A microwave transmission data encryption system and method

Abstract

The application provides a microwave transmission data encryption system and method, relates to the technical field of data encryption methods, and comprises the steps of constructing a Lorenz chaotic model by using a single-variable time delay method, iteratively updating chaotic variable values in the Lorenz chaotic model by using a fourth-order Runge-Kutta method, and simulating and generating unpredictable continuous chaotic trajectories; the symbol period of the chaotic trajectory is set, and the key stream corresponding to each symbol period is generated; the phase offset of the current symbol period is calculated by using a modulo operation, the frequency offset of the current symbol period is calculated by using a dynamic frequency modulation method, and a microwave carrier signal is generated. The key stream based on the Lorenz chaotic model has initial value sensitivity and long-term unpredictability, independent dynamic keys are generated in each symbol period, and the global security is not affected; through the modulo operation and the dynamic frequency modulation, the encrypted signal has both noise-like spectrum characteristics and time-varying characteristics.

Description

Technical Field

[0001] This invention relates to the field of data encryption methods, specifically to a microwave transmission-based data encryption system and method. Background Technology

[0002] Traditional microwave transmission encryption methods often employ static keys or single-parameter modulation techniques. Furthermore, key streams based on pseudo-random numbers or low-dimensional chaotic systems are easily predictable and difficult to resist phase analysis and tracing attacks. Single-parameter modulation, such as encryption signals with only phase or frequency shifts, has a single spectral characteristic and is easily overwhelmed by noise or cracked through spectral analysis. Moreover, existing methods struggle to achieve dynamic collaborative updates of keys and modulation parameters in time-varying channels, leading to the accumulation of decryption errors.

[0003] In the prior art, patent document CN106453398A discloses a method for encrypting data by setting up multiple control units for coordinated allocation. However, this method does not generate a highly complex chaotic trajectory based on the single-variable time-delay Lorenz chaotic model, nor does it combine nonlinear mapping to generate a dynamic key stream to avoid periodic characteristics and resist reverse engineering attacks. It also does not use phase offset and frequency offset dual-parameter joint modulation to expand the signal bandwidth and blur the spectral characteristics, making the encrypted signal exhibit noise-like characteristics in both the time and frequency domains, thus reducing the risk of interception. Furthermore, it does not introduce Gaussian white noise correction and coherent demodulation-phase compensation mechanisms to suppress channel noise while preserving encrypted information and achieve reliable decryption under high bit error rate environments. Therefore, there is an urgent need for a microwave transmission-based data encryption system and method.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a microwave-based data encryption system and method to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A microwave-based data encryption method includes the following steps:

[0008] S1: Calculate the target number of delayed steps and label them as historical steps by setting the time step and delay time. Set the initial chaotic variable values ​​and use the constant filling method to determine the chaotic variable values ​​corresponding to each historical step. Construct the Lorenz chaotic model using the univariate time delay method. Use the fourth-order Runge-Kutta method to iteratively update the chaotic variable values ​​inside the Lorenz chaotic model. Simulate and generate unpredictable continuous chaotic trajectories according to the set time step.

[0009] S2: Set the length of the symbol period of the chaotic trajectory, divide the chaotic trajectory into symbol periods, and use linear mapping to map the chaotic variable value of the last time step in each symbol period to a preset numerical range, and generate the key value corresponding to each symbol period.

[0010] S3: Based on the generated key value, the phase offset of each symbol period is calculated using modular arithmetic, and the frequency offset of each symbol period is calculated using dynamic frequency modulation. The microwave carrier signal to be encrypted is divided into several sub-signals of different lengths according to the symbol period. Based on the phase offset and frequency offset of each symbol period, the corresponding sub-signals are encrypted using dynamic dual-parameter method to generate the encrypted microwave carrier signal.

[0011] S4: The encrypted microwave carrier signal is corrected with Gaussian white noise to obtain the first microwave signal. The first microwave signal is then coherently demodulated to obtain the baseband signal. Based on the phase shift and frequency shift within each symbol period, the baseband signal is phase compensated. The compensated baseband signal is then integrated to obtain the decrypted original microwave carrier signal.

[0012] Furthermore, the constant filling method is used to determine the chaotic variable values ​​corresponding to each historical step. The specific steps are as follows:

[0013] Set the time step and delay time, set the ratio of delay time to time step as the historical step number, use the constant filling method to set the chaotic variable value corresponding to the historical step number, and constantly fill the chaotic variable values ​​of all historical steps with the preset initial value of the chaotic variable value.

[0014] Furthermore, the simulation generates unpredictable, continuous chaotic trajectories. The specific steps are as follows:

[0015] The Lorenz chaos model is constructed using the univariate time delay method:

[0016]

[0017] Indicates the first The values ​​of chaotic variables at each time step; Indicates the first The values ​​of chaotic variables at each time step; Indicates the first The value of a consecutive time point corresponding to a time step is the product of the discrete time step index and the time step size. Indices representing discrete time steps; This indicates a point in time. Chaotic variable value The instantaneous rate of change of the model; This represents the quotient of the delay time and the time step, which is the historical number of steps.

[0018] The fourth-order Runge-Kutta method is used to iteratively update the values ​​of chaotic variables, generating unpredictable, continuous chaotic trajectories:

[0019]

[0020] in,

[0021]

[0022]

[0023]

[0024]

[0025] , , , , , represent the initial instantaneous rate of change, the first intermediate instantaneous rate of change, the second intermediate instantaneous rate of change, and the final instantaneous rate of change, respectively; Indicates the first The values ​​of chaotic variables at each time step; Indicates the time step.

[0026] Further, the key value corresponding to each symbol period is generated, and the specific steps are as follows:

[0027] Define the symbol period as The chaotic trajectory is divided into symbolic periods, and a linear mapping is used to map the chaotic variable values ​​of the last time step in each symbolic period to an integer range. This indicates the number of steps contained within each symbol period;

[0028] The logic of the linear mapping is as follows: subtract the minimum chaotic variable value within the symbol period from the chaotic variable value at the last time step, then divide the difference by the difference between the maximum and minimum chaotic variable values ​​within the symbol period, multiply the quotient by 255 and round it to the nearest integer, then subtract 128 from the integer result to obtain the integer range of the key value. ;

[0029] Each symbol period is numbered by dividing the time step index by the number of steps contained in each symbol period to obtain the index number of each symbol period.

[0030] Further, the phase shift and frequency shift for each symbol period are calculated, and the specific steps are as follows:

[0031] Based on the key value, the phase shift for each symbol period is calculated using modular arithmetic:

[0032]

[0033] in, Indicates the first Phase shift per symbol period; This indicates a round-down operation; In the dynamic key stream based on chaotic systems, the first... The key value corresponding to the last time step of each symbol period; Indicates the symbol period index number;

[0034] The frequency offset for each symbol period is calculated using the dynamic frequency modulation method:

[0035]

[0036] in, Indicates the first Frequency offset per symbol period; This indicates the maximum permissible frequency offset.

[0037] Furthermore, the encrypted microwave carrier signal is generated using the dynamic two-parameter method. The specific steps are as follows:

[0038] The microwave carrier signal to be encrypted is divided into several sub-signals of varying lengths according to the symbol period. Based on the phase and frequency offsets of each symbol period, the corresponding sub-signals are encrypted using a dynamic two-parameter method to generate the encrypted microwave carrier signal. Specifically, the phase and frequency offsets of each symbol period are used as modulation parameters of the target carrier to generate the carrier microwave signal within each symbol period.

[0039]

[0040] in,

[0041]

[0042] in, Indicates the target carrier frequency; Indicates the signal amplitude of the target carrier; This represents the encrypted microwave carrier signal.

[0043] Furthermore, the first microwave signal is coherently demodulated to obtain the baseband signal. The specific steps are as follows:

[0044] The encrypted microwave carrier signal is corrected using Gaussian white noise. Specifically, Gaussian white noise is superimposed on the encrypted microwave carrier signal to obtain the first microwave signal. The corrected first microwave signal is then coherently demodulated to obtain the demodulated baseband signal.

[0045]

[0046] in, This represents the demodulated baseband signal; This indicates the corrected microwave carrier signal.

[0047] Further, the decrypted original microwave carrier signal is obtained through the following steps:

[0048] Phase compensation is performed on the baseband signal based on the phase and frequency shifts for each symbol period:

[0049]

[0050] in,

[0051]

[0052] in, This represents the baseband signal after phase compensation;

[0053] The compensated baseband signal is integrated to obtain the decrypted original signal:

[0054]

[0055] in, Indicates binary phase shift keying; This indicates the output decision signal.

[0056] The present invention also provides a microwave transmission data encryption system, the encryption system being used to perform the above-described encryption method, comprising:

[0057] The data acquisition module is used to calculate the target number of delayed steps and label them as historical steps by setting the time step and delay time. It sets the initial chaotic variable values ​​and uses the constant filling method to determine the chaotic variable values ​​corresponding to each historical step. It also uses the univariate time delay method to construct the Lorenz chaotic model and uses the fourth-order Runge-Kutta method to iteratively update the chaotic variable values ​​inside the Lorenz chaotic model. According to the set time step, it simulates and generates unpredictable continuous chaotic trajectories.

[0058] The key generation module is used to set the length of the symbol period of the chaotic trajectory, divide the chaotic trajectory into symbol periods, and use linear mapping to map the chaotic variable value of the last time step in each symbol period to a preset numerical range, thereby generating the key value corresponding to each symbol period.

[0059] The encryption module is used to calculate the phase offset of each symbol period based on the generated key value using modular arithmetic and to calculate the frequency offset of each symbol period using dynamic frequency modulation. The microwave carrier signal to be encrypted is divided into sub-signals of several lengths according to the symbol period, and the corresponding sub-signals are encrypted using dynamic dual-parameter method based on the phase offset and frequency offset of each symbol period to generate the encrypted microwave carrier signal.

[0060] The decryption module is used to correct the encrypted microwave carrier signal with Gaussian white noise, obtain the first microwave signal after correction, and coherently demodulate the first microwave signal to obtain the baseband signal. Based on the phase shift and frequency shift within each symbol period, the baseband signal is phase compensated, and the compensated baseband signal is integrated to obtain the decrypted original microwave carrier signal.

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] A highly complex chaotic trajectory is generated based on a univariate time-delay Lorenz chaotic model, and a dynamic key stream is generated by combining nonlinear mapping to avoid periodic characteristics and resist reverse engineering attacks. By using dual-parameter joint modulation of phase offset and frequency offset, the signal bandwidth is expanded and the spectral characteristics are blurred, so that the encrypted signal exhibits noise-like characteristics in both the time and frequency domains, reducing the risk of interception. Gaussian white noise correction and coherent demodulation-phase compensation mechanism are introduced to suppress channel noise while preserving encrypted information, achieving reliable decryption under high bit error rate environments. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0064] Figure 2 A graph showing the relationship between the key value and the phase offset at the last time step of each symbol period;

[0065] Figure 3 This is a schematic diagram of the overall device of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0067] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0068] Example:

[0069] Please see Figures 1-2 The present invention provides a technical solution:

[0070] A microwave-based data encryption method includes the following steps:

[0071] S1: Calculate the target number of delayed steps and label them as historical steps by setting the time step and delay time. Set the initial chaotic variable values ​​and use the constant filling method to determine the chaotic variable values ​​corresponding to each historical step. Construct the Lorenz chaotic model using the univariate time delay method. Use the fourth-order Runge-Kutta method to iteratively update the chaotic variable values ​​inside the Lorenz chaotic model. Simulate and generate unpredictable continuous chaotic trajectories according to the set time step.

[0072] The method of determining the chaotic variable value corresponding to each historical step using the constant filling method is as follows:

[0073] Set the time step and delay time, set the ratio of delay time to time step as the historical step number, use the constant filling method to set the chaotic variable value corresponding to the historical step number, and constantly fill the chaotic variable values ​​of all historical steps with the preset initial value of the chaotic variable value.

[0074] In the above process, the time step can be set to... The delay time is And set the initial values ​​of the chaotic variables. Using the constant filling method Previous The chaotic variable value of the step number is filled in, where, This represents the quotient of the delay time and the time step, which is the historical step count. Specifically, it sets all historical chaotic variable values ​​to 0.5.

[0075] Setting the initial chaotic variable value to 0.5 is primarily based on considerations of numerical stability and the initialization of the chaotic system. In the subsequent Lorenz chaotic model equations, the system requires sufficient historical data to drive its evolution at the start of iterations. 0.5, as a moderate intermediate value, avoids computational divergence or convergence to trivial solutions that might occur with extreme initial values. Furthermore, 0.5 falls within the common value range of typical chaotic variables, helping the system enter a chaotic state more quickly and ensuring that the generated trajectory possesses sufficient randomness and unpredictability, thus laying the foundation for the security and complexity of the subsequent keystream.

[0076] Setting all historical chaotic variable values ​​to 0.5 is a simple and effective "constant fill" initialization strategy. This ensures that the historical data is continuous and consistent, avoiding numerical instability or premature entry into a non-chaotic state that may be caused by random settings or mutations in historical data.

[0077] Chaotic systems are extremely sensitive to initial conditions and evolution processes. Excessively large time steps can rapidly amplify iteration errors, even causing the system to deviate from its true chaotic trajectory and lose its inherent nonlinear sensitivity and pseudo-randomness. Only by choosing a sufficiently small time step can numerical methods such as the fourth-order Runge-Kutta method effectively simulate continuous chaotic evolution in discrete iterations. This ensures that the generated trajectory continuously approximates the true solution in time while maintaining the inherent long-term unpredictability of chaotic systems. Therefore, in Lorenz systems, if the highest effective frequency component is several kilohertz, the time step should typically be less than 0.1 milliseconds. This order of magnitude ensures a sufficient number of sampling points within each cycle to accurately describe the system's rapid oscillations and sensitive evolution. If the step size is too large, such as close to 1 millisecond, numerical iterations will fail to accurately track the dynamic details of the system, leading to trajectory distortion or even computational divergence, thus losing the unpredictability of chaos.

[0078] The specific steps for simulating and generating unpredictable, continuous chaotic trajectories are as follows:

[0079] The Lorenz chaos model is constructed using the univariate time delay method:

[0080]

[0081] Indicates the first The values ​​of chaotic variables at each time step; Indicates the first The values ​​of chaotic variables at each time step; Indicates the first The value of a consecutive time point corresponding to a time step is the product of the discrete time step index and the time step size. Indices representing discrete time steps; This indicates a point in time. Chaotic variable value The instantaneous rate of change of the model; This represents the quotient of the delay time and the time step, which is the historical number of steps.

[0082] In the above process, a high-dimensional continuous Lorenz chaotic system is transformed into a single-variable discrete-time delay system that is easier to implement digitally while still retaining strong chaotic characteristics. The core idea is to use time-delay feedback to replace the coupling between multiple variables in the original Lorenz system by introducing historical values. The sine function creates a nonlinear interaction; simultaneously, a high-frequency sine term is added. As an external driver or disturbance to enhance the ergodicity and complexity of the system, the technical advantage of this design is that it only needs to iteratively update a single core variable. This significantly reduces computational complexity while retaining the extreme sensitivity of chaos to initial conditions, long-term unpredictability, and wide-spectrum characteristics.

[0083] Dependent variable Characterized at discrete time points At this point, the system's chaotic variables The instantaneous rate of change of the deterministic equation enables the iterative generation of highly complex and unpredictable chaotic trajectories from the initial values. The value is determined by three key terms, each corresponding to a different independent variable and its influencing mechanism. The first term... This indicates that it is affected by the current state variable. The direct impact constitutes a linear damping or negative feedback loop, playing a stabilizing role. The second term... The introduction of time-delay coupling makes the current rate of change dependent on the historical state. This establishes the system's memory effect and nonlinear interactions, which are key to generating complex dynamics. (The third term...) This is a relationship with absolute time. The directly related high-frequency periodic driving term, as an external forcing function, injects continuous disturbance into the system to prevent it from falling into a steady state. In this model, the dependent variable... With the current independent variable They show a negative correlation, which provides information about the system's dissipation characteristics; it is related to the time delay independent variable. and time independent variable Nonlinear correlations are established using sine functions.

[0084] The fourth-order Runge-Kutta method is used to iteratively update the values ​​of chaotic variables, generating unpredictable, continuous chaotic trajectories:

[0085]

[0086] in,

[0087]

[0088]

[0089]

[0090]

[0091] , , , , , represent the initial instantaneous rate of change, the first intermediate instantaneous rate of change, the second intermediate instantaneous rate of change, and the final instantaneous rate of change, respectively; Indicates the first The values ​​of chaotic variables at each time step; Indicates the time step.

[0092] In the above process, the fourth-order Runge-Kutta method is used for iterative updates to achieve high-precision numerical solutions to the continuous chaotic system described by the aforementioned nonlinear time-delay differential equation. This method cleverly calculates and weights the instantaneous rates of change at four different predicted points—the starting point, two intermediate points, and the ending point—within the current time step, thereby closely approximating the true evolution trajectory of the continuous system in discrete-time simulations. The technical advantage of this setup is that it significantly reduces numerical integration errors and ensures high accuracy even when using finite time steps. The generated chaotic sequence can still reflect the dynamic characteristics of the original system with high fidelity, effectively avoiding the degradation of chaotic characteristics or the decline in pseudo-randomness quality that may be caused by insufficient accuracy of numerical methods.

[0093] S2: Set the length of the symbol period of the chaotic trajectory, divide the chaotic trajectory into symbol periods, and use linear mapping to map the chaotic variable value of the last time step in each symbol period to a preset numerical range, and generate the key value corresponding to each symbol period.

[0094] The specific steps for generating the key value corresponding to each symbol period are as follows:

[0095] Define the symbol period as The chaotic trajectory is divided into symbolic periods, and a linear mapping is used to map the chaotic variable values ​​of the last time step in each symbolic period to an integer range. This indicates the number of steps contained within each symbol period;

[0096] The logic of the linear mapping is as follows: subtract the minimum chaotic variable value within the symbol period from the chaotic variable value at the last time step, then divide the difference by the difference between the maximum and minimum chaotic variable values ​​within the symbol period, multiply the quotient by 255 and round it to the nearest integer, then subtract 128 from the integer result to obtain the integer range of the key value. ;

[0097] Each symbol period is numbered by dividing the time step index by the number of steps contained in each symbol period to obtain the index number of each symbol period.

[0098] The formula upon which the above process is based is:

[0099]

[0100] in,

[0101]

[0102] in, Representing the value of chaotic variables The minimum fluctuation value; Representing the value of chaotic variables The maximum fluctuation value; Indicates the first The chaotic variable value corresponding to the end of a symbol cycle; In the dynamic key stream based on chaotic systems, the first... The key value corresponding to the last time step of each symbol period; Indicates the symbol period index number; This indicates the number of steps contained within each symbol period; This represents the rounding function.

[0103] In the above process, by linearly mapping and quantizing the chaotic state value at the end of each symbol period, the dynamic range of chaos is normalized to a fixed integer range, namely -128 to 127, ensuring that the numerical range and format of the key value meet the requirements of subsequent modulo operations and modulation; on the other hand, the key of each period... All of these depend uniquely and sensitively on the internal state of the chaotic system at that moment, causing the key stream to inherit the extreme sensitivity of the chaotic system to initial conditions, long-term unpredictability and quasi-randomness, thereby greatly enhancing the security and anti-cracking ability of the encryption system.

[0104] Mapping the key using the chaotic variable value at the last time step of each symbol period is primarily to ensure the uniqueness and synchronization of key generation. Because the trajectory of a chaotic system is continuous and inherently correlated, selecting any time point within the period might not adequately represent the overall evolutionary endpoint of the chaotic dynamics within that period. The value at the end of the period accumulates all the nonlinear iterative effects within that timeframe, reflecting the system's final dynamics to the greatest extent possible, thus extracting the most random and unpredictable key value. Simultaneously, strictly aligning key generation with the end of the symbol period facilitates precise time synchronization between encryption and decryption, ensuring that the key used in each symbol period strictly corresponds and avoiding encryption / decryption synchronization issues caused by inconsistent sampling times.

[0105] The target mapping range was set to -128 to 127 primarily for two reasons: First, this range contains 256 consecutive integer values, which corresponds precisely to the standard range of signed integers that can be represented by a single byte. This alignment allows the generated keystream to be stored, transmitted, and processed directly in bytes, ensuring high compatibility with common digital communication and computing architectures. Second, choosing a symmetrical range centered on zero helps generate phase modulation values ​​symmetrically distributed around the zero point in subsequent phase offset calculations. This optimizes the power distribution of the modulated signal and may simplify the design of synchronization and compensation algorithms at the receiver.

[0106] S3: Based on the generated key value, the phase offset of each symbol period is calculated using modular arithmetic, and the frequency offset of each symbol period is calculated using dynamic frequency modulation. The microwave carrier signal to be encrypted is divided into several sub-signals of different lengths according to the symbol period. Based on the phase offset and frequency offset of each symbol period, the corresponding sub-signals are encrypted using dynamic dual-parameter method to generate the encrypted microwave carrier signal.

[0107] The specific steps for calculating the phase shift and frequency shift for each symbol period are as follows:

[0108] Based on the key value, the phase shift for each symbol period is calculated using modular arithmetic:

[0109]

[0110] in, Indicates the first Phase shift per symbol period; This indicates a round-down operation; In the dynamic key stream based on chaotic systems, the first... The key value corresponding to the last time step of each symbol period; Indicates the symbol period index number;

[0111] In the above process, the dependent variable Indicates the first A phase shift of one symbol period will affect the key. The dynamic integer value is uniquely and unambiguously mapped to a standard phase circle. The specific angle within the carrier is used as a direct parameter for phase modulation, thereby enabling key-based physical layer encryption. The value is entirely determined by the independent variable. The decision is made through a linear transformation. The key value is initially converted into an angle value, and then... The operation is subtraction. The angle value is normalized periodically when it is an integer multiple of the given value. This makes it possible even if... The absolute value of the phase shift is large, and the resulting phase shift is always constrained within a complete phase period, ensuring the uniqueness and recoverability of phase information during modulation and demodulation. Dependent variable With independent variable They exhibit a positive correlation, but due to the introduction of modular arithmetic, the relationship is not a simple linear proportional relationship, but rather a relationship that varies with each... The correlation exhibits piecewise linear positive correlation within the period and resets at the period boundary, thus forming a periodic, bounded dependency.

[0112] In the above embodiments, 20 sets of data are provided for the key value and corresponding phase offset at the last time step of each symbol period, to reflect the change of phase offset as the key value changes, as shown in Table 1:

[0113] Table 1: Relationship between key value and corresponding phase offset

[0114]

[0115] As can be seen from Table 1 above, the dependent variable With independent variable They exhibit a positive correlation, but due to the introduction of modular arithmetic, the relationship is not a simple linear proportional relationship, but rather a relationship that varies with each... The correlation exhibits piecewise linear positive correlation within the period and resets at the period boundary, thus forming a periodic, bounded dependency.

[0116] The frequency offset for each symbol period is calculated using the dynamic frequency modulation method:

[0117]

[0118] in, Indicates the first Frequency offset per symbol period; This indicates the maximum permissible frequency offset.

[0119] In the above process, the dependent variable Indicates the first The frequency shift per symbol period, the technical effect is to dynamically adjust the key value. It is directly converted into a controllable frequency modulation parameter that changes synchronously with the key, realizing dynamic encryption perturbation of the carrier frequency, which is directly proportional to the key value. In other words, the key is the source driving the frequency offset change; at the same time, it is also proportional to the preset system parameters. , As a proportionality coefficient, it limits the absolute range of frequency offset variation, ensuring that the frequency offset of the modulated signal is constrained within a reasonable range allowed by the channel bandwidth or required by the system design.

[0120] For phase shift, the modulus is used. The operation is to ensure that, regardless of the key value, the final phase offset is always limited to a certain value. Within the standard period range, this avoids the ambiguity caused by phase winding, ensuring the uniqueness and reversibility of phase modulation. For frequency offset, the key value can be linearly scaled. It is directly mapped to a controlled, key-related frequency offset, where The maximum offset range was limited to meet channel bandwidth constraints. By directly injecting the dynamics of the chaotic key into the two fundamental parameters of the carrier—phase and frequency—deep binding between the key and the modulation signal was achieved, thus completing the encryption of the microwave signal at the physical layer.

[0121] The specific steps for generating the encrypted microwave carrier signal using the dynamic two-parameter method are as follows:

[0122] The microwave carrier signal to be encrypted is divided into several sub-signals of varying lengths according to the symbol period. Based on the phase and frequency offsets of each symbol period, the corresponding sub-signals are encrypted using a dynamic two-parameter method to generate the encrypted microwave carrier signal. Specifically, the phase and frequency offsets of each symbol period are used as modulation parameters of the target carrier to generate the carrier microwave signal within each symbol period.

[0123]

[0124] in,

[0125]

[0126] in, Indicates the target carrier frequency; Indicates the signal amplitude of the target carrier; This represents the encrypted microwave carrier signal.

[0127] In the above process, the dependent variable This represents the instantaneous amplitude of the final generated encrypted microwave carrier signal. Its technical effect is achieved by dynamically generating a phase offset from the chaotic key within each symbol period. and frequency offset Simultaneously injected into the standard carrier, the signal is directly encrypted at the physical layer, preventing unauthorized receivers from demodulating valid information. This achieves secure transmission based on chaotic keys and dynamic dual-parameter modulation (phase and frequency). The fundamental carrier consists of a center frequency... and time The encryption properties are determined by two dynamic modulation parameters: phase shift. A fixed phase transition is introduced at the beginning of the symbol period, while the frequency shift... This introduces an additional phase that accumulates linearly with time within the period. , With carrier term The total phase within the time frame exhibits a complex periodic correlation, with the total phase value changing with... , , and The amplitude increases with the increase of the phase, but the cosine function converts this linear phase growth relationship into a periodic oscillation of amplitude, thus forming the final modulated waveform.

[0128] Dividing the microwave carrier signal to be encrypted into sub-signals of several lengths according to the symbol period is mainly to segment the continuous data stream or modulation information and achieve strict synchronization with the dynamic key sequence generated by the chaotic system in time. Each symbol period corresponds to a key value, thereby determining a unique set of phase and frequency offset parameters. This division allows the encryption process to apply the dynamic randomness of chaos precisely and segment by segment to the carrier signal on a symbol-by-symbol basis, thus transforming the original regular modulation signal into an encrypted signal with randomly changing parameters, effectively masking the original characteristics of the signal.

[0129] In specific divisions, the length of the symbol period It is a fixed time interval preset by the system, divided according to a time axis, starting from the beginning of the signal, and... The continuous microwave carrier signal is divided into a series of sequentially arranged, non-overlapping time segments, or sub-signals, in the time domain at intervals of [ ]. The time range of each segment is [ ]. ,in It is the index number of the symbol period. This uniform division ensures that within each fixed time period, a constant combination of phase and frequency offsets determined by the corresponding periodic chaotic key is used for modulation and encryption, achieving a one-to-one correspondence and synchronous update of the encryption key and data symbols in time.

[0130] By applying the dynamically changing phase and frequency offsets generated by the chaotic key to carrier modulation, a dynamic two-parameter encryption mechanism at the physical layer is achieved. This is because the phase offset provides an instantaneous phase transition at the start of each symbol, while the frequency offset introduces a linearly changing additional phase over the symbol duration. The combination of these two factors results in the carrier signal for each symbol period possessing a complex phase trajectory uniquely determined by the key and varying over time. The technical effect is that it significantly increases the difficulty for unauthorized receivers to analyze or emulate the signal, as correct demodulation requires not only cracking the key but also precise compensation for this time-varying two-parameter perturbation. Simultaneously, for authorized receivers, as long as they possess the same keystream and can reproduce the phase and frequency offsets, they can accurately recover the baseband signal through synchronized phase and frequency compensation, thus achieving reliable and effective decryption while ensuring communication security.

[0131] S4: The encrypted microwave carrier signal is corrected with Gaussian white noise to obtain the first microwave signal. The first microwave signal is then coherently demodulated to obtain the baseband signal. Based on the phase shift and frequency shift within each symbol period, the baseband signal is phase compensated. The compensated baseband signal is then integrated to obtain the decrypted original microwave carrier signal.

[0132] The specific steps for coherently demodulating the first microwave signal to obtain the baseband signal are as follows:

[0133] The encrypted microwave carrier signal is corrected using Gaussian white noise. Specifically, Gaussian white noise is superimposed on the encrypted microwave carrier signal to obtain the first microwave signal. The corrected first microwave signal is then coherently demodulated to obtain the demodulated baseband signal.

[0134]

[0135] in, This represents the demodulated baseband signal; This indicates the corrected microwave carrier signal.

[0136] In the above process, under ideal encryption signal Superimposed Gaussian white noise is intended to model the additive noise interference that is unavoidable in actual wireless transmission. This makes the subsequent decryption and signal processing more closely resemble real-world application scenarios, allowing for the evaluation of the scheme's robustness in noisy environments. Subsequently, the signal is multiplied by the local carrier complex exponent. The purpose of coherent demodulation is to convert the received bandpass signal into a signal that is clear and transparent. From carrier frequency The signal was moved from the nearby area to the baseband to facilitate subsequent processing of the phase and frequency offset of the information carried. The signal conversion from radio frequency to baseband was completed at the receiving end, and the impact of channel noise was taken into account, which prepared the way for the next step of key-based accurate phase compensation and decryption to recover the original signal.

[0137] This represents the demodulated baseband signal, obtained by passing the received bandpass signal. Down-converting to zero intermediate frequency changes the signal's spectrum from the carrier frequency. The signal is moved from the nearby area to the baseband to extract the complex envelope containing encrypted information, namely phase and frequency offsets, for subsequent precise phase compensation and signal decryption processing; the demodulation process involves receiving the signal. This is multiplied by a local reference signal that is in phase and frequency with the transmitted carrier, i.e., in complex exponential form. Essentially, this performs a spectrum shift, which reduces the frequency and phase of the original signal. The spectral component centered on the frequency is shifted to zero frequency, thereby separating the baseband component that carries information; The complex magnitude and the independent variable There is a positive correlation, meaning that changes in the amplitude of the received signal are directly and linearly reflected in the amplitude of the demodulated baseband signal. The phase is equal to The phase minus the linearly changing carrier phase This is a phase subtraction relationship, and the entire operation is a linear multiplication process in the complex field.

[0138] The specific steps for obtaining the decrypted original microwave carrier signal are as follows:

[0139] Phase compensation is performed on the baseband signal based on the phase and frequency shifts for each symbol period:

[0140]

[0141] in,

[0142]

[0143] in, This represents the baseband signal after phase compensation;

[0144] In the above process, using phase and frequency offsets generated by the same chaotic key that are completely synchronized with the transmitting end, a phase rotation and frequency despinning of equal magnitude but opposite direction are applied to the received baseband signal. The technical effect of this is that it can completely remove the dynamic phase and frequency modulation components introduced by encryption from the signal, and realign the "disturbed" signal constellation points to the standard modulation positions, thus clearing a key obstacle for subsequent accurate symbol integration and decision-making, and finally decrypting the original data bits.

[0145] Dependent variable This indicates that the baseband signal after phase compensation, by canceling the dynamic phase and frequency shifts introduced by encryption, will receive a scrambled baseband signal. To restore it to a phase-aligned, clean signal. The complex magnitude and the independent variable The amplitudes are positively correlated, and in terms of phase, The phase is equal to The phase minus the total phase in the compensation factor is the phase. .

[0146] The compensated baseband signal is integrated to obtain the decrypted original signal:

[0147]

[0148] in, Indicates binary phase shift keying; This indicates the output decision signal.

[0149] In the above process, integrating the compensated signal within a single symbol period effectively accumulates all the energy carried by the symbol, while averaging out residual Gaussian white noise and minor phase errors, thereby maximizing the signal-to-noise ratio. The integration result is then fed into a decision unit for binary phase-shift keying modulation. Based on the polarity (or phase) of the integral value, it determines whether the original binary bit represented by the symbol is "0" or "1". This completes the final conversion from a continuous-time analog signal to a discrete digital bit stream and is the output of the entire decryption process. It directly determines whether the original transmitted data can be accurately recovered, ensuring high reliability of the decision.

[0150] Please see Figure 3 The present invention also provides a microwave transmission data encryption system, the encryption system being used to perform the above-described encryption method, comprising:

[0151] The data acquisition module is used to calculate the target number of delayed steps and label them as historical steps by setting the time step and delay time. It sets the initial chaotic variable values ​​and uses the constant filling method to determine the chaotic variable values ​​corresponding to each historical step. It also uses the univariate time delay method to construct the Lorenz chaotic model and uses the fourth-order Runge-Kutta method to iteratively update the chaotic variable values ​​inside the Lorenz chaotic model. According to the set time step, it simulates and generates unpredictable continuous chaotic trajectories.

[0152] The key generation module is used to set the length of the symbol period of the chaotic trajectory, divide the chaotic trajectory into symbol periods, and use linear mapping to map the chaotic variable value of the last time step in each symbol period to a preset numerical range, thereby generating the key value corresponding to each symbol period.

[0153] The encryption module is used to calculate the phase offset of each symbol period based on the generated key value using modular arithmetic and to calculate the frequency offset of each symbol period using dynamic frequency modulation. The microwave carrier signal to be encrypted is divided into sub-signals of several lengths according to the symbol period. Based on the phase offset and frequency offset of each symbol period, the encrypted microwave carrier signal is generated using dynamic dual-parameter method.

[0154] The decryption module is used to correct the encrypted microwave carrier signal with Gaussian white noise, obtain the first microwave signal after correction, and coherently demodulate the first microwave signal to obtain the baseband signal. Based on the phase shift and frequency shift within each symbol period, the baseband signal is phase compensated, and the compensated baseband signal is integrated to obtain the decrypted original microwave carrier signal.

[0155] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0156] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0157] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0158] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for encrypting data based on microwave transmission, characterized by the steps of Comprise: S1: calculate the delayed target step number by setting the time step and the delay time, and mark it as the history step number, set the initial chaotic variable value, determine the chaotic variable value corresponding to each history step number by using the constant filling method, and construct the Lorenz chaotic model by using the single variable time delay method, update the chaotic variable value in the Lorenz chaotic model by using the fourth-order Runge-Kutta method, simulate and generate the continuous chaotic trajectory which is unpredictable according to the set time step; S2: set the length of the symbol period of the chaotic trajectory, divide the chaotic trajectory by the symbol period, and map the chaotic variable value at the last time step in each symbol period to the preset numerical interval range by using the linear mapping to generate the key value corresponding to each symbol period; S3: based on the generated key value, calculate the phase offset of each symbol period by using the modulo operation, and calculate the frequency offset of each symbol period by using the dynamic frequency modulation method, divide the microwave carrier signal to be encrypted into sub-signals of several lengths according to the symbol period, and encrypt the corresponding sub-signals by using the dynamic double parameter method based on the phase offset and the frequency offset of each symbol period to generate the encrypted microwave carrier signal; S4: modify the encrypted microwave carrier signal by using the Gaussian white noise, obtain the first microwave signal after modification, and demodulate the baseband signal by coherent demodulation of the first microwave signal, compensate the baseband signal based on the phase offset and the frequency offset in each symbol period, and integrate the compensated baseband signal to obtain the decrypted original microwave carrier signal; Set the time step and the delay time, set the ratio of the delay time to the time step as the history step number, set the chaotic variable value corresponding to the history step number by using the constant filling method, and fill all the chaotic variable values of the history step number as the initial value of the preset chaotic variable value; Construct the Lorenz chaotic model by using the single variable time delay method: chaotic variable value at the th time step; chaotic variable value at the th time step; chaotic variable value at the th time step, which is the product of the discrete time step index and the time step length; index of the discrete time step; is the instantaneous rate of change of the model at the time point , with chaotic variable value ; is the quotient of the delay time and the time step length, which is the history step number; Update the chaotic variable value by using the fourth-order Runge-Kutta method to generate the continuous chaotic trajectory which is unpredictable: Based on the key value, calculate the phase offset of each symbol period by using the modulo operation: 、 、 、 , respectively, denote an initial instantaneous rate of change, a first intermediate instantaneous rate of change, a second intermediate instantaneous rate of change, a final instantaneous rate of change; denotes a chaotic variable value at the th time step; denotes a time step size; Calculate the frequency offset of each symbol period by using the dynamic frequency modulation method: wherein, denotes a phase offset of the th symbol period; denotes a floor operation; denotes a key value corresponding to the last time step of the th symbol period in the dynamic key stream based on the chaotic system; denotes a symbol period index number; The specific steps of generating the key value corresponding to each symbol period are: wherein, denotes the frequency offset of the th symbol period; denotes the maximum allowed frequency offset.

2. The method for microwave transmission data encryption according to claim 1, characterized in that, Number each symbol period, specifically: divide the time step index by the number of steps contained in each symbol period to obtain the index number of each symbol period. The symbol period is defined as The chaotic trajectory is divided into symbol periods, and the value of the chaotic variable at the last time step in each symbol period is mapped to an integer interval range using a linear mapping, where represents the number of steps contained in each symbol period; The logic of the linear mapping is: subtract the last time step of the chaotic variable value from the minimum chaotic variable value in the symbol period, divide the difference value by the difference between the maximum chaotic variable value and the minimum chaotic variable value in the symbol period, multiply the quotient value by 255 and round it to an integer, subtract 128 from the result of the integer, and the integer interval range of the key value is ; The specific steps of generating the encrypted microwave carrier signal by using the dynamic double parameter method are:

3. The method of claim 1, wherein the microwave transmission data is encrypted. Divide the microwave carrier signal to be encrypted into sub-signals of several lengths according to the symbol period, and encrypt the corresponding sub-signals by using the dynamic double parameter method based on the phase offset and the frequency offset of each symbol period to generate the encrypted microwave carrier signal, specifically: Take the phase offset and the frequency offset of each symbol period as the modulation parameters of the target carrier to generate the carrier microwave signal in each symbol period: The specific steps of demodulating the baseband signal by coherent demodulation of the first microwave signal are: Modify the encrypted microwave carrier signal by using the Gaussian white noise, specifically: wherein, represents a target carrier frequency; represents a signal amplitude of the target carrier; represents an encrypted microwave carrier signal.

4. The method for microwave transmission data encryption according to claim 3, characterized in that, ​ ​ The Gaussian white noise is superimposed on the encrypted microwave carrier signal, and a first microwave signal is obtained after correction, and the first microwave signal after correction is coherently demodulated to obtain a demodulated baseband signal: wherein represents a demodulated baseband signal; represents a corrected microwave carrier signal.

5. The method for microwave transmission data encryption according to claim 4, characterized in that, The decrypted original microwave carrier signal is obtained, and the specific steps are as follows: The baseband signal is phase compensated based on the phase offset and the frequency offset of each symbol period: Wherein, wherein denotes the phase-compensated baseband signal; The compensated baseband signal is integrated to obtain the decrypted original signal: wherein, represents binary phase shift keying; represents the output decision signal.

6. A microwave based transmission data encryption system characterized by: The encryption system is used to execute the encryption method of any one of claims 1-5, comprising: The data acquisition module is used to calculate the delayed target step number and calibrate it as the historical step number by setting the time step and the delay time, set the initial chaotic variable value, determine the chaotic variable value corresponding to each historical step number by using the constant filling method, construct the Lorenz chaotic model by using the single variable time delay method, update the chaotic variable value in the Lorenz chaotic model by using the fourth-order Runge-Kutta method, and simulate the generation of the unpredictable continuous chaotic trajectory according to the set time step; The key generation module is used to set the length of the symbol period of the chaotic trajectory, divide the chaotic trajectory by the symbol period, and map the chaotic variable value of the last time step in each symbol period to the preset numerical interval range by using linear mapping to generate the key value corresponding to each symbol period; The encryption module is used to calculate the phase offset of each symbol period by using the modulo operation based on the generated key value, calculate the frequency offset of each symbol period by using the dynamic frequency modulation method, divide the microwave carrier signal to be encrypted into sub-signals with a length according to the symbol period, and encrypt the corresponding sub-signals by using the dynamic double parameter method based on the phase offset and the frequency offset of each symbol period to generate the encrypted microwave carrier signal; The decryption module is used to correct the encrypted microwave carrier signal by using the Gaussian white noise, obtain the first microwave signal after correction, and coherently demodulate the first microwave signal to obtain the baseband signal, compensate the baseband signal based on the phase offset and the frequency offset in each symbol period, and integrate the compensated baseband signal to obtain the decrypted original microwave carrier signal.

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