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Abstract
An optical transmitter identification scheme based on optical chaotic phase space reconfiguration for secure communication is proposed to target injection attacks in the physical layer of optical networks. First, a feature fingerprint construction method based on reconfigured phase space of optical chaos is proposed. Then the fingerprint is controlled by the feedback intensity and filtering bandwidth of chaos. The in-phase and quadrature-phase encryption (IQE)/decryption (IQD) ensures the loading of fingerprints and realizes the confidential communication. In the experiment, the recognition rate of three transmitters is up to 99.3%. In the simulation, the recognition rate of five optical transmitters reaches 100% after 600 km transmission. The bit error rate of 25 GBaud QPSK signal after 300 km transmission at 25 dB OSNR is 1.6 × 10−3. Compared with the traditional optical transmitter identification methods, the fingerprint of this scheme is controllable. The IQE and IQD not only realize the chaotic fingerprint loading but also ensure the secure transmission of the signal avoiding the synchronization and time delay exposure problems in traditional chaotic communication systems. It is robust to device parameters, with low implementation difficulty and low cost. Therefore, this scheme has research and application value for secure communication in the physical layer of optical networks.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of bandwidth-intensive services such as 5G, cloud computing, and high-definition video, network data traffic has been growing explosively. As the main medium of high-speed and long-distance transmission of information, the optical network is increasingly important for its security. Security threats are mainly considered to occur at the physical layer in optical networks and can be divided into two categories: leakage attacks and injection attacks [1]. Leakage attack is a main way of optical network attacks, which does not disrupt normal optical communication and mainly refers to the purpose of eavesdropping information, such as fiber eavesdropping and monitoring port eavesdropping [2]. In addition to eavesdropping, injection attack can degrade communication quality and disrupts the network in optical networks by jamming attacks, tampering information attacks, and forgery attacks [3]. Facing the above security threats, it is crucial to ensure the information security of optical networks.
For eavesdropping attacks in physical layer optical networks, there are many encryption methods [4], such as code multiple access [5], optical steganography [6], chaotic optical encryption [7]. Among them, chaotic communication is one of the hot research topics. Chaos is the random signal generated by deterministic systems with uncertain, unrepeatable, and unpredictable properties [8]. Chaotic optical encryption uses chaos to modulate, mask, and key the signal [9–11], which has a good encryption effect and is compatible with optical networks. But the complexity of chaos needs to be increased to ensure security and the time delay signature (TDS) of chaos has to be suppressed [12]. The chaotic synchronization is also needed to ensure the correct decryption of information [13]. The high complexity of chaos, broadband characteristics, long transmission distances, and noise in the transmission links affect the effectiveness of synchronization, making it difficult to achieve secure chaotic communication over long distances at high speeds. Most importantly, the optical encryption can only ensure that the transmitted data isn’t bugged, but cannot identify malicious injection attacks.
To ensure the validity of received information, identity identification methods based on hardware features were proposed. On the one hand, some studies based on device differences were proposed. In 2019, [14] identified rogue ONUs in PON by optical spectrum feature analysis (OSFA) with a one-dimensional convolutional neural network. The identification accuracy can reach 100% within 12.6 milliseconds in experimental results. They analyzed the identification accuracy of the different algorithms. The accuracy of the support vector machine (SVM) was 98.54%, and the accuracy of one-dimensional convolutional neural network (1D-CNN) machine-learning OSFA is 100% [1]. In 2020, a signal decomposition method based on wavelet transform was used to extract feature matrices. A trained two-dimensional convolutional neural network (2D-CNN) was used to classify and identify the feature matrices. The experimental results showed that the method can successfully identify legal ONUs with an identification accuracy of 97.41%. The identification rate of detecting rogue ONUs was 100%, which effectively improved the ability of PON to resist identity spoofing attacks [15].
On the other hand, some identification methods based on channel characteristics have been proposed. In 2020, Jie Zhang et al. proposed security identification methods based on channel characteristics of optical networks, which used the dynamic changes of BER and SNR measured in the optical fiber channel as hardware fingerprints [16,17]. By measuring the change rate of bit error rate (BER) and SNR, it can determine whether the optical fiber channel was attacked. But excessive BER affected normal communication. The security identification can be also performed by measuring the change of the SNR, which didn’t affect the normal transmission of signals [16]. It had the advantages of simplicity, convenience, and low price. Although the above methods can achieve secure identity identification in optical networks under certain conditions, there are still some questions. First, the device hardware fingerprint used in the above solution comes from the systems themselves, which are susceptible to device aging and channel instability. Secondly, due to the differences between the equipment caused by the manufacturing process, it is difficult to manually control. The flexibility, and portability of the above solutions need to be improved.
In response to the above research status and problems in the physical layer of optical networks, a secure and controllable hardware fingerprint identification system based on electro-optical intensity chaos is proposed. The angle distance entire (ADE) feature fingerprint based on chaotic phase space reconstruction (PSR) is constructed to identify the optical transmitters. Since the chaos is generated by the nonlinear system and the attractor of the chaos has global stability, the invariant and unique feature can be extracted from optical chaos and used as the fingerprint of the system. Compared with hardware fingerprints based on device features or channel features, the optical chaotic fingerprint proposed in this paper has security and controllability. Therefore, fingerprint identification based on optical chaos has obvious advantages and important research significance. And this scheme can resist not only injection attacks but also eavesdropping attacks, without the need to increase the complexity of the chaos, chaotic bandwidth, and chaos synchronization.
The structure of this paper is arranged as follows, section 2 introduces the theoretical model of the optical transmitter with the chaotic fingerprint. Section 3 analyzes the chaotic fingerprint. The simulation results are shown in subsection 3.1. The experiment results of the chaotic fingerprint are discussed in subsection 3.2. Subsection 3.3 analyzes the resistance to the injection attack. Section 4 presents the communication system and analyze the performance of the chaotic fingerprint transmitter.
2. Model of the optical transmitter
This section proposes an optical transmitter structure with a chaotic fingerprint. The system consists of two main parts. One is to generate chaos using electro-optical feedback loops, and then construct chaotic fingerprints for fingerprint recognition. The second is to load fingerprints into the signal. The system diagram of the transmitter is shown in Fig. 1.
Fig. 1. System diagram of the optical transmitter with the chaotic fingerprint. DFB: distributed feedback laser, PC:polarization controller, AM: amplitude modulator, TD: time delay fiber, PD: photodiode, RF: radio frequency amplifier, ADC: analog-digital converter, S/P: serial-to-parallel conversion.
First, an electro-optical intensity feedback chaos generation system is established. A continuous wave (CW) is generated by a distributed feedback laser (DFB). Then the CW is injected into an amplitude modulation (AM). The output of the AM passes through an optical time delay line (TD). The optical wave passes through a photodetector (PD) and is amplified by a radio frequency (RF) amplifier. Finally, the electrical signal enters the AM as a modulated signal. The above devices are connected to form an optoelectronic feedback loop, which can generate a noise-like optical intensity chaotic signal [18].
Then the theoretical model of chaotic feature fingerprinting is introduced. The chaos is subjected to PSR, which is an effective method for analyzing nonlinear systems and has been widely used in nonlinear signal processing, such as quantitatively estimating the complexity of the system and estimating the dynamic behavior of the system. So we extract features from the reconstructed phase space (RPS) to reflect the nonlinear system. A phase space of a one-dimensional time series can be constructed using the embedding theorem. The time series is $x(n)$, where $n = 1, 2,\ldots, N$, and $N$ is the total length of the time series. The reconstructed phase space can be expressed as:
Then, the angle and distance between points in the RPS are analyzed. The angle between two points is calculated in Eq. (7). The distance between two points is in Eq. (8).
Since the AF, DF, and EF reflect part of the chaotic features respectively, we construct the angle distance (AD) feature by combining the angle and distance features in Eq. (12). Then the angle distance and entire (ADE) feature is constructed by combining the EF of the RPS, the AF of the angle matrix, and the DF of the distance matrix in Eq. (13).
Finally, the principle of fingerprint loading is introduced. The filtered optical chaos from low-pass filters$_{1}$ is used to extract the fingerprint. The data is transformed by serial-to-parallel conversion (S/P). Regarding [19], the fingerprint loading is implemented using the In-phase and Quadrature-phase encryption (IQE) in Eq. (14). The chaos signals from low-pass filters$_{1}$ and filters$_{2}$ are used for IQE. The data passing through the IQE is converted from analog to digital. Then, we select the appropriate electro-optical modulator according to the communication requirements, which means that this scheme is transparent regarding the modulation format. Due to the use of IQE to load fingerprints and encrypt signals in the transmitter, the receiver also needs corresponding I/Q decryption (IQD) to achieve signal decryption in Eq. (15).
3. Analysis of the chaotic fingerprint
In this section, the chaos is simulated first and the chaotic features are extracted. The effect of different parameters on the chaotic features is analyzed to choose the sensitive parameter as the fingerprint. The chaotic fingerprint is recognized by the support vector machines (SVM).
3.1 Chaotic fingerprint simulation
The electro-optical chaos is simulated with the fourth-order Runge-Kutta algorithm, and the simulation step is set to 10 ps. Each chaotic system is simulated 100 times with 10,000,000 points. The last 100,000 points are used for feature extraction. The false nearest neighbor method is utilized to get the embedding dimension $m=6$ [20] and the embedding delay is set to $\tau =2$ according to C-C method [21]. The $k$ is set to 101 at first, so the number of features is 100. The effects of different parameters of the chaotic system on angle, distance, and entire feature values are simulated in Fig. 2. The first row shows the features of five chaotic systems at different feedback coefficients $\beta = \{3, 3.5, 4, 4.5, 5\}$. Specifically, Fig. 2(${\rm a}$) shows the coordinates of three chaotic features ($F_{A}, F_{D}, F_{E}$). Three different features with $k$ changing are respectively shown in Figs. 2 (${\rm b},c,d$). The chaos with different $\beta$ are well distinguished in AF, DF, and EF. The second row shows the features of chaos with different time delay value $T\rm =\{6{\rm ns}, 7ns, 8ns, 9ns, 10ns\}$. There is no clear distinction in AF, DF, and EF with different $T$. Therefore, it is decided to choose $\beta$ as the fingerprint key for different chaotic systems. The chaos is initial value sensitive, which means the chaos waveforms are different with different initial values. The third row shows the features of chaos generated by the same system with different initial values. The results show the chaotic features extracted five times are indistinguishable in Fig. 2(${\rm i},j,k,l$). This indicates that the features of the same chaotic system have stable invariance and do not vary with the number of simulations. Thus, the RPS features of chaos have the essential properties of a fingerprint which have hardware parameter sensitivity and time invariance.
Fig. 2. Angle, distance, and entire features of the chaos with different $\beta$. The first column shows three different features in 3 dimension coordinates. The first row shows the features with the different gain coefficient $\beta$. The second row is with different time delay $T$. The third row is with different initial values of the chaotic system.
Figure 2 analyzes the distinction of chaotic features at different $k$. In the following, the distinction of different chaotic features is analyzed by the boxplots in Fig. 3. The chaos is controlled by feedback coefficient $\beta$. There are five boxplots in each subfigure, representing five chaotic systems with $\beta =\{3, 3.5, 4, 4.5, 5\}$. In each subplot, the boxplots of the five systems are differentiated, which means that the chaos can be identified by the AF, DF, and EF respectively.
Fig. 3. The boxplots of angular, distance, and entire features of five chaos with $\beta = \{3, 3.5, 4, 4.5,5\}$. (a)-(d) includes 4 different angular features $F_{A1}-F_{A4}$. In each boxplot, there are five different boxplots of different chaos. (e)-(h) are the corresponding distance features. (i)-(l) are the corresponding entire features.
Figure 4 shows the time domain plot of the chaos and the corresponding color contour map of the normalized ADE feature with 5 different $\beta$, $T=10 \rm ~ns$. The amplitude of the chaos becomes larger and the complexity becomes higher as $\beta$ increases in the first row of Fig. 4. The values of the features become higher as the $\beta$ increases in the second row of Fig. 4. The different colors represent the magnitude of the feature values, the black lines are five contour lines from 0.6 to 1. Therefore, the chaotic waveforms with different $\beta$ have different ADE features. So the identification of the transmitter can be achieved by using chaotic ADE features as fingerprints.
Fig. 4. Chaos and the corresponding ADE features with different $\beta$. The first row shows the time-domain waveforms of chaos. The second row shows the color contour map composed of ADE feature values.
Five chaotic ADE features are distinguished with SVM in Fig. 5. Each chaotic system is simulated one hundred times to produce 100 sets of chaotic ADE features. The first fifty simulations are used for training and the last fifty data are used for testing. Figure 5(a) shows the classification of five chaotic ADE features in the two-dimensional space of Feature 1 $F_{ADE1}$ and Feature 2 $F_{ADE2}$. The five chaos can be clearly distinguished. Figure 5(b) shows the confusion matrix of the five chaos. The column represents the prediction category, and the total number of each column is the number of data predicted as that category. The row represents the true category of the data. The five classification accuracy achieves 100%. Figure 5 verifies the feasibility of chaotic fingerprint identification using SVM.
Fig. 5. ADE fingerprint identification results. (a) shows the classification of five chaotic ADE features, and (b) shows the confusion matrix of the predicted class and the class.
We analyze the influence of different parameters on identification accuracy in Fig. 6. The SVM algorithm is used to classify the features. Five chaotic systems are simulated and their feedback coefficients are $\beta =\{3,3.2,3.4,3.6,3.8\}$. Figure 6(a) shows the effect of the number of features on the identification accuracy. The number of features is equal to $k-1$. the identification accuracy of the ADE features is mostly higher than those of the other four features. In Fig. 6(b), we analyze the effect of the feedback coefficient interval $\Delta \beta$ on the identification rate at $k=7$. As $\Delta \beta$ increases, the accuracy rates become higher. Because $\beta$ is the main factor affecting the nonlinear dynamics of electro-optical feedback chaotic systems [22]. And the PSR reflects the dynamic properties of the nonlinear system, so the PSR-based chaotic fingerprints are significantly affected by $\beta$. When $\Delta \beta$ is larger, the nonlinear dynamic difference of chaos is larger with the higher recognition rates. When $\Delta \beta$ is 0.2, the values of the identification accuracy of all five features are higher than 90%. The fingerprint identification rate of the ADE feature is the highest at 93.5%. When $\Delta \beta$ is 0.5, the identification accuracy of ADE features is 100%. In summary, ADE features have higher identification accuracy most of the time compared with the other four.
Fig. 6. Fingerprint identification accuracy of five chaotic systems as functions of different parameters. (a) is as a function of the number of features. (b) is as a function of the feedback coefficient interval.
To ensure the security of chaotic fingerprints, it is necessary to set the same filters at the transmitter and the receiver. Feature fingerprint extraction and identification are performed using filtered chaos. The influence of filters on chaos and identification accuracy is analyzed. Firstly, the impact of the filter on chaos is analyzed. The normalized permutation entropy (PE) is used to map the unpredictability of time series. PE is widely used in nonlinear dynamic quantitative analysis subsequently [23,24]. The calculation method for PE is: the time series $\left \{ x\left (i \right ), i=1,2,\ldots,N \right \}$ is reconstructed to $X_{j}=\left \{ x\left (j \right ),x\left (j+D \right ),x(j+2D),\ldots,x(j+(m-1)D) \right \}$, where $j=\{1,2,\ldots,N-(m-1)D\}$. $m$ is the ordinal pattern length and $D$ is the embedding delay. Calculate the ranks of the values in the sequence $X_{j}$ to get ordinal patterns $\pi _{j}=\{d_{1},d_{2},\ldots,d_{m}\}$ [25]. There are at most $m!$ ordinal patterns permutations. The probability of occurrence for a given ordinal pattern $\pi _{j}$ is $p\left (\pi _{j}\right )$. The normalized permutation entropy is PE in Eq. (16).
The range of PE is from 0 to 1. The higher the value of PE, the higher the complexity [26]. We take 120,000 points for PE calculation [27]. The ordinal pattern length $m = 6$ and the embedding delay $D = 2$ [7,27]. The PE of the chaos as functions of the bandwidth of low-pass filters and feedback coefficient $\beta$ is simulated in Fig. 7(a). As $\beta$ and the bandwidth increase, the PE values become larger, indicating that the chaos becomes more complex. When $\beta =5$ and the bandwidth of the low-pass filter is ${\rm BW}=1$ GHz, PE is ${\rm 0}.32$ and the largest Lyapunov exponent [28] is 0.01, which indicates that the output of the filter is chaos with low complexity. When someone wants to tamper or disguise attacks, he needs to reconstruct the fingerprint and then load the fingerprint into the fake information. The filter is the key to safeguarding the chaotic ADE fingerprint from being cracked. Then the effect of the filter’s bandwidth on the identification rate of chaotic ADE fingerprints is analyzed in Fig. 7(b). The filter’s bandwidth of the legal receiver is set as the horizontal axis, and the filter’s bandwidth of the illegal receiver is the vertical axis. The legal and illegal chaotic fingerprints are identified by SVM. The vast majority of the area is yellow, representing a 100% identification rate. When the illegal attacker happens to use the same filter as the legitimate transmitter, the identification rate is 50%, which means an illegal attacker cannot be recognized. The identification rate decreases slightly as the cut-off frequency of the low-pass filter increases. When the filter bandwidth is narrow and the filter bandwidth difference between legal and illegal transmitters is 1 GHz, the identification rate can reach 100%. Overall, the recognition rate of illegal chaotic fingerprints was 91.63% in the frequency range of 0 to 50 GHz.
Fig. 7. The effect of the filter bandwidth and the feedback coefficient on the PE of chaos, and the effect of the filter bandwidth on identification accuracy between legal and illegal transmitters. (a) is PE as a function of filter bandwidth and feedback coefficients (b) is identification rate as a function of filter bandwidth.
This section first introduces the theoretical model of the chaotic fingerprint, then discusses the identifiability and invariance of the electro-optical intensity chaotic ADE feature. The performance of the ADE feature fingerprint is analyzed by boxplot and SVM algorithm. Comparing the identification accuracy of the five types of fingerprints including $F_{A}$, $F_{D}$, $F_{E}$, $F_{AD}$ feature, and $F_{ADE}$ feature, the identification accuracy of ADE feature $F_{ADE}$ is the highest.
3.2 Performance analysis in experiment
This subsection verifies the performance of the ADE feature fingerprint in the experiment. We use a laser (EXFO FLS-2800) at $\lambda _{1}=1550$ nm with a linewidth of 100 kHz to generate continuous waves (CW). The laser is controlled by a Polarization Controller (PC) and amplified by an Erbium Doped Fiber Amplifier (EDFA Amonics AEDFA23-B-FA). The laser is injected into the Mach–Zehnder modulator (MZM, Mach-40, Thorlabs) to achieve intensity modulation. The modulated optical field is divided into two parts through a 50:50 optical coupler (OC). One part is passed through a fiber Delay line (DL), a photodiode (${\rm PD}_{1}$, RXM25AF, Thorlabs, 3 dB bandwidth of 25 GHz and a responsivity of 0.75 A/W), an RF amplifier (SHF-S126A), and then injected into the RF voltage port of MZM to form an intensity feedback loop. The other part goes through ${\rm PD}_{2}$ (XPDV2320R-VF-FP, Finisar) and is sampled by the 25 GS/s oscilloscope (OSC, Tektronix DPO 72004C). The chaotic signal collected by OSC is subjected to offline feature extraction, chaotic fingerprint construction, and identification. Because the features are sensitive to feedback coefficient $\beta$ in the simulation and the $\beta$ is linearly related to the injection power of the MZM. The EDFA is changing to be equivalent to the changing of $\beta$ in the experiment. At the same power, the systems are restarted to collect 100 sets of data.
Firstly, the identification accuracy of legal chaotic feature fingerprints distinguished from illegal fingerprints is analyzed. When there is only one legal chaotic fingerprint, all the collected data are divided into one legal chaotic fingerprint and other illegal chaotic fingerprints. When the EDFA power of the legal chaotic system is different, the identification accuracy is different in Table 1. All the accuracies are higher than 91.7%. When the power of EDFA is 20 dBm, the accuracy is the highest of 99.2%. Then we analyze the identification rate between legal chaotic fingerprints.
Table 1. The identification rate of legal chaotic ADE fingerprints distinguished from illegal fingerprints.
Multiple chaotic fingerprints are multi-classified in Fig. 8(a). Multiple chaos systems are generated by changing the power of EDFA, because $\beta$ is linearly related to the power of EDFA. The power values of EDFAs in chaotic systems are changed from 10 dBm to 20 dBm with 1 dBm power interval in the experiment. Figure 8(a) shows the recognition rate of 1 to 9 chaotic fingerprints. For example, we change the power of EDFA to 10 dBm and 11 dBm to generate two chaotic systems, and we change the power of EDFA from 10 dBm to 18 dBm to represent nine chaotic systems. The identification accuracy of ADE feature fingerprints is significantly higher than other feature fingerprints. When there is only one legal chaotic system, the accuracy rate is 100%. When there are five legal chaotic systems, the five-classification accuracy rate is 86.8%. As the number of legal systems increases, the accuracy rate decreases. Then the identification rates of three chaotic systems are analyzed in Fig. 8(b). The identification rates are different when the EDFA power value intervals are different. When the interval is larger, the accuracy rate is higher. When the interval is 1 dBm, the accuracy rate is 85.3%. When the power interval is 2 dBm, the accuracy rate is 98%. When the interval is 4 dBm, the accuracy rate reaches 99.3%.
Fig. 8. Identification rate of multiple chaotic systems in the experiment. $({\rm a})$ is the multi-classified identification rate of features of chaotic systems with a 1 dBm EDFA power interval. $({\rm b})$ is the identification rate of three chaotic systems with different power differences.
Compared with the traditional hardware fingerprint extraction from the transmission signal or channel, chaotic ADE feature fingerprint is variable and flexible. The cost of giving the transmitter a flexible and controllable fingerprint to achieve secure authentication is the introduction of an additional chaotic system. Therefore, the communication performance of the transmitter based on chaotic fingerprints will be analyzed later.
3.3 Attack scenario analysis
The attack scenarios and attack resistance results are evaluated for this scheme. Since the optical transmitter emits optical signals with chaotic fingerprints and chaotic light for authentication, the optical attack situations at two central wavelengths are analyzed separately. A schematic diagram of the attack scenario is shown in Fig. 9. Two chaotic transmitters in the optical network are simulated. The attacker1 injects the laser into the chaotic carrier of transmitter1. Attacker2 injects the signal into the wavelength of transmitter2. At the receiver, fingerprint recognition is performed on chaotic carriers, and chaos is used to decrypt information. Firstly, we analyze the first attack scenario. When the attacker1 injects laser into the chaos, the fingerprint of the transmitter1 at the receiver is changed, which also affects the decryption of the legitimate transmitter1. At this point, the injection attack is discovered and resisted through fingerprint recognition.
Fig. 9. System security performance analysis including injection attacks and the eavesdropping attack defense in optical networks.
Then we analyze the second attack scenario. When attacker2 injects illegal signals into the wavelength of transmitter2’s signal for tampering or impersonation, the chaotic fingerprint of transmitter2 is not affected. But before the receiver gets the signal sent by attacker2, the signal must go through a chaotic fingerprint processing stage of I/Q decryption. Although attacker2 can obtain the chaos from the public link, he cannot obtain the filtered chaos used for IDE. The receiver receives garbled information rather than messages sent by attacker2, which cannot achieve the purpose of tampering or impersonating. Therefore, regardless of whether the illegal injection attack is at the chaotic wavelength or the wavelength of the information, this scheme has resistance.
It is worth mentioning that the IDE also encrypts information, avoiding eavesdropping attacks, without the problems of key exposure and chaotic synchronization in traditional chaotic encryption. The chaos used for the encryption and the IQE are secure. If you want to get the signal, you need to get the IQE matrix, which dose not only include fixed matrix coefficients $a$ and $b$ as the keys, but also related to the different chaotic sequences generated each time, due to the initial value sensitivity of chaos. The chaos is also secured by the ADC resolution, sampling rate, bandwidth and two filters together. So, it is difficult for the illegals to obtain the IQE matrix. Overall, this scheme can resist injection attacks and eavesdropping attacks.
4. Transmission analysis
This section simulates the recognition rate of chaotic fingerprints and the bit error rate (BER) of signals under the influence of the transmission link. The transmission system based on the optical transmitter with a chaotic fingerprint is shown in Fig. 10. The optical chaos at the central wavelength of $\lambda _{1}$ and the signal at the central wavelength $\lambda _{2}$ are transmitted after a multiplexer (MUX). At the receiver, encrypted messages and chaos are separated by a demultiplexer (DEMUX). The identification process of the transmitter is divided into two steps. First, the chaos is filtered and the chaotic fingerprint is identified. Then the data is obtained by IQ decryption (IQD) and parallel-to-serial (P/S).
The transmission link is simulated by the split-step Fourier algorithm [29]. The time-domain waveform of the system is performed in Fig. 11. The signal is 25 GBaud QPSK. The OSNR is 20 dB. The fiber is 100 km, which contains 50 km of normal dispersion fiber and 50 km of anomalous dispersion compensated fiber with $\beta _{2}=\pm 20\times 10^{-27}{\rm s}^{2}/m$. The attenuation is $0.2\times 10^{-3} {\rm dB}/m$. The nonlinear index is $2.6\times 10^{-20} {\rm m}^{2}/W$. The wavelength of chaos is 193.1 THz. The wavelength of the signal is 193.2 THz. The chaos waveforms at the transmitter and the receiver are shown in Fig. 11(${\rm a},d$). Figure 11(${\rm b},e$) shows the I and Q of the initial signal at the transmitter and the final signal at the receiver. Figure 11(${\rm c},f$) shows the I and Q of the signal after IQE at the transmitter and the signal before IQD at the receiver. The amplitude of the chaos and the signal are normalized. The bandwidth of the low-pass filter of chaos is set to ${\rm BW}=10$ GHz, and the coefficients of chaos are $a=b=7$. 200,000 bits are taken for BER calculation by Monte Carlo method [30]. The BER of the signal after IQE is 0.0352. The BER after the transmission is 0.0475. The BER of the signal after IQD is $3.7\times 10^{-4}$. The BERs of the signals after IQE and after transmission are higher than the hard decision forward error correction (HD-FEC) threshold $3.8\times 10^{-3}$ [31]. The BER after decryption is lower than HD-FEC. IQE not only realizes the loading of chaotic ADE fingerprints but also ensures the security of transmitted information. So, the feasibility of this system is verified.
Fig. 11. Time domain waveforms of the chaos and signals at the transmitter and receiver. (a) Chaos at the transmitter, (b) the in-phase (I) signal at the transmitter and receiver, (c) the I part of the signal after IQE and before IQD, (d) chaos at the receiver, (e) the quadrature-phase (Q) signal at the transmitter and receiver, (f) the Q part of the signal after IQE and before IQD.
Then the effect of the transmission link on the chaos is analyzed. Figure 12 analyzes the cross-correlation coefficient (CC) [7] between the chaos after transmission and the chaos emitted. CC measures the correlation degree of the two sequences. The correlation coefficient is [?]:
Fig. 12. CC for chaos at transmitter and receiver. The first row is CC under the influence of dispersion, the second row is CC after dispersion compensation. (a),(b) show the CC curves at different feedback coefficients $\beta$. (c),(d) are the CC curves at different distances, (e),(f) are the CC curves at different OSNR.
Next, we analyze the effect of transmission on the identification rate of chaotic feature fingerprints. Five chaotic systems with $\beta =\{3, 3.5, 4, 4.5, 5\}$ are simulated and ADE feature fingerprints are extracted. In Fig. 13(a), the OSNR is 25 dB. The identification rate of the ADE feature fingerprint of chaos with $\beta =3$ is analyzed. Chaotic feature fingerprints of different transmission distances are constructed into a dataset and the fingerprints are identified using SVM. Due to transmission loss, amplifier noise is introduced if amplification is performed every 100 km. Therefore, as the transmission distance increases, the chaotic waveform changes and the ADE fingerprint identification rate decreases. When the transmission distance is within 600 km, the identification accuracy is close to 100% in all cases. Then the transmission distance is set to 500 km. The identification rate as a function of ONSR is shown in Fig. 13(b). The identification accuracy reaches 98% when the OSNR reaches 25 dB. Therefore, the chaotic ADE feature fingerprint can achieve an identification rate close to 100% after 600 km transmission at the OSNR of 25 dB.
Fig. 13. The effect of transmission link on identification rate. (a) is the effect of transmission distance on identification rate with $\beta =3$, ${\rm OSNR}=25~dB$. (b) is the effect of OSNR of transmission link on identification rate. with a transmission distance of 500 km.
The transmission performance of the signal in this system is analyzed in Fig. 14. The BER of the signal after IQE, transmission, and IQD is calculated first. And it is assumed that there is an illegal attacker Eve performing an injection attack before the receiver. The BER of the attack signal after IQD is calculated to determine whether Eve has achieved tampering or forgery.
Fig. 14. The BER as functions of system parameters and transmission links. (a) shows the effect of filter bandwidth on the signal BER. (b) shows the effect of coefficients $a$ and $b$ of chaos on BER. (c) is the effect of transmission distance on BER. (d) is the effect of OSNR on BER.
The bandwidth of filter$_{2}$ is 45 GHz, chaos coefficients are $a=b=7$, transmission distance is 100 km, and OSNR is 25 dB. The effect of bandwidth of filter$_{1}$ on BER is analyzed in Fig. 14(a). The signal after IQE, the signal after transmission, and the signal of Eve attack after IQD are almost unaffected by the bandwidth of filter$_{1}$. The BER of the signal after IQE is about 0.150. The BER of the transmitted signal is 0.158. After the IQD transform, the BER is about $2.8\times 10^{-3}$. Therefore, IQE can be considered encryption and IQD can be understood as decryption. The filter bandwidth has little effect on encryption and some effect on decryption. The BER of the low-bandwidth filter is smaller than the BER of the high-bandwidth filter. Figure 14(b) analyzes the effect of chaotic coefficients $a$ or $b$ on BER. The bandwidth values of filter$_{1}$ and filter$_{2}$ are 45GHz. If the chaos coefficient is larger, the BER after encryption and after decryption is larger. Similarly, the BER of illegal signals injected by Eve is also higher. When the chaos coefficient is less than 11, the BER of the decrypted signal is lower than HD-FEC, which satisfies the transmission requirement. Figure 14(c) analyzes the effect of the length of transmission fiber on BER. The bandwidth of filter$_{2}$ is 10 GHz, and chaos coefficients are $a=b=7$. When the transmission distance is 300 km, the BER of the decrypted signal is $1.6\times 10^{-3}$, the BER of the signal after IQE is 0.035, and the BER of the transmitted signal is 0.051. The BER of the Eve signal after IQD is 0.036. As the transmission distance increases, the BER of the decrypted signal is higher than that of HD-FEC. Figure 14(d) analyzes the effect of OSNR on BER. The bandwidth of filter$_{2}$ is 10 GHz, chaos coefficients are $a=b=7$ and the length of fiber is 100 km. When the OSNR is 20 dB, the BER of the decrypted signal is $3.2\times 10^{-4}$. In summary, this system can achieve safe and reliable transmission of 25GBaud QPSK signal for 300 km at OSNR of 25 dB.
5. Conclusion
In this paper, an optical transmitter identification scheme is proposed. An ADE fingerprint based on optical chaotic PSR is constructed. The chaotic fingerprint is loaded into the signal using IQE, and IQD is used to achieve the demodulation of the legal signal and the defense of illegal optical injection. The security of the ADE fingerprint is verified by the simulation and the experiment. The chaotic ADE fingerprint can be controlled dynamically by changing the chaotic feedback coefficients. The security of the fingerprint is guaranteed through the filter. In the experiment, the recognition rate of three legal transmitters is up to 99.3%. The recognition rate of illegal transmitters is up to 99.2%. The system achieves both controllable and effective recognition of legitimate chaotic fingerprints and resists injection attacks by illegals. The transmission performance of this scheme is then simulated. With an OSNR of 25 dB, five optical transmitters are 100% recognized after 600 km of transmission. The BER of the 25GBaud QPSK signal after 300 km transmission at the OSNR of 25dB is $1.6\times 10^{-3}$ without chaotic synchronization. This scheme uses low-complexity chaos for encryption in authentication and does not need to introduce additional nonlinearities for TDS hiding. Therefore, the scheme is resistant to injection and eavesdropping attacks, transparent to the signal format, and can be used for long-distance secure communication in the physical layer of the optical network.
Funding
National Natural Science Foundation of China (61831003, 62021005).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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