A physical layer key generation and distribution method based on WFRFT subcarrier index

Abstract

This invention discloses a physical layer key generation and distribution method based on WFRFT subcarrier indexing, belonging to the field of physical layer secure communication. This invention solves the problem of key vulnerability in traditional subcarrier index-based key generation and distribution methods. It utilizes the WFRFT communication system to enhance the concealment of subcarrier activation states by adjusting the WFRFT transform parameters to change the energy distribution of the WFRFT system in the time-frequency plane. Through energy redistribution, the energy distribution in the time-frequency plane of the WFRFT system tends to be uniform, making the signal exhibit Gaussian characteristics, thereby obtaining a more concealed subcarrier energy distribution pattern. This effectively solves the problem of vulnerability in traditional subcarrier index-based key generation and distribution methods. Simultaneously, the WFRFT system has better resistance to channel distortion than traditional OFDM systems, improving key authentication success rate without sacrificing key rate. This invention can be applied to the field of physical layer secure communication.

Description

Technical Field

[0001] This invention belongs to the field of physical layer secure communication, specifically relating to a key generation and distribution method based on WFRFT (Weighted Fractional Fourier Transform) subcarrier index. Background Technology

[0002] With the widespread adoption of the Internet of Things (IoT), wireless applications are becoming increasingly diverse and distributed. This trend makes the need for communication security more urgent to address potential security threats such as adversarial eavesdropping. When facing heterogeneous and ubiquitous IoT networks, key distribution and management present significant challenges and vulnerabilities. Traditional information confidentiality typically relies on upper-layer encryption technologies. However, due to the limited computing resources of IoT hardware devices, using traditional encryption algorithms or their variants faces significant challenges. Furthermore, traditional encryption key exchange protocols are easily attacked by adversaries, leading to security risks. Therefore, how to effectively and with low complexity implement a secret key sharing mechanism has become a pressing issue.

[0003] In recent years, physical layer key generation methods have gradually attracted attention from academia and industry. Unlike encryption key generation schemes that rely on computational complexity to achieve security, physical layer key generation methods utilize the inherent randomness of wireless channels to establish secret keys, offering advantages such as low cost and real-time updates, making them highly suitable for resource-constrained IoT applications. Existing key generation and distribution methods based on subcarrier indexing are implemented using OFDM (Orthogonal Fourier Divison Multiplexing) systems. Under this signaling system, unauthorized eavesdropping devices can easily monitor the subcarrier activation state by observing subcarrier energy in the frequency domain, thereby deciphering the key and posing a security threat. Therefore, there is an urgent need for a more covert and secure physical layer key generation and distribution method to protect the subcarrier activation state from being deciphered and ensure key security. Summary of the Invention

[0004] The purpose of this invention is to solve the problem that the keys of traditional key generation and distribution methods based on subcarrier indexes are easily cracked, and to propose a physical layer key generation and distribution method based on WFRFT subcarrier indexes.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] A physical layer key generation and distribution method based on WFRFT subcarrier indexing, the method specifically includes the following steps:

[0007] Step 1: Bob, the i-th valid receiver iThe pilot sequence, i = 1, 2, ..., N, is transmitted to the legitimate transmitter via the uplink channel. B N B This represents the total number of legitimate receivers, and each legitimate receiver transmits a pilot sequence of x = [x1, x2, ..., x]. N ], where N is the length of the pilot sequence x;

[0008] The frequency domain received signal Y from the i-th legitimate receiver by the legitimate transmitter is... s,i (f i ,t i ), and then according to Y s,i (f i ,t i Estimating the channel response f represents the set of complex numbers. i Let t be the frequency of the i-th legitimate receiver. i Let be the uplink timeslot of the i-th legitimate receiver;

[0009] Step Two, according to Generate the WFRFT order α of the i-th valid receiver. i and session key Then according to Generate group key sequence k G ;

[0010] Step 3: For the i-th valid receiver Bob i Using the i-th valid receiver Bob i Session key Group key sequence k G Encryption is performed to obtain the encrypted group key sequence k. Gi ;

[0011] legitimate transmitter to legitimate receiver Bob i Send group key sequence k Gi Group key sequence k Gi The length is k i Bits, including those of length k i,1 The bit index sequence c i,1 and length k i,2 The modulation sequence of bits c i,2 , i.e., k i,1 +k i,2 =k i ;

[0012] Step 4: Bob, the i-th legitimate receiver i Occupying M subcarriers for group key sequence k GiDistribution: Divide the M subcarriers into G sub-blocks, then each sub-block contains P subcarriers, where P = M / G. Then, group the key sequence k... Gi The index sequence c i,1 They are mapped onto the subcarriers of each sub-block, that is, for each sub-block, K of the P subcarriers are activated;

[0013] Group key sequence k Gi The modulation sequence c in i,2 Modulation is performed, and the modulated symbols are mapped onto the active subcarriers. After mapping, a data block D of length M×1 is obtained. i ;

[0014] Step 5: Process data block D i After zero-padding, an extended data block S of length N×1 is obtained. i =[0 M(i-1) ;D i ;0 N-Mi ], where the subscript of 0 indicates the length of the zero vector;

[0015] For data block S i For order α i The WFRFT is used to obtain the i-th valid receiver Bob. i The corresponding WFRFT result;

[0016] Step 6: For each legitimate receiver, execute steps 3 through 5.

[0017] The WFRFT results corresponding to each legitimate receiver are then merged, and the merged result is subjected to a WFRFT of order β to obtain the key signal y.

[0018] Step 7: Bob, the i-th legitimate receiver i The key signal y is equalized to obtain the equalized sequence u. Then, the equalized sequence u is processed to extract the sequence belonging to the i-th legitimate receiver Bob. i Sequence information

[0019] Step 8: Bob, the i-th legitimate receiver i For sequence information Subcarrier index detection is performed to obtain the detection results of subcarrier activation states. Based on the detection results of subcarrier activation states, the index sequence c is reconstructed. i,1 ;

[0020] Then according to Demodulate the subcarrier activation state detection result to reconstruct the modulation sequence c. i,2 After reconstructing the index sequence and modulation sequence, the group key sequence k is obtained. Gi ;

[0021] Step 9: Bob, the i-th legitimate receiver i The session key is reconstructed based on the channel estimation results.

[0022] Step 10: Perform steps 7 to 9 for each legitimate receiver to reconstruct the session key and group key sequence for each legitimate receiver.

[0023] Furthermore, the channel response for:

[0024]

[0025] Among them, P i (f i ) is the frequency domain sequence of the pilot sequence x.

[0026] Furthermore, the aforementioned according to Generate the WFRFT order α of the i-th valid receiver. i and session key The specific process is as follows:

[0027]

[0028] Where, α i Let be the WFRFT order of the i-th valid receiver. G is the session key for the i-th legitimate receiver. i and K i It is a predefined signature sequence used for key generation enhancement, F d (·) and F k (·) indicates the physical layer key generation method.

[0029] Furthermore, the aforementioned according to Generate group key sequence k G The specific process is as follows:

[0030]

[0031] Where, k G For group key sequence, This indicates the XOR operation.

[0032] Furthermore, the N B Each legitimate receiver sends pilot sequences to a legitimate transmitter in different time slots and in an agreed-upon order.

[0033] Furthermore, the pair key sequence k Gi The modulation sequence c in i,2 Modulation is performed using Q-order QAM or PSK.

[0034] Furthermore, the aforementioned Represents the number of combinations. Indicates rounding down, k i,2 ≤Klog2 Q.

[0035] Furthermore, the key signal y is:

[0036]

[0037] Where H represents the time-domain channel matrix, This represents a WFRFT operation of order β and length N. Indicates the order as α i A WFRFT operation of length N, where n is the channel noise.

[0038] Furthermore, the sequence information for:

[0039]

[0040] Among them, C i This represents the M(i-1)+1th to Mithth elements extracted from the balanced sequence u. This represents the inverse WFRFT operation of order -β and length N. Indicates the order as -α i The inverse WFRFT operation of length M.

[0041] Furthermore, the specific process of step nine is as follows:

[0042] Step 91, in the time slot The legitimate transmitter sends a message to the i-th legitimate receiver, Bob. i Preset pilot sequence for broadcast Bob, the i-th legitimate receiver i Channel estimation is performed based on the received signal.

[0043]

[0044] in, Bob is the i-th legitimate receiver. i The received frequency domain signal, P alice (f i (x) is the frequency domain sequence of the pilot sequence x′. Bob is the i-th legitimate receiver. i The channel estimation results;

[0045] Step 92, Bob, the i-th legitimate receiveri The session key is reconstructed based on the channel estimation results.

[0046]

[0047] The beneficial effects of this invention are:

[0048] This invention utilizes the WFRFT communication system to enhance the concealment of subcarrier activation states. By adjusting the transform parameters of WFRFT, it alters the energy distribution of the WFRFT system in the time-frequency plane. Through energy redistribution, it ensures that the energy distribution in the time-frequency plane of the WFRFT system tends to be uniform, making the signal exhibit Gaussian characteristics. This results in a more concealed subcarrier energy distribution pattern, effectively addressing the vulnerability of traditional subcarrier index-based key generation and distribution methods to decryption. Furthermore, compared to traditional OFDM systems, the WFRFT system has better resistance to channel distortion, improving key authentication success rate without sacrificing key rate. Attached Figure Description

[0049] Figure 1 A schematic diagram of the frame structure design for key generation and distribution;

[0050] Figure 2 This is a flowchart of the key distribution phase;

[0051] Figure 3a The diagram shows the time-frequency distribution of the key frame signal in an OFDM-based key distribution system.

[0052] Figure 3b (This is a time-frequency distribution diagram of the key frame signal in a WFRFT-based key distribution system.)

[0053] Figure 4 This is a comparison chart of the key leakage rate between the present invention and the traditional method;

[0054] Figure 5 The key sequence c of this invention and the conventional method i Authentication success rate comparison chart;

[0055] Figure 6 The chart shows a comparison of the key rate of this invention and the traditional method when the weighting parameters have errors. Detailed Implementation

[0056] The present application will now be described in further detail with reference to specific embodiments and accompanying drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention, and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are all within the scope of protection of the present invention.

[0057] Specific Implementation Method 1: Combination Figure 1 and Figure 2 This embodiment describes a physical layer key generation and distribution method based on WFRFT subcarrier indexing. The method specifically includes the following steps:

[0058] Step 1: Bob, the i-th valid receiver i The pilot sequence, i = 1, 2, ..., N, is transmitted to the legitimate transmitter via the uplink channel. B N B This represents the total number of legitimate receivers, and each legitimate receiver transmits a pilot sequence of x = [x1, x2, ..., x]. N ], where N is the length of the pilot sequence x;

[0059] The frequency domain received signal Y from the i-th legitimate receiver by the legitimate transmitter is... s,i (f i ,t i ), and then according to Y s,i (f i ,t i Estimating the channel response f represents the set of complex numbers. i Let t be the frequency of the i-th legitimate receiver. i Let be the uplink timeslot of the i-th legitimate receiver;

[0060] Step Two, according to Generate the WFRFT order α of the i-th valid receiver. i and session key Then according to Generate group key sequence k G ;

[0061] Step 3: For the i-th valid receiver Bob i Using the i-th valid receiver Bob i Session key Group key sequence k G Encryption is performed to obtain the encrypted group key sequence k. Gi ;

[0062] legitimate transmitter to legitimate receiver Bob i Send group key sequence k Gi Group key sequence k Gi The length is k i Bits, including those of length k i,1 The bit index sequence c i,1 and length k i,2 The modulation sequence of bits c i,2, i.e., k i,1 +k i,2 =k i ;

[0063] Step 4: Bob, the i-th legitimate receiver i Occupying M subcarriers for group key sequence k Gi Distribution: Divide the M subcarriers into G sub-blocks, then each sub-block contains P subcarriers, where P = M / G. Then, group the key sequence k... Gi The index sequence c i,1 The subcarriers are mapped to each sub-block, meaning that for each sub-block, K of the P subcarriers are activated; the index sequence is a 0-1 bit sequence, and the subcarrier mapping rules of the index sequence include, but are not limited to: the subcarrier position corresponding to 1 represents activation, and the subcarrier position corresponding to 0 represents inactivation;

[0064] Group key sequence k Gi The modulation sequence c in i,2 Modulation is performed, and the modulated symbols are mapped onto the active subcarriers. After mapping, a data block D of length M×1 is obtained. i ;

[0065] Step 5: Process data block D i After zero-padding, an extended data block S of length N×1 is obtained. i =[0 M(i-1) ;D i ;0 N-Mi ], where the subscript of 0 indicates the length of the zero vector;

[0066] For data block S i For order α i The WFRFT is used to obtain the i-th valid receiver Bob. i The corresponding WFRFT result;

[0067] Step 6: For each legitimate receiver, execute steps 3 through 5.

[0068] The WFRFT results corresponding to each legitimate receiver are then merged, and the merged result is subjected to a WFRFT of order β to obtain the key signal y.

[0069] Step 7: Bob, the i-th legitimate receiver i The key signal y is equalized to obtain the equalized sequence u. Then, the equalized sequence u is processed to extract the sequence belonging to the i-th legitimate receiver Bob. i Sequence information

[0070] Step 8: Bob, the i-th legitimate receiver i For sequence information Subcarrier index detection is performed to obtain the detection results of subcarrier activation states. Based on the detection results of subcarrier activation states, the index sequence c is reconstructed. i,1 ;

[0071] Then according to Demodulate the subcarrier activation state detection result to reconstruct the modulation sequence c. i,2 After reconstructing the index sequence and modulation sequence, the group key sequence k is obtained. Gi ;

[0072] Step 9: Bob, the i-th legitimate receiver i The session key is reconstructed based on the channel estimation results.

[0073] Step 10: For each legitimate receiver, execute steps 7 through 9 to reconstruct the session key and group key sequence for each legitimate receiver. During actual communication, the sender encrypts the transmitted data using the session key and group key sequence, and the receiver decrypts it using the reconstructed session key and group key sequence to reconstruct the information sent by the sender.

[0074] In this embodiment, the legitimate transmitter (named Alice) and Bob i (i = 1, ..., N) B Communication occurs on the same frequency band to ensure that the uplink and downlink channels are distinct. Steps one and two constitute the detection phase, and steps three to eight constitute the key distribution phase. Figure 1 The diagram shows a frame structure designed based on the channel coherence time T. The frame structure consists of two parts: the first part is the detection frame, with a number of frames Fr1; the second part is the group key distribution frame, with a number of frames Fr2. Fr1 and Fr2 can be flexibly set according to the coherence time and the number of legitimate receivers.

[0075] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the channel response... for:

[0076]

[0077] Among them, P i (f i ) is the frequency domain sequence of the pilot sequence x.

[0078] The other steps and parameters are the same as in Specific Implementation Method 1.

[0079] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the method described is based on... Generate the WFRFT order α of the i-th valid receiver. iand session key The specific process is as follows:

[0080]

[0081] Where, α i Let be the WFRFT order of the i-th valid receiver. G is the session key for the i-th legitimate receiver. i and K i It is a predefined signature sequence used for key generation enhancement, F d (·) and F k (·) indicates the physical layer key generation method.

[0082] In this embodiment, F d (·), F k (·) represents any possible encoding, mapping, and quantization methods during the physical layer key generation process.

[0083] Other steps and parameters are the same as in specific implementation method one or two.

[0084] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the method described is based on... Generate group key sequence k G The specific process is as follows:

[0085]

[0086] Where, k G For group key sequence, This indicates the XOR operation.

[0087] It should be noted that this embodiment only provides one method for generating group key sequences; other conventional methods for generating group key sequences can also be applied to this invention.

[0088] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0089] Specific Implementation Method Five: This implementation method differs from one of Specific Implementation Methods One to Four in that the N... B Each legitimate receiver sends pilot sequences to a legitimate transmitter in different time slots and in an agreed-upon order.

[0090] Its steps and parameters are the same as those in one of the specific implementation methods one to four.

[0091] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the pair key sequence k Gi The modulation sequence c in i,2 Modulation is performed using Q-order QAM or PSK.

[0092] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0093] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the... Represents the number of combinations. Indicates rounding down, k i,2 ≤Klog2 Q.

[0094] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0095] Specific Implementation Method Eight: This implementation method differs from one of Specific Implementation Methods One to Seven in that the key signal y is:

[0096]

[0097] Where H represents the time-domain channel matrix, This represents a WFRFT operation of order β and length N. Indicates the order as α i A WFRFT operation of length N, where n is the channel noise.

[0098] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0099] Each key frame consisting of N subcarriers can achieve key distribution to L legitimate receivers, where L = N / M ≥ 1. This implementation is applicable to L ≥ N. B In the case where L < N B At this time, multiple key frames can be sent to jointly complete the key distribution to multiple legitimate receivers. In this case, each key signal y contains only the merged result of the WFRFT result of the legitimate receiver corresponding to the current key frame.

[0100] The WFRFT operation on a complex sequence x0 of length N can be represented as:

[0101]

[0102] Among them, the weighting coefficient It is generated by the following formula:

[0103]

[0104] W N For WFRFT core, satisfying Among them, I N F represents the identity matrix. N R represents the DFT matrix, and R can be chosen freely.

[0105] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the sequence information... for:

[0106]

[0107] Among them, C i This represents the M(i-1)+1th to Mithth elements extracted from the balanced sequence u. This represents the inverse WFRFT operation of order -β and length N. Indicates the order as -α i The inverse WFRFT operation of length M.

[0108] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0109] Specific Implementation Method Ten: This implementation method differs from any of Specific Implementation Methods One to Nine in that the specific process of step Nine is as follows:

[0110] Step 91, in the time slot The legitimate transmitter sends a message to the i-th legitimate receiver, Bob. i Preset pilot sequence for broadcast Bob, the i-th legitimate receiver i Channel estimation is performed based on the received signal.

[0111]

[0112] in, Bob is the i-th legitimate receiver. i The received frequency domain signal, P alice (f i (x) is the frequency domain sequence of the pilot sequence x′. Bob is the i-th legitimate receiver. i The channel estimation results;

[0113] Step 92, Bob, the i-th legitimate receiver i The session key is reconstructed based on the channel estimation results.

[0114]

[0115] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0116] Figure 3a ( ) is a time-frequency distribution diagram of key frame signals in an OFDM-based key distribution system. Figure 3bThe image shows the time-frequency distribution of the key frame signal in a WFRFT-based key distribution system. It can be seen that under the OFDM key distribution method, the subcarrier activation state is more easily observed, leading to key information leakage. However, the introduction of WFRFT redistributes the time-frequency energy of the signal, resulting in a more uniform signal energy distribution and making the subcarrier activation state more concealed.

[0117] The security performance of the proposed method was verified using Monte Carlo simulation. With N = M = 1024, a subcarrier spacing of 15 kHz, QPSK mode was employed, considering five-path channels, MMSE equalization was used, and log-likelihood ratio detection was used for subcarrier detection. Figure 4 The graph compares the key leakage rates of WFRFT-IKG (this invention) and OFDM-IKG (the traditional method) at (P,K) = (4,2), (P,K) = (6,3), and (P,K) = (8,4). As can be seen from the graph, in the traditional method, key leakage increases significantly with increasing signal-to-noise ratio (SNR). However, the introduction of WFRFT improves this leakage, offering better concealment than β = 0.5 and β = 2.5. The leakage probability does not increase with changes in SNR because the time-frequency energy distribution is more uniform under these parameters, and the signal subcarriers exhibit Gaussianization.

[0118] and Figure 4 The simulation environment settings are consistent. Figure 5 For WFRFT-IKG (this invention) and OFDM-IKG (conventional method), key sequences of lengths 32bit, 64bit, 128bit, and 256bit are provided. i The authentication success rate comparison chart shows that as the signal-to-noise ratio increases, the authentication success rate of this invention is significantly improved compared to traditional methods. This is due to the introduction of the WFRFT communication system, which is better able to cope with channel distortion than the OFDM communication system.

[0119] and Figure 4 The simulation environment settings are consistent. Figure 6 The simulation results show a comparison of group key rates between WFRFT-IKG (this invention) and OFDM-IKG (the traditional method) at (P,K) = (4,2), (P,K) = (6,3), and (P,K) = (8,4) with errors in the weighting parameters. The simulation results demonstrate that even with weighting parameter errors, the key rate of this invention is still higher than that of OFDM-IKG at medium and high signal-to-noise ratios. The key rate increases with increasing signal-to-noise ratio, eventually converging without decreasing, achieving the same upper limit for group key rates as the traditional method.

[0120] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A physical layer key generation and distribution method based on WFRFT subcarrier indexing, characterized in that, The method specifically includes the following steps: Step 1: Bob, the i-th valid receiver i The pilot sequence, i = 1, 2, ..., N, is transmitted to the legitimate transmitter via the uplink channel. B N B This represents the total number of legitimate receivers, and each legitimate receiver transmits a pilot sequence of x = [x1, x2, ..., x]. N ], where N is the length of the pilot sequence x; The frequency domain received signal Y from the i-th legitimate receiver by the legitimate transmitter is... s,i (f i ,t i ), and then according to Y s,i (f i ,t i Estimating the channel response f represents the set of complex numbers. i Let t be the frequency of the i-th legitimate receiver. i Let be the uplink timeslot of the i-th legitimate receiver; Step Two, according to Generate the WFRFT order α of the i-th valid receiver. i and session key Then according to Generate group key sequence k G ; Step 3: For the i-th valid receiver Bob i Using the i-th valid receiver Bob i Session key Group key sequence k G Encryption is performed to obtain the encrypted group key sequence k. Gi ; legitimate transmitter to legitimate receiver Bob i Send group key sequence k Gi Group key sequence k Gi The length is k i Bits, including those of length k i,1 The bit index sequence c i,1 and length k i,2 The modulation sequence of bits c i,2 , i.e., k i,1 +k i,2 =k i ; Step 4: Bob, the i-th legitimate receiver i Occupying M subcarriers for group key sequence k Gi Distribution: Divide the M subcarriers into G sub-blocks, then each sub-block contains P subcarriers, where P = M / G. Then, group the key sequence k... Gi The index sequence c i,1 They are mapped onto the subcarriers of each sub-block, that is, for each sub-block, K of the P subcarriers are activated; Group key sequence k Gi The modulation sequence c i,2 Modulation is performed, and the modulated symbols are mapped onto the active subcarriers. After mapping, a data block D of length M×1 is obtained. i ; Step 5: Process data block D i After zero-padding, an extended data block S of length N×1 is obtained. i =[0 M(i-1) ;D i ;0 N-Mi ], where the subscript of 0 indicates the length of the zero vector; For data block S i For order α i The WFRFT is used to obtain the i-th valid receiver Bob. i The corresponding WFRFT result; Step Six: For each legitimate receiver, execute steps Three through Five. The WFRFT results corresponding to each legitimate receiver are then merged, and the merged result is subjected to a WFRFT of order β to obtain the key signal y. Step 7: Bob, the i-th legitimate receiver i The key signal y is equalized to obtain the equalized sequence u. Then, the equalized sequence u is processed to extract the sequence belonging to the i-th legitimate receiver Bob. i Sequence information Step 8: Bob, the i-th legitimate receiver i For sequence information Subcarrier index detection is performed to obtain the detection results of subcarrier activation states. Based on the detection results of subcarrier activation states, the index sequence c is reconstructed. i,1 ; Then according to Demodulate the subcarrier activation state detection result to reconstruct the modulation sequence c. i,2 After reconstructing the index sequence and modulation sequence, the group key sequence k is obtained. Gi ; Step 9: Bob, the i-th legitimate receiver i The session key is reconstructed based on the channel estimation results. Step 10: Perform steps 7 to 9 for each legitimate receiver to reconstruct the session key and group key sequence for each legitimate receiver.

2. The physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 1, characterized in that, The channel response for: Among them, P i (f i ) is the frequency domain sequence of the pilot sequence x.

3. The physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 2, characterized in that, According to Generate the WFRFT order α of the i-th valid receiver. i and session key The specific process is as follows: Where, α i Let be the WFRFT order of the i-th valid receiver. G is the session key for the i-th legitimate receiver. i and K i It is a predefined signature sequence used for key generation enhancement, F d (·) and F k (·) indicates the physical layer key generation method.

4. The physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 3, characterized in that, According to Generate group key sequence k G The specific process is as follows: Where, k G For group key sequence, This indicates the XOR operation.

5. The physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 1, characterized in that, The N B Each legitimate receiver sends pilot sequences to a legitimate transmitter in different time slots and in an agreed-upon order.

6. The physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 4, characterized in that, The pair key sequence k Gi The modulation sequence c i,2 Modulation is performed using Q-order QAM or PSK.

7. A physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 6, characterized in that, The Represents the number of combinations. Indicates rounding down, k i,2 ≤Klog2 Q.

8. A physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 7, characterized in that, The key signal y is: Where H represents the time-domain channel matrix, This represents a WFRFT operation of order β and length N. Indicates the order as α i A WFRFT operation of length N, where n is the channel noise.

9. A physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 8, characterized in that, The sequence information for: Among them, C i This represents the M(i-1)+1th to Mithth elements extracted from the balanced sequence u. This represents the inverse WFRFT operation of order -β and length N. Indicates the order as -α i The inverse WFRFT operation of length M.

10. A physical layer key generation and distribution method based on WFRFT subcarrier index according to claim 9, characterized in that, The specific process of step nine is as follows: Step 91, in the time slot The legitimate transmitter sends a message to the i-th legitimate receiver, Bob. i Preset pilot sequence for broadcast Bob, the i-th legitimate receiver i Channel estimation is performed based on the received signal. in, Bob is the i-th legitimate receiver. i The received frequency domain signal, P alice (f i (x) is the frequency domain sequence of the pilot sequence x′. Bob is the i-th legitimate receiver. i The channel estimation results; Step 92, Bob, the i-th legitimate receiver i The session key is reconstructed based on the channel estimation results.

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