A secure two-way real number comparison method and apparatus based on nonlinear mapping

Abstract

This application discloses a secure two-party real number comparison method and apparatus based on nonlinear mapping, relating to the field of wireless communication. The method includes: matching a corresponding secure two-party real number comparison protocol based on a real number comparison request; then, based on a first secure party node and a second secure party node, performing the secure two-party real number comparison protocol on the first and second secure party real numbers to obtain the first and second secure party calculation results, thereby determining the real number comparison result between the first and second secure party real numbers; wherein, the secure two-party real number comparison protocol is determined based on a secure two-party nonlinear mapping protocol and symbol conversion processing; the secure two-party nonlinear mapping protocol is determined based on vector space mapping transformation and a secure two-party scalar product protocol; the secure two-party scalar product protocol is determined based on random vectors, random numbers, auxiliary computing nodes, and secure data obfuscation techniques. This application achieves efficient, secure, and reliable privacy-preserving nonlinear numerical computation.

Description

Technical Field

[0001] This application relates to the field of wireless communication, and in particular to a secure two-way real number comparison method and apparatus based on nonlinear mapping. Background Technology

[0002] With the continuous innovation and application of artificial intelligence and big data technologies, data has become a crucial strategic resource. Regarding privacy-preserving data modeling in large-scale modeling scenarios, data alignment through privacy comparisons is typically required during data preprocessing and cleaning. Numerical comparisons are also involved in the max-pooling layer during model training. Furthermore, in scenarios requiring multi-party data ranking, such as decision tree models and KNN (K-Nearest Neighbor) models, the prediction process is inextricably linked to privacy comparison operations. However, currently, the following issues exist when dealing with secure two-party numerical comparisons:

[0003] (1) Existing solutions to secure two-party numerical comparison problems mostly adopt computational frameworks developed based on traditional cryptographic primitives such as homomorphic encryption, secret sharing, and obfuscated circuits. These methods rely on ciphertext space computation with extremely high time and space complexity, resulting in low practicality and efficiency. (2) The output of existing secure two-party numerical comparison protocols is not fair and consistent. The calculation results are usually obtained by one party first, and then the other party is notified of the comparison results. This mode has the problem that the output is too dependent on whether one party is trustworthy. Once the party that obtains the comparison results first withdraws from the protocol or broadcasts the wrong result, the output will be affected. If the result is incorrect, the final correct comparison result cannot be obtained; (3) Existing solutions to secure two-party numerical comparison problems aim to protect the difference by verifying whether the difference between the two values ​​to be compared is greater than zero and by introducing random obfuscation values. Therefore, there is a problem of overprotecting the difference result and introducing additional computational and memory overhead; (4) Existing applications of secure two-party numerical comparison schemes mostly rely on outsourced cloud service systems. However, the credibility of third-party cloud service computing platforms is not high or they may be attacked by malicious nodes, which may cause the leakage of intermediate calculation results or key key information, further triggering the security risk of privacy leakage of the original data party. Summary of the Invention

[0004] The purpose of this application is to provide a secure two-party real number comparison method and apparatus based on nonlinear mapping, which can realize efficient, secure, reliable privacy-preserving nonlinear numerical computation.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] In a first aspect, this application provides a secure two-way real number comparison method based on nonlinear mapping, including:

[0007] Obtain secure two-party real number comparison request information; the secure two-party real number comparison request information includes a real number comparison request, a first secure party node and its corresponding first secure party real number, a second secure party node and its corresponding second secure party real number;

[0008] Based on the real number comparison request, a corresponding secure two-party real number comparison protocol is matched. Then, based on the first secure party node and the second secure party node, the secure two-party real number comparison protocol is executed on the first secure party real number and the second secure party real number to obtain the first secure party calculation result and the second secure party calculation result.

[0009] The comparison result of the real numbers of the first and second security squares is determined based on the calculation results of the first and second security squares.

[0010] The secure two-party real number comparison protocol is determined based on a secure two-party nonlinear mapping protocol and symbol conversion processing; the secure two-party nonlinear mapping protocol is determined based on vector space mapping transformation and a secure two-party scalar product protocol; and the secure two-party scalar product protocol is determined based on random vectors, random numbers, auxiliary computing nodes, and secure data obfuscation technology.

[0011] Secondly, this application provides a secure two-way real number comparison device based on nonlinear mapping, comprising:

[0012] The task acquisition module is used to: parse and acquire the secure two-party real number comparison request information sent by the computation requester; the secure two-party real number comparison request information includes the real number comparison request, the first secure party node and the corresponding first secure party real number, the second secure party node and the corresponding second secure party real number;

[0013] The secure computing module is used to: match a corresponding secure two-party real number comparison protocol based on the real number comparison request;

[0014] The comparison calculation module is used to: based on the first security party node and the second security party node, perform the security two-party real number comparison protocol on the first security party real number and the second security party real number to obtain the first security party calculation result and the second security party calculation result;

[0015] The data sending module is configured to: return the calculation results of the first security party and the calculation results of the second security party to the calculation requester, and determine the comparison result of the real number of the first security party and the real number of the second security party based on the calculation results of the first security party and the calculation results of the second security party at the calculation requester;

[0016] The secure two-party real number comparison protocol is determined based on a secure two-party nonlinear mapping protocol and symbol conversion processing; the secure two-party nonlinear mapping protocol is determined based on vector space mapping transformation and a secure two-party scalar product protocol; and the secure two-party scalar product protocol is determined based on random vectors, random numbers, auxiliary computing nodes, and secure data obfuscation technology.

[0017] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a secure two-party real number comparison method and apparatus based on nonlinear mapping. It matches a corresponding secure two-party real number comparison protocol based on a real number comparison request. Then, based on a first secure party node and a second secure party node, the secure two-party real number comparison protocol is executed on the first and second secure party real numbers to obtain the first and second secure party calculation results, thereby obtaining the real number comparison result. It should be noted that the secure two-party real number comparison protocol plays a crucial role in this process. This protocol is determined based on a secure two-party nonlinear mapping protocol and symbol conversion processing. By invoking the secure two-party nonlinear mapping protocol and symbol conversion, privacy protection and fair output of the two-party comparison results are achieved with minimal computational cost. The secure two-party nonlinear mapping protocol is based on vector space mapping transformation and a secure two-party scalar product protocol. By calling the secure two-party scalar product protocol, it calculates the corresponding nonlinear mapping values ​​for each input. This addresses the problems of high computational complexity, high communication overhead, and low availability in existing schemes based on homomorphic encryption, secret sharing, and obfuscated circuits. It achieves a highly efficient and secure two-party numerical comparison scheme that does not rely on a third-party cloud service platform. The secure two-party scalar product protocol is based on random vectors, random numbers, auxiliary computing nodes, and secure data obfuscation technology. The protocol's design is based on the concept of secure data obfuscation. The secure two-party scalar product protocol does not require any key and, due to its inherent characteristic of obfuscating and encrypting data in the real number field, ensures "one-time pad" security while also considering lower computational costs. Attached Figure Description

[0018] 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.

[0019] Figure 1 This is a flowchart illustrating a secure two-way real number comparison method based on nonlinear mapping in one embodiment of this application;

[0020] Figure 2This is a schematic diagram of a secure data obfuscation technique in one embodiment of this application;

[0021] Figure 3 This is a schematic diagram of a secure two-party scalar product problem in one embodiment of this application;

[0022] Figure 4 This is a flowchart of a secure two-party scalar product calculation protocol in one embodiment of this application;

[0023] Figure 5 This is a schematic diagram of a secure two-party nonlinear mapping problem in one embodiment of this application;

[0024] Figure 6 This is a flowchart of a secure two-party nonlinear mapping protocol in one embodiment of this application;

[0025] Figure 7 This is a flowchart of a secure two-party numerical comparison protocol in one embodiment of this application;

[0026] Figure 8 This is a schematic diagram illustrating a secure two-party numerical comparison problem in one embodiment of this application;

[0027] Figure 9 This is a schematic diagram of a secure two-way real number comparison device based on nonlinear mapping in one embodiment of this application. Detailed Implementation

[0028] 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 of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0029] The following are explanations of some of the terms that appear in this application:

[0030] Semi-Honest Adversaries Security is a specific protocol that assumes all parties involved in the computation will participate in privacy-preserving computation honestly and strictly follow each step of the process. However, there is a risk that some corrupted parties may attempt to infer the privacy behavior of other parties by observing the intermediate or final results of the protocol execution process.

[0031] The Secure 2-Party DotProductProtocol (S2PDP) assumes that there are two mutually distrustful parties, P1 and P2. Each party holds a secret input vector x and y respectively, and they jointly execute a two-party dot product protocol f(x,y) = Output(v1,v2) = x⊙y. Eventually, each party obtains the corresponding output v1 and v2, and the output satisfies v1 + v2 = x⊙y. 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 parties.

[0032] The Secure 2-Party ComparisonProtocol (S2PC) assumes that there are two mutually distrustful parties, P1 and P2. Each party holds a secret real number x and y as inputs, and they jointly execute a two-party comparison protocol and U a = U b = Sign(δ) = Output{-1,0,1}. Eventually, each party knows the size relationship between each other. Here, "-1" represents x < y, "0" represents x = y, and "1" represents x > y. 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 parties.

[0033] The Non-LinearMapping specifically refers to a family of unary monotonic functions jointly coupled by a random element function in a set of an n + 1-dimensional parameter vector θ = {(θ0, θ1, θ2, …, θ n )|(θ i ∈R + , i = 1 ~ n)} defined in the positive real number domain and a set of odd power functions. The function can be formalized as where where is a power function randomly selected from the set , and the function vector F(x) = (1, f1(x), f2(x), …, f n (x)).

[0034] Secure Data Disguising Technology (SDDT) is a data protection method used to protect the intermediate results of secure multi-party computations. By constructing a reasonable computation protocol, the computation results are randomly split, so that the outputs of multiple parties can be combined in a linear manner to form the real target computation result, ultimately achieving the effect of one-time key data privacy protection.

[0035] Privacy-Preserving Computing Technology refers to a series of information security technologies that break down data silos, collaborate on multi-party computation, and ultimately achieve complex computation and modeling analysis of multi-source data without exposing the privacy of the private data of all parties, thus ensuring that data elements are "usable but not visible" during the circulation and integration process.

[0036] To make the 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.

[0037] In one exemplary embodiment, such as Figure 1 As shown, a secure two-party real number comparison method based on nonlinear mapping is provided. This method is executed by a computer device, specifically by a computer device such as a terminal or server alone, or by both a terminal and a server. In this embodiment, it includes the following steps 101 to 103.

[0038] Step 101: Obtain the secure two-party real number comparison request information; the secure two-party real number comparison request information includes the real number comparison request, the first secure party node and the corresponding first secure party real number, the second secure party node and the corresponding second secure party real number.

[0039] Step 102: Match the corresponding secure two-party real number comparison protocol based on the real number comparison request, and then execute the secure two-party real number comparison protocol on the first secure party real number and the second secure party real number based on the first secure party node and the second secure party node to obtain the first secure party calculation result and the second secure party calculation result.

[0040] Step 103: Determine the comparison result of the real numbers of the first and second security squares based on the calculation results of the first and second security squares.

[0041] The secure two-party real number comparison protocol is determined based on a secure two-party nonlinear mapping protocol and symbol conversion processing; the secure two-party nonlinear mapping protocol is determined based on vector space mapping transformation and a secure two-party scalar product protocol; and the secure two-party scalar product protocol is determined based on random vectors, random numbers, auxiliary computing nodes, and secure data obfuscation technology.

[0042] To more intuitively demonstrate the algorithm flow of the secure two-party real number comparison protocol, the following content will derive and describe it in the following order: secure data obfuscation technique, secure two-party scalar product protocol, secure two-party nonlinear mapping protocol, and secure two-party real number comparison protocol. Furthermore, in the following text, the first secure party node can be represented by the node Alice, and the second secure party node can be represented by the node Bob.

[0043] (a) Secure data obfuscation technology.

[0044] For most multi-party computations, achieving secure computation typically involves multiple interactive steps. During these interactions, the unavoidable challenge is ensuring the security of intermediate results. For example, when using the product of two matrices, A×B, as an intermediate result, regardless of whether Alice or Bob obtains the final matrix A×B, either node could potentially deduce the other's data. Therefore, privacy-preserving computation must guarantee not only the security of the initial input data but also the security of the intermediate results.

[0045] To address this issue, this application employs secure data obfuscation encryption technology. Specifically, it decomposes any multi-ary operation into a new multi-ary addition to obfuscate the result of intermediate value calculations. Taking a two-way operation as an example, the principle is as follows: Figure 2 As shown. Assume S k =F k (A i B i ), F k A is the objective function for the k-th step. i B is the private input data belonging to node Alice at step k. i This is the private input data belonging to node Bob at step k. During step k of the execution of the multi-party secure computation protocol, the intermediate result S... k The following constraint will be strictly followed: Alice will only know the calculation result A that belongs to her. k Bob only knows the result B k And A k +B k =S k . Formula [A i :B i ]→[A k :Bk |A k +B k =F k (A i B i The diagram represents the process of passing intermediate values. Throughout this process, nodes Alice and Bob are not allowed to exchange data with each other, including calculating the intermediate result A after splitting it. k and B k Similarly, for the (k+1)th step, its input... and The output A from node Alice and node Bob at step k k and B k Transmission constitutes, and and Its output A k+1 and B k+1 satisfy Node Alice only knows the calculation result A that belongs to herself. k+1 Node Bob only knows its result B k+1 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.

[0046] Based on this, this application further provides a secure two-party scalar product protocol.

[0047] (ii) Security two-party scalar product agreement.

[0048] Before determining the process of the secure two-party scalar product protocol, we first need to define the problem: Given two independent and mutually distrustful computational parties or nodes, Alice and Bob, node Alice holds an n-dimensional private vector α = (α1, α2, ..., α...). n ) T Node Bob holds an n-dimensional private vector β = (β1, β2, ..., β3) n ) T The two nodes hope to achieve f by jointly executing a secure two-way scalar product protocol. S2PDP (α,β)=α⊙β=W a +W b Ultimately, each computing node obtains its corresponding output W. a W bThe results are then sent to the requesting party to aggregate and obtain the desired two-way scalar product. 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. The problem defined above can be addressed as follows: Figure 3 As shown.

[0049] In response to the above issues, such as Figure 4 As shown, the process of the secure two-party scalar product protocol in this application includes:

[0050] (21) Obtain the first private vector generated at the first security node and the second private vector generated at the second security node; wherein, when the first private vector is the first security private parameter vector, the corresponding second private vector is the second security private input vector; when the first private vector is the first security private input vector, the corresponding second private vector is the second security private parameter vector.

[0051] It should be noted that this step is only required when executing the secure two-party nonlinear mapping protocol. If only the secure two-party scalar product protocol is called in the actual application, this step can be skipped directly, and the corresponding private vector as input can be obtained directly.

[0052] (22) Call the auxiliary computing node (CommodityServer, CS) and randomly generate a first random vector and a corresponding first random number, a second random vector and a corresponding second random number at the auxiliary computing node; wherein the sum of the first random number and the second random number is equal to the scalar product of the first random vector and the second random vector.

[0053] Specifically, the auxiliary computing nodes generate a first random vector R of dimension n. a A second random vector R of dimension n b and the first random number r a The second random number r b These random variables strictly satisfy the following constraint r a +r b =R a ⊙R b .

[0054] (23) The first random vector R is processed through the auxiliary computing node CS. a and the first random number r a Send to the first security node Alice; the second random vector R is then sent through the auxiliary computing node CS. b and the second random number r b Send to the second security node Bob.

[0055] (24) At the first security node Alice, according to the first random vector R a The first private vector α determines the first encryption vector. The specific calculation formula is as follows: Then the first encryption vector The data is sent to the second security node Bob, where a second private output W is randomly generated. b ∈R, and according to the second random number r b The second private output W b The first encryption vector The intermediate result t of the second private vector β is calculated using the following formula: The intermediate result t is then sent to the first security node Alice.

[0056] (25) At the second safe node Bob, according to the second random vector R b The second private vector β determines the second encryption vector. The specific calculation formula is as follows: Then the second encryption vector Send to the first security node Alice.

[0057] (26) At the first security node Alice, based on the intermediate result t and the second encryption vector The first random number r a and the first random vector R a Calculate the first private output W a The specific calculation formula is as follows:

[0058] (27) Mark the second private output as the second scalar product result or the fourth scalar product result, and mark the first private output as the first scalar product result or the third scalar product result; wherein, the sum of the first scalar product result and the second scalar product is equal to the scalar product of the first private vector α and the second private vector β, that is, α⊙β=W a +W b .

[0059] In practical applications, if only the secure two-party scalar product protocol is executed, the final obfuscation and decomposition result W can be obtained. a W b The product is sent to the computation requester, who then aggregates the results to obtain the final product, which can be verified within the computation requester.

[0060] (III) Secure two-party nonlinear mapping protocol.

[0061] Before determining the process of the secure two-party nonlinear mapping protocol, we first need to define the problem: Given two computational participants, Alice and Bob, who are independent of each other and do not trust each other, Alice holds private data a∈R and a private parameter vector θ stored only on her own computation node. a =(θ a0 ,θ a1 ,θ a2 ,…,θ an )∈R + Bob holds private data b∈R and a private parameter vector θ stored only on his own computing node. b =(θ b0 ,θ b1 ,θ b2 ,…,θ bn )∈R + Two computational participants, Alice and Bob, collaborate to compute a nonlinear mapping. Obtain the function value corresponding to each private data when x = a or b. Nonlinear mapping The parameter θ in the parameter vector is derived from the private parameter vector θ between the two parties. a and θ b Together they satisfy the relation θ=θ a +θ b Both parties keep their respective parameter vectors θ secret from each other. a and θ b Therefore, the problem is equivalent to: both parties need to know the function vector F(x) = (1, f1(x), f2(x), ..., f n (x) Given the specific form but with unknown parameter θ distribution, construct a two-way nonlinear mapping protocol ψ(a,b,θ). a ,θ b )=θ⊙F(x)=(U a U b And through collaborative computing, they obtain their respective corresponding mapping output results. This information is then sent to the requesting party. During the computation process, each participating node can only know its own input and output information and cannot obtain any intermediate computation results or final outputs from other participants. The problem defined above can be addressed as follows: Figure 5 As shown.

[0062] Based on the problems defined above, this application proposes the following design principles:

[0063] Firstly, in nonlinear mappings... For set Any power function randomly selected from the set can be replaced by a more general set of monotonically increasing functions; therefore, the set... It can be represented as a monotonically increasing function over the real number field. Differentiable, and f'(x)≥0}. Due to the first derivative of the family of nonlinear mapping functions. From the positive number field parameter θ i Even power function f' in nonnegative domain i =x 2k The structure is composed of k = 1, 2, ..., n, so it is easy to know that... It is always a monotonically increasing function. In practical applications, the parameter θ can be defined in the negative domain, and the set of power functions... It can be represented as a family of monotonically decreasing functions over the real number field such that the mapping still retains its monotonically increasing property.

[0064] It requires the collaboration of two distrustful parties to jointly compute the real number field. The nonlinear mapping, for participants Alice and Bob, without exposing their respective private data {a,θ} a} and {b,θ b Under the premise of}, both parties obtain their respective mapped output values. and To simplify the analysis, let f in this application i (x)=x 2i-1 Then the nonlinear mapping can be expressed as Furthermore, the nonlinear mapping is transformed into a tensor space representation for calculating the vector inner product. Where X is an (n+1)-dimensional vector X = (1, x, x) mapped from a univariate variable x. 3 ,…,x 2n-1 ).

[0065] Based on the problem definition above, participants Alice and Bob each hold a private parameter θ for the nonlinear mapping. a =(θ a0 ,θ a1 ,θ a2 ,…,θ an )∈R n+1 and θ b =(θ b0 ,θ b1 ,θ b2 ,…,θ bn )∈R n+1 And the private parameter satisfies θ = θ a +θ b Therefore, the problem can be further transformed into Clearly, when the input variable x belongs to the Alice side, the calculation process of the mapping function value for the corresponding Alice side can be represented as follows: At this point, only one call to the S2PDP protocol is needed to obtain f. S2PDP (X a ,θ b ) = V a1 +V b1 Then output V b =V b1 The results are sent to node Alice, who then aggregates the intermediate calculation results from both sides (V). a V b ) to obtain the corresponding x a mapping value Similarly, a similar derivation applies when the input variable x originates from the Bob side. At this point, only one S2PDP protocol call is needed. S2PDP (θ a ,X b ) = V a2 +V b2 Then output V a '=V a2 It is also sent to node Bob, who then aggregates the intermediate calculation results from both sides (V). a ',V b ') to obtain the corresponding mapping value

[0066] In response to the above issues, such as Figure 6 As shown, the process of the secure two-party nonlinear mapping protocol in this application includes:

[0067] (31) Obtain the first security node Alice and its corresponding first security real number a, the second security node Bob and its corresponding second security real number b.

[0068] (32) Generate a first security-side private parameter vector at the first security-side node Alice, and perform a vector space mapping transformation based on the first security-side real numbers to generate a first security-side private input vector; generate a second security-side private parameter vector at the second security-side node, and perform a vector space mapping transformation based on the second security-side real numbers to generate a second security-side private input vector. This completes the process. Figure 6 The processing within the preprocessing module.

[0069] Taking the steps executed at the first security party node Alice as an example, the steps for determining the first security party's private parameter vector and the first security party's private input vector include:

[0070] 321) Obtain the random parameter n determined by the first security node Alice and the second security node Bob through negotiation; in an application instance, n is a positive integer, n≥2.

[0071] 322) At the first security node Alice, generate a set of |n|+1 dimensional parameter vectors θ based on the random parameters. a =(θ a0 ,θ a1 ,θ a2 ,…,θ an )∈R + And marked as the private parameter vector of the first security party.

[0072] 323) At the first security node Alice, perform a mapping transformation from a univariate real number to an |n|+1 dimensional vector space based on the first security real number a. To obtain the private input vector X of the first security side a =(1,a,a) 3 ,…,a 2n-1 ).

[0073] The steps executed at the second security node Bob are similar and will not be repeated here. The corresponding private parameter vector of the second security node is θ. b =(θ b0 ,θ b1 ,θ b2 ,…,θ bn )∈R + The second security party's private input vector is X. b =(1,b,b) 3 ,…,b 2n-1 ).

[0074] (33) For the first security party's private input vector X a ∈R n+1 The second security party's private parameter vector θ b ∈R n+1 Execute the secure two-party scalar product protocol S2PDP by calculating f S2PDP (X a ,θ b )=θ b ⊙X a To obtain the first scalar integrand result V a1 ∈R, the result of the second scalar product V b1 ∈R, and are sent to the first security node Alice and the second security node Bob respectively. It should be noted that at this time, the formula: f S2PDP (X a ,θ b ) = Va1 +V b1 =θ b ⊙X a .

[0075] (34) The second scalar product result V is obtained through the second safe party node Bob. b1 ∈R is sent to the first security party node Alice; at the first security party node Alice, the first security party's private parameter vector θ is processed. a With the first security party's private input vector X a Perform a scalar product calculation to obtain the scalar product result of the first vector. The specific calculation formula is: T a =θ a ⊙X a Then, at the first safe party node Alice, based on the first vector scalar product result T... a The first scalar integrator result V a1 and the result of the second scalar integrator V b1 Determine the first safe party mapping result U a The specific calculation formula is: U a =(T a +V a1 )+V b1 .

[0076] (35) Regarding the second security party's private input vector X b ∈R n+1 The first security party's private parameter vector θ a ∈R n+1 To execute a secure two-party scalar product protocol, by calculating f S2PDP (X b ,θ a )=θ a ⊙X b To obtain the third scalar integrand result V a2 ∈R, fourth scalar product result V b2 ∈R, and are sent to the first security node Alice and the second security node Bob respectively. It should be noted that at this time, the formula: f S2PDP (X b ,θ a ) = V a2 +V b2 =θ a ⊙X b .

[0077] (36) The third scalar product result V is obtained through the first security node Alice. a2∈R is sent to the second security party node Bob; at the second security party node Bob, the second security party's private parameter vector θ is... b With the second security party's private input vector X b Perform a scalar product calculation to obtain the second vector scalar product result T. b The specific calculation formula is: T b =θ b ⊙X b Then, at the second safe node, based on the result T of the second vector scalar product... b The third scalar product result V a2 and the fourth scalar integrand result V a2 Determine the second security party mapping result U b The specific calculation formula is: U b =(T b +V b2 )+V a2 .

[0078] In practical applications, if only the secure two-party scalar product protocol is executed, the final private mapping function value U can be obtained. a U b Send to the computation requester, who then aggregates and verifies the data: For the participating node Alice: Similarly, this also applies to Bob, the participating node.

[0079] (iv) Agreement on comparison of real numbers between the two parties for security.

[0080] The problem of secure two-party comparison of real numbers is commonly found in applications such as privacy-preserving intersection in distributed databases, privacy-preserving ranking in online decision trees, and privacy-preserving deep neural networks, and has broad research value. Therefore, without loss of generality, let Alice's initial input to the participating nodes be real numbers a∈R, and Bob's initial input to the participating nodes be real numbers b∈R. Based on this, ... Figure 7 As shown, the process of the secure two-party real number comparison protocol in this application includes:

[0081] (41) Obtain the first security node Alice and its corresponding first security real number a, the second security node Bob and its corresponding second security real number b.

[0082] (42) Based on the first security party node Alice and the second security party node Bob, perform the S2PNLM two-party nonlinear mapping protocol on the first security party real number a and the second security party real number b to obtain the mapping result of the first security party. and the mapping results of the second safe side Due to the mapping process within the protocol and They are independent and unrelated to each other; therefore, they can be executed in parallel to improve computational efficiency.

[0083] (43) Map the first security party through the first security party node Alice. The data is sent to the second security party node Bob, and then combined with the second security party mapping result at the second security party node Bob. Perform a sign transformation to obtain the second safe side calculation result V. b .

[0084] In a specific practical application, the second safe party calculation result V b The determination process includes:

[0085] 431) Obtain the sign conversion function Sign(x) at the second security node as follows:

[0086]

[0087] x is the difference between the mapping result of the first security party and the mapping result of the second security party. Figure 7 The symbol conversion module contains the symbol conversion function.

[0088] 432) The difference between the first safe-side mapping result and the second safe-side mapping result is used as the input to the symbol conversion function to obtain the second safe-side calculation result V. b The specific formula is: V b =Sign(σ)=δ∈{-1,0,1};σ=U a -U b As input to the sign function Sign(x).

[0089] Since the nonlinear mapping function is a monotonically increasing function in the real number domain, the requester can easily deduce the relative magnitudes of Alice's private data 'a' and Bob's private data 'b' based on the sign of the final comparison function output δ.

[0090] (44) Map the second security party through the second security party node Bob. The data is sent to the first security party node Alice, and then combined with the first security party mapping result at the first security party node Alice. Perform a sign transformation to obtain the first safe side calculation result V. a .

[0091] In another specific practical application, step 103 includes:

[0092] (51) Obtain the calculation requester corresponding to the real number comparison request.

[0093] (52) The calculation result V of the first safe side a and the second safe calculation result V b All are sent to the computation requester.

[0094] (53) The calculation result V received from the first security party is calculated by the calculation requesting party. a and the second safe calculation result V b Perform a consistency comparison (this consistency comparison ensures the reliability of the comparison results because if the first safe party node Alice and the second safe party node Bob have calculated accurately and without lying, V...). a =V b If V holds true, a ≠V b (Therefore, one party must have made a calculation error); after a consistency comparison, the result V calculated by the first safe party is used. a Or the result V calculated by the second security party b Determine the real number comparison result; the real number comparison result is used to characterize the relative size relationship between the first safe real number and the second safe real number.

[0095] Specifically, assuming the results are reliable, the calculation result V is based on the first safe side. a Or the result V calculated by the second security party b The sign of V can be used to quickly infer the relative size relationship between Alice's private data 'a' and Bob's private data 'b'. a =V b When a = -1, <b,V a =V b When V = 0, a = b, V a =V b When =1, a>b.

[0096] Furthermore, from the perspective of the overall solution, this application solves the problem of comparing real numbers between two parties securely, which can be addressed as follows: Figure 8As shown: Given two independent and distrustful computational participants, Alice and Bob, Alice holds private data a∈R stored only on her own computational node, and Bob holds private data b∈R stored only on his own computational node. The two participants jointly execute a secure two-party real number comparison protocol π(a,b)=sign(ab)=V a =V b Ultimately, each participating node in the computation receives its corresponding output indicator V. a V b The input and output values ​​are assigned to each other in the range {1, 0, -1}, and sent to the requesting party to obtain the expected comparison result between the two values. During the calculation process, each participating node can only obtain its own input and output information, and cannot obtain the intermediate settlement results or private data information held by other participants.

[0097] To address the aforementioned problem of secure two-party real number comparison, this application provides a secure two-way scalar product protocol, S2PDP, based on secure data obfuscation technology. 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. This application also proposes for the first time a privacy-preserving solution for two-party collaborative computation of nonlinear mapping problems. Its key technical point lies in the introduction of a monotonically increasing family of functions jointly constructed by the two parties; its order preservation is crucial to ensuring the correctness and security of the final comparison result. This application ensures the reliability and fairness of the final output result by performing symbol conversion on the intermediate results of the two-way mapping protocol, solving the reliability and fairness problems caused by one party having priority access to the result in traditional schemes.

[0098] In practical applications, in order to improve computational efficiency, the secure two-party real number comparison method based on nonlinear mapping in this application further includes: the computational operations to be performed by the first secure party node and the computational operations to be performed by the second secure party node are executed asynchronously in parallel.

[0099] Based on the same inventive concept, this application also provides a secure two-party real number comparison device for implementing the secure two-party real number comparison method based on nonlinear mapping described above. The solution provided by this device is similar to the implementation described in the above method. Therefore, the specific limitations of one or more embodiments of the secure two-party real number comparison device based on nonlinear mapping provided below can be found in the limitations of the secure two-party real number comparison method based on nonlinear mapping described above, and will not be repeated here.

[0100] In one exemplary embodiment, such as Figure 9As shown, a secure two-party real number comparison device based on nonlinear mapping is provided, including a task acquisition module, a secure calculation module, a rule generation module, a consensus calculation module, and a data sending module.

[0101] The task acquisition module is used to: parse and acquire secure two-party real number comparison request information sent by the requesting party (such as a client); the secure two-party real number comparison request information includes a real number comparison request, a first secure party node and its corresponding first secure party real number, a second secure party node and its corresponding second secure party real number.

[0102] The secure computing module is used to: match the corresponding secure two-party real number comparison protocol based on the real number comparison request.

[0103] The comparison calculation module is used to: based on the first security party node and the second security party node, execute the secure two-party real number comparison protocol on the first security party real number and the second security party real number to obtain the first security party calculation result and the second security party calculation result. In a specific application example, the comparison calculation module includes a rule generation module and a consensus calculation module that communicate with each other.

[0104] The rule generation module is used to: determine the computational operations to be performed by the first secure party node and the second secure party node based on the secure two-party real number comparison protocol (that is, to realize the splitting of computational tasks so that different computational nodes can perform collaborative computation according to their respective self-rules), and construct an asynchronous parallel execution process; determine the computational operation instructions of the two nodes based on the asynchronous parallel execution process, and send them to the first secure party node and the second secure party node respectively, until the asynchronous parallel execution process ends and the first secure party computational result and the second secure party computational result are obtained.

[0105] The consensus calculation module is used to monitor the calculation operations in the first secure party node and the second secure party node, and match them with the asynchronous parallel execution process to ensure the order of real number comparison between the two secure parties, thereby ensuring the synchronization and consistency of calculation results between different nodes.

[0106] The data sending module is used to: return the calculation results of the first security party and the second security party to the calculation requester, and determine the comparison result of the real number of the first security party and the real number of the second security party based on the calculation results of the first security party and the second security party at the calculation requester.

[0107] The secure two-party real number comparison protocol is determined based on a secure two-party nonlinear mapping protocol and symbol conversion processing; the secure two-party nonlinear mapping protocol is determined based on vector space mapping transformation and a secure two-party scalar product protocol; and the secure two-party scalar product protocol is determined based on random vectors, random numbers, auxiliary computing nodes, and secure data obfuscation technology.

[0108] In a specific practical application, a computational framework is deployed based on the secure two-party real number comparison device based on nonlinear mapping of this application, and then participates in the computation of a two-party secure numerical comparison task. The process is as follows: A client outside the framework sends a request for two-party numerical comparison to a network terminal with a distributed computing service deployed via HTTP or gRPC communication protocol; when the task acquisition module of the network node receives the request for numerical comparison, it parses it and starts the secure computing service process of the corresponding computing participant nodes Alice and Bob; after the task acquisition module has parsed the corresponding computing requirements, it passes them to the secure computing module, which performs a joint query through its internal interface to match the corresponding secure computing protocol (which can be a secure two-party scalar product protocol, secure...). The two-party nonlinear mapping protocol (either of the two-party real number comparison protocol or the secure two-party real number comparison protocol) is synchronized to the rule generation module in the two participating nodes. The rule generation module will formulate different asynchronous parallel execution processes according to the different sub-tasks undertaken by the two different participating nodes, and maintain communication with the consensus calculation module at each step of the execution. While the two participating nodes execute each step of the calculation instructions, the consensus calculation module broadcasts and maintains the consistency of the results of the distributed computing nodes on the chain and controls the stability of the execution process. After the calculation protocol is completed, the two participating nodes Alice and Bob obtain the results of each other's calculations, and send the result sub-matrix after the two parties' confusion and splitting to the calculation requester, i.e., the client, through the data sending module, thereby obtaining the correct calculation result.

[0109] In practical application scenarios, depending on the actual scenario in which the client issues the computation request, there are two situations: First, the computation request is an intermediate computation requirement. In this case, the real number comparison result obtained can be used as the input for the next round of computation, such as the max pooling layer in the training stage of a deep neural network model or the multi-level decision process in a decision tree model. Second, the computation request is a standalone computation request. In this case, the real number comparison result obtained can be directly returned to the computation requester. A simple example is the size comparison required in a computation program.

[0110] In summary, compared with the prior art, this application has the following advantages:

[0111] (1) This application proposes a secure two-way scalar product protocol S2PDP based on secure data obfuscation technology in a semi-honest scenario. Compared with existing homomorphic encryption, secret sharing, and obfuscated circuit schemes, this protocol reduces the computational complexity to the O(n) level. At the same time, the number of constant rounds of interaction and the intermediate transmitted data are all real numbers, which ensures that the communication overhead cost is controlled within a low range. It balances the requirements of the three impossible triangles of security, lightweight and efficiency.

[0112] (2) This application proposes a numerical comparison method based on the secure two-party nonlinear mapping protocol S2PNLM. The method ensures computational security by having both parties share a portion of the parameters. It introduces a set of power functions to construct a family of nonlinear mapping functions and uses their monotonically increasing characteristics to ensure the relative size consistency between the output and the input. The original input is converted into dummy data in the nonlinear function space for comparison. Furthermore, the parallel calls of S2PDP directly improve the computational efficiency of this two-numerical mapping. These advantages directly avoid the problem of low efficiency caused by the extra computational overhead of the traditional method of comparing numerical differences.

[0113] (3) This application does not directly output the results of the S2PNLM protocol. Instead, it uses a symbol conversion module to convert the intermediate calculation results that may carry the characteristics of the original data into symbol elements Sig(x) = {-1,0,1} that only represent the relative size relationship between the two data. This method not only ensures that the final calculation requester cannot obtain any privacy related to the input through the output, but also ensures the reliability of the output through the consistency between the two. In particular, when the calculation requesters are Alice and Bob, both parties can obtain the final comparison results at the same time, which solves the problem of output unfairness in traditional methods.

[0114] (4) This application is a study on the key technologies of integrated blockchain performance model and multi-level continuous collaborative optimization.

[0115] In another exemplary embodiment, a computer device is 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 another 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 methods of 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, and when executed, it can include the processes of the embodiments of the above methods. 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-way real number comparison method based on nonlinear mapping, characterized in that, The secure two-way real number comparison method based on nonlinear mapping includes: Obtain secure two-party real number comparison request information; the secure two-party real number comparison request information includes a real number comparison request, a first secure party node and its corresponding first secure party real number, a second secure party node and its corresponding second secure party real number; Based on the real number comparison request, a corresponding secure two-party real number comparison protocol is matched. Then, based on the first secure party node and the second secure party node, the secure two-party real number comparison protocol is executed on the first secure party real number and the second secure party real number to obtain the first secure party calculation result and the second secure party calculation result. The comparison result of the real number of the first security square and the real number of the second security square is determined based on the calculation results of the first security square and the second security square. The secure two-party real number comparison protocol is determined based on a secure two-party nonlinear mapping protocol and symbol conversion processing; the secure two-party nonlinear mapping protocol is determined based on vector space mapping transformation and a secure two-party scalar product protocol; and the secure two-party scalar product protocol is determined based on random vectors, random numbers, auxiliary computing nodes, and secure data obfuscation technology.

2. The secure two-way real number comparison method based on nonlinear mapping according to claim 1, characterized in that, The process of the secure two-party real number comparison protocol includes: Obtain the first security party node and its corresponding first security party real number, the second security party node and its corresponding second security party real number; Based on the first security party node and the second security party node, a two-party nonlinear mapping protocol is executed on the first security party real number and the second security party real number to obtain the first security party mapping result and the second security party mapping result; The first security party node sends the first security party mapping result to the second security party node, and then the second security party node performs symbol conversion by combining the second security party mapping result to obtain the second security party calculation result; The second security party node sends the second security party mapping result to the first security party node, and then performs symbol conversion at the first security party node in combination with the first security party mapping result to obtain the first security party calculation result.

3. The secure two-way real number comparison method based on nonlinear mapping according to claim 2, characterized in that, At the second secure party node, a symbol transformation is performed in conjunction with the second secure party mapping result to obtain the second secure party calculation result. This includes: obtaining the symbol transformation function at the second secure party node; and using the difference between the first secure party mapping result and the second secure party mapping result as the input of the symbol transformation function to obtain the second secure party calculation result. The sign conversion function Sign(x) is: x is the difference between the first security mapping result and the second security mapping result.

4. The secure two-way real number comparison method based on nonlinear mapping according to claim 1, characterized in that, The comparison result between the first and second real numbers of the security square is determined based on the calculation results of the first and second security squares, including: Obtain the computation requester corresponding to the real number comparison request; Both the calculation results of the first security party and the calculation results of the second security party are sent to the calculation requesting party. The requesting party performs a consistency comparison on the received first security party calculation result and second security party calculation result, and after passing the consistency comparison, determines the real number comparison result based on the first security party calculation result or the second security party calculation result; the real number comparison result is used to characterize the relative size relationship between the first security party real number and the second security party real number.

5. The secure two-way real number comparison method based on nonlinear mapping according to claim 1, characterized in that, The process of the secure two-party nonlinear mapping protocol includes: Obtain the first security party node and its corresponding first security party real number, the second security party node and its corresponding second security party real number; A first security-side private parameter vector is generated at the first security-side node, and a vector space mapping transformation is performed based on the first security-side real number to generate a first security-side private input vector; a second security-side private parameter vector is generated at the second security-side node, and a vector space mapping transformation is performed based on the second security-side real number to generate a second security-side private input vector. The secure two-party scalar product protocol is executed on the first secure party's private input vector and the second secure party's private parameter vector to obtain the first scalar product result and the second scalar product result, which are then sent to the first secure party node and the second secure party node, respectively. The second scalar product result is sent to the first security node through the second security node; at the first security node, a scalar product is calculated between the first security private parameter vector and the first security private input vector to obtain the first vector scalar product result; then at the first security node, the first security mapping result is determined based on the first vector scalar product result, the first scalar product result, and the second scalar product result. The secure two-party scalar product protocol is executed on the second secure party's private input vector and the first secure party's private parameter vector to obtain the third scalar product result and the fourth scalar product result, which are then sent to the first secure party node and the second secure party node, respectively. The third scalar product result is sent to the second security node through the first security node; at the second security node, a scalar product is calculated between the second security private parameter vector and the second security private input vector to obtain the second vector scalar product result; then at the second security node, the second security mapping result is determined based on the second vector scalar product result, the third scalar product result, and the fourth scalar product result.

6. The secure two-way real number comparison method based on nonlinear mapping according to claim 5, characterized in that, At the first security party node, a first security party private parameter vector is generated, and a vector space mapping transformation is performed based on the first security party real number to generate a first security party private input vector, including: Obtain the random parameter n determined by the first security node and the second security node through joint negotiation; At the first security node, a set of |n|+1 dimensional parameter vectors is generated based on the random parameters and marked as the first security node's private parameter vector; At the first security node, a mapping transformation from a univariate real number to an |n|+1 dimensional vector space is performed based on the first security real number to obtain the first security private input vector.

7. The secure two-way real number comparison method based on nonlinear mapping according to claim 5, characterized in that, The process of the secure two-party scalar product protocol includes: Obtain a first private vector generated at the first security party node and a second private vector generated at the second security party node; wherein, when the first private vector is the first security party private parameter vector, the corresponding second private vector is the second security party private input vector; when the first private vector is the first security party private input vector, the corresponding second private vector is the second security party private parameter vector. An auxiliary computing node is invoked, and a first random vector and its corresponding first random number, a second random vector and its corresponding second random number are randomly generated at the auxiliary computing node; wherein, the sum of the first random number and the second random number is equal to the scalar product of the first random vector and the second random vector; The first random vector and the first random number are sent to the first security node through the auxiliary computing node; the second random vector and the second random number are sent to the second security node through the auxiliary computing node; At the first security node, a first encryption vector is determined based on the first random vector and the first private vector. Then, the first encryption vector is sent to the second security node. At the second security node, a second private output is randomly generated. An intermediate result is calculated based on the second random number, the second private output, the first encryption vector, and the second private vector. Then, the intermediate result is sent to the first security node. At the second security node, a second encryption vector is determined based on the second random vector and the second private vector, and then the second encryption vector is sent to the first security node. At the first secure node, a first private output is calculated based on the intermediate result, the second encryption vector, the first random number, and the first random vector. The second private output is labeled as the second scalar product result or the fourth scalar product result, and the first private output is labeled as the first scalar product result or the third scalar product result; wherein the sum of the first scalar product result and the second scalar product is equal to the value of the scalar product of the first private vector and the second private vector.

8. The secure two-party real number comparison method based on nonlinear mapping according to claim 1, 2, 4, or 5, characterized in that, The secure two-party real number comparison method based on nonlinear mapping further includes: the computational operations to be performed by the first secure party node and the computational operations to be performed by the second secure party node are executed asynchronously in parallel.

9. A secure two-way real number comparison device based on nonlinear mapping, characterized in that, The secure two-way real number comparison device based on nonlinear mapping includes: The task acquisition module is used to: parse and acquire the secure two-party real number comparison request information sent by the computation requester; the secure two-party real number comparison request information includes the real number comparison request, the first secure party node and the corresponding first secure party real number, the second secure party node and the corresponding second secure party real number; The secure computing module is used to: match a corresponding secure two-party real number comparison protocol based on the real number comparison request; The comparison calculation module is used to: based on the first security party node and the second security party node, perform the security two-party real number comparison protocol on the first security party real number and the second security party real number to obtain the first security party calculation result and the second security party calculation result; The data sending module is configured to: return the calculation results of the first security party and the calculation results of the second security party to the calculation requester, and determine the comparison result of the real number of the first security party and the real number of the second security party based on the calculation results of the first security party and the calculation results of the second security party at the calculation requester; The secure two-party real number comparison protocol is determined based on a secure two-party nonlinear mapping protocol and symbol conversion processing; the secure two-party nonlinear mapping protocol is determined based on vector space mapping transformation and a secure two-party scalar product protocol; and the secure two-party scalar product protocol is determined based on random vectors, random numbers, auxiliary computing nodes, and secure data obfuscation technology.

10. The secure two-way real number comparison device based on nonlinear mapping according to claim 9, characterized in that, The comparison calculation module includes a rule generation module and a consensus calculation module that communicate with each other. The rule generation module is used to: determine the computational operations to be performed by the first secure party node and the second secure party node based on the secure two-party real number comparison protocol, and construct an asynchronous parallel execution process; Based on the asynchronous parallel execution process, the computation operation instructions for the two nodes are determined and sent to the first security node and the second security node respectively, until the asynchronous parallel execution process ends and the computation results of the first security node and the second security node are obtained. The consensus calculation module is used to: monitor the calculation operations in the first secure party node and the calculation operations in the second secure party node, and match them with the asynchronous parallel execution process to ensure the order of real number comparison between the two secure parties.

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