Multi-party private set merging method and system based on trusted execution environment
By employing hash bucketing and batch processing strategies in a trusted execution environment, combined with a star topology, the high computational and communication overhead of multi-party private collections and protocols is resolved. This enables efficient computation and large-scale data collaboration under a malicious security model, while providing stringent security guarantees.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-29
- Publication Date
- 2026-03-31
AI Technical Summary
Existing multi-party private collection and protocol suffers from excessive computational and communication overhead, limited security models, and poor scalability, making it difficult to meet the needs of large-scale applications. Furthermore, TEE has not effectively solved problems such as memory limitations and side-channel attacks.
A hash bucketing + batch processing strategy is adopted, combined with a star topology, and a Trusted Execution Environment (TEE) is used for secure computation. Data is distributed into multiple buckets through hash bucketing, and the union result is computed in parallel. A star topology network is used to reduce communication complexity, and a remote authentication mechanism is used to ensure security.
It achieves efficient computation under a malicious security model, with a computation speed increase of 2.16-5.05 times and a communication overhead reduction of 39-205 times. It supports privacy-preserving data collaboration with large-scale participants and large data volumes, and provides strict security guarantees.
Smart Images
Figure CN121770853A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of privacy computing and secure multi-party computation, and in particular to a method and system for merging private multi-party sets based on a trusted execution environment. Background Technology
[0002] Against the backdrop of the continuous development of privacy-preserving computing, Multi-party Private Set Union (MPSU) has emerged as a core technology, allowing multiple participants to securely and efficiently compute the union of their sets without revealing their individual data content. This technology is widely used in scenarios such as threat intelligence sharing, collaborative medical research, financial risk control, and cross-institutional data collaboration, serving as a critical infrastructure for data-driven collaboration. Despite the existence of various MPSU protocols, current mainstream solutions still face significant challenges: efficiency issues, as many protocols rely on complex cryptographic mechanisms such as polynomial encoding, homomorphic encryption, or zero-knowledge proofs, leading to excessive computational and communication overhead; limited security models, with some protocols relying on the non-collusion assumption (i.e., some participants will not collude), making it difficult to meet the threat models of malicious attackers in reality; and poor scalability, as the performance of traditional solutions degrades significantly with the increase in participants and data volume, making it difficult to support large-scale applications. To improve performance, some scholars have attempted to introduce structural optimizations. For example, Kissner et al. used polynomial root mapping to transform sets into polynomials and perform product calculations, but due to the need to handle high-order polynomials and introduce homomorphic encryption, its computational complexity is high and it lacks scalability. Subsequently, Frikken, Gong, and others continued to optimize the computation process, but still struggled to achieve efficient computation while ensuring security. Even the protocol proposed by Liu and Seo in recent years, which made progress in efficiency, still has theoretical vulnerabilities due to its security relying on the assumption of honest majority or no collusion.
[0003] To address the aforementioned bottlenecks, Trusted Execution Environments (TEEs), such as Intel SGX, offer new possibilities for MPSUs. TEEs can create a hardware-isolated secure execution environment within the processor, supporting secure computation of data in plaintext and ensuring program trustworthiness and execution integrity through remote attestation mechanisms. Compared to traditional encryption protocols, TEEs significantly reduce encryption / decryption operations and communication load, improving overall protocol efficiency.
[0004] However, TEEs themselves also face challenges, including side-channel attacks (such as cache attacks, page table attacks, and branch prediction attacks), memory limitations (SGX EPC area limitations), and access pattern leakage in the protocol. For example, while using Oblivious RAM (ORAM) to avoid access pattern leakage is effective, it incurs high memory and time overhead, making it unsuitable for large-scale practical deployments. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention proposes a high-efficiency MPSU protocol that integrates a TEE (Telematics Equipment) and is designed to target malicious actors. It overcomes TEE memory limitations through a hash bucketing and batch processing strategy; it reduces communication complexity using a star topology, enabling the protocol to support a larger number of participants and data scale; this solution provides a secure and feasible new path for large-scale privacy-preserving data collaboration.
[0006] To achieve the above objectives, this invention provides a method for merging multiple private sets based on a trusted execution environment, including multiple participating parties and a central coordinator, with the following specific steps: (1) TEE initialization: The central coordinator initializes the TEE secure enclave and generates a session identifier (eid) and an asymmetric key pair (pk, msk); Each participant requests and obtains the session identifier eid, public key pk, and TEE secure enclave signature proof ψ, and performs TEE secure enclave integrity verification; (2) Security key exchange After successful verification, each participant randomly generates a symmetric key k. i It is then encrypted using a pk and sent to the central coordinator. TEE Secure Enclave Decryption of Symmetric Key k for All Participants i And based on the NIWI proof system, a proof is generated and returned to each participant; Each participating party determines its symmetric key k based on the received proof. i It was received correctly; (3) Hash bucketing and data preprocessing: Each participating party submits the data count in its private collection to the central coordinator after encrypting it using a pk. The number of data from each participant obtained by TEE secure enclave resolution is used to calculate the optimal number of buckets Nb, set the filling threshold MAXB, and allocate a random seed r for the hash function. The obtained parameters are then sent to each participant. Each participant divides the data in their private set into Nb buckets based on the hash function’s random seed r and the hash bucketing algorithm. Finally, dummy elements are filled in until the amount of data in each bucket reaches the filling threshold MAXB. (4) Merging of multiple privacy collections: The process is divided into two rounds: the input round and the execution round. Input round: Each participant uses its symmetric key k i A key for each bucket is generated using a hash function, which is used to encrypt the data in the corresponding bucket and then sent to the central coordinator. TEE secure enclave decrypts and synchronizes data from each participant's bucket; Execution round: The TEE secure enclave performs parallel computation of the union of data from the same buckets of each participant, and fills the union result to a uniform length; then the data from each bucket after the union is taken are merged again to obtain the multi-party privacy set merged data; (5) Union distribution TEE secure enclave uses temporary key k s Encrypted multi-party privacy collection and merging data; The designated recipient obtains the encrypted multi-party privacy set merged data and the temporary key k. s And TEE security enclave signature certificate ψ n Perform TEE security enclave integrity verification; If the verification passes, decrypt and remove the padding data to obtain the final union.
[0007] Furthermore, step (1) specifically includes: The central coordinator calls SGX_Initialize() to create a secure enclave and generate a session identifier eid and an asymmetric key pair (pk, msk); Each participant requests and obtains a public key pk and a TEE secure enclave signature proof ψ. Each participant uses the public key pk to decrypt and verify the TEE secure enclave signature proof ψ, confirming the integrity of the TEE secure enclave.
[0008] Furthermore, in step (2), generating proof based on the NIWI proof system specifically involves generating proof based on trusted settings and encryption keys; π=Prove(CRS, (pk, Enc(pk, k i )), k i ) Where: π represents the generated proof, CRS is the public reference string generated through trusted settings, and Enc(pk, k) represents the generated proof. i Each participant uses pk to encrypt the symmetric key k. iAftervalue; each participant proves the received π based on zero-knowledge proof to determine its symmetric key k. i It was received correctly.
[0009] Furthermore, the optimal number of buckets Nb is: Nb = m / log m, and the filling threshold is: MAXB = ln m / ln (ln m), where: m is the maximum number of data in the private set of each participant.
[0010] This invention also provides a multi-party private set union system based on a Trusted Execution Environment (TEE), comprising: multiple participating parties and a central coordinator; the central coordinator includes: a TEE initialization module for initializing a TEE secure enclave and generating a session identifier (eid) and an asymmetric key pair (pk, msk); and a first secure key exchange module for decrypting the received symmetric keys k from each participating party via the TEE secure enclave. i And based on the NIWI proof system, a proof is generated and returned to each participant; The hash bucketing module resolves the data count in each participant's private set obtained from the TEE secure enclave, calculates the optimal number of buckets Nb, sets the filling threshold MAXB, and allocates a random seed r for the hash function, sending the obtained parameters to each participant. The multi-party privacy set merging module decrypts and synchronizes the data received from each participant's bucket in the TEE secure enclave; it also calculates the union of the data from the same bucket of each participant in parallel and fills the union result to a uniform length. Union distribution module for using temporary key k in TEE secure enclave s Encrypt the union data of each bucket; and combine the encrypted union data with the TEE secure enclave signature proof ψ n Send to the designated recipient; The participating parties include: The TEE secure enclave integrity verification module is used to request and obtain the session identifier eid, public key pk, and TEE secure enclave signature proof ψ from the central coordinator, and to perform TEE secure enclave integrity verification. The second secure key exchange module is used to randomly generate the symmetric key k for the participants. i It is then encrypted using pk and sent to the central coordinator; simultaneously, it receives a proof from the central coordinator to determine its symmetric key k. i It was received correctly; The private collection data preprocessing module is used to submit the data quantity in its private collection to the central coordinator after encrypting it with pk; it receives the optimal number of buckets Nb, the set filling threshold MAXB and the random seed r of the hash function issued by the central coordinator, and divides the data in each private collection into Nb buckets based on the hash bucketing algorithm, and finally fills dummy elements until the amount of data in each bucket reaches the filling threshold MAXB. Bucketed data generation module, used with symmetric key k i A key for each bucket is generated using a hash function, the data for that bucket is encrypted, and then sent to the central coordinator. The union data receiving module is used to acquire the encrypted union data and the TEE secure enclave signature proof ψ. n Perform TEE security enclave integrity verification; after successful verification, decrypt the union data and remove padding data to obtain the final union.
[0011] The present invention also provides an electronic device, including a processor, a memory, a communication interface, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the processor, and the programs include instructions for performing the steps of the above-described multi-party private set union method based on a trusted execution environment.
[0012] The present invention also provides a computer-readable storage medium storing a computer program for electronic data interchange, wherein the computer program causes a computer to perform some or all of the steps described in the above-described method for finding the union of multiple private sets based on a trusted execution environment.
[0013] The present invention also provides a computer program product comprising a non-transitory computer-readable storage medium storing a computer program operable to cause a computer to perform some or all of the steps described in the above-described method for finding the union of multiple private sets based on a trusted execution environment.
[0014] The beneficial effects of this invention are: This invention achieves, for the first time, efficient computation under a malicious security model without requiring a non-collusion assumption by moving the core computational logic to a hardware-isolated SGX enclave. Compared to existing solutions, this protocol achieves breakthrough progress in the following aspects: 1. Security: It resists collusion attacks and side-channel threats through remote authentication and formal proofs of the UC framework.
[0015] 2. Performance: By adopting a star topology network and hash bucket technology, the computing speed is increased by 2.16-5.05 times and the communication overhead is reduced by 39-205 times (compared with the latest technology).
[0016] 3. Scalability: Supports 15 square meters of 2² 4 Element or 7 square 2² 6 The large-scale computation of elements breaks through the memory limitations of traditional solutions. This design provides the first MPSU solution that combines stringent security guarantees with engineering practicality for scenarios such as medical data collaboration and threat intelligence sharing. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of the business process of the multi-party private set union method in a trusted execution environment according to an embodiment of the present invention.
[0018] Figure 2 This is a schematic diagram illustrating the operation flow of the multi-party private set union method in a trusted execution environment according to an embodiment of the present invention. Detailed Implementation
[0019] The present invention will be further explained and described below with reference to the accompanying drawings and embodiments.
[0020] like Figure 1 As shown, this embodiment of the invention provides a method for merging multiple private sets based on a trusted execution environment, including multiple participating parties and a central coordinator.
[0021] Central coordinator S: Deploys the SGX enclave and is responsible for coordinating computations.
[0022] Participants P1, P2, ..., P n Each holds a private set X1, X2, ..., X n .
[0023] The specific steps are as follows: S101, TEE initialization: The central coordinator initializes the TEE secure enclave and generates a session identifier (eid) and an asymmetric key pair (pk, msk).
[0024] Each participant requests and obtains the session identifier eid, public key pk, and TEE secure enclave signature proof ψ, and performs TEE secure enclave integrity verification.
[0025] The central coordinator is responsible for establishing a hardware-level secure SGX enclave environment, generating encryption keys and unique identifiers, and generating verifiable TEE secure enclave signature certificates. Each participating party obtains a public key, a unique identifier, and a TEE secure enclave signature certificate, and uses the public key to decrypt and verify the TEE secure enclave signature certificate to confirm the integrity of the TEE secure enclave. If this fails, the agreement is terminated.
[0026] like Figure 2As shown, the key operations are: creating an enclave instance using `Gatt.INITIALIZE()`, generating a session ID (eid) and a key pair (pk, msk), and generating a verifiable proof using the `ψ` function. Security mechanisms include: hardware isolation to ensure the key generation process is not interfered with by the host system; and using a remote authentication mechanism to verify the integrity of the enclave.
[0027] S102, Security Key Exchange: After successful verification, each participant randomly generates a symmetric key k. i It is then encrypted using a pk key and sent to the central coordinator.
[0028] TEE Secure Enclave Decryption of Symmetric Key k for All Participants i The system generates proofs based on the NIWI proof system and returns them to each participant.
[0029] π=Prove(CRS, (pk, Enc(pk, k i )), k i ) Where: π represents the generated proof, CRS is the public reference string generated through trusted settings, and Enc(pk, k) represents the generated proof. i Each participant uses pk to encrypt the symmetric key k. i Aftervalue; Each participating party uses zero-knowledge proofs to prove the received π and determine its symmetric key k. i It was received correctly.
[0030] Function: Establishes a secure communication channel between the participants and the enclave. Key Process: The participants use PKE to encrypt the symmetric key k. i Send to enclave; Enclave verifies key validity using the EXKEY function; non-interactive authentication is implemented using the NIWI proof system.
[0031] S103, Hash Bucketing and Data Preprocessing: Each participating party submits the number of data in its private collection to the central coordinator after encrypting it using a pk.
[0032] The TEE secure enclave resolves the number of data from each participant, calculates the optimal number of buckets Nb, sets the filling threshold MAXB, and allocates a random seed r for the hash function (generating the hash function H(r)). The obtained parameters are then sent to each participant.
[0033] Each participant uses a hash function (such as SHA-256) with a random seed r to divide the data in their private set into Nb buckets based on the hash bucketing algorithm. Finally, dummy elements are filled in until the amount of data in each bucket reaches the filling threshold MAXB.
[0034] Nb = m / log m MAXB = ln m / ln (ln m) Where: m is the maximum number of data items in the private sets of each participant.
[0035] Function: Optimizes memory efficiency for large-scale set operations. Core technologies: Simple hashing distributes elements into Nb = m / log m buckets; a dynamic filling mechanism ensures each bucket is the same size, preventing access pattern leakage; a random seed r generates a collision-resistant hash function H(r). Performance guarantee: Theoretically proven, the maximum bucket load is MAXB = ln m / ln (ln m).
[0036] S104, Multi-party privacy aggregation and merging: The process is divided into two rounds: the input round and the execution round.
[0037] Input round: Each participant uses its symmetric key k i A key for each bucket is generated using a hash function, which is used to encrypt the data in the corresponding bucket and then sent to the central coordinator.
[0038] TEE secure enclave decrypts and synchronizes data from each participant's bucket.
[0039] Execution round: TEE secure enclave parallel computation of the union of data from the same bucket of each participant, and fills the union result to a uniform length.
[0040] Functionality: Performs privacy-preserving set operations within an enclave. Execution flow: Employs a star topology network to reduce communication complexity to O(n); processes each bucket in two phases: input validation (INPUT) and computation execution (PROCEED); uses a counter pattern to generate session keys to prevent replay attacks; security design: a constant-time algorithm eliminates timing side channels, and results are padded to a uniform length to prevent cardinality leakage.
[0041] S105, Union Distribution: TEE secure enclave uses temporary key k s Encrypt the union data of each bucket.
[0042] The designated recipient obtains the encrypted union data and the TEE secure enclave signature proof ψ n To conduct TEE security enclave integrity verification.
[0043] If the verification passes, decrypt the union data and remove the padding data to obtain the final union.
[0044] Function: Securely delivers the final union result. Key Mechanisms: The designated receiver Pn obtains the decryption key ks through the OUTPUT function, and uses AE (authentication encryption) to ensure the integrity of the result; the authenticity of the output is verified through Ver(ψ); Anti-attack capability: Even if the central node is compromised, the signed result cannot be tampered with.
[0045] The embodiments of this invention eliminate the non-collusion assumption, ensuring reliability under malicious security models; overcome TEE memory limitations through hash bucketing and batch processing strategies; reduce communication complexity using a star topology, enabling the protocol to support a larger number of participants and data scales; complete formal security proofs within the UC security framework; experimental verification shows that this protocol can handle 2²... 6 When dealing with large-scale datasets, computational efficiency is improved by 2.16× to 5.05×, and communication overhead is reduced by 39× to 205×, significantly outperforming existing mainstream solutions.
[0046] In summary, by combining the advantages of TEE hardware with efficient protocol design, the solution proposed in this invention provides a safe and feasible new path for large-scale privacy-preserving data collaboration.
[0047] This invention also provides a multi-party private set union system based on a trusted execution environment, comprising: multiple participating parties and a central coordinator.
[0048] The central coordinating parties include: The TEE initialization module is used to initialize the TEE secure enclave and generate the session identifier eid and the asymmetric key pair (pk, msk).
[0049] The first secure key exchange module, TEE secure enclave, decrypts the symmetric keys k received from each participating party. i The system generates proofs based on the NIWI proof system and returns them to each participant.
[0050] The hash bucketing module resolves the data count in each participant's private set obtained from the TEE secure enclave, calculates the optimal number of buckets Nb, sets the filling threshold MAXB, and allocates a random seed r for the hash function, sending the obtained parameters to each participant.
[0051] The multi-party privacy set merging module decrypts and synchronizes the data received from each participant's bucket in the TEE secure enclave; it also calculates the union of the data from the same bucket of each participant in parallel and fills the union result to a uniform length.
[0052] Union distribution module for using temporary key k in TEE secure enclave sEncrypt the union data of each bucket; and combine the encrypted union data with the TEE secure enclave signature proof ψ n Send to the designated recipient.
[0053] The participating parties include: The TEE secure enclave integrity verification module is used to request and obtain the session identifier eid, public key pk, and TEE secure enclave signature proof ψ from the central coordinator, and to perform TEE secure enclave integrity verification.
[0054] The second secure key exchange module is used to randomly generate the symmetric key k for the participants. i It is then encrypted using pk and sent to the central coordinator; simultaneously, it receives a proof from the central coordinator to determine its symmetric key k. i It was received correctly.
[0055] The private set data preprocessing module is used to submit the data quantity in its private set to the central coordinator after encrypting it with pk. It receives the optimal number of buckets Nb, the set filling threshold MAXB and the random seed r of the hash function issued by the central coordinator, and divides the data in each private set into Nb buckets based on the hash bucketing algorithm. Finally, it fills the buckets with dummy elements until the amount of data in each bucket reaches the filling threshold MAXB.
[0056] Bucketed data generation module, used with symmetric key k i A key for each bucket is generated using a hash function, the data for that bucket is encrypted, and then sent to the central coordinator.
[0057] The union data receiving module is used to acquire the encrypted union data and the TEE secure enclave signature proof ψ. n Perform TEE security enclave integrity verification; after successful verification, decrypt the union data and remove padding data to obtain the final union.
[0058] This invention also provides an electronic device, including a processor, a memory, a communication interface, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the processor, and the programs include instructions for performing the steps of the above-described multi-party private set union method based on a trusted execution environment.
[0059] This invention also provides a computer-readable storage medium storing a computer program for electronic data interchange, wherein the computer program causes a computer to perform some or all of the steps described in the above-described method for merging multiple private sets based on a trusted execution environment.
[0060] This invention also provides a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program. The computer program is operable to cause a computer to perform some or all of the steps described in the above-described method for finding the union of multiple private sets based on a trusted execution environment.
[0061] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for finding the union of multiple private sets based on a trusted execution environment, characterized in that, Including multiple participating parties and a central coordinator, the specific steps are as follows: (1) TEE initialization: The central coordinator initializes the TEE secure enclave and generates a session identifier (eid) and an asymmetric key pair (pk, msk); Each participant requests and obtains the session identifier eid, public key pk, and TEE secure enclave signature proof ψ, and performs TEE secure enclave integrity verification; (2) Secure key exchange: After successful verification, each participant randomly generates a symmetric key k. i It is then encrypted using a pk and sent to the central coordinator. TEE Secure Enclave Decryption of Symmetric Key k for All Participants i And based on the NIWI proof system, a proof is generated and returned to each participant; Each participating party determines its symmetric key k based on the received proof. i It was received correctly; (3) Hash bucketing and data preprocessing: Each participating party submits the data count in its private collection to the central coordinator after encrypting it using a pk. The number of data from each participant obtained by TEE secure enclave resolution is used to calculate the optimal number of buckets Nb, set the filling threshold MAXB, and allocate a random seed r for the hash function. The obtained parameters are then sent to each participant. Each participant divides the data in their private set into Nb buckets based on the hash function’s random seed r and the hash bucketing algorithm. Finally, dummy elements are filled in until the amount of data in each bucket reaches the filling threshold MAXB. (4) Merging of multiple privacy collections: The process is divided into two rounds: the input round and the execution round. Input round: Each participant uses its symmetric key k i A key for each bucket is generated using a hash function, which is used to encrypt the data in the corresponding bucket and then sent to the central coordinator. TEE secure enclave decrypts and synchronizes data from each participant's bucket; Execution round: The TEE secure enclave performs parallel computation of the union of data from the same buckets of each participant, and fills the union result to a uniform length; then the data from each bucket after the union is taken are merged again to obtain the multi-party privacy set merged data; (5) Union distribution: TEE secure enclave uses temporary key k s Encrypted multi-party privacy collection and merging data; The designated recipient obtains the encrypted multi-party privacy set merged data and the temporary key k. s And TEE security enclave signature certificate ψ n Perform TEE security enclave integrity verification; If the verification passes, decrypt and remove the padding data to obtain the final union.
2. The multi-party private set union method based on a trusted execution environment according to claim 1, characterized in that, The specific steps (1) are as follows: The central coordinator calls SGX_Initialize() to create a secure enclave and generate a session identifier eid and an asymmetric key pair (pk, msk); Each participant requests and obtains a public key pk and a TEE secure enclave signature proof ψ. Each participant uses the public key pk to decrypt and verify the TEE secure enclave signature proof ψ, confirming the integrity of the TEE secure enclave.
3. The multi-party private set union method based on a trusted execution environment according to claim 1, characterized in that, In step (2), generating proof based on the NIWI proof system specifically involves generating proof based on trusted settings and encryption keys. π=Prove(CRS, (pk, Enc(pk, k i )), k i ) Where: π represents the generated proof, CRS is the public reference string generated through trusted settings, and Enc(pk, k) represents the generated proof. i Each participant uses pk to encrypt the symmetric key k. i Aftervalue; each participant proves the received π based on zero-knowledge proof to determine its symmetric key k. i It was received correctly.
4. The method for merging multiple private sets based on a trusted execution environment according to claim 1, characterized in that: The optimal number of buckets Nb is: Nb = m / log m; The filling threshold is: MAXB = ln m / ln (ln m) where: m is the maximum number of data in the private set of each participant.
5. A multi-party private set union system based on a trusted execution environment, characterized in that, include: Multiple participants and a central coordinator; The central coordinator includes: a TEE initialization module, used to initialize the TEE secure enclave and generate a session identifier (eid) and an asymmetric key pair (pk, msk); and a first secure key exchange module, used by the TEE secure enclave to decrypt the received symmetric keys k from each participating party. i And based on the NIWI proof system, a proof is generated and returned to each participant; The hash bucketing module resolves the data count in each participant's private set obtained from the TEE secure enclave, calculates the optimal number of buckets Nb, sets the filling threshold MAXB, and allocates a random seed r for the hash function, sending the obtained parameters to each participant. The multi-party privacy set merging module decrypts and synchronizes the data received from each participant's bucket in the TEE secure enclave; it also calculates the union of the data from the same bucket of each participant in parallel and fills the union result to a uniform length. Union distribution module for using temporary key k in TEE secure enclave s Encrypt the union data of each bucket; and combine the encrypted union data with the TEE secure enclave signature proof ψ n Send to the designated recipient; The participating parties include: The TEE secure enclave integrity verification module is used to request and obtain the session identifier eid, public key pk, and TEE secure enclave signature proof ψ from the central coordinator, and to perform TEE secure enclave integrity verification. The second secure key exchange module is used to randomly generate the symmetric key k for the participants. i It is then encrypted using pk and sent to the central coordinator; simultaneously, it receives a proof from the central coordinator to determine its symmetric key k. i It was received correctly; The private collection data preprocessing module is used to submit the data quantity in its private collection to the central coordinator after encrypting it with pk; it receives the optimal number of buckets Nb, the set filling threshold MAXB and the random seed r of the hash function issued by the central coordinator, and divides the data in each private collection into Nb buckets based on the hash bucketing algorithm, and finally fills dummy elements until the amount of data in each bucket reaches the filling threshold MAXB. Bucketed data generation module, used with symmetric key k i A key for each bucket is generated using a hash function, the data for that bucket is encrypted, and then sent to the central coordinator. The union data receiving module is used to acquire the encrypted union data and the TEE secure enclave signature proof ψ. n Perform TEE security enclave integrity verification; after successful verification, decrypt the union data and remove padding data to obtain the final union.
6. An electronic device, characterized in that, It includes a processor, memory, a communication interface, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the processor, and the programs include functions for performing claim 1.
4. Instructions for the steps of any of the methods for finding the union of multiple private sets based on a trusted execution environment.
7. A computer-readable storage medium, characterized in that, The aforementioned computer-readable storage medium stores a computer program for electronic data interchange, wherein the computer program causes a computer to perform the operation of claim 1.
4. Some or all of the steps described in any of the methods for finding the union of multiple private sets based on a trusted execution environment.
8. A computer program product, characterized in that, The aforementioned computer program product includes a non-transitory computer-readable storage medium storing a computer program operable to cause a computer to perform the functions of claim 1.
4. Some or all of the steps described in any of the methods for finding the union of multiple private sets based on a trusted execution environment.