Time-delay Feature Extraction Method, System, Device and Medium Based on Weight Similarity

Abstract

The present invention belongs to the field of physical layer security, and discloses a time-delay feature extraction method, system, device and medium based on weight similarity. The method includes: generating a chaotic time series as a data set; constructing an echo state network; selecting multiple time delays, and constructing multiple data set pairs according to different time delays; translating a certain amount for each data set pair to generate a corresponding data set pair; training the network for two data set pairs with the same time delay respectively, and extracting weights; performing similarity measurement on the two extracted weight matrices; and inferring the time-delay information according to the statistical analysis result of the similarity measurement. The present invention can analyze the time-delay key of a two-dimensional or even higher-dimensional chaotic system, not limited to one-dimensional time delay, and does not require prior knowledge of the chaotic system structure and mathematical model. Only a small amount of data is needed to analyze the key, saving computing power and having high accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of physical layer security, and particularly relates to a time-delay feature extraction method, system, device and medium based on weight similarity. Background Art

[0002] In an optical chaotic secure communication system, a chaotic carrier is usually generated by a laser diode under the action of optoelectronic / all-optical time-delay feedback. One of the most important security considerations is the concealment of TDS (Time Delay Signature). So far, statistical analysis methods such as autocorrelation function and delay mutual information are usually used to reveal TDS. However, when the nonlinearity of the chaotic system increases, the effectiveness of these methods will decrease. At the same time, certain TDS hiding strategies have been designed based on statistical analysis. Convolutional neural networks have shown their effectiveness in TDS extraction of high-loop nonlinear chaotic systems. However, this method depends on the understanding of the detailed structure of the chaotic system.

[0003] Optical or electro-optic time-delay chaotic systems have unique advantages such as high dimensionality, high dynamic complexity and significant broadband spectrum, providing potential for high-speed data secure transmission. Since the early demonstration of optical chaotic secure communication, it has been widely studied and has become one of the most feasible hardware encryption methods. Without a matching device or parameter setting, it is difficult for eavesdroppers to recover the message embedded in the chaotic carrier. Currently, there are mainly two types of optical chaotic systems. One is based on the internal nonlinearity of the laser. When a semiconductor laser is subjected to external perturbations such as all-optical time-delay feedback and external optical injection, chaos will be generated. The other is an optoelectronic oscillator chaotic system, where chaos is generated through external nonlinear optoelectronic time-delay feedback. Generally speaking, these systems can be described by time-delay differential equations:

[0004]

[0005] where x(t) is the state variable and x(t - τ) is the time-delay variation. Usually, the cyclic delay parameter τ (i.e., TDS) is selected as the encryption key. Because by changing the loop length of the system circuit, the delay value can vary within a large range. At the same time, an adjustable optical delay line can be used to precisely match the delay values at the transmitter and receiver. In this way, a large time-domain key space can be obtained. Therefore, an important security consideration is the concealment of TDS.

[0006] So far, many studies have focused on hiding TDS. However, its security analysis takes some time to mature. To successfully recover TDS, different strategies can be adopted, such as permutation information analysis, radio frequency spectrum analyzer, singular value fractional measure, optimal transformation, autocorrelation function, delay mutual information, local linear fitting in a low-dimensional subspace, extreme value statistics, etc. Among the listed methods, ACF and DMI are widely used due to their effectiveness and robustness.

[0007] In recent years, deep learning technology has received increasing attention due to its advantages in dealing with complex non-linear time series analysis and non-linear modeling. Deep learning is an attractive technology for the security analysis of optical chaotic secure communication systems. Chaotic communication cryptanalysis for TDS remains a challenging open problem.

[0008] Through the above analysis, the problems and defects existing in the prior art are as follows:

[0009] (1) The existing time delay extraction methods have a large demand for data;

[0010] (2) The existing time delay extraction methods have low tolerance for system non-linearity and additive noise. Summary of the Invention

[0011] In view of the problems existing in the prior art, the present invention provides a time delay feature extraction method, system, device and medium based on weight similarity.

[0012] The present invention is implemented as follows. A time delay feature extraction method based on weight similarity, the time delay feature extraction method based on weight similarity includes:

[0013] Generate a chaotic time series as a data set; construct an echo state network; select multiple time delays, and construct multiple data set pairs according to different time delays; translate each data set pair by a certain amount to generate corresponding data set pairs; train the network for two data set pairs with the same time delay respectively, and extract weights; perform similarity measurement on the two extracted weight matrices; infer the time delay information according to the statistical analysis results of the similarity measurement.

[0014] Further, the data set is a chaotic optoelectronic oscillator system, and the fourth-order Runge-Kutta method is used to solve the chaotic optoelectronic oscillator system. The differential equation of the chaotic optoelectronic oscillator system is:

[0015]

[0016] where x 0 represents the initial value of x, y 0 represents the initial value of y, and f(x, y) represents a known function about time x and state y;

[0017] The calculation formula of the fourth-order Runge-Kutta method is:

[0018]

[0019] where h represents the solution step size, x i represents the state of x at the i-th step, y i represents the state of y at the i-th step, k1 , k 2 , k 3 , k 4 represents the tangent slope values of four points taken within the interval [x i , x i+1 ; The obtained discrete time series y is used as the data set.

[0020] Furthermore, the construction of the echo state network includes:

[0021] Initialize the neural network, determine the reservoir size, randomly generate the connection matrix W, scale the matrix so that the spectral radius < 1, and randomly generate the input connection weights W in and the output feedback weights W out ;

[0022] Set the hyperparameters of the neural network, where the reservoir size N = 1000; the spectral radius ρ = 0.9; the regularization factor is 1e-6; the leakage rate α = 0.3.

[0023] Furthermore, the specific process of constructing multiple data set pairs according to different time delays includes:

[0024] Use the delay differential equation to characterize the chaotic optoelectronic oscillator system, and the formula of the delay differential equation is:

[0025]

[0026] In the formula, x(t) is the state variable, and x(t - τ) is the time delay change;

[0027] The difference equation approximately represented by the delay differential equation is:

[0028] x(t + Δt) - x(t) = Δtf(x(t), x(t - τ))

[0029] In the formula, Δt is the unit time step;

[0030] Therefore, the function mapping obtained is:

[0031]

[0032] Select M consecutive data amounts from the discrete time series to obtain x, select the time delay candidate set {R 1 , …, R k}, and construct k data set pairs (Xtrain , Ytrain i ) according to the function mapping i , which is expressed as:

[0033] Xtrain i = x(t - Ri )

[0034] Ytrain i = x(t + Δt) - x

[0035] where i = 1, …, k, Xtrain i and Ytrain i represent the input and output of the neural network.

[0036] Furthermore, the dataset is translated by s data amounts, and then another dataset pair (XStrain i , YStrain i ) is generated, which is expressed as:

[0037] XStrain i = x(t - R i + s)

[0038] YStrain i = x(t + Δt + s) - x(t + s)

[0039] where i = 1, …, k; s < M.

[0040] Furthermore, the specific process of training the network for two dataset pairs with the same time delay and extracting the weights is as follows:

[0041] The state update method of the reservoir and the output of the network are:

[0042] x(t) = tanh(Wx(t - 1) + W in u(t))

[0043] f(x) = W out x(t)

[0044] where u(t), x(t) and f(t) represent the input, the state of the reservoir, and the output at time t respectively, tanh(·) is the activation function, W in represents the input weight matrix, W represents the intermediate weight matrix, and W out represents the output feedback weight matrix;

[0045] Loading the Xtrain i and Ytrain i into the input and output to train the neural network in sequence. After idling for a certain period of time, continuously update and record the state of the reservoir, and use linear regression to determine the output feedback weight W outi , where i = 1, …, k);

[0046] Loading the XStrain i and YStrain iLoad them into the input and output training neural networks in sequence. After idling for a certain period of time, continuously update the record of the reservoir state, and use linear regression to determine the output feedback weight WS outi , where i = 1,..., k).

[0047] Furthermore, the specific process of the similarity measurement includes:

[0048] Use the Pearson correlation coefficient to measure the similarity between the two output feedback weights W outi and WS outi The calculation formula of the Pearson correlation coefficient is:

[0049]

[0050] In the formula, cov(·) is the covariance function, is the variance of the output feedback weight W outi , is the variance of the output feedback weight WS outi .

[0051] Another object of the present invention is to provide a time-delay feature extraction system based on weight similarity for implementing the time-delay feature extraction method based on weight similarity. The time-delay feature extraction system based on weight similarity includes:

[0052] An input module, configured to generate a chaotic time series as a data set, construct multiple data set pairs according to different time delays, and translate each data set pair by a certain amount to generate a corresponding data set pair;

[0053] A training module, configured to train the network for two data set pairs with the same time delay respectively and extract weights;

[0054] A similarity measurement module, configured to measure the similarity between the two extracted weight matrices;

[0055] A statistical analysis module, configured to infer the time-delay information according to the statistical analysis result of the similarity measurement.

[0056] Another object of the present invention is to provide a computer device, which includes a memory and a processor. When the computer program stored in the memory is executed by the processor, the processor is caused to execute the steps of the time-delay feature extraction method based on weight similarity.

[0057] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which when executed by a processor, causes the processor to execute the steps of the time-delay feature extraction method based on weight similarity.

[0058] Another object of the present invention is to provide an information data processing terminal for implementing the time-delay feature extraction system based on weight similarity.

[0059] Combined with the above technical solutions and the technical problems solved, please analyze the advantages and positive effects of the technical solution to be protected by the present invention from the following aspects:

[0060] First, aiming at the technical problems existing in the above-mentioned prior art and the difficulty of solving this problem, closely combining the technical solution to be protected by the present invention and the results and data in the R & D process, etc., analyze in detail and deeply how the technical solution of the present invention solves the technical problems and the creative technical effects brought after solving the problems. The specific description is as follows:

[0061] (1) The present invention generates a chaotic time series as a data set, selects multiple time delays, and constructs multiple data set pairs according to different time delays;

[0062] (2) The present invention uses the Pearson correlation coefficient to measure the similarity of the two extracted weight matrices;

[0063] (3) The present invention conducts statistical analysis on the obtained multiple similarity coefficients and infers the time-delay information according to the statistical analysis results.

[0064] Second, regarding the technical solution as a whole or from the perspective of the product, the technical effects and advantages of the technical solution to be protected by the present invention are specifically described as follows:

[0065] Compared with the existing methods, the time-delay feature extraction method based on weight similarity proposed by the present invention does not require prior knowledge of the chaotic system structure and mathematical model, has a smaller minimum data size requirement, and has a higher tolerance for system nonlinearity and additive noise.

[0066] Third, as the creative auxiliary evidence of the claims of the present invention, it is also reflected in the following important aspects:

[0067] (1) The expected benefits and commercial value after the transformation of the technical solution of the present invention are:

[0068] The present invention can analyze the time-delay key of a two-dimensional or even higher-dimensional chaotic system, not limited to one-dimensional time delay, and does not require prior knowledge of the chaotic system structure and mathematical model. Only a small amount of data is needed to analyze the key, saving computing power, having high accuracy, and having great commercial value.

[0069] (2) The technical solution of the present invention fills the domestic and foreign technical gaps in the industry:

[0070] Deep learning is an attractive technology for the security analysis of optical chaotic secure communication systems. The chaotic communication cryptanalysis for TDS remains a challenging open problem. The present invention makes use of the advantages of deep learning technology in dealing with complex nonlinear time series analysis and nonlinear modeling, and proposes a method for extracting TDS based on weight similarity, which requires a smaller minimum data size and has a higher tolerance for system nonlinearity and additive noise.

[0071] (3) Does the technical solution of the present invention solve the technical problems that people have been eager to solve but have never been successful in obtaining?

[0072] The present invention aims to solve the problems in the prior art that the existing time delay extraction methods have a large demand for data and low tolerance for system nonlinearity and additive noise, and provides a time delay feature extraction method based on weight similarity, realizing the mining of time delay information of the optical chaotic system.

[0073] (4) Does the technical solution of the present invention overcome the technical prejudice? BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a flowchart of time delay feature extraction based on weight similarity provided by an embodiment of the present invention;

[0075] Figure 2 is a weight similarity graph of chaotic signals provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0076] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0077] I. Explanation of the embodiment. This part is an explanatory embodiment that expands and explains the technical solution of the claims in order to enable those skilled in the art to fully understand how the present invention is specifically implemented.

[0078] As Figure 1 shown, the time delay feature extraction method based on weight similarity provided by an embodiment of the present invention includes the following steps:

[0079] Step 1, generating a chaotic time series as a data set;

[0080] Step 2, constructing an echo state network;

[0081] Step 3, selecting multiple time delays and constructing multiple data set pairs according to different time delays;

[0082] Step 4: Translate each dataset pair by a certain amount to generate a corresponding dataset pair;

[0083] Step 5: Train the network for two dataset pairs with the same time delay respectively, and extract the weights;

[0084] Step 6: Perform similarity measurement on the two extracted weight matrices;

[0085] Step 7: After ensuring that all dataset groups corresponding to time delays have gone through Step 5 and Step 6, perform statistical analysis on the obtained multiple similarity coefficients, and infer the time delay information based on the results of the statistical analysis.

[0086] The time delay feature extraction system based on weight similarity provided by the embodiment of the present invention includes:

[0087] Input module: Used to generate a chaotic time series as a dataset, construct multiple dataset pairs according to different time delays, and translate each dataset pair by a certain amount to generate a corresponding dataset pair;

[0088] Training module: Used to train the network for two dataset pairs with the same time delay respectively, and extract the weights;

[0089] Similarity measurement module: Used to perform similarity measurement on the two extracted weight matrices;

[0090] Statistical analysis module: Used to perform statistical analysis on the obtained multiple similarity coefficients, and infer the time delay information based on the results of the statistical analysis.

[0091] Further, Step 1 specifically includes:

[0092] Select a chaotic optoelectronic oscillator (OEO) system as the dataset, and the system equation is shown as the following formula:

[0093]

[0094] Perform numerical simulation according to the above formula, set the parameters τ = 25ps, T D = 30ns, θ = 5μs, β = 5, Adopt the fourth-order Runge-Kutta algorithm with a sampling step of 25ps, and use the obtained discrete time series x as the dataset.

[0095] Further, Step 2 specifically includes:

[0096] (1.1) Initialize the neural network: Determine the reservoir size; randomly generate the connection matrix W; scale the matrix so that the spectral radius < 1; randomly generate the input connection weight W in and the output feedback weight W out ;

[0097] (1.2) The hyperparameters of the neural network are set as follows: the reservoir size N = 1000; the spectral radius ρ = 0.9; the regularization factor is 1e-6; the leakage rate α = 0.3.

[0098] Further, step three specifically includes:

[0099] The training data volume M = 3500. According to the parameters set in step one, it can be known that the dimensionless time delay of the system Therefore, the time delay candidate set {R 1 , …, R k} can be set as {800, …, 2600}, with a step size of 100.

[0100] The optical chaos system can be described by a delay differential equation:

[0101]

[0102] where x(t) is the state variable and x(t-τ) is the time delay change. It can be approximately written as the following difference equation:

[0103] x(t+Δt)-x(t) = Δtf(x(t), x(t-τ))

[0104] where Δt is the unit time step.

[0105] According to the above formula, the following function mapping can be obtained:

[0106]

[0107] Select M consecutive data volumes from the discrete time series obtained in step one to get x. According to the mapping Construct k training set pairs based on the time delay candidate set:

[0108] Xtrain i = x(t-R i )

[0109] Ytrain i = x(t+Δt)-x

[0110] where i = 1, …, k.

[0111] Further, step four specifically includes:

[0112] Translate each constructed data set by s data volumes, and then generate a data set pair:

[0113] XStrain i = x(t-R i +s)

[0114] YStrain i= x(t + Δt + s) - *x(t + s)

[0115] where i = 1, …, k; s = 500.

[0116] Further, step five specifically includes:[[]]

[0117] (3.1) The state update method of the reservoir and the output of the network are as follows:[[]]

[0118] x(t) = tanh(Wx(t - 1) + W in u(t))

[0119] f(x) = W out x(t)

[0120] u(t), x(t), and f(t) represent the input, the state of the reservoir, and the output at time t respectively, and the activation function is tanh(·);

[0121] (3.2) Load Xtrain i and Ytrain i into the input-output training neural network in sequence. After idling for a certain period of time, continuously update and record the state of the reservoir, and use linear regression to determine the output connection weight W outi (i = 1, …, k);

[0122] (3.3) Load XStrain i and YStrain i into the input-output training neural network in sequence. After idling for a certain period of time, continuously update and record the state of the reservoir, and use linear regression to determine the output connection weight WS outi (i = 1, …, k).

[0123] Further, step six specifically includes:[[]]

[0124] Perform similarity measurement on the two extracted weights W outi and WS outi using the Pearson correlation coefficient. The calculation formula of the Pearson correlation coefficient is as follows:[[]]

[0125]

[0126] where i = 1, …, k; cov(·) is the covariance function, is the variance of the weight W outi , is the variance of the weight WS outi .

[0127] II. Application Examples. To prove the creativity and technical value of the technical solution of the present invention, this part provides application examples of the technical solution of the claims on specific products or related technologies.

[0128] It should be noted that the embodiments of the present invention can be implemented through hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated designed hardware. Those of ordinary skill in the art can understand that the above devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code is provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits of programmable hardware devices such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above hardware circuits and software such as firmware.

[0129] III. Evidence of Related Effects of the Embodiment. Some positive effects have been achieved during the research and development or use of the embodiments of the present invention, and there are indeed great advantages compared with the prior art. The following content will be described in combination with data, charts, etc. of the test process.

[0130] The following further illustrates the effects of the present invention in combination with simulation experiments:

[0131] Figure 2 It is the weight similarity graph of the chaotic signal in the embodiment of the present invention. Figure 2 In it, the abscissa is the selected set of delay candidates, and the ordinate is the similarity coefficient. The delay information of the chaotic system can be deduced by finding the delay corresponding to the maximum similarity value in the graph.

[0132] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be covered by the protection scope of the present invention.

Claims

1. A time-delay feature extraction method based on weight similarity, characterized in that, the time-delay feature extraction method based on weight similarity includes: generating a chaotic time series as a data set; constructing an echo state network; selecting multiple time delays, and constructing multiple data set pairs according to different time delays; translating each data set pair by a certain amount to generate a corresponding data set pair; training the network for two data set pairs with the same time delay respectively, and extracting weights; performing similarity measurement on the two extracted weight matrices; inferring the time-delay information according to the statistical analysis result of the similarity measurement; the specific process of inferring the time-delay information from the statistical analysis result of the similarity measurement is as follows: taking the similarity of the obtained weight matrices as the ordinate and the corresponding time delay as the abscissa, drawing a scatter plot reflecting the relationship between the two, and the abscissa of the point with the largest ordinate value is the time-delay information to be inferred; the constructing of the echo state network includes: Initialize the neural network, determine the size of the reservoir, randomly generate the connection matrix W, scale the matrix so that the spectral radius < 1, and randomly generate the input connection weights W in and the output feedback weights W out ; setting neural network hyperparameters, where the reservoir size N = 1000; the spectral radius ρ = 0.9; the regularization factor is 1e-6; the leakage rate α = 0.3; the specific process of constructing multiple data set pairs according to different time delays includes: characterizing the chaotic optoelectronic oscillator system using a time-delay differential equation, and the formula of the time-delay differential equation is: where x(t) is the state variable and x(t - τ) is the time-delay change; the difference equation approximately represented by the time-delay differential equation is: x(t + Δt) - x(t) = Δtf(x(t), x(t - τ)) where Δt is the unit time step; therefore, the function mapping is obtained as: Select M consecutive data amounts from the discrete time series to obtain x, and select the time delay candidate set {R 1 , …, R k}. According to the function mapping and the time delay candidate set, construct k data set pairs (Xtrain i , Ytrain i ), which are expressed as: Xtrain i = x(t - R i ) Ytran i = x(t + Δt) - x where \(i = 1,\ldots,k\), \(X_{train}\ i and \(Y_{train}\ i represent the input and output of the neural network; The said data set is translated by s data volumes, and then a data set pair (XStrain i , YStrain i ) is generated, which is expressed as: XStrain i = x(t - R i + s) Y Strain i = x(t + Δt + s) - x(t + s) where i = 1, …, k; s < M; the specific process of training the network for two data set pairs with the same time delay respectively and extracting weights is: the state update method of the reservoir and the output of the network are: x(t) = tanh(Wx(t - 1)+W in u(t)) f(x) = W out x(t) where \(u(t)\), \(x(t)\) and \(f(t)\) represent the input, the state of the reservoir, and the output at time \(t\), respectively, \(\tanh(\cdot)\) is the activation function, \(W\) in represents the input weight matrix, \(W\) represents the intermediate weight matrix, \(W\) out represents the output feedback weight matrix; Load the Xtrain i and Ytrain i into the input and output training neural networks in sequence. After idling for a certain period of time, continuously update the record of the reservoir state, and use linear regression to determine the output feedback weight W outi , where i = 1, …, k); Load the XStrain i and YStrain i into the input and output training neural networks in sequence. After idling for a certain period of time, continuously update the recorded reservoir state, and use linear regression to determine the output feedback weight WS outi , where i = 1, …, k).

2. The time-delay feature extraction method based on weight similarity according to claim 1, characterized in that, the data set is a chaotic optoelectronic oscillator system, and the fourth-order Runge-Kutta method is used to solve the chaotic optoelectronic oscillator system, and the differential equation of the chaotic optoelectronic oscillator system is: where x 0 represents the initial value of x, y 0 represents the initial value of y, and f(x, y) represents a known function with respect to time x and state y; the calculation formula of the fourth-order Runge-Kutta method is: where h represents the solution step size, x i represents the state of x at the i-th step, y i represents the state of y at the i-th step, k 1 , k 2 , k 3 , k 4 represent the tangent slope values at four points within the interval [x i , x i+1 ; the obtained discrete time series y is used as the data set.

3. The time-delay feature extraction method based on weight similarity according to claim 1, characterized in that, the specific process of the similarity measurement includes: The Pearson correlation coefficient is used to measure the similarity between the two output feedback weights W outi and WS outi The calculation formula of the Pearson correlation coefficient is as follows: where cov(·) is the covariance function, is the variance of the output feedback weight W outi , is the variance of the output feedback weight WS outi .

4. A time-delay feature extraction system based on weight similarity for implementing the time-delay feature extraction method based on weight similarity according to any one of claims 1-3, characterized in that, the time-delay feature extraction system based on weight similarity includes: an input module, configured to generate a chaotic time series as a data set, construct multiple data set pairs according to different time delays, translate each data set pair by a certain amount to generate a corresponding data set pair; a training module, configured to train the network for two data set pairs with the same time delay respectively and extract weights; a similarity measurement module, configured to perform similarity measurement on the two extracted weight matrices; a statistical analysis module, configured to infer the time-delay information according to the statistical analysis result of the similarity measurement.

5. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor is caused to execute the steps of the time-delay feature extraction method based on weight similarity according to any one of claims 1-3.

6. A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the processor is caused to execute the steps of the time-delay feature extraction method based on weight similarity according to any one of claims 1-3.

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