Interactive user identity authentication method based on three-color problem

Abstract

The invention discloses an interactive user identity authentication method based on a three-color problem. The interactive user identity authentication method comprises the following steps that a user generates an undirected graph H composed of a point set and an edge set and a three-color graph corresponding to the undirected graph H; a user selects replacement of a coloring mode for the uncolored three-color diagram in advance, and generates a first random number for commitment; the first verification party interacts with the first communication equipment, and the second verification party interacts with the second communication equipment; and after repeating for m rounds, the first verification party and the second verification party carry out verification, and if all rounds of verification are passed, the user is recognized to have the three-color graph corresponding to the undirected graph H, that is, the identity information proof of the user is accepted. According to the method, through multiple rounds of interaction and in combination with the relativistic principle, the possibility that attackers destroy protocol security through mutual communication is limited; and the verification process is ensured to be safe and reliable, and meanwhile, the method also has relatively high efficiency, and is suitable for various scenes needing high security levels.

Description

Technical Field

[0001] The present invention relates to the technical field of identity security, and particularly relates to an interactive user identity authentication method based on the three-color problem. Background Art

[0002] Zero-knowledge proof is an important cryptographic tool that allows a prover to prove to a verifier that they know a certain secret without revealing any information about the secret itself to the verifier. This makes zero-knowledge proof have broad application prospects in fields such as identity authentication, digital signature, and access control. Existing zero-knowledge proof protocols, such as those based on ZK-SNARKs or ZK-STARKs, have achieved certain success in practical applications. However, most of these schemes rely on complex mathematical assumptions, such as the discrete logarithm problem or the elliptic curve discrete logarithm problem, and their security faces challenges in the face of increasingly powerful computing capabilities, especially the threat of quantum computing. Therefore, exploring zero-knowledge proof schemes resistant to quantum computing attacks has become an important research direction in the field of cryptography.

[0003] The three-color problem is a classic NP-complete problem, and its decision problem is to determine whether a graph can be colored with three colors such that any two adjacent vertices have different colors. The NP-completeness of the three-color problem means that there is currently no known algorithm that can solve this problem in polynomial time, and its computational complexity increases exponentially with the growth of the graph size; this computational complexity provides a solid foundation for constructing a secure and reliable cryptographic system.

[0004] In summary, in order to address the security threats posed by quantum computing to existing identity authentication mechanisms using zero-knowledge proof, how to combine the three-color problem with zero-knowledge proof technology to effectively resist various potential attacks (including quantum attacks) has become a technical problem that the industry urgently needs to solve. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide an interactive user identity authentication method based on the three-color problem, which solves the problem of insufficient security of existing identity authentication mechanisms using zero-knowledge proof in the face of quantum computing attacks. The present invention combines the three-color problem with zero-knowledge proof technology to construct a secure and efficient identity authentication mechanism that can resist quantum attacks, effectively improving the security of the identity authentication mechanism and resisting various potential attacks (including quantum attacks).

[0006] Technical Solution: An interactive user identity authentication method based on the three-color problem of the present invention includes the following steps:

[0007] (1) Generate a three - color graph: The user generates an undirected graph \(H\) consisting of a set of vertices and a set of edges, and its corresponding three - color graph, and uses this three - color graph as the user's identity information; then the uncolored three - color graph is made public.

[0008] (2) Preparation stage: The user pre - selects a permutation of a coloring method for the uncolored three - color graph according to the three - color graph, and generates a first random number for commitment; then, the user uses two communication devices to interact with two verifiers, that is, the user uses the first communication device to go to the first verifier for subsequent interaction, and the user uses the second communication device to go to the second verifier for subsequent interaction.

[0009] (3) Interaction stage: The first verifier sends a randomly generated second random number to the first communication device, and the first communication device calculates the commitment value and replies to the first verifier; the second verifier sends randomly generated interaction content to the second communication device, and the second communication device generates a reply according to the interaction content and sends it to the second verifier.

[0010] (4) Verification stage: Repeat steps (2) - (3) for \(m\) rounds, where the permutation of the coloring method and the first random number in each round are different from other rounds; then, the first verifier and the second verifier integrate the information of all rounds for verification. If all rounds of verification pass, the first verifier and the second verifier recognize that the user has the three - color graph corresponding to the undirected graph \(H\), that is, accept the user's identity information proof; otherwise, the first verifier and the second verifier do not recognize that the user has the three - color graph corresponding to the undirected graph \(H\), that is, reject the user's identity information proof.

[0011] Further, the generation process of the three - color graph in step (1) is as follows:

[0012] 1) The vertex set of the undirected graph \(H\) is denoted as \(U\), and the edge set is denoted as \(F\); the number of vertices of the undirected graph \(H\) is denoted as \(|U|\), and the number of edges is denoted as \(|F|\); among them, each edge \(f\in F\) of the undirected graph \(H\) is represented by an unordered pair \((a, b)\), \(a, b\in U\), which are the connecting vertices \(a\) and \(b\) of the edge \(f\).

[0013] 2) Then, for each vertex \(w\in U\) of the undirected graph \(H\), select a value from \(\{0, 1, 2\}\) for assignment, representing the selection of a coloring, that is, \(d(w)\in\{0, 1, 2\}\).

[0014] 3) For any two different vertices \(u, v\in U(u\neq v)\) in the undirected graph \(H\), if their initial colors are different, that is, \(d(u)\neq d(v)\), then with probability \(p\), add an edge \((u, v)\) between vertices \(u\) and \(v\) to the edge set \(F\); where \(0\lt p\lt1\).

[0015] 4) Repeat step 3) multiple times, and then verify whether the generated graph K(U,F) is connected. If the graph K(U,F) is connected, then this graph is the generated three-color graph; otherwise, continue to repeat step 3) multiple times until the generated graph K(U,F) is connected.

[0016] Furthermore, verifying whether the generated graph K(U,F) is connected in step 4) means: determining whether there exists a path from any vertex to all other vertices in the graph K(U,F). If so, then the graph K(U,F) is connected; otherwise, the graph K(U,F) is not connected.

[0017] Furthermore, in step (2), when the user pre-selects a permutation of the coloring method for the uncolored three-color graph and generates the first random number for commitment, it means:

[0018] A: Color permutation selection: The user pre-selects a permutation π of the coloring method for the uncolored three-color graph according to the three-color graph. This permutation π is a permutation acting on the three colors {0, 1, 2}, and the coloring of each vertex w ∈ U after permutation is represented as π[d(w)] ∈ {0, 1, 2};

[0019] B: First random number generation: The user pre-generates a first random number for each vertex of each round of the three-color graph respectively. The set of first random numbers generated for all vertices in one round is represented as B = {b w}, w ∈ U, where b w belongs to the finite field F Q , and Q is a pre-selected prime number.

[0020] Furthermore, the spatial distance between the first communication device and the second communication device is D.

[0021] Furthermore, the specific process steps of step (3) are:

[0022] At time t 1 , the first verifier randomly generates |U| numbers belonging to the finite field F Q for each vertex, represented as X = {x w}, w ∈ U, and sends them to the first communication device; the first communication device calculates the commitment value of each vertex's coloring, represented as A = {a w}, w ∈ U, where a w = x w · π[d(w)] + b w , and then sends the commitment value to the first verifier. The first verifier records t 1 , X, A, and the time t 2 when it receives A;

[0023] At time t 3At this moment, the second verifier randomly selects an edge C=(i,j)∈F of the three-color graph as the interaction content and sends it to the second communication device. The second communication device sends two numbers (b i ,b j ) as the reply Y to the second verifier. The second verifier records t 3 , C, Y and the moment t 4 when Y is received.

[0024] Furthermore, the specific process of the first verifier and the second verifier integrating the information of all rounds for verification in step (4) is as follows:

[0025] The first verifier and the second verifier integrate the information of all rounds for verification:

[0026] (a) Relativity constraint verification: The first verifier and the second verifier need to verify that in each round of interaction, whether |t 1 -t 4 | and |t 2 -t 3 | are less than D / c, where c represents the speed of light in a vacuum; if not satisfied, end the verification and announce that the verification fails; otherwise, if satisfied, continue to the next step of verification;

[0027] (b) Three-color verification: From the random numbers (x i ,x j ) and the commitment values (a i ,a j ) and the reply Y=(b i ,b j ) in each round, calculate the permuted coloring π[d(i)]=(a i -b i ) / x i and π[d(j)]=(a j -b j ) / x j , and judge whether π[d(i)]≠π[d(j)]; if so, the verification passes; otherwise, end the verification and announce that the verification fails;

[0028] When the verification of all rounds passes, the first verifier and the second verifier recognize that the user owns the three-color graph corresponding to the undirected graph H and recognize the user's identity information, that is, accept the user's identity information proof; otherwise, the first verifier and the second verifier do not recognize that the user owns the three-color graph corresponding to the undirected graph H, that is, reject the user's identity information proof.

[0029] Furthermore, the Q is a pre-selected prime number, which is represented by the following expression:

[0030] log 2 Q=[9 + 4log2 3 - 3 log 2 ε 1

[0031] where [], [] represents rounding up, and ε 1 represents the probability that the verifier obtains the coloring scheme from the commitment value. Further, the number of rounds m is represented by the following expression:

[0032] m = [-ln(ε 2 ) * |F|]

[0033] where ε 2 represents the probability that a user without a correct coloring scheme is recognized by the verifier.

[0034] Advantages of the present invention:

[0035] (1) The present invention utilizes a commitment scheme combined with the principle of relativity to implement a secure and efficient identity authentication mechanism, which can effectively resist various attack means including quantum attacks. Without revealing the solution to the three - color problem, the user can prove to the verifier that they know the solution to the problem;

[0036] (2) The method of the present invention restricts the possibility of an attacker destroying the security of the protocol by communicating with each other through multiple - round interactions and combining the principle of relativity; moreover, while ensuring the security and reliability of the verification process, it also has high efficiency. The number of multiple - round interactions is proportional to the number of edges of the graph and can be adjusted according to actual needs to balance security and efficiency;

[0037] (3) Since the three - color problem belongs to an NP - complete problem and can be transformed into any NP problem in polynomial time, the method proposed by the present invention is also applicable to zero - knowledge proofs of other NP problems and applicable to various scenarios requiring a high security level, etc. Brief Description of the Drawings

[0038] Figure 1 is a schematic diagram of a coloring scheme in the three - color graph of the present invention;

[0039] Figure 2 is a schematic diagram of the interactive user identity authentication method based on the three - color problem of the present invention;

[0040] Figure 3 is another three - color graph generated after permuting the coloring of the original three - color graph; Detailed Embodiments

[0041] The following further describes the present invention in conjunction with the drawings and embodiments:

[0042] ​The existing identity authentication mechanisms using zero - knowledge proofs have obvious security vulnerabilities and are difficult to resist increasingly complex attack methods. Especially when facing quantum computing attacks, their security is insufficient. Based on the current problems, how to combine the three - color problem with zero - knowledge proof technology to effectively resist various potential attacks (including quantum attacks) has become a technical problem that the industry urgently needs to solve.

[0043] In view of this, the present application proposes an interactive user identity verification method based on the three - color problem. This method constructs a secure, efficient, and quantum - attack - resistant zero - knowledge proof mechanism based on a commitment scheme combined with the theory of relativity, thereby providing reliable security guarantees for identity verification. It specifically includes the following steps:

[0044] (1) Generate a three - color graph: The user generates an undirected graph H composed of a set of vertices and a set of edges and its corresponding three - color graph, and uses this three - color graph as the user's identity information; then publicly disclose the uncolored three - color graph.

[0045] Among them, the generation process of the three - color graph is as follows:

[0046] 1) The vertex set of the undirected graph H is denoted as U, and the edge set is denoted as F; the number of vertices of the undirected graph H is denoted as |U|, and the number of edges is denoted as |F|; among them, each edge f ∈ F of the undirected graph H is represented by an unordered pair (a, b), where a, b ∈ U, and a and b are the connecting vertices of the edge f.

[0047] 2) Then, for each vertex w ∈ U of the undirected graph H, select a value from {0, 1, 2} for assignment, representing choosing a color, that is, d(w) ∈ {0, 1, 2}.

[0048] 3) For any two different vertices u, v ∈ U (u ≠ v) in the undirected graph H, if their initial colors are different, that is, d(u) ≠ d(v), then with probability p, add an edge (u, v) between vertices u and v to the edge set F; where 0 < p < 1, and the value of the probability p will affect the structure and complexity of the finally generated graph.

[0049] 4) Repeat step 3) multiple times. That is, after completing all possible edge additions, then verify whether the generated graph K(U, F) is connected. If the graph K(U, F) is connected, then this graph is the generated three - color graph; otherwise, continue to repeat step 3) multiple times until the generated graph K(U, F) is connected.

[0050] Verifying whether the generated graph K(U, F) is connected means: judging whether there is a path from any vertex to all other vertices in the graph K(U, F). If so, the graph K(U, F) is connected; otherwise, the graph K(U, F) is not connected. Thus, the three - color graph is as Figure 1As shown, it aims to assign one of three colors \(d(w)\in\{0,1,2\}\) to each vertex \(w\in U\) in Figure H, and also satisfy the condition that the colors of the two endpoints \(a\) and \(b\) of any edge \((a,b)\in F\) must be different, i.e., \(d(a)\neq d(b)\);

[0051] (2) Preparation stage: The user pre-selects a permutation of a coloring method for the uncolored three-color graph according to the three-color graph, and generates a first random number for commitment; as Figure 2 shown, then, the user uses two communication devices to interact with two verifiers, that is, the user uses the first communication device to go to the first verifier for subsequent interaction, and the user uses the second communication device to go to the second verifier for subsequent interaction;

[0052] Among them, the user pre-selects a permutation of a coloring method for the uncolored three-color graph according to the three-color graph, and generates a first random number for commitment means:

[0053] A: Color permutation selection: The user pre-selects a permutation \(\pi\) of a coloring method for the uncolored three-color graph according to the three-color graph. This permutation \(\pi\) is a permutation acting on the three colors \(\{0,1,2\}\), ensuring the independence of each round of interaction and preventing the attacker from inferring the information of subsequent rounds by analyzing the information of the previous rounds. After the permutation, the coloring of each vertex \(w\in U\) is represented as \(\pi[d(w)]\in\{0,1,2\}\); among them, the permutation \(\pi\) of the coloring method means permuting the colors of all vertices with the same color in the three-color graph. For example, permute the colors of all vertices originally colored 1 to color 2, and permute the colors of all vertices originally colored 2 to color 1; as Figure 3 shown, in the left three-color graph, the vertex colors of 1, 7, and 3 are the same, and the vertex colors of 2, 8, 9, and 5 are the same; now perform color permutation, and the vertex colors of 1, 7, and 3 are the same but are permuted to different colors. Similarly, the vertex colors of 2, 8, 9, and 5 are the same but are permuted to different colors. The above are 2 kinds of vertex color permutations. Of course, 3 kinds of vertex color permutations can also be performed.

[0054] B: First random number generation: The user pre-generates a first random number for each vertex of each round of the three-color graph respectively. The set of first random numbers generated for all vertices in one round is represented as \(B = \{b w \}, w\in U\), where \(b w \) belongs to the finite field \(F Q \), and \(Q\) is a pre-selected prime number. These random numbers will be used to construct commitments, ensuring the randomness and unpredictability of each round of interaction and preventing the attacker from destroying the security of the protocol by guessing the random numbers;

[0055] All first random numbers belong to the numbers in the finite field \(F Q \), \(Q\) is a pre-selected prime number, and is represented by the following expression:

[0056] log 2 Q = [9 + 4log 2 3 - 3log 2 ε 1

[0057] wherein, [] represents rounding up, and ε 1 represents the probability that the verifier obtains the coloring scheme from the commitment value, which is preset according to the security requirements.

[0058] The user uses two communication devices to interact with two verifiers, that is to say, both the first communication device and the second communication device have all the preparatory stage information of the user, and the spatial distance between the first communication device and the second communication device is D.

[0059] (3) Interaction stage: The first verifier sends a second random number randomly generated to the first communication device, and the first communication device calculates the commitment value and replies to the first verifier; the second verifier sends randomly generated interaction content to the second communication device, and the second communication device generates a reply according to the interaction content and sends it to the second verifier; the specific process steps are as follows:

[0060] At time t 1 , the first verifier randomly generates |U| numbers belonging to the finite field F Q for each vertex, denoted as X = {x w}, w ∈ U, and sends them to the first communication device; the first communication device calculates the commitment value of each vertex coloring, denoted as A = {a w}, w ∈ U, where a w = x w ·π[d(w)] + b w , and then sends the commitment value to the first verifier, and the first verifier records t 1 , X, A and the time t 2 when A is received;

[0061] At time t 3 , the second verifier randomly selects an edge C = (i, j) ∈ F of the three-color graph as the interaction content and sends it to the second communication device, and the second communication device sends two numbers (b i , b j ) as the reply Y to the second verifier, and the second verifier records t 3 , C, Y and the time t 4 when Y is received.

[0062] ​The first verifier and the second verifier use a synchronous timekeeping device provided by satellite signals to determine the exact times when messages are sent and received. Of course, other methods can also be used for time synchronization. For example, optical fibers connecting the first verifier and the second verifier can be used for time synchronization, etc. The first verifier and the second verifier each use a field-programmable gate array (FPGA) to handle tasks such as generating random numbers and sending and receiving messages. The first communication device and the second communication device each use an FPGA to handle tasks such as pre-generating permutations and random numbers, storing, performing operations, and sending and receiving messages.

[0063] (4) Verification stage: Repeat steps (2)-(3) for m rounds, where the permutation and the first random number of the coloring method in each round are different from those in other rounds; the number of rounds m is represented by the following expression:

[0064] m = [-ln(ε 2 ) * |F|]

[0065] where ε 2 represents the probability that a user without a correct coloring scheme is recognized by the verifier, which is preset according to security requirements. After repeating the m-round interaction, the permutation π and the set B of the first random numbers used by the user in each round are different and are pre-generated in the preparation stage. The first verifier will also generate a new commitment value A in each round, and the second verifier generates new interaction content.

[0066] Then, the first verifier and the second verifier integrate the information of all rounds for verification. If the verification of all rounds passes, the first verifier and the second verifier recognize that the user has a three-color graph corresponding to the undirected graph H, that is, accept the user's identity information proof; otherwise, the first verifier and the second verifier do not recognize that the user has a three-color graph corresponding to the undirected graph H, that is, reject the user's identity information proof;

[0067] Among them, the specific process of integrating the information of all rounds for verification is as follows:

[0068] The first verifier and the second verifier integrate the information of all rounds for verification:

[0069] (a) Relativistic constraint verification: The first verifier and the second verifier first check whether the time of information interaction satisfies the time constraints set by the theory of relativity. Specifically, it is necessary to verify that in each round of interaction, |t 1 -t 4 | and |t 2 -t 3 | are less than D / c, where c represents the speed of light in a vacuum; if not satisfied, end the verification and announce that the verification fails; otherwise, if satisfied, continue to the next verification;

[0070] (b) Three - color verification: If the interactions in all rounds satisfy the relativistic time constraint, the first verifier and the second verifier further verify whether the three - color condition is satisfied in each round. The specific verification method is as follows: From the random numbers (x i , x j ) and commitment values (a i , a j ), and the response Y=(b i , b j ), calculate the permuted coloring π[d(i)]=(a i - b i ) / x i and π[d(j)]=(a j - b j ) / x j , and determine whether π[d(i)]≠π[d(j)]; if so, the verification passes; otherwise, end the verification and announce that the verification fails;

[0071] When the verification in all rounds passes, the first verifier and the second verifier recognize that the user has the three - color graph corresponding to the undirected graph H and recognize the user's identity information, that is, accept the user's identity information proof; otherwise, the first verifier and the second verifier do not recognize that the user has the three - color graph corresponding to the undirected graph H, that is, reject the user's identity information proof.

[0072] The present invention combines a commitment scheme with the principle of relativity to implement a secure and efficient identity authentication mechanism, which can effectively resist various attack means including quantum attacks. The user can prove to the verifier that they know the solution to the three - color problem without disclosing the solution. This method limits the possibility of an attacker disrupting the protocol security through mutual communication through multiple - round interactions and by combining the principle of relativity. Moreover, while ensuring the security and reliability of the verification process, it also has high efficiency and is applicable to various scenarios requiring a high security level.

Claims

1. An interactive user identity verification method based on the three-color problem, characterized in that: The following steps are involved: (1) Generate a three-color graph: The user generates an undirected graph H consisting of a set of points and a set of edges and its corresponding three-color graph, and uses the three-color graph as the user's identity information; then the uncolored three-color graph is made public; (2) Preparation stage: The user selects a coloring permutation for the uncolored three-color map in advance according to the three-color map, and generates a first random number for commitment; then, the user uses two communication devices to interact with two verification parties, that is, the user uses the first communication device to go to the first verification party for subsequent interaction, and the user uses the second communication device to go to the second verification party for subsequent interaction; (3) Interaction phase: The first verification party sends a randomly generated second random number to the first communication device, and the first communication device calculates the commitment value and replies to the first verification party; The second verification party sends randomly generated interactive content to the second communication device, and the second communication device generates a reply based on the interactive content and sends it to the second verification party; (4) Verification phase: Steps (2) to (3) are repeated m times, wherein the permutation of the coloring method and the first random number in each round are different from those in other rounds. Then, the first verifier and the second verifier integrate the information of all rounds and perform verification. If the verification of all rounds is passed, the first verifier and the second verifier recognize that the user owns the three-color graph corresponding to the undirected graph H, i.e., they accept the user's identity information proof. Otherwise, the first verifier and the second verifier do not recognize that the user owns the three-color graph corresponding to the undirected graph H, i.e., they reject the user's identity information proof.

2. The interactive user identity verification method based on the three-color problem according to claim 1, characterized in that: The generation process of the three-color map in step (1) is as follows: 1) The vertex set of an undirected graph H is represented by U, and the edge set is represented by F. The number of vertices of the undirected graph H is represented by |U|, and the number of edges is represented by |F|. Each edge f∈F of the undirected graph H is represented by an unordered pair (a,b), where a,b∈U are the connecting vertices a and b of the edge f. 2) For each vertex w∈U of the undirected graph H, select a value from {0,1,2} to assign a value, which represents the selection of a color, that is, d(w)∈{0,1,2}; 3) For any two different vertices u, v∈U (u≠v) in the undirected graph H, if their initial colors are different, that is, d(u)≠d(v), then add an edge (u,v) between vertices u and v to the edge set F with probability p; where 0 <p<1; 4) Repeat step 3) multiple times, and then verify whether the generated graph K(U,F) is connected. If the graph K(U,F) is connected, then the graph is the generated three-color graph; otherwise, continue to repeat step 3) multiple times until the generated graph K(U,F) is connected.

3. The interactive user identity verification method based on the three-color problem according to claim 2, characterized in that: Verifying whether the generated graph K(U, F) is connected in step 4) means: determining whether there is a path from any vertex to all other vertices in the graph K(U, F). If so, the graph K(U, F) is connected; otherwise, the graph K(U, F) is not connected.

4. The interactive user identity verification method based on the three-color problem according to claim 2, characterized in that: In the step (2), the user selects a coloring method for the uncolored three-color image in advance according to the three-color image, and generates a first random number for commitment, which means: A: Color permutation selection: The user selects a coloring permutation π for the uncolored three-color graph in advance based on the three-color graph. The permutation π is a permutation acting on the three-color {0,1,2}. After the permutation, the coloring of each vertex w∈U is expressed as π[d(w)]∈{0,1,2}; B: First random number generation: The user generates a first random number for each vertex of the three-color graph in each round in advance. The set of first random numbers generated for all vertices in one round is expressed as B = {b w },w∈U, where b w belongs to a finite field F Q , Q is a pre-selected prime number.

5. The interactive user identity verification method based on the three-color problem according to claim 4 is characterized in that: The spatial distance D between the first communication device and the second communication device.

6. The interactive user identity verification method based on the three-color problem according to claim 5, characterized in that: The specific process steps of step (3) are: At time t1, the first verifier randomly generates |U| nodes belonging to the finite field F for each vertex. Q The number is represented by X={x w }, w∈U, and send it to the first communication device; the first communication device calculates the commitment value of each vertex coloring, expressed as A={a w },w∈U, where a w =x w ·π[d(w)]+b w , then sends the commitment value to the first verifier, who records t1, X, A and the time t2 when A is received; At time t3, the second verifier randomly selects an edge C = (i, j) ∈ F of the three-color graph as the interaction content and sends it to the second communication device. The second communication device sends two numbers (b i ,b j ) is sent as a reply Y to the second verifier, and the second verifier records t3, C, Y and the time t4 when Y is received.

7. The interactive user identity verification method based on the three-color problem according to claim 6, characterized in that: The specific process of the first verifier and the second verifier in step (4) integrating all rounds of information for verification is as follows: The first and second verifiers integrate all rounds of information for verification: (a) Relative constraint verification: The first verifier and the second verifier need to verify whether |t1-t4| and |t2-t3| are less than D / c in each round of interaction, where c represents the speed of light in a vacuum. If not, the verification ends and the verification is declared failed. Otherwise, the verification continues to the next step. (b) Three-color verification: Each round of random numbers (x i ,x j ) and commitment value (a i ,a j ), reply Y = (b i ,b j ), calculate the permuted coloring π[d(i)]=(a i -b i ) / x i and π[d(j)]=(a j -b j ) / x j , determine whether π[d(i)]≠π[d(j)]; if so, the verification is successful; otherwise, the verification is terminated and declared unsuccessful; When all rounds of verification are passed, the first verifier and the second verifier recognize that the user owns the three-color graph corresponding to the undirected graph H, and recognize the user's identity information, that is, accept the user's identity information proof; otherwise, the first verifier and the second verifier do not recognize that the user owns the three-color graph corresponding to the undirected graph H, that is, reject the user's identity information proof.

8. The interactive user identity verification method based on the three-color problem according to claim 4, characterized in that: Q is a pre-selected prime number, which is expressed by the following expression: log2 Q=[9+4log23-3log2ε1] Among them, [] indicates rounding up, and ε1 represents the probability that the verifier obtains the coloring scheme from the commitment value.

9. The interactive user identity verification method based on the three-color problem according to claim 2, characterized in that: The round number m is represented by the following expression: m=[-ln(ε2)*|F|] Among them, ε2 represents the probability that a user without the correct coloring scheme is recognized by the verification party.

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