A group user identity authentication system and method based on lattice password

Abstract

The present invention relates to a group user identity authentication system and method based on lattice cryptography, belonging to the field of identity authentication. The present invention adopts a lattice-based global parameter generation module to generate relevant parameters of the lattice puzzle, which can prevent any network attack including quantum computing attack; through the lattice-based group parameter generation module, a public and private key pair of each group is generated, and the security strength can resist quantum computing attack; through the lattice-based group user formation module, the group user components and the distribution of user keys are completed, and the security strength can resist quantum computing attack; through the lattice-based group user identity authentication module of the management end, the group user identity is verified, and the verification process can resist quantum computing attack. The present invention can realize the creation of groups and group user identity authentication on the basis of resisting quantum computing attack, and the verification process is safe and efficient, and can effectively prevent malicious attacks such as forgery, impersonation, and key exhaustive search.

Description

Technical Field

[0001] The present invention belongs to the field of user identity authentication, and relates to a group user identity authentication system and method based on a lattice password. Background Art

[0002] Identity authentication is widely used in many fields, such as cloud computing, the Internet of Things (IoT), remote conferencing, and radio frequency identification (RFID). Identity authentication can be categorized into two types: individual and group. Individual authentication involves only two users verifying each other's identities. Group authentication involves multiple users communicating within a group. For example, in RFID and IoT scenarios, group authentication is required to verify user identities and mitigate malicious tampering and identity theft.

[0003] Identity authentication is typically achieved using cryptographic systems. Traditional authentication algorithms are based on the discrete logarithm problem or the large prime number factorization problem. However, these problems are insecure against quantum computing attacks. Shor proposed a quantum algorithm capable of solving the discrete logarithm problem and the factorization problem with sub-exponential time complexity. Later, Ajtai first proposed a lattice-based cryptographic algorithm and demonstrated its resistance to quantum computing attacks. Therefore, designing a lattice-based cryptographic algorithm for group user authentication can help further improve the security of authentication algorithms.

[0004] Patent application number 202010679390.5 provides a user authentication system based on edge computing, which primarily involves a local user authentication process performed by a server and a remote user authentication process performed by a server. This method uses custom functions to calculate authentication values, specifically using trigonometric functions and addition operations. While this solution offers a simple and efficient authentication process, it lacks security and can be easily cracked using methods such as exhaustive enumeration.

[0005] Patent application number 202011421209.7 provides a unified authentication method for multiple applications based on UKEY, including issuing security credentials to authenticated users, providing the user's security credentials to other applications, and using the user's security credentials to obtain user information. This method is primarily based on the UKEY device and includes user authentication, UKEY device authentication, security credential acquisition, and identity information acquisition. However, this method relies on the UKEY device, cannot achieve two-way identity authentication, and cannot resist quantum computing attacks.

[0006] The patent application with application number 202110189022.7 provides a secure and reliable identity authentication method and device that supports multiple protocols and multiple modes, mainly including user identity authentication, session management, certificate management and policy management. Among them, user identity authentication is performed when the user accesses the system, session management uses cookies or URL rewriting to track the user's session ID, and certificate management uses SSL or HTTPS authentication protocols to achieve two-way authentication. All authentication processes of this scheme rely on existing encryption algorithms based on discrete logarithms or large prime number decomposition problems, and cannot resist quantum computing attacks.

[0007] Patent application number 202110716727.X provides a cross-chain system and a distributed user identity authentication method for cross-chain systems, including user ID registration, user ID update, and user ID authentication. The system generates an ID for each user based on their identity information and generates public and private keys and digital signatures for each user using an elliptic curve. During the user ID update phase, the user sends their new identity information and blockchain user ID to the cross-chain system via the blockchain. The cross-chain system then updates the user information and generates a new signature for the user. During the authentication phase, blockchain system A sends the user's signature to blockchain system B, which verifies the user's digital signature. Subsequently, blockchain system B initiates a random number challenge-response to blockchain system A to verify the correctness of blockchain system A. This method's key security is based on the discrete logarithm problem and is not resistant to quantum computing attacks.

[0008] Patent application number 202110696725.9 provides a blockchain-based method for synchronous user authentication, which primarily involves user registration, signature generation, and user identity verification. This method uses blockchain smart contracts to verify the identity of individual users. However, this solution relies on blockchain smart contracts for verification and is vulnerable to quantum computing attacks.

[0009] Patent application 202211518403.6 discloses a bidirectional authentication method, a first electronic device, and a second electronic device. This method provides a process for bidirectional authentication between two electronic devices. However, this scheme is only applicable to identity authentication between two parties. Furthermore, this method uses the Triple DES encryption algorithm as an encryption scheme, which has a short key length and cannot resist quantum computing attacks. Its security performance needs to be improved.

[0010] The May 2018 issue of the journal Computer Applications and Software features a paper titled "An Efficient Identity-Based Authentication Scheme on Lattice." This scheme includes a master key generation algorithm, a user private key extraction algorithm, and a verification protocol. While the scheme is secure against quantum computing attacks, it is not suitable for multi-user group authentication scenarios.

[0011] Shandong University's doctoral dissertation, "Research on Lattice-Based Designated Verifier Digital Signature Scheme and Identity Authentication Protocol," proposed a lattice-based zero-knowledge identity authentication protocol. Although the protocol scheme can resist quantum computing attacks, it is only applicable to multi-round probabilistic identity authentication of a single object and is not suitable for multi-user group environments.

[0012] The paper "An Improved Remote User Authentication Scheme," published in the November 2021 issue of the journal Computer Engineering & Science, proposes a remote user authentication scheme for IoT environments. This scheme uses a timestamp mechanism and is based on the Diffie-Hellman problem. While this scheme is resistant to replay attacks, the Diffie-Hellman problem is a discrete logarithm problem and can be cracked by quantum algorithms.

[0013] The paper "Research on Lightweight Identity Authentication and Secure Communication Technology," published in the February 2023 issue of the journal Information Technology and Informatization, addresses the issue of secure information transmission on embedded device networks. It proposes a lightweight identity authentication and authentication-based encryption transmission technology. This technology is suitable for mutual authentication between two nodes. It uses the elliptic curve ECC algorithm as an asymmetric encryption algorithm. However, the ECC algorithm is based on the discrete logarithm problem and is not resistant to quantum computing attacks. Summary of the Invention

[0014] To address the aforementioned challenges of quantum computing attacks and group user identity authentication, this paper designs a group user identity authentication system and method based on lattice cryptography. This solution is applicable to any group formation and user identity authentication within the group. Both the key generation and verification processes are designed based on lattice problems, making it impossible for attackers to forge keys or pass the verification process. This solution not only ensures effective group user identity authentication but also resists quantum computing attacks.

[0015] In order to achieve the above object, the present invention provides the following technical solutions:

[0016] A group user identity authentication system based on a grid password, comprising: a grid-based global parameter generation module, a grid-based group parameter generation module, a grid-based group user formation module, a grid-based group user identity authentication module on a management side, and a grid-based group user identity authentication module on a user side;

[0017] The lattice-based global parameter generation module is responsible for defining the global parameters of the lattice problem, the large prime number p, and the number field ring R. p , thus completing the grid-based parameter generation;

[0018] The grid-based group parameter generation module is responsible for generating group parameters and generating public and private key pairs for each group through global parameters;

[0019] The grid-based group user formation module is responsible for forming users into groups and includes two submodules: a first grid-based group user formation module and a second grid-based group user formation module. The grid-based group user formation module is responsible for providing user identity information and initiating group joining requests. The grid-based group user formation module is responsible for creating user groups and managing user joining.

[0020] The user-side grid-based group user identity authentication module is responsible for interacting with the management-side grid-based group user identity authentication module to complete the identity authentication process, is responsible for processing the challenge information from the management-side grid-based group user identity authentication module, and uses the group user key generated by the management-side grid-based group user formation module to generate response information, and then sends the response information to the management-side grid-based group user identity authentication module;

[0021] The management-side grid-based group user identity authentication module is responsible for interacting with the user-side grid-based group user identity authentication module to complete the identity authentication process, generating challenge information, and sending the challenge information to the user-side grid-based group user identity authentication module. After receiving the response information from the user-side grid-based group user identity authentication module, it is determined whether the response information meets the requirements. If the response information meets the requirements, the verification is considered to be successful; otherwise, the verification is considered to have failed and the access request is rejected.

[0022] As a further improvement of the present invention, the grid-based global parameter generation module specifically implements the following functions: select a security parameter n and a large prime number p, calculate the scale parameter and dimension parameter m≥5nlogp, o() represents the upper bound; Next, the grid-based global parameter generation module selects Gaussian parameters Where m is the dimension parameter, ω() represents the lower bound, m'=2n; define the integer polynomial ring in is an integer polynomial with coefficients in the range {0,…,p-1}, f(x)=x n +1 is an irreducible polynomial; define the tool vector g=(1,2,4,…,2 k-1 ) T ;Finally, output the public parameters sp={n,p,l,m,k,σ,m',f(x),g}.

[0023] As a further improvement of the present invention, the grid-based group parameter generation module specifically implements the following functions: running the trapdoor generation algorithm Generate a group public and private key pair as follows: Randomly select the public key to construct the vector Reversible label h∈R p ,in represents a vector of mk dimensions, where the elements of each dimension are taken from the integer polynomial ring R p , selected from the sub-Gaussian distribution with parameter σ calculate satisfy Among them I k represents the k-dimensional identity matrix; finally, the grid-based group parameter generation module outputs a and T, where a is made public and T is kept secret.

[0024] As a further improvement of the present invention, the first grid-based user group formation module and the second grid-based user group formation module specifically implement the following functions: the first grid-based user group formation module selects user identity information The first group user formation module based on the grid receives the group user key T sent by the second group user formation module based on the grid. j The second group user formation module based on the grid calculates the group user public key And use the trapdoor transmission algorithm DelTrap (a j ,T,h,σ) generates the group user key T j As follows: First, transform the equation Then use the Gaussian pre-image sampling algorithm SamplePre(a,T,h,b i ,σ) Generate partial group user keys Where 1≤i≤k; the final output Finally, the second group user formation module based on the grid converts the group user key T j The data is sent to the first grid-based user group formation module via a secure channel.

[0025] As a further improvement of the present invention, the user-side grid-based group user identity authentication module is responsible for interacting with the administrator-side grid-based group user identity authentication module to complete the identity authentication process; the user-side grid-based group user identity authentication module receives the challenge information r∈R from the administrator-side grid-based group user identity authentication module. p Then, the Gaussian pre-image sampling algorithm is used to generate the response vector d = SamplePre (a j ,T j ,h,σ,r) is as follows: First generate a perturbation vector And calculate the intermediate parameters Then according to gT z=v calculates the intermediate vector Then calculate At this time there where a j =[a|u j ]; Then the user end based on the grid group user identity verification module will answer the vector Sent to the administrator a grid-based group user authentication module.

[0026] As a further improvement of the present invention, the grid-based group user identity authentication module of the management end is responsible for interacting with the grid-based group user identity authentication module of the user end to complete the identity authentication process; the grid-based group user identity authentication module of the management end selects random challenge information r∈R p Then, the challenge information r is sent to the user-side grid-based group user identity authentication module, and the response information d from the user-side grid-based group user identity authentication module is waited for; after the management-side grid-based group user identity authentication module receives the response information d from the user-side grid-based group user identity authentication module, the management-side grid-based group user identity authentication module calculates r'=a j d, where a j =[a|u j ], and then determine whether r=r' is established. If the equation is established, it is considered that the verification is successful. Otherwise, it is considered that the verification fails and the user is denied access.

[0027] A group user identity authentication method based on a lattice password comprises the following steps:

[0028] The lattice-based group parameter generation module defines the global parameters of the lattice problem, a large prime number p, and defines the number field ring R p , thus completing the grid-based parameter generation;

[0029] The lattice-based group parameter generation module generates group parameters and generates public and private key pairs for each group through global parameters;

[0030] The grid-based group user formation module organizes users into groups. The grid-based group user formation module provides user identity information and initiates a request to join a group. The grid-based group user formation module implements user group creation and manages user joining.

[0031] The user-side grid-based group user authentication module and the management-side grid-based group user authentication module interact to complete the authentication process:

[0032] The user-side grid-based group user identity authentication module processes the challenge information from the management-side grid-based group user identity authentication module, generates a response information using the group user key generated by the management-side grid-based group user formation module, and then sends the response information to the management-side grid-based group user identity authentication module;

[0033] The grid-based group user identity authentication module on the management side generates a challenge message and sends the challenge message to the grid-based group user identity authentication module on the user side. After receiving the response message from the grid-based group user identity authentication module on the user side, it determines whether the response message meets the requirements. If the response message meets the requirements, the verification is considered to be successful. Otherwise, the verification is considered to have failed and the access request is rejected.

[0034] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0035] 1. This invention uses lattice puzzles to implement group creation, group user components, and group user identity authentication. The group's public and private key pairs are constructed based on lattice puzzles, providing security strength that can withstand quantum computing attacks. The group user's secret keys are also constructed based on lattice puzzles, providing security strength that can withstand quantum computing attacks. Furthermore, the group identity authentication process effectively resists quantum computing attacks, offering high security performance and effectively preventing malicious attacks such as identity spoofing. This invention is suitable for multi-user group scenarios, offering both simplicity and efficiency, as well as high security strength, and is suitable for a wide range of applications.

[0036] 2. The present invention adopts a self-designed lattice-based global parameter generation module to generate relevant parameters of lattice problems, which can prevent any network attacks including quantum computing attacks; through the self-designed lattice-based group parameter generation module, a public and private key pair for each group is generated, and its security strength can resist quantum computing attacks; through the self-designed lattice-based group user formation module, the group user components and the distribution of user keys are completed, and the security strength of the keys can resist quantum computing attacks; through the management end-based lattice-based group user identity authentication module, the group user identity is verified, and the verification process can resist quantum computing attacks. The present invention can realize the creation of groups and group user identity authentication on the basis of resisting quantum computing attacks. At the same time, the verification process is safe and efficient, and can effectively prevent malicious attacks such as forgery, impersonation, and key exhaustive search. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is an architecture diagram of the identity authentication system of the present invention.

[0038] Figure 2 This is a schematic diagram of a group user identity authentication method based on a grid password provided by the present invention.

[0039] Figure 3 It is a flow chart of group user formation of the present invention.

[0040] Figure 4 It is a flow chart of group user identity authentication of the present invention. DETAILED DESCRIPTION

[0041] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0042] like Figure 1 The figure shows the architecture diagram of the identity authentication system of the present invention, which is applicable to most Internet scenarios. The identity authentication system of the present invention mainly includes two types of entities, administrators and users. The administrator is responsible for the creation of groups and the management of group users. When creating a new group, the administrator will disclose the public key of the new group and keep the group private key secret. After the administrator receives the identity information sent by the user, he will generate a corresponding user key for the user and send the user key to the corresponding user through a secure channel. During the group user identity verification stage, the administrator is responsible for sending challenge information to the user and receiving and verifying the response information sent by the user. The user is a member of the group. When a user joins a group, he needs to send his identity information to the administrator, and then receive the user private key sent by the administrator through a secure channel. During the identity verification stage, the user needs to send a response message to the administrator.

[0043] like Figure 2 The figure shows the overall block diagram of the present invention. The present invention provides a group user identity authentication system based on lattice cryptography, which includes a lattice-based global parameter generation module 1, a lattice-based group parameter generation module 2, a lattice-based group user formation module 3, a user-side lattice-based group user identity authentication module 4, and a management-side lattice-based group user identity authentication module 5. The lattice-based global parameter generation module 1 is responsible for defining the global parameters of the lattice problem, the large prime number p, and defining the ring R p, thereby completing the grid-based parameter generation. The grid-based group parameter generation module 2 is responsible for generating group parameters and generating the public and private key pairs of each group through global parameters. The grid-based group user formation module 3 is responsible for forming users into groups, and includes two sub-modules, namely the grid-based first group user formation module 3-1 and the grid-based second group user formation module 3-2. The grid-based first group user formation module 3-1 is responsible for providing the user's identity information and initiating a request to join the group. The grid-based second group user formation module 3-2 is responsible for creating user groups and managing user joining. The user-side grid-based group user identity authentication module 4 is responsible for interacting with the management-side grid-based group user identity authentication module 5 to complete the identity authentication process, is responsible for processing the challenge information from the management-side grid-based group user identity authentication module 5, and uses the group user key generated by the management-side grid-based group user formation module 5 to generate response information, and then sends the response information to the management-side grid-based group user identity authentication module 4. The grid-based group user identity authentication module 5 on the management side is responsible for interacting with the grid-based group user identity authentication module 4 on the user side to complete the identity authentication process, and is responsible for generating challenge information and sending the challenge information to the grid-based group user identity authentication module 4 on the user side. After receiving the response information from the grid-based group user identity authentication module 4 on the user side, it is determined whether the response information meets the requirements. If the response information meets the requirements, the verification is considered to be successful; otherwise, the verification is considered to have failed and the access request is rejected.

[0044] Specifically, the lattice-based global parameter generation module 1 selects a security parameter n (n is a power of 2) and a large prime number p, and calculates the scale parameter and dimension parameter m≥5nlogp, o() represents the upper bound; Next, the grid-based global parameter generation module 1 selects the Gaussian parameters Where m is the dimension parameter, ω() represents the lower bound, m'=2n; define the integer polynomial ring in is an integer polynomial with coefficients in the range {0,…,p-1}, f(x)=x n +1 is an irreducible polynomial; define the tool vector g=(1,2,4,…,2 k-1 ) T Finally, the public parameters sp = {n, p, l, m, k, σ, m', f(x), g} are output.

[0045] like Figure 3 The group parameter generation module 2 based on the grid runs the trapdoor generation algorithm. Generate a group public and private key pair as follows: Randomly select the public key to construct the vector ( represents a vector of mk dimensions, where the elements of each dimension are taken from the integer polynomial ring R p ), reversible label h∈R p , select the trapdoor from the sub-Gaussian distribution with parameter σ Calculate the public key satisfy Among them I k represents the k-dimensional identity matrix. Finally, the grid-based group parameter generation module 2 outputs a and T. a is made public and T is kept secret.

[0046] The grid-based group user formation module 3 is responsible for forming users into groups; the grid-based group user formation module 3 includes a grid-based first group user formation module 3-1 and a grid-based second group user formation module 3-2; the grid-based first group user formation module 3-1 selects user identity information The second group user forming module 3-1 based on the grid receives the group user key T sent by the group user forming module 3-2 based on the grid. j . Grid-based group user formation module 3-2 calculates the group user public key And use the trapdoor transmission algorithm DelTrap (a j ,T,h,σ) generates the group user key T j As follows: First, transform the equation Then use the Gaussian pre-image sampling algorithm SamplePre(a,T,h,b i ,σ) Generate partial group user keys Where 1≤i≤k; the final output Finally, the lattice-based group user formation module 3-2 converts the group user key T j The data is sent to the grid-based group user forming module 3-1 through a secure channel.

[0047] like Figure 4 The figure shows the group user identity authentication flow chart of the present invention. The user-side grid-based group user identity authentication module 4 is responsible for interacting with the administrator-side grid-based group user identity authentication module 5 to complete the identity authentication process; the user-side grid-based group user identity authentication module 4 receives the challenge information r∈R from the administrator-side grid-based group user identity authentication module 5. p Then, the Gaussian pre-image sampling algorithm is used to generate the response vector d = SamplePre (a j ,T j ,h,σ,r) are as follows (where a j =[a|u j ]): First generate a perturbation vector And calculate the intermediate parameters Then according to g T z=v calculates the intermediate vector Then calculate At this time there Then the user end based on the grid group user identity verification module 4 will answer the vector Sent to the administrator's grid-based group user authentication module 5.

[0048] The grid-based group user identity authentication module 5 on the management side is responsible for interacting with the grid-based group user identity authentication module 4 on the user side to complete the identity authentication process; the grid-based group user identity authentication module 5 on the management side selects random challenge information r∈R p Then the challenge information r is sent to the user-side grid-based group user identity authentication module 4; the user-side grid-based group user identity authentication module 4 generates a response information The response information d is sent to the management end based on the grid group user identity authentication module 5; after the management end based on the grid group user identity authentication module 5 receives the response information d from the user end based on the grid group user identity authentication module 4, it calculates r'=a j d, where a j =[a|u j ], and then judge whether r=r' is established. If the equation is established, it is considered that the verification is successful. Otherwise, it is considered that the verification fails and the user access is denied.

[0049] The present invention also provides a group user identity authentication method based on a lattice password, which implements the functions of each module in a group user identity authentication system based on a lattice password. Specifically, it includes the following steps:

[0050] The lattice-based global parameter generation module defines the global parameters of the lattice problem, a large prime number p, and defines the ring R p , thus completing the grid-based parameter generation;

[0051] The lattice-based group parameter generation module generates group parameters and generates public and private key pairs for each group through global parameters;

[0052] The grid-based group user formation module organizes users into groups, wherein the first grid-based group user formation module provides the user's identity information and initiates a request to join the group; the grid-based group user formation module implements the creation of user groups and manages the joining of users;

[0053] The user-side grid-based group user authentication module and the management-side grid-based group user authentication module interact to complete the authentication process:

[0054] The user-side grid-based group user identity authentication module processes the challenge information from the management-side grid-based group user identity authentication module, generates response information using the group user key generated by the management-side grid-based group user formation module, and then sends the response information to the management-side grid-based group user identity authentication module;

[0055] The grid-based group user identity authentication module on the management side generates a challenge message and sends the challenge message to the grid-based group user identity authentication module on the user side. After receiving the response message from the grid-based group user identity authentication module on the user side, it determines whether the response message meets the requirements. If the response message meets the requirements, the verification is considered to be successful. Otherwise, the verification is considered to have failed and the access request is rejected.

[0056] For the specific functions implemented by each module, please refer to the specific functions of each module in the aforementioned group user identity authentication system based on grid password.

[0057] The technical means disclosed in the solutions of the present invention are not limited to those disclosed in the above-mentioned embodiments, but also include technical solutions composed of any combination of the above-mentioned technical features. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A group user identity authentication system based on lattice password, characterized in that: include: It includes a grid-based global parameter generation module, a grid-based group parameter generation module, a grid-based group user formation module, a grid-based group user identity authentication module on the management side, and a grid-based group user identity authentication module on the user side; The lattice-based global parameter generation module is responsible for defining the global parameters of the lattice problem, the large prime number p, and defining the integer polynomial ring R p , thus completing the grid-based parameter generation; The grid-based group parameter generation module is responsible for generating group parameters and generating public and private key pairs for each group through global parameters; The grid-based group user formation module is responsible for forming users into groups and includes two submodules: a first grid-based group user formation module and a second grid-based group user formation module. The grid-based group user formation module is responsible for providing user identity information and initiating group joining requests. The grid-based group user formation module is responsible for creating user groups and managing user joining. The user-side grid-based group user identity authentication module is responsible for interacting with the management-side grid-based group user identity authentication module to complete the identity authentication process, is responsible for processing the challenge information from the management-side grid-based group user identity authentication module, and uses the group user key generated by the management-side grid-based group user formation module to generate response information, and then sends the response information to the management-side grid-based group user identity authentication module; The management-side grid-based group user identity authentication module is responsible for interacting with the user-side grid-based group user identity authentication module to complete the identity authentication process, generating challenge information, and sending the challenge information to the user-side grid-based group user identity authentication module. After receiving the response information from the user-side grid-based group user identity authentication module, it is determined whether the response information meets the requirements. If the response information meets the requirements, the verification is considered to be successful; otherwise, the verification is considered to have failed and the joining request is rejected.

2. The group user identity authentication system based on lattice password according to claim 1 is characterized in that: The grid-based global parameter generation module specifically implements the following functions: select a security parameter n and a large prime number p, calculate the scale parameter and dimension parameter m≥5nlogp, o() represents the upper bound; Next, the grid-based global parameter generation module selects Gaussian parameters Where m is the dimension parameter, ω() represents the lower bound, m'=2n; define the integer polynomial ring in is an integer polynomial with coefficients in the range {0,…,p-1}, f(x)=x n +1 is an irreducible polynomial; define the tool vector g=(1,2,4,…,2 k-1 ) T ;Finally, output the public parameters sp={n,p,l,m,k,σ,m',f(x),g}.

3. The group user identity authentication system based on lattice password according to claim 2 is characterized in that: The grid-based group parameter generation module specifically implements the following functions: running the trapdoor generation algorithm Generate a group public and private key pair as follows: Randomly select the public key to construct the vector Reversible label h∈R p ,in represents a vector of mk dimensions, where the elements of each dimension are taken from the integer polynomial ring R p , selected from the sub-Gaussian distribution with parameter σ calculate satisfy Among them I k represents the k-dimensional identity matrix; finally, the grid-based group parameter generation module outputs a and T, where a is made public and T is kept secret.

4. The group user identity authentication system based on lattice password according to claim 3 is characterized in that: The first group user formation module based on the grid and the second group user formation module based on the grid specifically implement the following functions: the first group user formation module based on the grid selects user identity information The first group user formation module based on the grid receives the group user key T sent by the second group user formation module based on the grid. j The second group user formation module based on the grid calculates the group user public key And use the trapdoor transmission algorithm DelTrap (a j ,T,h,σ) generates the group user key T j As follows: First, transform the equation Then use the Gaussian pre-image sampling algorithm SamplePre(a,T,h,b i ,σ) Generate partial group user keys Where 1≤i≤k; the final output Finally, the second group user formation module based on the grid converts the group user key T j The data is sent to the first grid-based user group formation module via a secure channel.

5. The group user identity authentication system based on lattice password according to claim 4 is characterized in that: The user-side grid-based group user identity authentication module is responsible for interacting with the administrator-side grid-based group user identity authentication module to complete the identity authentication process; the user-side grid-based group user identity authentication module receives the challenge information r∈R from the administrator-side grid-based group user identity authentication module. p Then, the Gaussian pre-image sampling algorithm is used to generate the response vector d = SamplePre (a j ,T j ,h,σ,r) is as follows: First generate a perturbation vector And calculate the intermediate parameters Then according to g T z=v calculates the intermediate vector Then calculate At this time there where a j =[a|u j ]; Then the user end based on the grid group user identity verification module will answer the vector Sent to the administrator a grid-based group user authentication module.

6. The group user identity authentication system based on lattice password according to claim 5, characterized in that: The management end grid-based group user identity authentication module is responsible for interacting with the user end grid-based group user identity authentication module to complete the identity authentication process; the management end grid-based group user identity authentication module selects random challenge information r∈R p , then sending the challenge information r to the grid-based group user identity authentication module of the user terminal, and waiting for the response information d from the grid-based group user identity authentication module of the user terminal; After the management end's grid-based group user identity authentication module receives the response information d from the user end's grid-based group user identity authentication module, it calculates r'=a j d, where a j =[a|u j ], and then judge whether r=r' is established. If the equation is established, it is considered that the verification is passed, otherwise it is considered that the verification fails and the user is denied to join.

7. A group user identity authentication method based on a lattice password, characterized in that: The implementation of the group user identity authentication system based on a grid password according to any one of claims 1 to 6 comprises the following steps: The lattice-based group parameter generation module defines the global parameters of the lattice problem, a large prime number p, and defines the integer polynomial ring R p , thus completing the grid-based parameter generation; The lattice-based group parameter generation module generates group parameters and generates public and private key pairs for each group through global parameters; The grid-based group user formation module organizes users into groups. The grid-based group user formation module provides user identity information and initiates a request to join a group. The grid-based group user formation module implements user group creation and manages user joining. The user-side grid-based group user authentication module and the management-side grid-based group user authentication module interact to complete the authentication process: The user-side grid-based group user identity authentication module processes the challenge information from the management-side grid-based group user identity authentication module, generates a response information using the group user key generated by the management-side grid-based group user formation module, and then sends the response information to the management-side grid-based group user identity authentication module; The grid-based group user identity authentication module on the management side generates a challenge message and sends the challenge message to the grid-based group user identity authentication module on the user side. After receiving the response message from the grid-based group user identity authentication module on the user side, it determines whether the response message meets the requirements. If the response message meets the requirements, the verification is considered to be successful. Otherwise, the verification is considered to have failed and the joining request is rejected.

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