Hyperchaotic scrambling M-EWFRFT communication method based on joint transform

Abstract

The application provides a hyperchaotic scrambling code M-EWFRFT communication method based on a pair-join transformation, and relates to the technical field of secret communication.The application constructs a three-dimensional hyperchaotic mapping, so that the iteratively generated chaotic sequence can be directly used as a data encryption key;then, a phase encryption algorithm is designed by adopting a pair-join transformation and a ciphertext feedback mode, the availability of modulation encryption and the ability to resist differential attacks are enhanced;finally, an M-EWFRFT physical implementation model is constructed, and the two are organically combined, the baseband modulation signal is subjected to phase scrambling, and then M-EWFRFT two-stage encryption is implemented.Compared with the existing physical layer encryption algorithm, the application further improves the signal anti-detection ability and anti-attack ability in the communication process.

Description

Technical Field

[0001] This invention relates to the field of secure communication technology, and in particular to a hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation. Background Technology

[0002] Wireless communication technology is increasingly widely used in mobile communications, the Internet of Things, satellite communications, and many other fields, greatly changing people's lives and production methods. However, the broadcast characteristics and deterministic features of wireless channels provide opportunities for malicious attackers to crack systems using protocol analysis and signal parameters, posing a serious security threat. Physical layer security has thus become the first line of defense in building wireless communication systems.

[0003] In related technologies, physical layer security mainly includes modulation encryption and signal processing techniques. Modulation encryption techniques are mostly implemented by adding an algorithm module after baseband modulation. However, existing modulation encryption and decryption algorithms lack consistency, which restricts the widespread adoption and application of this technology. Existing signal processing techniques typically incorporate weighted fractional Fourier transform (WFRFT) technology. This technique can improve signal concealment, but it has inherent drawbacks such as low parameter dimensionality and significant periodic characteristics, making it easily detectable and cracked by higher-order cumulants, cyclic correlation methods, etc.

[0004] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions in order to further enhance the anti-detection and anti-attack capabilities of signals during communication.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation, so as to further enhance the anti-interception and anti-attack capabilities of the signal during the communication process.

[0007] This invention provides a hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation, the method comprising the following steps: The input signal is modulated by baseband modulation to form a modulated signal; A three-dimensional hyperchaotic map is constructed, and a chaotic sequence is generated iteratively, wherein the chaotic sequence includes a first state variable, a second state variable, and a third state variable; Using the first state variable as the phase encryption key, the modulated signal is phase encrypted through integrative transformation and ciphertext feedback to generate a phase encrypted signal. Using 4-WFRFT as the state function, a physical implementation model of M-EWFRFT is constructed. The second and third state variables are used as control parameters of M-EWFRFT. The phase encryption signal is encrypted by M-EWFRFT to complete hybrid carrier modulation. The receiving end receives the mixed carrier signal and forms the signal to be decrypted; The signal to be decrypted is decrypted using the second and third state variables to generate a phase-decrypted signal. Phase decryption is performed on the signal to be decrypted, and the demodulation process is completed.

[0008] In an exemplary embodiment of the present invention, the step of using the first state variable as a phase encryption key to perform phase encryption on the modulated signal through involution transformation and ciphertext feedback to generate a phase-encrypted signal includes: For the first modulated signal, its phase is subtracted from the phase encryption key to generate a phase encryption signal; For the second and subsequent modulation signals, the phase of the phase encryption signal of the previous modulation signal is added to the phase of the current modulation signal to obtain the first phase sum. Then, the first phase sum is subtracted from the phase encryption key to generate the phase encryption signal.

[0009] In an exemplary embodiment of the present invention, the step of constructing an M-EWFRFT physical implementation model using 4-WFRFT as the state function includes: The original signal is simultaneously input into M 4-WFRFT modules; Perform a weighted summation on M 4-WFRFT signals.

[0010] In an exemplary embodiment of the present invention, during the iteration process of the three-dimensional hyperchaotic mapping, the coordinate values ​​of the state points are determined by... The trajectory is folded by taking the modulus.

[0011] In an exemplary embodiment of the present invention, during the iteration process of the three-dimensional hyperchaotic mapping, the trajectory of the state point is limited to... .

[0012] In an exemplary embodiment of the present invention, the difference equations of the three-dimensional hyperchaotic mapping are: in, As the first state variable, For the second state variable, For the third state variable, The base is , and , To control variables, , Represents the number of chaotic iterations. For iteration The first state variable after that. For iteration The first state variable after that. For iteration The second state variable after that. For iteration The second state variable after that. For iteration The third state variable after that. For iteration The third state variable after that. The base is The index is The exponential function, The base is The index is The exponential function, The base is The index is The exponential function.

[0013] In an exemplary embodiment of the present invention, the step of using 4-WFRFT as the state function, constructing an M-EWFRFT physical implementation model, and using the second and third state variables as control parameters of the M-EWFRFT to encrypt the phase encryption signal using M-EWFRFT includes: The phase encryption signal is first divided into groups, and then each group of phase encryption signals is encrypted using M-EWFRFT.

[0014] In an exemplary embodiment of the present invention, the step of performing M-EWFRFT decryption on the signal to be decrypted using the second state variable and the third state variable to generate a phase-decrypted signal includes: The signal to be decrypted is divided into groups, and then each group of signals to be decrypted is decrypted using M-EWFRFT, wherein the length of the group during decryption is the same as the length of the group during encryption.

[0015] In an exemplary embodiment of the present invention, the step of performing phase decryption on the signal to be phase decrypted includes: The first signal to be decrypted by phase is obtained by subtracting the phase of the first signal to be decrypted by phase encryption key; For the second and subsequent phase-decrypted signals, the phase of the previous phase-decrypted signal is added to the phase of the current phase-decrypted signal to obtain the second phase sum, and then the second phase sum is subtracted from the phase encryption key.

[0016] The technical solution provided by this invention may include the following beneficial effects: This invention constructs a novel three-dimensional hyperchaotic mapping, enabling the iteratively generated chaotic sequence to be directly used as a data encryption key. Next, a phase encryption algorithm is designed using involutional transformation and ciphertext feedback, enhancing the usability of modulation encryption and its resistance to differential attacks. Finally, an M-EWFRFT physical implementation model is constructed and organically combined with the existing algorithm, first performing phase scrambling on the baseband modulation signal, and then implementing two-level M-EWFRFT encryption. Compared with existing physical layer encryption algorithms, this invention further improves the signal's resistance to detection and attacks during communication.

[0017] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0019] Figure 1 This diagram illustrates the steps of the hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation in an exemplary embodiment of the present invention. Figure 2 This diagram illustrates a system block diagram of the hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation in an exemplary embodiment of the present invention. Figure 3 This illustrates an exemplary embodiment of the present invention where every two state sequences in a three-dimensional hyperchaotic mapping follow the control variable. A changing bifurcation diagram; Figure 4 The control variables of the three-dimensional hyperchaotic mapping in an exemplary embodiment of the present invention are shown. A three-dimensional phase diagram of the trajectory of a state point in phase space; Figure 5 This illustrates the Lyapunov exponent of the three-dimensional hyperchaotic mapping under different control variables in an exemplary embodiment of the present invention. Figure 6 The spectral entropy of three state sequences in a three-dimensional hyperchaotic mapping is shown in an exemplary embodiment of the present invention. Figure 7 The approximate entropy of three state sequences of a three-dimensional hyperchaotic mapping is shown in an exemplary embodiment of the present invention; Figure 8 This diagram illustrates phase encryption in an exemplary embodiment of the present invention. Figure 9 This diagram illustrates the physical implementation model flow of M-EWFRFT in an exemplary embodiment of the present invention. Figure 10 This diagram illustrates the constellation of the QPSK modulated signal after M-EWFRFT processing in an exemplary embodiment of the present invention. Figure 11 This diagram illustrates phase decryption in an exemplary embodiment of the present invention. Figure 12 This diagram illustrates the constellation diagram after the transmitted information has been modulated and encrypted using QPSK and 16QAM in an exemplary embodiment of the present invention. Figure 13 The statistical characteristics of the QPSK encryption signal in an exemplary embodiment of the present invention are shown in the figure. Figure 14 A key sensitivity analysis diagram is shown in an exemplary embodiment of the present invention. Detailed Implementation

[0020] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0021] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0022] Physical layer security (PLS) eliminates the identifiability of signals from the source by means of mechanisms such as dynamic waveform randomized modulation and collaborative generation of channel fingerprint keys, thus achieving active defense against interception and low detection probability, and thus becoming the first line of defense in building wireless communication systems.

[0023] Physical layer security mainly includes techniques such as modulation encryption and signal processing. Among them, modulation encryption utilizes the characteristics of baseband modulation and uses random sequences to control the modulation process of phase, amplitude, subcarriers, etc., thereby eliminating the inherent characteristics of the waveform, increasing the randomness of the waveform, and achieving the purpose of parameter concealment.

[0024] In addition, most modulation encryption technologies are implemented by adding an algorithm module after baseband modulation. However, existing modulation encryption and decryption algorithms are not consistent, which also restricts the popularization and application of this technology.

[0025] Signal processing techniques typically incorporate traditional WFRFT. As a novel signal processing technique, traditional WFRFT can generate signals of various forms through different modulation orders, effectively masking the characteristics of the original signal and providing an important solution for covert signal transmission. However, traditional WFRFT, due to its use of weighted superposition of periodic state functions controlled by modulation order, suffers from inherent drawbacks such as low parameter dimensionality and significant periodic characteristics, making it easily detectable and cracked by higher-order cumulants, cyclic correlation methods, and other techniques.

[0026] Based on this, the present invention provides a hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation, referencing... Figure 1 As shown, the method includes the following steps S100-S700: Step S100: The input signal is modulated by baseband to form a modulated signal.

[0027] Baseband modulation processes the raw information to be transmitted in the time, frequency, or code domains to transmit as much information as possible with the smallest possible bandwidth. The modulation method used in this step can be PSK modulation, QPSK modulation, ASK modulation, or QAM modulation.

[0028] Step S200: Construct a three-dimensional hyperchaotic mapping and generate a chaotic sequence through iteration. The chaotic sequence includes a first state variable, a second state variable, and a third state variable.

[0029] This three-dimensional hyperchaotic map is a new non-degenerate hyperchaos constructed based on the needs of subsequent phase encryption steps and M-EWFRFT transformation parameter values. Furthermore, the three state variables generated by the iteration of this three-dimensional hyperchaotic map do not require further processing and can be directly used as the subsequent phase encryption key and M-EWFRFT control parameters.

[0030] Step S300: Using the first state variable as the phase encryption key, the modulated signal is phase encrypted by integrative transformation and ciphertext feedback to generate a phase encrypted signal.

[0031] The phase encryption algorithm is designed by adopting integrative transformation and ciphertext feedback, which not only ensures the consistency of encryption and decryption algorithms, but also enhances the ability to resist differential attacks.

[0032] Step S400: Using 4-WFRFT as the state function, construct the M-EWFRFT physical implementation model, use the second and third state variables as the control parameters of M-EWFRFT, and perform M-EWFRFT encryption on the phase encryption signal to complete the hybrid carrier modulation.

[0033] M-EWFRFT is a multinomial extended weighted fractional Fourier transform. By introducing multiple weight coefficients and a multi-periodic behavior function mechanism, it can significantly increase the diversity of signal morphology while expanding the parameter dimension.

[0034] Step S500: The receiving end receives the mixed carrier signal and forms the signal to be decrypted.

[0035] Specifically, the receiving end removes the cyclic prefix and performs analog-to-digital conversion on the received signal to form the signal to be decrypted.

[0036] Step S600: Use the second state variable and the third state variable to perform M-EWFRFT decryption on the signal to be decrypted to generate a phase decryption signal.

[0037] Step S700: Perform phase decryption on the signal to be decrypted and complete the demodulation process.

[0038] In embodiments of this invention, a novel three-dimensional hyperchaotic mapping is constructed, enabling the iteratively generated chaotic sequence to be directly used as a data encryption key. Next, a phase encryption algorithm is designed using involutional transformation and ciphertext feedback, enhancing the usability of modulation encryption and its resistance to differential attacks. Finally, an M-EWFRFT physical implementation model is constructed and organically combined with the existing model, first performing phase scrambling on the baseband modulation signal, and then implementing two-level M-EWFRFT encryption. Compared with existing physical layer encryption algorithms, this invention further improves the signal's resistance to detection and attacks during communication.

[0039] Figure 2 This is a system block diagram of the communication method of the present invention, which shows the entire process of signal from input to output in detail. According to this diagram, we can see that after the information is input, it first undergoes baseband modulation, and then phase encryption and M-EWFRFT encryption are performed in sequence. After that, it is sent to the receiving end through processes such as adding a cyclic prefix, digital-to-analog conversion, and up-conversion. The receiving end processes the received signal in reverse process as the transmitting end and then outputs the signal.

[0040] Therefore, step S200 does not necessarily have to occur after step S100; it only needs to occur before step S300. Similarly, the process of constructing the M-EWFRFT physical implementation model in step S400 does not necessarily have to occur after steps S100, S200, and S300; it only needs to be completed before M-EWFRFT encryption.

[0041] The steps of the method described above in this example implementation will now be explained in more detail.

[0042] In step S200, during the iteration process of the three-dimensional hyperchaotic mapping, the coordinate values ​​of the state points are determined by... The trajectory is folded by taking the modulus.

[0043] More specifically, limiting the trajectory of the state point to .

[0044] Furthermore, the system of difference equations for the three-dimensional hyperchaotic mapping is constructed as follows: (1) in, As the first state variable, For the second state variable, For the third state variable, The base is , and , To control variables, , Represents the number of chaotic iterations. For iteration The first state variable after that. For iteration The first state variable after that. For iteration The second state variable after that. For iteration The second state variable after that. For iteration The third state variable after that. For iteration The third state variable after that. The base is The index is The exponential function, The base is The index is The exponential function, The base is The index is The exponential function, where all parameters are double-precision floating-point numbers. This three-dimensional hyperchaotic map has no fixed points.

[0045] Let the base of this three-dimensional hyperchaotic mapping be . The initial value of the first state variable is The initial value of the second state variable is The initial value of the third state variable is The dynamic characteristics were verified using bifurcation diagrams and phase diagrams, Lyapunov exponents, spectral entropy, and approximate entropy.

[0046] Figure 3 This demonstrates that the mapping varies between every two state sequences with the control variable. A changing bifurcation diagram, in which, Figure 3 (a) is bifurcation diagram, Figure 3 (b) is bifurcation diagram, Figure 3 (c) is As can be seen from the bifurcation diagram, the three bifurcation diagrams are distributed throughout the three-dimensional value space, reflecting that the evolution path and state of the system under different control variable conditions have a high degree of uncertainty and irregularity.

[0047] Figure 4 Showing control variables The three-dimensional phase diagram of the trajectory of the state point in phase space shows that the chaotic attractor is distributed throughout the entire range of state variables, indicating the extensive ergodicity of the mapping in the state space.

[0048] The Lyapunov exponent measures the sensitivity of a chaotic map to initial conditions. This three-dimensional hyperchaotic map has three state variables, and the state trajectory can be stretched and folded in three directions. Its corresponding Jacobian matrix... for: ; The Lyapunov exponents of this three-dimensional hyperchaotic map under different control variables were calculated and plotted using the QR orthogonal decomposition method, as shown below. Figure 5 As shown, where, Figure 5 (a) is The Lyapunov index. Figure 5 (b) is The Lyapunov index. From Figure 5 As can be seen, the three Lyapunov indices LE s All are large positive values, and vary with the control variable. It increases with the increase of . Therefore, when At that time, the three-dimensional hyperchaotic mapping is a non-degenerate hyperchaotic mapping, and the trajectory of the system state points is extremely sensitive to small changes in the initial values, exhibiting strong chaos.

[0049] Spectral entropy (SE) provides a holistic description of the structural complexity of a chaotic sequence. A higher SE value indicates greater complexity and more significant unpredictability of the chaotic system. The spectral entropy of the three state sequences in this three-dimensional hyperchaotic map is shown below. Figure 6 As shown, the average values ​​of SEs are 0.9377, 0.9383 and 0.9381, respectively, indicating that the three-dimensional hyperchaotic mapping has high complexity.

[0050] Approximate entropy (ApEn) measures the complexity and irregularity of chaotic sequences. More complex time series correspond to larger approximate entropy, while more regular time series correspond to smaller approximate entropy. This three-dimensional hyperchaotic mapping varies with control variables. The approximate entropy value of the change, where the length of the three state sequences is 500, the embedding dimension is 1, and the similarity tolerance is 0.2 times the standard deviation of each sequence. For example... Figure 7 As shown, the approximate entropy averages of the three state sequences are 1.6058, 1.6054, and 1.6091, respectively, and increase with the control variable. The increase in , with slight oscillations around the average value, indicates that the three-dimensional hyperchaotic mapping sequence has good complexity and randomness, and can be directly used as a data encryption key.

[0051] In step S300, the step of using the first state variable as the phase encryption key and performing phase encryption on the modulated signal through involution transformation and ciphertext feedback to generate the phase-encrypted signal includes: For the first modulated signal, subtract its phase from the phase encryption key to generate a phase encryption signal; For the second and subsequent modulation signals, the phase of the phase encryption signal of the previous modulation signal is added to the phase of the current modulation signal to obtain the first phase sum. Then, the first phase sum is subtracted from the phase encryption key to generate the phase encryption signal.

[0052] For details, please refer to Figure 8 As shown, let the phase of the modulated signal formed after baseband modulation be... and , This indicates the phase of the first modulated signal, ... Let the phase of the nth modulated signal be ; let the phase of the phase-encrypted signal be . and , This indicates the phase of the first phase encryption signal, ... Indicates the phase of the nth phase encryption signal: but ,in The first state variable is the phase encryption key; ; To unify the formula, assume that the phase summed with the phase of the first modulated signal is... Then refer to Figure 8 The phase encryption process, the expression for phase encryption is: ; In step S400, during the construction of the M-EWFRFT physical implementation model, the 4-WFRFT is used as the state function to construct the M-EWFRFT physical implementation model.

[0053] Specifically, the physical implementation model flow of M-EWFRFT is as follows: Figure 9 As shown, the original signal is first input to... In the 4-WFRFT module, the first The transformation order of each module is ; Then, the M 4-WFRFT signals are weighted and summed to obtain the M-EWFRFT signal, where the first... Item weighting coefficient calculation expression for: The realizable expression of M-EWFRFT for: In the above formula, Represents the original signal; For control parameters and ; The element representing the control parameter and , Indicates the index value of the control parameter and ; The order is 4-WFRFT; Represents the imaginary unit; This indicates the number of 4-WFRFT modules.

[0054] Correspondingly, the inverse transform of M-EWFRFT for: In the above formula, Represents the original signal; For control parameters and ; The element representing the control parameter and , Indicates the index value of the control parameter and ; The order is 4-WFRFT; Represents the imaginary unit; This indicates the number of 4-WFRFT modules.

[0055] Taking 6-EWFRFT as an example, the constellation point distribution of the QPSK modulated signal after M-EWFRFT processing is analyzed, such as... Figure 10 As shown, where Figure 10 (a) is the original QPSK signal constellation diagram. Figure 10 (b) in the diagram represents the QPSK signal after passing through... The constellation diagram processed by M-EWFRFT, Figure 10 (c) in the text represents the QPSK signal after passing through... The constellation diagram processed by M-EWFRFT, Figure 10 In the diagram, (d) represents the QPSK signal after passing through... The constellation diagram processed by M-EWFRFT, Figure 10 (e) is Figure 10 The inverse transform of (d).

[0056] Depend on Figure 10 As shown in (d) and (e), by inverting the transformation parameters, the signal processed by M-EWFRFT can be accurately recovered to the original signal, indicating that the M-EWFRFT expression proposed in this invention is feasible. Furthermore, through... Figure 10 As can be seen from (a) to (d), with the change of transform parameters, the constellation points of the signal processed by M-EWFRFT exhibit rotation, diffusion, and aliasing. Therefore, if the transform parameters change randomly, the signal processed by M-EWFRFT will inevitably exhibit Gaussian-like distribution characteristics. This characteristic will make it extremely difficult for illegal eavesdroppers to detect the transmitted signal. Furthermore, compared to WFRFT, M-EWFRFT uses multiple independent transform parameters to control the signal form changes, resulting in stronger resistance to parameter scanning and better security.

[0057] In one embodiment, the second state variable Third state variable As control parameters of M-EWFRFT The phase encryption signal is encrypted using M-EWFRFT.

[0058] Furthermore, the phase encryption signal can be first grouped, and then each group of phase encryption signals can be encrypted using M-EWFRFT.

[0059] Assuming the phase encryption signal is The signal after M-EWFRFT encryption is ,and: The encrypted signal After adding a cyclic prefix and performing digital-to-analog conversion, it is transmitted via a wireless channel.

[0060] In step S500, the receiving end removes the cyclic prefix and performs analog-to-digital conversion on the received signal to form the signal to be decrypted. .

[0061] In step S600, the second state variable is still used. and the third state variable Treating decryption signals Perform M-EWFRFT decryption to generate the phase to be decrypted signal.

[0062] Furthermore, it can also be used to treat decrypted signals. The signal is divided into groups, and then each group of signals to be decrypted is decrypted using M-EWFRFT. The length of the decryption group is the same as the length of the encryption group. The signal after M-EWFRFT decryption is then... ,and: In step S700, refer to Figure 11 As shown, for the signal Phase decryption is performed while the signal amplitude remains unchanged, using the key. Subtract signal The phase of the first signal to be decrypted is obtained from the phase of the first signal to be decrypted. Begin with the key Subtract the second phase sum, which is the sum of the phases of the previous phase-to-decrypt signal and the current signal.

[0063] For ease of analysis, let's assume... The phase is , The phase of the decryption signal is Then the phase decryption expression is: , Finally, the decrypted signal is demodulated to recover the original information.

[0064] Furthermore, the expression for phase encryption and the expression for phase decryption. , Analyze the relationships between them.

[0065] Definition: For a transformation ,like If it is an identity transformation, then it is called... This is an integrative transformation.

[0066] Set the expression for phase encryption as follows: Then for any key have: On the one hand, as can be seen from the above definition, the phase encryption algorithm designed in this invention is an integrative transformation.

[0067] On the other hand, it can also be seen from the expression of phase decryption that the phase encryption and decryption algorithms in this invention are exactly the same, which once again confirms that the phase encryption algorithm designed in this invention is an integrative transformation.

[0068] Furthermore, as can be seen from the phase encryption expression, the phase of the encrypted signal in this invention... Not only with the phase of the current modulation signal It is related to, and due to the effect of the encrypted signal phase link, it is also related to the phase of the previous modulated signal. This not only effectively conceals the distribution pattern of the plaintext modulated signal, but also ensures that if an illegal eavesdropper tampers with the transmitted signal, the legitimate receiver, even with the shared key, cannot accurately recover the subsequent signal. This can, to some extent, identify whether the illegal eavesdropper has tampered with the encrypted transmitted signal by replaying, embedding, or deleting it.

[0069] Furthermore, computer simulation analysis was performed on the hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation provided by this invention to demonstrate its encryption effect: Physical layer encryption methods aim to disrupt the inherent patterns and characteristics of signals. This invention, in designing its physical layer encryption method, also fully considers scrambling and spreading the original information to enhance its resistance to attacks. Therefore, this invention conducts simulation analysis on the proposed encryption method from two aspects: signal anti-detection and information anti-attack. The indicators for signal anti-detection include constellation encryption characteristics, signal distribution patterns, and distance correlation coefficients. When analyzing information anti-attack performance, a classic 256×256 grayscale image is used as the test object, and the method is evaluated from aspects such as resistance to statistical attacks, differential attacks, and brute-force attacks. The simulation experimental platform is: CPU Intel Core i3-5005U 4G, GPU NVIDIA GeForce 920A 4G, Windows 10 Home Edition. Simulation parameters are shown in Table 1.

[0070] Table 1 Simulation Parameters Analysis 1. Constellation Encryption Characteristics The constellation diagram after the transmitted information is modulated and encrypted using QPSK and 16QAM is as follows: Figure 12 As shown, where, Figure 12 (a) is the original QPSK constellation diagram. Figure 12 (b) is the phase-encrypted constellation diagram of QPSK. Figure 12 (c) is the M-EWFRFT cryptographic constellation diagram of QPSK. Figure 12 (d) is the original 16-QAM constellation diagram. Figure 12 (e) is a phase-encrypted constellation diagram of 16-QAM. Figure 12 (f) is the M-EWFRFT encrypted constellation diagram of 16-QAM. During the baseband modulation stage, the constellation diagrams generated by QPSK and 16QAM signals exhibit obvious regularity. This regularity makes it easy for unauthorized eavesdroppers to deduce important information such as modulation parameters through constellation comparison and pattern recognition techniques. After phase encryption, the signal constellation points present a uniform circular distribution, effectively eliminating the identifiable characteristics of the modulation method and achieving physical layer concealment of the modulation pattern. When further processed by M-EWFRFT, the signal exhibits a randomized diffuse distribution in the constellation diagram. This dual encryption mechanism achieves anti-interception protection of the transmitted signal through deep obfuscation of the physical layer signal pattern.

[0071] Analysis 2. Signal Statistical Characteristics Further analysis of the statistical characteristics of the QPSK encrypted signal, such as Figure 13 As shown, Figure 13 (a) is a comparison between the Rayleigh distribution and the method of the present invention. Figure 13 (b) is a comparison between the Gaussian distribution and the method of the present invention. Figure 13 (c) compares the uniform distribution with the method of this invention. Specifically, the mean and variance of the Rayleigh distribution are equal to the mean and variance of the amplitude of the complex envelope of the encrypted signal, the mean and variance of the Gaussian distribution are equal to the mean and variance of the amplitude of the in-phase quantity of the encrypted signal, and the probability density function of the uniform distribution is... It is easy to see that the amplitude distribution of the encrypted signal's complex envelope basically matches the Rayleigh distribution, the amplitude distribution of the in-phase component approximates a Gaussian distribution, and the signal phase strictly obeys... The signal exhibits a uniform distribution within the interval. This joint distribution characteristic is intrinsically related to the statistical properties of Gaussian white noise: when the real and imaginary parts of a complex signal each follow an independent and identically distributed Gaussian process, its envelope exhibits a Rayleigh distribution, and its phase exhibits a uniform distribution. Therefore, after being encrypted using the method of this invention, the statistical properties of the QPSK signal approximate those of a Gaussian white noise signal, exhibiting noise-like random characteristics. This will cause pattern recognition algorithms that rely on the statistical characteristics of the signal to fail, thereby achieving covert signal transmission.

[0072] Analysis 3. Distance Correlation Coefficient The distance correlation coefficient measures the correlation between two random variables. It is zero if and only if the random variables are independent. It is calculated by dividing the distance covariance by the distance standard deviation, and its expression is: in, It is a random variable and The distance covariance; and They are and The distance variance.

[0073] Physical layer encryption technology essentially achieves covert signal transmission by disrupting the signal distribution pattern. Therefore, the encryption effect can be quantitatively evaluated by calculating the distance correlation coefficient between the original signal and the encrypted signal; the smaller the correlation coefficient, the better the encryption effect. The encryption method designed in this invention mainly consists of two parts: phase encryption and M-EWFRFT encryption. To deeply analyze the signal splitting performance, ablation experiments were first used to determine two encryption schemes: Scheme 1 (phase encryption) and Scheme 2 (M-EWFRFT encryption). Then, comparative experiments were conducted using references 1 and 2 in the same field, and the distance correlation coefficients of each encryption method were calculated, as shown in Table 2. The control parameters of Scheme 2 (M-EWFRFT) were controlled by 3D-EQCM. As can be seen from Table 2, the distance correlation coefficient after encryption using the method of this invention is small, indicating that the encrypted signal has almost no correlation with the original signal.

[0074] Table 2 Comparison of distance correlation coefficients for different encryption methods Analysis 4. Performance against statistical attacks Information entropy reflects the uniformity of pixel value distribution in an encrypted image and is often used to quantitatively analyze the resistance of encryption methods to statistical attacks. The calculation formula is as follows: In the formula: For pixels The probability of occurrence The pixel order. The number of pixels.

[0075] For a 256×256 grayscale image, when the image pixels are uniformly distributed, i.e. At this point, the information entropy reaches the theoretical maximum value of 8. Using the method of this invention, three grayscale images—Cammerman, Peppers, and Baboon—were encrypted sequentially, and their information entropy was calculated and compared with that of references 1 and 2, as shown in Table 3. Table 3 shows that the information entropy values ​​of the three images encrypted using the method of this invention are all close to the theoretical maximum value of 8, and the information entropy value of the same encrypted image is greater than that of other encryption methods in the same field. This indicates that the statistical characteristics of the encrypted image are closer to a random distribution, and the encryption effect is good.

[0076] Table 3 Information Entropy of Different Encrypted Images Analysis 5. Resistance to Differential Attacks This invention's phase encryption algorithm innovatively introduces a ciphertext feedback mechanism, which significantly improves the system's differential attack defense capability by enhancing plaintext sensitivity. Specifically, this mechanism works by: when a single pixel value in the plaintext image changes... A tiny change of 1 will cause a significant global change in the encrypted output. This robustness against differential attacks can be quantified using two metrics: Number of Pixels Change Rate (NPCR) and Unified Average Changing Intensity (UACI), defined as follows: in, The number of pixels in the image. To encrypt the image, An encrypted image obtained by changing one pixel value from the original image. Defined as In the experimental verification phase, pixels were randomly selected for testing. The grayscale value modification method was used to conduct 100 repeated experiments on different test images, and the statistical average was calculated. As shown in Table 4, compared with existing typical physical layer encryption methods, the encryption method of this invention shows significant advantages in both NPCR and UACI, two key indicators. Specifically, the NPCR value is improved by approximately 1500 times, and the UACI value is improved by approximately 4900 times. The experimental data fully verify that the encryption method of this invention has superior differential attack resistance compared with similar methods.

[0077] Table 4. Mean NPCR and UACI values ​​for images with different encryption methods. Analysis 6. Resistance to brute-force attacks The key system of the encryption method of this invention is based on the initial value of the 3D-EQCM hyperchaotic mapping. Base number Control variables The security of this system, comprised of two components, is reflected in two dimensions: a large key space and extreme sensitivity to key perturbations. To verify this sensitivity, a univariate perturbation test was used to quantitatively analyze the key parameters—applying a small perturbation to a single key each time, while keeping the remaining parameters at their precise values ​​during decryption. The experimental results are as follows: Figure 14 As shown, under the correct key condition, the bit error rate decreases exponentially with the increase of the signal-to-noise ratio, verifying the effectiveness of the constellation scrambling encryption method of this invention; while the key Each occurred Tiny perturbations, key occur Changes in these parameters all resulted in a stable bit error rate of 0.5, confirming the irreversibility of key parameter changes. Therefore, the key space of the encryption method of this invention is... Based on Frontier, currently the world's most powerful supercomputer. With a double-precision floating-point operation capability of 10 times / second, it would take approximately 10 seconds to perform a brute-force crack of the encryption method of this invention. Years of exhaustive calculations demonstrate the actual unbreakability of the encryption method of this invention.

[0078] In summary, to address security threats such as detection, interception, and decryption of wireless communications, this invention designs a hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation. It constructs a novel three-dimensional hyperchaotic mapping, allowing the iteratively generated chaotic sequence to be directly used as the data encryption key for phase encryption and M-EWFRFT. Next, a phase encryption algorithm is designed using involutional transformation and ciphertext feedback, enhancing the usability of modulation encryption and its resistance to differential attacks. Finally, an M-EWFRFT physical implementation model is constructed, and the two are organically combined. The baseband modulation signal is first phase-scrambled before implementing two-level M-EWFRFT encryption. Compared with existing physical layer encryption algorithms, the method provided by this invention can effectively eliminate the inherent constellation distribution characteristics of the modulation signal, achieving modulation pattern concealment and thus reducing the detectability of the wireless signal. Furthermore, it can resist typical security threats such as statistical attacks, differential attacks, and brute-force attacks. In particular, compared with existing physical layer encryption methods, its resistance to differential attacks is significantly improved.

[0079] It should be noted that although the steps of the method in this invention are described in a specific order in the accompanying drawings, this does not require or imply that these steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps. Furthermore, it is readily understood that these steps may be executed synchronously or asynchronously, for example, in multiple modules / processes / threads.

[0080] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the appended claims.

Claims

1. A hyperchaotic scrambling code M-EWFRFT communication method based on a pair-join transformation, characterized in that, Includes the following steps: The input signal is modulated by baseband modulation to form a modulated signal; A three-dimensional hyperchaotic map is constructed, and a chaotic sequence is generated iteratively, wherein the chaotic sequence includes a first state variable, a second state variable, and a third state variable; Using the first state variable as the phase encryption key, the modulated signal is phase encrypted through integrative transformation and ciphertext feedback to generate a phase encrypted signal. Using 4-WFRFT as the state function, a physical implementation model of M-EWFRFT is constructed. The second and third state variables are used as control parameters of M-EWFRFT. The phase encryption signal is encrypted by M-EWFRFT to complete hybrid carrier modulation. The receiving end receives the mixed carrier signal and forms the signal to be decrypted; The signal to be decrypted is decrypted using the second and third state variables to generate a phase-decrypted signal. Phase decryption is performed on the signal to be decrypted, and the demodulation process is completed.

2. The hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation according to claim 1, characterized in that, The step of using the first state variable as the phase encryption key to perform phase encryption on the modulated signal through involution transformation and ciphertext feedback to generate a phase-encrypted signal includes: For the first modulated signal, its phase is subtracted from the phase encryption key to generate a phase encryption signal; For the second and subsequent modulation signals, the phase of the phase encryption signal of the previous modulation signal is added to the phase of the current modulation signal to obtain the first phase sum. Then, the first phase sum is subtracted from the phase encryption key to generate the phase encryption signal.

3. The hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation according to claim 1, characterized in that, The steps for constructing the M-EWFRFT physical realization model using 4-WFRFT as the state function include: The original signal is simultaneously input into M 4-WFRFT modules; Perform a weighted summation on M 4-WFRFT signals.

4. The hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation according to claim 1, characterized in that, During the iteration process of the three-dimensional hyperchaotic mapping, the coordinate values ​​of the state points are determined by... The trajectory is folded by taking the modulus.

5. The hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation according to claim 4, characterized in that, During the iteration process of the three-dimensional hyperchaotic mapping, the trajectory of the state point is limited to... .

6. The hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation according to claim 5, characterized in that, The difference equations for the three-dimensional hyperchaotic mapping are as follows: in, As the first state variable, For the second state variable, For the third state variable, The base is , and , To control variables, , Represents the number of chaotic iterations. For iteration The first state variable after that. For iteration The first state variable after that. For iteration The second state variable after that. For iteration The second state variable after that. For iteration The third state variable after that. For iteration The third state variable after that. The base is The index is The exponential function, The base is The index is The exponential function, The base is The index is The exponential function.

7. The hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation according to claim 1, characterized in that, The step of constructing an M-EWFRFT physical implementation model using 4-WFRFT as the state function, and using the second and third state variables as control parameters of M-EWFRFT to encrypt the phase encryption signal using M-EWFRFT includes: The phase encryption signal is first divided into groups, and then each group of phase encryption signals is encrypted using M-EWFRFT.

8. The hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation according to claim 7, characterized in that, The step of performing M-EWFRFT decryption on the signal to be decrypted using the second and third state variables to generate a phase-decrypted signal includes: The signal to be decrypted is divided into groups, and then each group of signals to be decrypted is decrypted using M-EWFRFT, wherein the length of the group during decryption is the same as the length of the group during encryption.

9. The hyperchaotic scrambling code M-EWFRFT communication method based on involutional transformation according to claim 1, characterized in that, The steps for performing phase decryption on the signal to be phase decrypted include: The first signal to be decrypted by phase is obtained by subtracting the phase of the first signal to be decrypted by phase encryption key; For the second and subsequent phase-decrypted signals, the phase of the previous phase-decrypted signal is added to the phase of the current phase-decrypted signal to obtain the second phase sum, and then the second phase sum is subtracted from the phase encryption key.

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