A V-OFDM secure transmission method, system, device and medium based on a dynamic feedback chaotic system

Abstract

This invention discloses a V-OFDM secure transmission method, system, device, and medium based on a dynamic feedback chaotic system. The method constructs a three-dimensional Lorenz chaotic mapping model based on dynamic feedback factors, controls the row and column transformations of the orthogonal DFT matrix, and independently encrypts each vector block. The system, device, and medium are used to implement this method. The method fully utilizes the vector block characteristics of V-OFDM, introducing dynamic row and column permutations of the DFT matrix, resulting in a spherical chaotic state in the encrypted constellation diagram, making it difficult for eavesdroppers to crack. This greatly enhances the system's resistance to signal interception, effectively strengthens the security of the physical layer, and reduces the system's peak-to-average power ratio (PAPR).

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a V-OFDM secure transmission method, system, device, and medium based on a dynamic feedback chaotic system. Background Technology

[0002] Currently, Vector Orthogonal Frequency Division Multiplexing (V-OFDM), as a generalized extension of Orthogonal Frequency Division Multiplexing (OFDM), introduces a vector block processing mechanism. This not only achieves efficient spectrum utilization but also further enhances resistance to multipath interference and the flexibility of signal adaptation. Compared to traditional OFDM, V-OFDM breaks down large-scale Fast Fourier Transform (IFFT) operations into multiple small-scale vector IFFTs. This allows for flexible adjustment of the vector block size in different application scenarios, balancing data rate, computational complexity, and transmission reliability. However, V-OFDM systems still face several key technical challenges in practical applications: First, the high peak-to-average power ratio (PAPR) problem persists. Due to the superposition effect of subcarriers within the vector block, the instantaneous peak power of the time-domain signal may be higher, leading to signal distortion, increased amplifier nonlinear distortion, and reduced system transmission performance. Second, existing physical layer security technologies have not further improved the vector block structure of V-OFDM to enhance transmission security.

[0003] Existing technical solutions have attempted to improve upon PAPR reduction or physical layer security. Regarding PAPR reduction, clipping and filtering techniques lower PAPR by limiting the instantaneous peak power of the signal, but this distorts the original waveform, causing significant signal distortion and degrading transmission quality. Furthermore, traditional security encryption technologies rely on upper-layer encryption algorithms, which are highly complex. Additionally, the symmetry of encryption using constellation diagram rotation can still be exploited by eavesdroppers, posing a high risk of breach. Therefore, traditional technologies cannot effectively address the dual requirements of secure transmission and PAPR reduction in V-OFDM systems.

[0004] Wuhan Qing (Wuhan Qing. Research on Physical Layer Security Algorithms Based on OFDM Systems [D]. Jiangsu University of Science and Technology, 2018.) proposed a composite encryption scheme combining phase rotation, key matrix, and artificial noise. This scheme encrypts transmitted symbols using a dynamic diagonal key matrix and generates artificial noise masking signals based on OFDM system parameters. Using this method, the PAPR is reduced by approximately 1.5 dB while maintaining the illegal demodulation bit error rate at 0.5%.

[0005] While the aforementioned research has made some progress in physical layer security and PAPR optimization, schemes based on the traditional OFDM framework are difficult to adapt to the vector block structure of V-OFDM and fail to effectively utilize its multidimensional characteristics for dynamic optimization. Therefore, existing technologies cannot effectively address the dual requirements of PAPR optimization and physical layer security in V-OFDM systems under dynamic environments, and an innovative scheme that can simultaneously solve PAPR optimization and physical layer security in V-OFDM systems is urgently needed. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention aims to provide a V-OFDM secure transmission method, system, device, and medium based on a dynamic feedback chaotic system. By constructing a three-dimensional Lorenz chaotic mapping model based on dynamic feedback factors, controlling the row and column transformations of the orthogonal DFT matrix, and employing dynamic orthogonal DFT matrix encryption, the PAPR (PAPR) is reduced, avoiding the problem of easy derivation and cracking of traditional fixed matrices. It fully utilizes the vector block characteristics of V-OFDM, effectively improving the physical layer security of the system. Through isometric transformation of the dynamic orthogonal DFT matrix, each vector block is independently encrypted, resulting in a spherical chaotic characteristic of the encrypted signal on the constellation diagram, making it difficult for eavesdroppers to crack. Simultaneously, the parameters of the three-dimensional Lorenz chaotic mapping model can be flexibly adjusted according to the communication environment, thereby enhancing the robustness and anti-interference capability of the system and meeting the requirements of high-security, low-latency scenarios such as 5G communication and the Internet of Things. The method of this invention can achieve more efficient secure communication at a lower cost, providing reliable physical layer protection for V-OFDM systems. Furthermore, this method has low computational complexity, a simple generation process, is suitable for real-time communication scenarios, and can significantly reduce hardware and energy costs.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A V-OFDM secure transmission method based on a dynamic feedback chaotic system includes the following steps:

[0009] Step 1: Introduce a dynamic feedback factor into the classic 3D Lorenz chaotic model to construct a 3D Lorenz chaotic mapping model and generate a chaotic key sequence x. i y i and z i The chaotic key sequence x i y i and z i Quantization is performed by mapping to a discrete space;

[0010] Step 2: In the encryption stage, the input data is divided into M×L vector groups to obtain an M×L matrix, and the index vector is used to perform row and column permutations on the M×L matrix;

[0011] Step 3: Decompose the standard DFT matrix into a set of orthogonal row vectors, and perform row and column permutations on the decomposed DFT matrix using index vectors; multiply the M×L matrix after row and column permutations with the DFT matrix after row and column permutations to generate an M×L encrypted matrix;

[0012] Step 4: Perform an inverse fast Fourier transform on the M×L encryption matrix, dividing it into L points by row, to obtain the time-domain signal s = [s0, s1, ..., s]. L-1 ]; The time-domain signal s = [s0, s1, ..., s L-1 Perform parallel-to-serial conversion and add a cyclic prefix (CP) to generate the transmitted signal.

[0013] Step 5: Transmit signal The signal is transmitted wirelessly to the receiving end, generating a received signal. Then, the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as at the transmitting end is performed to obtain the time-domain received signal y = [y0, y1, ..., y]. L-1 Subsequently, a Fast Fourier Transform (FFT) is performed on the time-domain received signal y, with L points along each row, to obtain the frequency-domain signal Y = [Y0, Y1, ..., Y]. L-1 ];

[0014] Step 6: In the decryption stage, the frequency domain signal Y is subjected to inverse row and column permutation using the same index vector as in Step 2. At the same time, the DFT matrix decomposed in Step 3 is inverted to obtain the inverse DFT matrix, and the same index vector as in Step 3 is used to perform inverse row and column permutation. The frequency domain signal Y after inverse row and column permutation is multiplied with the inverse DFT matrix after inverse row and column permutation to generate an M×L decryption matrix.

[0015] Step 7: Perform parallel-to-serial conversion and quadrature phase shift keying inverse mapping demodulation on the M×L decryption matrix in sequence to output binary output data.

[0016] The expression for the three-dimensional Lorenz chaotic mapping model in step 1 is as follows:

[0017]

[0018] In the formula, a is Prandtl number, b is Rayleigh number, c is direction ratio, and variables (x, y, z) represent three dynamic variables of the system state, with a>0, b>0, and c>0; ζ0 represents the initial value of the dynamic feedback factor, ∈ represents the control parameter of the fluctuation amplitude of the dynamic feedback factor in the time domain, and μ represents the feedback modulation parameter, with ζ0>0, ∈>0, and μ>0.

[0019] In step 1, the random initial value (x0, y0, z0) shared by the cooperative communication sender and the legitimate user receiver is input as a seed key into the three-dimensional Lorenz chaotic mapping model, and the model parameters a, b, c, ζ0, ∈, μ are set to iteratively generate three sets of chaotic key sequences x. i y i and z i .

[0020] In step 1, the chaotic key sequence x i y i and z i The formula for quantification is as follows:

[0021]

[0022] In the formula, These represent the quantized chaotic key sequences.

[0023] The process of grouping the input data into M×L vectors in step 2 is as follows: First, the input data is a data block consisting of a pseudo-random binary sequence, and the length of the data block is set to N; the data block is sequentially subjected to serial-to-parallel transformation and orthogonal phase shift keying mapping, and then the mapped data block is grouped into M×L groups, that is, divided into L vector blocks, each vector block containing M symbols, satisfying N=LM, and an M×L matrix is ​​established.

[0024] In step 2, the index vector is obtained by applying the quantized chaotic key sequence D. xi and D yi The result is obtained by sorting, i.e., in the quantized chaotic key sequence D. xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D. x =[d1,d2,...,d M Similarly, in the quantized chaotic key sequence D... yi Randomly select a sequence of length L and sort it in ascending order to obtain the index vector D. y =[d1,d2,…,d L ].

[0025] The index vector in step 3 is obtained by applying the quantized chaotic key sequence D. xi and D zi The result is obtained by sorting, i.e., in the quantized chaotic key sequence D. xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D'. x =[d1,d2,…,d M From the chaotic key sequence D zi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D.z =[d1,d2,…,d M ].

[0026] The present invention also provides a V-OFDM secure transmission system based on a dynamic feedback chaotic system, comprising:

[0027] Model building module: Introduces a dynamic feedback factor into the classic 3D Lorenz chaotic model to construct a 3D Lorenz chaotic mapping model and generate a chaotic key sequence x. i y i and z i The chaotic key sequence x i y i and z i Quantization is performed by mapping to a discrete space;

[0028] Encryption Module: During the encryption phase, the input data is divided into M×L vector groups to obtain an M×L matrix, and the index vector is used to perform row and column permutations on the M×L matrix; at the same time, the standard DFT matrix is ​​decomposed into a set of orthogonal row vectors, and the index vector is used to perform row and column permutations on the decomposed DFT matrix; the M×L matrix after row and column permutations is multiplied with the DFT matrix after row and column permutations to generate an M×L encryption matrix;

[0029] Transmission module: Performs a fast inverse Fourier transform on the M×L encryption matrix by L points along each row to obtain the time-domain signal s=[s0,s1,...,s L-1 ]; The time-domain signal s = [s0, s1, ..., s L-1 Perform parallel-to-serial conversion and add a cyclic prefix (CP) to generate the transmitted signal. Then transmit the signal. The signal is transmitted wirelessly to the receiving end, generating a received signal. Then, the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as at the transmitting end is performed to obtain the time-domain received signal y = [y0, y1, ..., y]. L-1 Subsequently, a Fast Fourier Transform (FFT) is performed on the time-domain received signal y, with L points along each row, to obtain the frequency-domain signal Y = [Y0, Y1, ..., Y]. L-1 ];

[0030] Decryption module: Perform inverse row and column permutations on the frequency domain signal Y using the same index vector as in the encryption module. Simultaneously, invert the decomposed DFT matrix in the encryption module to obtain the inverse DFT matrix, and perform inverse row and column permutations on it using the same index vector as in step 3. Multiply the frequency domain signal Y after inverse row and column permutations with the inverse DFT matrix after inverse row and column permutations to generate an M×L decryption matrix.

[0031] Output module: Performs parallel-to-serial conversion and orthogonal phase shift keying inverse mapping demodulation on the M×L decryption matrix in sequence, and outputs binary output data.

[0032] The present invention also provides a V-OFDM secure transmission device based on a dynamic feedback chaotic system, comprising:

[0033] Memory: A computer program that stores the above-described V-OFDM secure transmission method based on a dynamic feedback chaotic system, and is a computer-readable device;

[0034] Processor: Used to implement the above-described V-OFDM secure transmission method based on a dynamic feedback chaotic system when executing the computer program.

[0035] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the implementation of the above-described V-OFDM secure transmission method based on a dynamic feedback chaotic system.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] 1. This invention is the first to combine chaotic encryption technology with a V-OFDM system, innovatively enhancing system security through an M×L matrix and an orthogonal DFT matrix. This method effectively addresses the security challenges of V-OFDM in highly dynamic environments, providing a solid foundation for future V-OFDM applications in highly dynamic communication scenarios, and offering theoretical basis and engineering reference for subsequent research and implementation of security and reliability technologies.

[0038] 2. This invention employs an improved three-dimensional Lorenz chaotic system, which significantly enhances the randomness and initial value sensitivity of the chaotic sequence by introducing a dynamic feedback factor, thereby generating a chaotic sequence with higher randomness and unpredictability.

[0039] 3. This invention combines chaotic sequence to generate index vectors to dynamically permutate the rows and columns of the input data, and introduces a randomized DFT matrix for encryption. It is easy to implement and makes the encrypted constellation diagram present a spherical chaotic state, which greatly improves the system's resistance to signal interception and effectively enhances the security of the physical layer.

[0040] 4. Traditional V-OFDM systems, due to their multi-carrier modulation, suffer from a high peak-to-average power ratio (PAPR), which can easily cause the power amplifier to enter the nonlinear operating region, leading to signal distortion and reduced energy efficiency. This invention optimizes the signal energy distribution in the frequency domain by introducing dynamic row and column permutations of the DFT matrix, significantly reducing instantaneous peak power and avoiding out-of-band interference and nonlinear distortion. Simultaneously, the randomization of the DFT matrix through chaotic indexing further enhances the complexity of the signal spectrum, effectively preventing energy accumulation and the occurrence of fixed spectral positions, thereby improving the system's transmission reliability and solving the signal quality degradation problem caused by excessively high PAPR in existing technologies. Attached Figure Description

[0041] Figure 1 This is a flowchart of the V-OFDM secure transmission method based on a dynamic feedback chaotic system according to the present invention.

[0042] Figure 2 This is a three-dimensional phase diagram based on the dynamic feedback factor chaotic model of the present invention.

[0043] Figure 3 This is the xy-plane singularity factor attraction diagram of the present invention.

[0044] Figure 4 This is the yz-plane singularity factor attraction diagram of the present invention.

[0045] Figure 5 This is the xz-plane singularity factor attraction diagram of the present invention.

[0046] Figure 6 A performance comparison of the traditional Lorenz chaos model and the improved dynamic feedback factor Lorenz model.

[0047] Figure 7 This is the original constellation diagram of the QPSK of this invention.

[0048] Figure 8 This is the constellation diagram after QPSK encryption according to the present invention.

[0049] Figure 9 This is a comparison chart of the CCDF curves of PAPR before and after encryption in this invention. Detailed Implementation

[0050] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0051] This invention combines a dynamic feedback factor chaotic system and a DFT matrix to construct a complete encryption-to-decryption process for cooperative communication between the sender and legitimate receiver in a V-OFDM system. In the encryption phase, the initial values ​​of the chaotic model are first used as a shared seed key between the legitimate sender and receiver. Then, the index vector obtained through quantization and sorting of the chaotic model is used to perform row and column permutations on the data after the V-OFDM vector is grouped. An orthogonal DFT matrix is ​​introduced to perform row and column permutations on this data. Due to the randomness of the chaotic sequence, multi-level encryption of the data matrix is ​​achieved, which improves physical layer security and effectively reduces the peak-to-average power ratio (PAPR) of the system. In the decryption phase, the legitimate receiver uses the shared seed key to efficiently restore the data. By performing the sender's reverse permutation process, the original signal arrangement is accurately recovered.

[0052] like Figure 1 As shown, a V-OFDM secure transmission method based on a dynamic feedback chaotic system specifically includes the following steps:

[0053] Step 1: Introduce a dynamic feedback factor into the classical 3D Lorenz chaotic model to construct a 3D Lorenz chaotic mapping model. The introduction of the dynamic feedback factor aims to make the system exhibit more complex chaotic attractors, higher Lyapunov exponents, and stronger initial value sensitivity by dynamically controlling the changes in nonlinear terms in real time. The expression of the classical 3D Lorenz chaotic model is as follows:

[0054]

[0055] The expression for the three-dimensional Lorenz chaotic mapping model based on dynamic feedback factors is as follows:

[0056]

[0057] In the formula, a is the Prandtl number, b is the Rayleigh number, c is the direction ratio, and the variables (x, y, z) represent the three dynamic variables of the system state, with a > 0, b > 0, and c > 0; ζ0 represents the initial value of the dynamic feedback factor, ∈ represents the control parameter for the fluctuation amplitude of the dynamic feedback factor in the time domain, and μ represents the feedback modulation parameter, with ζ0 > 0, ∈ > 0, and μ > 0. The introduction of the dynamic feedback factor enables the system to exhibit more complex dynamic characteristics in time-varying states. By reasonably setting the range and form of these parameters, it can be ensured that the system is always in a chaotic state.

[0058] In this embodiment, to verify the chaotic performance of the improved system, the system parameters were set as a = 10, b = 25, c = 8 / 3, ζ0 = 1, ∈ = 0.1, μ = 0.1, and the following results were obtained: Figure 2 , 3Figures 4 and 5 show the three-dimensional phase diagram of the three-dimensional Lorenz hyperchaotic mapping and the singular attractor diagrams of each plane. The attractor trajector paths of the three-dimensional Lorenz chaotic mapping model in three-dimensional space clearly demonstrate the complex yet regular motion trajectory of the system. Due to the introduction of dynamic feedback factors, the three-dimensional Lorenz chaotic mapping model makes the attractor morphology more complex than the classic three-dimensional Lorenz chaotic model, exhibiting significant chaotic characteristics.

[0059] like Figure 3 As shown, the projected trajectory in the xy-plane exhibits a typical double-helix structure, indicating a complex alternating attraction characteristic between the two attractors of the system model. This structure reflects the instability and sensitive dependence of the system model in this plane. Figure 4 As shown, the trajectory in the yz plane reveals the symmetry and periodicity of the attractor, accompanied by a complex spiral convergence structure, reflecting the chaotic dynamics of the system in different dimensions. Figure 5 As shown, a complex symmetrical morphological structure can be observed in the trajectory in the xz plane, which confirms that the dynamic feedback factor enhances the chaotic characteristics of the system.

[0060] To further analyze the advantages of the proposed three-dimensional Lorenz model based on dynamic feedback factors, the performance of the classical three-dimensional Lorenz chaotic model and the improved dynamic feedback factor Lorenz model in Lyapunov exponent calculation is compared, for example... Figure 6 As shown in the figure, the blue curve represents the Lyapunov exponent of the classic 3D Lorenz chaotic model, with a maximum value of 1.4410 and a Rayleigh number b of 197. In contrast, the green curve represents the improved 3D Lorenz chaotic mapping model, with a maximum Lyapunov exponent of 5.7300 and a Rayleigh number b of 165. The maximum Lyapunov exponent is 2.97 times higher than the original, and it exhibits a higher Lyapunov exponent across multiple parameter ranges, indicating a significantly enhanced chaotic nature. In the region where the Rayleigh number b > 300, the Lyapunov exponent of the classic 3D Lorenz chaotic model gradually stabilizes and remains at a low level, indicating weaker chaotic behavior. However, the improved 3D Lorenz chaotic mapping model exhibits significant volatility and a higher Lyapunov exponent within the same parameter range, indicating more complex chaotic behavior. This improvement benefits from the introduction of a dynamic feedback factor, which increases the system's sensitivity to initial conditions and its trajectory bifurcation characteristics, significantly enhancing the system's chaotic performance while maintaining good randomness and complexity, thus verifying the effectiveness and feasibility of the improvement scheme.

[0061] Step 2: Generate a chaotic key sequence x based on the 3D Lorenz chaotic mapping model.i y i and z i ;

[0062] The random initial value (x0, y0, z0) shared by the cooperative communication sender and the legitimate user receiver is input into the model as a seed key. The parameters a, b, c, ζ0, ∈, and μ of the same three-dimensional Lorenz chaotic mapping model as in step 1 are set. After a certain number of iterations, three sets of chaotic key sequences x are generated. i y i and z i The three-dimensional Lorenz chaotic mapping model based on dynamic feedback factors, due to its pseudo-randomness in sensitivity to small changes in initial values ​​(x0, y0, z0), can provide high-strength security for V-OFDM secure transmission systems.

[0063] Step 3: The continuous chaotic key sequence x from Step 2... i y i and z i The quantization is performed by mapping to a discrete space; the quantization formula is as follows:

[0064]

[0065] In the formula, These represent the quantized chaotic key sequences;

[0066] By analyzing three sets of chaotic key sequences x i y i and z i The number is amplified by multiplying it by 1000, and then restricted to the range of 0 to N by modulo operation. This quantization process can transform the floating-point sequence into a discrete integer sequence with finite precision while maintaining its pseudo-randomness, and it can be directly used as an index for a matrix.

[0067] Step 4: In the encryption stage, the input data is divided into M×L vector groups to obtain an M×L matrix, and the chaotic key sequence quantized in Step 3 is sorted to obtain an index vector; the index vector is used to perform row and column permutations on the M×L matrix.

[0068] First, the input data from the transmitter of the V-OFDM secure transmission system is a data block consisting of a pseudo-random binary sequence, and the length of the data block is set to N. The data block is then subjected to serial-to-parallel transformation and quadrature phase shift keying (QPSK) mapping in sequence. Then, the mapped data block is divided into M×L groups, that is, into L vector blocks, each containing M symbols, satisfying N=LM, and an M×L matrix is ​​established.

[0069] The l-th vector block can be represented as:

[0070] x l =x lM ,x lM+1 ,...,x lM+M-1 T ,l=0,1,...,L-1

[0071] In the formula, T represents transpose;

[0072] The expression for the M×L matrix is ​​as follows:

[0073]

[0074] Then, the quantized chaotic key sequence D in step 3 xi Randomly select a sequence of length M to form sequence D. xi =[x0,x1,...,x M ], for sequence D xi =[x0,x1,...,x M Sort the data in ascending order to obtain the index vector D. x =[d1,d2,...,d M ]; using index vector D x =[d1,d2,...,d M Rearrange the rows of an M×L matrix. The resulting M×L matrix after row permutation is represented as:

[0075] X′(i,:)=X(D x [i],:), i = 1, 2, ..., M

[0076] The sorting formula is as follows:

[0077]

[0078] In the formula, D x D y D z These represent the sorted index vectors;

[0079] The sorting operation here returns the index of the sorted data in ascending order. For example, if... Then D x =[3,1,2,0]. This index mapping extends randomness to the permutation dimension, transforming numerical randomness into permutation randomness, further shuffling the data order. The resulting permutation has higher dimensional complexity, making it difficult to crack through frequency or time domain analysis, thus offering greater security.

[0080] Similarly, the row permutation-derived M×L matrix X′ in the quantized chaotic key sequence D yi Randomly select a sequence of length L to form sequence D.yi =[y0,y1,...,y L ], for sequence D yi =[y0,y1,...,y L Sort the data in ascending order to obtain the index vector D. y =[d1,d2,...,d L ]; using index vector D y =[d1,d2,...,d L Rearrange the columns of an M×L matrix. The resulting M×L matrix X after column permutation is represented as:

[0081] X(:,j)=X′(:,D y [j]), j = 1, 2, ..., L

[0082] The sorting operation here returns the index of the sorted data in ascending order. For example, if... Then D x =[3,1,2,0]. This index mapping extends randomness to the permutation dimension, transforming numerical randomness into permutation randomness, further shuffling the data order. The resulting permutation has higher dimensional complexity, making it difficult to crack through frequency or time domain analysis, thus offering greater security.

[0083] Step 5: Decompose the standard DFT matrix into a set of orthogonal row vectors, and perform row and column permutations on the decomposed DFT matrix using index vectors; then compare the M×L matrix obtained from the row and column permutations in Step 4 with the DFT matrix F obtained from the row and column permutations. M×M Multiply to generate an M×L encrypted matrix;

[0084] To further enhance system security and address the high peak-to-average power ratio (PAPR) issue inherent in V-OFDM as a multi-carrier system, an orthogonal DFT matrix is ​​introduced based on the original M×L matrix transform. The DFT matrix plays a crucial role in signal processing; its orthogonality and spectral spreading capabilities result in a more uniform data distribution in the frequency domain, thereby reducing the signal's peak power. This not only optimizes the physical layer transmission performance but also adds greater complexity to encryption schemes. The standard DFT matrix expression is as follows:

[0085]

[0086] In the formula, m and n are the row and column indices of the DFT matrix, respectively, ranging from m,n = 1, 2, ..., N; the expanded standard DFT matrix takes the following form:

[0087]

[0088] This matrix can be decomposed into a set of orthogonal row vectors. Right now:

[0089]

[0090] Since the input data is divided into M×L matrices, N is set to M to maintain the orthogonality of the DFT matrices. For the DFT matrix F... M×M From the quantized chaotic key sequence D xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D'. x =[d1,d2,…,d M The rows of the DFT matrix are rearranged, and the resulting DFT matrix is ​​represented as follows:

[0091] F′ MM (i,:)=F MM (D′ x [i],:), i = 1, 2, ..., M

[0092] After completing the row permutation, the DFT matrix F′ after the row permutation is also processed. M×M (i,:) from the chaotic key sequence D zi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D. z =[d1,d2,…,d M The DFT matrix is ​​reordered, and the resulting DFT matrix F after column permutation is... M×M Represented as:

[0093] F MM (:,j)=F MM (:,D z [j]), j = 1, 2, ..., M

[0094] The row and column permutation steps described above also complete the dynamic randomization of the DFT matrix.

[0095] The expression for generating the M×L encryption matrix is:

[0096] S = F M×M X

[0097] Step 6: Perform an Inverse Fast Fourier Transform (IFFT) on the M×L encryption matrix, dividing it into L points by row, to obtain the time-domain signal s = [s0, s1, ..., s]. L-1 This enables the modulation of data; the time-domain signal s = [s0, s1, ..., s2] is converted into a time-domain signal. L-1 Perform parallel-to-serial conversion and add a cyclic prefix (CP) to generate the transmitted signal.

[0098] The expression for the time-domain signal is:

[0099]

[0100] Step 7: Transmit signal The signal is transmitted wirelessly to the receiving end, generating a received signal. Then, the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as at the transmitting end is performed to obtain the time-domain received signal y = [y0, y1, ..., y]. L-1 Subsequently, a Fast Fourier Transform (FFT) is performed on the time-domain received signal y, with L points arranged along each row, to obtain the frequency-domain signal Y = [Y0, Y1, ..., Y]. L-1 ];

[0101] The expression for the time-domain received signal is:

[0102]

[0103] In the formula, h is the impulse response of the channel, and w is additive white Gaussian noise;

[0104] The expression for the frequency domain signal is:

[0105]

[0106] Step 8: In the decryption stage, the same index vector as in Step 4 is used to perform inverse row and column permutations on the frequency domain signal Y, and simultaneously, the DFT matrix F decomposed in Step 5 is... M×M Find the inverse to obtain the DFT inverse matrix, and perform row and column inverse permutations using the same index vector as in step 5; multiply the frequency domain signal Y after row and column inverse permutation with the DFT inverse matrix after row and column inverse permutation to generate an M×L decryption matrix;

[0107] During the decryption phase, only legitimate user receivers and cooperative communication senders share the same key sequence, thus obtaining the same index vector. First, the DFT matrix F... M×M Find the inverse; since the matrix is ​​orthogonal, the DFT matrix F M×M The inverse matrix is ​​obtained by the conjugate transpose, expressed as:

[0108]

[0109] In the formula, H represents the conjugate transpose.

[0110] Then, perform the inverse operation of the same row and column permutation as in step 5, that is, first perform the same column transformation on the DFT inverse matrix, and then perform the same row transformation on the DFT inverse matrix to obtain the DFT inverse matrix F after the row and column inverse permutation. -1 .

[0111] Next, the frequency domain signal Y is decrypted. The same key sequence and index vector are shared with the sender. The same row and column permutation operation as in step 4 is performed. That is, the same column transformation is performed on the M×L matrix first, and then the row transformation is performed on the M×L matrix after the column transformation to obtain the original M×L matrix X1.

[0112] The M×L matrix X1 after row and column inverse permutation is compared with the DFT inverse matrix F after row and column inverse permutation. -1 Multiplying completes the decryption process, generating a decrypted signal of M×L matrix, expressed as:

[0113] X2 = F -1 X1

[0114] Step 9: Perform parallel-to-serial conversion and quadrature phase shift keying (QPSK) inverse mapping demodulation on the M×L decryption matrix in sequence to obtain the correct binary output data.

[0115] For the legitimate user recipient, since they share the same seed key sequence as the sender, they can decrypt the data at the receiving end through the aforementioned series of reverse operations, and then refer to... Figure 7 Demodulation yields the correct quadrature phase shift keying (QPSK) constellation diagram;

[0116] For an unauthorized recipient, the enhanced chaotic nature of the chaotic model and its sensitivity to initial values ​​make it difficult to obtain the same key sequence, thus hindering decryption. The initial conditions and parameters of the chaotic model are extremely sensitive to the output chaotic sequence; even minute changes can lead to drastically different results. Therefore, even if an unauthorized recipient obtains the encrypted data, they cannot accurately recover the corresponding key sequence and thus cannot decrypt the data. (Refer to...) Figure 8 The demodulated constellation diagram appears as a spherical mess, exhibiting noise-like characteristics, making it difficult to demodulate the correct data information.

[0117] refer to Figure 9 Compared to the peak-to-average power ratio (PAPR) of the traditional OFDM system (Wuhan Qing. Research on physical layer security algorithm based on OFDM system [D]. Jiangsu University of Science and Technology, 2018.), the PAPR of the encrypted V-OFDM system of this invention is reduced by 1.8 dB. This is because the row and column permutations of the V-OFDM system and the addition of the DFT matrix after the row and column permutations greatly disturb the autocorrelation between symbols, thereby reducing the PAPR of the system.

[0118] In summary, the above scheme provides a stable decryption process for legitimate users by using key complexity and a high degree of dependence on the initial conditions of the chaotic model, while greatly increasing the difficulty of cracking for illegitimate users, thus effectively ensuring the security of data transmission.

[0119] The present invention also provides a V-OFDM secure transmission system based on a dynamic feedback chaotic system, comprising:

[0120] Model building module: Introduces a dynamic feedback factor into the classic 3D Lorenz chaotic model to construct a 3D Lorenz chaotic mapping model and generate a chaotic key sequence x. i y i and z i The chaotic key sequence x i y i and z i Quantization is performed by mapping to a discrete space;

[0121] Encryption Module: During the encryption phase, the sender divides the input data into M×L vector groups to obtain an M×L matrix, and performs row and column permutations on the M×L matrix using index vectors; simultaneously, the standard DFT matrix is ​​decomposed into a set of orthogonal row vectors, and the decomposed DFT matrix is ​​subjected to row and column permutations using index vectors; the M×L matrix after row and column permutations is multiplied by the DFT matrix after row and column permutations to generate an M×L encryption matrix;

[0122] Transmission module: Performs a fast inverse Fourier transform on the M×L encryption matrix by L points along each row to obtain the time-domain signal s=[s0,s1,...,s L-1 ]; The time-domain signal s = [s0, s1, ..., s L-1 Perform parallel-to-serial conversion and add a cyclic prefix (CP) to generate the transmitted signal. Then transmit the signal. The signal is transmitted wirelessly to the receiving end, generating a received signal. Then, the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as at the transmitting end is performed to obtain the time-domain received signal y = [y0, y1, ..., y]. L-1 Subsequently, a Fast Fourier Transform (FFT) is performed on the time-domain received signal y, with L points along each row, to obtain the frequency-domain signal Y = [Y0, Y1, ..., Y]. L-1 ];

[0123] Decryption module: Perform inverse row and column permutations on the frequency domain signal Y using the same index vector as in the encryption module. Simultaneously, invert the decomposed DFT matrix in the encryption module to obtain the inverse DFT matrix, and perform inverse row and column permutations on it using the same index vector as in step 3. Multiply the frequency domain signal Y after inverse row and column permutations with the inverse DFT matrix after inverse row and column permutations to generate an M×L decryption matrix.

[0124] Output module: Performs parallel-to-serial conversion and orthogonal phase shift keying inverse mapping demodulation on the M×L decryption matrix in sequence, and outputs binary output data.

[0125] The present invention also provides a V-OFDM secure transmission device based on a dynamic feedback chaotic system, comprising:

[0126] Memory: A computer program that stores the above-described V-OFDM secure transmission method based on a dynamic feedback chaotic system, and is a computer-readable device;

[0127] Processor: Used to implement the above-described V-OFDM secure transmission method based on a dynamic feedback chaotic system when executing the computer program.

[0128] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the implementation of the above-described V-OFDM secure transmission method based on a dynamic feedback chaotic system.

Claims

1. A V-OFDM secure transmission method based on a dynamic feedback chaotic system, characterized in that, Includes the following steps: Step 1: Introduce a dynamic feedback factor into the classic 3D Lorenz chaotic model to construct a 3D Lorenz chaotic mapping model and generate a chaotic key sequence x. i y i and z i The chaotic key sequence x i y i and z i The model is mapped to a discrete space for quantization; the expression for the three-dimensional Lorenz chaotic mapping model is as follows: In the formula, a is Prandtl number, b is Rayleigh number, c is direction ratio, and variables (x, y, z) represent three dynamic variables of the system state, with a>0, b>0, and c>0; ζ0 represents the initial value of the dynamic feedback factor, ∈ represents the control parameter of the fluctuation amplitude of the dynamic feedback factor in the time domain, and μ represents the feedback modulation parameter, with ζ0>0, ∈>0, and μ>0. For the chaotic key sequence x i y i and z i The formula for quantification is as follows: In the formula, These represent the quantized chaotic key sequences; Step 2: In the encryption stage, the input data is divided into M×L vector groups to obtain an M×L matrix, and the row and column permutations of the M×L matrix are performed using index vectors; the index vectors are obtained by applying the quantized chaotic key sequence D. xi and D yi The result is obtained by sorting, i.e., in the quantized chaotic key sequence D. xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D. x =[d1,d2,...,d M Similarly, in the quantized chaotic key sequence D... yi Randomly select a sequence of length L and sort it in ascending order to obtain the index vector D. y =[d1,d2,...,d L ]; Step 3: Decompose the standard DFT matrix into a set of orthogonal row vectors, and perform row and column permutations on the decomposed DFT matrix using index vectors; multiply the resulting M×L matrix with the resulting DFT matrix to generate an M×L encryption matrix; the index vectors are used to manipulate the quantized chaotic key sequence D. xi and D zi The result is obtained by sorting, i.e., in the quantized chaotic key sequence D. xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D'. x =[d1,d2,...,d M From the chaotic key sequence D zi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D. z =[d1,d2,...,d M ]; Step 4: Perform an inverse fast Fourier transform on the M×L encryption matrix, dividing it into L points by row, to obtain the time-domain signal s = [s0, s1, ..., s]. L-1 ]; The time-domain signal s = [s0, s1, ..., s L-1 Perform parallel-to-serial conversion and add a cyclic prefix (CP) to generate the transmitted signal. Step 5: Transmit signal The signal is transmitted wirelessly to the receiving end, generating a received signal. Then, the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as at the transmitting end is performed to obtain the time-domain received signal y = [y0, y1, ..., y]. L-1 Subsequently, a Fast Fourier Transform (FFT) is performed on the time-domain received signal y, with L points along each row, to obtain the frequency-domain signal Y = [Y0, Y1, ..., Y]. L-1 ]; Step 6: In the decryption stage, the frequency domain signal Y is subjected to inverse row and column permutation using the same index vector as in Step 2. At the same time, the DFT matrix decomposed in Step 3 is inverted to obtain the inverse DFT matrix, and the same index vector as in Step 3 is used to perform inverse row and column permutation. The frequency domain signal Y after inverse row and column permutation is multiplied with the inverse DFT matrix after inverse row and column permutation to generate an M×L decryption matrix. Step 7: Perform parallel-to-serial conversion and quadrature phase shift keying inverse mapping demodulation on the M×L decryption matrix in sequence to output binary output data.

2. The V-OFDM secure transmission method based on a dynamic feedback chaotic system according to claim 1, characterized in that: In step 1, the random initial value (x0, y0, z0) shared by the cooperative communication sender and the legitimate user receiver is input as a seed key into the three-dimensional Lorenz chaotic mapping model, and the model parameters a, b, c, ζ0, ∈, μ are set to iteratively generate three sets of chaotic key sequences x. i y i and z i .

3. The V-OFDM secure transmission method based on a dynamic feedback chaotic system according to claim 1, characterized in that, The process of grouping the input data into M×L vectors in step 2 is as follows: First, the input data is a data block consisting of a pseudo-random binary sequence, and the length of the data block is set to N; the data block is sequentially subjected to serial-to-parallel transformation and orthogonal phase shift keying mapping, and then the mapped data block is grouped into M×L groups, that is, divided into L vector blocks, each vector block containing M symbols, satisfying N=LM, and an M×L matrix is ​​established.

4. A V-OFDM secure transmission system based on a dynamic feedback chaotic system, according to any one of claims 1-3, characterized in that, include: Model building module: Introduces a dynamic feedback factor into the classic 3D Lorenz chaotic model to construct a 3D Lorenz chaotic mapping model and generate a chaotic key sequence x. i y i and z i The chaotic key sequence x i y i and z i Quantization is performed by mapping to a discrete space; Encryption Module: During the encryption phase, the input data is divided into M×L vector groups to obtain an M×L matrix, and the index vector is used to perform row and column permutations on the M×L matrix; at the same time, the standard DFT matrix is ​​decomposed into a set of orthogonal row vectors, and the index vector is used to perform row and column permutations on the decomposed DFT matrix; the M×L matrix after row and column permutations is multiplied with the DFT matrix after row and column permutations to generate an M×L encryption matrix; Transmission module: Performs a fast inverse Fourier transform on the M×L encryption matrix by L points along each row to obtain the time-domain signal s=[s0,s1,...,s L-1 ]; The time-domain signal s = [s0, s1, ..., s L-1 Perform parallel-to-serial conversion and add a cyclic prefix (CP) to generate the transmitted signal. Then transmit the signal. The signal is transmitted wirelessly to the receiving end, generating a received signal. Then, the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as at the transmitting end is performed to obtain the time-domain received signal y = [y0, y1, ..., y]. L-1 Subsequently, a Fast Fourier Transform (FFT) is performed on the time-domain received signal y, with L points along each row, to obtain the frequency-domain signal Y = [Y0, Y1, ..., Y]. L-1 ]; Decryption module: Perform inverse row and column permutations on the frequency domain signal Y using the same index vector as in the encryption module. Simultaneously, invert the decomposed DFT matrix in the encryption module to obtain the inverse DFT matrix, and perform inverse row and column permutations on it using the same index vector as in step 3. Multiply the frequency domain signal Y after inverse row and column permutations with the inverse DFT matrix after inverse row and column permutations to generate an M×L decryption matrix. Output module: Performs parallel-to-serial conversion and orthogonal phase shift keying inverse mapping demodulation on the M×L decryption matrix in sequence, and outputs binary output data.

5. A V-OFDM secure transmission device based on a dynamic feedback chaotic system, characterized in that, include: Memory: A computer program for a V-OFDM secure transmission method based on a dynamic feedback chaotic system as described in any one of claims 1-3, and is a computer-readable device; Processor: Used to implement the V-OFDM secure transmission method based on a dynamic feedback chaotic system as described in any one of claims 1-3 when executing the computer program.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of the V-OFDM secure transmission method based on a dynamic feedback chaotic system as described in any one of claims 1-3.

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