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

Abstract

The application provides a homomorphic hash-based multi-party cooperative anti-quantum signature method and system, relates to the technical field of digital signature, and comprises a plurality of participants and a verifier, specifically: each participant generates a pair of public and private keys, wherein the public key is composed of a total public key of all participants, a total signature matrix and a total hash matrix; based on the public and private keys, all participants perform multi-party signature on a target message through a homomorphic hash function, and the generated signature is composed of a total hash challenge value of all participants, a total response vector of all participants and a commitment value high-bit difference value of all participants; according to the signature, the verifier recovers the total commitment value high-bit, and then calculates the total hash challenge value, and through comparison of the total hash challenge value, the legality of the signature is verified; the application realizes multi-user cooperative signature, and obtains security against malicious opponents under a quantum computer.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of digital signature, and in particular to a multi-party collaborative anti-quantum signature method and system based on homomorphic hash. BACKGROUND

[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 to protect data integrity, authenticate identity and ensure non-repudiation, plays a crucial role in it. However, the current application of digital signature is facing two serious challenges: the long-term security threat brought by quantum computing and the growing demand for collaborative signing reality, which is embodied in the following points:

[0003] First, the subversive threat of quantum computing to the foundation of traditional cryptography.

[0004] The current widely used digital signature schemes, such as RSA, ECDSA and ElGamal, are based on the computational complexity of mathematical problems such as integer factorization and discrete logarithm. However, in 1994, Peter Shor proposed Shor's algorithm, which can solve these problems in polynomial time on a quantum computer, making the security of the above classical signature schemes theoretically completely shattered. Although large-scale and stable quantum computers have not yet been realized, the threat of "storing first, breaking later" already exists, posing an imminent challenge to digital assets that require 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 in 2024 officially determined Dilithium algorithm as the standard anti-quantum digital signature algorithm, providing a secure foundation for single-party signature in the post-quantum era.

[0005] Second, the inherent limitations of traditional digital signature mode in collaborative scenarios.

[0006] In many fields such as finance, law, government affairs and enterprise governance, an electronic document or a transaction often needs to be signed by multiple authorized parties before it can take effect. The traditional digital signature scheme is essentially a single signature model, where each signer independently generates and attaches their own signature. This model in collaborative scenarios will result in long signature data, low verification efficiency, and the inability to form a compact, unified credential representing the entire signing group. More importantly, it is difficult to efficiently prove that all signers have indeed reached a consensus on the same, unaltered document, and there are problems of complexity and credibility in auditing and verification.

[0007] Third, the integration dilemma of existing collaborative signature schemes and post-quantum security.

[0008] Although there are some co-signature or multi-signature techniques in academia and industry, they are mostly based on traditional cryptographic assumptions and cannot resist quantum attacks. Directly applying the post-quantum signature algorithm (such as Dilithium) of NIST standard to the co-signature scenario will face new technical challenges: the computation and communication overhead of lattice-based schemes such as Dilithium are relatively high, and if multiple independent Dilithium signatures are simply combined, the signature size and verification time will linearly increase, which is difficult to meet the efficiency requirements of practical applications.

[0009] Therefore, the prior art cannot deeply integrate the efficiency advantage of co-signature and the security features of post-quantum signature, and it is difficult to balance between “resisting quantum computer attacks” and “supporting multiple signers to co-sign the same document”, and it is difficult to realize multi-user co-signature in the post-quantum era. SUMMARY

[0010] To solve the above problems, the present application provides a multi-party co-signature anti-quantum signature method and system based on homomorphic hash, which realizes multi-user co-signature and obtains security against malicious adversaries under quantum computers.

[0011] According to some embodiments, the present application adopts the following technical solutions:

[0012] The multi-party co-signature anti-quantum signature method based on homomorphic hash includes a plurality of participants and a verifier, specifically:

[0013] Each participant generates a pair of public and private keys, wherein the public key is composed of a total public key, a total signature matrix, and a total hash matrix of all participants;

[0014] Based on the public and private keys, all participants perform multi-party signature on the target message through a homomorphic hash function, and the generated signature is composed of a total hash challenge value of all participants, a total response vector of all participants, and a commitment value high bit difference of all participants;

[0015] According to the signature, the verifier recovers the total commitment value high bit, and then calculates the total hash challenge value, and verifies the legality of the signature by comparing the total hash challenge value.

[0016] According to some embodiments, the present application adopts the following technical solutions:

[0017] The multi-party co-signature anti-quantum signature system based on homomorphic hash includes a plurality of participants and a verifier, specifically:

[0018] The participant is configured to generate a pair of public and private keys, wherein the public key is composed of a total public key, a total signature matrix, and a total hash matrix of all participants;

[0019] Parties, configured to: based on the public and private key, through the homomorphic hash function, the target message is multi-party signed, the generated signature is composed of total hash challenge value, total response vector and commitment value high difference value;

[0020] Verification party, configured to: according to the signature, restore the total commitment value high, and then calculate the total hash challenge value, verify the signature legality through the comparison of the total hash challenge value.

[0021] According to some embodiments, the present application adopts the following technical solutions:

[0022] A computer program product comprising a computer program, which, when executed by a processor, implements the homomorphic hash-based multi-party collaborative quantum-resistant signature method.

[0023] According to some embodiments, the present application adopts the following technical solutions:

[0024] A non-transitory computer readable storage medium for storing computer instructions, which, when executed by a processor, implements the homomorphic hash-based multi-party collaborative quantum-resistant signature method.

[0025] According to some embodiments, the present application adopts the following technical solutions:

[0026] An electronic device comprising a processor, a memory and a computer program; wherein the processor is connected with the memory, and the computer program is stored in the memory; when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the homomorphic hash-based multi-party collaborative quantum-resistant signature method.

[0027] Compared with the prior art, the present application has the following advantages:

[0028] The present application combines the homomorphic hash technology and the Dilithium signature algorithm, so that the number of original signers is safely expanded from 1 to n, multi-user collaborative signature is realized, and the security against malicious adversaries under quantum computers is obtained; the expansion is not limited by physical hardware, the commitment is used to achieve secure sharing, and the private vector that may leak private key information is stopped in time in the signature process, so that the private key recovery attack is avoided. BRIEF DESCRIPTION OF DRAWINGS

[0029] The drawings accompanying the specification of the present application form part of the present application and serve to provide a further understanding of the present application, the illustrative embodiments thereof and the description thereof serve to explain the present application and do not constitute an improper limitation thereof.

[0030] Figure 1 It is a flowchart of the homomorphic hash-based multi-party collaborative quantum-resistant signature method of embodiment 1. DETAILED DESCRIPTION

[0031] The application will be further described below with reference to the drawings and examples.

[0032] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, 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 application belongs.

[0033] It is to be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments consistent with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0034] Example 1

[0035] An embodiment of the present application provides a homomorphic hash-based multi-party collaborative anti-quantum signature method, including a plurality of participants and a verifier, as shown in Figure 1 Specifically, the method comprises the following steps:

[0036] Step S1: Each participant generates a pair of public and private keys, wherein the public key is composed of a total public key of all participants, a total signature matrix, and a total hash matrix;

[0037] Step S2: Based on the public and private keys, all participants perform multi-party signature on the target message through a homomorphic hash function, and the generated signature is composed of a total hash challenge value of all participants, a total response vector of all participants, and a commitment value high bit difference of all participants;

[0038] Step S3: According to the signature, the verifier restores the total commitment value high bit, and then calculates the total hash challenge value. By comparing the total hash challenge value, the legality of the signature is verified.

[0039] As an embodiment, the homomorphic hash-based multi-party collaborative anti-quantum signature method of the present application realizes multi-user collaborative signature and obtains security against malicious adversaries under quantum computers. The specific implementation process is described below.

[0040] I. Preliminary knowledge

[0041] 1. Lattice

[0042] The concept of lattice originated from the intersection of number theory and geometry in the 18th century. The idea of lattice was used by mathematicians such as Euler and Lagrange when they studied the distribution of integer points. In the 19th century, Hermann Minkowski introduced the lattice structure in Euclidean space when he studied the geometric method in number theory, and proposed the famous "lattice theory" and "shortest vector problem in convex body", laying the foundation of modern lattice theory.

[0043] In cryptography, the importance of lattice theory was discovered in the late 20th century. Ajtai proposed the first average-worst case equivalent hard assumption based on lattice, marking the rise of lattice cryptography. This provides a solid foundation for constructing quantum-resistant cryptography, and makes lattice problems a core tool for constructing modern public key cryptography systems.

[0044] Let be linearly independent vectors, called a set of basis of a lattice. Then the lattice generated by this set of basis is defined as:

[0045]

[0046] where is the basis matrix of the lattice; is the rank of the lattice, if , the lattice is called full-rank lattice; is the discrete subset of all integer linear combinations, called a lattice (Lattice).

[0047] The security of lattice cryptography systems depends on several computationally difficult problems on lattices. The following only describes the difficult problems used in this embodiment.

[0048] (1) Shortest Vector Problem (SVP):

[0049] Given the lattice basis , find the shortest non-zero vector in the lattice except the zero vector, which is formally defined as finding such that .

[0050] (2) Short Integer Solution (SIS):

[0051] Given a matrix , find a non-zero integer vector such that:

[0052]

[0053] where, is small enough, the problem is essentially to find a short vector such that it is linearly dependent on the basis The security assumption of this problem is based on the difficulty of SVP in average case.

[0054] 2. Homomorphic Hashing

[0055] Homomorphic Hashing is a special kind of Hashing function that allows operations on data without exposing the original data. Its core feature is that if some operation is performed on the original data, the Hash value of the original data can also be calculated by the corresponding operation, that is,

[0056]

[0057] where, is a binary operator applied to the original data, is the corresponding binary operation applied to the Hash value.

[0058] Homomorphic Hashing is usually divided into the following categories according to the type of operation supported by the Hash function: additive homomorphic Hashing, multiplicative homomorphic Hashing, double homomorphic Hashing, and vector homomorphic Hashing. The first two types of Hashing are relatively simple to construct, i.e., the and operations in the original Hash function definition are simultaneously instantiated as addition or multiplication operations; double homomorphic Hashing supports both additive and multiplicative homomorphic Hashing. Vector homomorphic Hashing differs from the previous three types in that the original data type is different. The original data types of the previous three types are numerical types, while the original data type of vector homomorphic Hashing is structured data such as vectors and matrices, which is defined as .

[0059] The homomorphic Hashing used in this embodiment is an additive homomorphic Hashing based on the SIS problem, which is defined as follows:

[0060] Given a public key matrix , define the Hash function:

[0061]

[0062] where, is the input vector, is the Hash output. Based on this definition, if , then .

[0063] 3. Fait-Shamir whit Abort Schema

[0064] ​In 1986, Fait and Shamir proposed a general method to convert interactive zero-knowledge proof system into non-interactive signature, the core idea is: challenge No longer randomly generated by the verifier, but by a hash function Generation:

[0065]

[0066] Where, is the target message to be signed, is the commitment.

[0067] According to the author's description, the method is applied to the lattice signature algorithm instance as follows:

[0068] Public key , private key , message .

[0069] The signing party randomly selects a vector (usually take 2 or 4) in the distribution , calculates , gets according to , and sends the signature to the verifier.

[0070] The verifier verifies the validity of the signature by verifying whether the equation holds.

[0071] Where, the of the signature part needs to be range verified before sending, when the norm of is too large (which may leak the norm information of the private key ), does not conform to the distribution (which may leak the information of ), the signer aborts the process and generates a new value to execute the process again.

[0072] This paradigm uses the "abort" method, and multiple successful sampling avoids the private key recovery attack caused by leakage.

[0073] 4、Dilithium signature scheme

[0074] ​Dilithium is a lattice-based digital signature scheme, which is one of the signature standards selected in the post-quantum cryptography standardization process of the United States NIST. It has the characteristics of high security, resistance to quantum computing attacks, efficient signature and verification speed, and no need for centralized trapdoor. The signature scheme mainly includes three algorithms: key generation, signature generation, and signature verification.

[0075] 4.1 Key generation algorithm:

[0076] Input public security parameters , generate a pair of public and private keys, the specific steps are described as follows:

[0077] (1) According to the random seed of the security parameter , generate a random matrix .

[0078] (2) According to the random seed of the security parameter , generate the private key vector and .

[0079] (3) Calculate the public key vector , where is a large prime number.

[0080] (4) Share the public key , and internally save the private key .

[0081] 4.2 Signature generation algorithm:

[0082] Input message and private key , output signature , the specific steps are described as follows:

[0083] (1) According to the random seed of the security parameter , sample a random vector , and calculate .

[0084] (2) Calculate the hash challenge value .

[0085] (3) Calculate the response vector .

[0086] (4) If does not exceed the limit, output the signature ; otherwise, output abort and re-execute the algorithm.

[0087] 4.3 Signature verification algorithm:

[0088] Input public key , message and signature , verify the signature legality and output 1 or 0 to represent whether it is legal, the specific steps are described as follows:

[0089] (1) Check whether it is within the limit.

[0090] (2) Reconstruct .

[0091] (3) Check whether the equation is established.

[0092] If it is established, the signature is legal and outputs 1, otherwise it is not legal and outputs 0.

[0093] 5, commitment protocol

[0094] Commitment protocol is the basis of many cryptographic protocols, and commitment protocol allows the sender to make a commitment to a secret value to the receiver, and the sender will subsequently disclose the secret value to the receiver, and the receiver cannot obtain any information related to the commitment value before the sender discloses the commitment value to the receiver, which is called hiding (Hiding). At the same time, the sender cannot make any modification to the secret value after making a commitment to the secret value, which is called binding (Binding).

[0095] Specifically, the sender S and the receiver R, S has a string , the function function is:

[0096] (1) Commitment process: S inputs a string to , and R receives the output of .

[0097] (2) Open commitment process: at a later time, S sends the secret to R through .

[0098] II. The method

[0099] The method uses homomorphic hash and commitment technology to convert the digital signature scheme of Dilithium into a multi-party collaborative signature protocol, realizing the function of specifying participating parties to jointly sign and authenticate a message . In the following technical details, a total of participating parties are involved, and is used to represent the i participating party . The operation of the protocol requires that the enemy cannot give an unsigned message to any participating party regardless of the success of the attack. Falsifying a signature requires all participants to run identically to each other, which also facilitates the description of the protocol, which is described from the perspective of a participant, specifically:

[0100] 1. Key generation (performed by the participant):

[0101] (1) The participant generates a 32-bit random number seed denoted as , and calculates by using a general hash function, where are sub-hash values extracted from the hash value of .

[0102] (2) Obtain the dimensions and of the signature matrix corresponding to the planned security length from the Dilithium security level.

[0103] (3) Initialize the local signature matrix , and use the index coordinates and the iterative hash value of the seed to assign values to all elements in the matrix to instantiate it, which can be expressed by the formula:

[0104]

[0105] where , .

[0106] (4) Obtain the dimensions and of the signature matrix corresponding to the planned security length from the Dilithium security level.

[0107] (5) Initialize the local hash matrix , and use the index coordinates and the iterative hash value of the seed to assign values to all elements in the matrix to instantiate it, which can be expressed by the formula:

[0108]

[0109] where , .

[0110] (6) The participant broadcasts the matrices and to other participants . ​​​​

[0111] (7) Aggregate the total signature matrix and the total hash matrix .

[0112] (8) Initialize the secret vector and the perturbation vector , and assign all elements in the vectors with instantiated values using the index coordinates and the seed 's iteration hash value, which can be expressed in the formula as:

[0113]

[0114]

[0115] where, , .

[0116] (9) Calculate the local public key .

[0117] (10) Calculate the hash value of the public key .

[0118] (11) Based on the commitment protocol, output the commitment value, which is the hash value of the public key broadcasted to other participants .

[0119] (12) Based on the commitment protocol, open the commitment, which is the public key broadcasted to other participants , and other participants locally run the hash operation on the received public key to obtain the hash value of the public key , and compare the hash value received by broadcast with the hash value calculated locally . If they are the same, pass and continue to the next step; otherwise, consider that there is a malicious participant and interrupt the execution of the program.

[0120] (13) Calculate the total public key .

[0121] Output: public key and private key .

[0122] 2. Signature generation (executed by participants):

[0123] (1) Initialize the random vector , and use the index coordinates, seed ​​The iteration of the hash value assigns values to all elements in the vector, i.e.

[0124]

[0125] wherein, .

[0126] (2) Calculate the commitment value and the commitment value high bit , wherein The function implements the interception of the first bit of the incoming first parameter, i.e. Indicates the high bit of the commitment value .

[0127] (3) Using a homomorphic hash function, calculate the hash challenge value , wherein "||" represents the concatenation operation, represents the message to be signed, is the commitment value high bit of the participant .

[0128] (4) Calculate the hash value of the hash challenge value .

[0129] (5) Based on the commitment protocol, output the commitment value, i.e. broadcast the hash value of the hash challenge value to other participants .

[0130] (6) Based on the commitment protocol, open the commitment, i.e. broadcast the hash challenge value to other participants , and other participants locally run the hash operation on the received hash challenge value to get , compare and , same, pass, continue to the next step; otherwise, interrupt the program execution.

[0131] (7) Calculate the total hash challenge value .

[0132] (8) Calculate the response vector , and check the range of .

[0133] The requirement , wherein comes from the value range of the random vector in the corresponding security level of Dilithium, which realizes the function of increasing the secret vector challenge without leaking the secret vector, and too large will backtrack to the first step of the signature generation part and re-execute.

[0134] (9) Calculate hash value of response vector .

[0135] (10) Based on commitment protocol, output commitment value, i.e. broadcast to other participants .

[0136] (11) Based on commitment protocol, open commitment, i.e. broadcast response vector to other participants , other participants locally run hash operation on received response vector , compare and , if same, pass, continue to execute next step; otherwise, interrupt execution of program.

[0137] (12) Calculate total response vector .

[0138] (13) Calculate hash value of high bits of commitment value .

[0139] (14) Based on commitment protocol, output commitment value, i.e. broadcast to other participants .

[0140] (15) Based on commitment protocol, open commitment, i.e. broadcast high bits of commitment value to other participants , other participants locally run hash operation on received , compare and , if same, pass, continue to execute next step; otherwise, interrupt execution of program.

[0141] (16) Calculate total high bits of commitment value .

[0142] (17) Based on total signature matrix , total response vector , total hash challenge value and total public key , locally calculate high bits of commitment value .

[0143] (18) Calculate difference value of high bits of commitment value , wherein implements bit-by-bit difference of two input parameters, and the difference value is used to recover another bit parameter from one of the parameters.

[0144] ​​​​​​​​Output: signature .

[0145] 3. Signature verification (executed at the verification party):

[0146] (1) Check the response vector , if it is too large, return 0 directly.

[0147] (2) Calculate the total commitment value by the total signature matrix , the total response vector , the total hash challenge value and the total public key , and intercept the high bit of the total commitment value , which is expressed by the formula as follows:

[0148]

[0149] (3) Correct the high bit of the total commitment value using the commitment value high bit difference value , and take the corrected commitment value high bit as the recovered total commitment value high bit, which is expressed by the formula as follows:

[0150]

[0151] Among them, the first parameter is corrected according to the second parameter.

[0152] (4) Calculate the total hash challenge value using the total hash matrix , the target message and the total commitment value high bit , which is expressed by the formula as follows:

[0153]

[0154] (5) Compare and , if they are the same, it means that the signature is legal, and output 1, otherwise output 0.

[0155] Embodiment 2

[0156] In an embodiment of the present application, a multi-party cooperative anti-quantum signature system based on homomorphic hash is provided, which includes a plurality of participants and a verification party, specifically:

[0157] The participant is configured to generate a pair of public and private keys, wherein the public key is composed of a total public key, a total signature matrix and a total hash matrix of all participants.

[0158] The participant is configured to: based on the public-private key, multi-sign the target message through the homomorphic hash function, and the generated signature is composed of a total hash challenge value, a total response vector and a commitment value high difference value.

[0159] The verification party is configured to: according to the signature, restore the total commitment value high, and then calculate the total hash challenge value, and verify the legality of the signature through comparison of the total hash challenge value.

[0160] Embodiment 3

[0161] In an embodiment of the present application, a computer program product is provided, comprising a computer program, which, when executed by a processor, implements the homomorphic hash-based multi-party collaborative anti-quantum signature method.

[0162] Embodiment 4

[0163] In an embodiment of the present application, a non-transitory computer readable storage medium is provided, which is used to store computer instructions, and the computer instructions, when executed by a processor, implement the homomorphic hash-based multi-party collaborative anti-quantum signature method.

[0164] Embodiment 5

[0165] In an embodiment of the present application, an electronic device is provided, comprising a processor, a memory and a computer program; wherein the processor is connected with the memory, and the computer program is stored in the memory; when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the homomorphic hash-based multi-party collaborative anti-quantum signature method.

[0166] The present application is described with reference to flowcharts and / or block diagrams of the method, device (system) and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 The device for implementing the functions specified in one flow or multiple flows and / or blocks Figure 1 The device for implementing the functions specified in one flow or multiple flows and / or blocks

[0167] These computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable data processing devices to generate a computer implemented process, so that the instructions executed on the computer or other programmable data processing devices provide a process for implementing the functions specified in the flowchart Figure 1 one flow or multiple flows and / or the functions specified in the block Figure 1 one flow or multiple flows and / or the functions specified in the block

[0168] The above describes the specific embodiments of the present application in conjunction with the drawings, but is not a limitation on the scope of protection of the present application. Those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the scope of protection of the present application.

Claims

1. A multi-party collaborative anti-quantum signature method based on homomorphic hash, characterized in that, The method comprises a plurality of participants and a verifier, and specifically comprises the following steps: Step 1: Each participant calls the key generation algorithm part of Dilithium to generate a local signature matrix, a hash matrix, a secret vector and a disturbance vector, reconstructs a public key composed of a total public key, a total signature matrix and a total hash matrix of all participants through broadcasting and aggregation, obtains a public key and a private key of each participant, and the steps are as follows: According to a random seed of a security parameter, an i-th participant Pi locally generates a signature matrix Asigni, a hash matrix Ahashi, a secret vector s1i and a disturbance vector s2i; The local signature matrix Asigni and the hash matrix Ahashi are broadcast to other participants; The signature matrix Asignj and the hash matrix Ahashj broadcast by all other participants Pj are received, and the total signature matrix Asign and the total hash matrix Ahash are obtained through summation; Based on the total signature matrix Asign, the secret vector s1i and the disturbance vector s2i, a local public key ti is generated; The local public key ti is broadcast to other participants; The public key tj broadcast by all other participants Pj is received, and the total public key t is obtained through summation; The public key pk=(A=(Asign,Ahash),t) and the private key ski=(s1i,s2i) are obtained; Step 2: Based on the signature generation algorithm part of Dilithium, all participants use the public and private keys to perform multi-party signature on a target message through a homomorphic hash function, and the generated signature comprises a total hash challenge value of all participants, a total response vector of all participants and a high-bit difference value of all participants; the steps are as follows: Based on the random vector yi and the total signature matrix Asign, the commitment value wi is calculated, and the high-bit commitment value wiH is intercepted; Based on the total hash matrix Ahash, the target message μ and the high-bit commitment value wiH, the homomorphic hash function is used to calculate the hash challenge value ci, and the hash challenge values of all participants are aggregated through broadcasting to obtain the total hash challenge value c; Based on the random vector yi, the total hash challenge value c and the local secret vector s1i, the response vector zi is calculated, and the response vectors of all participants are aggregated through broadcasting to obtain the total response vector z; The high-bit total commitment value wH is obtained by aggregating the high-bit commitment values of all participants through broadcasting; Based on the total signature matrix Asign, the total response vector z, the total hash challenge value c and the total public key t, the local total commitment value is calculated, and the high-bit total commitment value wH is intercepted; The high-bit difference value h of the commitment value is calculated by bit-by-bit difference between the two high-bit total commitment values wH and wH; The signature σ=(z,h,c) is obtained; The high-order difference h = HintwH, wH is calculated for the commitment value, where Hint performs bit-by-bit subtraction on the two input parameters. This difference h is used to recover the other parameter given one of the parameters. The total commitment value high-order difference wH = w1H + w2H + ... +wnH mod q; Based on the total signature matrix Asign, the total response vector z, the total hash challenge value c and the total public key t, the local calculates the commitment value high bit wH=HighBitAsign z c t,2×q 1÷32; The HighBit function realizes intercepting the first q 1÷32 bits of the input first parameter; Step 3: According to the signature, the verifier restores the high-bit total commitment value, and then calculates the total hash challenge value, and verifies the legality of the signature by comparing the total hash challenge value.

2. The homomorphic hash-based multi-party cooperative anti-quantum signature method according to claim 1, characterized in that, In the broadcasting and aggregation, the hash value of the to-be-broadcast content is also broadcast, the participant receiving the broadcast content locally calculates the hash value of the broadcast content, whether there is a malicious participant is judged by comparing the two hash values, and whether the following steps are continued is finally determined.

3. The homomorphic hash based multi-party cooperative anti-quantum signature method according to claim 1, characterized in that, The recovery total commitment value high, specifically: by the total signature matrix , the total response vector , the total hash challenge value and the total public key , calculate the total commitment value, and intercept the high bit of the total commitment value ; The high-order difference value of the commitment value is used The high-order difference value of the total commitment value is corrected The corrected high-order difference value of the commitment value is used as the recovered high-order difference value of the total commitment value.

4. The homomorphic hash based multi-party cooperative anti-quantum signature method according to claim 1, characterized in that, The total hash challenge value is calculated using the total hash matrix , the target message , the total commitment value high bits , the total hash challenge value is calculated .

5. A multi-party collaborative anti-quantum signature system based on homomorphic hash, characterized in that, Including a number of participants and a verification party, using the homomorphic hash-based multi-party collaborative anti-quantum signature method according to any one of claims 1-4, comprising: The participant is configured to generate a pair of public and private keys, wherein the public key is composed of the total public key of all participants, the total signature matrix, and the total hash matrix; The participant is configured to generate a multi-party signature on the target message based on the public and private keys through the homomorphic hash function, and the generated signature is composed of the total hash challenge value, the total response vector, and the commitment value high difference value; The verification party is configured to recover the total commitment value high according to the signature, and then calculate the total hash challenge value, and verify the legality of the signature by comparing the total hash challenge value.

6. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the homomorphic hash-based multi-party collaborative anti-quantum signature method according to any one of claims 1-4.

7. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium is used to store computer instructions, which are executed by the processor to realize the homomorphic hash-based multi-party collaborative anti-quantum signature method according to any one of claims 1-4.

8. An electronic device, comprising: Including: The processor, the memory and the computer program; wherein the processor is connected with the memory, and the computer program is stored in the memory; when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the homomorphic hash-based multi-party collaborative anti-quantum signature method according to any one of claims 1-4.

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