Predicate encryption-based low-altitude networking of intelligence fine-grained group communication method and system

Abstract

The invention discloses a low-altitude networking of intelligence fine-grained group communication method and system based on predicate encryption, and belongs to the technical field of network security communication. The method comprises the four steps of system initialization, entity registration, secure communication and key updating. In a registration stage, a predicate key is split into two parts, a first key component is stored in an unmanned aerial vehicle, and a second key component containing a complex attribute coupling item is stored in a ground base station. And during communication, decryption is realized by utilizing a preset matching relationship between the attribute vector and the predicate vector, and point-to-point communication based on the anonymous attribute vector and group communication based on public attribute filling are supported. During key updating or cross-domain switching, the ground base station uses the stored components to undertake the first type of operation with relatively high calculation complexity, and the unmanned aerial vehicle can synthesize a new key only by executing the second type of operation with relatively low calculation complexity. According to the method, the calculation overhead of the unmanned aerial vehicle is effectively reduced, and the problems of difficulty in fine-grained group division and key management under dynamic networking are solved.

Description

A Fine-Grained Group Communication Method and System for Low-Altitude Intelligent Networks Based on Predicate Encryption Technical Field

[0001] This invention belongs to the field of network security communication technology, specifically relating to a fine-grained group communication method and system for low-altitude intelligent networks based on predicate encryption. Background Technology

[0002] With the development of the low-altitude economy, low-altitude intelligent networks composed of unmanned aerial vehicles (UAVs) are playing an increasingly important role in disaster relief, environmental monitoring, and military reconnaissance. Due to the diversity of missions and the complexity of the environment, UAV swarms typically need to be dynamically networked and perform complex collaborative tasks.

[0003] Compared to traditional networks, low-altitude unmanned aerial vehicle (UAV) networks are characterized by high dynamism, rapid topology changes, and limited computing resources. However, as the network scales up and members change dynamically, the network establishment process becomes time-consuming, and ensuring its communication security also becomes more time-consuming. For example, the attribute proxy signature scheme for UAV networks proposed by He Lei et al., while guaranteeing unforgeability under chosen attribute attacks, experiences a significant increase in overhead time as the number of clusters increases. Furthermore, UAV cluster information transmission sometimes needs to be limited to a subset of network entities performing specific tasks, i.e., communication within a specific group. Therefore, employing task-oriented group communication technology can achieve data communication more efficiently.

[0004] As drone networks expand, dividing large-scale networks into finely sized subnets can significantly improve information gathering and task execution efficiency. However, current solutions struggle with fine-grained subnetting. While attribute-based approaches can address this to some extent, they still suffer from excessive overhead. Furthermore, due to the dynamic and large-scale nature of drone networks, the addition and removal of drones can cause network topology changes, leading to substantial communication and computational overhead, which negatively impacts the overall network's collaborative efficiency. To maintain the integrity of the subnet communication structure and ensure that newly added members can access shared network data while excluding departing members from internal subnet communication, key updates are required for both joining and leaving members. Ground base stations only need to broadcast update requests to joining and leaving members; there is no need to modify the keys of existing members within the subnet.

[0005] Therefore, there is an urgent need for a low-altitude intelligent network security communication solution that can adapt to highly dynamic environments, support fine-grained partitioning, and has low computational overhead. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to address the shortcomings of existing technologies by providing a fine-grained group communication method and system for low-altitude intelligent networks based on predicate encryption. Through attribute hierarchical settings and computation offloading mechanisms, this invention solves the problems of difficulty in fine-grained group division and heavy computational burden of UAV key updates in existing technologies.

[0007] Technical solution: The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption described in this invention includes the following steps:

[0008] Step S1, System Initialization: The trusted authorization authority generates system public parameters and master key, and distributes secret parameters to ground base stations and drones;

[0009] Step S2, Entity Registration: The trusted authorization agency generates corresponding attribute vectors and predicate vectors for the drone based on its identity, and generates a predicate key related to the predicate vectors; wherein, the predicate key is split into a first key component and a second key component, the first key component contains the drone's private random number part, which is stored in the drone, and the second key component contains an aggregate part that couples attributes and random numbers, which is stored in the ground base station to which the drone belongs;

[0010] Step S3, Secure Communication: The sender uses system public parameters and the attribute characteristics of the receiving target to encrypt the plaintext message to generate ciphertext. The receiver uses the predicate key it holds to decrypt the ciphertext. The condition for successful decryption is that the attribute vector corresponding to the ciphertext and the receiver's predicate vector satisfy the preset predicate matching relationship.

[0011] Step S4, Key Update: When the UAV needs to update its attributes or key validity, the trusted authorization authority generates update data; the ground base station uses its stored second key component and the update data to perform a first type of operation to generate intermediate update parameters and sends them to the UAV; after receiving the data, the UAV uses its stored first key component and the intermediate update parameters to perform a second type of operation, combining the intermediate update parameters with local parameters to obtain the updated complete predicate key; wherein, the computational complexity of the first type of operation is higher than that of the second type of operation.

[0012] The first type of operation mainly refers to the construction of bilinear groups (such as...). , The first type of operation refers to modular exponentiation or scalar multiplication on a bilinear group; the second type of operation refers to group element multiplication, group element division or dot addition on a bilinear group.

[0013] The present invention also provides a low-altitude intelligent network secure communication system based on predicate encryption, including a trusted authorization module, a base station processing module, and a UAV terminal module, for executing the above method.

[0014] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows:

[0015] This invention employs a hierarchical key storage and computation offloading mechanism. During key updates and cross-domain switching, computationally complex Type I operations (such as scalar multiplication or exponential operations on bilinear groups) are offloaded to ground base stations with higher computing power. The UAV only needs to perform less computationally complex Type II operations (such as dot addition or simple group multiplication). This design significantly reduces the computational burden on the UAV in dynamic environments and extends mission endurance.

[0016] The "valid code" attribute is introduced. When a key needs to be revoked or updated, the base station can simply issue a new valid code by a trusted authorized agency. The base station can then help calculate the update parameters to eliminate the impact of the old code without redistributing all keys, thus achieving efficient key revocation and update.

[0017] Based on the improved predicate encryption scheme, and utilizing the orthogonal matching relationship between attribute vectors and predicate vectors, this invention simultaneously supports fine-grained group broadcast communication for specific attribute sets and point-to-point communication for individuals under the same key system.

[0018] In point-to-point communication, an anonymous attribute vector generation mechanism is employed. The receiver generates an anonymous vector orthogonal to its own predicate through blinding processing, enabling the sender to complete encryption without knowing the receiver's true and specific attributes, thus satisfying the security requirements of anonymity and non-associability.

[0019] By placing the base station identifier attribute at the beginning of the attribute vector, when a drone crosses a domain, the new base station only needs to update the corresponding base station attribute component. Combined with the key migration mechanism, access can be completed quickly, adapting to the high-speed mobility characteristics of drones. Attached Figure Description

[0020] Figure 1 is a schematic diagram of the system model architecture provided in an embodiment of the present invention;

[0021] Figure 2 is a comparison chart of the relationship between the computational cost of the UAV and the number of attributes in an embodiment of the present invention;

[0022] Figure 3 is a comparison chart of the relationship between UAV communication overhead and the number of attributes in an embodiment of the present invention. Detailed Implementation

[0023] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the embodiments described.

[0024] Example 1: To address the secure communication problem in low-altitude intelligent network groups in existing technologies, this invention, based on predicate encryption technology, achieves secure and reliable communication within fine-grained groups by hierarchically setting the attributes of UAV entities. This invention introduces valid code attributes into the attributes of UAV entities, enabling efficient updates of UAV attributes and predicate keys. Subsequently, to prevent the exposure of the UAV's true attributes in point-to-point communication, this invention utilizes the many-to-many relationship between attributes and predicates, using predicates to randomly generate anonymous attributes to ensure the security of the UAV's true attributes.

[0025] As shown in Figure 1, the low-altitude intelligent network security communication system based on predicate encryption in this embodiment mainly includes three entities: a Trusted Authority (TA), a Base Station (BS), and a UAV.

[0026] The TA (Task Controller) is responsible for generating system parameters, managing attribute sets and predicate sets, and generating a "Code" attribute to control key validity. The BS (Base Station) possesses strong computing and storage capabilities, storing partial key information for UAVs within its jurisdiction to assist in key updates. The UAV, as the terminal node, executes specific tasks.

[0027] The method in this embodiment specifically includes the following steps:

[0028] Step S1: System initialization, including a trusted authorized agency generating system public parameters and a master key, and distributing secret parameters to ground base stations and drones;

[0029] Step S2: Register the drone and ground base station, generate corresponding attributes, predicates and keys related to the predicates, and store some key information in trusted authorization institutions and base stations to facilitate subsequent update operations;

[0030] Step S3: Point-to-point communication. The receiver uses its predicate to randomly generate a set of anonymous attributes and returns them to the sender. The sender uses the public parameters and this set of anonymous attributes to encrypt the plaintext and sends the resulting ciphertext message to the receiver. The receiver uses its predicate key to decrypt the plaintext. If the relationship between the attributes and the predicate is met, the plaintext is decrypted.

[0031] In group communication, the sender selects corresponding common attributes based on the common characteristics of the receiving group, and fills all other attributes with 0. The resulting attribute set is used to encrypt the message to be sent to the group. If the receiver's key matches the relationship between the attributes and the predicate, it can decrypt the message to obtain the plaintext.

[0032] Step S4: Key update. When the drone needs to update its attributes, it updates the key information pre-stored during the registration phase. The complex multiplication operation is handed over to the base station, and the drone can obtain the updated key by performing a single addition operation.

[0033] Step S5, Cross-Domain Joining / Leaving: During the attribute setting phase, we set the first attribute of the attribute set to the drone base station attribute. This attribute is the base station ID and only changes when the drone crosses domains. When the drone crosses a domain, it only needs to obtain the attribute of the other base station and perform a key update operation.

[0034] Specifically, step S1 includes:

[0035] S1.1 Constructing a Bilinear Mapping Environment: Given a bilinear mapping Its effect is on prime numbers. bilinear group Above, the generators are respectively .

[0036] S1.2 Generation Parameters: The trusted authorization authority selects random numbers. and random numbers corresponding to the dimension of the attribute set. ,all random numbers And calculate:

[0037]

[0038] ;

[0039] S1.3 Constructing Validity Control Parameters: Generating Attribute Sets Based on Requirements from Trusted Authorization Agencies and predicate set Choose a public attribute "Code" to ensure key validity, and compute the corresponding Code predicate using orthogonal relations. , making and The inner product is 0;

[0040] S1.4 Release Parameters: Calculate Common Parameters and master key :

[0041] .

[0042] Step S2, Entity Registration and Key Distribution

[0043] S2.1 The drone sends its real identity to a trusted authorized agency. A trusted authorization authority assigns attribute vectors to it. and predicate vector .

[0044] S2.2 Trusted Authorization Agency Selects Random Number Calculate the predicate key :

[0045]

[0046] Base station storage and The trusted authorization authority stores all the drone's operational data. Although the validity code update must be performed by the trusted authorization authority itself, the updates of other attributes are managed by the drone's designated base station.

[0047] S2.3 Key Splitting Storage

[0048] Compared to drones, ground base stations have stronger computing and storage capabilities, and their predicate keys are... After the terrestrial base station registration is completed, a trusted authorization agency allocates a partial master key to the registered terrestrial base station. Ground base stations can utilize a portion of the master key. The trusted authority independently updates the attributes of drones within its jurisdiction. It is only responsible for updating the overall system's key validity, attribute sets, and predicates, without participating in the updating of individual drone attributes.

[0049] First key component (stored in the drone): Drone storage The initial value (or its constituent factors) and The second key component (stored at the base station): The ground base station stores the part containing attribute coupling operations, including... and This hierarchical storage allows ground base stations to perform subsequent algebraic operations using the stored components without needing to know the drone's full private key.

[0050] Step S3, Secure Communication

[0051] This system supports point-to-point (single-point communication between drones or between a ground base station and a drone) and group (communication between a ground base station and a drone group). The core condition for decryption is the ciphertext attribute vector. With receiver predicate vector Satisfying orthogonality .

[0052] S3.1 Point-to-point communication (anonymous mode): The receiver utilizes its own predicate vector and random numbers Generate anonymous attribute vectors ,satisfy This is achieved by blinding the predicate vector.

[0053] Send connection request to ;

[0054] Use your own predicates Randomly generate an anonymous attribute Send to ;

[0055] take over Select random number calculate:

[0056]

[0057] Send ciphertext Give ;

[0058] Accept ciphertext Use your own predicate key Perform decryption:

[0059]

[0060] when Orthogonal, that is ,but Able to decrypt and obtain the message The specific decryption steps are as follows:

[0061]

[0062]

[0063]

[0064] =

[0065]

[0066] if If the result is 0, then the plaintext will be obtained. .

[0067] S3.2 Group Communication:

[0068] The sender determines the set of common attributes of the target group (e.g., "execute task A") and constructs an encrypted attribute vector. The common attributes are filled into the corresponding dimensions of the vector, while the remaining irrelevant dimensions are filled with 0. This vector is used to encrypt the broadcast; members within the group can decrypt it because their predicates are orthogonal to the common attributes (irrelevant bits being 0 do not affect the inner product).

[0069] When a base station needs to communicate with or issue tasks to nearby drones performing similar missions, assuming Having the same attributes The base station selects a common encryption attribute within the group. Encrypt group communication.

[0070] Station selects random number calculate:

[0071]

[0072] The base station will receive the ciphertext Send to The plaintext can be decrypted using one's own predicate key. .

[0073] Step S4, Key Update

[0074] When a trusted authorization authority transfers valid code from Updated to Time: Generate a predicate And calculate a new key for each base station and the drones under its jurisdiction:

[0075]

[0076] in, For the updated data of the i-th base station, This is expired valid code information. This is the currently valid code information. These are the private random parameters selected by the trusted authorization authority for the i-th base station during registration. Upon receiving the update command, the ground base station... direct use Eliminate expired valid codes and integrate the newly generated valid codes into the predicate key.

[0077] Trusted Authorization Authority Selects All-Zero Vector and random numbers calculate:

[0078]

[0079] ;

[0080] Obtain the predicate key update information of a ground base station and all UAVs within the jurisdiction of that base station. .

[0081] Trusted authorized agencies update data and then... Send ciphertext The ground base station received Decryption and It then updates its own predicate key, and subsequently the ground base station uses the drone update information calculated by the trusted authorized agency. Send it to the drones under its jurisdiction.

[0082] Assumption Update information received, calculation:

[0083]

[0084] Obtain the updated key ;

[0085] Similarly, drone attribute updates follow almost the same process as described above, but the operation targets a single drone entity. After the base station completes the update, it transmits the relevant information to both the drone and the trusted authorized agency, and updates the drone information stored in the database accordingly.

[0086] Step S5, Cross-domain switching

[0087] The first component of the attribute vector is set as the base station identifier attribute. When the drone moves from base station A to base station B, base station A migrates the drone's second key component to base station B. Base station B performs a first type of operation similar to S4 to generate update parameters for the new base station identifier, and the drone performs a second type of operation to complete the base station attribute update of the local key.

[0088] When belonging to The drones in the middle want to join , All drone key information stored in the database must be sent to And delete the data;

[0089] Upon receiving the information, update the drone's first attribute (i.e., the base station attribute). After the update is complete, the drone's identity information will be added to... In the database, and The drone information will then be removed from its own list, and a trusted authorized agency will be notified to update the data.

[0090] In summary, this embodiment significantly reduces the computational burden on UAVs in low-altitude intelligent networks by using attribute layering and key updates, while ensuring security.

[0091] To facilitate understanding of the technical solution in this embodiment, the relevant variables are explained, and the specific details are shown in Table 1.

[0092] Table 1

[0093]

[0094] Table 2 presents the experimental configuration and other parameters of this embodiment.

[0095] Table 2

[0096] Parameter Configuration: Processor: Intel Core i7-10700; RAM: 32GB; Implementation Language: C++; Hash Function: SHA 256; Elliptic Curve: BLS12383; Cryptographic Library: Miracl; Core Measurement: Metrics: 100 times. surface

[0097] Table 3 presents a theoretical analysis of the computational overhead of the scheme at each stage of point-to-point communication.

[0098] Table 3

[0099]

[0100] in They represent Exponential calculation time in the group. This represents the average computation time of the pairing operation. The number of attributes / predicates involved in the operation.

[0101] Table 4 presents a theoretical analysis of the communication overhead at each stage of the scheme during point-to-point communication.

[0102] Table 4

[0103]

[0104] in, Indicates the bit length of each group element. This represents the number of attributes / predicates involved in the operation. Large integers occupy 65 bytes, while... and The dots on the group were compressed to 49, 98, and 294 bytes respectively. Due to the message... The length varies with the transmitted information rather than being fixed, and is therefore not considered here.

[0105] Figure 2 illustrates the impact of the number of attributes on computational and communication overhead in point-to-point communication. As the number of attributes on the UAV increases, the total computational overhead also increases accordingly. However, it's easy to observe in Figure 2 that the number of attributes and computational overhead do not exhibit a linear relationship; instead, the growth rate of computational overhead decreases as the number of attributes increases. This is because regardless of the number of attributes, the decryption operation only requires three pairing operations, and the number of pairing operations does not change with the number of attributes.

[0106] Figure 3 illustrates the relationship between communication overhead and the number of attributes in point-to-point communication between UAVs. The communication overhead increases linearly with the number of attributes. In point-to-point communication, UAVs need to generate corresponding anonymous attribute sets based on their own real predicate sets to ensure that the other party can use the correct anonymous attributes to encrypt information. As the number of UAV attributes increases, the communication overhead will also increase linearly.

[0107] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A fine-grained group communication method for low-altitude intelligent networks based on predicate encryption, characterized in that, Includes the following steps: Step S1, System Initialization: The trusted authorization agency generates system public parameters and a master key, and distributes secret parameters to the ground base station and the UAV; Step S2, Entity Registration: The trusted authorization agency generates corresponding attribute vectors and predicate vectors for the UAV based on its identity, and generates a predicate key associated with the predicate vectors; wherein, the predicate key is split into a first key component and a second key component, the first key component is stored in the UAV, and the second key component is stored in the ground base station to which the UAV belongs; Step S3, Secure Communication: The sender uses the system public parameters and the attribute characteristics of the receiving target to encrypt the plaintext message to generate ciphertext, and the receiver uses its predicate key to decrypt the ciphertext, if and Decryption is successful and plaintext is obtained only when the attribute vector corresponding to the ciphertext and the predicate vector of the receiver satisfy the preset predicate matching relationship; Step S4, Key Update: The update of non-valid code attributes can be initiated by any entity in the system; when valid code attributes need to be updated, the trusted authorized agency generates update data; the ground base station uses its stored second key component and update data to perform the first type of operation to generate intermediate update parameters and send them to the UAV; after receiving the data, the UAV uses its own stored first key component and intermediate update parameters to perform the second type of operation, synthesizes the intermediate update parameters with local parameters, and obtains the updated predicate key; wherein, the computational complexity of the first type of operation is higher than that of the second type of operation.

2. The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption according to claim 1, characterized in that, The system initialization in step S1 includes: Step S1.1, constructing a bilinear mapping environment: selecting a prime order. bilinear group and bilinear mapping Determine generator and Step S1.2: Generate random secret parameters: The trusted authorization agency selects random numbers. and random numbers corresponding to the dimension of the attribute set. All of the random numbers belong to And perform the following calculations: ， Step S1.3: Construct validity control parameters: Select a public valid code attribute. And calculate the corresponding predicate vector components. , making and The inner product is zero, thus obtaining the common parameters. and master key ： ； 。 3. The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption according to claim 2, characterized in that, The entity registration in step S2 includes: the drone registering its real identity. Send to a trusted authority, which then retrieves the attribute set. Select a set of attributes And calculate the attribute vector and predicate vector ： ， ;in, To verify the true identity of the drone, For valid code, The effective code predicate is calculated using orthogonal relations; the predicate key for: ;in, These are common system parameters. The key component stored in the UAV is a random number; The second key component stored in the ground base station includes 。 4. The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption according to claim 3, characterized in that, The attribute vector generated in step S2 includes hierarchically configured base station identifier attributes, functional attributes, and valid code attributes; the preset predicate matching relationship is an orthogonal relationship if and only if the vector inner product... When the predicate matching relationship is satisfied, the inner product of the valid code attribute and the generated corresponding predicate component is zero; the first type of operation includes dot multiplication on the group, the second type of operation includes dot addition, and the key update in step S4 includes: when a trusted authorization agency releases a new valid code attribute, the ground base station uses dot multiplication and combines it with the second key component corresponding to the stored old version of the valid code to calculate the intermediate update parameter to eliminate the influence of the old code; after receiving the intermediate update parameter, the UAV performs dot addition within the group to obtain an update key containing the new valid code attribute.

5. The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption according to claim 2, characterized in that, The key update in step S4 includes: when the valid code is changed by... Updated to At that time, the trusted authorization authority calculates the first Update data of each base station ： ,in, This indicates expired valid code information. This indicates the currently valid code information. The trusted authorization structure selects private random parameters for the i-th base station during registration; the UAV receives data containing... After updating the information, perform the second type of operation to calculate the updated key. ： Thus, the updated key set is obtained. 。 6. The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption according to claim 3, characterized in that, Step S3 includes a point-to-point communication mode between drones or between a ground base station and a drone. In this mode, the specific process by which the receiver generates anonymous attributes is as follows: the receiver utilizes its own predicate vector... Generate anonymous attribute vectors that hide the real attributes Send to the sender; the sender utilizes the anonymous attribute vector Select random numbers It encrypts the plaintext and sends it to the receiver; the receiver decrypts it using its own predicate key, when the conditions are met. The recipient is able to decrypt the ciphertext.

7. The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption according to claim 6, characterized in that, The encryption and decryption process of point-to-point communication in step S3 satisfies the following mathematical relationship: The sender selects a random number. The generated ciphertext satisfy: ;in, For plain text, ， An anonymous attribute vector is generated for the recipient; the recipient's decryption verification formula is: If and only if When the above equation holds true, the plaintext is restored. 。 8. The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption according to claim 3, characterized in that, Step S3 includes a group communication mode between a ground base station and a drone swarm. The sender is the ground base station, and the receiver is the target drone swarm. The process is as follows: the sender determines a common attribute set based on the common characteristics of the receivers; the sender constructs an encrypted attribute vector, where the dimensions corresponding to the common attribute set are filled with common attribute values, and the remaining dimensions are filled with zero values; the sender broadcasts ciphertext using the encrypted attribute vector; if the receiver's predicate vector... If the inner product of the encrypted attribute vector and the encrypted attribute vector is zero, then decryption is successful.

9. The fine-grained group communication method for low-altitude intelligent networks based on predicate encryption according to claim 5, characterized in that, The method further includes a cross-domain handover step: the first component of the attribute vector is set to the base station identifier attribute to which the UAV belongs; when the UAV crosses domain from the first ground base station to the second ground base station, the first ground base station sends the second key component of the UAV stored therein to the second ground base station and deletes it from its local storage; the second ground base station updates the first component of the attribute vector according to its own base station identifier and performs the first type of operation to generate update parameters for the base station identifier attribute and sends them to the UAV. The drone performs the second type of operation to update the local key.

10. A fine-grained group secure communication system for low-altitude intelligent networks based on predicate encryption, characterized in that, include: The trusted authorization module is used to generate system public parameters and master keys, generate attribute vectors, predicate vectors and initial predicate keys for registered entities, and is responsible for generating and publishing valid code attributes used to control the validity of keys; The base station processing module, deployed on a ground base station, is used to store a portion of the predicate key components of UAVs within its jurisdiction. It is configured to perform computationally complex scalar multiplication or exponential operations using the stored key components to generate intermediate update parameters during key updates or cross-domain switching, and then send the results to the UAV. The UAV terminal module, deployed on the UAV, is used to store its own key components; it is configured to perform encrypted communication using system public parameters and target attributes, or to perform point-to-point communication using anonymous attribute vectors. Upon receiving intermediate update parameters from the base station, perform a point addition operation with low computational complexity to synthesize the updated complete key.

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