Multi-party threshold Schnorr signature method, system and device based on trusted aggregation party and medium
By introducing trusted aggregators and security parameters to generate threshold keys, the signature process is optimized, and the problems of high computational complexity and risk of random number reuse in the existing technology are solved, and efficient and secure multi-party threshold Schnorr signature is achieved.
Patent Information
- Application Number
- CN202510561552.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-30
- Publication Date
- 2025-08-01
AI Technical Summary
The existing threshold Schnorr signature scheme has high computational complexity, high risk of random number reuse and lacks a credible coordinator, resulting in delays or failures in signatures.
The trusted aggregation party is introduced to generate threshold keys through security parameters and threshold key sharing mechanisms and Lagrangian interpolation method. The trusted execution environment is used to generate random challenges and signature application information, optimize the signature process, reduce the number of interaction rounds and prevent random number reuse.
It improves the security and computing efficiency of signatures, prevents single point of failure, and ensures the confidentiality and integrity of the signature process. It is suitable for blockchain, distributed identity authentication, and privacy protection computing scenarios.
Smart Images
Figure CN120415740A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of information security technology, and particularly to a multi-party threshold Schnorr signature method, system, device and medium based on a trusted aggregator. Background Art
[0002] Schnorr signature is a digital signature scheme based on elliptic curve cryptography (ECC), which has high security and computational efficiency. Its basic process is as follows: 1) Key generation: Select a base point G of an elliptic curve group, let the private key be x, and the public key be ; 2) Signature process: Select a random number r, calculate the commitment value ; Calculate the hash challenge value ; Calculate the signature value ; Output the Schnorr signature ; 3) Verification process: Calculate equation. If it holds, the signature is valid.
[0003] In order to avoid single point of failure and improve the fault tolerance of the private key, existing research has proposed a threshold Schnorr signature scheme, such as FROST (Flexible Round-Optimized Schnorr Threshold Signatures). Its core idea is to split the private key among multiple participants, and each participant holds a private key share. Only when t participants reach the threshold participate in the signature can a valid signature be generated. The main steps of the FROST scheme are as follows: First, the participants distribute the private key shares , and calculate the public key shares ; Then, each participant independently generates a random value and calculates the commitment value , then, interactively calculate the hash challenge value , M is the message to be signed. Then, calculate the partial signature , and submit it to the aggregator. Finally, the aggregator calculates the final signature .
[0004] Although threshold Schnorr signature schemes such as FROST solve the single point of failure problem, there are still the following problems: 1) High computational complexity: Existing threshold signature schemes require multiple rounds of interaction. For example, FROST requires multiple parties to negotiate random numbers and calculate partial signatures, resulting in high computational complexity.
[0005] 2) Random number reuse risk: If the random number r is reused in different signature processes, the attacker can deduce the private key, resulting in key leakage.
[0006] 3) The decentralized threshold signature scheme lacks a unified coordination party: The existing schemes rely on a decentralized signature aggregation method and lack a trusted coordination party to optimize the signature process, which may lead to signature delay or failure.
[0007] For the problems in the related technologies, no effective solution has been proposed yet. Summary of the Invention
[0008] Embodiments of the present invention provide a multi-party threshold Schnorr signature method, system, device and medium based on a trusted aggregator to solve the above-mentioned technical problems in the prior art.
[0009] To provide a basic understanding of some aspects of the disclosed embodiments, a simple summary is given below. This summary part is not a general review, nor is it intended to identify key / important constituent elements or delineate the protection scope of these embodiments. Its sole purpose is to present some concepts in a simple form as a prelude to the subsequent detailed description.
[0010] According to the first aspect of the embodiments of the present invention, a multi-party threshold Schnorr signature method based on a trusted aggregator is provided.
[0011] In one embodiment, the multi-party threshold Schnorr signature method based on a trusted aggregator includes the following steps: S1. Based on security parameters and threshold parameters, combined with the threshold key sharing mechanism and Lagrange interpolation method, generate a threshold key for collaborative signature with the trusted aggregator; S2. The trusted aggregator generates a random challenge and related signature application information, calculates partial signatures according to the threshold signature nodes, and aggregates the signatures through the trusted aggregator.
[0012] In one embodiment, the step of generating a threshold key for collaborative signature with the trusted aggregator based on security parameters and threshold parameters, combined with the threshold key sharing mechanism and Lagrange interpolation method, includes the following steps: S11. Set security parameters and select elliptic curve parameters , set threshold parameters , where E represents the elliptic curve group, q represents the order of the elliptic curve group, G represents the base point, n represents the total number of participating parties, and t represents the threshold value; S12. Based on the threshold key sharing mechanism and Lagrange interpolation method, generate two sets of public-private key pairs for collaborative signature with the trusted aggregator.
[0013] In one embodiment, generating two sets of public and private key pairs for collaborative signature with a trusted aggregator based on the threshold key sharing mechanism and Lagrange interpolation method includes the following steps: S121. Use the threshold key sharing mechanism to split the private key s into n parts, so that each participating party i obtains a private key share and the public key , and generate the private key by combining the Lagrange interpolation method, where represents the threshold interpolation coefficient, and represents the private key share of participating party j; S122. The signing party i calculates and generates two sets of public and private key pairs for collaborative signature with the trusted aggregator, and , , where represents the first public key of signing party i, represents the second public key of signing party i, represents the first private key of signing party i, and represents the second private key of signing party i.
[0014] In one embodiment, the trusted aggregator generates a random challenge and related signature application information, calculates partial signatures according to the threshold signature nodes, and aggregates signatures through the trusted aggregator, including the following steps: S21. The user terminal submits the signature message M to the trusted aggregator; S22. Based on the trusted execution environment, the trusted aggregator generates a random challenge and related signature application information and sends them to the signing party; S23. The signing party calculates partial signatures, challenge values, and signature shards through the key exchange algorithm, and returns the signature shards to the trusted aggregator; S24. The trusted aggregator aggregates the signature shards of each signing party to obtain a signature value, generates a Schnorr signature and returns it to the user terminal; the user terminal first calculates the challenge value and verifies the validity of the signature.
[0015] In one embodiment, based on the trusted execution environment, the trusted aggregator generates a random challenge and related signature application information and sends them to the signing party, including the following steps: S221. The trusted aggregator selects t online signing parties and generates a random challenge inside the trusted execution environment, and calculates the challenge commitment value ; S222. Calculate the random commitment value of each signing party j, and converge and calculate to obtain the global commitment , where represents the hash operation mapping to The integer ring, represents the first public key of the signer j, represents the second public key of the signer j; S223. The trusted aggregator sends the signature application information to t signers, where M represents the signature message.
[0016] In one embodiment, the signer calculates a partial signature, a challenge value, and a signature shard through a key exchange algorithm and returns the signature shard to the trusted aggregator, including the following steps: S231. Each signer j calculates a partial signature , where represents the hash operation mapped to the integer ring, represents the random factor of the signer j, represents the first private key of the signer j, represents the second private key of the signer j; S232. Calculate the challenge value and the signature shard , where || is string concatenation, and the signer returns the signature shard to the trusted aggregator.
[0017] In one embodiment, the trusted aggregator aggregates the signature shards of each signer to obtain a signature value, generates a Schnorr signature, and returns it to the user terminal; the user terminal first calculates the challenge value and verifies the validity of the signature, including the following steps: S241. The trusted aggregator aggregates the signature shards of each signer to obtain a signature value , generates a Schnorr signature , and returns it to the user terminal; S242. The user terminal first calculates the challenge value , and determines whether the equation holds. If so, the signature is valid; if not, the signature is invalid.
[0018] According to the second aspect of the embodiments of the present invention, a multi-party threshold Schnorr signature system based on a trusted aggregator is provided.
[0019] In one embodiment, the multi-party threshold Schnorr signature system based on a trusted aggregator includes a threshold signature generation initialization module and a user terminal signature execution module; Among them, the threshold signature generation initialization module is used to generate a threshold key for collaborative signature with the trusted aggregator based on security parameters and threshold parameters, combined with a threshold key sharing mechanism and Lagrange interpolation method. The user terminal signature execution module is used to generate a random challenge and related signature application information by the trusted aggregator, calculate partial signatures according to the threshold signature nodes, and aggregate the signatures through the trusted aggregator.
[0020] According to the third aspect of the embodiments of the present invention, a computer device is provided.
[0021] In some embodiments, the computer device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the above method are implemented.
[0022] According to the fourth aspect of the embodiments of the present invention, a computer-readable storage medium is provided.
[0023] In one embodiment, a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the above method are implemented.
[0024] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects: 1) By introducing a trusted aggregator, the present invention can effectively optimize the threshold Schnorr signature scheme.
[0025] 2) Improve security: prevent single point of failure and ensure the confidentiality and integrity of the signature process.
[0026] 3) Higher computing efficiency: reduce the number of interaction rounds and improve the signature efficiency.
[0027] 4) Defend against random number reuse attacks: the trusted aggregator actively generates random challenges to ensure that each signature value is different.
[0028] 5) Based on trusted computing: the trusted aggregator runs in the TEE to ensure computing isolation and data security.
[0029] 6) Applicable to a variety of application scenarios: blockchain, distributed identity authentication, privacy-preserving computing, etc.
[0030] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] The accompanying drawings herein are incorporated into the specification and form a part of the specification, showing embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention.
[0032] Figure 1 is a flowchart of a multi-party threshold Schnorr signature method based on a trusted aggregator shown according to an exemplary embodiment; Figure 2 It is a schematic diagram of a multi-party threshold Schnorr signature method based on a trusted aggregator shown according to an exemplary embodiment; Figure 3 It is a structural block diagram of a multi-party threshold Schnorr signature system based on a trusted aggregator shown according to an exemplary embodiment; Figure 4 It is a schematic structural diagram of a computer device shown according to an exemplary embodiment. Detailed implementation manners
[0033] The following description and the drawings fully illustrate the specific embodiments herein, enabling those skilled in the art to practice them. Parts and features of some embodiments may be included in or substituted for parts and features of other embodiments. The scope of the embodiments herein includes the entire scope of the claims and all available equivalents of the claims. In this document, terms such as "first", "second", etc. are only used to distinguish one element from another, without requiring or implying any actual relationship or order between these elements. In fact, the first element can also be called the second element, and vice versa. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a structure, device or equipment including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such structure, device or equipment. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the structure, device or equipment including the said element. The various embodiments herein are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other.
[0034] Terms such as "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. in this document indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing this document and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be construed as a limitation of the present invention. In the description of this document, unless otherwise specified and limited, the terms "installed", "connected", "coupled" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or it can be the communication inside two elements. It can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.
[0035] In this document, unless otherwise specified, the term "plurality" means two or more than two.
[0036] In this document, the character " / " means that the objects before and after are in an "or" relationship. For example, A / B means: A or B.
[0037] In this document, the term "and / or" is a description of the associated relationship of an object, indicating that three relationships can exist. For example, A and / or B means: A or B, or, the three relationships of A and B.
[0038] It should be understood that although the various steps in the flowchart are displayed sequentially according to the indication of the arrows, these steps are not necessarily executed sequentially in the order indicated by the arrows. Unless there is a clear description in this document, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, at least a part of the steps in the figure may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same moment, but can be executed at different moments, and the execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.
[0039] Each module in the device or system of this application can be implemented in whole or in part by software, hardware and their combination. The above-mentioned modules can be embedded in the processor in the computer device in hardware form or be independent of it, or can be stored in the memory in the computer device in software form, so that the processor can call and execute the operations corresponding to each of the above modules.
[0040] Without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.
[0041] Figure 1 - Figure 2 An embodiment of a multi-party threshold Schnorr signature method based on a trusted aggregator of the present invention is shown.
[0042] In this alternative embodiment, the multi-party threshold Schnorr signature method based on a trusted aggregator can be applied to scenarios such as blockchain, distributed identity authentication, and privacy protection computing to improve the security and computing efficiency of multi-party signatures. Specifically, it includes the following steps: S1. Threshold signature generation initialization stage: Based on security parameters and threshold parameters, combined with the threshold key sharing mechanism and Lagrange interpolation method, generate a threshold key for collaborative signature with the trusted aggregator; Among them, the generation of the threshold key for collaborative signature with the trusted aggregator based on security parameters and threshold parameters, combined with the threshold key sharing mechanism and Lagrange interpolation method, includes the following steps: S11. System parameter setting: Select elliptic curve parameters , and set the threshold parameter , where E represents the elliptic curve group, q represents the order of the elliptic curve group, G represents the base point, n represents the total number of participants, and t represents the threshold value (i.e., at least t participants are required to generate a valid signature); S12. Threshold key distribution: Based on the threshold key sharing mechanism and Lagrange interpolation method, generate two pairs of public and private keys for collaborative signature with the trusted aggregator; Specifically, the generating of two pairs of public and private keys for collaborative signature with the trusted aggregator based on the threshold key sharing mechanism and Lagrange interpolation method includes the following steps: S121. Use the threshold key sharing mechanism (such as Shamir secret sharing) to split the private key s into n parts, so that each participant i obtains the private key share and the public key , and generate the private key by combining the Lagrange interpolation method, where represents the threshold interpolation coefficient (constant), represents the private key share of participant j, is the threshold value ; S122. The signer i calculates and generates two pairs of public and private keys for collaborative signature with the trusted aggregator , and satisfies , , the public key is made public and the private key is kept secret, where represents the first public key of signer i, represents the second public key of signer i, represents the first private key of signer i, represents the second private key of signer i; S2. User terminal signature execution stage: The trusted aggregator generates a random challenge and relevant signature application information, calculates partial signatures according to the threshold signature nodes, and aggregates the signatures through the trusted aggregator.
[0043] Among them, the trusted aggregator generates a random challenge and relevant signature application information, calculates partial signatures according to the threshold signature nodes, and aggregates the signatures through the trusted aggregator includes the following steps: S21. The user terminal initiates a signature request: The user terminal submits the signature message M to the trusted aggregator (Trusted Aggregator, TA); S22. The trusted aggregator generates a random challenge and relevant signature application information: Based on the trusted execution environment, the trusted aggregator generates a random challenge and relevant signature application information and sends it to the signer; Specifically, based on the trusted execution environment, the trusted aggregator generates a random challenge and related signature application information and sends it to the signers, including the following steps: S221. The trusted aggregator selects t online signers and generates a random challenge inside the trusted execution environment (TEE). Calculate the challenge commitment value ; S222. Calculate the random commitment value of each signer j and aggregate and calculate the global commitment , where represents the hash operation mapping to the integer ring, represents the first public key of signer j, represents the second public key of signer j; S223. The trusted aggregator sends the signature application information to the t signers, where M represents the signature message; S23. The threshold signature node calculates the partial signature: The signer calculates the partial signature, the challenge value and the signature shard through the key exchange algorithm and returns the signature shard to the trusted aggregator; Specifically, the signer calculates the partial signature, the challenge value and the signature shard through the key exchange algorithm and returns the signature shard to the trusted aggregator, including the following steps: S231. Each signer j calculates the partial signature (here, according to the ECDH method, that is, Elliptic Curve Diffie-Hellman, we know ), where represents the hash operation mapping to the integer ring, represents the random factor of signer j, represents the first private key of signer j, represents the second private key of signer j; S232. Calculate the challenge value and the signature shard , where || is string concatenation, and the signer returns the signature shard to the trusted aggregator; S24. The trusted aggregator aggregates the signature shards of each signer to obtain the signature value, generates a Schnorr signature and returns it to the user terminal; The user terminal first calculates the challenge value and verifies the validity of the signature; Specifically, the trusted aggregator aggregates the signature shards of each signatory to obtain a signature value, generates a Schnorr signature, and returns it to the user terminal. The user terminal first calculates a challenge value and verifies the validity of the signature, including the following steps: S241. The trusted aggregator aggregates the signature shards of each signatory to obtain a signature value , generates a Schnorr signature , and returns it to the user terminal; S242. The user terminal first calculates a challenge value , and determines whether the equation holds. If it holds, the signature is valid; otherwise, the signature is invalid.
[0044] Figure 3 FIG. shows an embodiment of a multi-party threshold Schnorr signature system based on a trusted aggregator according to the present invention.
[0045] In this alternative embodiment, the multi-party threshold Schnorr signature system based on a trusted aggregator includes a threshold signature generation initialization module 1 and a user terminal signature execution module 2; Among them, the threshold signature generation initialization module 1 is used to generate a threshold key for collaborative signature with the trusted aggregator based on security parameters and threshold parameters, in combination with a threshold key sharing mechanism and Lagrange interpolation method; The user terminal signature execution module 2 is used for the trusted aggregator to generate a random challenge and related signature application information, calculate a partial signature according to the threshold signature node, and aggregate the signature through the trusted aggregator.
[0046] In one embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as shown in Figure 4 . The computer device includes a processor, a memory, and a network interface connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store static information and dynamic information data. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the steps in the above method embodiment are implemented.
[0047] Those skilled in the art can understand, Figure 4The structure shown is only a block diagram of some structures related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.
[0048] In addition, the present invention also provides a computer device, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.
[0049] Furthermore, the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.
[0050] Those of ordinary skill in the art can understand that all or part of the processes in the above method embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above method embodiments. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memories. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical memory, etc. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.
[0051] The present invention is not limited to the structures already described and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present invention is only limited by the appended claims.
Claims
1. A multi-party threshold Schnorr signature method based on a trusted aggregator, characterized in that It includes the following steps: S1. Based on security parameters and threshold parameters, combining the threshold key sharing mechanism and Lagrange interpolation method, generate a threshold key for collaborative signature with a trusted aggregator; S2. The trusted aggregator generates a random challenge and related signature application information, calculates partial signatures according to threshold signature nodes, and aggregates signatures through the trusted aggregator.
2. The multi-party threshold Schnorr signature method based on a trusted aggregator according to claim 1, characterized in that, The step of generating a threshold key for collaborative signature with a trusted aggregator based on security parameters and threshold parameters, combining the threshold key sharing mechanism and Lagrange interpolation method includes the following steps: S11. Select elliptic curve parameters , and set a threshold parameter , where E represents the elliptic curve group, q represents the order of the elliptic curve group, G represents the base point, n represents the total number of participating parties, and t represents the threshold value; S12. Based on the threshold key sharing mechanism and Lagrange interpolation method, generate two pairs of public and private keys for collaborative signature with a trusted aggregator.
3. The multi-party threshold Schnorr signature method based on a trusted aggregator according to claim 2, wherein, The step of generating two pairs of public and private keys for collaborative signature with a trusted aggregator based on the threshold key sharing mechanism and Lagrange interpolation method includes the following steps: S121. Split the private key s into n shares using the threshold key sharing mechanism so that each participating party i obtains a private key share and the public key , and generate the private key by combining the Lagrange interpolation method , where represents the threshold interpolation coefficient represents the private key share of the participating party j; S122. The signer i calculates and generates two pairs of public and private keys for collaborative signature with the trusted aggregator , and , , where represents the first public key of the signer i, represents the second public key of the signer i, represents the first private key of the signer i, represents the second private key of the signer i.
4. A multi-party threshold Schnorr signature method based on a trusted aggregator according to claim 3, characterized in that, The step that the trusted aggregator generates a random challenge and related signature application information, calculates partial signatures according to threshold signature nodes, and aggregates signatures through the trusted aggregator includes the following steps: S21. The user terminal submits a signature message M to the trusted aggregator; S22. Based on a trusted execution environment, the trusted aggregator generates a random challenge and related signature application information and sends them to the signer; S23. The signer calculates partial signatures, challenge values, and signature shards through a key exchange algorithm and returns the signature shards to the trusted aggregator; S24. The trusted aggregator aggregates the signature shards of each signer to obtain a signature value, generates a Schnorr signature and returns it to the user terminal; the user terminal first calculates the challenge value and verifies the validity of the signature.
5. A multi-party threshold Schnorr signature method based on a trusted aggregator according to claim 4, characterized in that The step that based on a trusted execution environment, the trusted aggregator generates a random challenge and related signature application information and sends them to the signer includes the following steps: S221. The trusted aggregator selects t online signers and generates a random challenge inside the trusted execution environment , and calculates the challenge commitment value ; S222. Calculate the random commitment value of each signatory j , and aggregate the calculations to obtain the global commitment , where represents the hash operation mapping to the integer ring represents the first public key of signatory j represents the second public key of signatory j; S223. The trusted aggregator sends the signature application information to t signers, where M represents the signature message.
6. A multi-party threshold Schnorr signature method based on a trusted aggregator according to claim 5, characterized in that, The step that the signer calculates partial signatures, challenge values, and signature shards through a key exchange algorithm and returns the signature shards to the trusted aggregator includes the following steps: S231. Each signatory j calculates a partial signature through a key exchange algorithm , where represents a hash operation mapped to the integer ring, represents the random factor of signatory j, represents the first private key of signatory j, represents the second private key of signatory j; S232. Calculate the challenge value and signature shards , where || is string concatenation, and the signer returns the signed business card to the trusted aggregator.
7. A multi-party threshold Schnorr signature method based on a trusted aggregator according to claim 6, characterized in that, The step that the trusted aggregator aggregates the signature shards of each signer to obtain a signature value, generates a Schnorr signature and returns it to the user terminal; the user terminal first calculates the challenge value and verifies the validity of the signature includes the following steps: S241. The trusted aggregator aggregates the signature shards of each signatory to obtain a signature value , generates a Schnorr signature , and returns it to the user terminal; S242. The user terminal first calculates the challenge value , and determines whether the equation holds. If it does, the signature is valid; if not, the signature is invalid.
8. A multi-party threshold Schnorr signature system based on a trusted aggregator, which is used to implement the steps of the multi-party threshold Schnorr signature method based on a trusted aggregator described in any one of claims 1 to 7, is characterized in that It includes a threshold signature generation initialization module and a user terminal signature execution module; Among them, the threshold signature generation initialization module is used to generate a threshold key for collaborative signature with a trusted aggregator based on security parameters and threshold parameters, combining the threshold key sharing mechanism and Lagrange interpolation method; The user terminal signature execution module is used for the trusted aggregator to generate a random challenge and related signature application information, calculate partial signatures according to threshold signature nodes, and aggregate signatures through the trusted aggregator.
9. A computer device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method described in any one of claims 1 to 7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method described in any one of claims 1 to 7.