A polarization mode dispersion based encryption transmission method and system

Abstract

This invention discloses an encrypted transmission method and system based on polarization mode dispersion (PMD). The method includes, executed by the transmitting end, acquiring an original signal and mapping the original signal using a chaotic model to obtain a chaotic sequence; introducing PMD coefficients to perform encrypted dynamic perturbation processing on the chaotic sequence to obtain a PMD perturbation matrix; and multiplying the PMD perturbation matrix and the original signal to obtain an encrypted signal. This invention improves the transmission security of communication systems, while maintaining digital domain compatibility with existing systems, exhibiting low complexity and good security performance.

Description

Technical Field

[0001] This invention belongs to the field of optical fiber communication technology, and in particular relates to an encrypted transmission method and system based on polarization mode dispersion. Background Technology

[0002] With the development of the information network era, the importance of information security has become increasingly prominent in all walks of life and even in people's daily lives. This has led to the development of a wealth of information encryption and decoding methods. Among them, optical information encryption strategies have the inherent advantage of high-speed parallelism, enabling rapid and low-power processing of large amounts of information data. Furthermore, photons possess multiple degrees of freedom, such as amplitude, phase, wavelength, polarization, and orbital angular momentum, serving as information carriers. Therefore, research on information encryption using photons has received widespread attention and is expected to play an irreplaceable role in applications such as civilian information security communication, aerospace remote sensing, and quantum information warfare.

[0003] Physical layer encryption (PLA), as an emerging technology, utilizes the physical characteristics of communication channels (such as polarization and phase) for encryption. It effectively prevents various attacks and enhances system security, providing efficient and real-time security guarantees. PLA achieves encryption by altering the physical properties of the signal, independent of traditional encryption algorithms. It mostly employs digital domain chaotic models to perturb different physical dimensions, achieving signal encryption. Chaotic models, used in communication systems since the 1990s, represent seemingly random motion that actually occurs within a deterministic nonlinear system, producing near-random behavior without the addition of any random factors. Because chaotic sequences are highly sensitive to initial values—even slight changes can significantly impact the generated sequence—the sensitivity and pseudo-randomness of chaos are leveraged to effectively encrypt signals, ensuring data security in optical communication.

[0004] In current domestic and international research, traditional physical layer encryption methods mainly utilize the characteristics of bits, wavelength, phase, and frequency for encryption. These methods typically require high equipment costs and complex optical components, and have compatibility issues with existing systems, limiting their widespread application in practice.

[0005] Therefore, there is an urgent need for an encrypted transmission method and system that can improve the security of communication systems, achieve compatibility with existing systems, and improve the transmission reliability of optical communication systems. Summary of the Invention

[0006] The purpose of this invention is to provide an encrypted transmission method and system based on polarization mode dispersion. This method can improve the system transmission security, while being compatible with existing systems in the digital domain, with low complexity and good security performance.

[0007] To achieve the above objectives, the present invention employs the following technical solution:

[0008] In a first aspect, the present invention provides an encrypted transmission method based on polarization mode dispersion, executed by a sending end, comprising:

[0009] The original signal is acquired, and a chaotic model is used to map and process the original signal to obtain a chaotic sequence.

[0010] The polarization mode dispersion coefficient is introduced to perform encrypted dynamic perturbation processing on the chaotic sequence, resulting in the polarization mode dispersion perturbation matrix;

[0011] The encrypted signal is obtained by multiplying the polarization mode dispersion perturbation matrix with the original signal.

[0012] Optionally, the chaos model is a 2D-LSIMM model.

[0013] Optionally, the chaotic sequence includes a first sequence and a second sequence, which are respectively expressed by the following formulas:

[0014] ;

[0015] in, This represents the state value at time t in the first sequence; This represents the state value at time t in the second sequence; Indicates a time interval; Indicating the first sequence The state value at any given time; Indicating the second sequence The state value at any given time; This indicates a modulo operation; α, β, δ, and γ are all control parameters.

[0016] Optionally, the step of introducing polarization mode dispersion coefficients to perform encrypted dynamic perturbation processing on the chaotic sequence to obtain a polarization mode dispersion perturbation matrix includes:

[0017] Discretize the first sequence and the second sequence in the chaotic sequence respectively to obtain the first discrete sequence and the second discrete sequence.

[0018] Based on the first discrete sequence and the second discrete sequence, the first polarization angle and the second polarization angle are calculated respectively.

[0019] The first dynamic polarization mode dispersion coefficient is calculated based on the first discrete sequence and the polarization mode dispersion coefficient, and the second dynamic polarization mode dispersion coefficient is calculated based on the second discrete sequence and the polarization mode dispersion coefficient.

[0020] The first dynamic phase difference and the second dynamic phase difference are calculated based on the first dynamic polarization mode dispersion coefficient and the second dynamic polarization mode dispersion coefficient, respectively.

[0021] A first polarization matrix is ​​constructed based on the first dynamic phase difference and the first polarization angle;

[0022] A second polarization matrix is ​​constructed based on the second dynamic phase difference and the second polarization angle;

[0023] Based on the first polarization matrix and the second polarization matrix, construct the polarization mode dispersion perturbation matrix.

[0024] Optionally, the formula for the discretization process is expressed as:

[0025] ;

[0026] in, This represents the discrete value at time t in the first discrete sequence; This represents the discrete value at time t in the second discrete sequence.

[0027] Optionally, the formulas for the first polarization angle and the second polarization angle are expressed as follows:

[0028] ;

[0029] in, This represents the first polarization angle at time t; This represents the second polarization angle at time t; , These represent the first initial polarization angle and the second initial polarization angle, respectively. , Both represent weight parameters.

[0030] Optionally, the calculation formulas for the first dynamic polarization mode dispersion coefficient and the second dynamic polarization mode dispersion coefficient are respectively expressed as follows:

[0031] ;

[0032] in, This represents the dispersion coefficient of the first dynamic polarization mode at time t; This represents the dispersion coefficient of the second dynamic polarization mode at time t; Represents the polarization mode dispersion coefficient; , Both represent weight parameters.

[0033] Optionally, the calculation formulas for the first dynamic phase difference and the second dynamic phase difference are respectively expressed as follows:

[0034] ;

[0035] in, This represents the first dynamic phase difference at time t; This represents the second dynamic phase difference at time t; Indicates the wavelength of the laser; This indicates the length of the optical fiber.

[0036] Optionally, the polarization mode dispersion perturbation matrix is ​​constructed as follows:

[0037] ;

[0038] ;

[0039] ;

[0040] in, Let represent the polarization mode dispersion perturbation matrix at time t; This represents the first polarization matrix at time t; This represents the second polarization matrix at time t; This represents the first polarization angle at time t; denoted by t, the second polarization angle at time t; e represents the natural constant; j represents the imaginary unit.

[0041] In a second aspect, the present invention provides an encrypted transmission system based on polarization mode dispersion (PMD) for implementing the encrypted transmission method based on PMD as described in the first aspect, comprising:

[0042] The initial module acquires the original signal and uses a chaotic model to map and process the original signal to obtain a chaotic sequence;

[0043] The encryption preprocessing module is used to introduce polarization mode dispersion coefficients to perform encryption dynamic perturbation processing on the chaotic sequence, and obtain the polarization mode dispersion perturbation matrix.

[0044] The encryption module is used to multiply the polarization mode dispersion perturbation matrix and the original signal to obtain the encrypted signal.

[0045] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0046] This invention provides an encrypted transmission method and system based on polarization mode dispersion (PMD). The method first acquires the original signal at the transmitting end and maps it using a chaotic model to obtain a chaotic sequence. Next, PMD coefficients are introduced to perform encrypted dynamic perturbation processing on the chaotic sequence, resulting in a PMD perturbation matrix. Then, the PMD perturbation matrix and the original signal are multiplied to obtain the encrypted signal. At the receiving end, the inverse matrix of the PMD perturbation matrix is ​​used to decrypt the encrypted signal, yielding the original signal. This invention creatively utilizes the unique characteristics of PMD to employ matrix perturbation in the digital domain (PMD perturbation matrix) as an encryption method in optical fiber transmission. By using a 2D-LSIMM model to perform overall matrix perturbation of the PMD parameters and performing dynamic encoding of PMD in the digital domain, it achieves a high level of security improvement in optical fiber communication systems. Chaotic sequences generated using chaotic models are unpredictable and highly random, which improves the security performance of the system. The method of encrypting signals can be quickly adjusted by changing the DSP algorithm or initial conditions. It is suitable for rapidly developing large-capacity communication systems to improve the security of system transmission. At the same time, it is compatible with existing systems in the digital domain, with low complexity and good security performance. Attached Figure Description

[0047] Figure 1 The diagram shown is a flowchart of an encrypted transmission method based on polarization mode dispersion in one embodiment of the present invention.

[0048] Figure 2 The diagram shown is a flowchart of an encrypted transmission method based on polarization mode dispersion in one embodiment of the present invention.

[0049] Figure 3 The diagram shown is a schematic flowchart of the encryption dynamic perturbation processing in one embodiment of the present invention;

[0050] Figure 4 The diagram shown is an overall architecture block diagram of an encrypted transmission system based on polarization mode dispersion in one embodiment of the present invention.

[0051] Figure 5 The diagram shown is an offline DSP flowchart of the transmitting and receiving ends in one embodiment of the present invention;

[0052] Figure 6 The diagram shown is a schematic representation of the 16QAM constellation diagram before and after encryption in one embodiment of the present invention.

[0053] Figure 7 The diagram shown is a receiver constellation recovery diagram in one embodiment of the present invention;

[0054] Figure 8 The figure shown is a frame-by-frame trend chart of the bit error rate in one embodiment of the present invention;

[0055] Figure 9 The figure shown is a frame-by-frame trend chart of the symbol error rate in one embodiment of the present invention. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0057] Example 1

[0058] like Figure 1 As shown in the figure, this embodiment of the invention introduces an encrypted transmission method based on polarization mode dispersion (PMD), which is executed by the sending end:

[0059] S1: Obtain the original signal and use a chaotic model to map and process the original signal to obtain a chaotic sequence;

[0060] S2: Introduce polarization mode dispersion coefficients to perform encrypted dynamic perturbation processing on chaotic sequences to obtain polarization mode dispersion perturbation matrix;

[0061] S3: Multiply the polarization mode dispersion perturbation matrix and the original signal to obtain the encrypted signal;

[0062] like Figure 2 As shown in the figure, this embodiment proposes an encrypted transmission method based on polarization mode dispersion. At the transmitting end, a chaotic sequence is generated using a chaotic model, and the chaotic sequence is dynamically perturbed by polarization mode dispersion. After introducing the polarization mode dispersion perturbation, signal encryption in the digital domain is achieved through the polarization mode dispersion perturbation matrix. At the receiving end, the reverse process is carried out. The chaotic sequence is reconstructed using the same key as at the transmitting end to drive the chaotic model, and the inverse polarization mode dispersion perturbation matrix is ​​solved to perform decryption. This realizes dynamic encoding and decoding in the digital domain, i.e., encrypted transmission.

[0063] In this embodiment, step S1 involves acquiring the original signal and mapping it using a chaotic model to obtain a chaotic sequence, specifically including:

[0064] S11: Obtain the raw signal:

[0065] Obtain the original dataset from the sending end, wherein the original dataset includes first original data and second original data;

[0066] The original dataset is converted from serial to parallel, and the binary string is converted from serial to parallel to obtain the first and second original data in parallel.

[0067] The first and second raw data, which are in parallel, are modulated by two I / Q channels to form the first polarization component. Second polarization state component ;

[0068] The original signal is obtained based on the first polarization state component and the second polarization state component. ;

[0069] Specifically, the original signal The formula is expressed as:

[0070] ;

[0071] in, and The first polarization state component and the second polarization state component are respectively the electric field components in the x and y directions; and , , and , respectively, represent the electric field amplitudes in the x and y directions; e is the natural constant; j represents the imaginary unit; and These are the phases in the x and y directions, respectively.

[0072] S12: The chaotic model is mapped to obtain a chaotic sequence:

[0073] The chaotic sequence includes a first sequence and a second sequence, which are obtained through mapping processing of the chaotic model, expressed by the formula:

[0074] ;

[0075] in, This represents the state value at time t in the first sequence; This represents the state value at time t in the second sequence; Indicates a time interval; Indicating the first sequence The state value at any given time; Indicating the second sequence The state value at any given time; The modulo operation is indicated; α, β, δ and γ are all control parameters. Among them, α≥0, β∊[0,1], γ≥0. When α=3.85, β=0.72, γ=5.10, and δ=2.95, 2D-LSIMM exhibits chaotic behavior. mod is the modulo operation, which mainly controls the output range to [0,1].

[0076] In this embodiment, the chaotic model adopts the 2D-LSIMM (Two-Dimensional Logistic Sine ICMICModulation Map) model. Its coupling modulation method allows the logical mapping, sine mapping and ICMIC mapping, which only have simple chaotic behavior, to be completely mixed. This not only expands the key space, but also provides a more secure encryption scheme.

[0077] In this embodiment, as Figure 3 Step S2, as shown, involves introducing polarization mode dispersion coefficients to perform encrypted dynamic perturbation processing on the chaotic sequence to obtain the polarization mode dispersion perturbation matrix. Specific steps include:

[0078] S21: Discretize the first sequence and the second sequence in the chaotic sequence respectively to obtain the first discrete sequence and the second discrete sequence.

[0079] S22: Calculate the first polarization angle and the second polarization angle based on the first discrete sequence and the second discrete sequence, respectively;

[0080] S23: Calculate the first dynamic polarization mode dispersion coefficient based on the first discrete sequence and the polarization mode dispersion coefficient, and calculate the second dynamic polarization mode dispersion coefficient based on the second discrete sequence and the polarization mode dispersion coefficient;

[0081] S24: Calculate the first dynamic phase difference and the second dynamic phase difference based on the first dynamic polarization mode dispersion coefficient and the second dynamic polarization mode dispersion coefficient, respectively;

[0082] S25: Construct the first polarization matrix based on the first dynamic phase difference and the first polarization angle;

[0083] S26: Construct a second polarization matrix based on the second dynamic phase difference and the second polarization angle;

[0084] S27: Construct the polarization mode dispersion perturbation matrix based on the first polarization matrix and the second polarization matrix.

[0085] Specifically, in step S21, the first discrete sequence and the second discrete sequence can be used to determine the polarization mode dispersion coefficient. Dynamic perturbation is applied to influence the group delay difference and phase difference of the polarization state, achieving dynamic encryption. Specifically, for the time series (first and second sequences) generated by the chaotic model, a first and second discrete sequence are generated using an appropriate discretization method (such as the Euler method). The discrete values ​​in these sequences are expressed by the following formula:

[0086] ;

[0087] in, This represents the discrete value at time t in the first discrete sequence; Represents the discrete value at time t in the second discrete sequence; 10 9 The introduction of this is to enhance randomness;

[0088] After processing by the above formula, the discrete values ​​in the first and second discrete sequences change to random numbers in the range (0, 100), representing the polarization mode dispersion coefficient. It changes randomly and dynamically within this range.

[0089] The polarization mode dispersion coefficient is defined as the broadening of optical fiber per kilometer due to the wavelength differential group delay, and its unit is ps / km. 1 / 2 The polarization mode dispersion coefficient gives the degree of time broadening of the polarization mode of an optical signal under random birefringence within a unit fiber length (1 km), and the unit is ps.

[0090] Specifically, S22: Calculate the first polarization angle and the second polarization angle based on the first discrete sequence and the second discrete sequence, respectively. The calculation formula is expressed as follows:

[0091] ;

[0092] in, This represents the first polarization angle at time t, i.e., the first polarization state component. The polarization angle; This represents the second polarization angle at time t, i.e., the second polarization state component. The polarization angle; , These represent the first initial polarization angle and the second initial polarization angle, respectively. , Both represent weight parameters, which adjust the influence of the chaotic sequence on the polarization angle.

[0093] Specifically, the formulas for calculating the dispersion coefficients of the first and second dynamic polarization modes in S23 are expressed as follows:

[0094] ;

[0095] in, This represents the dispersion coefficient of the first dynamic polarization mode at time t; This represents the dispersion coefficient of the second dynamic polarization mode at time t; Represents the polarization mode dispersion coefficient; , Both represent weight parameters.

[0096] Specifically, the calculation formulas for the first dynamic phase difference and the second dynamic phase difference in S24 are expressed as follows:

[0097] ;

[0098] Will Substituting the values, the above formula expands to:

[0099] ;

[0100] in, This represents the first dynamic phase difference at time t; This represents the second dynamic phase difference at time t; Indicates the wavelength of the laser; This indicates the length of the optical fiber.

[0101] Specifically, step S25: Construct a first polarization matrix based on the first dynamic phase difference and the first polarization angle, the construction formula of which is expressed as:

[0102] ;

[0103] in, Let represent the first polarization matrix at time t.

[0104] Specifically, step S26: Construct a second polarization matrix based on the second dynamic phase difference and the second polarization angle, the construction formula of which is expressed as:

[0105] ;

[0106] in, Let represent the second polarization matrix at time t.

[0107] Specifically, step S27: Construct the polarization mode dispersion perturbation matrix, expressed by the following formula:

[0108] ;

[0109] in, Let represent the polarization mode dispersion perturbation matrix at time t.

[0110] In this embodiment, step S3: multiply the polarization mode dispersion perturbation matrix and the original signal to obtain the encrypted signal, as specifically expressed by the formula:

[0111] ;

[0112] in, This represents the encrypted signal at time t.

[0113] Furthermore, because the refractive index of optical fiber fluctuates randomly due to environmental influences, the pulse broadening of the optical signal is also random. This polarization mode dispersion perturbation matrix is ​​used to encrypt the channel data. By introducing a random sequence generated by a chaotic model, the polarization mode dispersion coefficient of the optical signal is dynamically perturbed, causing the polarization state of the optical signal to change dynamically over time. This dynamic change introduces complex perturbations, making the signal difficult to crack in both the polarization and time domains.

[0114] In this embodiment, step S4: At the receiving end, the encrypted signal is decrypted by using the inverse matrix of the polarization mode dispersion perturbation matrix to obtain the original signal. Specifically:

[0115] The decryption process requires using the initial conditions of the first and second discrete sequences to recover the dynamic polarization angles and phases, reconstruct the dynamic polarization angles (first and second polarization angles) and the first and second dynamic polarization mode dispersion coefficients, thereby constructing the inverse Jones matrix and the inverse matrix of the polarization mode dispersion perturbation matrix. The inverse matrix is ​​then applied to the received encrypted signal to recover the original signal.

[0116] Specifically, the inverse matrix is ​​constructed based on the polarization angle and phase difference; the inverse matrix of the first polarization matrix at time t is... :

[0117] ;

[0118] Expand to obtain,

[0119] .

[0120] Similarly, for the second polarization matrix at time t have:

[0121] ;

[0122] Expand to obtain,

[0123] .

[0124] By combining the inverses of the first and second polarization matrices, the inverse of the polarization mode dispersion perturbation matrix is ​​obtained. :

[0125] .

[0126] For chaotic sequences, we still take α=3.85, β=0.72, γ=5.10, δ=2.95, and apply the inverse of the polarization mode dispersion perturbation matrix to the received encrypted signal. Decryption is performed to obtain the decrypted signal. for:

[0127] ;

[0128] Due to the invertibility of matrices, we have:

[0129] .

[0130] Specifically, such as Figure 2 As shown, modulation and demodulation processes are performed after signal encryption and before signal decryption, respectively. This modulation and demodulation process is implemented in the transceiver stage of the coherent communication link: the encrypted data is first sent to the coherent optical communication system for coherent modulation, transmitted through the optical fiber channel, and then coherently demodulated at the receiving end. Subsequently, the demodulated data is decrypted to restore the original signal.

[0131] At this point, the original signal was obtained, the polarization state of the input signal was recovered, and the signal was successfully decrypted.

[0132] In summary, this embodiment proposes an encrypted transmission method based on polarization mode dispersion (PMD). PMD is introduced as an encryption mechanism into the field of digital signal processing in optical communication, utilizing the time delay characteristics of different polarization states caused by polarization and group velocity mismatch during fiber transmission. By introducing a two-dimensional chaotic system (chaotic model), the generated sequence is used to dynamically adjust the polarization angle, thereby perturbing the Jones matrix to achieve encryption. The receiving end successfully decrypts the signal by reconstructing the chaotic sequence and calculating the inverse Jones matrix. This method combines the physical characteristics of PMD encryption with the dynamic characteristics of chaotic systems, providing a strong encryption method. By adjusting the initial conditions and dynamic parameters of the chaotic system, the security and randomness of the system can be further enhanced.

[0133] Example 2

[0134] This invention provides an encrypted transmission system based on polarization mode dispersion (PMD) to implement the encrypted transmission method based on PMD described in Embodiment 1, comprising:

[0135] The initial module acquires the original signal and uses a chaotic model to map and process the original signal to obtain a chaotic sequence;

[0136] The encryption preprocessing module is used to introduce polarization mode dispersion coefficients to perform encryption dynamic perturbation processing on the chaotic sequence, and obtain the polarization mode dispersion perturbation matrix.

[0137] The encryption module is used to multiply the polarization mode dispersion perturbation matrix and the original signal to obtain the encrypted signal;

[0138] Specifically, the encrypted transmission system also includes a decryption module, which uses the inverse matrix of the polarization mode dispersion perturbation matrix to decrypt the encrypted signal in reverse process to obtain the original signal.

[0139] Specifically, such as Figure 4 As shown in the figure, this diagram illustrates the overall architecture of an encrypted transmission system based on polarization mode dispersion.

[0140] At the transmitting end, the raw data is generated in the offline DSP (Digital Signal Processor). The initial module completes two core tasks: first, it acquires random binary raw data, processes it to generate the raw signals with the first polarization and the second polarization; second, it generates chaotic sequences corresponding to the two polarizations based on the 2D-LSIMM chaotic model for subsequent encryption processing.

[0141] The encryption preprocessing module receives the chaotic sequence output by the initial module, introduces the polarization mode dispersion coefficient to perform encryption dynamic perturbation processing on the chaotic sequence, and completes the four steps of sequence discretization, parameter perturbation, matrix construction and matrix synthesis in sequence, finally obtaining the polarization mode dispersion perturbation matrix and outputting it to the encryption module.

[0142] The encryption module receives two raw signals output from the initialization module and an encryption matrix output from the encryption preprocessing module. It multiplies the encryption matrix with the raw signals to encrypt the raw signals and generate an encrypted signal. The encrypted signal is then processed and sent to the optical fiber transmission channel for long-distance transmission.

[0143] At the receiving end, after the encrypted signal is transmitted through the optical fiber transmission channel, it undergoes the offline DSP processing flow. The decryption module uses the key parameters synchronized with the sending end to reconstruct the inverse matrix of the polarization mode dispersion perturbation matrix, performs the reverse decryption operation on the encrypted signal, and finally recovers the original signal, completing the entire encrypted transmission process.

[0144] Furthermore, such as Figure 5 As shown, this flowchart illustrates the offline DSP flowcharts for the transmitting and receiving ends, and consists of two parts: the transmitting end DSP flowchart and the receiving end DSP flowchart.

[0145] At the transmitting end, the process includes processing such as original signal input, 16QAM (16 Quadrature Amplitude Modulation) mapping, two-dimensional chaotic system perturbation, discretization, pulse shaping, and upsampling to generate a transmission signal that meets the transmission requirements.

[0146] At the receiving end, the signal sampled in the offline digital domain first undergoes resampling and IQ quadrature imbalance compensation to suppress constellation distortion. Then, dispersion compensation is performed to eliminate inter-symbol interference in fiber optic transmission. Next, frequency offset estimation and compensation are performed to suppress the overall rotation of the constellation. Then, polarization demultiplexing and channel equalization are completed to gradually shape the constellation points. Finally, carrier phase recovery is performed to eliminate residual phase noise, and data decision and bit error rate calculation are performed.

[0147] This embodiment not only uses a two-dimensional chaotic system to encrypt the signal perturbation at the transmitting end, but also combines multiple digital signal processing algorithms at the receiving end to complete signal compensation, recovery and demodulation, thereby ensuring the reliability and effectiveness of the encrypted transmission method.

[0148] Example 3

[0149] This embodiment takes randomly generated binary data as an example, and combines the encryption transmission method based on polarization mode dispersion in Embodiment 1 and the specific embodiment in Embodiment 2 to conduct offline digital signal processing simulation analysis on the system proposed in this invention, so as to verify the feasibility of the method in the process of encryption at the transmitting end, channel transmission and recovery at the receiving end, and obtain the following experimental results;

[0150] Experiment Description: The transmitting end first performs 16QAM mapping on the original data, converting the input bit sequence into complex modulation symbols. Then, a two-dimensional chaotic system is introduced to perturb the mapped signal, achieving encrypted preprocessing of the transmitted signal. Based on this, the perturbed signal is sequentially discretized, pulse-shaped, and upsampled to generate a transmitted signal that meets transmission requirements. The receiving end, after receiving the signal, sequentially performs offline DSP processing including resampling, IQ quadrature imbalance compensation, dispersion compensation, frequency offset estimation, equalization and demultiplexing, carrier phase recovery, and 16QAM demapping to recover and demodulate the received signal.

[0151] Experimental results: such as Figure 6 As shown in the figure, the analysis of the 16QAM constellation diagram before and after encryption is presented. The figure also shows the simulation results of the dual-polarization chaotic encrypted communication system during signal processing and encryption at the transmitting end. Figure 6 Figures (a), (b), and (c) correspond to the first polarization, respectively; figures (d), (e), and (f) correspond to the second polarization, respectively. Each sub-figure reflects the original signal, the encrypted signal, the shaped signal, and the characteristics of the chaotic sequence.

[0152] First, as shown in Figure (a), the constellation diagram of the original signal with the first polarization (i.e., the original X-polarization) is presented. This constellation diagram exhibits a typical 16QAM modulation structure, with constellation points regularly distributed in the complex plane, indicating that the signal modulated at the transmitting end has a clear modulation state and a stable symbol structure, which can be used as the input signal for subsequent encryption processing.

[0153] Subsequently, chaotic perturbations were introduced into the original modulated signal for encryption. Figure (b) shows the constellation distribution of the original first polarization signal after chaotic encryption (i.e., encrypted X-polarization). It can be seen that the originally regularly distributed 16QAM constellation points are significantly disturbed, exhibiting an approximately continuous random distribution in the complex plane, making the original modulation structure difficult to directly identify. This demonstrates that chaotic perturbations can effectively disrupt the original constellation structure, thereby achieving the concealment and protection of the original information.

[0154] After signal encryption, the signal is subjected to RRC pulse shaping. As shown in Figure (c), the constellation distribution of the first polarization encrypted signal after RRC pulse shaping (i.e., X-polarization after RRC shaping) is as follows. Due to the inter-symbol correlation introduced by pulse shaping filtering, the constellation points exhibit a ring-shaped diffusion distribution in the complex plane, but the overall structure still maintains the random structure after chaotic perturbation, further indicating that the signal remains encrypted after shaping.

[0155] Similar to the first polarization, the lower row of figures shows the simulation results for the second polarization. As shown in Figure (d), the constellation diagram of the original signal of the second polarization (i.e., the original Y-polarization) also presents a regular 16QAM constellation distribution structure, indicating that both polarization signals use the same modulation method at the transmitting end.

[0156] Figure (e) shows the constellation diagram of the original signal with second polarization after chaotic encryption (i.e., encrypted Y-polarization). Similar to the encryption result of the first polarization, the constellation points after encryption exhibit a random distribution in the complex plane, and the original modulation structure is significantly broken down, thereby effectively improving the confidentiality of the signal.

[0157] Figure (f) shows the constellation distribution of the second polarization encrypted signal after RRC pulse shaping (i.e., Y-polarization after RRC shaping). It can be seen that after pulse shaping, the constellation points exhibit certain diffusion characteristics, but the overall distribution remains random after chaotic perturbation, indicating that the system does not destroy the encryption effect while completing signal shaping.

[0158] like Figure 7As shown in the figure, this figure presents the constellation recovery result after digital signal processing at the receiver. In the figure, the horizontal axis Real represents the real part, the vertical axis Imag represents the imaginary part, and BER represents the bit error rate. The left figure shows the recovered constellation diagram of the first polarization (i.e., X Channel), and the right figure shows the recovered constellation diagram of the second polarization (i.e., Y Channel). It can be seen from the figure that after offline DSP processing such as receiver resampling, IQ imbalance compensation, dispersion compensation, frequency offset estimation, equalization and demultiplexing, and carrier phase recovery, both polarization signals can re-form a clear 16QAM constellation distribution structure. Although there is still a certain degree of diffusion around the constellation points, the overall constellation points have clearly clustered near the theoretical decision positions, indicating that the receiver can effectively recover the signal structure encrypted by the transmitter after chaotic perturbation.

[0159] Furthermore, the calculation results shown in the figure indicate that the bit error rate of the first polarization (i.e., the X Channel) is approximately 7.65 × 10⁻⁶. -3 The bit error rate of the second polarization (i.e., the Y Channel) is approximately 7.46 × 10⁻⁶. -3 The bit error rates of the two polarization signals are basically the same, indicating that the dual-polarization system has good stability and consistency during transmission. This result also demonstrates that the chaotic encryption and polarization multiplexing transmission scheme proposed in this invention, while handling signal security disturbances, can still achieve effective recovery at the receiving end through corresponding digital signal processing, thereby ensuring normal demodulation and information extraction of the communication system.

[0160] In summary, the simulation results demonstrate that introducing a chaotic encryption mechanism into the dual-polarization signal transmission system effectively disrupts the constellation structure of the original modulated signal, making it difficult to directly identify the original information from the undecrypted signal. Furthermore, the key sequence generated by the chaotic system possesses good randomness and complexity, serving as a key parameter in the encryption process and thus enhancing system security. These results indicate that the polarization mode dispersion-based encryption method proposed in this invention can effectively encrypt the original signal, providing a foundation for subsequent secure transmission and signal recovery.

[0161] Furthermore, to evaluate the system's performance stability across multiple data frames, statistical analysis was conducted on the changes in bit error rate (BER) and symbol error rate (SER) with frame variation.

[0162] like Figure 8As shown in the figure, the bit error rate (BER) changes frame by frame. In the figure, Frame Number represents the frame sequence number; the blue curve represents the BER change of the first polarization (i.e., X Channel), and the red curve represents the BER change of the second polarization (i.e., Y Channel); the blue and red dashed lines (Mean BER X = 7.65e-03) represent the average bit error rate of 10 frames of data from X and Y Channels. It can be seen from the figure that in the initial frame stage, the BER is relatively high because the system equalization and carrier recovery processes have not yet fully converged; as the DSP processing gradually stabilizes, the BER of both signals rapidly decreases and remains stable in subsequent frames.

[0163] Statistical results show that the average bit error rate of the first polarization (i.e., X Channel) is approximately 7.65 × 10⁻⁶. -3 The average bit error rate of the second polarization (i.e., the Y Channel) is approximately 7.46 × 10⁻⁶. -3 .

[0164] like Figure 9 The figure shows the frame-by-frame trend of the symbol error rate (SER). The blue curve represents the SER change for the first polarization (X Channel), and the red curve represents the SER change for the second polarization (Y Channel). The blue and red dashed lines (Mean SER X = 7.65e-03) represent the average bit symbol error rate (BER) of 10 frames of data from the X and Y Channels. It can be seen that the SER is high in the initial stage of the system, but as the equalization and carrier recovery at the receiver gradually stabilize, the SER rapidly decreases and tends to stabilize. Statistical results show that the average SER for the first polarization (X Channel) is approximately 1.91 × 10⁻⁶. -2 The average symbol error rate of the second polarization (i.e., the Y Channel) is approximately 1.85 × 10⁻⁶. -2 .

[0165] In summary, the polarization mode dispersion-based encrypted transmission method provided by this invention can reconstruct the corresponding 16QAM modulation constellation structure of dual-polarization signals after transmission through the combination of chaotic encryption processing at the transmitting end and offline DSP recovery process at the receiving end. This verifies the feasibility and effectiveness of the polarization mode dispersion-based encrypted transmission system proposed in this invention in practical communication systems.

[0166] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0167] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0168] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0169] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for encrypted transmission based on polarization mode dispersion, characterized in that, Executed by the sender, including: The original signal is acquired, and a chaotic model is used to map and process the original signal to obtain a chaotic sequence. The polarization mode dispersion coefficient is introduced to perform encrypted dynamic perturbation processing on the chaotic sequence, resulting in the polarization mode dispersion perturbation matrix; The polarization mode dispersion perturbation matrix is ​​multiplied by the original signal to obtain the encrypted signal to be transmitted.

2. The encrypted transmission method based on polarization mode dispersion according to claim 1, characterized in that, The chaos model adopted is the 2D-LSIMM model.

3. The encrypted transmission method based on polarization mode dispersion according to claim 2, characterized in that, The chaotic sequence includes a first sequence and a second sequence, which are expressed by the following formulas: ； in, This represents the state value at time t in the first sequence; This represents the state value at time t in the second sequence; Indicates a time interval; Indicating the first sequence The state value at any given time; Indicating the second sequence The state value at any given time; This indicates a modulo operation; α, β, δ, and γ are all control parameters.

4. The encrypted transmission method based on polarization mode dispersion according to claim 3, characterized in that, The introduction of polarization mode dispersion coefficients to perform encrypted dynamic perturbation processing on the chaotic sequence yields a polarization mode dispersion perturbation matrix, including: Discretize the first sequence and the second sequence in the chaotic sequence respectively to obtain the first discrete sequence and the second discrete sequence. Based on the first discrete sequence and the second discrete sequence, the first polarization angle and the second polarization angle are calculated respectively. The first dynamic polarization mode dispersion coefficient is calculated based on the first discrete sequence and the polarization mode dispersion coefficient, and the second dynamic polarization mode dispersion coefficient is calculated based on the second discrete sequence and the polarization mode dispersion coefficient. The first dynamic phase difference and the second dynamic phase difference are calculated based on the first dynamic polarization mode dispersion coefficient and the second dynamic polarization mode dispersion coefficient, respectively. A first polarization matrix is ​​constructed based on the first dynamic phase difference and the first polarization angle; A second polarization matrix is ​​constructed based on the second dynamic phase difference and the second polarization angle; Based on the first polarization matrix and the second polarization matrix, construct the polarization mode dispersion perturbation matrix.

5. The encrypted transmission method based on polarization mode dispersion according to claim 4, characterized in that, The formula for the discretization process is expressed as follows: ； in, This represents the discrete value at time t in the first discrete sequence; This represents the discrete value at time t in the second discrete sequence.

6. The encrypted transmission method based on polarization mode dispersion according to claim 5, characterized in that, The formulas for the first polarization angle and the second polarization angle are expressed as follows: ； in, This represents the first polarization angle at time t; This represents the second polarization angle at time t; , These represent the first initial polarization angle and the second initial polarization angle, respectively. , Both represent weight parameters.

7. The encrypted transmission method based on polarization mode dispersion according to claim 5, characterized in that, The calculation formulas for the first dynamic polarization mode dispersion coefficient and the second dynamic polarization mode dispersion coefficient are expressed as follows: ； in, This represents the dispersion coefficient of the first dynamic polarization mode at time t; This represents the dispersion coefficient of the second dynamic polarization mode at time t; Represents the polarization mode dispersion coefficient; , Both represent weight parameters.

8. The encrypted transmission method based on polarization mode dispersion according to claim 7, characterized in that, The calculation formulas for the first dynamic phase difference and the second dynamic phase difference are expressed as follows: ； in, This represents the first dynamic phase difference at time t; This represents the second dynamic phase difference at time t; Indicates the wavelength of the laser; This indicates the length of the optical fiber.

9. The encrypted transmission method based on polarization mode dispersion according to claim 8, characterized in that, The polarization mode dispersion perturbation matrix is ​​constructed as follows: ； ； ； in, Let represent the polarization mode dispersion perturbation matrix at time t; This represents the first polarization matrix at time t; This represents the second polarization matrix at time t; This represents the first polarization angle at time t; denoted by t, the second polarization angle at time t; e represents the natural constant; j represents the imaginary unit.

10. An encrypted transmission system based on polarization mode dispersion, characterized in that, include: The initial module acquires the original signal and uses a chaotic model to map and process the original signal to obtain a chaotic sequence; The encryption preprocessing module is used to introduce polarization mode dispersion coefficients to perform encryption dynamic perturbation processing on the chaotic sequence, and obtain the polarization mode dispersion perturbation matrix. The encryption module is used to multiply the polarization mode dispersion perturbation matrix and the original signal to obtain the encrypted signal.

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