Multi-party collaborative anti-quantum signature method and system based on homomorphic hash

Abstract

The invention provides a multi-party collaborative anti-quantum signature method and system based on homomorphic Hash, and relates to the technical field of digital signatures, the system comprises a plurality of participants and a verification party, and the method is specifically as follows: each participant generates a pair of public and private keys, the public key is composed of a total public key, a total signature matrix and a total Hash matrix of all participants; based on the public and private keys, all participants perform multi-party signature on the target message through a homomorphic hash function, and a generated signature is composed of total hash challenge values of all participants, total response vectors of all participants and commitment value high-order difference values of all participants; according to the signature, the verifier recovers the high order of the total commitment value, further calculates the total hash challenge value, and verifies the validity of the signature through comparison of the total hash challenge value; according to the method, multi-user collaborative signature is realized, and the security of resisting malicious opponents under a quantum computer is obtained.

Description

Technical Field

[0001] This invention relates to the field of digital signature technology, specifically to a multi-party collaborative quantum-resistant signature method and system based on homomorphic hashing. Background Technology

[0002] With the rapid development of network technology and the increasing frequency of online activities, information security has become a global focus. Digital signature technology, as a core means of ensuring data integrity, authenticating identity, and ensuring non-repudiation of operations, plays a crucial role in this process. However, the current application of digital signatures faces two major challenges: the long-term security threats posed by quantum computing and the growing practical demand for collaborative signing, specifically manifested in the following aspects: First, quantum computing poses a disruptive threat to the foundations of traditional cryptography.

[0003] Currently widely used digital signature schemes, such as RSA, ECDSA, and ElGamal, rely on the computational complexity of mathematical problems like integer factorization and discrete logarithms for security. However, Shor's algorithm, proposed by Peter Shor in 1994, can solve these problems on quantum computers in polynomial time complexity, theoretically undermining the security of these classical signature schemes. Although large-scale, stable quantum computers have not yet been developed, the threat of "store first, crack later" already exists, posing an imminent challenge to digital assets requiring long-term security. To address this threat, the National Institute of Standards and Technology (NIST) launched the Post-Quantum Cryptography (PQC) standardization project in 2016 and officially designated the Dilithium algorithm as the standard quantum-resistant digital signature algorithm in 2024, providing a secure foundation for unilateral signatures in the post-quantum era.

[0004] Second, the inherent limitations of traditional digital signature methods in collaborative scenarios.

[0005] In many fields such as finance, law, government affairs, and corporate governance, an electronic document or transaction often requires the joint signature of multiple authorized parties to become effective. Traditional digital signature schemes are essentially a unilateral signature model, where each signer independently generates and attaches their own signature. In collaborative scenarios, this model leads to verbose signature data, low verification efficiency, and fails to form a compact, unified credential representing the entire signing group. More importantly, it struggles to efficiently prove that all signers have indeed reached a consensus on the same tamper-proof document, resulting in complexity and credibility issues in auditing and verification.

[0006] Third, the dilemma of integrating existing collaborative signature schemes with post-quantum security.

[0007] While some collaborative signature or multi-party signature technologies exist in academia and industry, most are based on traditional cryptographic assumptions and are equally vulnerable to quantum attacks. Directly applying NIST standard post-quantum signature algorithms (such as Dilithium) to collaborative scenarios presents new technical challenges: lattice-based cryptography schemes like Dilithium have relatively high computational and communication overhead. Simply combining multiple independent Dilithium signatures leads to a linear increase in signature size and verification time, making it difficult to meet the efficiency requirements of practical applications.

[0008] Therefore, existing technologies cannot deeply integrate the efficiency advantages of collaborative signatures with the security features of post-quantum signatures. They are unable to simultaneously address the issues of "resisting attacks from quantum computers" and "supporting multiple signers to collaboratively sign the same document," making it difficult to achieve multi-user collaborative signatures in the post-quantum era. Summary of the Invention

[0009] To address the aforementioned issues, this invention proposes a multi-party collaborative quantum-resistant signature method and system based on homomorphic hashing, enabling multi-user collaborative signatures and achieving security against malicious adversaries in quantum computing environments.

[0010] According to some embodiments, the present invention adopts the following technical solution: A multi-party cooperative quantum-resistant signature method based on homomorphic hashing includes several participants and one verifier, specifically: Each participant generates a public-private key pair, wherein the public key consists of the total public key of all participants, the total signature matrix, and the total hash matrix; Based on public and private keys, all participants perform multi-party signature on the target message using a homomorphic hash function. The generated signature consists of the total hash challenge value of all participants, the total response vector of all participants, and the high-order difference of the commitment value of all participants. Based on the signature, the verifier restores the high bits of the total commitment value and then calculates the total hash challenge value. By comparing the total hash challenge values, the validity of the signature is verified.

[0011] According to some embodiments, the present invention adopts the following technical solution: A multi-party collaborative quantum-resistant signature system based on homomorphic hashing includes several participants and one verifier, specifically: The participants are configured to generate a public-private key pair, wherein the public key consists of the total public key, the total signature matrix, and the total hash matrix of all participants; The participants are configured to: perform multi-party signing of the target message based on public and private keys using a homomorphic hash function, and generate a signature consisting of the total hash challenge value, the total response vector, and the high-order difference of the commitment value; The verifier is configured to: restore the high bits of the total commitment value based on the signature, then calculate the total hash challenge value, and verify the validity of the signature by comparing the total hash challenge values.

[0012] According to some embodiments, the present invention adopts the following technical solution: A computer program product includes a computer program that, when executed by a processor, implements the aforementioned multi-party collaborative quantum-resistant signature method based on homomorphic hashing.

[0013] According to some embodiments, the present invention adopts the following technical solution: A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned multi-party cooperative quantum-resistant signature method based on homomorphic hashing.

[0014] According to some embodiments, the present invention adopts the following technical solution: An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the multi-party cooperative quantum-resistant signature method based on homomorphic hashing.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention combines homomorphic hashing technology with the Dilithium signature algorithm, enabling the number of signers to be securely expanded from 1 to n, achieving multi-user collaborative signing and gaining security against malicious adversaries under quantum computing. This expansion is not limited by physical hardware, uses commitments to securely share shares, and promptly stops privacy vectors that may leak private key information during the signing process, thereby avoiding private key recovery attacks. Attached Figure Description

[0016] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0017] Figure 1 This is a flowchart of the multi-party collaborative quantum-resistant signature method based on homomorphic hashing in Example 1. Detailed Implementation The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0019] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0020] Example 1 One embodiment of the present invention provides a multi-party cooperative quantum-resistant signature method based on homomorphic hashing, including several participating parties and a verifier, such as... Figure 1 As shown, specifically: Step S1: Each participant generates a public-private key pair, wherein the public key consists of the total public key, the total signature matrix, and the total hash matrix of all participants; Step S2: Based on public and private keys, all participants perform multi-party signature on the target message using a homomorphic hash function. The generated signature consists of the total hash challenge value of all participants, the total response vector of all participants, and the high-order difference of the commitment value of all participants. Step S3: Based on the signature, the verifier restores the high bits of the total commitment value, and then calculates the total hash challenge value. By comparing the total hash challenge values, the validity of the signature is verified.

[0021] As one embodiment, the multi-party collaborative quantum-resistant signature method based on homomorphic hashing of the present invention enables multi-user collaborative signatures and obtains security against malicious adversaries under quantum computers. The specific implementation process is described below.

[0022] I. Preliminary Knowledge 1. grid The mathematical concept of "lattice" originated from the interdisciplinary research of number theory and geometry, which can be traced back to the 18th century. Mathematicians such as Euler and Lagrange used similar ideas when studying the distribution of integer points. In the 19th century, Hermann Minkowski systematically introduced the lattice structure in Euclidean space when studying "geometric methods in number theory" and proposed the famous "lattice theory" and "the problem of the shortest vector in a convex body", laying the foundation for modern lattice theory.

[0023] In cryptography, the importance of lattice theory was discovered at the end of the 20th century, especially with Ajtai's proposal of the first suffering hypothesis based on the mean-worst-case equivalence of lattices, marking the rise of lattice cryptography. This provided a solid foundation for building quantum-resistant cryptography and made the lattice problem a core tool for constructing modern public-key cryptosystems.

[0024] set up If vectors are linearly independent, they are said to form a basis for a lattice. Then, the lattice generated from this basis is... Defined as:

[0025] in, It is the basis matrix of the lattice; It is the rank of the lattice, if If the rank is full, then the rank is called a full-rank ... A discrete subset consisting of all linear combinations of integers is called a lattice.

[0026] The security of lattice cryptosystems relies on several problems that are considered computationally difficult on lattices. The following only describes the difficult problems used in this embodiment.

[0027] (1) Shortest Vector Problem (SVP): Given a lattice basis Find the shortest non-zero vector in a lattice, excluding the zero vector. Formally, this is defined as finding... , making .

[0028] (2) Short Integer Solution (SIS): Given a matrix Find non-zero integer vectors , so that:

[0029] in, The problem is essentially about finding a short vector such that it is small enough to fit a given modulus. The following is The problem assumes a linear dependency, and its security is based on the difficulty of the SVP average case.

[0030] 2. Homomorphic hashing Homomorphic hashing is a special type of hash function that allows operations on data without exposing the original data. Its core characteristic is that if a certain operation is performed on the original data, the hash value of that original data can also be calculated using the corresponding operation.

[0031] in, It is a binary operator applied to raw data. This refers to the binary operation applied to the hash value.

[0032] Homomorphic hashing is typically categorized based on the types of operations supported by the hash function: additive homomorphic hashing, multiplicative homomorphic hashing, bihomogeneous hashing, and vector homomorphic hashing. The first two types are relatively simple to construct, essentially reproducing the hash values ​​defined in the original hash function definition. and Operations are instantiated as either addition or multiplication; bihomogeneous hashing supports both addition and multiplication homomorphism. Vector homomorphic hashing differs from the previous three in its primitive data type. The previous three use numeric types, while vector homomorphic hashing uses structured data such as vectors and matrices, specifically defined as... .

[0033] The homomorphic hashing used in this embodiment is additive homomorphic hashing based on the SIS problem, as detailed below: Given a public key matrix Define a hash function:

[0034] in, It is the input vector. It is a hash output, based on this definition, if ,but .

[0035] 3. Fait-Shamir with Abort paradigm In 1986, Fait and Shamir proposed a general method for converting interactive zero-knowledge proof systems into non-interactive signatures. The core idea was to challenge... Instead of being randomly generated by the verifier, it is generated by a hash function. generate:

[0036] in, This is the target message to be signed. It is a promise.

[0037] According to the original author's description, an example of applying this method to a signature algorithm on a lattice is as follows: Public Key private key ,information .

[0038] Signer in distribution Randomly select vectors ( The value is usually 2 or 4), calculation ,according to get and will sign Send it to the verifier.

[0039] The verifier verifies the equation. The validity of the signature is verified.

[0040] Among them, the signature part Range validation needs to be performed before sending. The norm is too large (indicating a possible leak of the private key). (norm information) Disobedience Distribution (potential leak) (Information), the signer suspends the current process and regenerates a new one. The process is executed again.

[0041] This paradigm uses a "stop" approach, and multiple samplings successfully avoid private key recovery attacks caused by leaks.

[0042] 4. Dilithium signature scheme Dilithium is a lattice-based digital signature scheme and one of the signature standards selected during the NIST post-quantum cryptography standardization process in the United States. It features high security, resistance to quantum computing attacks, efficient signature and verification speed, and no need for a centralized trapdoor. The signature scheme mainly includes three algorithms: key generation, signature generation, and signature verification.

[0043] 4.1 Key Generation Algorithm: Input public safety parameters Generate a public-private key pair. The specific steps are described below: (1) Random seed based on security parameters Generate random matrices .

[0044] (2) Random seed based on security parameters Generate private key vector and .

[0045] (3) Calculate the public key vector ,in, It is a large prime number.

[0046] (4) Sharing the public key The private key is stored internally. .

[0047] 4.2 Signature Generation Algorithm: Input message and private key Output signature The specific steps are described below: (1) Random seed based on security parameters Sampled random vector calculate .

[0048] (2) Calculate the hash challenge value .

[0049] (3) Calculate the response vector .

[0050] (4) If If the limit is not exceeded, output the signature. Otherwise, output "abort" and re-execute the algorithm.

[0051] 4.3 Signature Verification Algorithm: Enter public key ,information and signature The signature is verified and outputs either 1 or 0 to indicate whether it is valid. The specific steps are described below: (1) Inspection Do not exceed the limit.

[0052] (2) Reconstruction .

[0053] (3) Check the equation Whether it is valid or not.

[0054] If the signature is valid, output 1; otherwise, output 0.

[0055] 5. Commitment Agreement Commitment protocols are fundamental primitives in many cryptographic protocols. A commitment protocol allows a sender to commit to a secret value for a receiver, which the sender will subsequently disclose to the receiver. Before the sender discloses the committed value, the receiver cannot obtain any information related to it; this property is called hiding. At the same time, after committing to the secret value, the sender cannot modify the secret value; this property is called binding.

[0056] Specifically, the sender S and the receiver R, S has a string Function for: (1) Commitment process: S to Input a string R receives The output.

[0057] (2) Opening the commitment process: At some point later, S makes a commitment through Send secret to R .

[0058] II. This method This method uses homomorphic hashing and commitment techniques to transform Dilithium's digital signature scheme into a multi-party collaborative signature protocol, achieving the specified... Several participating parties jointly view a certain message The signature authentication function. The following detailed technical specifications cover... Each participant, using Indicates the first i Each participating party The protocol requires that, regardless of whether an attack is successful, no participating party can send an unsigned message. Forging a signature requires that all participating parties operate independently of each other, which also facilitates the description of the protocol. The following description of the protocol is based on the participating parties. It runs in the view, specifically: 1. Key generation (executed by the participating parties): (1) Participating parties The seed for generating 32-bit random numbers is denoted as . Simultaneously, it is calculated using a general hash function. ,in, From respectively The sub-hash value extracted from the hash value.

[0059] (2) Obtain the signature matrix corresponding to the planned security length from the Dilithium security level. Dimensions and .

[0060] (3) Initialize the local signature matrix and using index coordinates and seed The iterative hash value is used to instantiate all elements in the matrix, as expressed by the formula:

[0061] in, , .

[0062] (4) Obtain the signature matrix corresponding to the planned security length from the Dilithium security level. Dimensions and .

[0063] (5) Initialize the local hash matrix and using index coordinates and seed The iterative hash value is used to instantiate all elements in the matrix, as expressed by the formula:

[0064] in, , .

[0065] (6) Participating parties For other participating parties Broadcast Matrix and .

[0066] (7) Calculate the total signature matrix and total hash matrix .

[0067] (8) Initialize the secret vector ( (vector of the disturbance vector) and perturbation vector ( (vector), using index coordinates and seed The iterative hash value is used to instantiate all elements in the vector by assigning values, which can be expressed by the formula:

[0068]

[0069] in, , .

[0070] (9) Calculate the local public key .

[0071] (10) Calculate the hash value of the public key. .

[0072] (11) Based on the commitment protocol, the commitment value is output, which is the hash value of the public key broadcast to other participants. .

[0073] (12) Based on the commitment protocol, opening the commitment means broadcasting the public key to other participants. Other participating parties locally access the received public key The hash value of the public key is obtained by performing a hash operation. Compare the hash value received from the broadcast. And locally calculated hash value If the results are the same, the process proceeds to the next step; otherwise, it is considered that there is a malicious participant, and the program is terminated.

[0074] (13) Calculate the total public key .

[0075] Output: Public key and private key .

[0076] 2. Signature generation (executed by participating parties): (1) Initialize the random vector and using index coordinates, seed The iterative hash value is used to instantiate all elements in the vector by assigning values, that is...

[0077] in, .

[0078] (2) Calculate the commitment value and high commitment value ,in The function extracts the first part of the first passed parameter. Position, that is Indicates the commitment value At a high level.

[0079] (3) Use a homomorphic hash function to calculate the hash challenge value. Where "||" represents the join operation, This indicates a message awaiting signature. As a participant The commitment value is high.

[0080] (4) Calculate the hash value of the hash challenge. .

[0081] (5) Based on the commitment protocol, the commitment value is output, which is the hash value of the hash challenge value broadcast to other participants. .

[0082] (6) Based on the commitment protocol, the commitment is opened, which means broadcasting the hash challenge value to other participants. Other participants locally respond to the received hash challenge value The hash operation is performed to obtain ,contrast and If the results are the same, the process passes and continues to the next step; otherwise, the program execution is interrupted.

[0083] (7) Calculate the total hash challenge value .

[0084] (8) Calculate the response vector And verify The range.

[0085] Require ,in Random vectors from the corresponding security level of Dilithium The range of values ​​is used to increase the challenge of the secret vector without revealing the secret vector. If the value is too large, the process will backtrack to the first step of the signature generation part and re-execute.

[0086] (9) Calculate the hash value of the response vector .

[0087] (10) Based on the commitment protocol, the commitment value is output, which is broadcast to other participants. .

[0088] (11) Based on the commitment protocol, open the commitment, which means broadcasting the response vector to other participants. Other participants locally receive the response vector The hash operation is performed to obtain ,contrast and If the results are the same, the process passes and continues to the next step; otherwise, the program execution is interrupted.

[0089] (12) Calculate the total response vector .

[0090] (13) Calculate the hash value of the high-order bits of the commitment value. .

[0091] (14) Based on the commitment protocol, the commitment value is output, which is broadcast to other participants. .

[0092] (15) Based on the commitment agreement, the commitment is opened, which means broadcasting the high-order value of the commitment to other participants. Other participating parties locally receive The hash operation is performed to obtain ,contrast and If the results are the same, the process passes and continues to the next step; otherwise, the program execution is interrupted.

[0093] (16) Calculate the high-order value of the total commitment. .

[0094] (17) Based on the total signature matrix Total response vector Total hash challenge value and public key The high-order part of the locally calculated commitment value .

[0095] (18) Calculate the high-level difference of the commitment value ,in This function calculates the difference between two input parameters bit by bit. Used to recover one parameter when one of the parameters is known.

[0096] Output: Signature .

[0097] 3. Signature verification (executed by the verifier): (1) Verify the response vector If the range is too large, it will return 0 directly.

[0098] (2) Through the total signature matrix Total response vector Total hash challenge value Sum of public keys Calculate the total commitment value and extract the high-order bits of the total commitment value. This can be expressed as a formula:

[0099] (3) Utilizing the high-level difference of the committed value The total commitment value is at a high level. Perform correction, and transfer the high-order bits of the corrected commitment value. As the high-order value of the recovered total commitment, it is expressed by the formula:

[0100] in, This allows for the correction of the first parameter based on the second parameter.

[0101] (4) Using the total hash matrix Target message Total commitment value is high Calculate the total hash challenge value This can be expressed as a formula:

[0102] (5) Comparison and If the signatures match, the signature is valid and the output is 1; otherwise, the output is 0.

[0103] Example 2 One embodiment of the present invention provides a multi-party cooperative quantum-resistant signature system based on homomorphic hashing, comprising several participating parties and a verifier, specifically: The participants are configured to generate a public-private key pair, wherein the public key consists of the total public key, the total signature matrix, and the total hash matrix of all participants; The participants are configured to: perform multi-party signing of the target message based on public and private keys using a homomorphic hash function, and generate a signature consisting of the total hash challenge value, the total response vector, and the high-order difference of the commitment value; The verifier is configured to: restore the high bits of the total commitment value based on the signature, then calculate the total hash challenge value, and verify the validity of the signature by comparing the total hash challenge values.

[0104] Example 3 One embodiment of the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned multi-party collaborative quantum-resistant signature method based on homomorphic hashing.

[0105] Example 4 In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided for storing computer instructions. When the computer instructions are executed by a processor, they implement the multi-party cooperative quantum-resistant signature method based on homomorphic hashing.

[0106] Example 5 One embodiment of the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the multi-party cooperative quantum-resistant signature method based on homomorphic hashing.

[0107] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0108] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0109] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A multi-party cooperative quantum-resistant signature method based on homomorphic hashing, characterized in that, It includes several participants and one verifier, specifically: Each participant generates a public-private key pair, wherein the public key consists of the total public key of all participants, the total signature matrix, and the total hash matrix; Based on public and private keys, all participants perform multi-party signature on the target message using a homomorphic hash function. The generated signature consists of the total hash challenge value of all participants, the total response vector of all participants, and the high-order difference of the commitment value of all participants. Based on the signature, the verifier restores the high bits of the total commitment value and then calculates the total hash challenge value. By comparing the total hash challenge values, the validity of the signature is verified.

2. The multi-party cooperative quantum-resistant signature method based on homomorphic hashing as described in claim 1, characterized in that, The i-th participant The specific steps to generate a public-private key pair are as follows: Based on the random seed of the security parameters, the i-th participant Generate signature matrix locally Hash matrix Secret Vector and perturbation vector ; The local signature matrix Hash matrix Broadcast to other participants; Receive all other participants Signature matrix broadcast and hash matrix The total signature matrix is ​​obtained by summing the results of consecutive additions. Total hash matrix ; Based on the total signature matrix Secret Vector and perturbation vector Generate a local public key ; Use the local public key Broadcast to other participants; Receive all other participants The public key broadcast The public key is obtained by summing the results of consecutive additions. ; Obtain the public key Private key .

3. The multi-party cooperative quantum-resistant signature method based on homomorphic hashing as described in claim 1, characterized in that, In the i-th participant The above performs multi-party signature, and the specific steps are as follows: Based on random vectors Total signature matrix Calculate the commitment value And extract the high value of the commitment. ; Based on the total hash matrix Target message High commitment value Calculate the hash challenge value using a homomorphic hash function. The total hash challenge value is obtained by aggregating the hash challenge values ​​of all participants through broadcasting. ; Based on random vectors Total hash challenge value and local secret vector Calculate the response vector The response vectors of all participants are aggregated through broadcasting to obtain the total response vector. ; By aggregating the high bits of the commitment values ​​from all participants through broadcasting, we obtain the high bit of the total commitment value. ; Based on the total signature matrix Total response vector Total hash challenge value Sum of public keys The total commitment value is calculated locally, and the high-order bits of the total commitment value are extracted. ; Through two high total commitment values Calculate the difference of each digit to determine the high-order difference of the committed value. ; Get a signature .

4. The multi-party cooperative quantum-resistant signature method based on homomorphic hashing as described in claim 1, characterized in that, In broadcast aggregation, the process also includes broadcasting the content to be broadcast and its hash value separately. The participants receiving the broadcast content calculate the hash value of the broadcast content locally, compare the two hash values ​​to determine whether there is a malicious participant, and finally decide whether to continue with the subsequent steps.

5. The multi-party cooperative quantum-resistant signature method based on homomorphic hashing as described in claim 1, characterized in that, The high-order part of the total recovery commitment value is specifically: Through the total signature matrix Total response vector Total hash challenge value Sum of public keys Calculate the total commitment value and extract the high-order bits of the total commitment value. ; Using the high-order difference of the commitment value The total commitment value is at a high level. Perform correction, and transfer the high-order bits of the corrected commitment value. The total commitment value recovered is at a high level.

6. The multi-party cooperative quantum-resistant signature method based on homomorphic hashing as described in claim 1, characterized in that, The calculation of the total hash challenge value is performed using the total hash matrix. Target message Total commitment value is high Calculate the total hash challenge value .

7. A multi-party cooperative quantum-resistant signature system based on homomorphic hashing, characterized in that, It includes several participants and one verifier, specifically: The participants are configured to generate a public-private key pair, wherein the public key consists of the total public key, the total signature matrix, and the total hash matrix of all participants; The participants are configured to: perform multi-party signing of the target message based on public and private keys using a homomorphic hash function, and generate a signature consisting of the total hash challenge value, the total response vector, and the high-order difference of the commitment value; The verifier is configured to: restore the high bits of the total commitment value based on the signature, then calculate the total hash challenge value, and verify the validity of the signature by comparing the total hash challenge values.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the multi-party collaborative quantum-resistant signature method based on homomorphic hashing as described in any one of claims 1-6.

9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the multi-party collaborative quantum-resistant signature method based on homomorphic hashing as described in any one of claims 1-6.

10. An electronic device, characterized in that, include: The electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the multi-party cooperative quantum-resistant signature method based on homomorphic hashing as described in any one of claims 1-6.

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