Safe two-vector sigmoid calculation method based on addition and multiplication transformation and related device

Abstract

The invention discloses a secure two-direction vector sigmoid calculation method based on addition and multiplication transformation and a related device, and relates to the technical field of privacy computation.The method comprises the steps that a first input vector and a second input vector serve as two input vectors of a secure two-direction vector bit multiplication protocol, and the first input vector and the second input vector serve as the two input vectors of the secure two-direction vector bit multiplication protocol; obtaining a first bit multiplication calculation output vector and a second bit multiplication calculation output vector; after the first bit multiplication calculation output vector is subjected to fine tuning, the first bit multiplication calculation output vector and the second bit multiplication calculation output vector after fine tuning are used as two input vectors of a secure two-direction vector reciprocal protocol to obtain a first reciprocal calculation output vector and a second reciprocal calculation output vector, and the first reciprocal calculation output vector and the second reciprocal calculation output vector are sent to a calculation requester for aggregation; and a sigmoid calculation vector can be obtained. According to the method, the sigmoid function is split into reciprocal and bit multiplication operation, polynomial approximation or piecewise function replacement is not needed, and the function value of the sigmoid can be accurately calculated.

Description

Technical Field

[0001] This application relates to the field of privacy computing technology, and in particular to a secure two-directional sigmoid calculation method and related apparatus based on additive-multiplicative transformation. Background Technology

[0002] With the continuous advancement of big data technology, data plays a crucial role in modern society. Countries around the world have introduced data privacy protection policies, and how to effectively utilize data while ensuring privacy has become an urgent challenge. Privacy-preserving computing technology has emerged to address this need. Through secure multi-party computation, homomorphic encryption, differential privacy, and other encryption techniques, it achieves both data availability and invisibility, becoming a current research focus. An important application area of ​​privacy computing is privacy-preserving machine learning, encompassing the secure training of various artificial intelligence models such as logistic regression and multilayer perceptrons. In the secure training of these models, the sigmoid activation function plays a key role due to its ability to introduce nonlinear computation, making it an indispensable part of privacy-preserving machine learning.

[0003] Existing solutions to the secure two-directional sigmoid problem typically employ polynomial approximation techniques or linear piecewise function substitution methods for transformation, followed by processing using computational frameworks developed based on traditional cryptographic primitives such as homomorphic encryption, secret sharing, and obfuscated circuits. These methods rely on complex ciphertext space computations, resulting in enormous computational and communication overhead, low practicality, and insufficient efficiency. Furthermore, after converting nonlinear operations to linear operations, using large prime numbers for encryption increases the number of bits in the ciphertext or introduces differential noise, leading to a decrease in the accuracy of model training parameters, affecting the accuracy of numerical calculations and consequently the reliability of the results. Simultaneously, existing solutions often rely on third-party cloud service systems, which are often unreliable or vulnerable to malicious attacks, leading to the leakage of intermediate computation results or critical key information, increasing the risk of original data privacy breaches.

[0004] Therefore, how to achieve efficient, secure, and reliable bidirectional sigmoid computation is a technical challenge that urgently needs to be overcome in the field of privacy computing. Summary of the Invention

[0005] The purpose of this application is to provide a safe two-directional sigmoid calculation method and related apparatus based on additive-multiplicative transformation, which can realize efficient, safe and reliable two-directional sigmoid calculation.

[0006] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a method for calculating a secure two-directional sigmoid based on additive-multiplicative transformations, comprising the following steps: The first and second participating nodes perform privacy processing on their respective initial input vectors locally to obtain the first and second input vectors, respectively. The privacy processing involves processing the initial input vector of the first or second participating node according to the natural constant to obtain the first or second input vector.

[0007] The first participating node uses the first input vector as one input vector of the secure two-way matrix multiplication protocol, and the second participating node uses the second input vector as another input vector of the secure two-way matrix multiplication protocol. The first and second participating nodes obtain the first bit multiplication calculation output vector and the second bit multiplication calculation output vector, respectively. In the secure two-way matrix multiplication protocol, after matrixing the two input vectors, the calculation is performed based on the matrixed two input vectors according to the secure two-way matrix multiplication protocol, and the calculation result of the secure two-way matrix multiplication protocol is reduced in dimensionality.

[0008] The first participating node fine-tunes the first multiplication output vector locally to obtain the fine-tuned first multiplication output vector.

[0009] The first participating node uses the fine-tuned bit-multiplication calculation output vector as one input vector of the secure two-way vector reciprocal protocol, and the second participating node uses the second bit-multiplication calculation output vector as another input vector of the secure two-way vector reciprocal protocol. The first and second participating nodes obtain the first and second reciprocal calculation output vectors, respectively. In the secure two-way vector reciprocal protocol, calculation is performed based on the secure two-way vector addition-multiplication transformation protocol. After taking the reciprocal bit by bit of the calculation result of the secure two-way vector addition-multiplication transformation protocol, calculation is performed based on the secure two-way vector bit-multiplication protocol.

[0010] The first participating node and the second participating node send their respective first and second reciprocal calculation output vectors to the calculation requester for aggregation to obtain the sigmoid calculation vector.

[0011] Secondly, this application also provides another method for calculating the secure two-directional sigmoid based on additive-multiplicative transformation, including the following steps: The first and second participating nodes perform privacy processing on their respective initial input vectors locally to obtain the first and second input vectors, respectively. The privacy processing involves processing the initial input vector of the first or second participating node according to the natural constant to obtain the first or second input vector.

[0012] The first participating node uses the first input vector as one input vector of the secure two-way vector addition-multiplication transformation protocol, and the second participating node uses the second input vector as another input vector of the secure two-way vector addition-multiplication transformation protocol. The first participating node and the second participating node obtain the first addition-multiplication transformation calculation output vector and the second addition-multiplication transformation calculation output vector, respectively.

[0013] The first participating node and the second participating node respectively fine-tune the first addition-multiplication transformation calculation output vector and the second addition-multiplication transformation calculation output vector locally to obtain the fine-tuned first addition-multiplication transformation calculation output vector and the fine-tuned second addition-multiplication transformation calculation output vector.

[0014] The first participating node uses the fine-tuned first addition-multiplication transformation output vector as one input vector of the secure two-way matrix multiplication protocol, and the second participating node uses the fine-tuned second addition-multiplication transformation output vector as another input vector of the secure two-way matrix multiplication protocol. The first and second participating nodes obtain the first and second bit multiplication output vectors, respectively. In the secure two-way matrix multiplication protocol, after matrixing the two input vectors, the secure two-way matrix multiplication protocol is used to perform calculations based on the matrixed two input vectors, and the calculation results of the secure two-way matrix multiplication protocol are dimensionality reduced.

[0015] The first participating node and the second participating node send their respective first-bit multiplication output vectors and second-bit multiplication output vectors to the computation requester for aggregation to obtain the sigmoid computation vector.

[0016] Thirdly, this application also provides a secure two-way sigmoid computation system based on additive-multiplicative transformation. This secure two-way sigmoid computation system based on additive-multiplicative transformation is deployed at each participating node in the network. The secure two-way sigmoid computation system based on additive-multiplicative transformation includes: a task acquisition module, a secure computation module, a rule generation module, a consensus computation module, and a data transmission module.

[0017] The task acquisition module is used to receive and parse sigmoid calculation requests from the calculation requester.

[0018] The secure computation module is used to automatically match the corresponding secure computation protocol based on the parsed sigmoid computation request. The secure computation protocols include secure two-way matrix multiplication protocol, secure two-way variable bitwise multiplication protocol, secure two-way variable addition-multiplication transformation protocol, secure two-way variable reciprocal protocol, and secure two-way variable sigmoid protocol.

[0019] The rule generation module is used to split the sigmoid calculation request according to the asynchronous instruction set of the matched secure computing protocol. The two participating nodes in the sigmoid calculation request perform collaborative computing according to the secure two-way sigmoid calculation method based on addition-multiplication transformation as described above.

[0020] The consensus computation module is used to ensure the synchronization and consistency of results between the two participating nodes in the sigmoid computation request during collaborative computation.

[0021] The data sending module is used to send the first reciprocal calculation output vector obtained by the first participating node or the second reciprocal calculation output vector obtained by the second participating node to the calculation requester for aggregation to obtain the sigmoid calculation vector.

[0022] Fourthly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the secure two-directional sigmoid calculation method based on additive-multiplicative transformation described above.

[0023] Fifthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the aforementioned safe two-directional sigmoid calculation method based on additive-multiplicative transformation.

[0024] In a sixth aspect, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the aforementioned safe two-directional sigmoid calculation method based on additive-multiplicative transformation.

[0025] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a secure two-way sigmoid calculation method and related apparatus based on additive-multiplicative transformation. In this method, the first participating node and the second participating node each perform privacy processing on the initial input vector locally to obtain a first input vector and a second input vector, respectively. Then, the first input vector and the second input vector are used as two input vectors of a secure two-way bit multiplication protocol to obtain the first bit multiplication calculation output vector and the second bit multiplication calculation output vector. After fine-tuning the first bit multiplication calculation output vector, the fine-tuned first bit multiplication calculation output vector and the second bit multiplication calculation output vector are used as two input vectors of a secure two-way reciprocal protocol to obtain the first reciprocal calculation output vector and the second reciprocal calculation output vector. These are then sent to the calculation requester for aggregation to obtain the sigmoid calculation vector. The proposed solution decomposes the sigmoid function into its reciprocal and bitwise multiplication operations. By utilizing secure two-way vector bitwise multiplication and secure two-way vector reciprocal protocols, the sigmoid function value can be accurately calculated without polynomial approximation or piecewise function substitution. This effectively avoids the precision errors caused by techniques such as obfuscated circuits and homomorphic encryption in the conversion of nonlinear operations to linear operations. Specifically, the secure two-way vector reciprocal protocol converts the addition of the denominator into a multiplication operation using a secure two-way addition-multiplication transformation protocol, thus decomposing the fraction. The secure two-way vector bitwise multiplication protocol is then used to accurately calculate the reciprocal, providing support for the accurate calculation of the secure two-way vector sigmoid. Furthermore, since the protocol used does not rely on a third-party cloud platform, it avoids the risk of privacy data leakage due to attacks on third-party cloud platforms. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a schematic diagram illustrating the problem of calculating the secure two-way sigmoid in privacy computing.

[0028] Figure 2 This is a schematic diagram illustrating the principle of a secure data obfuscation and encryption technology proposed in this application.

[0029] Figure 3 The flowchart illustrates a safe two-directional sigmoid calculation method based on additive-multiplicative transformation, as provided in an embodiment of this application.

[0030] Figure 4This is a schematic diagram illustrating the problem of the secure two-way quantity multiplication protocol in a secure two-way quantity sigmoid calculation method based on additive-multiplicative transformation provided in an embodiment of this application.

[0031] Figure 5 This is a schematic diagram illustrating the principle of the secure two-way sigmoid calculation method based on additive-multiplicative transformation, provided in an embodiment of this application.

[0032] Figure 6 This is a schematic diagram illustrating the problem of the secure two-way matrix multiplication calculation protocol in a secure two-way sigmoid calculation method based on additive-multiplicative transformation provided in an embodiment of this application.

[0033] Figure 7 This is a schematic diagram illustrating the principle of a secure two-way matrix multiplication calculation protocol in a secure two-way sigmoid calculation method based on additive-multiplicative transformation, provided in an embodiment of this application.

[0034] Figure 8 This is a schematic diagram illustrating the problem of the reciprocal protocol of the safe two-way quantity in a safe two-way quantity sigmoid calculation method based on additive-multiplicative transformation provided in an embodiment of this application.

[0035] Figure 9 This is a schematic diagram illustrating the principle of the reciprocal protocol of a secure two-way sigmoid calculation method based on additive-multiplicative transformation, provided in an embodiment of this application.

[0036] Figure 10 This is a schematic diagram illustrating the problem of the secure two-way quantity addition-multiplication transformation protocol in a secure two-way quantity sigmoid calculation method based on addition-multiplication transformation provided in an embodiment of this application.

[0037] Figure 11 This is a schematic diagram illustrating the principle of the secure two-way sigmoid calculation method based on additive-multiplicative transformation, provided in an embodiment of this application.

[0038] Figure 12 This is a schematic diagram illustrating the principle of the secure two-way sigmoid protocol in a secure two-way sigmoid calculation method based on additive-multiplicative transformation, provided in an embodiment of this application.

[0039] Figure 13 The flowchart illustrates a safe two-directional sigmoid calculation method based on additive-multiplicative transformation, provided in another embodiment of this application.

[0040] Figure 14This is a schematic diagram illustrating the principle of the secure two-way sigmoid protocol in a secure two-way sigmoid calculation method based on additive-multiplicative transformation, provided in another embodiment of this application.

[0041] Figure 15 This is a functional module diagram of a secure two-directional sigmoid calculation system based on additive-multiplicative transformation, provided in an embodiment of this application.

[0042] Figure 16 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0043] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0044] A major application of privacy-preserving computation is privacy-preserving machine learning, including the secure training of many AI models such as logistic regression and multilayer perceptrons. During the secure training of these models, the sigmoid activation function plays a crucial role by introducing non-linear computation into the model, making it an important component of privacy-preserving machine learning. Therefore, how to securely achieve accurate computation of the sigmoid function is a very important research topic. The secure two-directional sigmoid problem is defined as: given the existence of two computational directions... , They are independent and distrustful of each other. Hold one m dimensional private vector , Hold one m dimensional private vector The two parties hope to achieve this by jointly implementing a secure two-way sigmoid protocol. Ultimately, each participating node in the computation receives its corresponding output. The results are then sent to the requesting node to aggregate and obtain the desired two-way sigmoid result. During the computation, each participating node can only know its own input and output information and cannot obtain the intermediate computation results or data held by other participants. The problem is formally described as follows: Figure 1 As shown below, the existing relevant technical solutions at home and abroad are summarized and described: 1) The ABY3 framework, proposed by Mohassel and Rindal, utilizes piecewise functions to approximate the calculation of the sigmoid function, transforming nonlinear operations into linear and comparison operations. This framework employs obfuscated circuitry, which enables comparison operations by converting the operations into fixed Boolean circuits. The framework also combines other related techniques to achieve approximate calculation of the sigmoid function. While the ABY3 framework can implement secure comparison operations based on obfuscated circuitry and support the calculation of piecewise functions to replace the sigmoid, this approach requires the construction of numerous circuits, resulting in high computational and space complexity and low computational efficiency. Furthermore, the use of piecewise function approximation introduces errors, leading to accuracy issues.

[0045] 2) The ScretFlow framework, proposed by Ma and Zheng et al., uses the idea of ​​secret sharing to achieve secure computation. This technique protects privacy by having each participant split their private data into shares and share them with other participants. The framework utilizes a polynomial approximation method to transform nonlinear computation into linear computation, thereby enabling the computation of the sigmoid function using techniques such as secret sharing. However, while the ScretFlow framework, based on the idea of ​​secret sharing, achieves secure computation by splitting private data and sharing it with other participants, it provides a security threshold to ensure that the private data can only be reconstructed when participants exceeding this threshold unite. However, this approach involves a large amount of message exchange between multiple parties, leading to inefficient communication.

[0046] 3) The TenSeal framework proposed by Ayoub and Bilal et al. combines the CKKS homomorphic encryption scheme to achieve privacy-preserving computation by having the data holder encrypt private data and send it to a third-party computing node for computation in the ciphertext space. This scheme also uses approximation to convert nonlinear operations into linear operations to implement the sigmoid activation function. However, while the TenSeal framework uses traditional cryptographic techniques and public-private key encryption for privacy protection, ensuring the security of the computation results, its complex ciphertext computation and reliance on a third-party cloud platform result in high computational, storage, and communication overhead costs, as well as the risk of data leakage should the third-party cloud platform be attacked.

[0047] Regarding scalability, most of the above schemes perform well in secure two-way sigmoid computations, but encounter problems when scaling to multi-party computations. Obfuscated circuit schemes result in massive circuit sizes and extremely high computational and communication overhead when dealing with large-scale data computations; secret-sharing schemes generate a large amount of information exchange and have low communication efficiency when handling multi-party computations. Homomorphic encryption, due to its inherent encryption technology, incurs very high computational costs when involving complex multi-party computations.

[0048] For most multi-party computations, achieving secure computation typically involves multiple interactive steps. An unavoidable challenge arises: how to ensure the security of intermediate results? For example, multiplying two matrices... When used as an intermediate result in computation, regardless of the participating nodes... or node The final matrix was obtained The results could potentially lead to the deduction of data from the other party. Therefore, privacy-preserving computation must ensure not only the security of the initial input data but also the security of the intermediate results.

[0049] To address this problem, this application first proposes a secure data obfuscation encryption technique. This technique involves decomposing any multi-ary operation into a new multi-ary addition to obfuscate the result of calculating intermediate values. To better illustrate its principle, this paper uses a two-way operation as an example. The principle is as follows: Figure 2 As shown. Assume ,in It is the first The objective function of the step is to compute the following. It belongs to the organization No. Step's private input data, It belongs to the organization No. Private input data for the first step. In the execution of the multi-party secure computation protocol... intermediate results during the step The following constraints will be strictly followed: Only know the results of your own calculations and Only the result is known ,and . formula This illustrates the process of passing intermediate values ​​throughout the entire process. and Exchanging data information with each other is not allowed, including the splitting of intermediate calculation results. and Similarly, for the first Step, its input and By the Step and Output and Transmission constitutes, and and Its output and satisfy , Only know the results of your own calculations and Only the result is known Therefore, as long as the intermediate value is split into two random data items and stored separately by the two computation participants at each step of the computation, it can be guaranteed that no party can deduce the original data item from this obfuscated and encrypted data, thus making the entire privacy computation process highly secure.

[0050] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] In one exemplary embodiment of this application, a safe two-directional sigmoid calculation method based on additive-multiplicative transformation is provided, such as... Figure 3 As shown, the safe two-directional sigmoid calculation method based on additive-multiplicative transformation includes the following steps: A1. The first and second participating nodes perform privacy processing on their respective initial input vectors locally, obtaining a first input vector and a second input vector, respectively. Privacy processing involves processing the initial input vector of the first or second participating node according to the natural constant to obtain the first or second input vector. In this embodiment, step A1 specifically includes the following steps: A11. The first participating node processes the initial input vector of the first participating node locally according to the natural constant to obtain the first input vector.

[0052] A12. The second participating node processes the initial input vector of the second participating node locally according to the natural constant to obtain the second input vector.

[0053] Specifically, in this embodiment, the first participating node Alice performs a secret computation locally. ,in Similarly, the second participating node, Bob, secretly computes the computation locally. ,in .in, e is a natural constant, here representing . eExponentiation with a base of 0. Exponentiation uses a vector as the exponent, meaning it calculates the exponent for each element of that vector, and the result is still a vector.

[0054] A2. The first participating node uses the first input vector as one input vector of the secure two-way matrix multiplication protocol, and the second participating node uses the second input vector as another input vector of the secure two-way matrix multiplication protocol. The first and second participating nodes obtain the first bit multiplication calculation output vector and the second bit multiplication calculation output vector, respectively. In the secure two-way matrix multiplication protocol, after matrixing the two input vectors, calculations are performed based on the matrixed two input vectors according to the secure two-way matrix multiplication protocol, and the calculation results of the secure two-way matrix multiplication protocol are subjected to dimensionality reduction. In this embodiment, step A2 specifically includes the following steps: A21. The first participating node performs matrix transformation on the first input vector to obtain the first input matrix.

[0055] A22. The second participating node performs matrix processing on the second input vector to obtain the second input matrix.

[0056] A23. The first participating node uses the first input matrix as one input matrix of the secure two-party matrix multiplication protocol, and the second participating node uses the second input matrix as another input matrix of the secure two-party matrix multiplication protocol. The first participating node and the second participating node obtain the first matrix multiplication calculation output matrix and the second matrix multiplication calculation output matrix, respectively.

[0057] A24. The first participating node performs dimensionality reduction on the output matrix of the first matrix multiplication calculation to obtain the first multiplication calculation output vector.

[0058] A25. The second participating node performs matrix transformation on the output matrix of the second matrix multiplication calculation to obtain the output vector of the second bitwise multiplication calculation.

[0059] Specifically, the secure two-way bitwise multiplication protocol problem can be defined as: given two participating nodes... , They are independent and distrustful of each other. Hold one m dimensional private vector , Hold one m dimensional private vector The two parties hope to achieve this by jointly implementing a secure two-way vector multiplication protocol. Ultimately, each participating node in the computation receives its corresponding output. The input and output information is then sent to the requesting node to aggregate and obtain its desired two-way vector bitwise product result. During the computation, each participating node can only know its own input and output information and cannot obtain the intermediate computation results or held data information of other participants. A formal description of the problem can be found in [link to problem description]. Figure 4 The secure two-way quantity multiplication protocol includes the following steps: Step (a1): Participants Nodes and Participants The nodes jointly negotiate a positive integer. Each of them splits each element of the private vector they hold into n A set of distinct, random positive numbers. (Participants) The node will After being split into parts n dimensional private vector Participants The node will After being split into parts n dimensional private vector .

[0060] Step (a2): Participants The node will n dimensional private vector Transform into a Private vectors of dimension Specifically, by vectors The vector is obtained by concatenating the elements in order. Then the vector group { The private matrix is ​​constructed by sequentially dividing the rows from top to bottom. .

[0061] Step (a3): Participants The node will have each private vector Convert to private variable First, private vectors middle n Perform all permutations of the elements and convert each permutation into a vector, resulting in a total of... A random sorted vector, the process of which is represented as follows: , perms Function representation of pairs n element (a full permutation operation), then from Random selection n vectors The private matrix is ​​formed by row vectors. Then the matrix Dimensionality reduction to vector Specifically, the matrix Each column vector is concatenated to achieve the transformation from matrix space to vector space. Finally, the vectors are... Each column of the matrix is ​​used in turn to form the matrix. .

[0062] Step (a4): Participants Nodes and Participants The node is based on a secure two-way matrix multiplication computation protocol. Enter their respective private data. and Perform a round of safe two-sided matrix multiplication calculations .exist After the protocol calculation is completed, this round of calculation... Based on secure data obfuscation technology, it was split into... The two results were sent to the participants respectively. Nodes and Participants Each node serves as its private output, and these two private output matrices satisfy the following relation: .

[0063] Step (a5): Participants Nodes and Participants Each node obtains a private matrix. Then, each local unit sets the main diagonal of the matrix. n Each element is extracted and quantized to obtain a private vector. and ,in m 2 v The function represents the bitwise conversion of the elements of a diagonal matrix into their corresponding vectors. diag The function represents extracting the diagonal elements of any matrix to construct a diagonal matrix. Then... and The data is sent to the computation requester, who then aggregates it to obtain the results. .

[0064] It can be easily verified using the following formula: .

[0065] Its overall principle is as follows Figure 5 As shown, the secure two-way matrix multiplication computation protocol used in step (a4) can be defined as follows: given that there are two computation methods... , They are independent and distrustful of each other. Holding a dimension as Private data matrix stored only on its own computing node , Holding a dimension as Private data matrix The two parties hope to achieve this by jointly implementing a secure matrix multiplication protocol. Ultimately, each participating node in the computation receives its corresponding dimension. The output matrix The results are then sent to the requesting party to aggregate and obtain the desired two-way matrix product. During the calculation process, each participating node can only know its own input and output information and cannot obtain the intermediate settlement results or held data information of other participants. A formal description of the problem can be found in [link to problem description]. Figure 6 The secure two-party matrix multiplication computation protocol includes the following steps: Step (b1): The auxiliary computing node, also known as the commodity service node, is used. Generate two pairs of random matrices, specifically in the form of a matrix with dimension 1. random matrix Dimensions random matrix and dimensions Two random matrices These random matrices must strictly satisfy the following constraints. Then by The auxiliary node will pair the random matrix Send to the participants Calculate nodes, pair random matrices Send to the participants Compute nodes.

[0066] Step (b2): Participants Upon receiving the corresponding random matrix pair Then, its internal calculation and send it to the participating nodes. .

[0067] Step (b3): ​​Participants Upon receiving the corresponding random matrix pair Then, its internal calculation and send it to the participating nodes. .

[0068] Step (b4): Participants The node received from Matrix sent by the node Then, a random matrix is ​​secretly generated internally. And secretly calculate the matrix locally. Send to node.

[0069] Step (b5): Participants Node received Then, the matrix is ​​obtained through local secret computation. .

[0070] Step (b6): Participants node, Each node represents its corresponding final obfuscated split result. , The matrix multiplication is sent to the two parties requesting the matrix multiplication calculation, who then sums the results to obtain the final product. .

[0071] It can be easily verified using the following formula: Its overall principle is as follows: Figure 7 As shown.

[0072] A3. The first participating node fine-tunes the first-order multiplication output vector locally to obtain the fine-tuned first-order multiplication output vector. Specifically, in this embodiment, the participating node... Nodes compute locally ,in .

[0073] A4. The first participating node uses the fine-tuned bit-multiplication calculation output vector as one input vector of the secure two-way vector reciprocal protocol, and the second participating node uses the second bit-multiplication calculation output vector as another input vector of the secure two-way vector reciprocal protocol. The first and second participating nodes obtain the first and second reciprocal calculation output vectors, respectively. In the secure two-way vector reciprocal protocol, calculation is performed based on the secure two-way vector addition-multiplication transformation protocol. After taking the reciprocal bit by bit of the calculation result of the secure two-way vector addition-multiplication transformation protocol, calculation is performed based on the secure two-way vector bit-multiplication protocol. In this embodiment, step A4 specifically includes the following steps: A41. The first participating node uses the fine-tuned first bit multiplication calculation output vector as an input vector of the secure two-way vector addition-multiplication transformation protocol, and the second participating node uses the second bit multiplication calculation output vector as another input vector of the secure two-way vector addition-multiplication transformation protocol. The first participating node and the second participating node obtain the first addition-multiplication transformation calculation output vector and the second addition-multiplication transformation calculation output vector, respectively.

[0074] A42. The first participating node performs a bitwise reciprocal operation on the output vector of the first addition-multiplication transformation locally to obtain the output vector of the reciprocal of the first addition-multiplication transformation.

[0075] A43. The second participating node performs a bitwise reciprocal operation on the output vector of the second addition-multiplication transformation locally to obtain the output vector of the reciprocal of the second addition-multiplication transformation.

[0076] A44. The first participating node uses the first addition-multiplication transformation to calculate the reciprocal output vector as an input vector of the secure two-way multiplication protocol, and the second participating node uses the second multiplication calculation output vector as another input vector of the secure two-way multiplication protocol. The first participating node and the second participating node obtain the first reciprocal calculation output vector and the second reciprocal calculation output vector, respectively.

[0077] Specifically, the participating parties Alice Nodes and Participants Bob The node is based on the secure two-way reciprocal protocol. Each inputs its own private vector. and Perform a round of secure two-way reciprocal protocol calculation The results were obtained respectively. .

[0078] The secure two-way reciprocal protocol problem can be defined as: given the existence of two computational methods... , They are independent and distrustful of each other. Hold one m dimensional private vector , Hold one m dimensional private vector The two parties hope to achieve this by jointly implementing a secure two-way reciprocal protocol. Ultimately, each participating node in the computation receives its corresponding output. The input and output information is then sent to the requesting node to aggregate and obtain the expected inverses of the two vectors. During the computation, each participating node can only know its own input and output information and cannot obtain the intermediate computation results or data held by other participants. A formal description of this problem can be found in [link to problem description]. Figure 8 The secure two-way reciprocal protocol includes the following steps: Step (c1): Participants Alice Nodes and Participants Bob Nodes based on a secure two-way vector addition-multiplication transformation protocol Each inputs its own private vector. and Perform a round of safe two-way multiplication and transformation protocol calculation. The results were obtained respectively. .

[0079] Step (c2): Participants Alice Nodes perform secret computations locally ,in Participants Bob Nodes perform secret computations locally ,in .

[0080] Step (c3): Participants Alice Nodes and Participants Bob The node is based on a secure two-way bitwise multiplication protocol. Each inputs its own private vector. and Perform a round of secure two-way quantity multiplication protocol calculation The results were obtained respectively. .

[0081] Step (c4): Participants Alice Nodes and Participants Bob Each node sets its private result vector. Send the request to the party requesting the secure two-way variable addition-multiplication transformation calculation, satisfying... It is easy to verify that: .

[0082] Its overall principle is as follows Figure 9 As shown, the secure two-way quantity addition-multiplication transformation protocol used in step (c1) above can be defined as follows: Given that there are two computational methods... , They are independent and distrustful of each other. Hold one m dimensional private vector , Hold one m dimensional private vector The two parties hope to achieve this by jointly implementing a secure two-way vector addition-multiplication transformation protocol. Ultimately, each participating node in the computation receives its corresponding output. The results are then sent to the requesting party to aggregate and obtain the desired outcome. During the computation process, each participating node can only know its own input and output information and cannot obtain the intermediate computation results or held data information of other participants. A formal description of the problem can be found in [link to problem description]. Figure 10 The secure two-way vector multiplication and transformation protocol includes the following steps: Step (d1): Participants Alice The node secretly generates a random vector locally. .

[0083] Step (d2): Participants Alice Nodes perform secret computations locally , .in This is obtained by taking the reciprocal of each digit of the random vector. Taking the reciprocal digit by digit specifically refers to taking the reciprocal digit of any input vector. Perform the bitwise reciprocal operation to convert the result into a vector. The process.

[0084] Step (d3): Participants Alice Nodes and Participants Bob The node is based on a secure two-way bitwise multiplication protocol. Each inputs its own private vector. and Perform a round of secure two-way quantity multiplication protocol calculation The results were obtained respectively. .

[0085] Step (d4): Participants Alice Nodes perform secret computations locally ,in Then will Send to the participants Bob node.

[0086] Step (d5): Participants Bob The node receives the participants Alice Node sent Later, it was secretly calculated locally. ,in .

[0087] Step (d6): Participants Alice Nodes and Participants Bob Each node sets its private result vector. Send the request to the party requesting the secure two-way variable addition-multiplication transformation calculation, satisfying... .

[0088] It is easy to verify that: Its overall principle is as follows: Figure 11 As shown.

[0089] A5. The first participating node and the second participating node send their respective first and second reciprocal calculation output vectors to the calculation requester for aggregation to obtain the sigmoid calculation vector.

[0090] Specifically, the first participating node Alice and the second participating node Bob each set their private result vectors. Send the request to the party requesting the secure two-way variable addition-multiplication transformation calculation, satisfying... .

[0091] It can be easily verified using the following formula: The principle of the safe two-directional sigmoid calculation method based on additive-multiplicative transformation provided in this embodiment is as follows: Figure 12 As shown.

[0092] The method provided in the above embodiments of this application utilizes a secure two-way quantity multiplication protocol. S2PVEM Implemented secure two-way variable addition-multiplication transformation protocol S2PVATM This protocol is lightweight, low-overhead, and computationally efficient, solving the problems of high communication overhead, high computational complexity, and low usability caused by the mixed use of homomorphic encryption, secret sharing, unintentional transmission, and obfuscated circuits in existing cryptographic schemes. It also utilizes a secure two-way vector addition-multiplication transformation protocol. S2PVATM Implemented secure two-way reciprocal protocol S2PVR This protocol is based on accurate calculation of reciprocals in the real number field, requiring only one call to the secure two-way quantity addition-multiplication transformation protocol and one call to the secure two-way quantity bitwise multiplication protocol. It has high calculation accuracy and low communication overhead. Based on this, a secure two-way quantity sigmoid protocol is proposed. S2PVS By decomposing the sigmoid function into its reciprocal and bitwise multiplication operations, and utilizing secure two-way vector bitwise multiplication and secure two-way vector reciprocal protocols, the sigmoid function value can be accurately calculated without polynomial approximation or piecewise function substitution. This effectively avoids the precision errors caused by techniques such as obfuscated circuits and homomorphic encryption in the conversion of nonlinear operations to linear operations. Finally, the secure two-way vector reciprocal protocol proposed in the above embodiments... S2PVR With secure bidirectional sigmoid protocol S2PVS It offers greater security, as neither protocol relies on a third-party cloud platform, thus avoiding the risk of privacy data leakage due to attacks on third-party cloud platforms.

[0093] In another exemplary embodiment of this application, another method for calculating the secure two-directional sigmoid based on additive-multiplicative transformation is also provided, such as... Figure 13 As shown, the safe two-directional sigmoid calculation method based on additive-multiplicative transformation includes the following steps: B1. The first participating node and the second participating node perform privacy processing on their respective initial input vectors locally, obtaining a first input vector and a second input vector, respectively. The privacy processing involves processing the initial input vector of the first participating node or the second participating node according to the natural constant to obtain the first input vector or the second input vector. Specifically, in this embodiment, the first participating node, Alice, secretly computes the following locally. ,in The second participating node, Bob, performs secret computation locally. ,in .

[0094] B2. The first participating node uses the first input vector as one input vector of the secure two-way vector addition-multiplication transformation protocol, and the second participating node uses the second input vector as another input vector of the secure two-way vector addition-multiplication transformation protocol. The first and second participating nodes respectively obtain the first addition-multiplication transformation calculation output vector and the second addition-multiplication transformation calculation output vector. In this embodiment, step B2 specifically includes the following steps: B21. The first participating node generates a first random vector locally, and takes the reciprocal of each digit of the first random vector to obtain the first random reciprocal vector.

[0095] B22. The first participating node performs a bitwise multiplication on the first random inverse vector and the first input vector locally to obtain the first bit multiplied input vector.

[0096] B23. The first participating node uses the first random reciprocal vector as an input vector of the secure two-way vector bit multiplication protocol, and the second participating node uses the second input vector as another input vector of the secure two-way vector bit multiplication protocol. The first participating node and the second participating node obtain the first bit multiplication calculation output vector and the second bit multiplication calculation output vector, respectively.

[0097] B24. The first participating node sums the first sum vector locally based on the first multiplier input vector and the first multiplier calculation output vector, and sends the first sum vector to the second participating node.

[0098] B25. The second participating node sums the output vector locally based on the first summation vector and the second bitwise multiplication to obtain the second summation vector.

[0099] B26. The first participating node uses the first random vector as the first addition-multiplication transformation to calculate the output vector, and the second participating node uses the second summation vector as the second addition-multiplication transformation to calculate the output vector.

[0100] Specifically, the first participating node Alice and the second participating node Bob are based on a secure two-way vector addition-multiplication transformation protocol. Each inputs its own private vector. and Perform a round of secure two-way quantity multiplication protocol calculation The results were obtained respectively. The specific process is detailed in the above embodiment regarding the secure two-way vector addition-multiplication transformation protocol.

[0101] B3. The first participating node and the second participating node fine-tune the first multiplication transformation calculation output vector and the second multiplication transformation calculation output vector locally, respectively, to obtain the fine-tuned first multiplication transformation calculation output vector and the fine-tuned second multiplication transformation calculation output vector. In this embodiment, the first participating node Alice calculates locally. ,in The second participating node, Bob, performs local computation. ,in .

[0102] B4. The first participating node uses the fine-tuned first addition-multiplication transformation output vector as one input vector of the secure two-way matrix multiplication protocol, and the second participating node uses the fine-tuned second addition-multiplication transformation output vector as another input vector of the secure two-way matrix multiplication protocol. The first and second participating nodes obtain the first multiplication calculation output vector and the second multiplication calculation output vector, respectively. In the secure two-way matrix multiplication protocol, after matrixing the two input vectors, the secure two-way matrix multiplication protocol is used to perform calculations based on the matrixed two input vectors, and the calculation results of the secure two-way matrix multiplication protocol are dimensionality reduced.

[0103] Specifically, in this embodiment, the first participating node Alice and the second participating node Bob are based on a secure two-way bitwise multiplication protocol. Each inputs its own private vector. and Perform a round of secure two-way reciprocal protocol calculation The results were obtained respectively. The specific process is detailed in the above embodiment regarding the secure two-way vector reciprocal protocol.

[0104] B5. The first participating node and the second participating node send their respective first-bit multiplication output vectors and second-bit multiplication output vectors to the computation requester for aggregation, resulting in the sigmoid computation vector. In this embodiment, the first participating node Alice and the second participating node Bob each send their private result vectors... Send the request to the party requesting the secure two-way variable addition-multiplication transformation calculation, satisfying... .

[0105] It can be easily verified using the following formula: The principle of the safe two-directional sigmoid calculation method based on additive-multiplicative transformation provided in this embodiment is as follows: Figure 14As shown. In this embodiment, compared to the previous implementation, the S2PVR protocol is omitted, and only the S2PVEM and S2PVATM protocols need to be called once. The aforementioned implementation requires calling the S2PVEM and S2PVR protocol once, and the S2PVR protocol is composed of S2PVATM and S2PVEM once. Therefore, compared to this embodiment, the previous embodiment is more complex.

[0106] Based on the same inventive concept, this application also provides a system for implementing the aforementioned safe two-way sigmoid calculation method based on additive-multiplicative transformation. This safe two-way sigmoid calculation system based on additive-multiplicative transformation is deployed at each participating node in the network. In an exemplary embodiment, such as... Figure 15 As shown, a secure two-directional sigmoid computation system based on additive-multiplicative transformation is provided, including the following modules: task acquisition module, secure computation module, rule generation module, consensus computation module, and data transmission module.

[0107] The task acquisition module is used to receive and parse sigmoid calculation requests from the calculation requester.

[0108] The secure computation module is used to automatically match the corresponding secure computation protocol based on the parsed sigmoid computation request. The secure computation protocols include secure two-way matrix multiplication protocol, secure two-way variable bitwise multiplication protocol, secure two-way variable addition-multiplication transformation protocol, secure two-way variable reciprocal protocol, and secure two-way variable sigmoid protocol.

[0109] The rule generation module is used to split the sigmoid calculation request according to the asynchronous instruction set of the matched secure computing protocol. The two participating nodes in the sigmoid calculation request perform collaborative computing according to the secure two-way sigmoid calculation method based on addition-multiplication transformation as described above.

[0110] The consensus computation module is used to ensure the synchronization and consistency of results between the two participating nodes in the sigmoid computation request during collaborative computation.

[0111] The data sending module is used to send the first reciprocal calculation output vector obtained by the first participating node or the second reciprocal calculation output vector obtained by the second participating node to the calculation requester for aggregation to obtain the sigmoid calculation vector.

[0112] certainly, Figure 15 The architecture shown is merely exemplary; it can be omitted as needed when implementing different functionalities. Figure 15 One or at least two components of the system shown.

[0113] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 16 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage medium. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it can implement the secure two-way sigmoid calculation method based on additive-multiplicative transformation provided in any of the preceding embodiments.

[0114] Those skilled in the art will understand that Figure 16 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0115] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0116] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0117] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0118] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0119] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0120] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0121] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0122] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A secure two-direction vector sigmoid calculation method based on multiplication-addition transformation, characterized in that, The method comprises the following steps: The first participant node and the second participant node locally perform privacy processing on respective initial input vectors to obtain a first input vector and a second input vector respectively; the privacy processing is processing the initial input vector of the first participant node or the second participant node according to a natural constant to obtain the first input vector or the second input vector; The first participant node takes the first input vector as one input vector of a secure two-party vector bit multiplication protocol, the second participant node takes the second input vector as another input vector of the secure two-party vector bit multiplication protocol, and the first participant node and the second participant node obtain a first bit multiplication calculation output vector and a second bit multiplication calculation output vector respectively; in the secure two-party vector bit multiplication protocol, after matrix processing of the two input vectors, calculation is performed based on a secure two-party matrix multiplication protocol according to the two matrix-processed input vectors, and dimension reduction processing is performed on the calculation result of the secure two-party matrix multiplication protocol; The first participant node locally fine-tunes the first bit multiplication calculation output vector to obtain a fine-tuned first bit multiplication calculation output vector; The first participant node takes the fine-tuned first bit multiplication calculation output vector as one input vector of a secure two-party vector reciprocal protocol, the second participant node takes the second bit multiplication calculation output vector as another input vector of the secure two-party vector reciprocal protocol, and the first participant node and the second participant node obtain a first reciprocal calculation output vector and a second reciprocal calculation output vector respectively; in the secure two-party vector reciprocal protocol, calculation is performed based on a secure two-party vector multiplication and addition conversion protocol, and then calculation is performed based on a secure two-party vector bit multiplication protocol after taking the reciprocal of the calculation result of the secure two-party vector multiplication and addition conversion protocol bit by bit; The first participant node and the second participant node send the first reciprocal calculation output vector and the second reciprocal calculation output vector obtained respectively to a calculation request party for aggregation to obtain a sigmoid calculation vector.

2. The secure two-directional vector sigmoid calculation method based on the multiplication-addition transformation according to claim 1, characterized in that, The first participant node and the second participant node locally perform privacy processing on respective initial input vectors to obtain a first input vector and a second input vector respectively, and the specific steps comprise: The first participant node locally processes the initial input vector of the first participant node according to a natural constant to obtain the first input vector; The second participant node locally processes the initial input vector of the second participant node according to a natural constant to obtain the second input vector. 3.The secure two-direction vector sigmoid calculation method based on the multiplication-addition transformation of claim 1, wherein, The first participant node takes the first input vector as one input vector of a secure two-party vector bit multiplication protocol, the second participant node takes the second input vector as another input vector of the secure two-party vector bit multiplication protocol, and the first participant node and the second participant node obtain a first bit multiplication calculation output vector and a second bit multiplication calculation output vector respectively, and the specific steps comprise: The first participant node performs matrix processing on the first input vector to obtain a first input matrix; The second participant node performs matrix processing on the second input vector to obtain a second input matrix; The first participant node takes the first input vector as one input vector of a secure two-party vector bit multiplication protocol, the second participant node takes the second input vector as another input vector of the secure two-party vector bit multiplication protocol, and the first participant node and the second participant node obtain a first bit multiplication calculation output vector and a second bit multiplication calculation output vector respectively, and the specific steps comprise: The first participant node performs matrix processing on the first input vector to obtain a first input matrix; The second participant node performs matrix processing on the second input vector to obtain a second input matrix; The first participant node takes the fine-tuned first bit multiplication calculation output vector as one input vector of a secure two-party vector reciprocal protocol, the second participant node takes the second bit multiplication calculation output vector as another input vector of the secure two-party vector reciprocal protocol, and the first participant node and the second participant node obtain a first reciprocal calculation output vector and a second reciprocal calculation output vector respectively; in the secure two-party vector reciprocal protocol, calculation is performed based on a secure two-party vector multiplication and addition conversion protocol, and then calculation is performed based on a secure two-party vector bit multiplication protocol after taking the reciprocal of the calculation result of the secure two-party vector multiplication and addition conversion protocol bit by bit; The first participant node takes the first input matrix as one input matrix of the secure two-party matrix multiplication protocol, the second participant node takes the second input matrix as another input matrix of the secure two-party matrix multiplication protocol, and the first participant node and the second participant node obtain the first matrix multiplication calculation output matrix and the second matrix multiplication calculation output matrix respectively; The first participant node performs dimension reduction processing on the first matrix multiplication calculation output matrix to obtain the first bit multiplication calculation output vector; The second participant node performs matrix processing on the second matrix multiplication calculation output matrix to obtain the second bit multiplication calculation output vector.

4. The secure two-directional vector sigmoid calculation method based on the multiplication-addition transformation according to claim 1, wherein, The first participant node takes the fine-tuned first bit multiplication calculation output vector as one input vector of the secure two-way vector reciprocal protocol, the second participant node takes the second bit multiplication calculation output vector as another input vector of the secure two-way vector reciprocal protocol, and the first participant node and the second participant node obtain the first reciprocal calculation output vector and the second reciprocal calculation output vector respectively, which specifically includes: The first participant node takes the fine-tuned first bit multiplication calculation output vector as one input vector of the secure two-way vector reciprocal protocol, the second participant node takes the second bit multiplication calculation output vector as another input vector of the secure two-way vector reciprocal protocol, and the first participant node and the second participant node obtain the first reciprocal calculation output vector and the second reciprocal calculation output vector respectively, which specifically includes: The first participant node takes the fine-tuned first bit multiplication calculation output vector as one input vector of the secure two-way vector reciprocal protocol, the second participant node takes the second bit multiplication calculation output vector as another input vector of the secure two-way vector reciprocal protocol, and the first participant node and the second participant node obtain the first reciprocal calculation output vector and the second reciprocal calculation output vector respectively, which specifically includes: The first participant node takes the fine-tuned first bit multiplication calculation output vector as one input vector of the secure two-way vector reciprocal protocol, the second participant node takes the second bit multiplication calculation output vector as another input vector of the secure two-way vector reciprocal protocol, and the first participant node and the second participant node obtain the first reciprocal calculation output vector and the second reciprocal calculation output vector respectively, which specifically includes: The first participant node and the second participant node locally perform privacy processing on their respective initial input vectors to obtain the first input vector and the second input vector respectively; the privacy processing is to process the initial input vector of the first participant node or the second participant node according to a natural constant to obtain the first input vector or the second input vector; 5. A secure two-direction vector sigmoid calculation method based on a multiplication-addition transformation, characterized by, The first participant node takes the first input vector as one input vector of the secure two-way vector reciprocal protocol, the second participant node takes the second input vector as another input vector of the secure two-way vector reciprocal protocol, and the first participant node and the second participant node obtain the first reciprocal calculation output vector and the second reciprocal calculation output vector respectively, which specifically includes: The first participant node and the second participant node respectively fine-tune the first multiplication calculation output vector and the second multiplication calculation output vector locally to obtain the fine-tuned first multiplication calculation output vector and the fine-tuned second multiplication calculation output vector; ​ ​ The first participant node takes the fine-tuned first multiplication transformation calculation output vector as one input vector of a secure two-way vector bit multiplication protocol, the second participant node takes the fine-tuned second multiplication transformation calculation output vector as another input vector of the secure two-way vector bit multiplication protocol, and the first participant node and the second participant node obtain a first bit multiplication calculation output vector and a second bit multiplication calculation output vector respectively; in the secure two-way vector bit multiplication protocol, after matrix processing of the two input vectors, calculation is performed based on a secure two-way matrix multiplication protocol according to the two matrix-processed input vectors, and dimension reduction processing is performed on the calculation result of the secure two-way matrix multiplication protocol; The first participant node and the second participant node send the first bit multiplication calculation output vector and the second bit multiplication calculation output vector obtained by themselves to the calculation request party for aggregation to obtain a sigmoid calculation vector.

6. The secure two-directional vector sigmoid calculation method based on the multiplication-addition transformation according to claim 5, wherein, The first participant node takes the first input vector as one input vector of a secure two-way vector multiplication transformation protocol, the second participant node takes the second input vector as another input vector of the secure two-way vector multiplication transformation protocol, and the first participant node and the second participant node obtain a first multiplication transformation calculation output vector and a second multiplication transformation calculation output vector respectively, and specifically include: The first participant node generates a first random vector locally, and takes the reciprocal of each bit of the first random vector to obtain a first random reciprocal vector; The first participant node performs bit multiplication locally according to the first random reciprocal vector and the first input vector to obtain a first bit multiplication input vector; The first participant node takes the first random reciprocal vector as one input vector of a secure two-way vector bit multiplication protocol, the second participant node takes the second input vector as another input vector of the secure two-way vector bit multiplication protocol, and the first participant node and the second participant node obtain a first bit multiplication calculation output vector and a second bit multiplication calculation output vector respectively; The first participant node locally performs summation according to the first bit multiplication input vector and the first bit multiplication calculation output vector to obtain a first summation vector, and sends the first summation vector to the second participant node; The second participant node locally performs summation according to the first summation vector and the second bit multiplication calculation output vector to obtain a second summation vector; The first participant node takes the first random vector as a first multiplication transformation calculation output vector, and the second participant node takes the second summation vector as a second multiplication transformation calculation output vector.

7. A secure two-directional vector sigmoid calculation system based on a multiplication-addition transformation, characterized by The secure two-way vector sigmoid calculation system based on multiplication transformation is arranged in each participant node in networking, and includes a task acquisition module, a secure calculation module, a rule generation module, a consensus calculation module and a data sending module. The task acquisition module is used for receiving and analyzing a sigmoid calculation request from a calculation request party. The security calculation module is configured to automatically match a corresponding security calculation protocol according to the parsed sigmoid calculation request; the security calculation protocol includes a secure two-party matrix multiplication protocol, a secure two-party vector bit multiplication protocol, a secure two-party vector multiplication and transformation protocol, a secure two-party vector reciprocal protocol, and a secure two-party vector sigmoid protocol. The rule generation module is configured to split the sigmoid calculation request according to an asynchronous instruction set of the matched security calculation protocol, and two participant nodes participating in the sigmoid calculation request perform collaborative calculation according to the secure two-party vector sigmoid calculation method based on multiplication and transformation of any one of claims 1-4 or claims 5-6. The consensus calculation module is configured to ensure the synchronization and result consistency of the two participant nodes participating in the sigmoid calculation request during collaborative calculation. The data sending module is configured to send the first reciprocal calculation output vector obtained by the first participant node or the second reciprocal calculation output vector obtained by the second participant node to the calculation request party for aggregation to obtain a sigmoid calculation vector.

8. A computer device comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that the processor executes the computer program to implement the secure two-party vector sigmoid calculation method based on multiplication and transformation of any one of claims 1-4 or claims 5-6.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the secure two-party vector sigmoid calculation method based on multiplication and transformation of any one of claims 1-4 or claims 5-6.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to implement the secure two-party vector sigmoid calculation method based on multiplication and transformation of any one of claims 1-4 or claims 5-6.

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