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Abstract
In recent years, the transmission capacity of chaotic secure communications has been greatly expanded by combining coherent detection and multi-dimensional multiplexing. However, demonstrations over 1000 km fiber are yet to be further explored. In this paper, we propose a coherent optical secure transmission system based on analog-digital hybrid chaos. By introducing an analog-digital converter (ADC) and a bit extraction into the feedback loop of entropy source, the broadband analog chaos is converted into a binary digital signal. This binary digital signal is then mapped to a 65536-level pulse amplitude modulation (PAM) signal and injected into the semiconductor laser (SL) to regenerate the analog chaos, forming a closed loop. The binary digital signal from the chaos source and the encrypted signal are transmitted via wavelength division multiplexing (WDM). By using conventional digital signal processing (DSP) algorithms and neural networks for post-compensation, long-haul high-quality chaotic synchronization and high-performance secure communication are achieved. In addition, the probability density distribution of the analog chaotic signal is effectively improved by adopting the additional higher-order mapping operation in the digital part of the chaos source. The proof-of-concept experimental results show that our proposed scheme can support the secure transmission of 100 Gb/s quadrature phase shift keying (QPSK) signals over 1000 km of standard single-mode fiber (SSMF). The decrypted bit error rate (BER) reaches 9.88 × 10−4, which is well below the 7% forward error correction (FEC) threshold (BER = 3.8 × 10−3). This research provides a potential solution for high-capacity long-haul chaotic optical communications and fills the gap in secure communications based on analog-digital hybrid chaos.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber optic communication systems have the advantages of low transmission loss, large bandwidth and low cost, which can realize high-speed and long-haul transmission and carry more than 90% of the global data exchange. However, the eavesdropping technologies are also becoming more and more mature with the popularity of fiber optic communication [1]. In order to ensure the security of optical networks, the common method is to use upper-layer security protocols. But the rapid development of quantum computing makes the encryption algorithms face the threat of brute force cracking. How to guarantee the security of optical networks has always been a research hotspot [2,3]. A variety of new long-haul and high-rate secure communication schemes have emerged [4–6]. The physical layer can provide irreplaceable security for the entire optical network. The rapid development of physical layer security encryption schemes in recent years has built another powerful line of defense for network security.
Chaotic secure communication is one of the highly promising physical layer security encryption schemes. This scheme uses optical chaotic carriers to scramble the phase or intensity of the transmitted data, and decrypts it at the receiving end by chaotic synchronization. It can be built with commercial devices, is less difficult to implement, and is compatible with existing communication networks. In 2005, A. Argyris et al. first demonstrated 2.4 Gbit/s secure transmission over 120 km in the metropolitan area network of Athens, Greece [7]. In 2010, R. Lavrov et al. realized 10 Gbit/s differential phase shift keying (DPSK) signal secure transmission over 100 km [8]. In 2018, Ke et al. reported a successful 30 Gbit/s signal transmission of a duobinary message encrypted by a chaotic optical carrier over 100 km fiber [9]. In 2022, Gao et al. achieved secure transmission of 32 Gbit/s on-off-key (OOK) signal over 200 km fiber through self-feedback phase encryption [10]. Lin et al. used a trained deep learning model to generate chaotic waveforms and demonstrated 56 Gbit/s 4-level pulse amplitude modulation (PAM) secure transmission over 100 km [11].
The application of multi-dimensional multiplexing is a key way to enhance the transmission rate. Several chaotic secure communication schemes based on wavelength division multiplexing (WDM) have been experimentally demonstrated. In 2019, Fu et al. realized secure transmission of 2 × 10 Gbit/s signals over 100 km [12]. In 2021, Zhao et al. demonstrated secure transmission of 4 × 12.5 Gbit/s signals over 50 km [13]. In addition, using space division multiplexing (SDM) can also achieve a large capacity expansion. In 2022, we proposed a chaotic optical communication scheme based on a 7-core fiber and demonstrated the secure transmission of 6 × 40 Gbit/s 16 quadrature amplitude modulation (QAM) signals over 10 km [14]. In 2023, Shen et al. realized the secure transmission of 7 × 10 Gbit/s OOK signals over 130 km [15].
Adopting higher-order modulation formats and coherent detection techniques can improve the spectrum efficiency, thus further enhancing the single-wave secrecy data rate. In 2022, Yang et al. combined coherent detection and deep learning to achieve chaotic synchronization in the digital domain and demonstrated the secure transmission of a 30 Gbit/s quadrature phase shift keying (QPSK) signal over 340 km [16]. In the same year, we proposed a coherent optical communication scheme based on hybrid chaotic encryption and achieved the secure transmission of 60 Gbit/s QPSK signals over 100 km [17].
By combining coherent communication and multi-dimensional multiplexing, the bit rate-distance product of chaotic secure communication has been substantially improved in the past few decades. However, the transmission distance has always been difficult to exceed the order of 1000 km due to the fiber transmission impairment of analog signals. In 2021, Jiang et al. introduced an orthogonal basis between the analog chaotic carrier and the message, and achieved chaotic decryption by digital signal processing (DSP) algorithms. They demonstrated the secure transmission of a 112 Gbit/s signal over 1040 km fiber [18]. Due to the orthogonal basis, there is a trade-off between its security and practicality. In 2023, Wang et al. explored the limiting distance of analog chaotic hardware synchronization. They achieved co-driven synchronization over 1040 km fiber using a hybrid amplification of an erbium-doped fiber amplifier (EDFA) and a distributed fiber Raman amplifier (DFRA). And the synchronization coefficient was calculated as 0.9041, which reached the minimum requirement for chaotic communication [19].
To further enhance the transmission distance, using analog-digital hybrid optical chaos as an entropy source is a feasible solution. By introducing an analog-digital converter (ADC) and a bit extraction into the feedback loop of chaos source, the conversion of a broadband analog signal to a binary digital signal is achieved. Then, the binary digital signal is used as the driving signal for the nonlinear conversion module to regenerate the analog chaotic signal. Since the binary digital driving signal can resist channel impairment well, the analog-digital hybrid chaos source can realize long-haul synchronization. What’s more, the hybrid chaos-based scheme can also fill the gap between analog and digital systems. The key space of analog chaotic systems is limited by the range of physical parameters. Digital chaotic systems, on the other hand, have a relatively large key space. However, limited by the computation speed of DSP chips, digital systems often need to use a key stream with short periodicity, leading to security vulnerabilities. By combining analog and digital systems, security can be effectively enhanced. In our previous works, we have experimentally demonstrated high-quality chaotic synchronization over 200 km [20]. But the hybrid chaos-based scheme still has some limitations. Firstly, the complex structure imposes more stringent requirements on the chaotic synchronization technique, including the synchronization of the original analog system, and the relative synchronization between the digital signals and the analog signals. Secondly, how to achieve synergy between the analog hardware structure and the DSP algorithms is also a major challenge. In addition, due to the use of binary digital signals as driving signals, the resulting analog chaos has poor distribution characteristics and the system security is affected. Limited by the above factors, the long-haul communication experiment of this scheme has not been completed.
In this paper, we propose a coherent optical secure communication scheme based on analog-digital hybrid chaos. By using conventional DSP algorithms and neural networks for post-compensation, long-haul high-quality chaotic synchronization and high-performance secure communication are achieved. In the proof-of-concept experiments, the proposed scheme can support the secure transmission of 100 Gbit/s QPSK signal over 1000 km fiber and the decrypted bit error rate (BER) performance is below the 7% forward error correction (FEC) threshold (BER = 3.8 × 10−3). This is the first long-haul, high-capacity experimental verification of secure communication based on hybrid chaos. Further, we analyze the security of this scheme in details and discuss its feasibility in the multi-node communication system.
2. Principle
The structure of the proposed system consists of three main components: a transmitter with analog-digital hybrid chaos source and chaotic encryption, a fiber optic link with WDM, and a receiver with chaotic synchronization and chaotic decryption, as depicted in Fig. 1.
Fig. 1. Schematic diagram of analog-digital hybrid chaos-based coherent optical secure communication.
At the transmission side, the analog chaotic signal generated by the hybrid chaos source is sampled and converted into a digital sequence {Ai}. It is used to encrypt data symbols {Ti} together with another digital chaotic sequence {Di} generated by a mathematical formula. The procedure can be expressed by
Then, the encrypted data {Ti'} and the digital driving signal {Ci} from the entropy source are transmitted on the same fiber link after WDM.
At the receiver side, after demultiplexing and two coherent detections, the recovered digital driving signal {Ci'} and the received encrypted data {Ri'} can be obtained respectively. The digital drive signal is then used to realize chaotic synchronization. Similarly, this analog chaotic synchronization signal is sampled and converted into a digital sequence {Ai'}. Thus, the decrypted data can be expressed as
If the channel impairment is perfectly compensated and there is no synchronization error, it can be assumed that Ci = Ci’, Ai = Ai’, Ri'=Ti’. Consequently, the recovered data signal can be expressed as
As one of the most important components of the proposed scheme, the specific structure of the analog-digital hybrid chaos source is shown in Fig. 2.
Fig. 2. Schematic diagram of analog-digital chaos source. LD, laser diode; SL, semiconductor laser; EA, electrical amplifier; PD, photodetector; IM, intensity modulator; OC, optical circulator; ADC, analog-digital converter; DAC, digital-analog converter.
The basic principal of the hybrid entropy source is similar to those in our previous works [21]. In this paper, we use the inner nonlinear effects of semiconductor lasers (SL) and the nonlinearity of modulators to generate chaotic signals. Here an intensity modulator (IM) is adopted to load a digital electrical signal onto an optical carrier. This intensity modulated signal is injected into the SL through an optical circulator (OC). The strong nonlinearity of SL can effectively enhance the bandwidth of chaotic signals. Thus, a broadband noise-like chaotic signal is generated. This chaotic signal is then converted to a digital electrical signal by the photodetector (PD) and analog-digital converter (ADC), creating an analog-digital hybrid feedback system. To further improve the performance of the chaotic source, we introduce an additional operation of mapping in the digital part. As shown in Fig. 2, the binary electrical signal at point A is mapped to the 65536-level PAM signal at point B through a table of basis [22].
This mapping operation does not require a complicated mathematical operation process, which almost does not affect the computational complexity. The injection of the ultra-high-order PAM signal can make the probability density distribution of the chaotic signal at point C closer to the Gaussian distribution, which effectively improves the randomness of the analog chaos. Meanwhile, through coherent detection and DSP algorithms, the binary data at point A can be transmitted error-free over 1000 km fiber. This implies the realizability of long-haul co-drive synchronization.
3. Experimental setup and results
The experimental setup is shown in Fig. 3. In the chaos generation part, the light from a laser diode (LD1, Alnair Labs, TLG-200) at ∼1549.700 nm with ∼100 kHz linewidth is modulated by IM1. The drive voltage of the IM1 reaches 2.77 times half-wave voltage of it. This intensity-modulated signal is injected into the SL1 (SWLD-1550100122-02) through an OC with an injected intensity of −23.04 dBm, which is the optimal value in the experiment. The threshold current of SL1 is 12.65 mA, and its bias current is set to 39 mA. And the center wavelength is set to 1549.654 nm, at which optimal chaotic synchronization can be achieved. Then the analog chaotic signal is obtained from PD1 with a bandwidth of 40 GHz. The analog chaotic sequence {Ai} is obtained by a real-time digital oscilloscope (DSO) (Tektronix, DPO73304D) and used for offline encryption. Note that in the proof-of-concept experiments we directly mapped a 215−1 pseudo-random bit sequence (PRBS) to a 65536-level PAM signal, which was loaded onto the IM via a 64 GSa/s arbitrary waveform generator (AWG, Keysight M9502A Axle Chassis). The feedback loop of this entropy source is not fully constructed. We will consider perfecting this via the Field-Programmable Gate Array (FPGA) in the future. In the message generation part, the data signal is mapped onto QPSK format and is encrypted by {Ai} and {Di}. The encryption depths k1 and k2 are both set to π/2 here. Next, pre-compensation is used to overcome the frequency roll-off of devices to improve the transmission performance of high-rate signals [23]. After digital pre-processing, the encrypted data signal is modulated onto the carrier with a central wavelength of 1550.0 nm through AWG and IQM1. Thus, a 100 Gbit/s phase-encrypted QPSK signal is obtained. Meanwhile, the 20 Gbit/s binary signal from the hybrid chaotic source is also mapped onto QPSK format and loaded onto another carrier with a central wavelength of 1548.1 nm, called the driving signal. Note that, although the high-rate driving signal produces a high bandwidth chaotic signal, it also increases the cost of implementation. It is essential to select the appropriate rate of driving signals for different demands.
Fig. 3. Experimental setup of the proposed coherent optical secure communication system. LD, laser diode; SL, semiconductor laser; EA, electrical amplifier; PD, photodetector; IM, intensity modulator; ES, electric splitter; OC, optical circulator; ADC, analog-digital converter; DAC, digital-analog converter; IQM, in-phase and quadrature modulator; MUX, wavelength division multiplexing; SSMF, standard single-mode fiber; EDFA, erbium-doped fiber amplifier; DMUX, wavelength division demultiplexing; ICR, integrated coherent receiver; DSP, digital signal processing.
Then the encrypted data signal and the driving signal are transmitted over the same fiber optic link after WDM. Here we achieve a long-haul transmission via a fiber ring. The transmission link consists of 20 spans of 50 km of standard single-mode fiber (SSMF). Each span of the fiber is equipped with an EDFA to compensate for optical power attenuation.
After demultiplexing, error-free recovery of the driving signal can be achieved through coherent detection and common DSP algorithms. After QPSK de-mapping, a binary signal consistent with that in the chaos source can be obtained. Through the same mapping operation, this binary signal is transformed into a 65536-level PAM signal and injected into SL2 via IM2 and OC2 to achieve chaotic synchronization. The threshold current of SL2 is 12.87 mA, the bias current is set to 45.6 mA, and the center wavelength is set to 1549.654 nm. The analog chaotic synchronization signal is transformed into an analog chaotic sequence {Ai'} by PD3 with a bandwidth of 40 GHz and DSO. At the same time, the encrypted data signal is converted into electrical signal by coherent detection. Then the channel impairment compensation and chaotic decryption are performed in the digital domain.
We use MATLAB R2022a to perform the data signal pre-processing and post-processing offline. In the pre-progressing, the roll-off factor of the filter is set as 0.1. At the receiver side, after resampling, the dispersion impairment is first compensated by digital back propagation algorithm (DBP) [24]. Then, we use the frequency offset estimation, matched filtering, IQ delay imbalance compensation, Gram–Schmidt Orthogonalization Procedure (GSOP) [25], Constant Modulus Algorithm (CMA) [26], chaotic decryption Viterbi–Viterbi Phase Estimation (VVPE) [27], Decision-Directed Least Mean Square (DD-LMS), QPSK de-mapping, and bit error rate (BER) calculation in turn. Here, The IQ delay is set to 2.3 ps. The tap coefficient of CMA is set to 75, and the step size is 3 × 10–4. The length of adjacent data averaged in VVPE is 10. For DD-LMS, the tap coefficient is 45, and the step size is 3 × 10–4.
The performance of the entropy source can directly affect the system security. We first analyze the characteristics of the hybrid chaotic source. Figures 4(a) and (b) show the case of injecting binary signal into SL. In this situation, the probability density distribution of the analog chaos is highly skewed relative to the Gaussian distribution. Figures 4(c) and (d) show the case of injecting 65536-level PAM signal into SL. Obviously, the probability density function of the analog chaos becomes closer to the Gaussian distribution, which implies a stronger randomness. Moreover, the spectrum of the analog chaos becomes flatter. Here, the effective bandwidth is adopted to quantify the bandwidth of chaotic signals, which is defined as the span between the direct current (DC) component and the frequency where 80% of energy is contained in the power spectrum. It is calculated that the effective bandwidth of the analog chaos after injecting 65536-level PAM signal is increased to 9.58 GHz.
Fig. 4. Probability density distribution (a) and power spectra (b) under the case of injecting binary signal; Probability density distribution (c) and power spectra (d) under the case of injecting 65536-level PAM signal.
In practical applications, the limited computational performance of devices will limit the complexity of the table of basis in the mapping operation. The table of basis is often reused for easier storage, transfer and processing. We analyzed the system security in this case by simulation in VPItransmissionMaker9.1. Figures 5(a) and (b) show the autocorrelation functions (ACF) of the 65536-level PAM signal and the analog chaotic signal, respectively. Due to the reused table of basis, there are multiple pairs of side peaks at nonzero delay time in Fig. 5(a). After injecting the PAM signal into the SL, these side peaks disappear. This means that the reused table of basis in the mapping operation can’t reduce the complexity of analog chaos.
Chaotic synchronization performance after 1000 km transmission is also analyzed. It should be noted that in order to optimize the correlation performance, the long short term memory (LSTM) is adopted in the offline processing to make minor corrections to the hardware synchronization. Figures 6(a) and (b) show the chaotic waveforms in the transmitter and receiver, respectively. The correlation plots in Fig. 6(c) show that the chaotic signals at both sides are well synchronized. The maximum cross correlation coefficient is calculated as 0.924, which meets the requirement for implementing chaos communication successfully.
Figure 7 illustrates the main results of the proposed scheme. Figures 7(a) and (b) show the constellation diagrams of the decrypted 100 Gb/s QPSK signal under back-to-back (B2B) and after 1000 km transmission, respectively. For the authorized receiver, the QPSK signal can be recovered correctly. Due to the channel impairment, the BER performance degrades from 1.94 × 10−4 to 9.88 × 10−4 after long-haul transmission. Figure 7(c) shows the constellation diagram of the eavesdroppers. It can be seen that when the secure keys are unknown, the phase of the QPSK signal is scrambled by chaos and the subsequent DSP algorithms will not work properly.
Fig. 7. (a) Decrypted QPSK signal under B2B; (b) decrypted QPSK signal after 1000 km transmission; (c) coherent detected signal without chaos decryption.
The received optical power (ROP) is one of the important parameters to measure the performance of optical communication systems. Figure 8(a) shows the BER under B2B and after 1000 km transmission with different ROPs. Due to the high sensitivity of coherent detection, the decrypted BER in the B2B case reaches the FEC threshold when the ROP drops to −23 dBm. And after 1000 km transmission, the minimum ROP of the system will be raised to −21 dBm.
Fig. 8. BER of legal decryption as a function of (a) ROP, (b) masking depth, and (c) proportion of digital chaos.
In our proposed scheme, the encryption depth is an important secure key. We define the sum of k1 and k2 as the masking depth, the ratio of k1 to (k1 + k2) as the proportion of digital chaos (k). Figure 8(b) shows the BER under B2B and after 1000 km transmission with different masking depths. The value of k is set to 0.5. For the B2B case, the decrypted BER is much less than 3.8 × 10−3 even if the masking depth reaches 1.5π. And after 1000 km transmission, the masking depth needs to be set below 1.25π. The smaller the masking depth is, the less the phase distortion introduced by the chaotic signal is, and the system security will be reduced. Considering the transmission performance and security, the masking depth needs to be kept between 1π and 1.25π. Figure 8(c) shows the BER under B2B and after 1000 km transmission with different values of k, where the masking depth is kept at 1π. When the proportion of digital chaos decreases, the phase noise introduced by the synchronization error becomes larger, which leads to poor BER performance. The minimum k over B2B and 1000 km are 0.25 and 0.5, respectively. On the other hand, the increase of k makes the periodic characteristic of digital chaos become more obvious, resulting in a low complexity of hybrid chaotic sequences, which means lower system security [17]. In order to trade-off the transmission performance and security, it is appropriate to set the proportion of digital chaos to 0.5 and the masking depth to 1π. The encryption depths can also be flexibly tuned according to specific application scenarios.
The above experimental results demonstrate the application potential of analog-digital hybrid chaos-based physical layer encryption technologies. It will be an important direction to explore for realizing high-speed and long-haul secure communication. At present, the bit rate-distance product of the analog chaotic encryption scheme is up to 30 Gb/s × 340 km [16], while the limit of analog chaotic synchronization distance is 1040 km [19]. The distance of analog chaotic encryption scheme is difficult to exceed the order of thousands of kilometers, due to the channel impairments of analog signals. In our proposed scheme, the distance of chaotic synchronization is determined by the distance of error-free transmission of digital driving signals. For coherent optical communication, 1000 km is far from the limit of 20 Gb/s QPSK signals, which means the transmission distance of our scheme can be greatly increased. However, due to laboratory conditions, we have only verified the secure transmission of 100 Gb/s QPSK signals over 1000 km fiber.
4. Discussion
4.1 Application in multi-node systems
In the proposed scheme, we generate high-complexity intensity chaos by injecting digitally modulated signals into the SL. Due to the complex internal nonlinear effects of the SL, the accuracy of ordinary neural networks (e.g., LSTM) is difficult to meet the demand of chaotic synchronization. Therefore, hardware synchronization needs to be accomplished by using parameter-matched SL at the receiver side. Although this synchronization method has high security, the need for multiple parameter-matched lasers limits its application in multi-node systems. To further reduce the chaotic synchronization requirements and simplify the system structure, we propose an alternative scheme. The signal after IM’s nonlinear modulation (i.e., the signal at point D in Fig. 2) is directly used at the transmitter side to encrypt the data offline, and at the receiver side, the nonlinear dynamics of IM is learned by LSTM to achieve chaotic synchronization in the digital domain. Figures 9(a) and (b) show the chaotic waveforms at transmitter and receiver, respectively. As shown in Fig. 9(c), good chaotic synchronization in the digital domain can be achieved based on the trained deep learning model. The maximum mutual relationship number is calculated as 0.993, which is higher than the hardware synchronization scheme. This better synchronization performance means lower decryption BER, which also indicates higher communication rates.
Based on the alternative scheme, we do not need to deploy multiple pairs of matched-parameter devices, and only need to change the table of basis used for the mapping operation in the digital part to achieve secure communication between different nodes. As shown in Fig. 10, node A1 and node A2 use the table of basis M for secure communication, while nodes A1 and A3 use the table of basis N for secure communication. If node A1 uses the table of basis M when generating chaotic signals at the transmitting end, then only nodes A1 and A2 can achieve chaotic synchronization and complete data exchange. Conversely, when A1 changes the table of basis to N, secure communication between A1 and A3 can be realized. However, the security of this alternative scheme is reduced compared to the hardware synchronization scheme due to the lack of the complex internal nonlinear effects of SL. This is actually a trade-off between security and practicality.
4.2 Bottlenecks and outlook
In the above proof-of-concept experiment, we achieved secure transmission of 100 Gb/s QPSK signals over 1000 km fiber. However, this scheme still has bottlenecks in practical applications. On the one hand, the generation of 65536-level PAM signals in the chaos source requires a high-resolution ADC, which will undoubtedly lead to a significant increase in cost. On the other hand, although the polarization multiplexing technique can further enhance the secure communication rate, the special chaotic encrypted signal will make the conventional demultiplexing algorithm associated with the modulation format ineffective. How to achieve polarization demultiplexing of long-haul phase-encrypted signals will be the focus of our future research. Adding training sequences to the transmit data may be a feasible solution.
5. Conclusion
In conclusion, we propose a coherent optical chaotic secure communication based on analog-digital hybrid chaos. By introducing the interconversion between digital and analog signals in the chaos source, long-haul chaotic synchronization is achieved. And the probability density distribution characteristics of the analog chaotic signal are effectively improved by using the higher-order mapping operation. Due to the flexibility of the mapping operation, the proposed scheme can also be applied in multi-node communication systems. The feasibility of this scheme is verified by 100 Gb/s encrypted QPSK signal transmission over 1000 km fiber. Our future work is to perfect the proposed system using FPGAs and further enhance the transmission capacity by multi-dimensional multiplexing.
Funding
National Key Research and Development Program of China (2021YFB2900901); National Natural Science Foundation of China (62175077); Science and Technology Planning Project of Shenzhen Municipality (JCYJ20200109144012410, JCYJ20200109142010888); Key Research and Development Program of Hubei Province (2023BAB00B); Fund of State Key Laboratory of Advanced Optical Communication System and Networks, Shanghai Jiao Tong University (2022GZKF013).
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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