Robust efficient physical layer key generation method based on edge federated learning

Abstract

The invention discloses a robust efficient physical layer key generation method based on edge federated learning. The method comprises the steps that an edge server prepares a channel state information data set; the edge server divides the local beta-VAE model into a shared part and a private part, and cooperates with the base station to perform personalized federated learning to complete training of the local beta-VAE model; the edge server stores an encoder part of the trained personalized local beta-VAE model; the communication party carries out channel estimation to obtain channel state information; the communication party and the base station perform feature extraction and quantification on the channel state information by using a local encoder; and the communication party and the base station carry out information negotiation, and the bit mismatching rate is recorded. And if the bit mismatching rate is greater than a threshold value, carrying out privacy protection model aggregation and key generation model switching, otherwise, carrying out privacy amplification on key bits, and obtaining a consistent final key of the two parties. According to the invention, through a lightweight pre-training and fine tuning mode, the key generation cost is greatly reduced.

Description

Technical Field

[0001] The present invention relates to the field of cyberspace security, and more specifically, to a physical layer key generation method based on edge federated learning. Background Art

[0002] The rapid development of wireless communication technology is profoundly reshaping the way humans connect. From the massive access of Internet of Things (IoT) terminals to the real-time interaction of vehicle-to-everything (V2X) networks, from the precise control of industrial Internet to the intelligent services of mobile terminals, wireless networks have become an indispensable infrastructure in the digital age. However, the characteristics of the open and shared transmission medium make wireless communication systems naturally exposed to security threats such as eavesdropping, forgery, and man-in-the-middle attacks. Traditional encryption technologies rely on computational complexity or pre-distributed key mechanisms, and are facing severe challenges in scenarios with resource-constrained mobile terminals, edge computing nodes, etc. Overly complex encryption and decryption algorithms consume a large amount of computing power, which cannot be borne by resource-limited mobile devices; while key distribution protocols rely on a centralized architecture and are prone to single-point failures, and the lag in key updates in dynamic topology networks is more likely to trigger chain security vulnerabilities. Against this background, how to build a lightweight and low-latency security system has become the focus of common concern in academia and industry.

[0003] To solve the above problems, wireless channel key generation technology based on physical layer characteristics has gradually come to the forefront. This technology abandons the "pre-set key" paradigm of traditional cryptography and instead exploits the physical characteristics of the wireless channel itself as the security foundation. Due to the influence of multipath effects, Doppler frequency shift, environmental scattering, etc. on the propagation of wireless signals, the channel state information (CSI) or received signal strength (RSS) of the two communication parties has high reciprocity and spatio-temporal uniqueness within a short time window. The high reciprocity of these physical layer characteristics of the two communication parties ensures that they are the same at the same moment, while their spatio-temporal uniqueness ensures that they are different with the growth of time and different spatial positions. By quantifying these time-varying characteristics to generate a random sequence, PSKG can achieve identity binding and key negotiation of communication entities without pre-sharing keys. Taking CSI as an example, its phase and amplitude information can form a multi-dimensional random source, containing more channel information than RSS commonly used in traditional schemes. Therefore, the key generation rate is several times higher than that of traditional RSS schemes. At the same time, noise interference is suppressed through a joint quantization algorithm to ensure the consistency of keys between the transceiver parties. Potential eavesdroppers cannot obtain the same channel characteristics as legitimate communication parties due to their positions, and thus cannot steal legitimate communication keys. This concept of "the environment is the password" not only greatly reduces the computational overhead, but also naturally adapts to dynamic network environments, providing a new security paradigm for resource-sensitive scenarios such as drone swarms and wearable devices.

[0004] However, the practical application process of PSKG technology is still restricted by multiple challenges. First, the openness of physical layer characteristics can be a double-edged sword. Potential attackers can predict the key generation pattern by long-term monitoring of statistical characteristics, which poses a great challenge to the security of wireless channel key generation algorithms. In more complex key generation protocols, attackers can launch attacks at different links of the protocol, increasing the difficulty of secure key generation. Second, in resource-constrained scenarios, the limited computing power, energy consumption, and communication bandwidth of terminal devices restrict the efficiency of key generation algorithms. For example, although high-dimensional CSI quantization can improve key randomness, it consumes more computing resources, which mobile devices may not be able to bear, while lightweight solutions may lead to a decrease in key entropy due to insufficient feature dimensions. More critically, the dynamic environment further exacerbates system complexity: device mobility shortens the channel coherence time, forcing the key generation period to be compressed, and asynchronous measurements in fast time-varying channels may cause feature offsets between the transmitter and receiver, adding difficulties to maintaining key consistency between communication parties. These challenges are intertwined, requiring researchers to collaborate and innovate from multiple dimensions such as channel modeling, protocol optimization, and key generation algorithms in order to build a reliable security barrier in an open, dynamic, and resource-constrained wireless environment. Summary of the Invention

[0005] In view of the problems mentioned in the background art, the present invention provides a robust and efficient physical layer key generation method. The present invention uses a β-VAE neural network to extract channel features and utilizes the data utilization and privacy protection capabilities of personalized federated learning to train the model, realizing a lightweight fine-tuning method, improving the key rate of physical layer key generation, and efficiently calculating physical layer keys.

[0006] The present application provides a robust and efficient physical layer key generation method based on edge federated learning, which is characterized by including the following steps:

[0007] Step 1. The edge server prepares a channel state information dataset;

[0008] Step 2. The edge server divides the local β-VAE model into a shared part and a private part, and collaborates with the base station to complete the training of the local β-VAE model through personalized federated learning;

[0009] Step 3. The edge server saves the encoder part of the trained personalized local β-VAE model;

[0010] Step 4. The communication party performs channel estimation to obtain channel state information;

[0011] Step 5. The communication party and the base station use the local encoder to extract and quantize the features of the channel state information;

[0012] Step 6. The communicating party and the base station negotiate information and record the bit mismatch rate; if the bit mismatch rate is greater than the set threshold, a privacy protection model aggregation switching key generation model is performed, and the process starts from step 5 again; otherwise, privacy amplification is performed on the key bits to obtain the final consistent key for both parties; if more keys need to be generated, the process starts from step 4 again.

[0013] Preferably, step 1 includes:

[0014] Step 1.1. The base station sends a pilot signal X to the edge server a , and based on the channel model, the signal received by the edge server is

[0015] Y b =H ae X a +N e

[0016] where N e ~CN(0,σ 2 ) is the additive white Gaussian noise accumulated during the propagation of the signal in the channel, and CN(0,σ 2 ) refers to a complex Gaussian distribution with a mean of 0 and a variance of σ 2 . H ae is the channel state information from the base station to the edge server;

[0017] Step 1.2. The edge server performs channel feature estimation to obtain the channel state information; here, the least squares method is used to obtain the estimation result:

[0018]

[0019] Here, X a and Y b represent the pilot signal sent by the base station to the edge server and the signal received by the edge server respectively, represents the square of the Frobenius norm of the matrix. The meaning of this formula is to find a matrix H whose value minimizes the square of the Frobenius norm of Y b -HX a .

[0020] Step 1.3. Repeat steps 1 and 2 in a loop to accumulate a sufficient dataset of channel state information at each edge server.

[0021] Preferably, step 2 includes:

[0022] Step 2.1. Each edge server i initializes its own local β-VAE model θ i , and the base station initializes the global β-VAE model θ global .

[0023] The local β-VAE model consists of an encoder and a decoder. The encoder receives the input data x and outputs a mean vector μ and a standard deviation vector σ to define the distribution q(z|x) in the latent space, where z represents the latent variable. The decoder receives the sample z sampled from the latent space and reconstructs the original input data through inverse transformation. Each edge server divides the local β-VAE model θ i into a shared part and a private part where the private part contains the last layer of the model encoder and the first layer of the decoder, and the remaining part is the shared part.

[0024]

[0025] Similarly, for the base station's global β-VAE model θ global :

[0026]

[0027] Step 2.2: The base station sends the shared part in the global β-VAE model to each edge server, and each edge server uses it to initialize the shared part of its own local β-VAE model:

[0028]

[0029] Step 2.3: The edge server trains the local β-VAE model using the channel state information dataset accumulated in Step 1.3, repeats it T lt times, and updates the local β-VAE model parameters using the gradient descent method:

[0030]

[0031] θ i ←θ i +α·g lt

[0032] where: H i is the channel state information dataset of edge server i, L recon is the reconstruction loss, and here the mean squared error is adopted. L KL is the KL divergence calculation, β is a hyperparameter used to adjust the weight of the KL divergence term, and α is the learning rate used to adjust the step size of the gradient descent;

[0033] Step 2.4: The edge server sends the shared part in the local β-VAE model with updated parameters to the server, and the local β-VAE model retains the private part

[0034] Step 2.5: The base station collects the shared parameters of all edge servers, aggregates these parameters, and when aggregating, the weight of each edge server is proportional to the size of its training set. Finally, the global model is updated:

[0035]

[0036] where |H sum | is the sum of the sizes of the training sets of all edge servers;

[0037] Step 2.6: Repeat Steps 2.2 to 2.5 until the model converges.

[0038] Preferably, in Step 3, each edge server saves the encoder part M i of the local β-VAE model θ i The encoder part M i contains some shared parameters and some private parameters.

[0039] Preferably, Step 4 includes:

[0040] Step 4.1: The user and the base station send pilot signals X b , X a to each other for channel feature estimation. The signals received by the user and the base station are respectively

[0041] Y b = H ab X a + N b

[0042] Y a = H ba X b + N a

[0043] where N a , N b ~ CN(0, σ 2 ) is the additive white Gaussian noise accumulated during the propagation of the signal in the channel, and H ab , H ba are the channel state information from the base station to the edge server;

[0044] Step 4.2: The user and the base station respectively perform channel estimation to obtain

[0045]

[0046] That is the channel state information obtained by the user and the base station, and these two are approximately equal:

[0047]

[0048] Preferably, step 5 includes:

[0049] Step 5.1: The user and the base station use their own same encoder θ kg As a key generation model, use the channel estimation H as the input of the model, and use the output μ of the encoder as the extracted feature for subsequent quantization;

[0050] Step 5.2: For each output bit x, perform Q-bit quantization, and the output x ∈ [-1, 1]. The quantization formula is

[0051]

[0052] Preferably, step 6 includes:

[0053] Step 6.1: The user and the base station conduct information negotiation and record the bit mismatch rate. Assume that the initial bit strings of the user and the base station are k a and k b , respectively divide them into K small blocks, and calculate the parity check bits of each small block j (u = a, b) as follows:

[0054]

[0055] where n is the length of this block, represents the exclusive OR operation. If the parity check bits of the user and the base station are inconsistent, then this block needs to be further subdivided to determine which specific bit is incorrect. After counting the incorrect bits, calculate and record the key bit mismatch rate:

[0056]

[0057] Step 6.2: If the recorded bit mismatch rate exceeds the set threshold τ, then execute steps 6.3 - 6.5 for re-aggregation and switching of the model; if the bit mismatch rate is less than the set threshold τ, then execute step 6.6;

[0058] Step 6.3: Based on the location information of the user, select the K edge servers with the closest topology to construct a dynamic aggregation group. For each selected edge server model M i , extract its latent representation, that is, the encoder output O i = M i(H) ∈ [-1, 1], where H is the channel state information collected locally by the user. To meet the differential privacy requirements, a Laplace noise with a scale parameter of is imposed on each potential representation, where ∈ is the privacy budget:

[0059]

[0060] Step 6.4: Average the potential representations of all selected edge servers:

[0061]

[0062] Step 6.5: Fine-tune the local β-VAE model using the averaged potential representation, and send the fine-tuned model to the base station and the user. Then, start from Step 5. The loss function used for fine-tuning is as follows:

[0063] L total = L recon + β · L KL + γ · L soft

[0064] where L soft is the minimum mean square error between the output of the user model and the average potential representation of the selected edge servers. The final loss function is a linear combination of L recon 、L KL and L soft in the following calculation method:

[0065]

[0066] Here, θ kg is the model parameter of the β-VAE model for key generation, and refer to the encoder part and the decoder part of the model respectively. refers to the reconstructed version after the input x is encoded and decoded. E x～H refers to the mathematical expectation when the input x follows the channel state information distribution H. L recon calculates the mean square error between the original input x and the reconstructed . L KL calculates the difference between the posterior distribution of the latent variable output by the encoder and the prior distribution of the latent variable. L soft calculates the mean square error between the encoding result and the potential output O of the edge server. Among them, the calculation method of the KL divergence is as follows:

[0067]

[0068] Step 6.6: Perform privacy amplification on the key bits after information negotiation to obtain the final key; the privacy amplification uses a hash function h to map the original longer bit string to a shorter bit string, thereby obtaining the final key; if more keys need to be generated continuously, continue to execute from step 4.

[0069] The technical solution provided by this application has at least the following technical effects or advantages:

[0070] 1. The present invention utilizes the powerful feature extraction ability of β-VAE and the additional randomness introduced by the β term to improve the key rate of physical layer key generation and reduce the key bit inconsistency rate.

[0071] 2. The present invention reduces the computational cost of key generation on the basis of ensuring the efficient key generation effect through pre-training of a one-time model and lightweight fine-tuning. Description of the Drawings

[0072] Figure 1 It is a flowchart of the specific implementation manner of the present invention.

[0073] Figure 2 It is a schematic diagram of the model structure of the β-VAE network adopted in the specific implementation manner of the present invention.

[0074] Figure 3 It is a relationship diagram and data flow diagram between the main modules in the specific implementation manner of the present invention. Specific Embodiment

[0075] The present invention provides a robust and efficient physical layer key generation method based on edge federated learning, as Figures 1-3 shown, including the following steps:

[0076] Step 1: The edge server prepares a channel state information data set, and the specific steps are as follows:

[0077] Step 1.1: The base station sends a pilot signal X a , and based on the channel model, the signal received by the edge server is

[0078] Y b = H ae X a + N e

[0079] where N e ~ CN(0, σ 2 ) is the additive white Gaussian noise accumulated during the propagation of the signal in the channel, and CN(0, σ 2 ) refers to a complex Gaussian distribution with a mean of 0 and a variance of σ 2 The Hae Namely, it is the channel state information from the base station to the edge server;

[0080] Step 1.2: The edge server performs channel feature estimation to obtain the channel state information. Here, the least squares method is used to obtain the estimation result:

[0081]

[0082] X a and Y b respectively represent the pilot signal sent by the base station to the edge server and the signal received by the edge server. represents the square of the Frobenius norm of the matrix. The meaning of this formula is to find a matrix H whose value minimizes the square of the Frobenius norm of Y b - HX a .

[0083] Step 1.3: Repeat the above steps multiple times to accumulate a sufficient dataset of channel state information at each edge server.

[0084] Step 2: The edge server divides its local β-VAE model into a shared part and a private part, and collaborates with the base station to complete the training of the model through personalized federated learning. The specific steps are as follows:

[0085] Step 2.1: Each edge server i initializes its local β-VAE model θ i , and the base station initializes the global β-VAE model θ global . The β-VAE model consists of an encoder and a decoder. As Figure 2 shown, the encoder receives the input data x and outputs two vectors: the mean vector μ and the standard deviation vector σ. These two vectors are used to define the distribution q(z|x) in the latent space, where z represents the latent variable. The decoder receives the sample z sampled from the latent space and attempts to reconstruct the original input data through a series of inverse transformations Each edge server divides its local model θ i into a shared part and a private part where the private part contains the last layer of the model encoder and the first layer of the decoder, and the remaining part of the model is the shared part

[0086]

[0087] The base station performs the same operation:

[0088]

[0089] After that, repeat steps 2.2 - 2.5 until the model converges.

[0090] Step 2.2: The base station sends the shared part in the global model to each edge server, and each edge server uses it to initialize the shared part of its local model:

[0091]

[0092] Step 2.3: Repeat T lt times. The edge server trains the local β-VAE model using the local dataset and updates the local model parameters using the gradient descent method:

[0093]

[0094] θ i ←θ i +αHg lt

[0095] where H i is the channel state information dataset of edge server i. L recon is the reconstruction loss. In this embodiment, we use the mean squared error. L KL is the KL divergence calculation. β is a hyperparameter used to adjust the weight of the KL divergence term, and its value needs to be adjusted according to the actual situation. α is the learning rate used to adjust the step size of the gradient descent.

[0096] Step 2.4: The edge server sends the shared part in the local update of the model to the server and retains the private part locally

[0097] Step 2.5: The base station collects the shared parameters of all edge servers, aggregates these parameters, and when aggregating, the weight of each edge server is proportional to the size of its training set. Finally, the global model is updated:

[0098]

[0099] where |H sum | is the sum of the sizes of the training sets of all edge servers.

[0100] Step 3: The edge server saves the encoder part of the trained personalized β-VAE. Each edge server saves the encoder part M i of its local β-VAE model θ i . This part contains a part of shared parameters and a part of private parameters. The training is only carried out once, and the encoder part will not change after training.

[0101] Step 4: The communicating party performs channel estimation to obtain channel state information. The steps include:

[0102] Step 4.1: The user and the base station mutually send pilot signal X b , X a to perform channel characteristic estimation. The signals received by both are

[0103] Y b = H ab X a + N b

[0104] Y a = H ba X b + N a

[0105] where N a , N b ~ CN(0, σ 2 ) is the additive white Gaussian noise accumulated during the propagation of the signal in the channel, and H ab , H ba is the channel state information from the base station to the edge server.

[0106] Step 4.2: The user and the base station respectively perform channel estimation to obtain

[0107]

[0108] which are the channel state information obtained by the user and the base station. These two should be approximately equal:

[0109]

[0110] Step 5: The communicating party and the base station use a local encoder to perform feature extraction and quantization on the channel state information.

[0111] Step 5.1: The user and the base station use their own identical encoder θ kg as the key generation model, take the channel estimation H as the input of the model, and use the output μ of the encoder as the extracted feature for subsequent quantization.

[0112] Step 5.2: In this embodiment, for each output x during quantization, Q-bit quantization is used. The tanh activation function is used in the model of this embodiment, and the output x is restricted within [-1, 1]. The quantization formula is

[0113]

[0114] Step 6. The communicating party and the base station conduct information negotiation and record the bit mismatch rate. If the bit mismatch rate is greater than the set threshold, switch to the privacy protection model aggregation key generation model and restart from Step 5. Otherwise, perform privacy amplification on the key bits to obtain the final consistent key for both parties. If more keys need to be generated, restart from Step 4. The specific steps are as follows:

[0115] Step 6.1. The user and the base station conduct information negotiation and record the bit mismatch rate. Assume the initial bit strings of the user and the base station are k a and k b , respectively. Divide them into K small blocks and calculate the parity check bits for each small block j (u = a, b) as follows:

[0116]

[0117] where n is the length of the block, represents the exclusive OR operation. If the parity check bits of the user and the base station are inconsistent, the block needs to be further divided to determine which specific bit is incorrect. After counting the incorrect bits, the key bit inconsistency rate can be calculated and recorded:

[0118]

[0119] Step 6.2. If the recorded bit inconsistency rate exceeds the set threshold τ, it indicates that the current model performance is poor and the model needs to be re-aggregated and switched. In this case, execute Step 6.3 - Step 6.5; if the bit inconsistency rate is less than the set threshold τ, start from Step 6.6.

[0120] Step 6.3. Based on the user's location information, select the K edge servers with the closest topology to form a dynamic aggregation group. For each selected edge server model M i , extract its latent representation (i.e., the encoder output) O i = M i (H) ∈ [-1, 1], where H is the channel state information collected locally by the user. To meet the differential privacy requirements, apply Laplace noise with a scale parameter of to each latent representation, where ∈ is the privacy budget:

[0121]

[0122] Step 6.4. Average the latent representations of all selected edge servers:

[0123]

[0124] Step 6.5 Fine-tune the local β-VAE model using the averaged latent representation, and send the fine-tuned model to the base station and the user, then start from Step 5. The loss function used for fine-tuning is as follows:

[0125] L total = L recon + β·L KL + γ·L soft

[0126] Among them, the first two terms are the loss functions of β-VAE, which have been introduced in Step 2.3, and the third term L soft is the mean squared error between the output of the user model and the averaged latent representation of the selected edge server. The final loss function is a linear combination of these three terms. The calculation methods of these three terms are as follows:

[0127]

[0128]

[0129] Here, θ kg are the model parameters of the β-VAE model for key generation, and refer to the encoder part and the decoder part of the model respectively. refers to the reconstructed version of the input x after encoding and decoding. E x～H refers to the mathematical expectation when the input x follows the channel state information distribution H. L recon calculates the mean squared error between the original input x and the reconstructed . L KL calculates the difference between the posterior distribution of the latent variables output by the encoder and the prior distribution of the latent variables. L soft calculates the mean squared error between the encoding result and the latent output O of the edge server. Among them, the calculation method of the KL divergence is as follows:

[0130]

[0131] Step 6.6 Perform privacy amplification on the key bits after information negotiation to obtain the final key. Privacy amplification aims to reduce the amount of information about the key obtained by potential eavesdroppers, ensuring that even if part of the key information is leaked, the eavesdropper cannot recover the complete key. In this embodiment, the hash function h is used to map the original longer bit string to a shorter bit string, which is the obtained final key. If more keys need to be generated, start from Step 4.

[0132] The present invention utilizes the powerful feature extraction ability of β-VAE to extract features from channel state information, introduces personalized federated learning for training the key generation model, and makes lightweight fine-tuning of the model for the problem of channel environment changes caused by the movement of communication parties. The present invention can dynamically switch the model, quantize features into key bits, and obtain the final key bits through information negotiation and privacy amplification.

[0133] In practical applications, the model training part (Steps 1 - 3) will only be executed once, while the key generation part (Steps 4 - 6) may be executed multiple times according to the need for the number of key generations. On the one hand, the method proposed in the present invention improves the robustness of key generation through the feature extraction ability and dynamic fine-tuning of the β-VAE model; on the other hand, the method proposed in this paper greatly reduces the cost of key generation through the lightweight pre-training plus fine-tuning method.

[0134] To better understand the above technical solution, the following gives an example introduction of a physical layer key generation method based on edge federated learning.

[0135] Assume that the legitimate communication parties are users and the base station, and there are 4 edge servers in total. First, the 4 edge servers collect their own channel state information datasets, and the datasets are as follows:

[0136] Table 1

[0137]

[0138] These four edge servers act as clients to be responsible for local training tasks, and the base station acts as a server to be responsible for model aggregation tasks for federated learning until convergence. After training is completed, each edge server saves a personalized model of its own for aggregating to generate a user model later.

[0139] Assume that the channel state information estimated by the user and the base station is as follows, and their channel state information is roughly the same:

[0140] Table 2

[0141]

[0142] Calculated through the encoder on the user side:

[0143] Table 3

[0144]

[0145] Using 3-bit quantization, the quantization result on the user side is 111000111100, and the quantization result on the base station side is 101101000111. There are 8 bits inconsistent. After key negotiation, the errors in these 8 bits can be found. At this time, the key bit error rate is recorded as 8 / 12 = 0.67. This exceeds the threshold of 0.25 we set, so the model is triggered to re-aggregate. At this time, the channel state information on the user side is used as the data set, and the encoded output of the model saved on the edge server is obtained, and it is used to fine-tune the key generation model on the user side. After the fine-tuning is completed, the encoder output of the fine-tuned user-side model is used for quantization, and the following results are obtained:

[0146] Table 4

[0147]

[0148]

[0149] Using 3-bit quantization, the quantization result on the user side is 100 001 101 111, and the quantization result on the base station side is 100 001 101 111. The key bits are exactly the same. After key negotiation, it can be verified that there is no key bit error; then privacy amplification will be performed. This step uses a hash function. Taking the Toeplitz matrix as an example of the hash function, first determine that the length of the final key is 4, calculate the corresponding Toeplitz matrix H, and multiply it by the key:

[0150] K′ = H·K

[0151] The final key bits K' = 1101 are obtained.

[0152] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A robust and efficient physical layer key generation method based on edge federated learning, characterized in that It includes the following steps: Step 1. The edge server prepares a channel state information data set; Step 2. The edge server divides the local β-VAE model into a shared part and a private part, and collaborates with the base station to perform personalized federated learning to complete the training of the local β-VAE model; Step 3. The edge server saves the encoder part of the trained personalized local β-VAE model; Step 4. The communicating party performs channel estimation to obtain channel state information; Step 5. The communicating party and the base station use the local encoder to extract features from the channel state information and quantize it; Step 6. The communicating party and the base station perform information negotiation and record the bit mismatch rate; if the bit mismatch rate is greater than the set threshold, switch to the key generation model for privacy-preserving model aggregation and re-execute from Step 5; otherwise, perform privacy amplification on the key bits to obtain the final consistent key for both parties; if more keys need to be generated, re-execute from Step 4.

2. The robust and efficient physical layer key generation method based on edge federated learning according to claim 1, wherein, The said Step 1 includes: Step 1.

1. The base station sends a pilot signal X to the edge server a , based on the channel model, the signal received by the edge server is Y b = H ae X a + N e where N e ~CN(0, σ 2 ) is the additive white Gaussian noise accumulated during the signal propagation in the channel. CN(0, σ 2 ) refers to a complex Gaussian distribution with a mean of 0 and a variance of σ 2 , and H ae is the channel state information from the base station to the edge server; Step 1.

2. The edge server performs channel feature estimation to obtain channel state information; here, the least squares method is used to obtain the estimation result: where X a and Y b represent the pilot signal sent by the base station to the edge server and the signal received by the edge server, respectively, represents the square of the Frobenius norm of the matrix; Step 1.

3. Repeat Steps 1 and 2 in a loop to accumulate a sufficient channel state information data set at each edge server.

3. The robust and efficient physical layer key generation method based on edge federated learning according to claim 1, wherein The said Step 2 includes: Step 2.1: Each edge server i initializes its own local β-VAE model θ i , and the base station initializes the global β-VAE model θ global , The local β-VAE model consists of an encoder and a decoder. The encoder receives the input data x and outputs the mean vector μ and the standard deviation vector σ to define the distribution q(z|x) in the latent space, where z represents the latent variable. The decoder receives the sample z sampled from the latent space and reconstructs the original input data through the inverse transformation Each edge server divides the local β-VAE model θ i into a shared part and a private part where the private part contains the last layer of the model encoder and the first layer of the decoder, and the remaining part is the shared part Similarly, the base station global β-VAE model θ global : Step 2.

2. The base station sends the shared part in the global β-VAE model to each edge server, and each edge server uses to initialize the shared part of its local β-VAE model: Step 2.3: The edge server uses the channel state information dataset accumulated in Step 1.3 to train the local β-VAE model, and repeats the execution for T lt times, and updates the local β-VAE model parameters using the gradient descent method: θ i ←θ i +α·g lt Where: H i is the channel state information data set of edge server i, L recon is the reconstruction loss, and here the minimum mean square error is adopted, L KL is the KL divergence calculation, β is a hyperparameter used to adjust the weight of the KL divergence term, and α is the learning rate used to adjust the step size of gradient descent; Step 2.4: The edge server sends the shared part of the local β-VAE model with updated parameters to the server and retains the private part of the local β-VAE model Step 2.

5. The base station collects the shared parameters of all edge servers, aggregates these parameters, and when aggregating, the weight of each edge server is proportional to the size of its training set, and finally updates the global model: Among them, |H sum | is the sum of the number of training sets of all edge servers; Step 2.

6. Repeat Steps 2.2 to 2.5 until the model converges.

4. The robust and efficient physical layer key generation method based on edge federated learning according to claim 1, characterized in that, In step 3, each edge server stores the local β-VAE model θ i 's encoder part M i , and the encoder part M i includes some shared parameters and some private parameters.

5. The robust and efficient physical layer key generation method based on edge federated learning according to claim 1, wherein The said Step 4 includes: Step 4.1: The user and the base station send pilot signal X to each other b ,X a Channel characteristic estimation is performed, and the signals received by the user and the base station are respectively Y b = H ab X a + N b Y a = H ba X b + N a where N a , N b ~CN(0, σ 2 ) is the additive white Gaussian noise accumulated during the signal propagation in the channel, and H ab , H ba are the channel state information from the base station to the edge server; Step 4.

2. The user and the base station respectively perform channel estimation to obtain which is the channel state information obtained by the user and the base station, and these two are approximately equal:

6. The robust and efficient physical layer key generation method based on edge federated learning according to claim 5, wherein, The said Step 5 includes: Step 5.1: The user and the base station use their own identical encoder θ kg As the key generation model, the channel estimation H is used as the input of the model, and the output μ of the encoder is used as the extracted feature for subsequent quantization; Step 5.

2. For each output bit x, Q-bit quantization is adopted, and the output x ∈ [-1, 1]. The quantization formula is 7. The robust and efficient physical layer key generation method based on edge federated learning according to claim 6, characterized in that The said Step 6 includes: Step 6.1: The user and the base station perform information negotiation and record the bit mismatch rate. Assume that the initial bit strings of the user and the base station are k a and k b , respectively divide them into K small blocks, and calculate the parity check bits of each small block j as follows: where n is the length of the block, represents the exclusive OR operation. If the parity check bits of the user and the base station are inconsistent, the block needs to be further divided to determine which specific bit is in error. After counting the error bits, calculate and record the key bit inconsistency rate: Step 6.

2. If the recorded bit inconsistency rate exceeds the set threshold τ, then execute Steps 6.3 - 6.5 to perform re-aggregation and switching of the model; if the bit inconsistency rate is less than the set threshold τ, then execute Step 6.6; Step 6.3: Based on the user's location information, select the K edge servers with the closest topology to construct a dynamic aggregation group. For each selected edge server model M i , extract its latent representation, i.e., the encoder output O i = M i (H) ∈ [-1, 1], where H is the channel state information collected locally by the user. To meet the differential privacy requirements, a Laplace noise with a scale parameter of is applied to each latent representation, where ∈ is the privacy budget: Step 6.

4. Average the latent representations of all selected edge servers: Step 6.

5. Use the averaged latent representation to fine-tune the local β-VAE model, and send the fine-tuned model to the base station and the user, and then start to execute from the said Step 5. The loss function used for fine-tuning is as follows: L total = L recon + β·L KL + γ·L soft where L soft is the minimum mean square error between the output of the user model and the average latent representation of the selected edge server, and the final loss function is L recon , L KL and L soft is a linear combination of the three, and the calculation method is as follows: Where: θ kg are the model parameters of the β-VAE model for key generation, and refer to the encoder part and the decoder part of the model respectively; refers to the reconstructed version of the input x after encoding and decoding; E x～H refers to the mathematical expectation when the input x follows the channel state information distribution H; L recon calculates the mean square error between the original input x and the reconstructed ; L KL calculates the posterior distribution of the latent variable output by the encoder and the prior distribution of the latent variable ; L soft calculates the mean square error between the encoding result and the potential output O of the edge server; Step 6.

6. Perform privacy amplification on the key bits after information negotiation to obtain the final key; the privacy amplification uses a hash function h to map the original longer bit string to a shorter bit string, thereby obtaining the final key; if more keys need to be generated continuously, continue to execute from Step 4.

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