A puf-based group authentication and key agreement method and system

Abstract

This invention discloses a group authentication and key negotiation method and system based on PUF, relating to the field of identity authentication technology. The method includes system initialization, drone registration, group authentication and key negotiation, secret share calculation and verification, key recovery, threshold adjustment, and dynamic group adjustment steps. This invention employs the aforementioned PUF-based group authentication and key negotiation method and system, achieving reliable drone identity authentication and secure negotiation of group session keys without relying on a trusted execution environment or dedicated security hardware modules, by introducing PUF and a verifiable secret sharing mechanism.

Description

Technical Field

[0001] This invention relates to the field of identity authentication technology, and in particular to a group authentication and key negotiation method and system based on PUF. Background Technology

[0002] With the rapid development of drone technology, drones have been widely used in complex scenarios such as emergency rescue, disaster monitoring, intelligent transportation, and public safety. Especially in emergency rescue and disaster response missions, multiple drones typically work in swarms to perform information collection, communication relay, and task collaboration. They collaborate with ground or vehicle-mounted communication nodes to achieve rapid deployment and information transmission across large areas and complex environments. In these applications, emergency communication vehicles often serve as temporary communication hubs or control nodes, forming a linked system with the drone swarm to provide support functions such as drone authentication, task scheduling, and data aggregation. This places higher demands on the security, reliability, and real-time performance of drone swarm communication. However, the open wireless communication environment and the highly distributed nature of drone nodes expose such collaborative communication systems to various security threats.

[0003] Existing drone swarm communication solutions mostly employ pre-shared keys, centralized key distribution, or key management mechanisms based on a single control node. In scenarios where emergency communication vehicles are involved in management, these vehicles often assume centralized authentication and key management responsibilities. While such solutions are applicable when the node scale is small or the network structure is relatively stable, they are prone to revealing numerous shortcomings in real-world emergency environments. For example, if the pre-shared key is leaked, attackers can illegally access the communication system by disguising legitimate drones. When the emergency communication vehicle, acting as the centralized key management node, is attacked, malfunctions, or its privileges are abused internally, the security and availability of the entire drone swarm communication system may be severely impacted. Furthermore, traditional solutions still have limited overall protection capabilities against identity forgery, replay attacks, and malicious attacks launched by legitimate internal entities.

[0004] On the other hand, in real-world emergency applications, drone nodes frequently join or leave groups due to factors such as battery depletion, mission switching, communication link interruptions, or changes in the operating environment, making drone swarms highly dynamic. Simultaneously, emergency communication vehicles themselves may frequently establish temporary collaborative relationships with drone swarms of varying sizes due to mobile deployment, changes in communication load, or adjustments to mission areas. In this context, traditional key management mechanisms based on static keys or fixed membership assumptions struggle to adapt to frequently changing group structures, easily leading to excessive key update overhead, increased communication latency, and even service interruptions, thereby affecting the overall stability and real-time response capabilities of the emergency communication system.

[0005] Furthermore, drones are typically limited by factors such as size, weight, and energy consumption, resulting in relatively limited computing power, storage resources, and security capabilities. They generally lack trusted execution environments or dedicated security hardware modules. When faced with attacks such as physical capture, side-channel analysis, or storage medium reading, traditional security mechanisms relying on software-based key storage are insufficient to provide effective protection, posing a risk of key theft or tampering. Meanwhile, although emergency communication vehicles possess relatively stronger computing and communication capabilities, they often need to manage and authenticate a large number of drone nodes simultaneously in emergency scenarios. Their own computing and management load is also considerable, and it cannot be simply assumed that they possess unlimited trustworthiness or unlimited resources. Summary of the Invention

[0006] The purpose of this invention is to provide a group authentication and key negotiation method and system based on PUF, which solves the problems mentioned in the background art.

[0007] To achieve the above objectives, this invention provides a PUF-based group authentication and key negotiation method, comprising the following steps: S1. During the system initialization phase, the system administrator determines the system public parameters for each emergency communication vehicle. Each emergency communication vehicle calculates the corresponding public key based on the long and short private keys, and then publishes the system public parameters and public key to the outside world. S2. The drone generates a challenge-response pair to the challenge information, processes it, generates a response value, generates physical security based on the response value, and completes the drone's identity registration. S3. The drone terminal generates authentication parameters based on the challenge response. Each drone group performs group authentication, verifies the legality, negotiates the key, and calculates the session key. S4. The emergency communication vehicle secretly divides the session key, generates multiple secret shares, and distributes them to the drones. Each drone receives a secret share and verifies it. If the verification fails, the drone rejects the share and performs an exception handling. S5. When the minimum number of shares corresponding to the threshold parameter is met, each drone will work together to execute the secret recovery algorithm to reconstruct the group session key. S6. The emergency communication vehicle dynamically updates the threshold parameters, recalculates and distributes secret shares that match each updated threshold parameter. S7. When a drone node is detected joining, leaving, or exhibiting abnormal behavior, the emergency communication vehicle updates the group member list and updates the group session key.

[0008] Preferably, S1 includes: S11. The system administrator selects the identity identifier for the emergency communication vehicle. And determine its validity period. Then select a random seed number for the Chebyshev polynomial. Then choose a large prime number. The generator is addition cyclic group as well as Another generator in ; S12. The system administrator selects a one-way hash function. : Then select one that satisfies the cyclic group condition. integers The system administrator then Securely transmitted to all emergency communication vehicles; in, Represents a hash function. Modulus The integer multiplication group, mod represents the modulo operation. This represents the set of parameters to be transmitted. It is the smallest positive integer that satisfies this expression. ; S13. The emergency communication vehicle generates its long-term key. And calculate the corresponding public key Simultaneously, the emergency communication vehicle configuration can verify the relevant parameters required for the secret sharing mechanism and set initial threshold parameters. Limit the minimum number of secret shares required to recover the group session key; in, This represents one of the operations performed on a Chebyshev polynomial. S14. The system publishes parameters and distributes them to each UAV node through pre-configuration or secure communication methods; Wherein, the parameter is .

[0009] Preferably, S2 includes: S21. Drone managers select a unique identifier for each drone. Its long-term private key and random numbers And calculate the corresponding long-term public key. Furthermore, the built-in PUF and fuzz extractor work together to protect the security of long-term private keys, and it only needs to save the corresponding auxiliary data locally to recover the private key; S22, Calculation , Then select the current timestamp. Send registration request To its assigned emergency communication vehicle; in, and Each of these represents an unknown parameter that needs to be calculated in this step. This indicates the identification code of the emergency communication vehicle. Indicates the corresponding public key The specific operations of the hash function; S23, Emergency communication vehicle received Then, first select the current timestamp. verify If the entry into S24 is successful, otherwise an error message is returned to the drone; in, The maximum time interval for a message to be valid; S24. Emergency communication vehicles randomly select an unknown parameter. And calculate , , , ; in, , , and Each of these represents an unknown parameter that needs to be calculated in this step. Indicates drone The katakana; S25, Emergency Communication Vehicle Generation Valid time interval In addition to this This will be invalid; S26, Emergency Communication Vehicle Generation A unique challenge and select the current timestamp. Send message To drones; in, This represents the K unique challenges generated by the emergency communication vehicle within the final effective timeframe; S27, the drone received Then, select the current timestamp. verify and If valid, proceed to S28; otherwise, return an error message to the emergency communication vehicle. S28, UAVs In Each challenge generates a unique new challenge. Then, based on the built-in PUF input Generate the corresponding response ; in, This indicates the drone's response via PUF, taking the corresponding challenge as input. S29. The drone selects the current system timestamp. And calculate parameters And according to the re-parameter calculate ; in, This indicates the unknown parameters that need to be calculated in this step. This represents one of the operations performed on a Chebyshev polynomial. parameter Calculated using the following formula: ; S210, Sending information To emergency communication vehicles.

[0010] Preferably, S3 includes: S31, Emergency communication vehicle received the group's message. Different messages sent by various drones Next, verify the validity of the timestamp in each message according to the steps in S24. If it is valid, proceed to S32; otherwise, return an error message to the drone and terminate the mission. S32, Emergency Communication Vehicle calculates the corresponding data for each drone. and corresponding ; in, and "All" represents the unknown parameters that need to be calculated in this step, using the following formula: ; ; S33, The first verification parameter required to be calculated during the emergency communication vehicle verification protocol process. Is it a second verification parameter that needs to be calculated during the protocol process? If they are equal, the drone is considered legitimate and enters S34; otherwise, the process ends. in, Indicates the first The parameter names of the drones, Indicates the unknown parameters that need to be calculated; S34, Random selection parameters for emergency communication vehicles And calculate the session key ; S35, Emergency Communication Vehicle Computation Group Session Key and and Calculated using the following formula: ; ; in, This represents one of the operations performed on a Chebyshev polynomial. S36. Select the current system timestamp Send message To the corresponding drone; S37, the corresponding drone received Then, verify according to the steps described in S23. The validity of the internal timestamp is checked. If it is valid, proceed to S38; otherwise, return an error message to the emergency communication vehicle and terminate the mission. S38, Drone Verification Is it equal to If they are equal, the emergency communication vehicle is considered legitimate and its parameters are calculated. and ; in, and These represent one operation of a Chebyshev polynomial. This indicates the unknown parameters that need to be calculated in this step. Indicates the session key. This indicates that the parameters are obtained by the UAV through open channel transmission, rather than parameters calculated by the UAV itself.

[0011] Preferably, S4 includes: S41, Emergency Communications Vehicles will connect a group of drone nodes to the same challenge Made The response is as their respective coordinates and Coordinates, select from them Construct a polynomial from each node ; Among them, polynomial As shown in the following formula: ; parameter Calculated using the following formula: ; in, This represents one of the operations performed on a Chebyshev polynomial. S42. The emergency communication vehicle calculates the offsets of these m UAV nodes. To obtain the final share of each node, represented as This allows each node to participate; Among them, for drones The calculation process for the offset and its share is as follows: ; ; in, This indicates the challenges of drones. This represents the corresponding response to the challenges posed by drones, calculated using PUF. S43. Emergency communication vehicles also need to generate a hidden polynomial. Calculate the hidden polynomial And broadcast Then get the current timestamp. Send message to ; in, This example represents a set of share verification parameters for drones. This represents the calculated share; S44 use Decryption get and It will select the current timestamp. examine If the condition is not met, the process will terminate; otherwise... exist Randomly select one polynomials of degree Then use the verification formula Complete the Whether the share distributed to other drones by emergency communication vehicles is based on the same number of times Verification of polynomials using examples represent , represent ,in If the equation holds true, then proceed to S45; otherwise, consider... Illegal; in, Indicates an individual Finite field of an element Indicates the first One example is for drones. Share verification parameters, and These represent a polynomial with input and a parameter, respectively. S45, drones Reuse verify The validity of an equation is determined by whether the equation is true.

[0012] Preferably, S5 includes: S51, Within the same group Each drone, based on its respective share, calculates the group session key using Lagrange interpolation. ; Group session keys are calculated using the following formula: ; S52, Drone recovery of outgoing session key As shown in the following formula: .

[0013] Preferably, S6 includes: S61. Assume the initial threshold for secret sharing within this group is... The updated threshold is The number of updates is (Initialized to 1, updated each time) Add 1), where ; S62, of dot becomes , Point to conduct The next hash operation, based on the group... Nodes Proceed according to S4.

[0014] Preferably, S7 includes: S71. Drone Addition: Assuming a new drone... Due to mission requirements, it needs to be added to the group managed by the emergency communications vehicle. Two private keys are obtained during the registration phase. and the corresponding two public keys , ; S72. After registration is completed, the emergency communication vehicle will select a new one. calculate and judge If the legitimacy of the connection is not established, the process terminates; otherwise, the emergency communication vehicle calculates its connection with... Session key ; The following equation for the hash function is used to determine this. Legality: ; S73, Emergency Communication Vehicle Select Short-Term Key Then, use a short-lived key. Calculate group session key The emergency communication vehicle then selects the current timestamp. Send message }to , The legality of the emergency communication vehicle's identity is verified according to procedure S38. If invalid, the process terminates; otherwise, unknown parameters are calculated. and session key ; in, This represents one of the operations performed on a Chebyshev polynomial. S74. With the addition of new members, the share of each node is updated synchronously, and emergency communication vehicles send information. to The process will then proceed according to S5 and S6. in, This indicates that encryption is performed using a symmetric key. The parameters to be encrypted. Indicates share; S75. Drone Departure: Suppose that one or more drones need to leave a drone swarm, either voluntarily or involuntarily, due to task scheduling, external interference, or malicious behavior. The departure of drones mainly affects the update of the group session key, and the process is as follows: Emergency communication vehicles select short-term keys Calculate the group session key later Then, the original members' shares within the group are updated according to the S74 procedure.

[0015] A system for group authentication and key negotiation based on PUF, comprising: The emergency communication vehicle module is used to perform system initialization, group authentication, secret share generation and distribution, threshold adjustment, and dynamic group management. The drone module is used to perform private key derivation, identity authentication, secret share verification, and key recovery based on physically unclonable functions and fuzz extractors; The system is configured to perform the method according to any one of claims 1 to 8.

[0016] Preferably, the fuzz extractor includes an error correction module and an auxiliary data generation module. The error correction module is used to perform noise-tolerant processing on the original response output by the physically non-clonable function. The auxiliary data generation module is used to generate auxiliary information to support the stable reconstruction of the response value under different environmental conditions. The auxiliary information does not disclose valid information related to the private key.

[0017] Therefore, the present invention employs the above-mentioned PUF-based group authentication and key negotiation method and system, which has the following beneficial effects: (1) This method achieves reliable authentication of UAV identity and secure negotiation of group session keys by introducing PUF and verifiable secret sharing mechanism without relying on trusted execution environment or dedicated security hardware module.

[0018] (2) In the collaborative scenario where emergency communication vehicles serve as communication hubs and management nodes, this method reduces the reliance on absolute trustworthiness, enhances the system's fault tolerance to internal attacks and node failures, and supports the dynamic addition, removal, and expulsion of abnormal nodes of UAV nodes, thereby improving the security, stability, and scalability of UAV swarm communication systems in complex emergency environments.

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0020] Figure 1 This is a flowchart of a PUF-based group authentication and key negotiation method according to the present invention. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0023] Example Please see Figure 1 This invention provides a PUF-based group authentication and key negotiation method, comprising the following steps: S1. System Initialization Steps: During the system initialization phase, the system administrator determines system parameters for each emergency communication vehicle. Each emergency communication vehicle selects its own long-short-term private key and calculates the corresponding public key. Then, the system's public parameters and its public key are publicly announced. The specific implementation steps are as follows: S11. The system administrator selects the identity identifier for the emergency communication vehicle. And determine its validity period. Next, we choose a random seed number for the Chebyshev polynomial. Then choose a large prime number. The generator is addition cyclic group as well as Another generator in ; S12. The system administrator selects a one-way hash function. : Then select one that satisfies the cyclic group condition. integers The administrator then Secure transmission of values ​​to all emergency communication vehicles; in, Represents a hash function. Modulus The integer multiplication group, mod represents the modulo operation. This represents the set of parameters to be transmitted. It is the smallest positive integer that satisfies this expression. .

[0024] S13. The emergency communication vehicle generates its long-term key. And calculate the corresponding public key ,in, This represents one of the operations of a Chebyshev polynomial. Simultaneously, the emergency communication vehicle configuration can verify the relevant parameters required for the secret sharing mechanism and set initial threshold parameters. This is used to limit the minimum number of secret shares required for group session key recovery.

[0025] The verifiable secret sharing mechanism generates corresponding verification information for each secret share while generating the secret share, enabling the drone to perform validity verification on the received secret share without recovering the group session key.

[0026] S14, System Public Parameters Distribute to each drone node via pre-configuration or secure communication methods.

[0027] S2. Drone Registration Steps: The drone calls the built-in physically unclonable function to generate challenge-response pairs related to the physical characteristics of the drone hardware based on the challenge information integrated from the emergency communication vehicle and its own identity information. The drone then uses a fuzz extractor to correct and stabilize the original response, generating a stable response value and corresponding auxiliary information to complete the drone's identity registration.

[0028] The challenge response pair is a temporary authentication parameter used only once in each authentication process, thereby preventing replay attacks and identity impersonation attacks. Subsequent uses are all derived from the challenge response pair generated at the initial time through a series of hash functions.

[0029] During the drone registration phase, each drone performs the following operations upon its initial connection to the system: S21. Drone managers select a unique identifier for each drone. Its long-term private key and random numbers And calculate the corresponding long-term public key. Furthermore, relying on the built-in PUF and fuzz extractor to protect the security of long-term private keys, it only needs to store the corresponding auxiliary data locally for recovering the private key; The drone's private key is not permanently stored in the drone's non-volatile memory during use. Instead, it is dynamically restored on demand during the registration process by the drone's physical non-clonable function based on the microscopic physical differences within its hardware.

[0030] S22, Calculation , Then select the current timestamp. Send registration request To its assigned emergency communication vehicle; in, and Each of these represents an unknown parameter that needs to be calculated in this step. This indicates the identification code of the emergency communication vehicle. Indicates the corresponding public key The specific operations of the hash function.

[0031] S23, Emergency communication vehicle received Then, first select the current timestamp. verify ,in This is the maximum time interval for a valid message. If valid, proceed to S24; otherwise, return an error message to the drone. S24. Emergency communication vehicles randomly select an unknown parameter. And calculate the following unknown parameters: , , , ; in, , , and Each of these represents an unknown parameter that needs to be calculated in this step. Indicates drone The pseudonym.

[0032] S25, Emergency Communication Vehicle Generation Valid time interval In addition to this This will be invalid; S26, Emergency Communication Vehicle Generation A unique challenge and select the current timestamp. Send message To drones; in, This represents the K unique challenges generated by the emergency communication vehicle within the final effective timeframe; S27, the drone received Then, select the current timestamp. verify and If valid, proceed to S28; otherwise, return an error message to the emergency communication vehicle. S28, UAVs In Each challenge generates a unique new challenge. Then, based on the built-in PUF input Generate the corresponding response ; in, This indicates the drone's response via PUF, taking the corresponding challenge as input.

[0033] S29. The drone selects the current system timestamp. And calculate parameters ,in Then combine this formula to calculate ; in, This indicates the unknown parameters that need to be calculated in this step. This represents one of the operations performed on a Chebyshev polynomial.

[0034] S210, Sending information To emergency communication vehicles.

[0035] S3. Group Authentication and Key Negotiation Steps: The drone generates authentication parameters based on the challenge response and sends them to the emergency communication vehicle. The emergency communication vehicle receives and verifies the validity of the group authentication request information from each drone. After verifying the legitimacy of the drone's identity, the emergency communication vehicle, together with multiple authenticated drones, performs the group authentication and key negotiation process, generating a session key between itself and each drone, as well as a group session key. Then, it sends the authentication parameters to each drone in the group. Each drone receives the parameters and verifies the validity of the information sent by the emergency communication vehicle in S3-2. If valid, it authenticates the emergency communication vehicle's identity based on the authentication parameters and then calculates the session key with the emergency communication vehicle. The specific implementation steps are as follows: S31, Emergency communication vehicle received the group's message. Different messages sent by various drones Then, first verify the validity of the timestamp in each message according to the steps described in S24. If it is valid, proceed to S32; otherwise, return an error message to the drone and terminate the mission. S32, Emergency Communication Vehicle calculates the corresponding data for each drone. and corresponding , in, and "All" represents the unknown parameters that need to be calculated in this step, using the following formula: ; ; S33, The first verification parameter required to be calculated during the emergency communication vehicle verification protocol process. Is it a second verification parameter that needs to be calculated during the protocol process? If they are equal, the drone is considered legitimate and enters S34; otherwise, the process ends. in, Indicates the first The parameter names of the drones, This indicates the unknown parameters that need to be calculated.

[0036] S34, Random selection parameters for emergency communication vehicles And calculate the session key ; S35, Emergency Communication Vehicle Computation Group Session Key and Calculated using the following formula: ; ; in, This represents one of the operations performed on a Chebyshev polynomial.

[0037] S36. Select the current system timestamp Send message To the corresponding drone; S37, the corresponding drone received Then, verify according to the steps described in S23. The validity of the internal timestamp is checked. If it is valid, proceed to S38; otherwise, return an error message to the emergency communication vehicle and terminate the mission. S38, Drone Verification Is it equal to If they are equal, the emergency communication vehicle is considered legitimate and its parameters are calculated. and .

[0038] in, and These represent one operation of a Chebyshev polynomial. This indicates the unknown parameters that need to be calculated in this step. Indicates the session key. This indicates that the parameters are obtained by the UAV through open channel transmission, rather than parameters calculated by the UAV itself.

[0039] S4. Secret Share Calculation, Distribution, and Verification Steps: Based on the group session key material, the emergency communication vehicle uses a verifiable secret sharing algorithm to secretly segment the session key; multiple secret shares are generated according to the current threshold parameter, and each secret share is encrypted using the session key generated in S3 and distributed to the corresponding UAV; each UAV performs integrity and consistency verification on the received secret share; when verification fails, the corresponding secret share is rejected and an exception handling process is triggered. The specific implementation steps are as follows: S41, Emergency Communications Vehicles will connect a group of drone nodes to the same challenge Made The response is as their respective coordinates and Coordinates, select from them Each node is constructed in the form of... polynomial The following formula is used to calculate: .

[0040] in, This represents one of the operations performed on a Chebyshev polynomial.

[0041] The coefficient can be derived from Calculate, where, yes The Vandermonde matrix of a point. yes Vector of a point It is the coefficient matrix of the polynomial.

[0042] S42. The emergency communication vehicle needs to calculate the offset of these m drone nodes. To obtain the final share of each node, that is This allows each node to participate.

[0043] Among them, for drones The calculation process for the offset and its share is as follows: ; ; in, This indicates the challenges of drones. This represents the corresponding response to the challenges posed by drones, calculated using PUF. S43. Emergency communication vehicles also need to generate a hidden polynomial. Its form is as follows As shown, calculate the hidden polynomial. And broadcast Then get the current timestamp. send to ; in, This represents an instance, specifically the set of share verification parameters for drones. This represents the calculated share.

[0044] S44 use Decryption get and It will select the current timestamp. examine If the condition is not met, the process will terminate. Otherwise... exist Randomly select one polynomials of degree Then use the verification formula. Complete the Whether the share distributed to other UAVs by emergency communication vehicles is based on the same number of times To verify the polynomial, we will use an example for clarity. represent , represent ,in If the equation holds true, proceed to S45; otherwise, consider... Illegal; in, Indicates an individual Finite field of an element Indicates the first One example is for drones. Share verification parameters, and These represent a polynomial with input and a parameter, respectively.

[0045] S45, drones Reuse verify The validity of an equation is determined by whether the equation is true.

[0046] S5. Key Recovery Step: When the minimum number of shares corresponding to the threshold parameter is met, multiple drones within the group collaboratively execute the secret recovery algorithm to reconstruct the group session key for subsequent group communication data encryption and integrity protection. Emergency communication vehicles are configured not to participate in the final recovery process of the group session key, and their distributed secret shares must be verified through the drone's end-user verification mechanism before participating in key recovery, thereby preventing emergency communication vehicles from unilaterally controlling the group key recovery process. The specific implementation steps are as follows: S51. Within the same group Each drone, combined with its respective share, was calculated using Lagrange interpolation. ; Group session keys are calculated using the following formula: ; S52, Drones can recover outgoing session keys. As shown in the following formula: .

[0047] S6. Threshold Adjustment Step: Based on changes in drone swarm size, security level, or communication requirements, the emergency communication vehicle dynamically updates the threshold parameters; it then recalculates and distributes the secret share matching the updated threshold parameters. The specific implementation steps are as follows: S61. Assume the initial threshold for secret sharing within this group is... The updated threshold is The number of updates is (Initialized to 1, updated each time) Add 1), where This process is similar to the initial S4 process; only the differences are explained here. The emergency communication vehicle still utilizes the challenge response pair to generate a new round of secret polynomials. ; S62, of dot becomes , Point to conduct The next hash operation, based on the group... Nodes Just follow S4.

[0048] S7. Group Dynamic Adjustment Steps: When a drone node is detected joining, leaving, or exhibiting abnormal behavior, the emergency communication vehicle updates the group member list. The emergency communication vehicle marks the drone node as an invalid node and removes it from the group member list. This triggers the group session key update process to ensure forward and backward security of group communication.

[0049] When a drone node joins the group, it needs to re-execute the registration or authentication process and obtain a new secret share; when a drone node leaves the group, the emergency communication vehicle triggers a group session key update process to ensure that the leaving node cannot obtain subsequent group communication content. The specific implementation steps are as follows: S71. Drone Addition: Assuming a new drone... Due to mission requirements, it needs to be added to the group managed by emergency communication vehicles. Two private keys need to be obtained during the registration phase. and the corresponding two public keys , The subsequent process is similar to that described in S2, and will not be elaborated on here. This section mainly describes the authentication key negotiation process with emergency communication vehicles, the group session key, and the share update process. S72. After registration is completed, the emergency communication vehicle will select a new one. calculate And judge according to the equation of the hash function. The legality is as follows: ; If the equation does not hold true, the process terminates; otherwise, the emergency communication vehicle calculates its relationship with... Session key ; S73, Emergency Communication Vehicle Selection Then use this to calculate the group session key. The emergency communication vehicle then selects the current timestamp. 'send }to , The S38 procedure verifies the legitimacy of the emergency communication vehicle's identity; if invalid, the procedure terminates; otherwise, it calculates unknown parameters. and session key ; in, This represents one of the operations performed on a Chebyshev polynomial. S74. With the addition of new members, the share of each node also needs to be updated synchronously. For newly added drones, the process follows the S4 procedure.

[0050] For members within the original group, emergency communication vehicle calculation parameters and share Calculated using the following formula: ; and ; and broadcast instances Then the emergency communication vehicle sent a message. to The process will then proceed according to steps S5 and S6. S75. Drone Departure: Suppose that one or more drones need to leave a drone swarm, either voluntarily or involuntarily, due to task scheduling, external interference, or malicious behavior. The departure of these drones mainly affects the update of the group session key, and the process is as follows: Emergency communication vehicles select short-term keys The group session key is then calculated using the following formula: ; Then, update the original members' shares in the group according to the S74 procedure.

[0051] A system for group authentication and key negotiation based on PUF is configured to execute steps S1-S7. These include: The emergency communication vehicle module is used to perform system initialization, group authentication, secret share generation and distribution, threshold adjustment, and dynamic group management; the drone module is used to perform private key derivation, identity authentication, secret share verification, and key recovery based on physically unclonable functions and fuzz extractors.

[0052] The fuzz extractor includes an error correction module and an auxiliary data generation module. The error correction module performs noise-tolerant processing on the raw response output of the physically non-clonable function, while the auxiliary data generation module generates auxiliary information to support stable reconstruction of the response value under different environmental conditions. The auxiliary information does not disclose valid information related to the private key. Therefore, this invention employs the aforementioned PUF-based group authentication and key negotiation method and system. Without relying on a trusted execution environment or dedicated security hardware modules, it achieves reliable authentication of UAV identities and secure negotiation of group session keys by introducing PUF and a verifiable secret sharing mechanism. Simultaneously, in collaborative scenarios where emergency communication vehicles act as communication hubs and management nodes, it reduces the reliance on absolute trustworthiness, enhances the system's fault tolerance to internal attacks and node failures, and supports the dynamic joining, leaving, and expulsion of abnormal UAV nodes, thereby improving the security, stability, and scalability of the UAV swarm communication system in complex emergency environments.

[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A PUF-based group authentication and key agreement method, characterized by, Includes the following steps: S1. During the system initialization phase, the system administrator determines the system public parameters for each emergency communication vehicle. Each emergency communication vehicle calculates the corresponding public key based on the long and short private keys, and then publishes the system public parameters and public key to the outside world. S2. The drone generates a challenge-response pair to the challenge information, processes it, generates a response value, generates physical security based on the response value, and completes the drone's identity registration. S3. The drone terminal generates authentication parameters based on the challenge response. Each drone group performs group authentication, verifies the legality, negotiates the key, and calculates the session key. S4. The emergency communication vehicle secretly divides the session key, generates multiple secret shares, and distributes them to the drones. Each drone receives a secret share and verifies it. If the verification fails, the drone rejects the share and performs an exception handling. S5. When the minimum number of shares corresponding to the threshold parameter is met, each drone will work together to execute the secret recovery algorithm to reconstruct the group session key. S6. The emergency communication vehicle dynamically updates the threshold parameters, recalculates and distributes secret shares that match each updated threshold parameter. S7. When a drone node is detected joining, leaving, or exhibiting abnormal behavior, the emergency communication vehicle updates the group member list and updates the group session key.

2. The PUF-based group authentication and key agreement method of claim 1, wherein, S1 includes: S11. The system administrator selects the identity identifier for the emergency communication vehicle. And determine its validity period. Then select a random seed number for the Chebyshev polynomial. Then choose a large prime number. The generator is addition cyclic group as well as Another generator in ; S12. The system administrator selects a one-way hash function. : Then select one that satisfies the cyclic group condition. integers The system administrator then Securely transmitted to all emergency communication vehicles; in, Represents a hash function. Modulus The integer multiplication group, mod represents the modulo operation. This represents the set of parameters to be transmitted. It is the smallest positive integer that satisfies this expression. ; S13. The long-term key is generated by the emergency communication vehicle. And calculate the corresponding public key Simultaneously, the emergency communication vehicle configuration can verify the relevant parameters required for the secret sharing mechanism and set initial threshold parameters. Limit the minimum number of secret shares required to recover the group session key; in, This represents one of the operations performed on a Chebyshev polynomial. S14. The system publishes parameters and distributes them to each UAV node through pre-configuration or secure communication methods; Wherein, the parameter is .

3. The PUF-based group authentication and key negotiation method according to claim 2, characterized in that, S2 includes: S21. Drone managers select a unique identifier for each drone. Its long-term private key and random numbers And calculate the corresponding long-term public key. Furthermore, the built-in PUF and fuzz extractor work together to protect the security of long-term private keys, and it only needs to save the corresponding auxiliary data locally to recover the private key; S22, Calculation , Then select the current timestamp. Send registration request To its assigned emergency communication vehicle; in, and Each of these represents an unknown parameter that needs to be calculated in this step. This indicates the identification code of the emergency communication vehicle. Indicates the corresponding public key The specific operations of the hash function; S23, Emergency communication vehicle received Then, first select the current timestamp. verify If the entry into S24 is successful, otherwise an error message is returned to the drone; in, The maximum time interval for a message to be valid; S24. Emergency communication vehicles randomly select an unknown parameter. And calculate , , , ; in, , , and Each of these represents an unknown parameter that needs to be calculated in this step. Indicates drone The katakana; S25, Emergency Communication Vehicle Generation Valid time interval In addition to this This will be invalid; S26, Emergency Communication Vehicle Generation A unique challenge and select the current timestamp. Send message To drones; in, This represents the K unique challenges generated by the emergency communication vehicle within the final effective timeframe; S27, the drone received Then, select the current timestamp. verify and If valid, proceed to S28; otherwise, return an error message to the emergency communication vehicle. S28, UAVs In Each challenge generates a unique new challenge. Then, based on the built-in PUF input Generate the corresponding response ; in, This indicates the drone's response via PUF, taking the corresponding challenge as input. S29. The drone selects the current system timestamp. And calculate parameters And according to the re-parameter calculate ; in, This indicates the unknown parameters that need to be calculated in this step. This represents one of the operations performed on a Chebyshev polynomial. parameter Calculated using the following formula: ； S210, Sending information To emergency communication vehicles.

4. The PUF-based group authentication and key negotiation method according to claim 3, characterized in that, S3 includes: S31, Emergency communication vehicle received the group's message. Different messages sent by various drones Next, verify the validity of the timestamp in each message according to the steps in S24. If it is valid, proceed to S32; otherwise, return an error message to the drone and terminate the mission. S32, Emergency Communication Vehicle calculates the corresponding data for each drone. and corresponding ; in, and "All" represents the unknown parameters that need to be calculated in this step, using the following formula: ； ； S33, The first verification parameter required to be calculated during the emergency communication vehicle verification protocol process. Is it a second verification parameter that needs to be calculated during the protocol process? If they are equal, the drone is considered legitimate and enters S34; otherwise, the process ends. in, Indicates the first The parameter names of the drones, Indicates the unknown parameters that need to be calculated; S34, Random selection parameters for emergency communication vehicles And calculate the session key ; S35, Emergency Communication Vehicle Computation Group Session Key and and Calculated using the following formula: ； ； in, This represents one of the operations performed on a Chebyshev polynomial. S36. Select the current system timestamp Send message To the corresponding drone; S37, the corresponding drone received Then, verify according to the steps described in S23. The validity of the internal timestamp is checked. If it is valid, proceed to S38; otherwise, return an error message to the emergency communication vehicle and terminate the mission. S38, Drone Verification Is it equal to If they are equal, the emergency communication vehicle is considered legitimate and its parameters are calculated. and ; in, and These represent one operation of a Chebyshev polynomial. This indicates the unknown parameters that need to be calculated in this step. Indicates the session key. This indicates that the parameters are obtained by the UAV through open channel transmission, rather than parameters calculated by the UAV itself.

5. The PUF-based group authentication and key negotiation method according to claim 4, characterized in that, S4 includes: S41, Emergency Communications Vehicles will connect a group of drone nodes to the same challenge Made The response is as each coordinates and Coordinates, select from them Construct a polynomial from each node ; Among them, polynomial As shown in the following formula: ； parameter Calculated using the following formula: ； in, This represents one of the operations performed on a Chebyshev polynomial. S42. The emergency communication vehicle calculates the offsets of these m UAV nodes. To obtain the final share of each node, represented as This allows each node to participate; Among them, for drones The calculation process for the offset and its share is as follows: ； ； in, This indicates the challenges of drones. This represents the corresponding response to the challenges posed by drones, calculated using PUF. S43. Emergency communication vehicles also need to generate a hidden polynomial. Calculate the hidden polynomial And broadcast Then get the current timestamp. Send message to ; in, This example represents a set of share verification parameters for drones. This represents the calculated share; S44 use Decryption get and It will select the current timestamp. examine If the condition is not met, the process will terminate; otherwise... exist Randomly select one polynomials of degree Then use the verification formula Complete the task Whether the share distributed to other drones by emergency communication vehicles is based on the same number of times Verification of polynomials using examples represent , represent ,in If the equation holds true, then proceed to S45; otherwise, consider... Illegal; in, Indicates an individual Finite field of an element Indicates the first One example is for drones. Share verification parameters, and These represent a polynomial with input and a parameter, respectively. S45, drones Reuse verify The validity of an equation is determined by whether the equation is true.

6. The PUF-based group authentication and key negotiation method according to claim 5, characterized in that, S5 includes: S51, Within the same group Each drone, based on its respective share, calculates the group session key using Lagrange interpolation. ; Group session keys are calculated using the following formula: ； S52, Drone recovery of outgoing session key As shown in the following formula: 。 7. The PUF-based group authentication and key negotiation method according to claim 6, characterized in that, S6 includes: S61. Assume the initial threshold for secret sharing within this group is... The updated threshold is The number of updates is (Initialized to 1, updated each time) Add 1), where ; S62, of dot becomes , Point to conduct The next hash operation, based on the group... Nodes Proceed according to S4.

8. The PUF-based group authentication and key negotiation method according to claim 7, characterized in that, S7 includes: S71. Drone Addition: Assuming a new drone... Due to mission requirements, it needs to be added to the group managed by the emergency communications vehicle. Two private keys are obtained during the registration phase. and the corresponding two public keys , ; S72. After registration is completed, the emergency communication vehicle will select a new one. calculate and judge If the legitimacy of the connection is not established, the process terminates; otherwise, the emergency communication vehicle calculates its connection with... Session key ; The following equation for the hash function is used to determine this. Legality: ； S73, Emergency Communication Vehicle Select Short-Term Key Then, use a short-lived key. Calculate group session key The emergency communication vehicle then selects the current timestamp. Send message }to , The legality of the emergency communication vehicle's identity is verified according to procedure S38. If invalid, the process terminates; otherwise, unknown parameters are calculated. and session key ; in, This represents one of the operations performed on a Chebyshev polynomial. S74. With the addition of new members, the share of each node is updated synchronously, and emergency communication vehicles send information. to The process will then proceed according to S5 and S6. in, This indicates that encryption is performed using a symmetric key. The parameters to be encrypted. Indicates share; S75. Drone Departure: Suppose that one or more drones need to leave a drone swarm, either voluntarily or involuntarily, due to task scheduling, external interference, or malicious behavior. The departure of drones mainly affects the update of the group session key, and the process is as follows: Emergency communication vehicles select short-term keys Calculate the group session key later Then, the original members' shares within the group are updated according to the S74 procedure.

9. A system applied to the PUF-based group authentication and key negotiation method described in claim 8, characterized in that, include: The emergency communication vehicle module is used to perform system initialization, group authentication, secret share generation and distribution, threshold adjustment, and dynamic group management. The drone module is used to perform private key derivation, identity authentication, secret share verification, and key recovery based on physically unclonable functions and fuzz extractors; The system is configured to perform the method according to any one of claims 1 to 8.

10. The system for a PUF-based group authentication and key negotiation method according to claim 9, characterized in that: The fuzz extractor includes an error correction module and an auxiliary data generation module. The error correction module is used to perform noise-tolerant processing on the original response output by the physically non-clonable function. The auxiliary data generation module is used to generate auxiliary information to support the stable reconstruction of the response value under different environmental conditions. The auxiliary information does not disclose valid information related to the private key.

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