Intelligent power grid group key negotiation method and system based on phase characteristics

Abstract

The invention discloses an intelligent power grid group key negotiation method and system based on phase characteristics, and mainly solves the problems that an existing intelligent power grid is large in calculation and communication overhead and is difficult to adapt to large-scale equipment access. According to the implementation scheme, a central node and a demand response group are arranged in a smart power grid, and interactive detection between the central node and the demand response group is carried out to obtain an initial key; performing quantization, exclusive-or operation and decoding on the initial key in sequence to obtain an error-corrected key; enhancing the error-corrected secret key through a hash function and a pseudo-random number generator to generate a final dual-communication node secret key; the central node aggregates all the dual-communication node keys, generates a global group key through Hash operation, and encrypts and distributes the global group key by using each node key; and according to the joining or quitting of the node, recombining the key library by using a forward or backward security principle, generating a new group key, encrypting and broadcasting the new group key to a legal node. The method can reduce the calculation and communication overhead, ensures the safety when the node dynamically joins or quits, and can be used for a complex smart grid environment.

Description

Technical Field

[0001] The present invention belongs to the field of network security technology. Specifically, it relates to a smart grid group key negotiation method and system. The method and system can be used in smart grid scenarios that rely on real-time communication and have high security and lightweight requirements, especially in scenarios with limited device resources, frequent dynamic group changes, or the need to integrate physical layer security. Background Art

[0002] Smart grid group key agreement is a secure communication mechanism for dynamic groups of devices. It establishes a unified encryption key for terminal devices such as smart meters and sensors. This ensures efficient and secure key sharing in a dynamic environment where members frequently join and leave, while also protecting against threats such as man-in-the-middle and collusion attacks. Existing technologies optimize key generation and distribution efficiency through schemes such as hierarchical key derivation, elliptic curve cryptography, physical channel feature fusion, and blockchain consensus. However, these technologies still face bottlenecks such as centralization risks, environmental noise interference, and insufficient real-time performance.

[0003] Currently, a wide variety of authentication and key agreement schemes exist in smart grids, most of which enhance system security and communication efficiency through methods such as pre-keying, elliptic curve cryptography, and physical layer feature extraction. Traditional solutions, such as factory pre-keying, generate and embed an initial key for each smart meter. After network access, key updates and management are accomplished through session key encryption. However, these solutions still rely on key synchronization mechanisms between the manufacturer and the power company.

[0004] In recent years, some research proposals have begun to incorporate lightweight cryptography and physical layer information to enhance the authentication capabilities and robustness of systems. For example, Harbin Institute of Technology proposed an anonymous authentication and key agreement method for smart meters that combines elliptic curves and physically unclonable functions. This method achieves privacy protection of meter identities and dynamic key generation through collaboration between the authentication platform and the service provider. However, this solution involves complex parameter generation, multiple rounds of hashing, and a centralized authentication platform, resulting in high computational and communication overhead, making it difficult to adapt to large-scale device access scenarios.

[0005] In addition, to address the challenges of communication reliability and channel security, some solutions adopt dual-mode communication mechanisms, leveraging the physical layer characteristics of wireless channels to achieve key generation and negotiation. For example, patent document CN202410036011.9 discloses a "network information electromagnetic anti-interference method based on dual-mode communication." It establishes a physical feature extraction mechanism under dual-mode conditions and combines it with error correction coding to achieve secure key sharing. However, this dual-mode hardware support and real-time physical feature extraction place high demands on the equipment, and error correction coding may introduce additional delays, affecting authentication efficiency in highly dynamic environments.

[0006] Other research attempts to address the physical foundations of smart grids. Patent application number CN202311182063.9 discloses a "method for authenticating wireless terminal devices in distribution networks based on device hardware fingerprints." This method uses stable physical parameters such as voltage, current, and frequency to construct a behavioral profile of the device, enabling unique identification and dynamic authentication of the terminal device. However, this method is susceptible to environmental fluctuations, leading to feature drift and requiring frequent updates to the fingerprint database, increasing system maintenance costs. Furthermore, concurrent authentication of multiple devices faces computing bottlenecks in resource-constrained scenarios. Summary of the Invention

[0007] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and provide a phase-feature-based smart grid group key negotiation method and system to simplify computational complexity, reduce communication delay and maintenance costs, reduce the strong dependence of equipment on the smart grid center, and improve the dynamic access and secure multicast communication performance and environmental adaptability of smart meters.

[0008] The technical ideas for achieving the purpose of the present invention are: by introducing a lightweight symmetric encryption algorithm, the system has the advantages of lightweight and high efficiency, thereby improving the security of multicast communication; by establishing a demand response group in the smart grid, the dynamic management of the smart grid is strengthened and the maintenance cost of the grid system is simplified.

[0009] According to the above ideas, the technical solution of the present invention includes:

[0010] 1. A smart grid group key negotiation method based on phase characteristics, characterized by comprising:

[0011] (1) A central node P0 and a demand response (DR) group are set up in the smart grid. P0 is used to perform interactive detection with each smart meter node in the DR group through a wireless channel, and the phase estimation value obtained by the detection is used as the initial key.

[0012] (2) The initial key is converted into a binary bit sequence using the quantization order q to generate a quantized initial key, and the quantized initial key is subjected to an XOR operation and decoding using a codeword sequence in the error correction coding library to eliminate the phase quantization error and obtain the error-corrected key;

[0013] (3) The randomness of the corrected key is enhanced by using a hash function and a pseudo-random number generator to generate the final dual-communication node key;

[0014] (4) The central node aggregates the keys of all dual-communication nodes, randomly combines the aggregated keys, and generates a global group key through a hash operation, which is then encrypted and distributed using the keys of each node;

[0015] (5) According to the joining or leaving of the node, the key base is reorganized using the forward or backward security principle, and a new group key is generated and encrypted and broadcast to the legitimate nodes.

[0016] Furthermore, in step (1), P0 is interactively detected with each smart meter node in the demand response DR group through a wireless channel, and its implementation includes:

[0017] 1a) The central node P0 generates a probe signal with a random phase and sends it to a single node P in the demand response DR group on multiple subcarrier frequencies. j ;

[0018] 1b) Node P j Receive the detection signal, extract the phase estimation value on each sub-carrier frequency, and obtain the phase from P0 to P j Phase information on the path;

[0019] 1c)P j Generate a sounding signal with a random phase and send it to P0 on multiple subcarrier frequencies for reverse channel sounding;

[0020] 1d) P0 receives P j The signal sent is combined with the transmitted signal to extract the phase estimate θ′ on the reverse path i .

[0021] Furthermore, the step (2) converts the initial key into a binary bit sequence through the quantization order q to generate a quantized initial key, which is based on the range of the phase θ.

[0022] If the phase of the central node and the phase of the individual nodes in the DR group are both within the set range The existing formula Q(θ)=l is used to calculate the central node index l0 and the single node index l j , and then l0 and l j Convert to binary and obtain the initial key sequence of the central node through quantization and a single node initial key sequence

[0023] Otherwise, use the existing formula θ i =θmod2π to normalize the phase θ that does not meet the range until the phase value meets the range.

[0024] Furthermore, in step (2), the codeword sequence in the error correction coding library is used to perform an XOR operation and decoding on the quantized initial key, and its implementation includes the following:

[0025] 2a) The central node P0 selects a codeword sequence c from a preset error correction codeword library;

[0026] 2b) The central node P0 sends its initial key sequence Perform an XOR operation with the selected codeword sequence c to generate intermediate data s, and send it to a single node P in the DR group j ;

[0027] 2c) Single node P in the DR group j After receiving the intermediate data s, combined with its own initial key sequence Perform an XOR operation to recover the selected codeword sequence c;

[0028] 2d) Single node P in DR group j Then perform XOR operation on the recovered codeword sequence c and the received intermediate data s to generate the synchronization key To keep its key consistent with that of the central node P0 and achieve key synchronization.

[0029] Furthermore, the step (4) randomly combines the aggregated keys and generates a global group key through a hash operation, which is implemented as follows:

[0030] 4a) The central node P0 and each member node P in the group j They negotiate to establish one-to-one communication keys, and the central node saves the key K of all members. j , and each member only saves the corresponding key K related to it j ;

[0031] 4b) The central node P0 communicates the key K to each member j Perform random permutations and combinations, extract partial key information from the combination results, and generate a combined key g for group communication k ;

[0032] 4c) The central node P0 uses the communication key K corresponding to each member j The group key is encrypted to obtain ciphertext, and the ciphertext is sent to the target member node so that it can decrypt and obtain the complete group key, thus realizing group sharing. Compared with the existing technology, the present invention has the following advantages:

[0033] First, the present invention proposes a phase quantization method based on the quantization order q, which, combined with phase normalization technology and bit operation, can convert continuous phase information into a binary key, effectively improving the randomness and uniqueness of the initial key generation, and ensuring the consistency and repeatability of the key generation.

[0034] Secondly, the present invention introduces an error correction coding library mechanism, which corrects and synchronizes the initial quantization key by performing XOR exchange and reconstructing codewords between the central node and the DR group node. It can effectively offset the differences caused by channel disturbances or phase quantization errors, achieve key consistency synchronization with low overhead, and improve the reliability and practicality of key negotiation.

[0035] Third, the present invention proposes a group key generation scheme that aggregates member keys and encrypts and distributes them, which can support large-scale group communication while having forward and backward security and adapting to the actual needs of dynamic changes in nodes.

[0036] Fourthly, the present invention does not require an external trust organization and can complete key negotiation only by relying on interaction between nodes. It is easy to deploy and is suitable for complex heterogeneous environments such as smart grids. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is an interactive diagram of the smart grid group key negotiation method based on phase characteristics of the present invention;

[0038] Figure 2 This is a flow chart for implementing the interactive detection signal in the method of the present invention;

[0039] Figure 3 Flowchart of the implementation of quantization and error correction processing in the method of the present invention;

[0040] Figure 4 This is a block diagram of the smart grid group key negotiation system based on phase characteristics of the present invention. DETAILED DESCRIPTION

[0041] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0042] Example 1: Smart Grid Group Key Negotiation Method Based on Phase Characteristics

[0043] The present invention is applicable to smart grids, a new energy network that integrates modern communications and sensor technologies with traditional power systems. Its core features are bidirectional flow of electrical energy, state awareness, and intelligent control. Compared to traditional power grids, various terminal devices in smart grids, such as smart meters, substation monitors, and distributed energy devices, can be dynamically connected to the system, participating in real-time interaction and the transmission of control commands.

[0044] Reference Figure 1 The implementation steps of this example include the following:

[0045] Step 1: Phase acquisition and path detection to obtain the i-th phase estimate θ i .

[0046] In the smart grid system, a central node P0 is first established as the core coordination unit, and several smart meter nodes belonging to the demand response DR group are configured to form a terminal set that can participate in key negotiation;

[0047] The central node P0 constructs a wireless detection signal with random phase characteristics through its internal signal generation module and transmits it across multiple predefined subcarrier frequency channels. After the wireless detection signal propagates through the wireless channel to the target smart meter node, the receiving end completes signal acquisition and processing, extracting the phase response value corresponding to each subcarrier frequency as the physical layer parameter used to construct the initial key.

[0048] To achieve bidirectional path consistency and enhance key entropy, the target node will reversely generate a set of its own detection signals and send them back to the central node. The central node combines the received reverse signal with the reference information to calculate the phase response information in the reverse path, thereby forming a complete key basis for the bidirectional channel.

[0049] Reference Figure 2 , the implementation of this step includes the following:

[0050] 1.1) The central node P0 generates a detection signal and sends it to the DR node:

[0051] 1.1.1) The central node P0 generates a detection signal with a random phase, which is implemented by:

[0052] The central node generates a set of detection signals s(t) with random phase perturbations. The central node P0 initializes a random seed value based on a preset pseudo-random number generator and calls the generator to generate a random seed value for each subcarrier frequency f. i Assign a phase perturbation value φ i ;

[0053] The phase perturbation value φ i Loaded onto each sub-carrier sinusoidal signal, the detection signal s(t) is obtained:

[0054]

[0055] Where N is the number of subcarrier frequencies, φ i is the phase disturbance value of the i-th subcarrier frequency.

[0056] 1.1.2) The generated detection signal s(t) is modulated on multiple sub-carrier frequencies, and the signal phase φ on each sub-carrier frequency isi Generated based on the i-th pseudo-random number generator rand(i), it can be expressed as:

[0057] φ i =2π·rand(i),i=1,2,…,D

[0058] Where D represents the number of subcarrier frequencies, rand(i) is the output of the i-th pseudo-random number generator;

[0059] The detection signal s(t) is sent out at a certain period, and the central node P0 records the initial phase value φ of each subcarrier signal i As a reference, the signal is sent to the target smart meter node within the DR group through the wireless channel;

[0060] 1.2) The DR node receives the probe signal and extracts the phase estimate:

[0061] After receiving the detection signal s(t), the target smart meter node in the DR group uses its local synchronous sampling module to demodulate the signal on each subcarrier frequency and extract the corresponding received i-th phase θ i , under ideal noise-free conditions, the phase value is:

[0062] θ i =φ i +Δθ i

[0063] where the i-th Δθ i Phase variation introduced to the channel;

[0064] 1.3) The DR node generates a reverse detection signal and sends it to the central node:

[0065] The DR node generates the i-th detection signal s(i) in reverse and sends it to the central node P0, that is, modulating the signal ψ with random phase disturbance on the same D subcarrier frequencies i :

[0066] ψ i =2π·rand(i),i=1,2,…,D

[0067] Among them, rand(i) is the i-th pseudo-random number generator;

[0068] The i-th detection signal ψ i Send it back to the central node P0 to form a reverse detection path. The DR node will change the initial phase θ of its own signal to i Reserved so that the central node can calculate the phase offset of the reverse channel based on the known information.

[0069] 1.4) The central node receives the reverse detection signal and extracts the reverse path phase:

[0070] The central node P0 receives the i-th reverse detection signal ψ i Then, by comparing the i-th signal φ received on each sub-carrier frequency i and the i-th signal θ randomly generated by the DR node i Perform difference calculation to extract the i-th phase estimate θ on the reverse path i ′:

[0071] θ i ′=ψ i +Δθ i '

[0072] where the i-th Δθ i ′ is the phase offset on the reverse channel path. Theoretically, this value should be similar to that on the forward path, but due to the influence of multipath effects and noise, there may be slight deviations.

[0073] Step 2: Quantization mapping and error correction.

[0074] After obtaining the phase response value, each node needs to convert it into binary data for key generation to facilitate digital key storage and subsequent processing. Based on a pre-set quantization standard in the system, the continuously varying phase value is divided into several discrete intervals, and each interval is mapped into a fixed-length bit sequence, thus forming structured initial key data.

[0075] This example takes into account the fact that in actual applications, wireless channels may be affected by noise, path changes, etc., resulting in slight errors in phase values. The central node P0 first selects a specific codeword sequence from a preset error-correcting coding library, performs a logical operation with its own initial key data to generate an intermediate result, and then sends the result to the target node; the target node then combines the initial key generated locally with itself and recovers the corresponding error-correcting codeword through a logical operation process.

[0076] Reference Figure 3 , the implementation of this step includes the following:

[0077] 2.1) Quantization processing:

[0078] 2.1.1) Set the phase estimate θ i The range of the phase estimation value θ i Is it in this range:

[0079] If the estimated value θ i In the range [0,2π], the quantization order is set to q, which divides the phase space [0,2π] into 2 q intervals, define each interval as corresponding to a q-bit code, and use the estimated value θ iQuantize to get the quantized i-th phase estimation value k i for:

[0080]

[0081] If the estimated value θ i If it exceeds the legal range [0,2π], it is first processed by the normalization function to obtain the normalized i-th phase estimate: θ′ i =θ i mod 2π, and then set the quantization order to q, which divides the phase space [0,2π] into 2 q intervals, define each interval as corresponding to a q-bit code, and normalize the estimated value θ′ i Quantize to get the quantized i-th phase estimation value k i for:

[0082]

[0083] 2.1.2) Generate the initial key sequence through binary encoding:

[0084] For the quantized i-th phase estimation value k i Perform binary coding to obtain the ith phase estimation value Bin(k i );

[0085] Each binary-coded phase estimate Bin(k i ) are spliced in the form of bit strings to obtain the initial key sequence K init :

[0086] K init =Bin(k1)||Bin(k2)||…||Bin(k D )

[0087] Where || represents the bit string concatenation operation, and D represents the number of subcarrier frequencies;

[0088] 2.2) Error Correction Coding:

[0089] Quantize the central node P0 to obtain the quantized key sequence

[0090] The central node P0 selects a set of code words C from the preset error correction code word library, and the length of the code word C is the same as its own quantized key sequence. consistent length;

[0091] The key sequence after the central node P0 is quantified Perform bit-level XOR operation with codeword C to obtain the error correction key M:

[0092]

[0093] Step 3: Hashing and pseudo-random enhancement.

[0094] 3.1) The central node p0 and the target node each perform a hash operation on the synchronized error correction key M to obtain a set of highly irreversible summary data;

[0095] 3.2) Inputting a set of highly irreversible summary data as a seed into a pseudo-random number generator to generate a pseudo-random bit sequence with a longer length and more uniform distribution;

[0096] 3.3) Select multiple representative position bit segments from the pseudo-random bit sequence and extract them to form the final shared key between the two communicating nodes to ensure that the key has higher information entropy and enhance the system's resistance to attacks such as eavesdropping and replay.

[0097] Step 4: Communication key aggregation and group distribution.

[0098] 4.2) The central node p0 negotiates with each member node to generate a unique communication key, and each node saves the relevant information;

[0099] 4.3) The central node p0 processes all communication keys in a random permutation and combination manner, and constructs a global group key through hashing;

[0100] 4.4) To ensure the security of key transmission, the central node P0 encrypts the group key with the point-to-point communication key corresponding to each member node to form the corresponding ciphertext;

[0101] 4,5) The ciphertext is distributed to the legal member nodes through encrypted broadcast or unicast. Each node can decrypt it using the local key and obtain the group key, thereby realizing information encryption communication and a unified key system within the entire DR group.

[0102] Step 5: Forward and backward secure key reconstruction.

[0103] The forward direction refers to when a new node joins the group, the central node p0 will regenerate a new group key based on the updated key set, and encrypt and distribute it using the new node's unique key and the original group key respectively, ensuring that the new node cannot decrypt any historical communication content before it joins, thereby preventing information from being traced back;

[0104] The backward direction means that when a node exits the group, the central node P0 immediately removes its key from the key library and regenerates a new group key based on the remaining legitimate nodes. It is encrypted and distributed only to the current members to ensure that the exited node cannot access any subsequent communication information of the group.

[0105] The forward and backward security key reconstruction in this step is actively triggered and executed by the central node P0 on the member node's joining and exit operations:

[0106] When a new node applies to join the group, the central node P0 will negotiate with the node to generate its own key and add it to the existing key database. Then, based on the complete key set, a new group key will be reconstructed, encrypted with the old group key, and sent to existing members. At the same time, a copy of the key will be sent to each member separately using the new node key to ensure forward security.

[0107] When the central node P0 detects that a member node has exited or is offline, it immediately removes the node key from the key library, generates a new group key based on the current remaining key, and then broadcasts a copy of the new encryption key to all nodes still online to prevent the exited node from continuing to participate in decryption through the stored old key, thereby ensuring backward security.

[0108] Example 2: Smart Grid Group Key Agreement System Based on Phase Characteristics

[0109] Reference Figure 4 This example includes a quantization module 1, an error correction module 2, a group key generation module 3, a hash enhancement module 4, a pseudo-random number generation module 5, and a key distribution module 6. The working principle of the entire system is as follows:

[0110] Quantization module 1 is responsible for converting the phase estimation value θ received by each DR node into i The phase estimation value θ is calculated by the preset quantization order q. i Discretize the phase estimate θ i Convert the continuous binary bit sequence into a binary bit sequence, then convert the continuous binary bit sequence into an initial key sequence that meets the encryption requirements, and transmit it to the error correction module;

[0111] Error correction module 2 performs error correction on the quantized initial key sequence through an XOR operation. That is, it selects a suitable codeword sequence from a preset error correction codeword library and performs an XOR operation with the node's initial key sequence to eliminate differences caused by channel disturbances or phase quantization errors. The consistent key generated after error correction is then transmitted to the group key generation module.

[0112] The group key generation module 3 first negotiates with each member node through the central node P0 to establish a point-to-point communication key K init Then, a part of the information is extracted from the key of the member node by random arrangement, and the group key g is generated by hash operation. k , and the group key g kDistribute to all legitimate nodes through a secure channel to ensure that each node can securely obtain the key g k , and the key g k Transfer to the hash enhancement module;

[0113] The hash enhancement module 4 generates the group key g k Perform hash enhancement to obtain the enhanced group key g k ′, to ensure that the group key g k ′ is irreversible, so even if the attacker obtains the group key g k ′, and the group key g cannot be recovered by any reverse method k ′, in addition, the group key g can be enhanced by hashing k The randomness and security of ' are further enhanced, and the ability to resist replay attacks and eavesdropping attacks is improved. k 'Transmit to the pseudo-random number generation module;

[0114] The pseudo-random number generation module 5 is used to generate a pseudo-random sequence to further enhance the group key g k ′ is random, that is, by inputting a random seed, a random sequence g with good distribution characteristics can be output through the pseudo-random number generation module ′ k ′ , in order to further improve the security of the group key, reduce the risk of the group key being predicted or cracked, and the final enhanced key g ′ k ′ Transmit to the key distribution module;

[0115] The key distribution module 6 is responsible for converting the final enhanced group key g ′ k ′ Encrypt and securely distribute to each legal node, each node uses point-to-point encryption to encrypt the group key g ′ k ′ Only the node with the corresponding decryption key can successfully decrypt and obtain the group key g ′ k ′ To ensure that the group key g ′ k ′ Security and confidentiality during transmission. This module ensures that all members in the group can obtain the correct group key g ′ k ′ .

[0116] It should be noted that the step numbers in the specification and claims of the present invention are only for the purpose of clearly describing the embodiments of the present invention and facilitating understanding, and the order of the step numbers is not limited.

Claims

1. A smart grid group key negotiation method based on phase characteristics, characterized in that: include: (1) A central node P0 and a demand response (DR) group are set up in the smart grid. P0 is used to perform interactive detection with each smart meter node in the DR group through a wireless channel, and the phase estimation value obtained by the detection is used as the initial key. (2) The initial key is converted into a binary bit sequence using the quantization order q to generate a quantized initial key, and the quantized initial key is subjected to an XOR operation and decoding using a codeword sequence in the error correction coding library to eliminate the phase quantization error and obtain the error-corrected key; (3) The randomness of the corrected key is enhanced by using a hash function and a pseudo-random number generator to generate the final dual-communication node key; (4) The central node aggregates the keys of all dual-communication nodes, randomly combines the aggregated keys, and generates a global group key through a hash operation, which is then encrypted and distributed using the keys of each node; (5) According to the joining or leaving of the node, the key base is reorganized using the forward or backward security principle, and a new group key is generated and encrypted and broadcast to the legitimate nodes.

2. The method according to claim 1, characterized in that In step (1), P0 is interactively detected with each smart meter node in the demand response DR group through a wireless channel, and its implementation includes: 1a) The central node P0 generates a probe signal with a random phase and sends it to a single node P in the demand response DR group on multiple subcarrier frequencies. j ; 1b) Node P j Receive the detection signal, extract the phase estimation value on each sub-carrier frequency, and obtain the phase from P0 to P j Phase information on the path; 1c)P j Generate a sounding signal with a random phase and send it to P0 on multiple subcarrier frequencies for reverse channel sounding; 1d) P0 receives P j The signal sent is combined with the transmitted signal to extract the phase estimate θ′ on the reverse path i .

3. The method according to claim 1, characterized in that The step (2) converts the initial key into a binary bit sequence through the quantization order q to generate the quantized initial key, which is performed as follows according to the range of the phase θ: If the phase of the central node And request the phase of a single node in the DR group Then use the existing formula Q(θ)=l to calculate the central node index l0 and the single node index l j , and then l0 and l j Convert to binary and obtain the initial key sequence of the central node through quantization and a single node initial key sequence If the phase of the central node Or request a response from a single node within the DR group Then use the existing formula θ i =θmod2π to normalize the phase θ that does not meet the range until the phase value meets the range.

4. The method according to any one of claims 1 to 3, characterized in that In step (2), the codeword sequence in the error correction coding library is used to perform an XOR operation and decoding on the quantized initial key, and its implementation includes the following: 2a) The central node P0 selects a codeword sequence c from a preset error correction codeword library; 2b) The central node P0 sends its initial key sequence Perform an XOR operation with the selected codeword sequence c to generate intermediate data s, and send it to a single node P in the DR group j ; 2c) Single node P in the DR group j After receiving the intermediate data s, combined with its own initial key sequence Perform an XOR operation to recover the selected codeword sequence c; 2d) Single node P in DR group j Then perform XOR operation on the recovered codeword sequence c and the received intermediate data s to generate the synchronization key To keep its key consistent with that of the central node P0 and achieve key synchronization.

5. The method according to any one of claims 1 to 3, characterized in that In step (3), randomness enhancement is performed on the corrected key by using a hash function and a pseudo-random number generator, and its implementation includes the following steps: 3a) Central node P0 and single node P in DR group j Perform hash operations on each initial synchronization key to obtain the corresponding central node hash sequence and the hash sequence of a single node within the DR group 3b) Central node hash sequence and the hash sequence of a single node within the DR group As seeds, they are input into the pseudo-random number generator to generate the corresponding pseudo-random sequence and 3c) Pseudo-random sequence at the central node and pseudo-random sequences of individual nodes within the DR group Extract the bit fragments at the same position as the enhanced dual communication node key K j .

6. The method according to any one of claims 1 to 5, characterized in that The step (4) randomly combines the aggregated keys and generates a global group key through a hash operation, which is implemented as follows: 4a) The central node P0 and each member node P in the group j They negotiate to establish one-to-one communication keys, and the central node saves the key K of all members. j , and each member only saves the corresponding key K related to it j ; 4b) The central node P0 communicates the key K to each member j Perform random permutations and combinations, extract partial key information from the combination results, and generate a combined key g for group communication k ; 4c) The central node P0 uses the communication key K corresponding to each member j The group key is encrypted to obtain a ciphertext, and the ciphertext is sent to the target member node so that it can decrypt and obtain the complete group key to achieve group sharing.

7. The method according to claim 1, characterized in that In step (5), the key base of the joined node is reorganized using the forward security principle, which is implemented as follows: 5a) Central node P0 and newly added node P j+1 Negotiate and generate its own key K j+1 and add the key to the keystore; 5b) The central node P0 regenerates a new group key g based on the updated key set k , and use the original group key g k Encrypt the new group key to generate a new group key g k 'Send to the original group members; 5c) For the newly added node P j+1 Use the key K corresponding to the new node j+1 Encrypt to generate a new group key g k " is sent to newly joined nodes to ensure that new nodes cannot decrypt historical communication content after access, achieving forward security.

8. The method according to claim 1, characterized in that In step (5), the backward security principle is used to reconstruct the key base of the exited node, and its implementation includes the following: 5d) The central node P0 detects the node P j After exiting, immediately remove the key K corresponding to the node j , and based on the remaining key K j The collection regenerates a new group key g k '; 5e) The central node P0 sends the remaining members’ respective keys K j After encryption, a new group key g is generated k ′, and the new group key g′ k The key is distributed to each node without any encryption operation to prevent the exited nodes from obtaining the new group key, thus ensuring backward security.

9. The method according to claim 2, characterized in that In step 1a), the central node P0 generates a detection signal with a random phase, which is implemented by: 1a1) The central node P0 initializes a random seed value based on a preset pseudo-random number generator and calls the generator for each subcarrier frequency f i Assign a phase perturbation value φ i ; 1a2) The phase perturbation value φ i Loaded onto each sub-carrier sinusoidal signal, the detection signal s(t) is obtained: Where N is the number of subcarrier frequencies, φ i is the phase disturbance value of the i-th subcarrier frequency.

10. The method according to claim 2, characterized in that In step 1c), a single node P in the DR group responds j Generate a probe signal with a random phase, which includes: 1c1) Response to a single node P in the DR group j Initialize a random seed value based on a preset pseudo-random number generator and call the generator for each subcarrier frequency f j Assign a random phase perturbation value φ j ; 1c2) The random phase perturbation value φ j are loaded into each sub-carrier sinusoidal signal to obtain the total detection signal s j (t): Where N is the number of subcarrier frequencies, φ j is the phase disturbance value of the j-th subcarrier frequency.

11. A smart grid group key negotiation method based on phase characteristics, characterized in that: include: Quantization module 1 is used to convert the phase estimation value θ received by each DR node into i The phase estimation value θ is calculated by the preset quantization order q. i Perform discretization and binary conversion, and then convert the binary bit sequence into an initial key sequence that meets encryption requirements; Error correction module 2 is used to perform error correction on the quantized initial key sequence. That is, it selects a suitable codeword sequence from a preset error correction codeword library and performs an XOR operation with the node's initial key sequence to eliminate differences caused by channel disturbances or phase quantization errors. The group key generation module 3 is used to negotiate with the central node P0 and each member node to establish a point-to-point communication key K init , extract part of the information from the key of the member node by random arrangement, and generate the group key g through hash operation k , and distributed to all legal nodes; Hash enhancement module 4 is used to generate the group key g k Perform hash enhancement to obtain the enhanced group key g k ′, to ensure that the group key g k Irreversibility of ′; The pseudo-random number generation module 5 is used to generate a pseudo-random sequence for the enhanced group key g k ' is enhanced again to obtain the group key g" with good distribution characteristics k , to reduce the risk of group keys being predicted or cracked; The key distribution module 6 is used to distribute the final enhanced group key g″ k Encrypt and securely distribute to each legal node, each node uses point-to-point encryption to encrypt the group key g″ k Only the node with the corresponding decryption key can successfully decrypt and obtain the group key g″ k .

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