Safe two-direction vector bit multiplication method based on space dimension reduction and related device

Abstract

The invention discloses a safe two-direction vector bit multiplication method based on spatial dimensionality reduction and a related device, and relates to the technical field of block chain security, the method comprises the following steps: preprocessing an obtained private vector of a first participant and an obtained private vector of a second participant to obtain a first participant private matrix and a second participant private matrix; based on a secure two-party matrix multiplication calculation protocol, performing secure two-party matrix multiplication calculation on the two participant private matrixes to obtain a first participant private output matrix and a second participant private output matrix; performing dimension reduction conversion processing on the private output matrixes of the two participants to obtain a first dimension reduction private vector and a second dimension reduction private vector; and summarizing the two dimensionality reduction private vectors to obtain a safe two-direction vector bit multiplication result. According to the method, the practicability can be improved, the communication efficiency is improved, meanwhile, the requirements for higher calculation precision and lower calculation cost are considered, and data leakage is not likely to be caused.

Description

Technical Field

[0001] The present invention relates to the field of blockchain security technology, and in particular to a secure two-way quantization bitwise multiplication method based on space dimensionality reduction and a related device. Background Art

[0002] With the development of big data and artificial intelligence, data has become an important resource for promoting innovation and economic growth. Privacy computing is a computing method that ensures data privacy and security. Its purpose is to protect the confidentiality of personal information when multiple parties collaborate to process data. Existing privacy-preserving computing technology (PPCT) uses homomorphic encryption, differential privacy, secret sharing and other technologies. By reducing computing efficiency and accuracy and increasing communication overhead, it breaks the inherent data island model and drives the circulation of multi-party data, realizing the mining of the value behind data elements.

[0003] In the training and inference process of AI large model scenarios, the activation function Sigmoid, the output layer Softmax, and the chain propagation of gradient parameters in the back propagation process all involve vector bitwise multiplication operations, which greatly improve the parallelization of privacy computing. Therefore, under the premise of meeting privacy requirements, it is of great research significance to realize the bitwise multiplication of two or even multiple directions. The following summarizes the existing related technologies at home and abroad:

[0004] In the existing technology, the Obliv-C framework proposed by Zahur and Evans and the ABY framework proposed by Demmler, Schneider and others both use obfuscated circuit technology, which converts mathematical operations (addition and multiplication) into Boolean circuits and combines encryption technologies such as secure shuffling and oblivious transfer to protect the circuit outputs corresponding to each input.

[0005] The MP-SPDZ framework proposed by Keller and the Crypten framework provided by Knott, Venkataraman and others use the idea of ​​secret sharing technology to hide secret values. They randomly split each secret value into multiple slices and use a threshold number of nodes to reconstruct and combine them when necessary through interactions among various participants, which can realize the privacy vector bit multiplication problem.

[0006] Lin, Zhao and others proposed a SOCI framework by combining the ElGamal homomorphic encryption scheme with the Paillier primitive. The SOCI framework can encrypt the privacy vector to be calculated locally and then participate in the calculation. Finally, the answer identical to the plaintext calculation can be obtained through decryption with the private key, which can solve the privacy vector bit multiplication problem.

[0007] However, the above technical solution has the following advantages and disadvantages:

[0008] Obliv-C and ABY frameworks both have general secure two-party computation solutions based on obfuscated circuits. Obfuscated circuit technology can support secure two-way bitwise multiplication of quantities, but such solutions require the construction of a large number of circuits, resulting in high computational and spatial complexity and low computational efficiency. At the same time, this technology is essentially for Boolean operations, and there are precision issues in the processing of floating-point numbers, making it insufficiently practical.

[0009] MP-SPDZ and Crypten frameworks are based on the idea of ​​secret sharing. They divide the value into several shares for sharing to hide the true value of the two parties. This ensures that the secret value can only be reconstructed when enough parties join together. However, such schemes involve a large number of message exchanges between multiple parties, which leads to low communication efficiency.

[0010] Lin, Zhao and others proposed a SOCI framework based on the Paillier primitive, which uses public key encryption to calculate the ciphertext and then uses the private key to decrypt the result. Although the security of the calculation results is guaranteed, due to the complexity of the ciphertext calculation itself and its reliance on a third-party cloud platform for calculation, there are problems with high computing storage and communication overhead costs, as well as the risk of data leakage once the third-party cloud platform is attacked.

[0011] Therefore, how to design a secure two-way multiplication method and related devices that can improve practicality and communication efficiency while taking into account higher computing accuracy and lower computing cost requirements and not easily cause data leakage has become a technical problem that needs to be urgently solved in this field. Summary of the invention

[0012] The purpose of the present invention is to provide a secure two-way quantization multiplication method and related devices based on spatial dimensionality reduction, which can realize efficient, secure and reliable privacy numerical calculation, improve practicality, improve communication efficiency, take into account higher calculation accuracy and lower calculation cost requirements, and are not prone to data leakage.

[0013] To achieve the above object, the present invention provides the following solutions:

[0014] In a first aspect, the present invention provides a secure two-way quantization bitwise multiplication method based on space dimension reduction, the secure two-way quantization bitwise multiplication method based on space dimension reduction comprising:

[0015] Get the private vector of the first participant and the private vector of the second participant.

[0016] The private vector of the first participant and the private vector of the second participant are preprocessed to obtain a first participant private matrix and a second participant private matrix.

[0017] Based on the secure two-party matrix multiplication calculation protocol (S2PM), the first participant's private matrix and the second participant's private matrix are subjected to secure two-party matrix multiplication calculation to obtain the first participant's private output matrix and the second participant's private output matrix; the secure two-party matrix multiplication calculation protocol is a protocol designed based on secure data obfuscation technology (SDDT); the secure data obfuscation technology is a technology that decomposes any multi-objective operation into a new multi-objective addition to obfuscate the calculation results of intermediate values; the sum of the first participant's private output matrix and the second participant's private output matrix is ​​the product result of the first participant's private matrix and the second participant's private matrix.

[0018] Perform dimensionality reduction conversion processing on the first participant's private output matrix and the second participant's private output matrix respectively to obtain a first reduced-dimensionality private vector and a second reduced-dimensionality private vector.

[0019] The first reduced-dimensionality private vector and the second reduced-dimensionality private vector are aggregated to obtain a secure two-way vector bitwise multiplication result.

[0020] In a second aspect, the present invention provides a secure two-way quantization bitwise multiplication device based on spatial dimension reduction, the secure two-way quantization bitwise multiplication device based on spatial dimension reduction comprising:

[0021] The private vector acquisition module is used to acquire the private vector of the first participant and the private vector of the second participant.

[0022] The preprocessing module is used to preprocess the private vector of the first participant and the private vector of the second participant to obtain the first participant's private matrix and the second participant's private matrix.

[0023] A secure two-party matrix multiplication calculation module is used to perform secure two-party matrix multiplication calculation on the first participant's private matrix and the second participant's private matrix based on a secure two-party matrix multiplication calculation protocol to obtain a first participant's private output matrix and a second participant's private output matrix; the secure two-party matrix multiplication calculation protocol is a protocol designed based on secure data obfuscation technology; the secure data obfuscation technology is a technology that decomposes any multi-objective operation into a new multi-objective addition for obfuscating the calculation results of intermediate values; the sum of the first participant's private output matrix and the second participant's private output matrix is ​​the product result of the first participant's private matrix and the second participant's private matrix.

[0024] The dimensionality reduction conversion processing module is used to perform dimensionality reduction conversion processing on the first participant's private output matrix and the second participant's private output matrix respectively to obtain a first dimensionality reduction private vector and a second dimensionality reduction private vector.

[0025] The aggregation module is used to aggregate the first reduced-dimensionality private vector and the second reduced-dimensionality private vector to obtain a secure two-way vector bitwise multiplication result.

[0026] In a third aspect, the present invention provides a computer device comprising: 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 any of the above-described secure two-way quantization bitwise multiplication methods based on spatial dimensionality reduction.

[0027] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-mentioned secure two-way quantization bitwise multiplication methods based on spatial dimensionality reduction.

[0028] In a fifth aspect, the present invention provides a computer program product, including a computer program, which, when executed by a processor, implements any of the above-mentioned secure two-way quantization bitwise multiplication methods based on spatial dimensionality reduction.

[0029] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0030] The present invention provides a secure two-way quantization bitwise multiplication method and related devices based on spatial dimensionality reduction. First, a private vector of a first participant and a private vector of a second participant are obtained; the private vector of the first participant and the private vector of the second participant are preprocessed to obtain a first participant private matrix and a second participant private matrix; secondly, based on a secure two-party matrix multiplication calculation protocol, a secure two-party matrix multiplication calculation is performed on the first participant private matrix and the second participant private matrix to obtain a first participant private output matrix and a second participant private output matrix; then, a dimensionality reduction conversion process is performed on the first participant private output matrix and the second participant private output matrix respectively to obtain a first reduced-dimensional private vector and a second reduced-dimensional private vector; finally, the first reduced-dimensional private vector and the second reduced-dimensional private vector are aggregated to obtain a secure two-way quantization bitwise multiplication result. The present invention designs a secure two-party matrix multiplication calculation protocol based on secure data obfuscation technology. The protocol does not need to introduce any secret key and due to its own characteristics of obfuscating encrypted data based on the real number field, it ensures the security of "one-time one-key" while also taking into account higher calculation accuracy and lower calculation cost requirements; at the same time, the present invention solves the problem of low communication efficiency caused by the need for a large amount of information exchange in secret sharing technology through dimensionality reduction conversion processing; in addition, the present invention does not need to rely on a third-party cloud platform, and can solve the risk of data leakage caused by attacks on the third-party cloud platform in homomorphic encryption technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0032] Figure 1 A flowchart of a secure two-way quantization multiplication method based on spatial dimensionality reduction is provided in accordance with an embodiment of the present invention.

[0033] Figure 2 A schematic diagram of a secure two-way bitwise multiplication problem provided by an embodiment of the present invention.

[0034] Figure 3 A schematic diagram of the security data obfuscation technology provided by one embodiment of the present invention.

[0035] Figure 4 A schematic diagram of a secure two-square matrix multiplication calculation problem provided by an embodiment of the present invention.

[0036] Figure 5 A flowchart of a secure two-party matrix multiplication calculation protocol provided by one embodiment of the present invention.

[0037] Figure 6 A flow chart of a secure two-way bitwise multiplication protocol provided by an embodiment of the present invention.

[0038] Figure 7 A schematic diagram of a secure multi-directional bitwise multiplication problem provided by an embodiment of the present invention.

[0039] Figure 8 A flow chart of a secure multi-directional bitwise multiplication protocol provided by an embodiment of the present invention.

[0040] Fig. 9 A schematic diagram of functional modules of a secure two-way quantization multiplication device based on spatial dimension reduction provided by one embodiment of the present invention.

[0041] Fig.10 A diagram of an implementation device of a secure two-way quantizer bitwise multiplication algorithm applied to distributed computing nodes provided in one embodiment of the present invention.

[0042] Fig.11 A schematic diagram of the structure of a computer device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] Terminology explanation:

[0046] Semi-honest model: The semi-honest model (Semi-Honest Adversaries Security) is a specific protocol that assumes that all participants in the calculation will honestly participate in the privacy calculation and strictly follow each step of the process. However, there is a risk that some corrupted participants will try to infer the privacy of other participants through the intermediate or final results of the protocol execution process.

[0047] Secure two-party matrix multiplication calculation protocol: As the name suggests, the secure two-party matrix multiplication calculation protocol assumes that there are two participants P1 and P2 who do not trust each other. Each participant holds a secret input matrix x and y, and jointly executes a two-party multiplication protocol f(x,y)=Output(v1,v2)=x·y. In the end, each participant obtains the corresponding output v1,v2, and the output satisfies v1+v2=x·y. During the entire calculation process, each participant node only knows the input and output data involved in its own calculation process, and cannot obtain any intermediate calculation results about other participants.

[0048] Secure 2-Party Vector Element-wise Multiplication Protocol: Secure 2-Party Vector Element-wise Multiplication Protocol (S2PVEM), as the name suggests, assumes that there are two participants P1 and P2 who do not trust each other. Each participant holds a secret input vector x and y and jointly executes a secure two-way vector multiplication protocol Finally, each participant obtains the corresponding output v1, v2, and the output satisfies During the entire calculation process, each participating node only knows the input and output data involved in its own calculation process and cannot obtain any intermediate calculation results of other participants.

[0049] Secure N-Party Vector Element-wise Multiplication Protocol: Secure N-Party Vector Element-wise Multiplication Protocol (SNPVEM), as the name suggests, assumes that there are N mutually untrusting parties P1, P2, ..., P N , each participant holds a secret input vector α1, α2, …, α N ∈R m , jointly implement a secure multi-directional bitwise multiplication protocol Finally, each participant gets the corresponding output W1, W2, ..., W N , and the output satisfies During the entire calculation process, each participating node only knows the input and output data involved in its own calculation process and cannot obtain any intermediate calculation results of other participants.

[0050] Secure data obfuscation technology: Secure data obfuscation technology is a data protection method used to protect the intermediate results of multi-party secure computing. By rationally constructing the computing protocol, the computing results are randomly split, so that the outputs of multiple parties together constitute the real target computing results in a linear combination, ultimately achieving a one-time, one-key data privacy protection effect.

[0051] Privacy computing technology: Privacy computing technology specifically refers to a series of information security technologies that break down data silos, coordinate multi-party computing, and ultimately achieve complex computing and modeling analysis of multi-source data without exposing the privacy of private data of all parties, thereby ensuring that data elements are "available but invisible" during the circulation and integration process.

[0052] The present invention mainly focuses on the problem of secure bitwise multiplication of quantities in two directions to achieve efficient, secure and reliable privacy numerical calculation. Therefore, based on the above objectives, the technical problems to be solved by the present invention are as follows:

[0053] 1) Existing solutions to the problem of secure bitwise multiplication of quantities in two directions mostly use computing frameworks developed based on traditional basic cryptographic primitives such as homomorphic encryption, secret sharing, and obfuscated circuits. These methods rely on ciphertext space calculations with extremely high time and space complexities, which leads to low practicality and efficiency.

[0054] 2) Existing solutions to the problem of secure two-way bitwise multiplication of quantities use large prime number encryption, which increases the number of ciphertext bits in the computational space or introduces differential noise, which causes the loss of model training parameter precision, directly leading to insufficient numerical calculation precision and affecting the reliability of the calculation results.

[0055] 3) Existing application scenarios involving secure two-way quantization bitwise multiplication schemes mostly rely on outsourced cloud service systems for implementation. However, the low credibility of third-party cloud service computing platforms or attacks by malicious nodes may cause the leakage of intermediate calculation results or key key information, further causing security risks of privacy leakage of the original data party.

[0056] In an exemplary embodiment, Figure 1 As shown, a secure two-way vector bitwise multiplication method based on spatial dimension reduction is provided, and the method includes the following steps S1 to S5. Among them:

[0057] S1: Obtain the private vector of the first participant and the private vector of the second participant.

[0058] S2: Preprocessing the private vector of the first participant and the private vector of the second participant to obtain a first participant private matrix and a second participant private matrix.

[0059] S3: Based on the secure two-party matrix multiplication calculation protocol, the first participant's private matrix and the second participant's private matrix are subjected to secure two-party matrix multiplication calculation to obtain the first participant's private output matrix and the second participant's private output matrix; the secure two-party matrix multiplication calculation protocol is a protocol designed based on secure data obfuscation technology; the secure data obfuscation technology is a technology that decomposes any multi-objective operation into a new multi-objective addition to confuse the calculation of intermediate value results; the sum of the first participant's private output matrix and the second participant's private output matrix is ​​the product result of the first participant's private matrix and the second participant's private matrix.

[0060] S4: Perform dimensionality reduction conversion processing on the first participant's private output matrix and the second participant's private output matrix respectively to obtain a first reduced-dimensionality private vector and a second reduced-dimensionality private vector.

[0061] S5: Aggregate the first dimension-reduced private vector and the second dimension-reduced private vector to obtain a secure two-way vector bitwise multiplication result.

[0062] By implementing the above-mentioned steps S1 to S5, the present invention designs a secure two-party matrix multiplication calculation protocol S2PM based on the secure data obfuscation technology SDDT. The protocol does not need to introduce any secret key and due to its own characteristics of obfuscating encrypted data based on the real number field, it ensures the security of "one-time one-key" while also taking into account higher calculation accuracy and lower calculation cost requirements; at the same time, the present invention solves the problem of low communication efficiency caused by the need for a large amount of information exchange in secret sharing technology through dimensionality reduction conversion processing; in addition, the present invention does not need to rely on a third-party cloud platform, and can solve the risk of data leakage caused by attacks on the third-party cloud platform in homomorphic encryption technology.

[0063] The safe two-way scalar multiplication problem is defined as follows:

[0064] It is known that there are two computing parties, Alice and Bob, who are independent and do not trust each other. Alice holds an n-dimensional private vector α = (α1, α2, …, α n ) T , Bob holds an n-dimensional private vector β = (β1, β2, …, β n ) T The two parties wish to achieve this by jointly executing a secure two-way quantum multiplication protocol. Finally, each computing participant node gets its corresponding output W a , W b, and sent to the computation requester to aggregate and obtain the desired scalar product result of the two parties. During the computation process, each participant node can only understand its own input and output information, and cannot obtain the intermediate computation results and held data information of other participants. The formal description of the problem can be found in Figure 2 .

[0065] The secure data obfuscation techniques are as follows:

[0066] For most multi-party computations, the process of achieving secure computation usually involves multiple steps of interaction. Inevitably, we need to face a problem: how to ensure the security of intermediate results. For example, when the product of two matrices A×B is used as the intermediate result of the computation, whether the participating node Alice or node Bob obtains the result of the final matrix A×B, it is possible to infer the data information of the other party. Therefore, in the privacy computing process, we must not only ensure the security of the initial input data, but also the security of the intermediate results of the computation.

[0067] To solve this problem, the present invention proposes a secure data obfuscation encryption technology, that is, by disassembling any multi-objective operation into a new multi-objective addition to obfuscate the result of calculating the intermediate value. To make it easier to explain its principle, this article takes the two-party operation type as an example. The principle is as follows Figure 3 Assume S k =F k (A i ,B i ), where F k is the target calculation function of the kth step, A i is the private input data of Alice in step k, B i is the private input data of the kth step belonging to the organization Bob. When executing the kth step of the multi-party secure computation protocol, the intermediate result S k The following constraints will be strictly followed: Alice only knows her own calculation result A k and Bob only knows the result B k , and A k +B k =S k . Formula [A i :B i ]→[A k :B k |A k +B k =F k (A i ,B i )] represents the process of transferring the intermediate value. During the whole process, Alice and Bob are not allowed to exchange each other’s data information, including the calculation of the intermediate result after the splitting of A k and B k; Similarly, for the k+1th step, the input and The output A of Alice and Bob at step k k and B k The transmission structure, and and Its output A k+1 and B k+1 satisfy Alice only knows her own calculation result A k+1 and Bob only knows the result B k+1 Therefore, as long as the intermediate value is split into two random data items and stored separately in the two computing participants at each step of the calculation, it can be guaranteed that no party can reverse the original data item from the obfuscated encrypted data, making the entire privacy computing process more secure.

[0068] The secure two-party matrix multiplication computation protocol problem is defined as follows:

[0069] It is known that there are two computing parties, Alice and Bob, who are independent and do not trust each other. Alice holds a private data matrix A with a dimension of n×s and is only stored in her own computing node, and Bob holds a private data matrix B with a dimension of s×m. The two participants hope to implement f(A,B)=AB=V by jointly executing a secure matrix multiplication protocol a +V b Finally, each computing participant node obtains its own output matrix V with dimensions of n×m a 、V b , and sent to the calculation requester to aggregate and obtain the expected two-way matrix product result. During the calculation process, each participant node can only understand its own input and output information, and cannot obtain the intermediate settlement results and holding data information of other participants. The formal description of the problem is shown in Figure 4 .

[0070] like Figure 5 As shown, the secure two-party matrix multiplication calculation protocol process is as follows:

[0071] Step A1: The auxiliary computing node, also known as the commodity service node CS (CommodityServer), generates two sets of random matrix pairs, which are in the form of random matrices R with dimensions n×s a , a random matrix R with dimension s×m b and two random matrices r of dimension n×m a 、r b These random matrices must strictly satisfy the following constraints: a +r b =R a·R b Then the CS auxiliary node converts the random matrix pair (R a ,r a ) is sent to the participant Alice’s computing node, and the random matrix pair (R b ,r b ) is sent to the computing node of participant Bob.

[0072] Step A2: Upon receiving the corresponding random matrix pair (R a ,r a ) after which the node internally calculates And send it to the participating node Bob.

[0073] Step A3: After receiving the corresponding random matrix pair (R b ,r b ) after which the node internally calculates And send it to the participating node Alice.

[0074] Step A4: Participant Bob's node receives the matrix sent from Alice's node After that, a random matrix V is generated secretly inside b ∈R n×m , and secretly compute the matrix locally Send to Alice node.

[0075] Step A5: After receiving T, the participant Alice's node calculates the matrix locally

[0076] Step A6: Participants Alice and Bob respectively generate their corresponding final obfuscated split results V a 、V b Sent to the two parties requesting matrix multiplication, which will summarize and obtain the final product AB = V a +V b .

[0077] It is easy to verify that:

[0078]

[0079] The protocol for secure two-way bitwise multiplication is as follows:

[0080] The problem of secure two-way vector multiplication usually occurs in application scenarios such as logistic regression, parallel computing of activation functions of multilayer perceptrons, and privacy-preserving matrix multiplication, and has extensive research value. Therefore, in order to maintain generality, let the initial input of Alice's calculation of the participating nodes in the protocol be an m-dimensional private vector α = (α1, α2, …, αm ), Bob calculates the initial input of the participating nodes as an m-dimensional private vector β = (β1, β2, …, β m ), and on this basis, a Figure 6 An efficient parallelized secure two-way quantizer bitwise multiplication protocol for the shown process.

[0081] Specifically, the secure two-way bitwise multiplication protocol process is as follows:

[0082] Step B1: Participant Alice and participant Bob jointly negotiate a positive integer n ≥ 2, and each splits each element of the private vector held by them into n mutually unequal random positive numbers. Participant Alice will i (1≤i≤m) is split into n-dimensional private vectors Participant Bob's node will β i (1≤i≤m) is split into n-dimensional private vectors

[0083] Step B2: Participant Alice's node converts the n-dimensional private vector Convert to an n 2 Private vector of dimension Specifically, by transforming n vectors Splice them together in order to get a new vector Then the vector group The private matrix A∈R is constructed from top to bottom in sequence. m×n2 .

[0084] Step B3: Participant Bob's node sends each private vector Convert to private variables First private vector The n elements in the array are fully arranged and each arrangement is converted into a vector, resulting in a total of s = n! random ordering vectors. The process is expressed as Among them, perms is for m elements A function of a full permutation operation, then from Randomly select n vectors from Together they form a private matrix in the form of row vectors Then the matrix Dimensionality reduction to vector Specifically, the matrix Each column vector is concatenated together to realize the transformation from matrix space to vector space. Sequentially as a column of the matrix together constitute a private matrix

[0085] Step B4: Participant Alice’s node and participant Bob’s node input their respective private data based on the secure two-party matrix multiplication protocol S2PM. and Perform a round of secure two-way matrix multiplication calculation f S2PM (A,B)=A×B. After the S2PM protocol calculation is completed, the calculation f S2PM (A, B) is split into V based on secure data obfuscation technology a 、V b ∈R m×m The two results are sent to the participant Alice node and the participant Bob node as their private outputs, and the two private output matrices satisfy the relationship f S2PM (A,B)=A×B=V a +V b .

[0086] Step B5: Participant Alice’s node and participant Bob’s node obtain the private matrix V respectively a 、V b ∈R m×m After that, each local takes out the n elements of the main diagonal of the matrix and vectorizes them to obtain the private vector W a =m2v(diag(V a )) and W b =m2v(diag(V b )), where W a is the first dimension-reduced private vector (Alice’s dimension-reduced private vector), W b is the second dimension reduction private vector (Bob's dimension reduction private vector), m2v is a function that converts the elements of the diagonal matrix into corresponding vectors bit by bit, and diag is a function that extracts the diagonal elements of any matrix to form a diagonal matrix. Then W a and W b Send it to the computing requester, who will summarize it and get

[0087] It is easy to verify that:

[0088] In an exemplary embodiment, in step S2, it specifically includes:

[0089] S21: Determine a splitting positive integer; the splitting positive integer is greater than or equal to 2.

[0090] S22: Split each element of the private vector of the first party according to the split positive integer to obtain a plurality of first split private vectors.

[0091] S23: Split each element of the second party's private vector according to the split positive integer to obtain a plurality of second split private vectors.

[0092] S24: transforming and sorting the plurality of first split private vectors to obtain a first participant private matrix.

[0093] S25: transforming and sorting the plurality of second split private vectors to obtain a second participant private matrix.

[0094] In an exemplary embodiment, in step S3, it specifically includes:

[0095] S31: Generate two groups of random matrix pairs based on the auxiliary computing node; the two groups of random matrix pairs include: random matrix pairs (R a ,r a ) and random matrix pairs (R b ,r b ), where the random matrix R a The dimension is n×s, and the random matrix R b The dimension is s×m, and the random matrix r a and the random matrix r b The dimension is n×m; r a +r b =R a ·R b .

[0096] S32: The random matrix pair (R a ,r a ) is sent to the first party.

[0097] S33: The random matrix pair (R b ,r b ) is sent to the second party.

[0098] S34: The first participant receives a random matrix pair (R a ,r a ), calculate the private matrix of the first participant and the random matrix R a , obtain a first matrix and, and send the first matrix and to the second participant.

[0099] S35: The second participant receives the random matrix pair (R b ,r b ), calculate the second party's private matrix and the random matrix R b , obtain a second matrix and, and send the second matrix and to the first participant.

[0100] S36: After receiving the first matrix and the second participant, a second participant private output matrix is ​​generated.

[0101] S37: Calculate a confusion matrix according to the private output matrix of the second participant; and send the confusion matrix to the first participant; the calculation formula of the confusion matrix is: Where T is the confusion matrix, is the first matrix and, B is the private matrix of the second participant, V b It is the private output matrix of the second participant, which is a random matrix generated by an internal secret.

[0102] S38: After receiving the confusion matrix, the first participant calculates and obtains the first participant's private output matrix; the calculation formula of the first participant's private output matrix is: Among them, V a is the private output matrix of the first participant, is the second matrix and .

[0103] The present invention is a secure two-party matrix multiplication calculation protocol designed based on secure data obfuscation technology. The protocol does not need to introduce any secret key and due to its own characteristics of obfuscating encrypted data based on the real number field, it ensures the security of "one-time one-pad" while also taking into account higher calculation accuracy and lower calculation cost requirements.

[0104] The present invention proposes a secure two-way vector bitwise multiplication protocol, which transforms numerical values ​​into a two-dimensional matrix space through scaling, and then compresses them into a one-dimensional vector space through spatial dimensionality reduction, thereby realizing the operation of transforming vector bitwise multiplication into matrix multiplication. According to the distributive law and associative law of numerical multiplication, it is ensured that only one round of secure two-way matrix multiplication protocol needs to be called to obtain the final result through parallel calculation, thus solving the problem of low communication efficiency caused by the need for a large amount of information exchange in secret sharing technology.

[0105] The secure two-way bitwise multiplication protocol and the secure multi-way bitwise multiplication protocol proposed in the present invention do not need to rely on a third-party cloud platform, and can solve the risk of data leakage caused by attacks on the third-party cloud platform in homomorphic encryption technology.

[0106] It should be noted that the alternative solution for safe bitwise multiplication of quantities in two directions is as follows:

[0107] Protocol ideas:

[0108] Step 1: Convert the numerical multiplication in the secure two-party numerical multiplication protocol into a vector inner product: If there are other secure two-party numerical multiplication protocols that convert the numerical multiplication a×b into the matrix multiplication A×B, then based on the idea of ​​the secure two-way bitwise multiplication protocol preprocessing module, the matrices A and B in this protocol can be compressed into two vectors, thereby converting the numerical multiplication a×b into the form of a vector inner product.

[0109] Step 2: Convert the vector bitwise multiplication in the secure two-way vector bitwise multiplication protocol into matrix multiplication: Based on the method of converting the numerical multiplication in the secure two-way numerical multiplication protocol in step 1 into the vector inner product, the vector can be converted into a matrix composed of several row or column vectors, and the vector bitwise multiplication can be converted into matrix multiplication. Then, the secure two-way matrix multiplication protocol can be used to realize the secure two-way vector bitwise multiplication.

[0110] In terms of scalability, most existing solutions perform well in secure bitwise multiplication of two-way quanta, but many problems arise when expanding to bitwise multiplication of multi-way quanta. The obfuscated circuit solutions used by Obliv-C and ABY frameworks will result in large circuit scales when encountering large-scale data calculations, and the computational and communication overheads are very high; the secret sharing scheme will generate more information exchange when processing multi-directional quanta multiplication, and the communication efficiency is low. Since homomorphic encryption uses encryption technology itself, the computational cost is very high when it comes to multi-directional quanta multiplication.

[0111] In another exemplary embodiment of the present invention, the problem definition of the secure multi-directional bitwise multiplication protocol is as follows:

[0112] Given N computing parties P1, P2, ..., P N , are independent and do not trust each other, each holding a private vector data stored only in its own computing node, α1, α2, …, α N ∈R m N participants jointly execute a multi-directional bitwise multiplication protocol Finally, each computing participant node obtains its corresponding output W1, W2, ..., W N , and sent to the calculation requester to obtain the desired multi-directional multiplication calculation result. During the calculation process, each participant node can only obtain its own input and output information during the calculation process, and cannot obtain the intermediate settlement results and private data information held by other participants. The formal description of the problem is shown in Figure 7 .

[0113] like Figure 8 As shown, the secure multi-directional bitwise multiplication protocol process is as follows:

[0114] Step C1: Participant P1 node and participant P2 node input their respective private vectors α1∈R based on the secure two-way vector multiplication protocol S2PVEM m and α2∈R m , conduct the <1> Layer-Secure Two-Way Quantity Multiplication Protocol Computation Get the results respectively

[0115] Step C2: Loop and execute the following process N-2 times: For the i-th (1≤i≤N-2) cycle, based on the secure two-way bitwise multiplication protocol S2PVEM,<i+1> The i+2 computing participants at the layer execute a total of i+1 rounds of the S2PVEM protocol (e.g. Fig. 9 middle The jth (1≤j≤i+1) round of secure two-way multiplication is performed by the participant P j Nodes and Participants P i+2 Nodes enter their own private data and α i+2 ∈R m ,calculate Get the results respectively Then the participant P i+2 Nodes compute locally

[0116] Step C3: All parties P i (1≤i≤N) nodes get private vectors After that, you can get Then W i Send it to the computing requester, who will summarize it and get

[0117] It is easy to verify that:

[0118] The present invention extends the secure two-way bitwise multiplication protocol S2PVEM and proposes a secure multi-way bitwise multiplication protocol SNPVEM. It also uses the idea of ​​scale transformation and space dimension reduction to transform vector bitwise multiplication into matrix multiplication. The final result can be obtained by calculating the round-safe two-way quantum bitwise multiplication protocol S2PVEM, which solves the problem of poor scalability of obfuscated circuits, secret sharing and homomorphic encryption technology.

[0119] In summary, the present invention utilizes a secure two-party matrix multiplication computing protocol S2PM implemented based on secure data obfuscation technology. The protocol has the characteristics of lightweight, low overhead, and high computational efficiency. It solves the problems of high communication overhead, high computational complexity, and low availability caused by the mixed calls of technologies such as homomorphic encryption, secret sharing, oblivious transmission, and obfuscated circuits used in existing cryptographic schemes.

[0120] This invention proposes for the first time a privacy protection solution for the problem of secure two-way vector multiplication. The key technical point is to introduce a scaling method that converts the numerical space into a matrix space and then reduces the space dimension into a vector space. Based on the positive integer n jointly agreed by the two parties, the elements in the vector are split into vectors, and then converted into a matrix and reduced to vectors. Therefore, vector multiplication can be converted into matrix multiplication to achieve. This conversion process involves the privacy of the original data of the participating nodes and is an important step to ensure security.

[0121] The present invention performs calculations through a secure two-party matrix multiplication protocol S2PM based on secure data obfuscation technology, and generates the final answer through a local solution module. These two steps respectively ensure the security of the calculation process and the non-disclosure of the private answer of each participating node when obtaining the answer from the main diagonal.

[0122] The present invention also provides an application scenario, which applies the above-mentioned secure two-way quantization bitwise multiplication method based on spatial dimensionality reduction. Specifically: The secure two-way quantization bitwise multiplication method based on spatial dimensionality reduction provided in this embodiment can be applied in a semi-honest scenario. The semi-honest scenario includes: a private vector acquisition link, a preprocessing link, a secure two-party matrix multiplication calculation link, a dimensionality reduction conversion link, and a summary link; preprocessing the acquired private vector of the first participant and the private vector of the second participant to obtain the first participant's private matrix and the second participant's private matrix; based on the secure two-party matrix multiplication calculation protocol, the first participant's private matrix and the second participant's private matrix are subjected to secure two-party matrix multiplication calculation to obtain the first participant's private output matrix and the second participant's private output matrix; respectively perform dimensionality reduction conversion processing on the first participant's private output matrix and the second participant's private output matrix to obtain a first reduced dimensionality private vector and a second reduced dimensionality private vector; summarize the first reduced dimensionality private vector and the second reduced dimensionality private vector to obtain a secure two-way quantization bitwise multiplication result.

[0123] Based on the same inventive concept, an embodiment of the present invention further provides a secure two-way quantization bitwise multiplication device for implementing the secure two-way quantization bitwise multiplication method based on spatial dimensionality reduction involved above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in one or more embodiments of the secure two-way quantization bitwise multiplication device based on spatial dimensionality reduction provided below can refer to the limitations of the secure two-way quantization bitwise multiplication method based on spatial dimensionality reduction above, and will not be repeated here.

[0124] In an exemplary embodiment, Fig. 9 As shown, a secure two-way quantization bitwise multiplication device based on space dimension reduction is provided, and the secure two-way quantization bitwise multiplication device based on space dimension reduction comprises:

[0125] The private vector acquisition module M1 is used to acquire the private vector of the first participant and the private vector of the second participant.

[0126] The preprocessing module M2 is used to preprocess the private vector of the first participant and the private vector of the second participant to obtain the first participant's private matrix and the second participant's private matrix.

[0127] The secure two-party matrix multiplication calculation module M3 is used to perform secure two-party matrix multiplication calculation on the first participant's private matrix and the second participant's private matrix based on a secure two-party matrix multiplication calculation protocol to obtain a first participant's private output matrix and a second participant's private output matrix; the secure two-party matrix multiplication calculation protocol is a protocol designed based on secure data obfuscation technology; the secure data obfuscation technology is a technology that decomposes any multi-objective operation into a new multi-objective addition for obfuscating the calculation results of intermediate values; the sum of the first participant's private output matrix and the second participant's private output matrix is ​​the product result of the first participant's private matrix and the second participant's private matrix.

[0128] The dimensionality reduction conversion processing module M4 is used to perform dimensionality reduction conversion processing on the first participant's private output matrix and the second participant's private output matrix respectively to obtain a first dimensionality reduction private vector and a second dimensionality reduction private vector.

[0129] The aggregation module M5 is used to aggregate the first dimension-reduced private vector and the second dimension-reduced private vector to obtain a secure two-way vector bitwise multiplication result.

[0130] As an optional implementation, Fig.10 As shown, the execution process is as follows:

[0131] First, it is necessary to deploy the corresponding distributed computing framework on the computing nodes of the two-party secure numerical multiplication task. The framework consists of five modules. Specifically, it includes: task acquisition module, secure computing module, rule generation module, consensus computing module and data sending module. The task acquisition module is responsible for receiving and decoding the privacy computing request from the client; the secure computing module automatically matches the corresponding secure computing protocol according to the parsed computing request; the rule generation module implements the computing task splitting according to the asynchronous instruction set of the secure computing protocol, and different computing nodes perform collaborative computing according to their corresponding self-rules; after receiving the sub-rules assigned to each, the consensus computing module ensures the synchronization of the calculation and the consistency of the results through the consensus protocol; after the calculation is completed, the data sending module collects and transmits the calculation results of each participant node to the calculation requester.

[0132] In an exemplary embodiment, an external client sends a computation request for a two-way vector bitwise multiplication to a network terminal where a distributed computing service is deployed through an HTTP or GRPC communication protocol. When the task acquisition module of the node on the group network receives the computation request Request for the vector bitwise multiplication, it parses it and starts the security computing service process of the corresponding computing participants, nodes 1 and 2. When the task acquisition module completes the parsing of the corresponding computing requirements, it passes them to the security computing module, performs a joint query through its internal interface, and synchronizes to the rule generation modules in the two participating nodes after matching the corresponding security computing protocol. The rule generation module formulates different asynchronous parallel execution processes according to the different subtasks undertaken by the two different participating nodes, and maintains communication with the consensus computing module at each step of the execution. While the two participating nodes execute each step of the computing instructions, the consensus computing module broadcasts and maintains the consistency of the results of the distributed computing nodes on the chain and the stability of the control execution process. After waiting for the final computing protocol to be executed and the two participating nodes obtain the sub-results of each other's calculations, the sub-vectors after the confusion and splitting of the two parties are sent to the computing requester through the data sending module to obtain the correct computing results.

[0133] Compared with the prior art, the present invention has the following advantages:

[0134] 1) Based on the secure data obfuscation technology, this paper proposes a secure two-party matrix multiplication calculation protocol S2PM in a semi-honest scenario. Compared with the existing homomorphic encryption, secret sharing, and obfuscated circuit schemes, this protocol reduces the computational complexity to O(n 3 ) level, and the number of interactions in the constant round and the intermediate transmission data are all real numbers, which ensures that the communication overhead cost is controlled in a low range, taking into account the balance of the three impossible triangles of security, lightness, and efficiency.

[0135] 2) The present invention proposes a secure two-way quantization bitwise multiplication protocol S2PVEM, which converts vector bitwise multiplication into matrix multiplication through scaling and spatial dimension reduction after two participating nodes jointly negotiate an n, thereby using the secure two-party matrix multiplication protocol S2PM to achieve parallel computing, high computing efficiency, few communication rounds, and no need to introduce any secret key encryption operation. At the same time, due to the characteristics of the secure two-way quantization bitwise multiplication protocol S2PVEM based on real number domain operations, it is not limited to integer computing tasks, and can well avoid the accuracy problems caused by technologies such as obfuscated circuits and homomorphic encryption in the processing of floating-point numbers.

[0136] 3) Based on the concept of the secure two-way bitwise multiplication protocol S2PVEM, the present invention proposes a secure multi-way bitwise multiplication protocol SNPVEM. For N participating nodes, a total of The final answer can be obtained by the round-safe two-way quantization multiplication protocol S2PVEM. The process is based on real number field operations, which can ensure high calculation accuracy and embody scalability. It avoids the need to build a huge circuit network when expanding based on obfuscated circuit technology and the generation of a large amount of information interaction when expanding based on secret sharing technology.

[0137] 4) The secure two-way bitwise multiplication protocol S2PVEM and the secure multi-way bitwise multiplication protocol SNPVEM proposed in the present invention have more security guarantees. Since the two protocols do not rely on a third-party cloud platform, they can avoid the risk of privacy data leakage due to attacks on the third-party cloud platform.

[0138] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Fig.11 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store the private vector of the first participant and the private vector of the second participant. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a secure two-way vector multiplication method based on spatial dimensionality reduction is implemented.

[0139] Those skilled in the art will understand that Fig.11 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0140] In an exemplary embodiment, a computer device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the above-mentioned method embodiments are implemented when the processor executes the computer program.

[0141] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the above-mentioned method embodiments are implemented.

[0142] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the above-mentioned method embodiments are implemented.

[0143] 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, stored data, displayed data, etc.) involved in the present invention are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0144] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided by the present invention 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), magnetoresistive 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 may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0145] The database involved in each embodiment provided by the present invention may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided by the present invention may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0146] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, 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.

[0147] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A secure two-way multiplication method based on spatial dimension reduction, characterized in that: The secure two-way vector multiplication method based on spatial dimension reduction includes: Obtaining a private vector of the first participant and a private vector of the second participant; Preprocessing the private vector of the first participant and the private vector of the second participant to obtain a first participant private matrix and a second participant private matrix; Based on the secure two-party matrix multiplication calculation protocol, the first participant's private matrix and the second participant's private matrix are subjected to secure two-party matrix multiplication calculation to obtain the first participant's private output matrix and the second participant's private output matrix; the secure two-party matrix multiplication calculation protocol is a protocol designed based on secure data obfuscation technology; the secure data obfuscation technology is a technology that decomposes any multi-objective operation into a new multi-objective addition to obfuscate the calculation results of intermediate values; the sum of the first participant's private output matrix and the second participant's private output matrix is ​​the product result of the first participant's private matrix and the second participant's private matrix; Performing dimensionality reduction conversion processing on the first participant's private output matrix and the second participant's private output matrix respectively to obtain a first reduced-dimensionality private vector and a second reduced-dimensionality private vector; The first reduced-dimensionality private vector and the second reduced-dimensionality private vector are aggregated to obtain a secure two-way vector bitwise multiplication result.

2. The secure two-way multiplication method based on spatial dimension reduction according to claim 1, characterized in that: Preprocessing the private vector of the first participant and the private vector of the second participant to obtain a first participant private matrix and a second participant private matrix specifically includes: Determine a split positive integer; the split positive integer is greater than or equal to 2; Splitting each element of the private vector of the first participant according to the splitting positive integer to obtain a plurality of first split private vectors; Splitting each element of the private vector of the second participant according to the splitting positive integer to obtain a plurality of second split private vectors; Transforming and sorting the first split private vectors to obtain a first participant private matrix; A plurality of the second split private vectors are transformed and sorted to obtain a second participant private matrix.

3. The secure two-way multiplication method based on spatial dimension reduction according to claim 1, characterized in that: Based on a secure two-party matrix multiplication calculation protocol, performing secure two-party matrix multiplication calculation on the first participant's private matrix and the second participant's private matrix to obtain the first participant's private output matrix and the second participant's private output matrix, specifically comprising: Two groups of random matrix pairs are generated based on the auxiliary computing node; the two groups of random matrix pairs include: random matrix pairs (R a ,r a ) and random matrix pairs (R b ,r b ), where the random matrix R a The dimension is n×s, and the random matrix R b The dimension is s×m, and the random matrix r a and the random matrix r b The dimension is n×m; r a +r b =R a ·R b ; The random matrix pair (R a ,r a ) is sent to the first party; The random matrix pair (R b ,r b ) is sent to the second party; The first participant receives a random matrix pair (R a ,r a ), calculate the private matrix of the first participant and the random matrix R a , obtain a first matrix and, and send the first matrix and to the second participant; The second participant receives a random matrix pair (R b ,r b ), calculate the second party's private matrix and the random matrix R b , obtain a second matrix and, and send the second matrix and to the first participant; After receiving the first matrix and the second participant, the second participant generates a second participant private output matrix; According to the private output matrix of the second participant, a confusion matrix is ​​calculated; and the confusion matrix is ​​sent to the first participant; the calculation formula of the confusion matrix is: Where T is the confusion matrix, is the first matrix and, B is the private matrix of the second participant, V b is the private output matrix of the second participant, which is a random matrix generated by an internal secret; After receiving the confusion matrix, the first participant calculates and obtains the first participant's private output matrix; the calculation formula of the first participant's private output matrix is: Among them, V a is the private output matrix of the first participant, is the second matrix and .

4. The secure two-way multiplication method based on spatial dimension reduction according to claim 1, characterized in that: Performing dimensionality reduction conversion processing on the first participant's private output matrix and the second participant's private output matrix respectively to obtain a first dimensionality reduction private vector and a second dimensionality reduction private vector specifically includes: Extract several elements of the main diagonal of the private output matrix of the first participant and vectorize them to obtain a first reduced-dimensional private vector; Several elements of the main diagonal of the second participant's private output matrix are taken out and vectorized to obtain a second reduced-dimensional private vector.

5. The secure two-way multiplication method based on spatial dimension reduction according to claim 4 is characterized in that: The calculation formula of the first dimension-reduced private vector is: W a =m2v(diag(V a )); The calculation formula of the second dimension-reduced private vector is: W b =m2v(diag(V b )); Among them, W a is the first dimension-reduced private vector, W b is the second dimension reduction private vector, m2v is a function that converts the elements of a diagonal matrix into corresponding vectors bit by bit, and diag is a function that extracts the diagonal elements of an arbitrary matrix to form a diagonal matrix.

6. The secure two-way multiplication method based on spatial dimension reduction according to claim 1, characterized in that: The first reduced-dimensional private vector and the second reduced-dimensional private vector are aggregated to obtain the calculation formula for the bitwise multiplication result of the secure two-way vector: Among them, f S2PVEM (·) is a secure two-way bitwise multiplication protocol, α is the n-dimensional private vector of the first participant, β is the n-dimensional private vector of the second participant, W a is the first dimension-reduced private vector, W b is the second dimension-reduced private vector, Multiply two quantities in order to be safe.

7. A secure two-way multiplication device based on spatial dimension reduction, characterized in that: The secure two-way quantization multiplication device based on spatial dimension reduction comprises: A private vector acquisition module, used to acquire the private vector of the first participant and the private vector of the second participant; A preprocessing module, used for preprocessing the private vector of the first participant and the private vector of the second participant to obtain a private matrix of the first participant and a private matrix of the second participant; A secure two-party matrix multiplication calculation module is used to perform secure two-party matrix multiplication calculation on the first participant's private matrix and the second participant's private matrix based on a secure two-party matrix multiplication calculation protocol to obtain a first participant's private output matrix and a second participant's private output matrix; the secure two-party matrix multiplication calculation protocol is a protocol designed based on secure data obfuscation technology; the secure data obfuscation technology is a technology that decomposes any multi-objective operation into a new multi-objective addition to obfuscate the calculation results of intermediate values; the sum of the first participant's private output matrix and the second participant's private output matrix is ​​the product result of the first participant's private matrix and the second participant's private matrix; A dimensionality reduction conversion processing module, used to perform dimensionality reduction conversion processing on the first participant's private output matrix and the second participant's private output matrix respectively, to obtain a first dimensionality reduction private vector and a second dimensionality reduction private vector; The aggregation module is used to aggregate the first reduced-dimensionality private vector and the second reduced-dimensionality private vector to obtain a secure two-way vector bitwise multiplication result.

8. A computer device comprising: 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 secure two-way quantization multiplication method based on spatial dimensionality reduction as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the secure two-way quantization multiplication method based on spatial dimension reduction described in any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the secure two-way quantization multiplication method based on spatial dimension reduction described in any one of claims 1 to 6 is implemented.

Images