A method for finding the intersection of two-way threshold privacy sets for large datasets

Abstract

This invention belongs to the field of information security technology and provides a two-party threshold privacy set intersection method supporting large datasets. This method designates a judge and an initiator from the participating parties. The initiator randomly generates a secret and assigns a corresponding secret share and index to each element in the set. By introducing a confusion Bloom filter, the set elements are associated with their secret shares and indices. The judge verifies whether a sufficient number of correct sub-shares can be recovered to reconstruct the original secret, thereby determining whether the number of intersection elements meets a preset threshold, and further calculates the intersection content accordingly, effectively avoiding the leakage of the intersection cardinality. This invention avoids the use of complex public-key cryptographic operations such as homomorphic encryption, resulting in high computational efficiency and low implementation complexity. Its computational efficiency is significantly better than existing schemes for large datasets. Simultaneously, the protocol effectively resists attacks under the semi-honest adversary model, meeting the security requirements of this attack model.

Description

Technical Field

[0001] This invention belongs to the field of information security technology, specifically relating to a method for finding the intersection of two-party threshold privacy sets that supports large datasets. Background Technology

[0002] Threshold Privacy Set Intersection (TPSI) is an enhanced privacy-preserving technology used to securely compute the intersection of set elements in multi-party scenarios. Unlike traditional Privacy Set Intersection (PSI) protocols, TPSI introduces a "threshold" concept, allowing participants to output the intersection only if its size meets a preset threshold. If the intersection size does not reach the threshold, no information is disclosed, further protecting privacy. TPSI can also be used in applications such as fingerprint matching, online social recommendations, and privacy-preserving ride-sharing. By introducing a threshold mechanism, TPSI achieves a better balance between privacy protection and data sharing, providing a more powerful tool for secure multi-party computation and privacy protection.

[0003] Most current TPSI protocols calculate the cardinality of the intersection and then compare it with a threshold value to determine if the intersection size meets a preset requirement. While this method is simple, it suffers from the problem of leaking the intersection cardinality. To protect the intersection cardinality, the TPSI protocol proposed by Hallgren et al. combines the phasing protocol with a threshold key encapsulation mechanism (T-KEM). However, their protocol has excessive computational overhead in the threshold determination step, which relies on polynomial interpolation, and requires trying all possible continuous point sets. The protocol's time cost becomes extremely high when the user dataset is very large, as it involves multiple possible combinations to reconstruct the key. Therefore, this scheme is only suitable for small-scale datasets and is difficult to deploy in practical applications in big data environments due to its excessive computational time cost. Furthermore, Zhao et al.'s protocol introduces additional overhead in its Bloom filter-based construction to ensure the privacy of the intersection cardinality, involving numerous homomorphic encryption operations to sever element associations. Secondly, the encrypted transmission and polynomial reconstruction of the Bloom filter in the threshold judgment process incur excessive computational overhead.

[0004] In summary, the existing TPSI protocol has the following problems: In the threshold determination process, existing solutions either face the risk of intersection cardinality leakage or are difficult to construct efficiently and feasible protocols due to the introduction of high computational or communication overhead.

[0005] Most existing TPSI protocols rely on public-key cryptographic primitives, which have high computational overhead, resulting in low overall operating efficiency and making it impossible to effectively implement the protocol.

[0006] When dealing with large-scale datasets, the runtime increases rapidly as the dataset size increases, making it difficult to effectively scale to even larger datasets. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a method for finding the intersection of two-party threshold privacy sets for large datasets, thereby resolving the issues in the prior art. The technical solution adopted by this invention is as follows: A method for finding the intersection of two-party threshold privacy sets for large datasets includes: S1 Setup Phase: Initiator P 1. Select a secret value s, and call the share generation algorithm of elastic secret sharing to obtain the secret share set. Share With the corresponding set of index shares Index Subsequently, the initiator P 1. Using sets X Secret share set Share With index share set Index Construct a blomber filter GBF1 with obfuscation, and the receiver uses a set. Y Construct a Bloom filter (BF); S2 extended unintentional transmission phase: Judgment method P 2 and the initiator P 1. Construct an intersection obfuscation Bloom filter GBF2 by executing the OT protocol; S3 Calculation Phase: Judgment Method P 2. Decode to obtain the secret share set Share ′ and index share set Index Then, it checks whether the secret value reconstructed using the secret reconstruction algorithm of elastic secret sharing is correct, and determines whether the intersection size reaches a threshold value. t ; S4 query output phase: If the intersection size reaches the threshold t Then the judgment method P 2. Verify the validity of the shares and calculate the intersection; if the intersection size does not reach the threshold. t The protocol is terminated and a terminator is output.

[0008] Furthermore, the initiator P 1 and judgment method P 2. Each has its own private collection: X = { x 1,..., x n}and Y = { y 1,..., y n}

[0009] Furthermore, S1 includes: S11: Initiator P 1 and judgment method P 2. Generate random numbers using a pseudo-random generator.n A length of λ random seed sequence seed P1 ∈{0,1} λ and seed P2 ∈{0,1} λ Subsequently, both parties send their respective generated random seed sequences to the other party and each calculates the merge seed. seed = seed P1 ⊕ seed P2 ; S12: Based on merging seeds seed Both parties use the same pseudo-randomization function to generate the data. n - t Both parties generate a consistent virtual element; each party adds the generated virtual element to its original private set, forming an expanded set: X ′ ={ x 1, x 2,...., x n ,..., x 2n-t}and Y ′= { y 1, y 2,..., y n ,..., y 2n-t}; S13: Initiator P 1. Randomly generate a set of index shares. Index = { ind 1,..., ind 2n-t}, targeting secrets s Execute the share generation algorithm for elastic secret sharing: based on 2 n - t Choose the highest power among the indices. t - The Secret Polynomial of 1 f ( x (), meets the conditions f (0) = s； Calculating secret shares s i = f ( ind i ), ind i It is the first i The index value corresponding to each sub-share is used to obtain the secret value. s The corresponding 2 n - t A set of secret sharesShare = { s 1,..., s 2n-t}; S14: Initiator P 1 H ( s )Sent to the judgment party P 2, H ( s () indicates the initiator P 1. The Secret of Output s The hash value; S15: Initiator P 1. Input its extended set X ',based on k hash functions h 1,..., h k Construct a Bloom filter GBF1; the Bloom filter GBF1 satisfies: for each element x i ∈ X ′( i ∈[2 n - t ]), its corresponding k The XOR result of the values ​​stored in each hash location is equal to s i || ind i , represented as: GBF1[ h 1( x i )]⊕GBF1[ h 2( x i )]⊕...⊕GBF1[ h k ( x i )] = s i || ind i Fill the unoccupied remaining positions in the obfuscated Bloom filter GBF1 with a randomly generated 2. λ Bit string; S16: Judgment Method P 2. Input its extended set Y ',based on k Same hash function h 1,..., h k Construct a Bloom filter (BF); the Bloom filter (BF) satisfies: for each element yi ∈ Y ′( i ∈[2 n - t ]) and each of its hash positions j ∈[ k ], has BF[ h j ( y i )] = 1; The unused positions in the Bloom filter BF are assigned a value of 0.

[0010] Furthermore, S2 includes: S21: Judgment Method P 2. With the initiator P 1. Execute the extended OT protocol; P 2. Using a Bloom filter (BF) as the selection input, P 1. Use a blomber filter GBF1 as the message input; S22: P 2. Output the intersection confusion Bloom filter GBF2 constructed from this.

[0011] Furthermore, S21 includes: for each position index b ∈[ m ]: If BF[ b If ] = 0, then the judgment method P 2. Obtain a random value corresponding to the selection in the OT protocol. r 1, and GBF2[ b ] = r If BF[b] = 1, then the judgment method... P 2. Obtain GBF1 via OT protocol [ b The true value r 2, and let GBF2[ b ] = r 2= ​​GBF1[ b ].

[0012] Furthermore, S3 includes: S31: Judgment Method P 2. Input its extended set Y ′, for each element y i ∈ Y ′( i ∈[2 n - t Based on the same k hash functions h 1, ..., h k calculate: result = GBF2[ h 1(y i )]⊕GBF2 h 2( y i )]⊕...⊕GBF2 h k ( y i )]; result It represents the decoding result obtained after performing an exclusive OR operation on the corresponding positions in the confused Bloom filter GBF2: When y i belongs to the intersection of both parties, this value is the secret information embedded by the initiator during the construction phase, that is s i || ind i ; otherwise, result it appears as a random value; Let the security parameter be λ represented as the bit length, then result has a total length of 2 λ bits. Parse the first result bits of λ into the share s i ′, and the remaining λ bits into the corresponding index ind i ′, thus obtaining 2 n - t groups of corresponding shares and index values; S32: Add the share s i ′ to the secret share set Share ′; add the index ind i ′ to the index share set Index ′; P 2 Invoke the secret reconstruction algorithm to recover a polynomial t of degree up to g ( x ) that satisfies the interpolation condition: g ( ind i ′) = s i ′; S33: Party P 2 calculates g (0) to obtain the reconstructed secret candidate value s ′, and verifies the cryptographic hash equation H ( s ) = H ( sDoes the equation hold true? If it does, it means the receiver has decoded at least... t The correct sub-shares are used to reconstruct the secret. s The initiator P 1 and judgment method P The intersection size between 2 reaches the threshold t If the protocol terminates normally, the intersection result is output; otherwise, the protocol is terminated.

[0013] Furthermore, S4 includes: S41: Regarding i ∈[2 n - t ], P 2 Calculation g ( ind i If there is s i ′ = g ( ind i '), but y i It is the element in the intersection of the two participating parties, which will y i Add to intersection I = X ∩ Y middle; S42: Judge P 2. Obtain the intersection I Output the intersection result.

[0014] The present invention has the following beneficial effects: (1) In order to reduce computational overhead and improve operating efficiency, this invention designs an improved GBF decoding algorithm to store the secret shared share and its index value corresponding to the set element, thereby reducing the computational overhead of threshold judgment under the premise of privacy protection.

[0015] (2) An elastic secret sharing algorithm is introduced to reconstruct the secret, which effectively prevents the leakage of the intersection cardinality and avoids exhaustively enumerating all possible combinations of secret shares. The error correction and verification functions of the elastic secret sharing algorithm ensure that the secret can be reconstructed in a single calculation, thereby greatly reducing the number of reconstruction operations.

[0016] (3) In the design process, this invention avoids the use of complex public key cryptographic operations such as homomorphic encryption. Only a small number of base OT operations are required to realize the interactive function between the two parties, thereby significantly reducing the computational burden.

[0017] (4) Compared with existing TPSI implementation schemes, the present invention can support larger datasets. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0019] The following will be described in conjunction with embodiments of the present invention. Figure 1 The technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0020] This invention aims to address the limitations of traditional LSRTM methods in terms of resolution and amplitude fidelity under band-limited illumination, as well as the poor geological adaptability of traditional regularization methods. Experiments using synthetic and real-world data demonstrate that the proposed method significantly outperforms traditional LSRTM in terms of deep interface continuity, amplitude fidelity, and artifact suppression, achieving a comparable residual threshold with fewer iterations, thus synergistically improving imaging quality and computational efficiency.

[0021] The overall technical concept of this invention is as follows: (1) Both parties interact to generate a consistent pseudo-random seed through pseudo-random number generation technology, and generate a unified set of virtual elements based on the seed. The virtual elements are then extended to their respective original private sets to construct the extended set, thereby improving the matching coverage capability in large-scale data scenarios.

[0022] (2) A share generation algorithm based on elastic secret sharing technology generates secret shares that meet the threshold reconstruction conditions and binds the shares to the corresponding index to support subsequent recovery and verification.

[0023] (3) Based on the extended unintentional transmission technology and the obfuscated Bloom filter structure, selective information transmission between the initiator and the judge is realized, so that the judge can obtain the data obfuscation result of the target location without disclosing the unmatched information.

[0024] (4) Use Bloom filter to encode and query the extended set of the judgment party, locate the corresponding position through multi-hash function mapping technology and perform XOR recovery to obtain candidate secret share and index information.

[0025] (5) The secret reconstruction algorithm based on elastic secret sharing technology interpolates the recovered share to calculate the recovered secret value, and judges whether the intersection size reaches the threshold value through hash consistency verification, thereby outputting the final privacy set intersection result.

[0026] Specifically, such as Figure 1 This invention proposes a method for finding the intersection of two-party threshold privacy sets for large datasets, wherein the two-party threshold privacy set intersection protocol includes two participants: the initiator and the third party. P 1 and judgment methodP 2. The method specifically includes the following steps: S1 Setup Phase: Initiator P 1. Select secret value s, and call ( t , n The share generation algorithm of Flexible Secret Sharing (RSS) yields the set of secret shares. Share With the corresponding set of index shares Index Subsequently, the initiator P 1. Using sets X , Share and Index Construct a blomber filter GBF1 with obfuscation, and the receiver uses a set. Y Construct a Bloom filter (BF).

[0027] Initiator P 1 and judgment method P 2 Each has its own set X = { x 1,..., x n}and Y = { y 1,..., y n}

[0028] S2 extended unintentional transmission phase: Judgment method P 2 and the initiator P 1. Construct an intersection obfuscation Bloom filter GBF2 by executing the OT protocol.

[0029] S3 Calculation Phase: Judgment Method P 2. Decode to obtain the secret share set Share ′ and index share set Index Then, based on whether the secret value reconstructed by the RSS secret reconstruction algorithm is correct, it is determined whether the intersection size has reached the threshold value. t .

[0030] S4 query output phase: If the intersection size reaches the threshold t Then the judgment method P 2. Verify the validity of the shares and calculate the intersection. If the intersection size does not reach the threshold... t The protocol is terminated and a terminator (⊥) is output.

[0031] Furthermore, the S1 setup phase includes the following steps: S11: Initiator P 1 and judgment method P 2. Generate random numbers using a pseudo-random generator. n A length of λ random seed sequence seedP1 ∈{0,1} λ and seed P2 ∈{0,1} λ Subsequently, both parties send their generated random seed sequences to the other party and each calculates the merge seed. seed = seed P1 ⊕ seed P2 .

[0032] S12: Based on merging seeds seed Both parties use the same pseudo-randomization function to generate the data. n - t Each party generates a consistent virtual element. The generated virtual element is then added to their original private set by both parties, forming an expanded set. X ′ ={ x 1, x 2,...., x n ,..., x 2n-t}and Y ′= { y 1, y 2,..., y n ,..., y 2n-t}

[0033] S13: Initiator P 1. Randomly generate a set of index shares. Index = { ind 1,..., ind 2n-t To improve tolerance for erroneous shares, a lightweight redundant verification step is introduced to filter out abnormal shares during the reconstruction phase, specifically targeting secrets. s implement( t , n The algorithm for generating RSS shares through flexible secret sharing: based on these 2 n - t Choose the highest power among the indices. t - The Secret Polynomial of 1 f ( x (), meets the conditions f (0) = s Calculate the secret share s i = f ( ind i ), ind i It is the first iThe index value corresponding to each sub-share is used to obtain the secret value. s The corresponding 2 n - t A set of secret shares Share = { s 1,..., s 2n-t}

[0034] Alternatively, the standard can be adopted. Shamir ( t , 2 n - t The secret sharing algorithm generates shares, but it needs to introduce additional "index redundancy and hash verification" steps to compensate for the resilience of RSS. The RSS algorithm has built-in error correction and verification functions and is currently the most powerful in theory.

[0035] S14: Initiator P 1 H ( s )Sent to the judgment party P 2, H ( s () indicates the initiator P 1. The Secret of Output s The hash value; S15: Initiator P 1. Input its extended set X ',based on k hash functions h 1,..., h k Construct GBF1. This construction satisfies the following relation: for each element x i ∈ X ′( i ∈[2 n - t ]), its corresponding k The XOR result of the values ​​stored in each hash location is equal to s i || ind i That is, GBF1[ h 1( x i )]⊕GBF1[ h 2( x i )]⊕...⊕GBF1[ h k ( x i )] = s i || ind i The remaining positions in GBF1 not occupied by the above process should be filled with a randomly generated 2. λBit string.

[0036] S16: Judgment Method P 2. Input its extended set Y ',based on k Same hash function h 1,..., h k Construct BF. This construction satisfies the following relation: for each element y i ∈ Y ′( i ∈[2 n - t ]) and each of its hash positions j ∈[ k ], has BF[ h j ( y i )] = 1. This sets the value to 0 for any unused position in the BF.

[0037] Furthermore, the S2 extended unintentional transmission phase includes the following steps: S21: As the party making the judgment P 2. With the initiator P 1. Execute the extended OT protocol. P 2 uses its Bloom filter (BF) as the selection input. P 1 uses its obfuscated Bloom filter GBF1 as message input. Specifically, for each position index... b ∈[ m ]: If BF[ b If ] = 0, then P 2. Obtain a random value corresponding to the selection in the OT protocol. r 1, and GBF2[ b ] = r If BF[b] = 1, then P 2. Obtain GBF1 via OT protocol [ b The true value r 2, and let GBF2[ b ] = r 2= ​​GBF1[ b ].

[0038] S22: P 2. Output the intersection confusion Bloom filter GBF2 constructed from this.

[0039] Furthermore, the S3 calculation stage includes the following steps: S31: Judgment Method P 2. Input your own set Y ′, for each elementy i ∈ Y ′( i ∈[2 n - t ) is based on the same k hash functions h 1, ..., h k Calculate: result = GBF2 h 1( y i )]⊕GBF2 h 2( y i )]⊕...⊕GBF2 h k ( y i )].

[0040] result Denote the decoding result obtained by performing an exclusive OR operation on the corresponding positions in the obfuscated Bloom filter GBF2: When y i belongs to the intersection of both parties, this value is the secret information embedded by the initiator in the construction phase, that is s i || ind i ; Otherwise, result appears as a random value; Let the security parameter λ be represented as the bit length, then result has a total length of 2 λ bits. Parse the first result bits of λ into the share s i ′, and the remaining λ bits into the corresponding index ind i ′, thus obtaining 2 n - t groups of corresponding shares and index values; S32: Add s i ′ to the set Share ′; Add ind i ′ to the set Index ′( i ∈[2 n - t )]. Based on the constructed share set Share ′ = { s 1′, s 2′,..., s 2n-t ′} and the corresponding index setIndex ′= { ind 1′, ind 2′,..., ind 2n-t ′}, P 2. Call the RSS secret reconstruction algorithm to recover a maximum of [number of times]. t - A polynomial of degree 1 g ( x To ensure that it meets the interpolation conditions: g ( ind i ′) = s i ′.

[0041] S33: P 2 Calculation g (0) Obtain the candidate value for reconstructing the secret. s ′, and verify the cryptographic hash equation. H ( s ) = H ( s Does the equation hold true? If the equation holds true, it means the receiver has decoded at least... t The correct sub-shares reconstruct the secret s That is, the participating parties P 1 and P The intersection size between 2 reaches the threshold t If the protocol terminates normally, the intersection result is output; otherwise, the protocol is terminated.

[0042] Finally, the S4 query output stage includes the following steps: S41: Regarding i ∈[2 n - t ], P 2 Calculation g ( ind i If there is s i ′ = g ( ind i '), but y i Both parties involved P 1 and P The elements in the intersection of the two sets will y i Add to intersection I = X ∩ Y middle.

[0043] S42: P 2. Obtain the intersection I Output the intersection result.

[0044] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, alterations, or substitutions made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for finding the intersection of two-party threshold privacy sets for large datasets, characterized in that, Include: S1 Setup Phase: Initiator P 1. Select a secret value s, and call the share generation algorithm of elastic secret sharing to obtain the secret share set. Share With the corresponding set of index shares Index Subsequently, the initiator P 1. Using sets X Secret share set Share With index share set Index Construct a blomber filter GBF1 with confusion, and the receiver uses a set. Y Construct a Bloom filter (BF); S2 extended unintentional transmission phase: Judgment method P 2 and the initiator P 1. Construct an intersection obfuscation Bloom filter GBF2 by executing the OT protocol; S3 Calculation Phase: Judgment Method P 2. Decode to obtain the secret share set Share ′ and index share set Index Then, it checks whether the secret value reconstructed using the secret reconstruction algorithm of elastic secret sharing is correct, and determines whether the intersection size reaches a threshold value. t ; S4 query output phase: If the intersection size reaches the threshold t Then the judgment method P 2. Verify the validity of the shares and calculate the intersection; if the intersection size does not reach the threshold. t The protocol is terminated and a terminator is output.

2. The method for finding the intersection of two-party threshold privacy sets for large datasets according to claim 1, characterized in that, Initiator P 1 and judgment method P 2. Each has its own private collection: X = { x 1,..., x n }and Y = { y 1,..., y n } 3. The method for finding the intersection of two-party threshold privacy sets for large datasets according to claim 1, characterized in that, S1 includes: S11: Initiator P 1 and judgment method P 2. Generate random numbers using a pseudo-random generator. n A length of λ random seed sequence seed P1 ∈{0,1} λ and seed P2 ∈{0,1} λ Subsequently, both parties send their respective generated random seed sequences to the other party and each calculates the merge seed. seed = seed P1 ⊕ seed P2 ; S12: Based on merging seeds seed Both parties use the same pseudo-randomization function to generate the data. n - t Both parties generate a consistent virtual element; each party adds the generated virtual element to its original private set, forming an expanded set: X ′ ={ x 1, x 2,...., x n ,..., x 2n-t }and Y ′= { y 1, y 2,..., y n ,..., y 2n-t }; S13: Initiator P 1. Randomly generate a set of index shares. Index = { ind 1,..., ind 2n-t }, targeting secrets s Execute the share generation algorithm for elastic secret sharing: based on 2 n - t Choose the highest power of each index. t - The Secret Polynomial of 1 f ( x (), meets the conditions f (0) = s； Calculating Secret Shares s i = f ( i ), ind i It is the first i The index value corresponding to each sub-share is used to obtain the secret value. s The corresponding 2 ind A set of secret shares n - t = { s 1,..., s 2n-t }; S14: Initiator P 1 H ( s )Sent to the judgment party P 2, H ( s () indicates the initiator P 1. The Secret of Output s The hash value; S15: Initiator P 1. Input its extended set X ',based on k hash functions h 1,..., h k Construct a Bloom filter GBF1; the Bloom filter GBF1 satisfies: for each element x i ∈ X ′( i ∈[2 ]), its corresponding k The XOR result of the values ​​stored in each hash location is equal to s i || Share i , represented as: GBF1[ h 1( x i )]⊕GBF1[ h 2( x i )]⊕...⊕GBF1[ h k ( x i )] = s i || n - t i Fill the unoccupied remaining positions in the obfuscated Bloom filter GBF1 with a randomly generated 2. Bit string; S16: Judgment Method P 2. Input its extended set Y ',based on k Same hash function h 1,..., h k Construct a Bloom filter (BF); the Bloom filter (BF) satisfies: for each element y i ∈ Y ′( i ∈[2 ind ]) and each of its hash positions j ∈[ k ], has BF[ h j ( y i )] = 1; The unused positions in the Bloom filter BF are assigned a value of 0.

4. The method for finding the intersection of two-party threshold privacy sets for large datasets according to claim 1, characterized in that, S2 ind S21: Judgment Method P 2. With the initiator P 1. Execute the extended OT protocol; P 2. Using a Bloom filter (BF) as the selection input, P 1. Use a blomber filter GBF1 as the message input; S22: P 2. Output the intersection confusion Bloom filter GBF2 constructed from this.

5. The method for finding the intersection of two-party threshold privacy sets for large datasets according to claim 4, characterized in that, S21 includes: for each location index b ∈[ m ]: If BF[ b If ] = 0, then the judgment method P 2. Obtain a random value corresponding to the selection in the OT protocol. r 1, and GBF2[ b ] = r If BF[b] = 1, then the judgment method... P 2. Obtain GBF1 via OT protocol [ b The true value r 2, and let GBF2[ b ] = r 2 = GBF1[ b ].

6. The method for finding the intersection of two-party threshold privacy sets for large datasets according to claim 1, characterized in that, S3 λ S31: Judgment Method P 2. Input its extended set Y ′, for each element y i ∈ Y ′( i ∈[2 n - t Based on the same k hash functions h 1, ..., h k calculate: = GBF2[ h 1( y i )]⊕GBF2[ h 2( y i )]⊕...⊕GBF2[ h k ( y i )]; Include: This represents the decoding result obtained after performing an XOR operation on the corresponding positions in the obfuscated Bloom filter GBF2: when y i When the two parties' values ​​intersect, this value is the secret information embedded by the initiator during the construction phase, i.e. s i || Include: i ;otherwise, n - t It appears as a random value; Set safety parameters Expressed as bit length, then result The total length is 2 result Bit. ind The former result Bit resolution to share s i ′, remaining λ Bit parsing to the corresponding index result i ′, thus obtaining 2 λ The share and index value corresponding to the group; S32: Add the share s i ′ to the set of secret shares result ′; add the index λ i ′ to the set of index shares λ ′; P 2 Call the secret reconstruction algorithm to recover a polynomial t of degree at most g - 1 x ( g () ind i ′) = s i ′; S33: Judge P 2 Calculation g (0) Obtain the candidate value for reconstructing the secret. s ′, and verify the cryptographic hash equation. H ( s ) = H ( s Does the equation hold true? If it does, it means the receiver has decoded at least... t The correct sub-shares are used to reconstruct the secret. s The initiator P 1 and judgment method P The intersection size between 2 reaches the threshold t If the protocol terminates normally, the intersection result is output; otherwise, the protocol is terminated.

7. The method for finding the intersection of two-party threshold privacy sets for large datasets according to claim 6, characterized in that, S4 n - t S41: Regarding i ∈[2 ], P 2 Calculation g ( Share i If there is s i ′ = g ( ind Index ind Include: n - t ind ind i '), but y i It is the element in the intersection of the two participating parties, which will y i Add to intersection I = X ∩ Y middle; S42: Judge P 2. Obtain the intersection I Output the intersection result.

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