Local area network integral security encryption and decryption method and system based on coding graph group

Abstract

The invention relates to the technical field of computers, in particular to a local area network overall security encryption and decryption method and system based on a coding graph group. The method comprises the steps of selecting an initial basic diagram, obtaining topological structure changes of a local area network, adjusting the initial basic diagram in real time in combination with the topological structure changes of the local area network to obtain an optimized basic diagram, constructing a topological diagram set based on the optimized basic diagram, then coding the topological diagram set and constructing a topological coding diagram group, finally, the local area network communities and topological signatures of communication paths between the communities are defined, the signatures are updated when communication between the local area network communities changes, and the defined topological signatures are used for generating encryption keys to encrypt data. The coding graph group matched with the network topology is constructed, the key generation and management process is simplified, and the data security protection capability is improved.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and particularly to a method and system for overall security encryption and decryption of a local area network based on an encoded graph group. Background Art

[0002] With the rapid development of computer network technology, the local area network (LAN) has become the core platform for information exchange and resource sharing within various institutions and enterprises. However, the data transmission within the local area network is facing increasingly severe security challenges. In a complex network environment, the communication between multiple users, devices, and communities is vulnerable to threats such as malicious attacks, data leakage, or tampering.

[0003] Traditional encryption technologies, such as symmetric encryption algorithms, although they have played a certain role in data protection, have significant deficiencies in dealing with complex network topologies and ensuring the dynamics and flexibility of encrypted transmission. Especially in the multi-community communication scenario, the existing technologies are difficult to effectively distinguish the security of different communities and communication paths, and the complexity of key management and distribution is likely to lead to key conflicts and security vulnerabilities. In addition, while improving security, traditional methods often sacrifice the efficiency of encryption and decryption, and it is difficult to achieve a balance between security and performance. Summary of the Invention

[0004] The object of the present invention is to address the problems in the background art and propose a method and system for overall security encryption and decryption of a local area network based on an encoded graph group.

[0005] The technical solution of the present invention:

[0006] On the one hand, the present application provides a method for overall security encryption and decryption of a local area network based on an encoded graph group, including:

[0007] Select an initial base graph, obtain the topological structure changes of the local area network, adjust the initial base graph in real time in combination with the topological structure changes of the local area network to obtain an optimized base graph, and construct a topological graph set based on the optimized base graph;

[0008] Encode the topological graph set;

[0009] Define the topological signatures of the local area network communities and the communication paths between communities, update the signatures when the communication between the local area network communities changes, and generate encryption key pairs with the defined topological signatures to encrypt the data.

[0010] Preferably, selecting an initial base graph, obtaining the topological structure changes of the local area network, adjusting the initial base graph in real time in combination with the topological structure changes of the local area network to obtain an optimized base graph, and constructing a topological graph set based on the optimized base graph, includes:

[0011] Randomly select an initial basic graph with the number of vertices being m, where m is greater than or equal to the number of local area network communities;

[0012] Obtain the change in the local area network topology structure to adjust the number of vertices of the initial basic graph, and obtain the optimized basic graph H1;

[0013] Copy the optimized basic graph m - 1 times, denoted as H2,...,H m , to obtain the topology graph set F = {H1, H2,..., H m}}.

[0014] Preferably, encode the topology graph set, including:

[0015] Define the encoding function of the optimized basic graph H1 through Formula 1;

[0016] h1: V(H1) → {1, 2,..., m} Formula 1;

[0017] Where h1 is the encoding function of the optimized basic graph H1, m is the number of vertices of the optimized basic graph H1, and V(H1) is the vertex set of the optimized basic graph H1;

[0018] Define the encoding functions of the optimized basic graphs H2,..., H m through Formula 2;

[0019] h i (x) = (h i-1 (x) + 1)(mod m) Formula 2;

[0020] Where h i is the encoding function of the i-th optimized basic graph, and 2 ≤ i ≤ m, x is the vertex element of the optimized basic graph H i .

[0021] Preferably, encoding the topology graph set also includes:

[0022] Combining Formula 1 and Formula 2, construct the topology coding graph group through Formula 3;

[0023]

[0024] Where h i is the encoding function of the i-th optimized basic graph, H i is the i-th optimized basic graph, and i, j, k ∈ [1, m], x is the vertex element of the optimized basic graph H i , and H k is the specified zero element.

[0025] Preferably, define the topological signatures of the local area network communities and the communication paths between the communities, update the signatures when the communication between the local area network communities changes, and encrypt the defined topological signatures to generate encryption key pairs for data, including:

[0026] For each community in the local area network, randomly assign a topological coding graph to each community in turn, and use the assigned topological coding graph as the topological signature of the community;

[0027] For any two communities in the local area network, determine whether there is communication between the two communities;

[0028] If there is communication between the two communities, assign a communication zero element to the communication path;

[0029] Calculate the topological coding graph corresponding to the communication zero element of the communication path through Formula 3, and record the topological coding graph as the topological signature of the communication path.

[0030] Preferably, the topological coding graph includes the adjacent matrix, e - adjacent matrix, and full coding matrix of the topological coding graph.

[0031] Preferably, define the topological signatures of the local area network communities and the communication paths between the communities, update the signatures when the communication between the local area network communities changes, and encrypt the defined topological signatures to generate encryption key pairs for data, further including:

[0032] Derive the topological signature string pairs and topological digital string pairs of the adjacent matrix, e - adjacent matrix, and full coding matrix of the topological coding graph;

[0033] Make the coding graph public key and coding graph private key based on the topological signature string pairs and topological digital string pairs of the adjacent matrix, e - adjacent matrix, and full coding matrix of the topological coding graph;

[0034] Derive the topological signature string pairs and topological digital string pairs of the adjacent matrix, e - adjacent matrix, and full coding matrix of the topological signature of the communication path;

[0035] Make the communication public key and communication private key based on the topological signature string pairs and topological digital string pairs of the adjacent matrix, e - adjacent matrix, and full coding matrix of the topological signature of the communication path.

[0036] Preferably, define the topological signatures of the local area network communities and the communication paths between the communities, update the signatures when the communication between the local area network communities changes, and encrypt the defined topological signatures to generate encryption key pairs for data, further including:

[0037] Send the coding graph public key;

[0038] Send the communication public key;

[0039] Determine whether a reply message is received;

[0040] If no reply information is received, decryption and identification processing is performed using the communication private key.

[0041] On the other hand, the present application also provides a local area network overall security encryption and decryption system based on a coded graph group, including an encryption component and a control component. The public key and private key are generated by the encryption component. The public key includes a communication public key and a coded graph public key, and the private key includes a communication private key and a coded graph private key. The control component is communicatively connected to the encryption component, and the control component executes the method for local area network overall security encryption and decryption based on a coded graph group described in any one of the foregoing.

[0042] Preferably, the control component includes a sending end and a receiving end. The public key is sent through the sending end, and it is determined whether the receiving end has received the public key.

[0043] Compared with the prior art, the above technical solution of the present invention has the following beneficial technical effects:

[0044] By selecting an initial base graph, obtaining the topological structure change of the local area network, adjusting the initial base graph in real time in combination with the topological structure change of the local area network to obtain an optimized base graph, constructing a topological graph set based on the optimized base graph, encoding the topological graph set, finally defining the topological signature of the local area network community and the communication path between communities, and updating the signature when the communication between local area network communities changes, encrypting the defined topological signature to generate an encryption key pair for data encryption. The present application can dynamically monitor the change of the local area network topological structure, adjust the initial base graph accordingly, construct a coded graph group matching the network topology, simplify the key generation and management process, and improve the data security protection ability. Description of the Drawings

[0045] Figure 1 It is a schematic flowchart of a method for local area network overall security encryption and decryption based on a coded graph group proposed by the present invention;

[0046] Figure 2 It is a schematic structural diagram of a local area network overall security encryption and decryption system based on a coded graph group proposed by the present invention;

[0047] Figure 3 It is a graph group based on finite modular Abelian additive operation of a method for local area network overall security encryption and decryption based on a coded graph group proposed by the present invention;

[0048] Reference numerals: 100, encryption component; 200, control component; 201, sending end; 202, receiving end. Detailed Embodiments

[0049] Example 1, as Figure 1As shown in the figure, a method for overall security encryption and decryption of a local area network based on an encoded graph group proposed by the present invention includes:

[0050] S100, select an initial basic graph, obtain the topological structure change of the local area network, adjust the initial basic graph in real time in combination with the topological structure change of the local area network to obtain an optimized basic graph, and construct a topological graph set based on the optimized basic graph;

[0051] S200, encode the topological graph set;

[0052] S300, define the topological signature of the local area network community and the communication path between communities, update the signature when the communication between local area network communities changes, and generate an encryption key pair with the defined topological signature to encrypt the data.

[0053] In the present invention, by selecting an initial basic graph, obtaining the topological structure change of the local area network, adjusting the initial basic graph in real time in combination with the topological structure change of the local area network to obtain an optimized basic graph, constructing a topological graph set based on the optimized basic graph, then encoding the topological graph set, and finally defining the topological signature of the local area network community and the communication path between communities, updating the signature when the communication between local area network communities changes, and generating an encryption key pair with the defined topological signature to encrypt the data, this application can dynamically monitor the changes in the topological structure of the local area network, adjust the initial basic graph accordingly, construct an encoded graph group matching the network topology, simplify the key generation and management process, and improve the data security protection ability.

[0054] In an optional embodiment, the S100 includes:

[0055] S110, randomly select an initial basic graph with m vertices, where m is greater than or equal to the number of local area network communities;

[0056] S120, obtain the topological structure change of the local area network to adjust the number of vertices of the initial basic graph and obtain an optimized basic graph H1;

[0057] S130, copy the optimized basic graph m - 1 times, denoted as H2,...,H m , to obtain a topological graph set F = {H1, H2,...,H m}.

[0058] It should be noted that the graph set F is an encoded graph group based on the finite modular Abelian addition operation, specifically denoted as {F(H); [+][-]}. The finite modular Abelian additive operation of the everywhere-zero element graph group is defined by formula 3, denoted as "H i [+ k H j :=H i [+]H j [-]H k =Hλ "It satisfies:

[0059] (i) Closure: That is, for any i, j ∈ [1, m], H i [+ k H j :=H i [+]H j [-]H k =H λ , where λ = (i + j - k)(mod m), there is H λ ∈ {F(H); [+][-]}.

[0060] (ii) Identity element: Each topological coding graph H i ∈ {F(H); [+][-]} can be used as the identity element for the finite modular Abelian additive operation;

[0061] (iii) Inverse element: For the specified identity element H k ∈ {F(H); [+][-]}, the inverse element of H i is H (2k-i)(modm) , then there is H i [+ k H (2k-i)(modm) :=H i [+]H (2k-i)(modm) [-]H k =H k。

[0062] In an alternative embodiment, the S200 includes:

[0063] S210, defining the encoding function of the optimized base graph H1 through Formula 1;

[0064] h1: V(H1) → {1, 2,..., m} Formula 1;

[0065] where h1 is the encoding function of the optimized base graph H1, m is the number of vertices of the optimized base graph H1, and V(H1) is the vertex set of the optimized base graph H1;

[0066] S220, defining the encoding functions of the optimized base graphs H2,..., H m ;

[0067] h i (x) = (h i-1 (x) + 1)(mod m) Formula 2;

[0068] where h i is the encoding function of the i-th optimized base graph, and 2 ≤ i ≤ m, and x is the vertex element of the optimized base graph H i .

[0069] It should be noted that, as Figure 3 shown, a coded graph group {F(H); [+][-]} is given, where the coded graph set F(H) = {H i : i ∈ [1, 9]}, and each coded graph H i admits a code h i , i ∈ [1, 9]. Arbitrarily select a coded graph H k as the "zero element", and define the finite modular Abelian additive operation of the coded graph set F(H) as: H i [+]H j [-]H k = H λ , λ = (i + j - k)(mod 9), where the finite modular Abelian additive operation is calculated according to the following formula (h i (x) + h j (x) - h k (x))(mod 9) = h λ (x), λ = (i + j - k)(mod 9).

[0070] Note that the coded graphs in the coded graph set F(H) are isomorphic to each other. Therefore, there is a vertex x ∈ V(H i ) = V(H1), and the code h i of each edge uv ∈ E(H i )(uv) = |h i (u) - h i (v)|, or h i (uv) = 9 - |h i (u) - h i (v)|, such that the edge code set h i (E(H i )) = {1, 3, 5, 6, 7} (i ∈ [1, 9]). It is not difficult to verify that the topological coded graph set F(H) meets the requirements of a finite modular Abelian additive group. Therefore, this finite modular Abelian additive operation is denoted as {F(H); [+][-]}, and is called a topological coded graph group with an everywhere zero element based on the finite modular Abelian additive operation.

[0071] By defining the coded graph group of the coding function and the finite modular Abelian additive operation, this method optimizes the key generation process. The topological signatures of each community and communication path are used as the encryption and decryption keys, which not only ensures the security of the keys but also simplifies the key management by virtue of the characteristics of group operations. When the network topology changes, the central platform can quickly adjust the topological signature and regenerate the keys, improving the efficiency of encryption and decryption and reducing the complexity and cost of key management.

[0072] In an alternative embodiment, the S200 further includes:

[0073] S230, combine Formula 1 and Formula 2 to construct a topological coding graph group through Formula 3;

[0074]

[0075] where h i is the coding function of the i-th optimized basic graph, H i is the i-th optimized basic graph, and i, j, k ∈ [1, m], x is the vertex element of the optimized basic graph H i , and H k is the specified zero element;

[0076] Specifically, for each edge of the initial basic graph, define the coding of the edge through Formula 4 as:

[0077] h i (uv) = |h i (u) - h i (v)| or h i (uv) = m - |h i (u) - h i (v)| Formula 4

[0078] where E(H i ) is the edge set of the optimized basic graph H i , h i is the coding function of the i-th optimized basic graph, and x is the vertex element of the optimized basic graph H i .

[0079] It should be noted that by continuously monitoring the changes in the local area network topology and obtaining the network topology information in real time, when it is detected that the number n of communities in the local area network changes, dynamically adjust the value of m to ensure that m ≥ n, and reconstruct the initial basic graph H1 according to the updated value of m.

[0080] In an alternative embodiment, the S300 includes:

[0081] S310, for each community in the local area network, randomly assign a topological coding graph to each community in turn, and use the assigned topological coding graph as the topological signature of the community;

[0082] S320, for any two communities in the local area network, determine whether there is communication between the two communities;

[0083] S330, if there is communication between the two communities, assign a communication zero element to the communication path;

[0084] S340, calculate the topological coding graph corresponding to the communication zero element of the communication path through Formula 3, and record the topological coding graph as the topological signature of the communication path.

[0085] It should be noted that for each community N in the local area network N k (k ∈ [1, n]), a topological coding graph H i ∈ F (1 ≤ i ≤ m) is randomly assigned as the topological signature of this community, and it is ensured that the topological coding graphs of any two communities are different. For two communities N u and N v (u, v ∈ [1, n]) that communicate in the local area network N(t), the communication path is assigned a communication zero element H λ ∈ F (1 ≤ λ ≤ m), and the topological coding graph H i ∈ F (1 ≤ i ≤ m) obtained in the foregoing steps is used as the topological signature of this communication path N u N v . Dynamically detect changes in communication between communities in the local area network N, allocate communication zero elements in real time, and use step S100 to update the topological coding graph of the communication path.

[0086] Each community and communication path has its own topological signature as the encryption and decryption key, effectively preventing data from being stolen, tampered with, and forged, ensuring the integrity and confidentiality of data transmission. This application is applicable to the local area network environment containing multiple communities, can be flexibly expanded to meet the growing user and device needs, while maintaining communication security, and guarantees communication security and flexibility in the multi-community environment.

[0087] In an optional embodiment, the topological coding graph includes an adjacent matrix of the topological coding graph, an e-adjacent matrix, and a full coding matrix.

[0088] It should be noted that the topological coding graph is input and stored in a computer by matrices such as the adjacent matrix of the graph, the incidence matrix of the graph, the e-adjacent matrix of the graph, and the full coding topological matrix of the graph, and can implement the following functions:

[0089] ⑴ Uniqueness of topological signature: Since the adjacent matrix of a graph is one-to-one corresponding to itself, it has uniqueness of topological signature in practical applications, calculations, and topological identity authentication.

[0090] ⑵ "One-to-many" topological signature key: The full coding topological matrix is not one-to-one corresponding to the topological coding graph. Therefore, a full coding topological matrix usually corresponds to multiple non-isomorphic topological coding graphs, resulting in the establishment of a "one-to-many" topological signature key.

[0091] ⑶ Graph homomorphism graph set: The full coding topological matrix corresponds to the graph set of the topological coding graph, realizing the graph homomorphism of the topological coding graph, not only realizing the privacy and security of cloud computing data, but also realizing the diversity, complexity, and computational security of the asymmetric topological coding graph.

[0092] In an optional embodiment, the S300 further includes:

[0093] S350, exporting the topological signature string pairs and topological digital string pairs of the adjacent matrix, e - adjacent matrix and full - coding matrix of the topological coding graph;

[0094] S351, generating a coding - graph public key and a coding - graph private key based on the topological signature string pairs and topological digital string pairs of the adjacent matrix, e - adjacent matrix and full - coding matrix of the topological coding graph;

[0095] S352, exporting the topological signature string pairs and topological digital string pairs of the adjacent matrix, e - adjacent matrix and full - coding matrix of the topological signature of the communication path;

[0096] S353, generating a communication public key and a communication private key based on the topological signature string pairs and topological digital string pairs of the adjacent matrix, e - adjacent matrix and full - coding matrix of the topological signature of the communication path.

[0097] It should be noted that the topological coding graph depends on the adjacent matrix, e - adjacent matrix (technological innovation) and full - coding topological matrix for input and storage in the computer, and corresponding operations are performed. Under matrix similarity operations, the topological signature is unique. The full - coding topological matrix does not have a one - to - one correspondence with the topological coding graph. It corresponds to a set of topological coding graphs, generating a "one - to - many" and "many - to - many" topological signature key group.

[0098] Since the topological coding graph is composed of theoretical knowledge in two essentially different mathematical fields, namely "topological structure" and "mathematical constraints", the uniqueness of the topological structure makes the topological coding graph naturally become a topological signature, just like a mathematical fingerprint, ensuring the uniqueness, provable security and integrity of the topological signature identity.

[0099] In an optional embodiment, the S300 includes:

[0100] S354, sending the coding - graph public key;

[0101] S355, sending the communication public key;

[0102] S356, determining whether a reply message is received;

[0103] S357, if no reply message is received, performing decryption and identification processing through the communication private key.

[0104] It should be noted that the topological signature string pairs and topological digital string pairs are derived from the adjacent matrix, e - adjacent matrix and full - coding matrix of the topological coding graph for key generation. The public key Gnum and private key Snum are generated by encrypting a file using the topological coding graph. The data sender sends the public key Gnum to the data receiver.

[0105] Derive topological signature string pairs and topological digital string pairs using the adjacent matrix, e - adjacent matrix, and full - encoding matrix of the communication path topology encoding graph for making keys, and use topological encoding Figure 2 For the secondary - encrypted file, derive the public key TGnum and the private key TSnum. The private key TSnum is stored in the central platform. During data inspection or exception handling, use TSnum for decryption and identification processing, and send the public key TGnum to both communication parties.

[0106] Meanwhile, when the network topology changes, the topological signature can be adjusted and the key can be regenerated, and the key management process can be simplified by leveraging the characteristics of group operations.

[0107] The digital string and string of the topological signature are used to make the encryption key for the data stream and are associated with the identifier of the data stream. Serialize the topological signature into a string, and then convert it into a fixed - length digital string as the encryption key. During data transmission, use this key to encrypt the data stream to ensure confidentiality and integrity during the transmission process.

[0108] To enhance security, the system stores the key in association with the meta - information of the data packet (such as the topological signatures of the sender and the receiver) to ensure the traceability of the key. In addition, when the network topology changes, the system can regenerate the topological signature and update the key, and simplify the key management process by using the group operation characteristics of the encoding graph group, significantly improving the efficiency and security of encryption and decryption. This method not only adapts to complex network environments but also effectively prevents data theft, tampering, and forgery, providing a flexible, efficient, and scalable security solution for local - area network communication.

[0109] As Figure 2 shown, this application also provides a local - area network overall security encryption and decryption system based on an encoding graph group, including an encryption component and a control component. Generate a public key and a private key through the encryption component. The public key includes a communication public key and an encoding - graph public key, and the private key includes a communication private key and an encoding - graph private key. The control component is communicatively connected to the encryption component and executes the local - area network overall security encryption and decryption method based on an encoding graph group as described in any one of the first embodiments through the control component.

[0110] It should be noted that the control component monitors in real - time the changes in the communication relationships between communities in the local - area network. When a new communication path is detected, allocate a communication zero - element for this communication path, and use step S100 to generate a topological encoding graph corresponding to this communication path as the topological signature of this communication path.

[0111] In an optional embodiment, the control component includes a sender and a receiver. Send the public key through the sender and determine whether the receiver has received the public key.

[0112] It should be noted that the sender and the receiver use a combination of public keys and private keys for encryption and decryption, which further enhances the security of the data and makes it more difficult to be cracked during the transmission process.

[0113] After the receiver completes the verification, it uses the public key TGnum to decrypt the first layer of data encryption, then conducts another verification, and uses the public key Gnum to decrypt the second layer of data encryption to obtain the plaintext data. For the data returned by the receiver, the sender uses the private key Snum to obtain the plaintext data after completing the authentication.

[0114] When the data receiver decrypts the data, it needs to authenticate the receiver:

[0115] (i) Authenticate the topology signature of the receiver to identify the identity; (ii) Authenticate the data encryption public key Gnum. The receiver regenerates the key based on the same topology signature and uses the public key Gnum and TGnum with the same encryption algorithm to decrypt the data and restore the original information.

[0116] In addition, when the network topology changes, the central platform promptly coordinates and adjusts. The receiver can complete the identity verification based on the updated topology signature and receive the public keys Gnum and TGnum to verify the data source and decrypt the data.

[0117] For the data returned by the receiver, the sender completes the authentication:

[0118] (i) Authenticate the topology signature of the sender to identify the identity;

[0119] (ii) Authenticate the data encryption private key Snum. Use the private key Snum and the public key TGnum to obtain the plaintext data. When the network topology changes, the central platform promptly coordinates and adjusts, and the sender updates the relevant keys.

[0120] The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to this. Various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those skilled in the art to which the present invention pertains.

Claims

1. A method for overall security encryption and decryption of a local area network based on an encoded graph group, characterized in that, Including: Select an initial base graph, obtain the topological structure changes of the local area network, adjust the initial base graph in real time in combination with the topological structure changes of the local area network to obtain an optimized base graph, and construct a topological graph set based on the optimized base graph; Encode the topological graph set; Define the topological signatures of the local area network communities and the communication paths between the communities, update the signatures when the communication between the local area network communities changes, and generate encryption key pairs with the defined topological signatures to encrypt the data.

2. The overall security encryption and decryption method for local area network based on encoded graph group according to claim 1, characterized in that, Select an initial base graph, obtain the topological structure changes of the local area network, adjust the initial base graph in real time in combination with the topological structure changes of the local area network to obtain an optimized base graph, and construct a topological graph set based on the optimized base graph, including: Randomly select an initial base graph with the number of vertices m, where m is greater than or equal to the number of local area network communities; Obtain the topological structure changes of the local area network to adjust the number of vertices of the initial base graph to obtain an optimized base graph H1; Copy the optimized basic graph m - 1 times, denoted as H2,..., H m , to obtain the topological graph set F = {H1, H2,..., H m}.

3. The overall security encryption and decryption method for a local area network based on an encoded graph group according to claim 2, characterized in that, Encode the topological graph set, including: Define the encoding function of the optimized base graph H1 through Formula 1; h1:V(H1)→{1,2,...,m} Formula 1; Where h1 is the encoding function of the optimized base graph H1, m is the number of vertices of the optimized base graph H1, and V(H1) is the vertex set of the optimized base graph H1; Define the optimized base graphs H2,...,H through Equation 2 m 's encoding function; h i (x) = (h i-1 (x) + 1) (mod m); Equation 2 Among them, h i is the encoding function of the i-th optimized basic graph, where 2 ≤ i ≤ m, and x is the vertex element of the optimized basic graph H i of the vertex element.

4. A method for overall security encryption and decryption of a local area network based on an encoded graph group according to claim 3, characterized in that, Encoding the topological graph set also includes: Combining Formula 1 and Formula 2, construct a topological coding graph group through Formula 3; where h i is the encoding function of the i-th optimized basic graph, H i is the i-th optimized basic graph, and i, j, k ∈ [1, m], x is the vertex element of the optimized basic graph H i , and H k is the specified zero element.

5. A method for overall security encryption and decryption of a local area network based on an encoded graph group according to claim 4, characterized in that, Define the topological signatures of the local area network communities and the communication paths between the communities, update the signatures when the communication between the local area network communities changes, and generate encryption key pairs with the defined topological signatures to encrypt the data, including: For each community in the local area network, randomly assign a topological coding graph to each community in turn, and use the assigned topological coding graph as the topological signature of the community; For any two communities in the local area network, determine whether there is communication between the two communities; If there is communication between the two communities, assign a communication zero element to the communication path; Calculate the topological coding graph corresponding to the communication zero element of the communication path through Formula 3, and record the topological coding graph as the topological signature of the communication path.

6. The overall security encryption and decryption method for a local area network based on an encoded graph group according to claim 5, characterized in that The topological coding graph includes the adjacent matrix, e-adjacent matrix and full coding matrix of the topological coding graph.

7. A method for overall security encryption and decryption of a local area network based on an encoded graph group according to claim 6, characterized in that Define the topological signatures of the local area network communities and the communication paths between the communities, update the signatures when the communication between the local area network communities changes, and generate encryption key pairs with the defined topological signatures to encrypt the data, and also include: Derive the topological signature string pairs and topological digital string pairs of the adjacent matrix, e-adjacent matrix and full coding matrix of the topological coding graph; Make a coding graph public key and a coding graph private key based on the topological signature string pairs and topological digital string pairs of the adjacent matrix, e-adjacent matrix and full coding matrix of the topological coding graph; Derive the topological signature string pairs and topological digital string pairs of the adjacent matrix, e-adjacent matrix and full coding matrix of the topological signature of the communication path; Make a communication public key and a communication private key based on the topological signature string pairs and topological digital string pairs of the adjacent matrix, e-adjacent matrix and full coding matrix of the topological signature of the communication path.

8. A method for overall security encryption and decryption of a local area network based on an encoded graph group according to claim 7, characterized in that Define the topological signature of the local area network community and the communication path between communities, and update the signature when the communication between local area network communities changes. Encrypt the generated encryption key pair data with the defined topological signature, further including: Send the encoded graph public key; Send the communication public key; Judge whether a reply message is received; If no reply message is received, perform decryption and identification processing through the communication private key.

9. A local area network overall security encryption and decryption system based on an encoded graph group, characterized in that, Including: An encryption component that generates a public key and a private key through the encryption component; the public key includes a communication public key and an encoded graph public key, and the private key includes a communication private key and an encoded graph private key; A control component that is communicatively connected to the encryption component and executes the overall security encryption and decryption method for the local area network based on the encoded graph group as described in any one of claims 1 to 8 through the control component.

10. A local area network overall security encryption and decryption system based on an encoded graph group, characterized in that, The control component includes a sending end and a receiving end, and sends the public key through the sending end and judges whether the receiving end receives the public key.

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