Block chain right confirmation and responsibility investigation method based on dual-path verifiable threshold signature

Abstract

The invention discloses a double-path verifiable threshold signature-based block chain right confirmation and responsibility investigation method, which comprises the following steps of: S1, receiving right confirmation data, processing the data to obtain normalized data, and calculating a data abstract of the normalized data; submitting the data abstract and the associated information thereof to a block chain for evidence storage to form a right confirmation request record; s2, in response to the right confirmation request record, selecting a committee member set from candidate nodes based on a preset strategy, and cooperatively generating a global public key and a private key share corresponding to each committee member by the committee member set through a distributed key generation protocol; and S3, each committee member generates a partial signature for the data abstract by using the private key share of the committee member, and generates a verifiable proof for proving the correctness of the calculation process of the partial signature of the committee member at the same time. According to the invention, independent verification and accurate responsibility tracing of individual signature behaviors of committee members can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of blockchain and cryptography technology, and in particular to a blockchain authentication and accountability method based on a double-path verifiable threshold signature. BACKGROUND

[0002] With the growing demand for government-enterprise collaboration data circulation, more application scenarios require trusted authentication and traceable management of data resources. In the process of on-chain authentication involving government affairs, security and sensitive resources, it is often necessary for multiple authorized parties (or committee members) to jointly endorse the authenticity, integrity and legality of a certain data resource to form a reliable credential for subsequent regulatory departments to verify. To avoid single-point trust risks, such multi-party authentication often uses threshold signature or multi-party signature schemes based on cryptography, allowing multiple committee members to participate in and generate a final aggregated signature, thereby ensuring the decentralization, security and tamper resistance of the authentication process while dispersing power.

[0003] However, existing mainstream threshold signature schemes (such as TSS-DSA, TSS-BLS, TSS-EdDSA, etc.) usually only output a final aggregated signature, which cannot reflect the individual behavior of each participant. Once a committee member submits an incorrect partial signature, refuses to participate in the signature process, or commits malicious behavior during the process, such schemes cannot locate the specific responsible subject, and the system can only perceive that the entire signature group is abnormal, lacking accountability for individual malicious nodes. Although some existing research has attempted to provide group-level accountability (such as DeTAPS), the accountability mechanism still cannot support independent on-chain verification of the specific behavior of each committee member during the signature calculation phase, resulting in final accountability remaining at the "signature group level" and making it difficult to meet the needs of government-enterprise application scenarios requiring precise real-name supervision.

[0004] In the key generation phase, existing research has used zero-knowledge proof (such as ZK-DKG technology based on Feldman VSS) to verify the correctness of the distributed key generation (DKG) process. However, these technologies mainly focus on the verifiability of the key material generation phase and fail to cover the more critical "signature calculation phase", making it impossible to effectively prove and audit the correctness of the members' calculations during the signature process.

[0005] In addition, there are other contradictions in the system implementation level: if the real-time verification of signing and proof completely relies on the blockchain, it will generate high computing and storage overhead, seriously affecting the system throughput performance; if the off-chain verification method is completely adopted, the regulatory party cannot obtain the necessary on-chain visibility, making it difficult to meet the compliance requirements of "on-chain checkable, traceable and accountable". At the same time, the existing system architecture generally lacks a dual-path unified verification framework that can support efficient proof based on trusted execution environment (TEE) and strong privacy proof based on zero-knowledge proof (ZK-proof). This makes it difficult for committee members to choose proof methods flexibly according to their hardware conditions and security requirements, making it difficult for the system to achieve a good balance between performance, privacy protection and verifiability.

[0006] In summary, the existing technology mainly has the following defects: 1) unable to locate specific malicious nodes in the threshold signature process, lacking individual-level accountability; 2) lacking effective and independently verifiable proof mechanism for signature calculation phase; 3) regulatory party has difficulty in tracing and auditing the signature behavior of individual nodes on the chain; 4) the verification cost of the proof is high, and there is a lack of flexible technical path that takes into account performance and trusted verification. The present application aims to provide an innovative solution to the above problems. SUMMARY

[0007] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide a blockchain authentication and accountability method based on dual-path verifiable threshold signature, which generates verifiable proof for part of the signature process of each member by introducing optional TEE or zero-knowledge proof and uploads it to the chain, combines asynchronous batch verification and on-chain accountability mechanism, and realizes independent verification and accurate responsibility tracing of individual signature behavior of committee members.

[0008] The blockchain authentication and accountability method based on dual-path verifiable threshold signature comprises the following steps: S1, receiving data to be authenticated, processing the data to obtain normalized data, and calculating the data digest of the normalized data; submitting the data digest and its associated information to the blockchain for storage, forming an authentication request record; S2, in response to the authentication request record, electing a set of committee members from candidate nodes based on a preset strategy, and generating a global public key and a private key share corresponding to each committee member by a distributed key generation protocol; S3, each committee member generates a partial signature for the data digest using its private key share, and generates a verifiable proof for proving the correctness of its partial signature calculation process; wherein the verifiable proof includes hardware proof generated based on trusted execution environment or cryptographic proof generated based on zero-knowledge proof; S4, submitting the partial signature generated by each committee member and its corresponding verifiable proof to the blockchain, associating with the right request record; the submitted verifiable proof is verified asynchronously in batches by the verification service, and the verification result is recorded; S5, when the number of valid partial signatures verified reaches a preset threshold, generating an aggregated signature for the data digest according to the valid partial signatures and their corresponding verification results; S6, verifying the validity of the aggregated signature, and generating a right certificate containing the data digest, the aggregated signature, the list of valid committee members and the timestamp after verification, and storing the right certificate on the blockchain; S7, when the right certificate needs to be traced or disputed, based on the right request record and all verifiable proof records associated with it stored on the blockchain, the committee members participating in the signature are verified one by one to locate the abnormal nodes and perform corresponding accountability processing.

[0009] Further, in S2, the distributed key generation protocol is a commitment-based verifiable secret sharing protocol; generating a global public key and a private key share includes: each committee member generates a random polynomial and calculates a corresponding commitment vector, distributes shares among members in secret, the receiver verifies the validity of the received share based on the commitment vector, and after verification, aggregates to generate its own private key share, and calculates the global public key based on the commitment vectors of all members.

[0010] Further, in S3, the partial signature is generated by a Schnorr-based threshold signature scheme; the committee member generates a random number and calculates a corresponding random number commitment, and then calculates a partial signature value based on the data digest, the global public key, its own private key share and Lagrange coefficient; wherein the Lagrange coefficient is determined according to the node index of the member itself and the set of signature participants agreed by the threshold signature scheme; the random number commitment is submitted together with the partial signature.

[0011] Further, in S3, the hardware proof generated based on the trusted execution environment is a platform proof report containing execution environment measurement value, signature output information and timestamp.

[0012] Furthermore, in S3, the cryptographic proof generated based on zero-knowledge proof is generated by constructing a zero-knowledge proof circuit; the public input of the circuit includes a global commitment, node index, data digest, and random number commitment generated by the distributed key generation protocol, and the private witness includes the node's private key share and random number; the constraints of the circuit include at least: consistency verification between the private key share and the global commitment, consistency verification between the random number and the random number commitment, and correctness verification of the partial signature calculation relationship.

[0013] Furthermore, in S4, the asynchronous batch verification specifically involves: the verification service periodically reading records in the pending verification state from the blockchain, calling the trusted execution environment verification interface to verify records that use hardware proofs, calling the zero-knowledge proof verifier to verify records that use cryptographic proofs, and writing the verification results back to the blockchain to update the state of the corresponding records.

[0014] Furthermore, S5 specifically includes: obtaining all valid partial signatures and their associated information from the blockchain to determine the set of valid signature members; recalculating the Lagrange coefficient of each member based on the set of valid signature members; combining the partial signature values ​​using the Lagrange coefficients and aggregating the random number commitments to obtain the aggregated signature.

[0015] Furthermore, in S6, the validity of the aggregated signature is verified by a verification equation; the equation involves the aggregated signature, the aggregated random number commitment, the global public key, and a hash value for verification, which is calculated from the aggregated random number commitment, the global public key, and the data digest.

[0016] Furthermore, in S7, the accountability process includes at least one of the following: imposing penalties on abnormal nodes, lowering the reputation score of abnormal nodes, adding abnormal nodes to a blacklist, and triggering a re-authorization process for the data digest.

[0017] Furthermore, in step S1, the data processing includes data desensitization; the data digest is obtained by performing a cryptographic hash operation on the normalized data; during notarization, the data digest and its metadata are submitted to the blockchain smart contract, and the storage reference information of the original data is also submitted.

[0018] Compared with existing technologies, the beneficial effects of this invention are as follows: the blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures has significant advantages in terms of security, verifiability, performance, and regulatory availability, specifically: 1. This invention introduces a dual-path verification mechanism of TEE (Trusted Execution Environment) and ZK-proof on the basis of the traditional threshold signature system. Unlike existing schemes that rely solely on a single cryptographic proof or trusted hardware, this invention allows committee members to choose an appropriate proof method based on their own computing resources and security level. TEE provides efficient trusted computing capabilities, while ZK-proof provides strong security guarantees that can be executed in a pure software environment. Through the dual-path parallel mechanism, this invention achieves a balance between security and flexibility, ensuring the correctness of signature calculation while also taking into account node heterogeneity and performance optimization.

[0019] 2. The multi-layered rights confirmation and accountability mechanism proposed in this invention achieves a complete closed loop from signature generation to responsibility identification. Traditional threshold signature schemes cannot identify specific malicious nodes when signatures are abnormal, while this invention, through on-chain stored proof records, achieves verifiability and accountability for individual committee members. When the government or arbitration institution discovers an anomaly in the rights confirmation certificate, it can re-verify the proofs of each node based on the on-chain evidence, accurately locating the malicious actor, thereby improving the system's auditability and judicial credibility.

[0020] 3. The architecture of this invention achieves traceability and anti-counterfeiting for on-chain rights confirmation certificates. By integrating information such as data hash, aggregate signature, valid node list, and timestamp into the rights confirmation certificate, it ensures consistency and immutability between the certificate and the blockchain state, solving the trust gap problem that exists in traditional digital certificates in multi-institutional collaboration scenarios. Overall, this invention outperforms existing solutions in terms of security, performance, and regulatory compliance, and is particularly suitable for scenarios with extremely high trust requirements, such as government rights confirmation, financial supervision, and judicial evidence collection. Attached Figure Description

[0021] Fig. 1 This is a flowchart of a blockchain-based method for establishing and tracing ownership and accountability based on dual-path verifiable threshold signatures, as described in an embodiment of the present invention. Fig. 2 This is a flowchart illustrating the blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures in an embodiment of the present invention. Fig. 3 This is a schematic diagram of the architecture of the blockchain ownership confirmation and accountability method based on dual-path verifiable threshold signature in an embodiment of the present invention. Detailed Implementation

[0022] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the various embodiments or technical features described below can be arbitrarily combined to form new embodiments.

[0023] This invention provides a blockchain-based method for establishing and holding accountable rights based on dual-path verifiable threshold signatures. This method combines Feldman VSS DKG, TEE proof, zero-knowledge proof (ZK-proof), threshold signature aggregation, on-chain / off-chain collaborative verification, and a rights certificate generation and accountability mechanism to achieve complete verifiability and locatable accountability for the signing behavior of committee members, overcoming the technical deficiency of existing threshold signature methods that cannot identify malicious members.

[0024] like Figs. 1-3 As shown, the blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to an embodiment of the present invention includes the following steps: S1. Receive the data to be confirmed, process the data to obtain standardized data, and calculate the data digest of the standardized data; submit the data digest and its associated information to the blockchain for storage to form a confirmation request record.

[0025] In this embodiment, the submission of a right confirmation request specifically includes the following: Users submit the original data D to be confirmed to an external platform or client. The platform then performs data standardization and anonymization processing locally to obtain the data. And calculate the data summary: H can be SHA-256 / SM3, and the output can be used as a hash or mapped to Zq for group operation input. The system calls the contract submitDataHash(m,meta) on the blockchain for notarization. The contract record contains {m,submitter,txHash,blockNumber,timestamp}. For privacy and efficiency, only m and the proof-hash are stored on the chain (if the original text is stored on external storage, its address digest is written). This write event simultaneously triggers committee elections or the start of the next round of candidate preparation.

[0026] S2. In response to the confirmation request record, a set of committee members is elected from the candidate nodes based on a preset strategy, and the set of committee members collaboratively generates a global public key and a private key share corresponding to each committee member through a distributed key generation protocol.

[0027] In this embodiment, committee election and key generation specifically include the following: The contract CommitteeSC selects n committee members based on a preset strategy (reputation weight, rotation, on-chain random seed) and broadcasts the CommitteeID. Members execute Feldman VSS in parallel: each member i randomly generates a polynomial: in Let t be the secret polynomial generated by committee member i, and t be the threshold size. For the private coefficients of the polynomial, Let be a finite field modulo q.

[0028] And calculate the commitment vector Then, privately send the share to member j. Recipient verification: in, The coefficient commitment published for node i The commitment result calculated using the received share.

[0029] If the transaction fails, a Complaint(i) can be submitted for contract arbitration or a resend / penalty can be triggered. All verified shares are aggregated into their private key shares on each node j: in, Let be the final share of the private key for node j. Let n be the share received from node i, and n be the total number of committee members.

[0030] Write a global commitment in the contract. PK= global public key The DKG process guarantees that no single point of contact can control the complete private key and promises that it can be used as a public input for subsequent proof circuitry.

[0031] S3. Each committee member uses their own private key share to generate a partial signature on the data digest, and at the same time generates a verifiable proof to prove the correctness of their partial signature calculation process; wherein, the verifiable proof includes a hardware proof generated based on a trusted execution environment or a cryptographic proof generated based on zero-knowledge proof.

[0032] In this embodiment, partial signature generation + proof generation (TEE / ZK dual path) specifically includes the following: When a signature is required to confirm ownership of m, committee members each compute their local signature. Schnorr is used, and nodes generate random nonces. ,calculate And calculate local signatures in, The Lagrange interpolation coefficients are based on the participating set T. Let e ​​be the partial signature of node j, and e be the challenge value. This represents the private key share of node j. Each node must also generate a proof to demonstrate the correctness of its signature calculation; nodes can choose between two paths: TEE path (efficient): Perform signature computation and generate attestation within a trusted execution environment. The attestation contains execution environment metrics and an output summary, which can be checked by contracts or remote verification services to verify the issuer's signature and MRENCLAVE whitelist.

[0033] ZK path (strong proof): Construct a zero-knowledge circuit, with common inputs including: global commitments. Node index j, message hash m, possible Private witness is , The circuit should include at least the following constraints: 1. (Consistency of share) ; 2. (Nonce consistency) ; 3. (Signature Relationship) .

[0034] Generate proof (e.g., Groth16 / PLONK, etc.), and { , }or{ Submit to the contract's pending pool. To save on-chain storage, large proofs can be stored off-chain (IPFS / enterprise storage) and the proof hash submitted on-chain.

[0035] S4. Submit the partial signature generated by each committee member and its corresponding verifiable proof to the blockchain and associate it with the confirmation request record; the verification service performs asynchronous batch verification of the submitted verifiable proof and records the verification results.

[0036] In this embodiment, on-chain recording + asynchronous verification specifically includes the following: The contract receives submissions and marks the records as PENDING (including submission time, proof type, and proof hash). To balance throughput and security, asynchronous batch verification is used: the Verifier Daemon periodically reads pending items in batches and executes VerifyTEE in parallel. (Verify attestation signature, MRENCLAVE, output consistency) or VerifyZK ( (Calls the local zkverifier or on-chain verifier contract). The verification result is written back to the contract and the corresponding status is updated to VALID or INVALID. When the number of VALIDs is greater than or equal to t, the contract triggers an aggregation event. This design places the expensive proof computation off-chain and reduces the on-chain burden by using parallelization and batch verification (batch techniques can be used for zk).

[0037] S5. When the number of verified valid partial signatures reaches a preset threshold, an aggregate signature for the data digest is calculated and generated based on the valid partial signatures and their corresponding verification results.

[0038] In this embodiment, the aggregation signature generation is detailed below: After the contract specifies VALID≥t, the aggregator (which can be a rotating aggregator node or a dedicated aggregator service) retrieves the valid participant set T and calculates the Lagrange interpolation coefficients. Where T is the set of nodes that participated in signing and valid verification in this round, and l is the index of other nodes in set T.

[0039] Merge each , Overall and and calculate Perform final verification. Aggregator submits { The `T,proofRefs` property is given to the contract to record the aggregator's signature and time, facilitating subsequent accountability.

[0040] S6. Verify the validity of the aggregated signature. If the verification is successful, generate a certificate of authorization containing the data digest, the aggregated signature, a list of valid committee members, and a timestamp, and store the certificate of authorization on the blockchain.

[0041] In this embodiment, the verification formula in the on-chain verification and certificate generation is as follows: Where g is a generator of group G, and s is the s-part of the final aggregated Schnorr threshold signature. After successful verification, a certificate of ownership (Cert) is generated and written to the blockchain. The certificate contains {m, `T,proofMode,proofHashes,blockNumber,timestamp}`. Simultaneously, events are emitted for regulators or indexing services to archive complete off-chain proof data (for use in judicial evidence collection).

[0042] S7. When it is necessary to trace the source of the confirmation certificate or when a dispute arises, the committee members who participated in the signing are verified one by one based on the confirmation request record and all verifiable proof records associated with it stored on the blockchain, so as to locate the nodes with abnormal behavior and carry out corresponding accountability.

[0043] In this embodiment, the accountability mechanism is as follows: If a dispute occurs (user complaint, audit, or certificate verification failure), the government / regulatory node invokes the accountability process: the smart contract reads the Cert and the corresponding submission record of each member, and calls VerifyTEE one by one. ) or VerifyZK ( Any INVALID / MISSING entry is marked as Faulty; the contract automatically executes slashes, reputation deductions, or blacklisting of nodes according to the policy, and can revoke certs and trigger re-establishment of rights. If the ZK path involves privacy, the contract should define legal trigger conditions, allowing nodes to disclose restricted witness portions to support proof, provided compliance is guaranteed; if a node refuses to disclose in compliance, the contract can make a judgment according to the rules.

[0044] The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures, as described in this invention, has the following advantages: 1. This invention innovatively introduces a dual-path verifiable mechanism, achieving a balance between security, flexibility, and efficiency. By integrating Trusted Execution Environment (TEE) and zero-knowledge proof (ZK) technologies into the same threshold signature framework, committee members can choose between efficient TEE proofs or privacy-preserving ZK proofs based on their hardware capabilities, computing resources, and security requirements. This design also considers node heterogeneity, ensuring signature calculation correctness through verifiable proofs while providing flexible access methods for different participants, thus optimizing the overall system performance and compatibility.

[0045] 2. This invention constructs a complete closed loop for individual-level behavior tracing and accountability, enhancing the system's auditing capabilities and judicial credibility. By requiring each member to simultaneously generate verifiable proof and store it on the blockchain when generating partial signatures, the signature behavior of any single committee member can be independently verified and audited post-event. When disputes or anomalies arise in the confirmation results, regulatory agencies can accurately locate specific nodes of misconduct based on the immutable records on the blockchain, thereby achieving effective accountability for individual nodes and enhancing the system's audit transparency and the admissibility of judicial evidence in highly regulated scenarios.

[0046] 3. This invention employs an asynchronous verification architecture that combines on-chain and off-chain collaboration, ensuring both auditability and high system throughput. To address the performance bottleneck caused by fully on-chain verification, an asynchronous batch verification mechanism is designed that coordinates smart contracts with off-chain verification services. This transfers the computationally expensive proof verification calculations to off-chain parallel execution, only writing the verification result summary back to the blockchain. This model avoids the performance bottleneck of the blockchain while ensuring the on-chain verifiability and non-repudiation of all key verification evidence, effectively balancing regulatory transparency and system operating efficiency.

[0047] 4. This invention generates a structurally complete, on-chain stored ownership certificate, ensuring the immutability and complete traceability of the ownership document. The final generated digital ownership certificate is a structured data record deeply embedded in the blockchain state, integrating core data digests, aggregate signatures, participant lists, timestamps, and corresponding metadata, and its generation logic is closely linked to the multi-step evidence storage records on the blockchain. This design not only utilizes blockchain characteristics to ensure the authenticity of the certificate but also establishes a complete evidence chain tracing back from the ownership certificate to the original data and the actions of all parties, solving the trust connection and traceability problems of traditional certificates in cross-institutional collaboration.

[0048] 5. The overall solution of this invention possesses both high practicality and wide applicability. Through a series of collaborative designs, including dual-path verification, on-chain individual behavior, asynchronous verification optimization, and structured certificates, a secure, efficient, reliable, and superviseable multi-party collaborative rights confirmation system is constructed. Its technical characteristics are particularly well-suited to application scenarios with extremely high requirements for data authenticity, process compliance, and post-event accountability, such as government data asset rights confirmation, compliant financial transaction evidence storage, and judicial electronic evidence fixation.

[0049] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures, characterized in that: Includes the following steps: S1. Receive the data to be confirmed, process the data to obtain standardized data, and calculate the data digest of the standardized data; submit the data digest and its associated information to the blockchain for notarization to form a confirmation request record; S2. In response to the confirmation request record, a set of committee members is elected from the candidate nodes based on a preset strategy, and the set of committee members collaboratively generates a global public key and a private key share corresponding to each committee member through a distributed key generation protocol. S3. Each committee member uses their own private key share to generate a partial signature on the data digest, and at the same time generates a verifiable proof to prove the correctness of their partial signature calculation process; wherein, the verifiable proof includes a hardware proof generated based on a trusted execution environment or a cryptographic proof generated based on zero-knowledge proof; S4. Submit the partial signature generated by each committee member and its corresponding verifiable proof to the blockchain and associate it with the rights confirmation request record; the verification service performs asynchronous batch verification of the submitted verifiable proof and records the verification results; S5. When the number of verified valid partial signatures reaches a preset threshold, calculate and generate an aggregate signature for the data digest based on the valid partial signatures and their corresponding verification results. S6. Verify the validity of the aggregated signature. If the verification is successful, generate a certificate of authorization containing the data digest, the aggregated signature, a list of valid committee members, and a timestamp, and store the certificate of authorization on the blockchain. S7. When it is necessary to trace the source of the confirmation certificate or when a dispute arises, the committee members who participated in the signing are verified one by one based on the confirmation request record and all verifiable proof records associated with it stored on the blockchain, so as to locate the nodes with abnormal behavior and carry out corresponding accountability.

2. The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to claim 1, characterized in that, In step S2, the distributed key generation protocol is a commitment-based verifiable secret sharing protocol; the collaborative generation of the global public key and private key shares includes: each committee member generating a random polynomial and calculating the corresponding commitment vector, secretly distributing the shares among the members, the recipient verifying the validity of the received shares based on the commitment vector, and after verification, aggregating to generate their respective private key shares, and calculating the global public key based on the commitment vectors of all members.

3. The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to claim 2, characterized in that, In step S3, the partial signature is generated using a Schnorr-based threshold signature scheme; committee members generate random numbers and calculate corresponding random number commitments, and then calculate the partial signature value based on the data digest, the global public key, their own private key share, and the Lagrange coefficient; wherein, the Lagrange coefficient is determined according to the member's own node index and the set of signature participants agreed upon by the threshold signature scheme; the random number commitment is submitted together with the partial signature.

4. The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to claim 1, characterized in that, In S3, the hardware proof generated based on the trusted execution environment is a platform proof report that includes execution environment metrics, signature output information, and timestamps.

5. The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to claim 2, characterized in that, In step S3, the cryptographic proof generated based on zero-knowledge proof is generated by constructing a zero-knowledge proof circuit; the public input of the circuit includes a global commitment, node index, data digest, and random number commitment generated by the distributed key generation protocol, and the private witness includes the node's private key share and random number; the constraints of the circuit include at least: consistency verification between the private key share and the global commitment, consistency verification between the random number and the random number commitment, and correctness verification of the partial signature calculation relationship.

6. The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to claim 1, characterized in that, In S4, the asynchronous batch verification specifically involves: the verification service periodically reading records in the pending verification state from the blockchain, calling the trusted execution environment verification interface to verify records that use hardware proofs, calling the zero-knowledge proof verifier to verify records that use cryptographic proofs, and writing the verification results back to the blockchain to update the state of the corresponding records.

7. The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to claim 3, characterized in that, S5 specifically includes: obtaining all valid partial signatures and their associated information from the blockchain to determine the set of valid signature members; recalculating the Lagrange coefficient of each member based on the set of valid signature members; combining the partial signature values ​​using the Lagrange coefficients and aggregating the random number commitments to obtain the aggregated signature.

8. The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to claim 7, characterized in that, In step S6, the validity of the aggregated signature is verified by a verification equation; the equation involves the aggregated signature, the aggregated random number commitment, the global public key, and a hash value for verification, which is calculated from the aggregated random number commitment, the global public key, and the data digest.

9. The blockchain-based method for establishing ownership and accountability based on dual-path verifiable threshold signatures according to claim 1, characterized in that, In S7, the accountability process includes at least one of the following: imposing penalties on abnormal nodes, lowering the reputation score of abnormal nodes, adding abnormal nodes to a blacklist, and triggering a re-authorization process for the data digest.

10. The blockchain ownership confirmation and accountability method based on dual-path verifiable threshold signatures according to claim 1, characterized in that, In step S1, the data processing includes data desensitization; the data digest is obtained by performing a cryptographic hash operation on the normalized data; during notarization, the data digest and its metadata are submitted to the blockchain smart contract, and the storage reference information of the original data is also submitted.

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