Robust fast covert channel construction method using CSS spread spectrum modulation on amplitude

Abstract

The application discloses a kind of robust fast secret channel construction methods for amplitude using CSS spread spectrum modulation, mainly solve the problems, such as the limited transmission distance and capacity of secret channel in the existing low-power wide-area network environment, steps include: the modulation method design of secret channel;Signal frame structure design and frame detection;The demodulation method design of secret channel;Analysis is carried out to the information loss in the demodulation process of secret signal.The application designs the LoRa physical layer secret channel modulated by amplitude using CSS spread spectrum modulation method, designs the modulation and demodulation method of secret channel, analyzes the information loss in the demodulation process of secret signal, constructs the robust fast secret channel, widens the construction scene of secret channel, and the operation method is simple and clear, has practical value.

Description

Technical Field

[0001] This invention belongs to the fields of Internet of Things and low-power wireless networks, and relates to a method for constructing covert channels. In particular, it relates to a robust and fast covert channel construction method using CSS spread spectrum modulation in amplitude, which can be used to transmit additional information or launch attacks in covert channels during communication, thereby improving communication speed and robustness. Background Technology

[0002] The Internet of Things (IoT) is a revolutionary and innovative technology that extends and expands upon the internet, tightly integrating various information sensing devices with the internet to achieve ubiquitous interconnection between people, machines, and things. In my country, the IoT is considered one of the important digital infrastructures, providing key support and innovative impetus for the digital transformation of the economy and society and supply-side structural reform.

[0003] Low Power Wide Area Network (LPWAN) is an emerging and innovative Internet of Things (IoT) technology. Its goal is to enable power-limited end devices (such as battery-powered devices) to operate for extended periods and communicate at low speeds with gateways several kilometers away. LPWAN technology significantly improves IoT connectivity, expands IoT coverage, and provides broad application prospects and practical value for vertical industries such as public utilities and industrial control. This technology has been widely applied in security, transportation, logistics, industry, home, and agriculture.

[0004] With the ongoing development of 5G, low-power wide-area networks (LPWANs) are further promoting the interconnection of all elements—people, machines, and things—providing support for the digital empowerment of various industries and helping to realize the vision of the Internet of Everything. Currently, LWAN technologies include NB-IoT, Weightless-P, Sigfox, and LoRaWAN. Among them, LoRaWAN boasts the longest communication distance and the lowest power consumption, and adopts an open data standard, allowing users to deploy their networks as needed without paying operators. Therefore, LoRaWAN has received widespread attention in both industry and academia in recent years.

[0005] In recent years, significant efforts have been made to improve the performance of LoRaWAN and its physical layer standard, LoRa. These efforts include extending communication range, improving multiple access mechanisms, and resolving collisions. Furthermore, many innovative applications have been developed based on LoRa / LoRaWAN, including target localization, remote transmission, and aggregation querying.

[0006] However, besides the aforementioned research on performance improvements and application development, the security of LoRa / LoRaWAN is also an important research issue. Although computer communications face common threats such as interference replay attacks, imitation attacks, and key leakage attacks, there is little discussion about covert channel attacks.

[0007] Covert channels can breach the logical protections of computer systems, leaking confidential or sensitive information, a long-standing security concern in the network research community. Recent research indicates that partners can use covert channels to enhance the communication of legitimate applications, rather than having them exploited by attackers to compromise computer security. This further expands the potential applications of covert channels.

[0008] Nevertheless, the design and implementation of covert channels in low-power wide-area network (LPWAN) environments have not been widely discussed. Currently, the most advanced covert channel on LoRa is CloakLoRa, which uses on-off keying (OOK) to modulate LoRa amplitude information. However, CloakLoRa has limited communication range because OOK is not robust to noise. Furthermore, CloakLoRa generates different symbols by attenuating the transmitted power; due to power limitations in the ISM band and power attenuation, CloakLoRa's communication range is severely restricted, achieving only a 250-meter range.

[0009] Innovative ideas and research are needed to improve the performance and range of covert channels. By improving modulation schemes, enhancing noise robustness, and optimizing transmission power control, the reliability and coverage of covert channels in LoRaWAN can be improved. Furthermore, other modulation techniques and channel coding methods can be explored to further improve the performance of covert channels.

[0010] In light of this situation, the application research of a robust and fast covert channel construction method for LoRa amplitude modulation using CSS spread spectrum modulation is of great significance. It can effectively promote the application of covert channel transmission of additional information or attacks in communication, and improve communication speed and robustness. Summary of the Invention

[0011] This invention focuses on physical layer modulation and demodulation methods for low-power wide-area networks (LPWANs), proposing a robust and fast covert channel built upon amplitude modulation and demodulation at the physical layer. This invention innovatively applies CSS chirped spread spectrum modulation, originally used in the frequency domain, to the amplitude of LoRa signals, thus constructing a covert channel. This invention designs a demodulation method for this covert information modulation method, utilizing shared phase information to generate the imaginary part, thereby achieving information recovery and extraction under certain noise conditions. This invention designs a robust and fast covert channel construction method using CSS spread spectrum modulation to modulate LoRa amplitude: embedding real part information into the signal power amplitude, recovering the imaginary part information at the receiver, and demodulating using a method similar to classical chirped spread spectrum demodulation, achieving a breakthrough in noise tolerance.

[0012] The technical solution of the present invention is as follows:

[0013] A robust and fast covert channel construction method using CSS spread spectrum modulation on amplitude is characterized by comprising the following steps:

[0014] (1) The hidden chirped signal is generated by the chirped spread spectrum modulation (CSS) method, and the real part of the hidden chirped signal is taken as the hidden signal to be embedded.

[0015] (2) The frame structure of the covert signal is designed as a synchronization bit and data content. That is, the frame structure of the covert signal is a synchronization bit and data content payload, both of which are composed of CSS chirp.

[0016] (3) Embed the covert signal into the power amplitude of the LoRa legitimate channel so that the signal carries both legitimate and covert information;

[0017] (4) Locate the data packet according to the synchronization word of the legal signal, and align the data packet according to the synchronization word of the secret signal;

[0018] (5) Use a receiver for the hidden signal to sample the signal and extract the signal amplitude to obtain the real part of the hidden signal;

[0019] (6) Based on the real part of the hidden signal, the imaginary part of the hidden signal is generated using the information of the shared phase;

[0020] (7) By using the obtained real and imaginary parts, demodulation is performed using a method similar to classical chirped spread spectrum demodulation, thereby breaking through the noise tolerance and demodulating the hidden information in the background of noise.

[0021] (8) Analyze the information loss during the demodulation of the covert signal, that is, analyze the impact of information loss on the demodulation of the final covert information, and prove that the impact can be accepted under the covert channel conditions, and finally complete the construction of a robust and fast covert channel.

[0022] Furthermore, in step (1), the specific steps for generating the hidden chirp signal include: given CSS hidden signal parameters, including bandwidth BW and spreading factor SF, generating the hidden signal using the chirp signal generation method; the specific steps for taking the real part of the hidden chirp signal as the hidden signal to be embedded include: taking the real part of the time domain signal of the hidden chirp signal and discarding the imaginary part as the hidden signal to be embedded.

[0023] Furthermore, in step (2), the synchronization word contains the real part of a standard up-chirp and the opposite of the real part of a standard down-chirp. Since the real parts of the standard up-chirp and down-chirp are exactly the same, they are set to be the opposite of the down-chirp for distinction. The data content payload consists of the real parts of chirps at different starting frequency positions to represent different secret information.

[0024] Furthermore, in step (3), the specific steps of embedding the hidden signal to be embedded into the power amplitude of the LoRa legitimate channel include: changing the amplitude of the legitimate signal from a constant in the time domain to the same waveform as the hidden signal to be embedded, so as to ultimately carry legitimate information in frequency and hidden information in amplitude.

[0025] Furthermore, in step (4), the data packet positioning and alignment process includes the following steps:

[0026] ① Locate the data packet based on the synchronization word of the original legal information in each data packet of the legal signal, and perform an autocorrelation operation with the locally generated template to obtain the approximate location of the data packet containing both legal and hidden information; the template is generated using parameters that have been agreed upon by both the sender and receiver.

[0027] ② Utilizing the sync word of the hidden signal, through autocorrelation or de-chirping operations in demodulation methods,

[0028] Align data packets using templates.

[0029] Furthermore, the process of locating data packets is performed through cross-correlation; the process of data packet alignment is accelerated using GPU computation.

[0030] Furthermore, in step (5), the process of sampling the signal using a receiver of the covert signal and extracting the signal amplitude includes the following steps: sampling the I and Q signals in the signal and performing a sum-of-squares operation on the I and Q signals to obtain the signal power amplitude.

[0031] Furthermore, in step (6), the specific steps for generating the imaginary part of the hidden signal include: obtaining the phase of the real part of the hidden signal mathematically, based on the fact that the real and imaginary parts of any signal have the same phase, and obtaining the imaginary part with information loss through the trigonometric function method.

[0032] Furthermore, in step (7), the demodulation using a method similar to the classic chirped spread spectrum demodulation method includes the following steps: using the standard demodulation method of chirped spread spectrum modulation, de-chirping, multiplying the signal composed of the real part signal and the imaginary part signal with the corresponding down-chirp signal in the locally generated template, and performing downsampling and FFT operations to break through the noise tolerance, thereby demodulating the hidden information in the background of noise.

[0033] Furthermore, in step (8), the information loss during the demodulation of the covert signal is analyzed. The specific steps include: analyzing the impact of information loss on the final demodulation of the covert information, proposing and calculating the estimation error and demodulation error for this scenario, and proving that the impact can be accepted under the covert channel conditions.

[0034] The beneficial effects of this invention are as follows:

[0035] 1. This invention fully utilizes the time-accumulated energy characteristic of CSS chirped spread spectrum modulation, which can overcome the noise limit, and applies CSS to amplitude modulation, thus broadening the application scope of CSS. Existing research uses OOK modulation to construct covert channels, but this method has extremely low robustness to noise, and useful information is easily submerged by noise during transmission. This invention finds a novel method—combining CSS modulation with amplitude modulation—to construct a more noise-resistant and faster covert channel, and innovatively designs a demodulation method to form a complete covert channel system.

[0036] 2. This invention designs a frame structure for a covert channel and defines the covert signal frame structure as a synchronization bit and data content. By utilizing the synchronization bit of the covert signal, which has a unique identifier, the capture and alignment of data packets are achieved through autocorrelation or de-chirping operations in demodulation methods, providing a new approach for packet structure design in other scenarios.

[0037] 3. This invention addresses modulation systems combining CSS modulation and amplitude modulation by designing a demodulation method based on shared phase. This method fully considers the characteristics of CSS modulation and demodulation, achieving energy accumulation in the time domain and overcoming noise limits, thus avoiding problems such as high bit error rates caused by signal transmission. Furthermore, based on the characteristics of classic CSS demodulation, this invention significantly improves noise robustness, enabling longer communication distances and greatly enhancing the establishment of covert channels. Attached Figure Description

[0038] Figure 1 This is a general flowchart of an embodiment of the present invention.

[0039] Figure 2 This is a comparison of signals before and after embedding a covert channel in an embodiment of the present invention.

[0040] Figure 3 This is a schematic diagram of the covert channel demodulation process according to an embodiment of the present invention.

[0041] Figure 4 These are the different maximum bandwidths and maximum bit rates corresponding to different spreading factors of the covert channel in embodiments of the present invention. Detailed Implementation

[0042] The technical solution and effects of the present invention will be further described in detail below with reference to the accompanying drawings.

[0043] Before introducing the robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude provided by this invention, we will briefly explain the basic principle of chirped spread spectrum modulation and demodulation used in the LoRa physical layer.

[0044] In CSS modulation, the signal is modulated into chirps. Each chirp sweeps a specified bandwidth BW linearly with time during its symbol time Ts. The basic up-chirp increases linearly with time from its initial frequency, reaching a maximum frequency f. max and continue from the minimum frequency f min It sweeps back to its initial frequency, while down-chirp does the opposite.

[0045] To retrieve the encoded data, the receiver estimates the initial frequency of the chirp. The receiver first performs a de-chirping process by multiplying the received chirp by a locally generated down-chirp. The de-chirped signal is then transformed into a constant-frequency sine wave, which is precisely the initial frequency of the chirp. Therefore, the receiver finds the 2- of the de-chirped signal. SF The frequency is recovered by using the peak value of the point FFT.

[0046] Covert channels can affect communication over public channels. Maximizing the use of physical layer redundancy to establish covert channels for communication and security applications while maintaining communication quality over public channels presents a series of challenges, including limited modulation methods, short communication distances, and low communication rates. To address these challenges, this invention proposes a robust and fast covert channel design method by applying CSS chirped modulation to amplitude modulation. Figure 1 The implementation steps of this invention are as follows:

[0047] Step 1: We plan to establish a covert channel at the physical layer based on the amplitude of the LoRa signal and modulate the amplitude, such as using chirped spread spectrum modulation, to improve the communication range of the covert channel. Specifically, assuming there is a chirp of a LoRa signal, it can be represented as...

[0048]

[0049] Step 2: Taking chirped spread spectrum as an example, we perform covert channel modulation on its amplitude A(t) so that its real part, i.e., the signal I(t), exhibits the same chirp as chirped spread spectrum.

[0050]

[0051] Note that t′ here refers to the duration of a chirp in the covert channel, which is not necessarily the same as the original chirp.

[0052] To embed the esoteric chirp, the power level amplitude of the LoRa chirp is modulated using CSS. This amplitude modulation is performed on a channel where frequency modulation has already been completed. Therefore, esoteric channel embedding does not affect the initial frequency of the legitimate LoRa chirp, as it is a scaling process for each sample point. When the esoteric channel has a high bandwidth, new frequency components may be introduced. However, the dechirping process can converge the spectral power of the chirp to a frequency point that is much larger than the power of the introduced frequency components. For simplicity, the amplitude of the power level is expressed as the amplitude in the following sections. Ideally, the amplitude of the legitimate chirp, denoted by A(t), remains constant over its symbol time. Note that the amplitude of the signal is not a complex value. Therefore, to embed the esoteric chirp into the amplitude, we replace the original A(t) of the legitimate chirp with the real part of the esoteric chirp (i.e., the value of i), as follows: Figure 2 The image shows a comparison of the signal before and after embedding the covert channel.

[0053] Step 3: The covert channel frame consists of two parts: a covert channel synchronization word containing a covert upper chirp and a covert lower chirp, and a payload of multiple data items. We cannot distinguish between the covert upper chirp and the covert lower chirp based on their real parts, as they are identical. Therefore, the unique pattern of the synchronization word is set to the inverse of the covert upper chirp and the covert lower chirp. The covert frame does not contain a preamble because the system modulates the amplitude of the legitimate channel, meaning the receiver does not need to use a preamble to correct carrier frequency offset. In the covert channel, covert chirp modulation begins at the start of the LoRa legitimate frame.

[0054] Step 4: To detect frames of espionage, the receiver employs a two-step approach: (1) Valid LoRa frame detection: The last uplink chirp of the sync word and the first downlink chirp of the SFD exhibit a unique “peak” pattern, which can be used as a template. During operation, the receiver cross-correlates the received signal and locates the LoRa frame. LoRa frame detection can be implemented in various ways, including folding, the Schmidl-Cox algorithm, and deep learning. (2) Espionage frame detection: A method similar to that used for standard LoRa detection is employed. The sync word in the espionage frame exhibits a unique pattern. However, as mentioned in Step 2, only the real part of the espionage chirp differs from the regular chirp, meaning the receiver cannot distinguish between the espionage uplink chirp and the espionage downlink chirp. Therefore, we use the inverse of the espionage uplink chirp and the espionage downlink chirp as the correlation template. The receiver generates the template locally and cross-correlates it with the received signal. Furthermore, we can utilize a GPU to accelerate the frame detection process.

[0055] Step 5: The real part of the covert chirp signal is already on the baseband, therefore, we do not need to perform additional signal processing to achieve downconversion. For a legitimate receiver, it does not check the amplitude of the data packet. The amplitude of the received LoRa frame is...

[0056]

[0057] Where I(t) and Q(t) are the in-phase and quadrature values ​​captured by the covert receiver.

[0058] Step Six: The hidden chirp is embedded in the amplitude, which is a real value. However, in CSS modulation, the receiver needs both the real and imaginary parts to converge the spectral power of the chirp to a certain frequency. To achieve this signal-to-noise ratio gain, the receiver needs to generate a corresponding imaginary part based on the real part. Using a phase-sharing method, taking advantage of the fact that the real and imaginary parts are in phase, the corresponding imaginary part is generated using the mathematical principles of trigonometric functions.

[0059]

[0060] Step 7: By merging the obtained real and imaginary parts, a complete ChirpC of the amplitude-concealed channel can be obtained. a (t'), the expression is For the amplitude information A(t) of a chirp within an existing channel, we can customize the length of the hidden channel chirp so that... After obtaining the imaginary part, we can use the locally generated hidden dechirping to perform dechirping and retrieve hidden information, such as... Figure 3 The diagram shown illustrates the demodulation process of a covert channel.

[0061] Step 8: Since the amplitude is real, the covert channel embeds and transmits the real part of the covert chirp, discarding the imaginary part. The imaginary part needs to be generated locally at the receiver to achieve dechirping in the covert channel. The generated imaginary part retains the positive part corresponding to the original signal, but modifies the negative part to the opposite number. Mathematically, arccos is a multivalued function with values ​​in the range [0, π]. Therefore, quadrant information of phase φ is lost. We theoretically analyze the information loss in the generation of the imaginary part. We analyze the information loss in the demodulation process of the covert signal, that is, analyze the impact of information loss on the demodulation of the final covert information, and prove that this impact is acceptable under the conditions of the covert channel. Finally, we realize a complete system for constructing a robust and fast covert channel.

[0062] By following the above methods, a complete, robust, and fast system for constructing covert channels can be built.

[0063] This invention, on the one hand, fully utilizes the time-accumulated energy characteristic of CSS chirped spread spectrum modulation, thereby overcoming the noise limit, and applies CSS to amplitude modulation, broadening the application scope of CSS. Compared with traditional methods, the proposed method achieves higher robustness to noise, making useful information less likely to be submerged by noise during transmission. This invention finds a novel method—combining CSS modulation and amplitude modulation—to construct a more noise-resistant and faster covert channel. On the other hand, this invention designs a demodulation method based on shared phase for the modulation system combining CSS modulation and amplitude modulation, fully considering the characteristics of CSS modulation and demodulation, realizing energy accumulation in the time domain, overcoming the noise limit, and avoiding problems such as high bit error rate caused by signal transmission.

[0064] The effects of the method proposed in this invention will be further described below with reference to the embodiments.

[0065] Example 1:

[0066] To understand the performance limitations of the covert channel, we further implemented it in GNU Radio. Specifically, we performed simulations to explore the maximum covert channel bandwidth and maximum covert channel bit rate. In CSS modulation, when the sampling rate of the SDR receiver is constant, the bandwidth affects the maximum bit rate. Therefore, understanding the maximum bandwidth of the covert channel is crucial. The number of samples per symbol, denoted by n, can be represented as...

[0067]

[0068] Among them, sr s T represents the sampling rate of the SDR receiver. sc This represents the symbol time in the covert channel. For an SDR receiver, its sampling rate sr s It is fixed when receiving the signal and can be considered a constant. Therefore, given a fixed sr s and SF c The number of samples for each symbol Ns is a decisive factor, and is related to BW. c The inverse relationship Ns has a lower bound to ensure the decoding accuracy of the covert channel. Mathematically, CSS requires at least 2SF per chirp. c We use sampling points to perform an FFT to recover the initial frequency. Then, we calculate the number of samples per symbol point-by-point for each spreading factor, and obtain the minimum value that satisfies the requirement of a bit error rate of 0 through simulation. We can find that 2SF... c The relationship between the minimum sample size per symbol verifies Nyquist's theorem.

[0069] The transmission rate of a covert channel can be expressed as:

[0070]

[0071] Among them SF c T is the spreading factor. sc For symbolic time, BW c For bandwidth. Bit rate and bandwidth (BW) c Numerically proportional to the spreading factor SF c Based on the previous maximum bandwidth results, we can calculate the maximum bit rate under different spreading factors. When sr s With a clock speed of 1 MHz and SF = 3, the maximum bit rate of a covert channel can reach 150 kbps. (Maximum bit rate sr) s With SF c The bit rate decreases as the receiver's sampling rate (sr) increases. Similar to bandwidth, the bit rate decreases as the receiver's sampling rate (sr) increases. s Proportional, such as Figure 4 As shown, this represents the different maximum bandwidths and maximum bit rates corresponding to different spreading factors in a covert channel.

[0072] The above description is merely a preferred embodiment of the present invention. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention using the methods and techniques disclosed above, or modify them into equivalent embodiments with equivalent changes, without departing from the scope of the technical solutions of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall still fall within the protection scope of the technical solutions of the present invention.

Claims

1. A robust and fast covert channel construction method using CSS spread spectrum modulation on amplitude, characterized in that, Includes the following steps: (1) The hidden chirped signal is generated by the chirped spread spectrum modulation (CSS) method, and the real part of the hidden chirped signal is taken as the hidden signal to be embedded. (2) The frame structure of the hidden signal is designed as a synchronization bit and data content. That is, the frame structure of the hidden signal is a synchronization bit syncword and data content payload, both of which are composed of CSS chirp; (3) Embed the covert signal into the power amplitude of the LoRa legitimate channel so that the signal carries both legitimate and covert information; (4) Locate the data packet according to the sync word of the legitimate signal, and align the data packet according to the sync word of the secret signal; (5) Use a receiver for the hidden signal to sample the signal and extract the signal amplitude to obtain the real part of the hidden signal; (6) Based on the real part of the hidden signal, the imaginary part of the hidden signal is generated using the information of the shared phase; (7) By using the obtained real and imaginary parts, demodulation is performed using a method similar to classical chirped spread spectrum demodulation, thereby breaking through the noise tolerance and demodulating the hidden information in the background of noise. (8) Analyze the information loss during the demodulation of the covert signal, that is, analyze the impact of information loss on the demodulation of the final covert information, and prove that the impact can be accepted under the covert channel conditions, and finally complete the construction of a robust and fast covert channel.

2. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 1, characterized in that, In step (1), the specific steps for generating the hidden chirp signal include: given CSS hidden signal parameters, including bandwidth BW and spreading factor SF, generating the hidden signal using the chirp signal generation method; the specific steps for taking the real part of the hidden chirp signal as the hidden signal to be embedded include: taking the real part of the time domain signal of the hidden chirp signal and discarding the imaginary part as the hidden signal to be embedded.

3. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 1, characterized in that, In step (2), the synchronization word contains the real part of a standard up-chirp and the opposite of the real part of a standard down-chirp; the data payload consists of the real parts of chirps at different starting frequency positions to represent different secret information.

4. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 1, characterized in that, In step (3), the specific steps of embedding the hidden signal to be embedded into the power amplitude of the LoRa legitimate channel include: changing the amplitude of the legitimate signal from a constant in the time domain to the same waveform as the hidden signal to be embedded, so as to ultimately carry legitimate information in frequency and hidden information in amplitude.

5. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 1, characterized in that, In step (4), the data packet positioning and alignment process includes the following steps: ① Locate the data packet based on the sync word of the original legal information in each data packet of the legal signal, and perform an autocorrelation operation with the locally generated template to obtain the approximate location of the data packet that contains both legal and hidden information; ②Using the synchronization word of the hidden signal, the data packets are aligned by means of the template through autocorrelation or the de-chirping operation in the demodulation method.

6. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 5, characterized in that, The process of locating data packets is performed through cross-correlation; the process of data packet alignment is accelerated using GPU computation.

7. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 1, characterized in that, In step (5), the process of sampling the signal using a receiver of the covert signal and extracting the signal amplitude includes the following steps: sampling the I and Q signals in the signal and performing a sum-of-squares operation on the I and Q signals to obtain the signal power amplitude.

8. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 1, characterized in that, In step (6), the specific steps for generating the imaginary part of the hidden signal include: obtaining the phase of the real part of the hidden signal mathematically, based on the fact that the real and imaginary parts of any signal have the same phase, and obtaining the imaginary part with information loss through the trigonometric function method.

9. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 1, characterized in that, In step (7), the demodulation using a method similar to the classic chirped spread spectrum demodulation method includes the following steps: using the standard demodulation method of chirped spread spectrum modulation, de-chirping, multiplying the signal composed of the real part signal and the imaginary part signal with the corresponding down-chirp signal in the locally generated template, and performing downsampling and FFT operations to break through the noise tolerance, thereby demodulating the hidden information in the background of noise.

10. The robust and fast covert channel construction method using CSS spread spectrum modulation and amplitude as described in claim 1, characterized in that, In step (8), the information loss during the demodulation of the covert signal is analyzed. The specific steps include: analyzing the impact of information loss on the demodulation of the final covert information, proposing and calculating the estimation error and demodulation error for this scenario, and proving that the impact can be accepted under the covert channel conditions.

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