A method for enhancing the dynamic characteristics of chaotic encryption systems based on echo state networks

Abstract

The present invention discloses a method for enhancing the dynamic characteristics of a chaotic encryption system based on an echo state network. The method employs a method of constructing an enhanced 3-D HICM cascade chaotic map by combining two chaotic cascade maps to generate a chaotic sequence with improved performance. The chaotic sequence is input into an echo state network (ESN) for training to obtain an output sequence. The ESN output sequence is processed to obtain a key group, which is used to sequentially encrypt bits, constellation diagrams, and subcarrier information. The trained ESN is used to obtain the same key group, and after receiving a signal at a receiving end, the signal is decrypted. The present invention can generate a chaotic sequence with improved performance, increase the key space of the chaotic sequence, and improve the complexity of the chaotic system. The adopted ESN can effectively simplify the network structure compared to other traditional neural network structures, reducing the computational complexity and training time of network training.

Description

Technical Field

[0001] The present invention relates to a method for enhancing the dynamic characteristics of a chaotic encryption system based on an echo state network, and is mainly applied to an orthogonal frequency division multiplexing passive optical network transmission system. Background Art

[0002] With the advancement of communications technology, demand for broadband access has steadily increased, and optical access network technology has gradually become a key component of internet access. In recent years, Orthogonal Frequency Division Multiplexing (OFDM), an excellent multi-carrier modulation technology, has been widely adopted in passive optical networks (PONs) due to its advantages such as high spectrum utilization and strong resistance to multipath fading. As a pure dielectric network, PONs avoid electromagnetic interference from external devices and the effects of lightning, significantly improving system reliability. PONs have become a popular technology due to their high capacity, long transmission distance, low cost, and full service support. Meanwhile, passive optical networks such as TDM-PON and WDN-PON are now gradually being commercialized. However, in PON networks, components such as PSCs and erbium-doped fiber amplifiers are vulnerable to active eavesdropping attacks, making it impossible to guarantee information confidentiality. Consequently, many currently superior optical communication systems still face numerous transmission vulnerabilities, and their security performance still needs to be further improved.

[0003] To address the security challenges of optical network systems, numerous researchers have proposed various models of physical-layer encryption techniques for optical systems. Optimizing and improving these techniques is currently a hot research topic. Existing encryption technologies primarily utilize chaotic systems, which iteratively generate sequences and use these sequences as a factor sequence in encryption transformations. Chaotic encryption leverages the self-similarity of chaos, ensuring that locally selected chaotic key sets have a similar distribution to the overall set. Chaotic systems are highly sensitive to initial states, exhibit complex dynamical behavior, and exhibit distributions that do not conform to the principles of probability and statistics. These systems are quasi-random sequences with complex structures, exhibiting excellent randomness, correlation, and complexity, making them difficult to reconstruct, analyze, and predict. However, due to the limited computational precision of computer simulation software and digital hardware, the chaotic sequences generated by chaotic systems no longer maintain strict chaotic dynamical properties. These systems often suffer from dynamical degradation, which severely impacts the security and transmission efficiency of communication encryption systems based on chaotic systems. Generally, improvements in chaotic dynamical properties can be achieved through improving computational precision, cascading chaotic systems, and applying external perturbations.

[0004] Recurrent neural networks (RNNs) are a common network architecture used in most deep learning models. However, because they require gradient descent to calculate their weight matrices, the computational cost is extremely high and network training is challenging. The echo state network (ESN), a computational framework derived from RNNs, aims to alleviate the difficulties of learning recurrent connections within RNNs. In ESNs, the connection weights at the input layer and within the network are randomly generated and, after initialization, are not adjusted throughout the training process. ESNs can be trained with a simple readout mechanism to read the states of neurons in the network and map them to the desired outputs. Training occurs only during the output phase, during which the input, internal weight matrix, and reservoir dynamics remain unchanged. This approach uses a chaotic sequence generated by a 3-D high-intensity matrix (HICM) chaotic map to assign values to the network's internal connection weights. Experimental and computational studies have shown that this method achieves superior training results and effectively reduces the normalized root mean square error (NRMSE) during network training. Compared to traditional RNNs, ESNs possess superior computational power, significantly reducing the computational cost and training time. Summary of the Invention

[0005] Purpose of the invention: The present invention proposes a method for enhancing the dynamic characteristics of a chaotic encryption system based on an echo state network. While enhancing the chaotic dynamic characteristics and ensuring the transmission quality of the communication system, the method can effectively simplify the neural network structure, reduce the computational complexity and training time of the system, and improve the reliability of the communication system.

[0006] Technical solution: The method for enhancing the dynamic characteristics of a chaotic encryption system based on an echo state network described in the present invention specifically includes the following steps:

[0007] (1) An enhanced 3-D HICM cascade chaotic map is constructed by combining two chaotic cascade maps to generate chaotic sequences with better performance.

[0008] (2) Inputting the chaotic sequence obtained in step (1) into the echo state network (ESN) for training to obtain the output sequence;

[0009] (3) The ESN output sequence is processed to obtain a key group, which is used to encrypt the bits, constellation diagram, and subcarrier information in sequence;

[0010] (4) Use the trained ESN to obtain the same key group, and decrypt the signal after receiving it at the receiving end.

[0011] Furthermore, the implementation process of step (1) is as follows:

[0012] Henon map as seed map:

[0013]

[0014] ICMIC chaotic mapping is used to improve the performance of seed mapping:

[0015] x i+1 =sin(c / x i )

[0016] After dimensionality expansion, the Henon map and ICMIC map are cascaded to form a 3-D HICM cascade map:

[0017]

[0018] Among them, x i 、y i 、z i are the state variables of the three dimensions of the chaotic system at time i, x i+1 、y i+1 、z i+1 are the state variables of the three dimensions of the chaotic system at time (i+1), a and b are the control variables that control the state of the Honon chaotic system, and c is the control variable that controls the state of the ICMIC chaotic system.

[0019] Furthermore, the implementation process of step (2) is as follows:

[0020] During the training process, ESN randomly selects the weight of the loop so that the hidden state captures the evolutionary history of the input information and trains the weight from the hidden state to the output state. The hidden layer calculation process is as follows:

[0021] h t+1 =f(W in u t+1 +Wh t )

[0022] Among them, W in is the input weight matrix, which is uniformly sampled from the range [-ω, ω], where ω is a hyperparameter; W is the reserve pool weight matrix, and the output weight matrix W out Regularized least squares regression training is used to alleviate overfitting, and the output expression is:

[0023] y t =g(W out h t )

[0024] After the data passes through the enhanced 3-D HICM cascade chaotic system, a chaotic sequence (x, y, z) is generated. The sequence z is used to assign the internal weights of the ESN to obtain a random weight matrix. Then, after ESN training and prediction, the enhanced output sequence (x', y', z') is obtained.

[0025] Furthermore, the implementation process of step (3) is as follows:

[0026] After the echo state network outputs three sets of output sequences (x', y', z'), the network prediction sequence is processed to obtain the key group (X, Y, Z); bit encryption is performed before QAM mapping. The original data is preprocessed to obtain a binary bit stream to send data. Each character is encrypted by performing a bitwise XOR operation with the key X:

[0027]

[0028] Where, mo$(·) represents the remainder function, floor(·) represents the floor function; s is the original binary bit stream, and S is the encrypted binary bit stream;

[0029] After the above encryption process, X becomes a chaotic sequence of only 0 and 1, and the unmodulated original binary bit stream is encrypted. After the first layer of encryption is completed, the constellation point phase in the constellation is encrypted:

[0030]

[0031] Where θ is the angle of the unencrypted constellation point in the polar coordinate system, θ' is the angle of the encrypted constellation point in the polar coordinate system, and Y becomes a chaotic sequence with only integers between 0 and 360, which is used to randomly rotate the constellation to achieve encryption of the constellation phase information;

[0032] The combination of the subcarriers of the OFDM signal and the symbols on each subcarrier is regarded as a two-dimensional matrix. Each column of the two-dimensional matrix represents each subcarrier, and each element represents a symbol on the corresponding subcarrier. The order of the subcarriers is disrupted according to the order of the elements of the key sequence Z, thereby completing the encryption of the subcarriers.

[0033] Furthermore, the implementation process of step (4) is as follows:

[0034] The received signal is restored to its subcarrier, constellation and bits, and then the original data is output through parallel-to-serial conversion to complete the decryption.

[0035] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are: the present invention adopts an innovative 3-DHICM cascade chaotic mapping. On the basis of expanding the dimension, the mapping can generate a chaotic sequence with better performance, increase the key space of the chaotic sequence, and improve the complexity of the chaotic system; the ESN adopted by the present invention can effectively simplify the network structure compared with other traditional neural network structures, reduce the computational complexity and training time of network training; the present invention encrypts the optical physical layer through a chaotic dynamics enhancement method based on the echo state network, which can effectively make up for the defect of degradation of the dynamic characteristics of the chaotic system, and uses a key sequence group to encrypt information in three dimensions, effectively improving the overall reliability of the encryption system. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a schematic diagram of the dynamic performance of the enhanced chaotic encryption system based on the echo state network;

[0037] Figure 2 A schematic diagram comparing the bifurcation diagrams of two chaotic maps;

[0038] Figure 3 Schematic diagram for comparing the LE maximum values of two chaotic maps;

[0039] Figure 4 This is a schematic diagram of the echo state network structure;

[0040] Figure 5 This is a schematic diagram of the structure of the echo state network training unit;

[0041] Figure 6 This is a comparison chart of the effects of using chaotic sequences to generate reserve internal weights;

[0042] Figure 7 Schematic diagram of the specific process of OFDM signal encryption in the frequency domain subcarrier;

[0043] Figure 8 Schematic diagram of the three-dimensional intelligent perturbation optical transmission system model structure. DETAILED DESCRIPTION

[0044] The present invention will be described in further detail below with reference to the accompanying drawings.

[0045] The present invention proposes a method for enhancing the dynamic characteristics of chaotic encryption systems based on echo state networks, which is mainly applied to orthogonal frequency division multiplexing passive optical network transmission systems. Figure 1As shown, a 3-D HICM chaotic map is enhanced by cascading chaotic systems. The chaotic sequence generated by the 3-D HICM chaotic map is input into the ESN for training, resulting in a generative model with excellent performance. This generative model is used to predict and generate new chaotic sequence groups, which, to a certain extent, improve the dynamic degradation problem of the chaotic system. In the encryption module, the chaotic sequence group generated by the ESN is processed to obtain a key sequence group, which is used to encrypt the signal bits, constellation diagram, and subcarrier information respectively. This method can resist the security risks caused by the dynamic degradation of the chaotic system and ensure that important information is not easily leaked or stolen during transmission. Compared with encryption schemes with other network structures, this network structure can reduce computational complexity and effectively shorten computation time. While ensuring that the system transmission efficiency is not affected, it greatly enhances the reliability of the chaotic encryption system. The specific implementation process is as follows:

[0046] Step 1: Using the Henon map as a seed map in a chaotic system, we extend the Henon map to three dimensions and cascade it with the infinite folding iterative map (ICMIC) to obtain the enhanced three-dimensional Henon-infinite folding iterative (3-D HICM) chaotic map. This improvement allows for better initial value sensitivity and significantly enhances the ergodicity of its chaotic trajectory diagrams.

[0047] The Henon map, as the seed map of the system, is a classic two-dimensional discrete chaotic map, and its equation is:

[0048]

[0049] a and b are the control variables that control the state of the Honon chaotic system. The variables a and b in the formula are control parameters. When a = 1 and b = 0.3, the sequence generated by the system has good chaotic characteristics.

[0050] ICMIC chaotic mapping is used to improve the performance of the original mapping. ICMIC chaotic mapping is a one-dimensional chaotic mapping, which is mathematically defined as:

[0051] x i+1 =sin(c / x i )

[0052] After the dimension is expanded, the Henon map and ICMIC map are cascaded, and the 3-D HICM cascade map is defined as:

[0053]

[0054] Among them, x i 、y i 、z iare the state variables of the three dimensions of the chaotic system at time i, x i+1 、y i+1 、z i+1 are the state variables of the three dimensions of the chaotic system at time (i+1), c is the control variable that controls the state of the ICMIC chaotic system, c∈(0,+∞).

[0055] The bifurcation diagrams of the Henon map and the 3-D HICM cascade chaos map are shown in Figure 2. Figure 2 As shown. Figure 2 It can be seen that some areas of the Henon map have low ergodicity and there are some blank areas in the phase trajectory diagram, which will lead to poor performance of the sequence generated by the chaotic system. By expanding the dimension and cascading, the newly constructed 3D-HICM cascade chaotic map has higher ergodicity and better chaotic performance.

[0056] In addition, the maximum values of the Lyapunov exponents (LE) of the Henon map and the 3-D HICM cascade chaotic map are analyzed to further compare the changes in their performance. Figure 3 As shown, when the value of a ranges from 0 to 5, the maximum LE index of the 3-D HICM cascade mapping is always greater than 0, indicating that the mapping fails to converge to a stable orbit or stable point, satisfying the excellent conditions for a chaotic system. Compared with the Henon mapping, the 3-D HICM cascade mapping is more likely to achieve chaotic conditions. Through cascading, the disadvantage of the sequence obtained within a certain range of parameter a values not maintaining chaotic properties is improved, and the resulting chaotic sequence has more excellent chaotic properties.

[0057] Step 2: Input the chaotic sequence obtained in step 1 into the echo state network (ESN) for training to obtain the output sequence.

[0058] The operation unit used in ESN is similar to the standard structure of RNN. The difference is that the input and internal weights of ESN are randomly generated to meet the echo state properties of the reservoir and create a large and rich dynamic library. Only the weights of the output layer will be trained. The specific reservoir unit information transmission principle diagram is as follows Figure 4 As shown. During the training process, ESN randomly selects the weight of the loop so that the hidden state captures the evolution history of the input information. On this basis, the weight from the hidden state to the output state is trained. The hidden layer is represented by the function form and the calculation process is as follows:

[0059] h t+1 =f(W in u t+1 +Wh t )

[0060] Among them, W inis the input weight matrix, which is uniformly sampled from the range [-ω,ω], where ω is a hyperparameter. W is the reservoir weight matrix, and the output weight matrix W out Regularized least squares regression training is used to alleviate overfitting, and the output expression is:

[0061] y t =g(W out h t )

[0062] The data is passed through the enhanced 3-D HICM cascade chaotic system to generate a chaotic sequence (x, y, z). The sequence z is used to assign the internal weight of the ESN to obtain a random weight matrix. Then, after ESN training and prediction, the enhanced chaotic sequence (x', y', z') is obtained. The reserve pool calculation training unit is as follows: Figure 5 As shown. In the reserve pool calculation training unit, the internal state h at time t t Iteratively update the hidden layer calculation formula to generate h t+1 , where u t+1 is the input signal at time t+1. In the reservoir computation training unit, the reservoir weight matrix W is assigned values based on the enhanced chaotic output sequence generated by the 3D-HICM system, maintaining a random and disordered state. After training, the input signal is updated and re-input into the reservoir computation unit at the next moment for iteration.

[0063] In the process of training ESN, using the sequence generated by 3-D HICM cascade chaotic mapping to generate the internal weights of the reserve pool can achieve better training results. In 100 different prediction tasks, the same sequence is predicted using two methods. In the original network, each input weight and internal weight are randomly generated. In this invention, the internal weight of the reserve pool is generated using the chaotic sequence z. Figure 6 The results show that this method makes the ESN network have smaller NRMASE and higher prediction accuracy than the original network in most tasks.

[0064] Step 3: After processing the ESN output sequence, a key group is obtained, and the key group is used to encrypt the bits, constellation diagram, and subcarrier information in sequence.

[0065] After the echo state network outputs three sets of prediction sequences (x', y', z'), the network prediction sequences are processed to obtain the key group (X, Y, Z), which is passed to the three-dimensional encryption module of bits, constellations, and subcarriers for encryption.

[0066] Bit encryption is performed before QAM mapping. The original data is preprocessed to obtain a binary bit stream for transmission. Each character can be encrypted by performing a bitwise XOR operation with the key X. During the decryption process, it is only necessary to perform a bitwise XOR operation on the encrypted result and the key X again. The generation process of X and the encryption process are as follows:

[0067]

[0068] Where mo$(·) represents the remainder function, and floor(·) represents the floor function. s is the original binary bit stream, and S is the encrypted binary bit stream.

[0069] After the above processing, X becomes a chaotic sequence of only 0s and 1s, encrypting the original unmodulated binary bit stream. After the first layer of encryption is completed, the constellation point phase in the 16QAM constellation is encrypted. The specific process is as follows:

[0070]

[0071] Where θ is the angle of the unencrypted constellation point in the polar coordinate system, and θ' is the angle of the encrypted constellation point in the polar coordinate system. After processing, Y becomes a chaotic sequence consisting of integers between 0 and 360, which is used to randomly rotate the constellation and encrypt the constellation phase information.

[0072] like Figure 7 As shown in Figure 1, the combination of the OFDM signal's subcarriers and the symbols on each subcarrier can be viewed as a two-dimensional matrix. Each column of the two-dimensional matrix represents a subcarrier, and each element represents a symbol on the corresponding subcarrier. The subcarrier order is scrambled according to the order of the elements in the key sequence Z. The scrambled subcarrier data is arranged randomly and unordered, achieving the requirements of subcarrier encryption.

[0073] Step 4: Use the trained ESN to obtain the same key group, and decrypt the signal after receiving it at the receiving end.

[0074] The decryption steps at the receiving end follow the same principles as the encryption, but in reverse order. The trained echo state network model is used to derive the same key set. After receiving the signal, the receiving end decrypts it. The subcarriers, constellation, and bits of the received signal are first restored. Then, a parallel-to-serial conversion is performed to output the original data, completing the decryption.

[0075] like Figure 8As shown, at the transmitter, an echo state network (ESN) generates a key group, and the signal encryption module encrypts the original data. First, the binary bit stream is encrypted. The signal then undergoes quadrature amplitude modulation (QAM) to generate a 16QAM signal, with the constellation points subjected to phase perturbation. Subcarrier information is then perturbed and encrypted during OFDM modulation. After passing through an arbitrary waveform generator (AWG), the data is sent to the modulator, modulated into an optical signal. This signal is then coupled with another beam of light to generate an electrical signal, which is then transmitted through an optical amplifier. At the receiver, the received signal is first attenuated for power adjustment before being captured by a photodetector and displayed on an oscilloscope. The key group generated by the ESN is used to decrypt the bits, constellation, and subcarrier information of the received data, restoring the transmitted binary data stream and obtaining the original data. Throughout this process, three key sequences are generated to encrypt information in three dimensions. These key sequences are generated by a chaotic sequence generated by a cascaded 3-D HICM chaotic map and enhanced by an ESN. This method significantly improves the reliability of the entire system.

[0076] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A method for enhancing the dynamic characteristics of a chaotic encryption system based on an echo state network, characterized in that: The following steps are involved: (1) An enhanced 3-D HICM cascade chaotic map is constructed by combining two chaotic cascade maps to generate chaotic sequences with better performance. (2) Inputting the chaotic sequence obtained in step (1) into the echo state network (ESN) for training to obtain the output sequence; (3) The ESN output sequence is processed to obtain a key group, which is used to encrypt the bits, constellation diagram, and subcarrier information in sequence; (4) Using the trained ESN to obtain the same key group, the signal is decrypted after being received at the receiving end; The implementation process of step (1) is as follows: Henon map as seed map: ICMIC chaotic mapping is used to improve the performance of seed mapping: x i+1 =sin(c / x i ) After dimensionality expansion, the Henon map and ICMIC map are cascaded to form a 3-D HICM cascade map: Among them, x i 、y i 、z i are the state variables of the three dimensions of the chaotic system at time i, x i+1 、y i+1 、z i+1 are the state variables of the three dimensions of the chaotic system at time i+1, a and b are the control variables that control the state of the Honon chaotic system, and c is the control variable that controls the state of the ICMIC chaotic system.

2. The method for enhancing the dynamic characteristics of a chaotic encryption system based on an echo state network according to claim 1, characterized in that: The implementation process of step (2) is as follows: During the training process, ESN randomly selects the weight of the loop so that the hidden state captures the evolutionary history of the input information and trains the weight from the hidden state to the output state. The hidden layer calculation process is as follows: h t+1 =f(W in u t+1 +Wh t ) Among them, W in is the input weight matrix, which is uniformly sampled from the range [-ω, ω], where ω is a hyperparameter; W is the reserve pool weight matrix, and the output weight matrix W out Regularized least squares regression training is used to alleviate overfitting, and the output expression is: y t =g(W out h t ) The data passes through the enhanced 3-D HICM cascade chaotic system to generate a chaotic sequence (x, y, z). The sequence z is used to assign the internal weights of the ESN to obtain a random weight matrix. Then, the enhanced output sequence (x', y', z') is obtained through ESN training and prediction.

3. The method for enhancing the dynamic characteristics of a chaotic encryption system based on an echo state network according to claim 1, characterized in that: The implementation process of step (3) is as follows: After the echo state network outputs three sets of output sequences (x', y', z'), the network prediction sequence is processed to obtain the key group (X, Y, Z); bit encryption is performed before QAM mapping. The original data is preprocessed to obtain a binary bit stream to send data. Each character is encrypted by performing a bitwise XOR operation with the key X: Where mod(·) represents the remainder function, floor(·) represents the floor function; s is the original binary bit stream, and S is the encrypted binary bit stream; After the above encryption process, X becomes a chaotic sequence of only 0 and 1, and the unmodulated original binary bit stream is encrypted. After the first layer of encryption is completed, the constellation point phase in the constellation is encrypted: Where θ is the angle of the unencrypted constellation point in the polar coordinate system, θ' is the angle of the encrypted constellation point in the polar coordinate system, and Y becomes a chaotic sequence with only integers between 0 and 360, which is used to randomly rotate the constellation to achieve encryption of the constellation phase information; The combination of the subcarriers of the OFDM signal and the symbols on each subcarrier is regarded as a two-dimensional matrix. Each column of the two-dimensional matrix represents each subcarrier, and each element represents a symbol on the corresponding subcarrier. The order of the subcarriers is disrupted according to the order of the elements of the key sequence Z, thereby completing the encryption of the subcarriers.

4. The method for enhancing the dynamic characteristics of a chaotic encryption system based on an echo state network according to claim 1, characterized in that: The implementation process of step (4) is as follows: The received signal is restored to its subcarrier, constellation and bits, and then the original data is output through parallel-to-serial conversion to complete the decryption.

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