edge node communicates with the master node three times.

9. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 8 is characterized in that: Step S32 specifically includes: S321, perform the first communication and send the current task of the edge node to , modular exponential parameters Send to the master node, and the master node sends the auxiliary variable and the negative of the Lagrange multiplier vector After quantization and confusion, segmentation is performed to generate the first segmentation parameters and the second segmentation parameter , and send it to the edge node, where represents the confusion function; S322. After the first communication is completed, the master node calculates the current task of the edge node in space Modulo exponential parameter on ,Right now: ； Then, the master node modulus index parameter Perform collaborative decryption, inverse quantize and splice the data to be recovered At the same time, the edge nodes have the first segmentation parameter and the second segmentation parameter Perform modular exponential calculation to generate the third intermediate parameter , the fourth intermediate parameter ,Right now: ； ； S323, the second communication is carried out, and the edge node sends the three intermediate parameters , the fourth intermediate parameter Send to the master node; S324. After the second communication is completed, the master node and the negative of the Lagrange multiplier vector Perform deobfuscation, encryption, and segmentation to generate segmentation auxiliary variables and the negative of the Lagrange multiplier vector of the partition ; S325, the third communication is carried out, the master node divides the auxiliary variables and the negative of the Lagrange multiplier vector of the partition Send to edge nodes; S326. Determine whether the maximum number of iterations has been reached or the mean square error has reached the convergence threshold. If so, terminate the iteration; otherwise, proceed to the next homomorphic iterative calculation.

10. The parallel collaborative privacy computing method under the condition of uneven edge network computing power according to claim 9 is characterized in that: GPU parallel methods are also introduced to accelerate and optimize the encryption and decryption calculation process, specifically: First, the plaintext data is converted into a set base vector. If multiplication operation of two converted base vectors is involved, the fast Fourier transform method is introduced for calculation. At the same time, multiplication and shift operations are used to replace the division operation in the modular exponential calculation.

Images