Identity authentication method and system based on graph theory

Abstract

The invention discloses an identity authentication method and system based on a graph theory, and the method comprises the steps: firstly, a user and an authorization server preset a numerical value m and a numerical value n, then the authorization server generates a sequence composed of k non-repeated numerical values based on the numerical value n, and then the sequence is used as a private key to be issued to the user; the authorization server generates an undirected graph G (E, V, k) based on a sequence formed by k numerical values, and broadcasts the undirected graph G (E, V, k); the user verifies whether the private key owned by the user represents a k-maximum group of the broadcasted undirected graph G (E, V, k), and if not, the private key is returned and regenerated; if so, the user acknowledges the validity of the authorization. According to the method, the graph theory problem is taken as the complexity of NP completeness, and an attacker is difficult to find the maximum clique in the graph without a private key, so that an illegal user is effectively prevented from pretending to be a legal user for identity authentication; therefore, the method provided by the invention has higher security assurance in the aspect of identity authentication, and effectively resists various attack means.

Description

Technical Field

[0001] The present invention relates to the technical field of cryptography, and in particular to an identity authentication method and system based on graph theory. Background Art

[0002] The public-private key cryptography system is the foundation of modern cryptography, which uses a pair of public and private keys to achieve information encryption and identity authentication. The public key can be published publicly, while the private key is kept secret by the user. The public key is used to encrypt information, and only the user with the private key can decrypt the information. Similarly, the private key can be used to generate a digital signature, while the public key can be used to verify the signature, thereby ensuring the authenticity and integrity of the source of the information.

[0003] The public key can be used to encrypt messages that can only be decrypted using the private key. Known public key encryption systems rely on cryptographic algorithms based on mathematical problems. For example, the RSA public key encryption system relies on the difficulty of integer factorization, and the elliptic curve-based public key encryption relies on the difficulty of discrete logarithms. However, with the development of quantum technology, the most widely used public key cryptosystems, namely RSA and elliptic curve cryptography (ECC), will be cracked by universal quantum computers and become no longer secure.

[0004] Cryptography based on NP problem solutions is one of the hot topics of research. It uses the difficulty of NP problems to build a secure identity authentication mechanism. NP problems refer to problems whose solutions can be verified in polynomial time on non-deterministic Turing machines, but finding the solution may take exponential time. By using the solution to the NP problem as the user's private key and the problem itself as the public key, the user can prove his identity by providing his private key, while it is difficult for an attacker to find the solution to the problem without the private key.

[0005] Graph theory problems have unique advantages in cryptography based on NP problem solutions because they can provide rich and diverse structures and characteristics, thereby building more secure and flexible authentication protocols. Compared with other NP problems, graph theory problems have the following advantages in authentication: graph theory problems can describe various complex relationships, such as social networks, transportation networks, communication networks, etc., providing a rich structural foundation for building flexible authentication protocols; graph theory problems can control the difficulty of the problem by adjusting the structural parameters of the graph, such as the number of nodes, the number of edges, the edge weights, etc., to meet different security requirements; high resistance to attacks, some problems in graph theory problems, such as the maximum clique problem, are highly complex, and even when the solution is known, it is difficult for attackers to find other solutions, thereby improving the security of authentication.

[0006] It can be seen that graph theory problems have potential application value in the field of cryptography; however, there is currently no method to use graph theory problems to generate private keys and public keys for further identity authentication, which makes it difficult to promote and develop in practical applications. Summary of the invention

[0007] Purpose of the invention: In order to solve the relevant technical problems raised in the background technology, the purpose of the present invention is to provide an identity authentication method and system based on graph theory. The method utilizes the complexity and controllability of graph theory problems to provide users with safer and more reliable identity authentication services; and it solves the problem that the public key and private key of the current cryptographic system are easily cracked by quantum computers; at the same time, the method is flexible and easy to use, and can be easily integrated into the existing identity authentication system, thereby improving the security of identity authentication and expanding its scope of application.

[0008] Technical solution: The present invention provides an identity authentication method based on graph theory, comprising the following steps:

[0009] (1) Generate a private key: First, the user and the authorization server pre-set two values ​​m and n. Then the authorization server generates a sequence of k non-repeating values ​​based on the value n, and then issues the generated sequence to the user as a private key, denoted as key. The maximum value of the sequence does not exceed n.

[0010] (2) Generate a public key: The authorization server generates an undirected graph G(E, V, k) based on a sequence of k numerical values, where E represents a set of edges, with a total of m edges; V represents a set of nodes, with a total of n nodes; and k represents the maximum clique of the undirected graph, with k nodes. Then, the authorization server broadcasts the generated undirected graph G(E, V, k).

[0011] (3) Private key verification: The user verifies whether the private key he / she owns represents a k-maximal clique of the broadcast undirected graph G(E, V, k). If not, return to step (1) to regenerate the private key. If yes, the user acknowledges the validity of the authorization.

[0012] (4) Identity authentication: When a user needs to authenticate himself to the authentication server, he sends the private key to the authentication server. The authentication server obtains the corresponding undirected graph G(E,V,k) from the broadcast and verifies whether the obtained private key represents a k-maximal clique in the undirected graph G(E,V,k). If so, the identity authentication is passed; otherwise, the identity authentication is rejected.

[0013] Furthermore, the specific process steps of the authorization server generating an undirected graph G(E, V, k) based on a sequence consisting of k numerical values ​​are as follows:

[0014] 1) First, the authorization server generates an n×n adjacency matrix, assigns all matrix elements except the diagonal elements in the adjacency matrix to 1, and assigns the matrix elements of the diagonal elements to 0;

[0015] 2) The authorization server randomly generates two unequal numbers p and q (p≠q and p,q≤n) that are both not greater than n; then the two numbers p and q are judged. If both numbers p and q belong to the private key, the authorization server does not perform any operation; if both numbers p and q do not belong to the private key, the authorization server changes the values ​​of the matrix element (p,q) in the pth row and qth column of the adjacency matrix and the matrix element (q,p) in the qth row and pth column of the matrix to 0;

[0016] 3) The authorization server repeats step 2) until only 2m matrix elements in the generated n×n adjacency matrix are assigned a value of 1, and then uses this matrix as the adjacency matrix representing an undirected graph G(E,V,k) and outputs it as the public key.

[0017] Furthermore, the step 1) further comprises: counting the matrix elements assigned with a value of 1 in the n×n adjacency matrix, recording the count value as i, and the initial value of i is i(0)=n×nn;

[0018] Step 2) also includes: in response to the authorization server changing the values ​​of the matrix element (p, q) in the pth row and qth column of the adjacency matrix and the matrix element (q, p) in the qth row and pth column of the matrix to 0 for the ath time, the count value i is updated to i(a)=i(a-1)-2=n×nn-2a.

[0019] Furthermore, the specific process of the authorization server generating a sequence consisting of k non-repeating numerical values ​​based on the numerical value n is as follows:

[0020] 1) The authorization server converts the value n into a binary data format, and obtains a data length x of the binary data format of the value n;

[0021] 2) The authorization server generates k true random numbers with a length not greater than x, and then converts the generated k true random numbers into k values ​​that are consistent with the base of the value n; then the k values ​​are judged, and if there is a value greater than n or two or more repeated values, the corresponding value is discarded, and the authorization server regenerates the corresponding number of true random numbers with a length not greater than x according to the number of discarded values, and then converts the values ​​and judges; repeats the above operation until k values ​​less than or equal to n and non-repeating are generated;

[0022] 3) The authorization server combines the k generated values ​​into a sequence.

[0023] Furthermore, the specific process of the authorization server generating a sequence consisting of k non-repeating numerical values ​​based on the numerical value n is as follows:

[0024] a) The authorization server converts the value n into a binary data format, and obtains a data length x of the binary data format of the value n;

[0025] b) The authorization server generates a true random number with a length no greater than x, and then converts the generated true random number into a value consistent with the base of the value n, and then judges the converted value. If the value is greater than n or has been obtained through true random number conversion before, it is discarded and a new true random number is generated;

[0026] c) Repeat step b) multiple times until k values ​​less than or equal to n and not repeated are obtained;

[0027] d) The authorization server combines the k generated values ​​into a sequence.

[0028] Furthermore, the combining of the generated k numerical values ​​to form a sequence means: arranging and combining the k numerical values ​​in order to form a sequence according to the order in which the k numerical values ​​are generated; or, after the authorization server generates k numerical values, arranging the k numerical values ​​in random order and then combining them to form a sequence.

[0029] The present invention also includes a system for the identity authentication method based on graph theory according to the above claims, the system comprising users, an authentication server and an authorization server connected in pairs;

[0030] The user receives the private key issued by the authorization server and uses the private key to prove the legitimacy of his identity to the authentication server;

[0031] The authorization server is used to generate private keys and public keys, issue the generated private keys to users, and broadcast the generated public keys;

[0032] The authentication server is used to verify the legitimacy of the user's identity based on the user's private key.

[0033] Further, the authorization server includes an input unit, a data format conversion unit, a true random number generator, a sequence generation unit, a key issuance unit and a transmission unit connected in sequence, the sequence generation unit is also connected to an undirected graph generation unit, and the undirected graph generation unit is connected to the key issuance unit;

[0034] The input unit is used to input two preset numerical values ​​m and n;

[0035] The data format conversion unit is used to convert the value n into a binary data format, and obtain the data length of the binary data format of the value n as x;

[0036] The true random number generator is used to generate true random numbers;

[0037] The sequence generation unit is used to convert the generated true random number into a value consistent with the base of the value n and make a judgment until k values ​​less than or equal to n and not repeated are obtained; and the generated k values ​​are combined to form a sequence;

[0038] The undirected graph generation unit is used to generate an undirected graph according to the generated sequence;

[0039] The key issuing unit is used to transmit the received private key and public key to the transmission unit;

[0040] The transmission unit is used to issue the private key to the user and broadcast the public key.

[0041] Beneficial effects of the present invention:

[0042] (1) Based on the complexity of graph theory problems as NP-complete, it is difficult for an attacker to find the largest group in the graph without a private key, thereby effectively preventing illegal users from impersonating legitimate users for identity authentication; this makes the method of the present invention have higher security in identity authentication and effectively resists various attack methods;

[0043] (2) By controlling the structural parameters of the graph, such as the number of nodes and edges, the difficulty of identity authentication can be adjusted to meet different security requirements. For example, for a highly sensitive system, the difficulty of identity authentication can be increased by increasing the complexity of the graph. This controllability enables the method of the present invention to flexibly adjust parameters according to actual application scenarios to achieve optimal security. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A schematic diagram of the identity authentication method based on graph theory of the present invention;

[0045] Figure 2 A schematic diagram of an identity authentication system based on graph theory of the present invention;

[0046] Figure 3 This is a schematic diagram of the authorization server structure. DETAILED DESCRIPTION

[0047] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0048] The present invention provides an identity authentication method based on graph theory, the process of which is described as follows: Figure 1 As shown, the present invention utilizes the characteristics of graph theory problems to provide users with passwords that are difficult to crack, thereby constructing an identity authentication scheme with security advantages, which specifically includes the following steps:

[0049] (1) Generate a private key: First, the user and the authorization server pre-set two values ​​m and n. Then the authorization server generates a sequence of k non-repeating values ​​based on the value n, and then issues the generated sequence to the user as a private key, denoted as key. The maximum value of the sequence does not exceed n.

[0050] The authorization server, as the generator of the sequence, issues the generated sequence as a private key to the user. Specifically, the specific process of generating a sequence consisting of k non-repeating values ​​based on the value n is as follows:

[0051] 1) A data format conversion unit is provided in the authorization server, which is used to convert the value into a binary format. First, the value n is converted into a binary data format, and the data length of the binary data format of the value n is obtained as x;

[0052] 2) The authorization server is provided with a true random number generator for generating k true random numbers with a length not greater than x, and then converting the generated k true random numbers into k values ​​consistent with the base of the value n; then judging the k values, if there is a value greater than n or two or more repeated values, the corresponding values ​​are discarded, and the authorization server regenerates the corresponding number of true random numbers with a length not greater than x according to the number of discarded values, and then converts the values ​​and judges; repeating the above operation until k values ​​less than or equal to n and not repeated are generated;

[0053] 3) The authorization server combines the k generated values ​​into a sequence.

[0054] Or the specific process of the authorization server generating a sequence of k non-repeating values ​​based on the value n is as follows:

[0055] a) The authorization server converts the value n into a binary data format, and obtains a data length x of the binary data format of the value n;

[0056] b) The authorization server generates a true random number with a length no greater than x, and then converts the generated true random number into a value consistent with the base of the value n, and then judges the converted value. If the value is greater than n or has been obtained through true random number conversion before, it is discarded and a new true random number is generated;

[0057] c) Repeat step b) multiple times until k values ​​less than or equal to n and not repeated are obtained;

[0058] d) The authorization server combines the k generated values ​​into a sequence.

[0059] Combining the generated k numerical values ​​to form a sequence means: arranging and combining the k numerical values ​​in order to form a sequence according to the order in which the k numerical values ​​are generated; or, after the authorization server generates the k numerical values, arranging the k numerical values ​​in random order and then combining them to form a sequence.

[0060] (2) Generate a public key: Based on the sequence of k numerical values, the authorization server regards it as a representation of a k-maximum clique in an undirected graph and generates an undirected graph G(E, V, k), where E represents a set of edges, with a total of m edges; V represents a set of nodes, with a total of n nodes, n>k; k represents that the maximum clique of the undirected graph has k nodes; then, the authorization server broadcasts the generated undirected graph G(E, V, k);

[0061] The specific process steps for generating an undirected graph G(E,V,k) are as follows:

[0062] 1) First, the authorization server generates an n×n adjacency matrix, assigns all matrix elements except the diagonal elements in the adjacency matrix to 1, and assigns the matrix elements of the diagonal elements to 0;

[0063] The n×n matrix is ​​an adjacency matrix. The matrix element (i, j) in the i-th row and j-th column of the adjacency matrix represents the connection relationship between node i and node j (i≠j). If there is an edge between node i and node j, the value of the matrix element (i, j) is 1; if there is no edge between node i and node j, the value of the matrix element (i, j) is 0; the value of the diagonal element is 0; of course, the matrix elements assigned a value of 1 in the n×n adjacency matrix can be counted, and the count value is recorded as i, and the initial value of i is i(0)=n×nn;

[0064] 2) The authorization server uses a true random number generator to randomly generate two unequal numerical values ​​p and q (p≠q and p, q≤n) that are both not greater than n; then the two numbers p and q are judged. If the two numbers p and q both belong to the private key key, the authorization server does not perform any operation; if the two numbers p and q do not both belong to the private key key, the authorization server changes the values ​​of the matrix element (p,q) in the pth row and qth column of the adjacency matrix and the matrix element (q,p) in the qth row and pth column of the matrix to 0; that is, in response to the authorization server changing the values ​​of the matrix element (p,q) in the pth row and qth column of the adjacency matrix and the matrix element (q,p) in the qth row and pth column of the matrix to 0 for the ath time. Then, the count value i is updated to i(a)=i(a-1)-2=n×nn-2a.

[0065] 3) The authorization server repeats step 2) until only 2m matrix elements in the generated n×n adjacency matrix are assigned a value of 1. This can also be regarded as comparing the size of i(a) and 2m. Step 2) is repeated until i(a) is equal to 2m, and then this matrix is ​​used as the adjacency matrix representing an undirected graph G(E,V,k) and output as the public key.

[0066] (3) Private key verification: The user verifies whether the private key he / she owns represents a k-maximal clique of the broadcast undirected graph G(E, V, k). If not, return to step (1) to regenerate the private key. If yes, the user acknowledges the validity of the authorization.

[0067] The maximum clique problem refers to finding the largest clique in an undirected graph. A clique is defined as a subset of the set V of undirected graph nodes, where each node in the subset is connected to any node in the subset by an edge; a k-maximum clique means that the largest clique in the clique of an undirected graph has k nodes. The maximum clique problem is an NP-complete problem, and its solution is a k-maximum clique, which is represented in this patent as the set of numbers of the nodes involved in the maximum clique.

[0068] The method for a user to verify whether the private key he owns represents a k-maximum clique of the broadcasted undirected graph G(E,V,k) can be achieved through the Bron-Kerbosch algorithm or the backtracking method.

[0069] (4) Identity authentication: When a user needs to authenticate himself to the authentication server, he sends the private key to the authentication server. The authentication server obtains the corresponding undirected graph G(E,V,k) from the broadcast and verifies whether the obtained private key represents a k-maximal clique in the undirected graph G(E,V,k). If so, the identity authentication is passed; otherwise, the identity authentication is rejected.

[0070] It can be seen that the identity authentication method based on graph theory proposed in the present invention is based on the complexity of graph theory problems as NP-complete. It is difficult for attackers to find the largest group in the graph without a private key, thereby effectively preventing illegal users from impersonating legal users for identity authentication; this makes the method of the present invention have higher security in identity authentication and effectively resists various attack methods. The present invention can also adjust the difficulty of identity authentication by controlling the structural parameters of the graph, such as the number of nodes, the number of edges, etc., to meet different security requirements. For example, for highly sensitive systems, the difficulty of identity authentication can be increased by increasing the complexity of the graph. This controllability enables the method of the present invention to flexibly adjust parameters according to actual application scenarios to achieve optimal security.

[0071] The present invention also proposes a system for identity authentication method based on the above graph theory, such as Figure 2As shown, the system includes two-way connected users 1, authentication server 2 and authorization server 3; user 1, the owner of the private key, is used to receive the private key issued by the authorization server 3, and prove the legitimacy of its identity to the authentication server 2 through the private key; the authorization server 3 is a private key and public key generation and issuance agency, which is used to generate private keys and public keys, and issue the generated private key to user 1, and broadcast the generated public key; the authentication server 2 is an identity legitimacy certification agency, which is used to verify the legitimacy of the identity of user 1 based on the user's private key, and the user 1 who passes its authentication process is a legitimate user.

[0072] like Figure 3 As shown, the authorization server 3 includes an input unit 31, a data format conversion unit 32, a true random number generator 33, a sequence generation unit 34, a key issuance unit 35 and a transmission unit 36 ​​which are connected in sequence, the sequence generation unit 34 is also connected to an undirected graph generation unit 37, and the undirected graph generation unit 37 is connected to the key issuance unit 35;

[0073] The input unit 31 is used to input two preset values ​​m and n;

[0074] The data format conversion unit 32 is used to convert the value n into a binary data format, and obtain the data length of the binary data format of the value n as x;

[0075] The true random number generator 33 is used to generate true random numbers;

[0076] The sequence generation unit 34 is used to convert the generated true random number into a value consistent with the base of the value n and make a judgment until k values ​​less than or equal to n and not repeated are obtained; and the generated k values ​​are combined to form a sequence;

[0077] The undirected graph generating unit 37 is used to generate an undirected graph according to the generated sequence;

[0078] The key issuing unit 35 is used to transmit the received private key and public key to the transmission unit 36;

[0079] The transmission unit 36 ​​is used to issue the private key to the user 1 and broadcast the public key.

[0080] The present invention is flexible and easy to use, and can be conveniently integrated into an existing identity authentication system, thereby improving the security of identity authentication and expanding its application scope.

Claims

1. A graph-based identity authentication method, characterized in that: The following steps are involved: (1) Generate a private key: First, the user and the authorization server pre-set two values ​​m and n. Then the authorization server generates a sequence of k non-repeating values ​​based on the value n, and then issues the generated sequence to the user as a private key, denoted as key. The maximum value of the sequence does not exceed n. (2) Generate a public key: The authorization server generates an undirected graph G(E, V, k) based on a sequence of k numerical values, where E represents a set of edges, with a total of m edges; V represents a set of nodes, with a total of n nodes; and k represents the maximum clique of the undirected graph, with k nodes. Then, the authorization server broadcasts the generated undirected graph G(E, V, k). (3) Private key verification: The user verifies whether the private key he / she owns represents a k-maximal clique of the broadcast undirected graph G(E, V, k). If not, return to step (1) to regenerate the private key. If yes, the user acknowledges the validity of the authorization. (4) Identity authentication: When a user needs to authenticate himself to the authentication server, he sends the private key to the authentication server. The authentication server obtains the corresponding undirected graph G(E,V,k) from the broadcast and verifies whether the obtained private key represents a k-maximal clique in the undirected graph G(E,V,k). If so, the identity authentication is passed; otherwise, the identity authentication is rejected.

2. According to claim 1, a method for identity authentication based on graph theory is characterized in that: The specific process steps of the authorization server generating an undirected graph G(E, V, k) based on a sequence of k numerical values ​​are as follows: 1) First, the authorization server generates an n×n adjacency matrix, assigns all matrix elements except the diagonal elements in the adjacency matrix to 1, and assigns the matrix elements of the diagonal elements to 0; 2) The authorization server randomly generates two unequal numbers p and q (p≠q and p,q≤n) that are both not greater than n; then the two numbers p and q are judged. If both numbers p and q belong to the private key, the authorization server does not perform any operation; If the two numbers p and q do not both belong to the private key, the authorization server changes the values ​​of the matrix element (p,q) in the pth row and qth column of the adjacency matrix and the matrix element (q,p) in the qth row and pth column of the matrix to 0; 3) The authorization server repeats step 2) until only 2m matrix elements in the generated n×n adjacency matrix are assigned a value of 1, and then uses this matrix as the adjacency matrix representing an undirected graph G(E,V,k) and outputs it as the public key.

3. According to claim 2, a method for identity authentication based on graph theory is characterized in that: The step 1) further includes: counting the matrix elements assigned a value of 1 in the n×n adjacency matrix, recording the count value as i, and the initial value of i is i(0)=n×nn; Step 2) also includes: in response to the authorization server changing the values ​​of the matrix element (p, q) in the pth row and qth column of the adjacency matrix and the matrix element (q, p) in the qth row and pth column of the matrix to 0 for the ath time, the count value i is updated to i(a)=i(a-1)-2=n×nn-2a.

4. The identity authentication method based on graph theory according to claim 1, characterized in that: The specific process of the authorization server generating a sequence consisting of k non-repeating values ​​based on the value n is as follows: 1) The authorization server converts the value n into a binary data format, and obtains a data length x of the binary data format of the value n; 2) The authorization server generates k true random numbers with a length not greater than x, and then converts the generated k true random numbers into k values ​​that are consistent with the base of the value n; then the k values ​​are judged, and if there is a value greater than n or two or more repeated values, the corresponding value is discarded, and the authorization server regenerates the corresponding number of true random numbers with a length not greater than x according to the number of discarded values, and then converts the values ​​and judges; repeats the above operation until k values ​​less than or equal to n and non-repeating are generated; 3) The authorization server combines the k generated values ​​into a sequence.

5. The identity authentication method based on graph theory according to claim 1, characterized in that: The specific process of the authorization server generating a sequence consisting of k non-repeating values ​​based on the value n is as follows: a) The authorization server converts the value n into a binary data format, and obtains a data length x of the binary data format of the value n; b) The authorization server generates a true random number with a length no greater than x, and then converts the generated true random number into a value consistent with the base of the value n, and then judges the converted value. If the value is greater than n or has been obtained through true random number conversion before, it is discarded and a new true random number is generated; c) Repeat step b) multiple times until k values ​​less than or equal to n and not repeated are obtained; d) The authorization server combines the k generated values ​​into a sequence.

6. The identity authentication method based on graph theory according to claim 4 or 5, characterized in that: Combining the generated k numerical values ​​to form a sequence means: arranging and combining the k numerical values ​​in order to form a sequence according to the order in which the k numerical values ​​are generated; or, after the authorization server generates k numerical values, arranging the k numerical values ​​in random order and then combining them to form a sequence.

7. A system based on the graph-theory-based identity authentication method according to any one of claims 1 to 6, characterized in that: The system includes users, authentication servers and authorization servers connected in pairs; The user receives the private key issued by the authorization server and uses the private key to prove the legitimacy of his identity to the authentication server; The authorization server is used to generate private keys and public keys, issue the generated private keys to users, and broadcast the generated public keys; The authentication server is used to verify the legitimacy of the user's identity based on the user's private key.

8. The system according to claim 7, characterized in that The authorization server comprises an input unit, a data format conversion unit, a true random number generator, a sequence generation unit, a key issuance unit and a transmission unit which are connected in sequence, wherein the sequence generation unit is also connected to an undirected graph generation unit, and the undirected graph generation unit is connected to the key issuance unit; The input unit is used to input two preset numerical values ​​m and n; The data format conversion unit is used to convert the value n into a binary data format, and obtain the data length of the binary data format of the value n as x; The true random number generator is used to generate true random numbers; The sequence generation unit is used to convert the generated true random number into a value consistent with the base of the value n and make a judgment until k values ​​less than or equal to n and not repeated are obtained; and the generated k values ​​are combined to form a sequence; The undirected graph generation unit is used to generate an undirected graph according to the generated sequence; The key issuing unit is used to transmit the received private key and public key to the transmission unit; The transmission unit is used to issue the private key to the user and broadcast the public key.

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