A method and apparatus for synchronously generating a group key and a pairwise key

Abstract

This invention relates to the field of physical layer secure communication technology, and provides a method and apparatus for synchronously generating group keys and paired keys. The method includes: a central node acquiring the azimuth angles and corresponding channel complex gains of each edge node, designing the switching array parameters of a time modulation array based on the azimuth angles of each edge node, calculating the average radiation pattern coefficients of all edge nodes, and transmitting them collectively; the central node generating a group key and modulating it into a modulated signal using the time modulation array and transmitting it; the central node generating corresponding paired keys for each edge node and encrypting them to obtain paired key ciphertext, which is then sent to the corresponding edge node; each edge node receiving the modulated signal performs coherent demodulation to obtain demodulated symbols, performs hard decision on the demodulated symbols, and obtains the group key; each edge node decrypts the paired key ciphertext using the average radiation pattern coefficients and the demodulated symbols to obtain the paired key.

Description

Technical Field

[0001] This invention relates to the field of physical layer secure communication technology, and in particular to a method and apparatus for synchronously generating group keys and paired keys. Background Technology

[0002] The Internet of Things (IoT) is one of the most influential technologies in the 6G wireless communication ecosystem. The convergence of IoT and 6G has given rise to emerging application scenarios such as intelligent transportation and industrial IoT. As 6G networks continue to improve their support for IoT, the number of connected devices is growing exponentially, accompanied by a simultaneous increase in network scale and data interaction complexity. Therefore, security has become a key bottleneck limiting the large-scale deployment of IoT. Confidentiality, integrity, and availability are core requirements of information security, providing fundamental guarantees for the reliable operation of IoT applications. The security level and lightweight nature of these requirements directly determine the deployment value of an IoT system.

[0003] Traditional security solutions for the Internet of Things (IoT) primarily rely on upper-layer encryption protocols or pre-shared key mechanisms. These protocols are inherently susceptible to high computational overhead, delayed key updates, and dependence on trusted third parties. These drawbacks make them incompatible with the resource-constrained nature and dynamically changing topologies of 6G IoT devices. Physical layer security technologies leverage the inherent characteristics of wireless channels, providing an innovative paradigm for lightweight security mechanisms. Physical layer security avoids complex mathematical operations, achieving security protection by utilizing the unique properties of physical layer transmission, thus effectively addressing the limitations of traditional cryptographic schemes. Furthermore, time-modulated arrays introduce time as an additional design dimension to adjust the activation state and complex weights of array elements. Time-modulated arrays possess unique spatiotemporal radiation characteristics, offering significant advantages over traditional phased arrays in the field of physical layer security.

[0004] Physical layer security has made some progress in its application in the Internet of Things (IoT). However, most existing research focuses on authentication, a pre-defense mechanism. For example, authentication schemes based on channel state information, received signal strength, or inherent hardware characteristics effectively defend against spoofing attacks and unauthorized access by leveraging the unique correlation between the device and the channel. However, as a core advantage of physical layer security and a fundamental prerequisite for encrypted communication, physical layer secure key generation still faces significant research gaps in multi-device collaboration scenarios within the IoT.

[0005] In multi-device collaboration scenarios within the Internet of Things (IoT), the coordination and guarantee of group keys and pair keys are particularly important. Group keys support one-to-many multicast communication, ensuring the confidentiality and consistency of collaboration instructions, configuration parameters, and other information synchronously issued by the controller to multiple terminals. In contrast, pair keys are geared towards one-to-one interaction, ensuring the secure exclusive transmission of sensitive data in peer-to-peer communication between a single terminal and a central node, or between terminals. The efficient collaborative generation of these two keys is the core of balancing IoT communication efficiency and data security, directly determining the operational reliability of multi-device collaboration scenarios.

[0006] The collaborative, multi-device nature of the Internet of Things (IoT) highlights the concurrent need for group keys and pairwise keys in many critical scenarios. In the Industrial IoT, edge controllers must broadcast adjustment commands to all sensors via group keys, while simultaneously receiving sensitive device data reported by individual sensors via pairwise keys to prevent data leakage or command tampering. In intelligent transportation vehicle ad hoc networks, roadside units need to use group keys to push real-time traffic information to vehicles within the area, while pairwise keys are required between vehicles and roadside units to transmit authentication information and precise location data, thereby avoiding traffic chaos caused by identity forgery. In drone swarm missions, the control center publishes formation coordination strategies via group keys, and individual drones transmit their status parameters and local mission data back to the center via pairwise keys, satisfying the dual requirements of swarm coordination and single-point privacy protection.

[0007] However, traditional cryptographic schemes face bottlenecks due to computational resource constraints, and most physical layer key generation schemes focus on a single key type. Existing solutions do not achieve the synchronous generation of group keys and paired keys. Summary of the Invention

[0008] Traditional cryptographic schemes face limitations due to computational resource constraints, and most physical layer key generation schemes focus on a single key type, failing to achieve simultaneous generation of group keys and paired keys. This invention proposes a method and apparatus for simultaneously generating group keys and paired keys.

[0009] In a first aspect, the present invention provides a method for synchronously generating group keys and paired keys, comprising:

[0010] The central node obtains the azimuth angles of each edge node and the corresponding channel complex gain;

[0011] The central node designs the switching array related parameters of the time modulation array based on the azimuth angle of each edge node. Based on the switching array related parameters and the azimuth angle of each edge node, the average radiation pattern coefficient of all edge nodes is calculated and common transmission is performed.

[0012] The central node generates a group key, modulates the group key into a modulation signal using a time modulation array, and transmits it. The central node generates corresponding pair keys for each edge node, and encrypts the pair keys using the average pattern coefficient and the modulation signal to obtain the pair key ciphertext, which is then sent to the corresponding edge node.

[0013] Each edge node receives the modulation signal, performs coherent demodulation on the modulation signal to obtain demodulated symbols, performs hard decision on the demodulated symbols to obtain a pair key, and uses the average pattern coefficients and the demodulated symbols to decrypt the pair key ciphertext to obtain a pair key.

[0014] Furthermore, the switch array related parameters include the average value and variance of the complex excitation weights caused by the switch array, and the average radiation pattern coefficient is the average value of the far-field radiation pattern of all edge nodes under the switch array parameters.

[0015] Furthermore, the central node generates a group key, modulates the group key into a modulated signal using a time modulation array, and transmits it, specifically including:

[0016] The central node randomly selects the first and second bits as the group key.

[0017] The central node modulates the group key into a modulated signal using a time modulation array; wherein the modulated signal is:

[0018]

[0019] in, Indicates the modulated signal. Indicates the first bit, Indicates the second bit;

[0020] exist The modulated signal transmitted in the direction is:

[0021]

[0022] In the formula,

[0023]

[0024]

[0025] in, Indicates in Modulated signals sent in the direction, This represents the far-field radiation pattern. This indicates the number of antenna elements in the time-modulated array. Indicates the first Complex excitation weights caused by a single switching component express Phase difference in orientation Indicates wave number, Indicates the carrier wavelength. Represents the spacing between array elements. The angle of the array normal of the edge node relative to the center node.

[0026] Furthermore, the central node generates corresponding pairwise keys for each edge node, and encrypts the pairwise keys using the average pattern coefficients corresponding to each edge node and the modulation signal to obtain the pairwise key ciphertext, which is then sent to the corresponding edge node. Specifically, this includes:

[0027] The central node randomly selects the third bit of each edge node as the pairwise key;

[0028] The central node performs a hard decision on the modulated signal using the pattern coefficients corresponding to each edge node:

[0029]

[0030]

[0031] in, The modulated signal calculated by the central node The corresponding demodulation symbols, express Expectations This indicates the hard decision result executed by the central node. express In the Independent implementation within each time modulation period;

[0032] The central node uses the hard decision result to encrypt the paired keys to obtain the paired key ciphertext.

[0033] Furthermore, each edge node receives the modulated signal, performs coherent demodulation on the modulated signal to obtain demodulated symbols, and performs hard decision on the demodulated symbols to obtain a group key, specifically including:

[0034] The edge node receives the modulated signal and performs coherent demodulation on the modulated signal to obtain a demodulated symbol; wherein the demodulated symbol comprises a real part and an imaginary part, and the real part is represented as... ,in express A noise-free version This represents additive white Gaussian noise;

[0035] The real part of the demodulation symbol Perform a hard decision to obtain an estimate of the real part of the modulated signal:

[0036]

[0037]

[0038] in, Indicates in Estimates of the real part of the modulated signal over a consecutive time modulation period. represent In the Independent implementation within each time modulation period. Represents the real part of the demodulation symbol The result of enforcing a hard judgment;

[0039] By deriving the estimate of the real part of the modulated signal, the estimate of the first bit is obtained:

[0040]

[0041] in, This represents the estimated value of the first bit;

[0042] The same hard decision and derivation are performed on the imaginary part of the demodulated symbol to obtain an estimate of the second bit;

[0043] The estimated value of the first bit and the estimated value of the second bit are combined to form the estimated value of the group key.

[0044] Furthermore, each edge node uses the average direction pattern coefficient and the demodulation symbol to decrypt the pairwise key ciphertext to obtain the pairwise key, specifically including:

[0045] Each edge node performs a hard decision on the demodulation symbol using the corresponding pattern coefficients:

[0046]

[0047]

[0048] in, Indicates demodulation symbols. This represents the expectation of the demodulation symbols. This indicates the hard decision result executed by the edge node. express In the Independent implementation within each time modulation period;

[0049] Each edge node uses the hard decision result to decrypt the paired key ciphertext to obtain the paired key.

[0050] In a second aspect, the present invention provides a device for synchronizing the generation of group keys and paired keys, comprising:

[0051] The channel acquisition module is used by the central node to acquire the azimuth angles of each edge node and the corresponding channel complex gain.

[0052] The parameter configuration module is used by the central node to design the switching array related parameters of the time modulation array according to the azimuth angle of each edge node, and to calculate the average radiation pattern coefficient of all edge nodes and perform common transmission based on the switching array related parameters and the azimuth angle of each edge node.

[0053] The key generation and transmission module is used for the central node to generate a group key, and to modulate the group key into a modulation signal through a time modulation array and transmit it; the central node generates corresponding pair keys for each edge node, and encrypts the pair keys using the average pattern coefficient and the modulation signal to obtain the pair key ciphertext and sends it to the corresponding edge node.

[0054] The key receiving and decryption module is used for each edge node to receive the modulation signal, perform coherent demodulation on the modulation signal to obtain demodulation symbols, perform hard decision on the demodulation symbols to obtain a pair key; and each edge node uses the average pattern coefficient and the demodulation symbols to decrypt the pair key ciphertext to obtain a pair key.

[0055] Thirdly, the present invention provides a system for synchronously generating group keys and paired keys, including a central node and M edge nodes, wherein the central node is equipped with a conventional antenna for public communication and an N-ary time modulation array for broadcasting time modulation signals;

[0056] The central node is used to acquire the azimuth angles and corresponding channel complex gains of each edge node; it is also used to design the switching array related parameters of the time modulation array based on the azimuth angles of each edge node, calculate the average radiation pattern coefficients of all edge nodes based on the switching array related parameters and the azimuth angles of each edge node, and transmit them in a common manner; it is also used to generate a group key, modulate the group key into a modulation signal through the time modulation array, and transmit it; it is also used to generate corresponding pair keys for each edge node, encrypt the pair keys using the average radiation pattern coefficients and the modulation signal, obtain the pair key ciphertext, and send it to the corresponding edge node;

[0057] The edge node is configured to receive the modulation signal, perform coherent demodulation on the modulation signal to obtain demodulated symbols, perform hard decision on the demodulated symbols to obtain a group key, and also to decrypt the pairwise key ciphertext using the average pattern coefficients and the demodulated symbols to obtain a pairwise key.

[0058] Fourthly, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in the first aspect.

[0059] Fifthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0060] The beneficial effects of this invention are as follows:

[0061] This invention proposes a method for synchronously generating group keys and pairwise keys, which can generate both simultaneously using a time modulation array. The method provided by this invention effectively addresses the core limitation of existing research, which focuses only on a single key type and therefore cannot well adapt to multi-device collaborative communication in the Internet of Things (IoT). It offers an integrated security solution for one-to-many multicast and one-to-one interactive communication scenarios.

[0062] This invention overcomes the limitations of traditional time-modulated arrays that rely on pseudo-random sequence optimization. It employs an innovative probabilistic control strategy to flexibly configure the expectation and variance of the complex weights of array elements. Utilizing the multi-main-lobe characteristics of the far-field radiation of the time-modulated array, it achieves directional broadcasting of group keys to legitimate devices; and leverages the directionality of the variance to provide a unique random source for paired keys. This method not only maintains the low hardware complexity requirements of IoT devices but also balances the directionality and randomness of key transmission. Attached Figure Description

[0063] Figure 1 A time modulation array model diagram provided for an embodiment of the present invention;

[0064] Figure 2 A flowchart illustrating a method for synchronously generating group keys and paired keys according to an embodiment of the present invention;

[0065] Figure 3 This is a structural diagram of a group key and pair key synchronization generation device provided in an embodiment of the present invention;

[0066] Figure 4 This is a schematic diagram of a group key and pair key synchronization generation system provided in an embodiment of the present invention;

[0067] Figure 5 This is a structural diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0069] To facilitate understanding of this invention, the time modulation array involved will first be introduced. The overall model of the time modulation array is as follows: Figure 1 As shown, by Each antenna element and It consists of a switch array of individual switching components. The input signal is divided into equal power components by a power divider. The path. Each switching component is time-modulated, applying a complex excitation weight to each path. Specifically, it is controlled by a complex programmable logic device. The values ​​of the complex excitation weights, under time modulation, exhibit the characteristics of a complex random variable, possessing a mean... and variance ;

[0070] Due to the random nature of the complex excitation weights in the time-modulated array, the far-field radiation pattern It is also a complex random variable. From a mathematical perspective, the far-field radiation pattern can be represented as... ,in express Phase difference in orientation Indicates wave number, It is the carrier wavelength. Represents the spacing between array elements. Defined as the angle relative to the array normal.

[0071] like Figure 2 As shown, this embodiment of the invention provides a method for synchronously generating group keys and paired keys, including:

[0072] S1: Each edge node sends a pilot signal to the central node. The central node uses the received pilot signal to obtain the azimuth angle of each edge node and the corresponding channel complex gain.

[0073] Specifically, the directions of the M edge nodes satisfy... By sending pilot signals, the central node can obtain the azimuth angles of each edge node. and the channel complex gain between the central node and the edge nodes. .

[0074] In this embodiment, the central node can be a trusted institution or roadside unit, and the edge node can be a vehicle; or the central node can be a centralized cloud server or key management server, and the edge node can be an industrial gateway or edge controller; or the central node can be a base station or cluster head, and the edge node can be an IoT sensor device or microcontroller; or the central node can refer to a cloud center or master station system, and the edge node can be a power distribution terminal or smart meter.

[0075] S2: The central node designs the switching array related parameters of the time modulation array according to the azimuth angle of each edge node. Based on the switching array related parameters and the azimuth angle of each edge node, the average radiation pattern coefficient of all edge nodes is calculated and common transmission is performed. Among them, the switching array related parameters include the average value and variance of the complex excitation weights caused by the switching array, and the average radiation pattern coefficient is the average value of the far-field radiation pattern of all edge nodes under the switching array parameters.

[0076] Specifically, the central node can design the average value of the complex excitation weights caused by the switching array of the time modulation array based on the azimuth angles of each edge node. and variance At the same time, the central node according to and Calculate the average value of the far-field radiation pattern for all edge nodes under the switching array parameters. Then it is broadcast publicly. The calculation formula is:

[0077] ;

[0078] Its phase is represented as ,Right now .

[0079] S3: The central node generates a group key and modulates the group key into a modulation signal through a time modulation array and sends it; the central node generates corresponding pair keys for each edge node and encrypts the pair keys using the average pattern coefficient and the modulation signal to obtain the ciphertext of the pair keys and sends it to the corresponding edge node.

[0080] S4: Each edge node receives the modulated signal, performs coherent demodulation on the modulated signal to obtain demodulated symbols, performs hard decision on the demodulated symbols to obtain the group key; each edge node uses the average pattern coefficient and the demodulated symbols to decrypt the pairwise key ciphertext to obtain the pairwise key.

[0081] The method provided in this invention utilizes the multi-main-lobe characteristics of far-field radiation from a time-modulated array to achieve directional broadcasting of group keys to legitimate devices. By leveraging the directionality of variance to provide a unique random source for paired keys, it not only maintains the low hardware complexity requirements of IoT devices but also balances the directionality and randomness of key transmission. It can simultaneously generate group keys and paired keys.

[0082] As one possible implementation, a design method for a time modulation array is provided, which addresses key parameters in the time modulation array, including the average of complex excitation weights. and variance The design logic is as follows.

[0083] First of all The design considers edge nodes based on their location. Generate complex weights Its amplitude satisfies a low-sidelobe Chebyshev distribution, and its phase satisfies a beam pointing direction of... ,Right now

[0084]

[0085]

[0086] in, This represents the average value of the complex excitation weights generated by the nth switch array for the mth edge node. For its sidelobe level value, choose a sufficiently low value so that the linearity of the sidelobe level can be approximated as 0, and then let...

[0087]

[0088] Then to The modulus value is normalized. express The design target value. It's called a target value because it cannot necessarily be achieved by adjusting the parameters of the time modulation array. Therefore, for edge nodes, their orientation corresponds to... Both are relatively large, while for those not in For eavesdroppers in a specific direction, the mean can be approximated as 0.

[0089] And variance The design principle is relatively simple, aiming to ensure that signal radiation from different directions is independent of each other. Only... A simple way to achieve a low sidelobe distribution is:

[0090]

[0091] in, The value is low enough that the linearity of the sidelobe level can be approximated as 0. Similarly, Too The design target value. The key to the low sidelobe tapering distribution of the array antenna lies in the ratio between the weights of each element. Therefore, in this embodiment, the target values ​​of both the mean and variance are multiplied by a coefficient, i.e. and ,in and It is a positive number.

[0092] As one possible implementation method, the group key generation process specifically includes:

[0093] The central node randomly selects the first bit. Second bit As a group key, that is:

[0094] ;

[0095] The central node modulates the group key into a modulated signal using a time modulation array; the modulated signal is:

[0096]

[0097] in, Indicates the modulated signal;

[0098] Central node at The modulated signal transmitted in the direction is:

[0099]

[0100] In the formula,

[0101]

[0102]

[0103] in, Indicates in Modulated signals sent in the direction, This represents the far-field radiation pattern. This indicates the number of antenna elements in the time-modulated array. Indicates the first Complex excitation weights caused by a single switching component express Phase difference in orientation Indicates wave number, Indicates the carrier wavelength. Represents the spacing between array elements. The angle is relative to the array normal.

[0104] The edge node receives the modulated signal and performs coherent demodulation on the modulated signal to obtain the demodulated symbol; the real part of the demodulated symbol is represented as... ,in express A noise-free version This represents additive white Gaussian noise;

[0105] Specifically, the modulated signal received by the edge node can be coherently demodulated to obtain a demodulated symbol. The demodulated symbol contains two signal components: a real part and an imaginary part, corresponding to the real and imaginary parts of the modulated signal. This embodiment of the invention uses... Let's take the real part as an example to illustrate how Bobm obtains the group key and pairwise keys. The same operation can also be applied to... The imaginary part.

[0106] The real part of the demodulation symbol Perform a hard decision to obtain an estimate of the real part of the modulated signal:

[0107]

[0108]

[0109] in, Corresponding to . This only refers to the symbols Bobm acquires within one time modulation period. To reduce Bobm's influence... The estimated bit error rate per QPSK symbol. Transmission occurs within a continuous time modulation period. Without loss of generality, assume... It's an odd number, so Bobm can collect it. A separate symbol, denoted as . Indicates in Estimates of the real part of the modulated signal over a consecutive time modulation period. represent In the Independent implementation within each time modulation period;

[0110] By deriving the estimate of the real part of the modulated signal, the estimate of the first bit is obtained:

[0111]

[0112] in, Describing the 1-norm, This represents the estimated value of the first bit, based on... The number of "1"s in the first bit is used to derive the estimated value of the first bit.

[0113] Similarly, the edge nodes perform the same hard decision and derivation on the imaginary part of the demodulated symbol to obtain the estimate of the second bit;

[0114] The estimated value of the first bit and the estimated value of the second bit are combined to form the estimated value of the group key.

[0115] As one possible implementation, the pairwise key generation step includes:

[0116] The central node randomly selects the third bit of each edge node as the pairwise key;

[0117] The central node performs hard decision-making on the modulated signal using the pattern coefficients corresponding to each edge node:

[0118]

[0119]

[0120] in, The modulated signal calculated by the central node The corresponding demodulation symbols can be calculated by the central node based on the information it possesses. The specific form is expressed as ; express Expectations This indicates the hard decision result executed by the central node. express In the Independent implementation within each time modulation period;

[0121] The central node uses the hard decision result to encrypt the pairwise keys, thus obtaining the ciphertext of the pairwise keys.

[0122] Specifically, the central node will transmit through public channels Transmitted to Bobm, where It is modulo 2 addition.

[0123] Each edge node performs a hard decision on the demodulation symbol using the corresponding pattern coefficients:

[0124]

[0125]

[0126] in, Indicates demodulation symbols. This represents the expectation of the demodulation symbols. This indicates the hard decision result executed by the edge node. express In the Independent implementation within each time modulation period;

[0127] Each edge node uses the hard decision result to decrypt the paired key ciphertext to obtain the paired key.

[0128] Specifically, edge nodes receive Afterwards, with Performing modulo-2 addition yields the following result: Then, Bobm obtains the result based on the number of "1"s in the resulting sequence. The estimated value :

[0129]

[0130] Alice and Bob secretly shared the key. and Similarly, Alice can generate... and use The imaginary part is negotiated with Bobm. Bob can also obtain... The estimated value .

[0131] At this point, Alice and Bobs have completed the sharing of the group key and the pair key. Since both the group key and the pair key were chosen independently by Alice, they are independent of each other.

[0132] like Figure 3 As shown, this embodiment of the invention also provides a device for synchronizing and generating group keys and paired keys, comprising:

[0133] The channel acquisition module is used by the central node to acquire the azimuth angles of each edge node and the corresponding channel complex gain.

[0134] The parameter configuration module is used by the central node to design the switching array related parameters of the time modulation array according to the azimuth angle of each edge node, and to calculate the average radiation pattern coefficient of all edge nodes and perform common transmission based on the switching array related parameters and the azimuth angle of each edge node.

[0135] The key generation and transmission module is used by the central node to generate a group key, and modulate the group key into a modulation signal through a time modulation array and transmit it; the central node generates corresponding pair keys for each edge node, and encrypts the pair keys using the average pattern coefficient and the modulation signal to obtain the ciphertext of the pair keys and sends it to the corresponding edge node.

[0136] The key receiving and decryption module is used by each edge node to receive the modulated signal, perform coherent demodulation on the modulated signal to obtain demodulated symbols, perform hard decision on the demodulated symbols to obtain the group key; each edge node uses the average pattern coefficient and the demodulated symbols to decrypt the pair key ciphertext to obtain the pair key.

[0137] like Figure 4 As shown, this embodiment of the invention also provides a system for synchronously generating group keys and paired keys, including one central node (Alice). There are one edge node (Bob1, Bob2, ..., BobM) and one passive eavesdropper (Eve). In this embodiment of the invention, the edge nodes are legitimate IoT devices. Alice is equipped with a conventional antenna for public communication and a time-modulated signal for broadcasting. A time-modulated array. Alice is capable of channel state detection, direction finding, and random bit generation. Bob can be configured with a single antenna or multiple antennas. In a single-antenna configuration, the antennas are time-division multiplexed for both common communication and receiving signals broadcast by the time-modulated array. In a dual-antenna configuration, one antenna is dedicated to receiving signals from the time-modulated array, while the other is used for common communication, avoiding mutual interference.

[0138] The central node is used to obtain the azimuth angles and corresponding channel complex gains of each edge node; it is also used to design the switching array related parameters of the time modulation array based on the azimuth angles of each edge node, calculate the average radiation pattern coefficients of all edge nodes based on the switching array related parameters and the azimuth angles of each edge node, and transmit them in a common manner; it is also used to generate a group key, modulate the group key into a modulation signal through the time modulation array, and transmit it; it is also used to generate corresponding pair keys for each edge node, encrypt the pair keys using the average radiation pattern coefficients and the modulation signal, obtain the pair key ciphertext, and send it to the corresponding edge node;

[0139] Edge nodes are used to receive modulated signals, perform coherent demodulation on the modulated signals to obtain demodulated symbols, perform hard decision on the demodulated symbols to obtain the group key, and also use the average pattern coefficients and demodulated symbols to decrypt the pairwise key ciphertext to obtain the pairwise key.

[0140] Figure 5 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 5 As shown, the electronic device may include a processor 501, a communications interface 502, a memory 503, and a communication bus 504. The processor 501, communications interface 502, and memory 503 communicate with each other via the communication bus 504. The processor 501 can call logical instructions stored in the memory 503 to execute the group key and pairwise key synchronization generation method provided in the above-described method embodiments, which includes embodiments S1 to S4.

[0141] Furthermore, when the logical instructions in the aforementioned memory 1503 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0142] This invention also provides a computer program product, which includes a computer program stored on a computer-readable storage medium. The computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute the group key and pair key synchronization generation method provided in the above-described method embodiments, including embodiments S1 to S4.

[0143] This invention also provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the group key and pair key synchronization generation method provided in the above-described method embodiments, including embodiments S1 to S4.

[0144] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for synchronously generating group keys and paired keys, characterized in that, include: The central node obtains the azimuth angles of each edge node and the corresponding channel complex gain; The central node designs the switching array related parameters of the time modulation array based on the azimuth angle of each edge node. Based on the switching array related parameters and the azimuth angle of each edge node, the average radiation pattern coefficient of all edge nodes is calculated and common transmission is performed. The central node generates a group key, modulates the group key into a modulation signal using a time modulation array, and transmits it. The central node generates corresponding pair keys for each edge node, and encrypts the pair keys using the average pattern coefficient and the modulation signal to obtain the pair key ciphertext, which is then sent to the corresponding edge node. Each edge node receives the modulation signal, performs coherent demodulation on the modulation signal to obtain demodulated symbols, and performs hard decision on the demodulated symbols to obtain the group key; Each edge node uses the average directional pattern coefficient and the demodulation symbol to decrypt the paired key ciphertext to obtain the paired key.

2. The method for synchronously generating group keys and paired keys according to claim 1, characterized in that, The switch array-related parameters include the average value and variance of the complex excitation weights caused by the switch array, and the average radiation pattern coefficient is the average value of the far-field radiation pattern of all edge nodes under the switch array parameters.

3. The method for synchronously generating group keys and paired keys according to claim 1, characterized in that, The central node generates a group key, modulates the group key into a modulated signal using a time modulation array, and then transmits it. Specifically, this includes: The central node randomly selects the first and second bits as the group key. The central node modulates the group key into a modulated signal using a time modulation array; wherein the modulated signal is: in, Indicates the modulated signal. Indicates the first bit, Indicates the second bit; exist The modulated signal transmitted in the direction is: In the formula, in, Indicates in Modulated signals sent in the direction, This represents the far-field radiation pattern. This indicates the number of antenna elements in the time-modulated array. Indicates the first Complex excitation weights caused by a single switching component express Phase difference in orientation Indicates wave number, Indicates the carrier wavelength. Represents the spacing between array elements. The angle of the array normal of the edge node relative to the center node.

4. The method for synchronously generating group keys and paired keys according to claim 1, characterized in that, The central node generates corresponding pairwise keys for each edge node, and encrypts the pairwise keys using the average pattern coefficients of each edge node and the modulation signal to obtain the ciphertext of the pairwise keys, which is then sent to the corresponding edge node. Specifically, this includes: The central node randomly selects the third bit of each edge node as the pairwise key; The central node performs a hard decision on the modulated signal using the pattern coefficients corresponding to each edge node: in, The modulated signal calculated by the central node The corresponding demodulation symbols, express Expectations This indicates the hard decision result executed by the central node. express In the Independent implementation within each time modulation period; The central node uses the hard decision result to encrypt the paired keys to obtain the paired key ciphertext.

5. The method for synchronously generating group keys and paired keys according to claim 3, characterized in that, Each edge node receives the modulated signal, performs coherent demodulation on the modulated signal to obtain demodulated symbols, and performs hard decision on the demodulated symbols to obtain a group key, specifically including: The edge node receives the modulated signal and performs coherent demodulation on the modulated signal to obtain a demodulated symbol; wherein the demodulated symbol comprises a real part and an imaginary part, and the real part is represented as... ,in express A noise-free version This represents additive white Gaussian noise; The real part of the demodulation symbol Perform a hard decision to obtain an estimate of the real part of the modulated signal: in, Indicates in Estimates of the real part of the modulated signal over a consecutive time modulation period. represent In the Independent implementation within each time modulation period Represents the real part of the demodulation symbol The result of enforcing a hard judgment; By deriving the estimate of the real part of the modulated signal, the estimate of the first bit is obtained: in, This represents the estimated value of the first bit; The same hard decision and derivation are performed on the imaginary part of the demodulated symbol to obtain an estimate of the second bit; The estimated value of the first bit and the estimated value of the second bit are combined to form the estimated value of the group key.

6. The method for synchronously generating group keys and paired keys according to claim 4, characterized in that, Each edge node uses the average direction pattern coefficient and the demodulation symbol to decrypt the pairwise key ciphertext to obtain the pairwise key, specifically including: Each edge node performs a hard decision on the demodulation symbol using the corresponding pattern coefficients: in, Indicates demodulation symbols. This represents the expectation of the demodulation symbol. This indicates the hard decision result executed by the edge node. express In the Independent implementation within each time modulation period; Each edge node uses the hard decision result to decrypt the paired key ciphertext to obtain the paired key.

7. A device for synchronizing group keys and paired keys, characterized in that, include: The channel acquisition module is used by the central node to acquire the azimuth angles of each edge node and the corresponding channel complex gain. The parameter configuration module is used by the central node to design the switching array related parameters of the time modulation array according to the azimuth angle of each edge node, and to calculate the average radiation pattern coefficient of all edge nodes and perform common transmission based on the switching array related parameters and the azimuth angle of each edge node. The key generation and transmission module is used for the central node to generate a group key, and to modulate the group key into a modulation signal through a time modulation array and transmit it; the central node generates corresponding pair keys for each edge node, and encrypts the pair keys using the average pattern coefficient and the modulation signal to obtain the pair key ciphertext and sends it to the corresponding edge node. The key receiving and decryption module is used to receive the modulation signal at each edge node, perform coherent demodulation on the modulation signal to obtain demodulated symbols, and perform hard decision on the demodulated symbols to obtain a group key; Each edge node uses the average directional pattern coefficient and the demodulation symbol to decrypt the paired key ciphertext to obtain the paired key.

8. A system for synchronously generating group keys and paired keys, comprising a central node and M edge nodes, characterized in that, The central node is equipped with a conventional antenna for public communication and an N-ary time modulation array for broadcasting time-modulated signals. The central node is used to acquire the azimuth angles and corresponding channel complex gains of each edge node; it is also used to design the switching array related parameters of the time modulation array based on the azimuth angles of each edge node, calculate the average radiation pattern coefficients of all edge nodes based on the switching array related parameters and the azimuth angles of each edge node, and transmit them in a common manner; it is also used to generate a group key, modulate the group key into a modulation signal through the time modulation array, and transmit it; it is also used to generate corresponding pair keys for each edge node, encrypt the pair keys using the average radiation pattern coefficients and the modulation signal, obtain the pair key ciphertext, and send it to the corresponding edge node; The edge node is used to receive the modulation signal, coherently demodulate the modulation signal to obtain demodulated symbols, and perform hard decision on the demodulated symbols to obtain a group key; It is also used to decrypt the paired key ciphertext using the average pattern coefficients and the demodulation symbols to obtain the paired key.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the method as described in any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 6.

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