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Abstract
We propose and demonstrate a novel secure optical communication scheme, in which the message signal is encrypted and decrypted by two synchronized wideband complex signals. In our scheme, the wideband complex signals are generated by two private chaotic driving signals which are obtained from two local conventional external-cavity semiconductor lasers (ECSLs) subject to a common injection. Both the experimental and simulation results show that, the effective bandwidths of the chaotic driving signals are significantly improved and the time-delay signatures are completely suppressed, in virtue of the spectral broadening effect of chaotic phase-modulation and the phase-to-intensity conversion effect of dispersive components. Furthermore, the generated wideband complex signals are used as the optical carriers for achieving secure transmission. The message signal with a bit rate up to 10 Gb/s can be well hidden into the carrier, and cannot be recognized by the eavesdropper. The high-quality synchronization ensures that the message signal can be correctly recovered at the receiver.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical chaos generated by external-cavity semiconductor laser (ECSL) has been widely applied for securing the physical layer of optical communication systems [1–6]. The noise-like and unpredictable characteristics of chaotic signal make it sufficient to hide the message and realize secure transmission. However, the practical applications of ECSL-based chaos are limited by two aspects. On the one hand, since the message is buried within the frequency bandwidth of chaotic carrier, the bandwidth of chaotic carrier restricts the signal transmission capacity of chaos-based communication systems. So far as we know, the maximum bandwidth of the chaotic signal which has been experimentally demonstrated in secure communication system is only 10 GHz [7]. On the other hand, in ECSL-based systems, the external cavity resonance induces a periodic modulation pattern in the power spectrum, which results in an obvious time-delay signature (TDS) in the ECSL-based chaos. The TDS threatens the security of chaotic optical communication, since the eavesdropper can figure out the information of the feedback delay time, by identifying the TDS using several analysis methods such as the autocorrelation function (ACF), the delayed mutual information (DMI) and the spectrum analysis [8–10]. Moreover, TDS degrades the randomness and complexity of chaotic source [11–13].
In recent years, many methods have been proposed to improve the bandwidth of chaotic signal and suppress the TDS. For example, the bandwidth of chaotic signal can be enhanced by utilizing heterodyning [14,15], delayed self-interference [16], injecting chaos into a fiber ring resonator [17], cascaded-coupling ring lasers [18], mutual injection [19], and chaotic self-phase-modulation [20,21]. The TDS characteristic can be suppressed by using grating feedback [22,23], double optical feedback [24], feedback with parallel-coupling ring resonators [25], optical fiber [26] and a compact phased array of semiconductor lasers [27]. However, the above methods mainly focused on the stand-alone chaos source, experimental investigations on secure communication using wideband and TDS-suppressed physical sources are rare and deserve further exploration.
In this work, we propose and demonstrate a new scheme for generating two synchronized wideband complex signals, and investigate its application in secure optical communication. The wideband complex signals are obtained from two initial chaotic driving signals which are generated by a common-injection-induced synchronization configuration. The bandwidth and complexity of initial chaos can be greatly improved by the chaotic phase modulation and the dispersion. Then the generated wideband complex signals are used as the optical carriers to encrypt and decrypt the message signal. The results indicate that high-security message transmission with a bit rate over Gb/s and satisfactory BER performance can be achieved.
2. Experimental setup
The experiment setup of the proposed secure optical communication system is shown in Fig. 1. A closed-loop configuration under unidirectional injection is adopted to obtain the initial chaos, where two ECSLs are subjected to the common injection of a constant-amplitude random-phase (CARP) light [28,29]. The CARP light is generated by modulating a drive laser (DL) with a noise phase. A 25-Gb/s arbitrary waveform generator (AWG) is employed as the noise generator, which sends a white Gaussian noise signal to the RF input of a phase modulator (PM1). The CARP light is equally split into two beams by a fiber coupler (FC). The two beams are then sent to two slave lasers (SLs), respectively, after they pass through optical isolators (ISOs) and variable optical attenuators (VOAs). The DL and the two SLs are distributed-feedback (DFB) lasers, which are monitored by a current-temperature controller. The operation wavelength of the DL is set to 1549.6 nm, and the frequency detuning between the DL and SLs is set to 0.06 nm [21]. The delay times of the feedback loops in ECSLs are 82.78 ns, and the feedback strengths are fixed to −20 dB. The emissions of two continuous-wave lasers (CWL1 and CWL2) with a central wavelength of 1550 nm are sent to PM2 and PM3, respectively. The linewidth and the emission power of the CWLs are 100 kHz and 8 dBm, respectively. The chaotic-phase-modulated lights are subsequently passed through two dispersive components (D1 and D2) for generating wideband complex signals at positions A and B, respectively. At the transmitter (Alice), the message is embedded into the carrier through an intensity modulator with a 3-dB bandwidth of 10 GHz. At the receiver (Bob), the message is recovered by the subtraction of the local wideband complex carrier generated by Bob from the encoded transmitted signal. Here, these two wideband complex carriers are collected by an oscilloscope in which the synchronization and the subtraction are performed. The recovered message is subsequently filtered by a digital low-pass four-order Butterworth filter with a cut-off frequency of 0.8R, where R is the bit rate of message. In our experiment, two 50-km single-mode fibers (SMFs) with a dispersion coefficient of 16 ps/nm/km are adopted as the dispersive components, which can also be replaced by fiber gratings or dispersion compensation fibers. Two erbium doped fiber amplifiers (EDFAs) are used to compensate the loss of the two SMFs, respectively. The splitting ratio of all the fiber couplers used in the experiment is 50:50. The bandwidths of the phase modulators are 20 GHz, with a half-wave voltage of 3.8 V. The bandwidths of all PDs are 30 GHz. The peak-to-peak amplitudes of the driving signals of PM2 and PM3 are approximately 6.1 V (corresponds to a maximum modulation depth of 1.6), while that of PM1 is approximately 3.9 V (corresponds to a maximum modulation depth of 1). The maximum power gain of the RF amplifiers is 35 dB. All the electronic signals are measured and recorded by a 100 GS/s real-time digital oscilloscope with four 25-GHz bandwidth channels.
Fig. 1. Experimental setup of the proposed secure optical communication system. DL, drive laser, SL, slave laser; CWL, continuous-wave laser; AWG, arbitrary waveform generator; PM, phase modulator; FC, 3-dB fiber coupler; PD, photodetector; RF, radio-frequency amplifier; VOA, variable optical attenuator; M, mirror; ISO, optical isolator, D1 and D2, dispersive components, IM, intensity modulator; LF, low-pass filter; EDFA, erbium doped fiber amplifier; m(t): original message; m’(t): recovered message.
3. Results and discussions
3.1 Generation of wideband complex signals
Figure 2 illustrates the temporal waveforms, power spectra and ACF traces of the initial chaos generated from ECSL1 and the output signal measured at Alice end (refer to position A in Fig. 1). Here, the commonly-used effective bandwidth is adopted to quantify the bandwidth characteristic [14–21]. The power spectra are computed from the time domain signals which are recorded by the oscilloscope, based on fast Fourier transform (FFT). It is observed that the power spectrum of the generated wideband signal as shown in Fig. 2(e) is greatly expanded and becomes much flatter than that of the initial chaos as shown in Fig. 2(b). The effective bandwidth of the initial chaos is only 10.6 GHz, while that of the generated wideband signal is significantly enhanced to 21.9 GHz. The bandwidth enhancement is attributed to the combined effects of PM-induced spectral broadening and dispersion-induced phase-modulation to intensity-modulation conversion [29]. Moreover, the ACF trace of the initial chaos is depicted in Fig. 2(c), where an obvious peak appears at the position of feedback delay time, indicating that the TDS can be easily identified. In contrast, for the output signal as shown in Fig. 2(f), there is no distinguishable peak appears at the position near the feedback delay in the ACF trace, the TDS is completely suppressed under the joint nonlinearity effects of the chaotic phase modulation and the dispersion. The elimination of TDS also means that the complexity of chaos is greatly enhanced [11,12].
Fig. 2. Experimental temporal intensity waveforms (first column), power spectra (second column) and ACF traces (third column) of the initial chaos generated by ECSL1 (first row) and the output signal measured at position A in Fig. 1 (second row).
Figure 3 illustrates the synchronization performance of the wideband complex signals measured at positions A and B. To quantify the synchronization quality, the frequently used cross-correlation (CC) coefficient is adopted, which is defined as [7,21,30]:
Fig. 3. Experimental temporal waveforms of (a) the common injection signal, as well as the output signals measured at (b) position A and (c) position B in Fig. 1; (d) the correlation plot between the common injection and the output signal at position A; (e) the correlation plot between the two output signals.
In our system, the modulation depth of the PM is the key parameter for enhancing the bandwidth and suppressing the TDS. Figures 4(a) and 4(b) present the PM modulation depth-dependent behaviors of the effective bandwidth and the TDS value of the output signal measured at position A, respectively. Here the TDS value is defined as the maximum value in the vicinity of the feedback delay time in ACF trace. The PM modulation depth is controlled by adjusting the peak-to-peak amplitude of the PM driving signal. As shown in Fig. 4(a), the effective bandwidth gradually increases from 13.3 GHz to 23.1 GHz, as the modulation depth increases from 0.4 to 1.9. When the modulation depth is larger than 1.3, the effective bandwidth can reach a value greater than 20 GHz. On the other hand, the evolution trend of TDS value in Fig. 4(b) shows that, with the increase of modulation strength, the TDS value gradually decreases to an indistinguishable level. When the modulation strength is larger than 1.5, the TDS value keeps at a very low level close to 0. Here the bandwidth and TDS value of the output signal measured at position B are similar to those measured at position A, which are not presented. In addition, Fig. 4(c) investigates the sensitivity of the PM modulation depth, which is realized by fixing the parameter of Alice and changing that of Bob. The PM modulation depth at Alice is fixed to 1.6. It is observed that high-quality synchronization with a CC value of 0.94 can be achieved when the parameter mismatch is controlled in a minimal range, and the synchronization performance is sensitive to the modulation depth mismatch. The above results indicate that the synchronized wideband TDS-suppressed outputs can be easily obtained in the proposed scheme, by properly selecting the PM modulation depth.
Fig. 4. The influence of PM modulation depth on (a) the effective bandwidth and (b) the TDS value in the ACF traces of the output signal measured at position A. (c) The influence of PM modulation depth mismatch on CC value.
3.2 Performance of secure communication
Next, we investigate the application of the proposed wideband complex signals in secure optical communication. In the experiment, the message is generated from a 25-Gb/s arbitrary waveform generator, which is a non-return-to-zero pseudorandom bit sequence. At the transmitter (Alice), the message is embedded into the carrier through an intensity modulator. At the receiver (Bob), the message is recovered by the subtraction of the synchronized massage-free signal from the encoded transmitted signal. The message modulation amplitude is set to 0.2, which is determined by the optical power of message signal and the carrier [31]. Figure 5 presents the performance of message encryption and recovering, where two bit rate cases, 5 Gb/s (first column) and 10 Gb/s (second column) are considered. The original message signals are directly measured by oscilloscope as shown in the black lines of Figs. 5(a) and 5(b), while the recovered messages are depicted in the red lines. For both of the 5 Gb/s and 10 Gb/s back-to-back transmission cases, the comparisons between the original message signals and the recovered message signals indicate that the messages are correctly recovered. Regarding the corresponding encrypted signals as illustrated in Figs. 5(c) and 5(d), the temporal waveforms exhibit a noise-like characteristic with randomly oscillating intensities, indicating that the message signals are well hidden in the carriers.
Fig. 5. Experimental temporal intensity waveforms of (a), (b) the original messages (black) and the recovered messages (red), as well as (c), (d) the encrypted messages, in the cases of 5 Gb/s (first column) and 10 Gb/s (second column) back-to-back transmission.
To demonstrate the security of the proposed communication system against illegal interception, the message recovered by the eavesdropper is investigated. Here we consider a possible attack scenario namely direct detection with linear filtering (DDLF) [5,32]. In this attack method, the eavesdropper directly detects the encrypted signal from the public link by PD and then adopts a filter with a cut-off frequency equaling the message bit rate to recover the message. Figure 6 illustrates the eye diagrams of the encrypted message, the intercepted message of DDLF attack scenario and the recovered message, in the 5 Gb/s transmission case. The eye diagrams of the intercepted message and the encrypted message are all closed, which indicate that the message cannot be correctly recovered without the correct decryption. While for the recovered message as shown in Fig. 6(c), the eye diagram is widely opened.
Fig. 6. The eye diagrams of (a) the encrypted message, (b) the intercepted message and (c) the recovered message.
Furthermore, Fig. 7(a) illustrates the BER performances of the encrypted, the decrypted and the intercepted messages as a function of the message bit rate. Here 2 × 106 bits are used to calculate the BER, by comparing the recovered message with the original one. The BER for both of the intercepted message and the recovered message gradually increases with increasing the message bit rate, while the BER for the encrypted message is maintained at a high level (larger than 0.1). For the legal recovered message, the BER is always below 3.8 × 10−3, which is the hard decision forward error correction (HD-FEC) threshold. It is indicated that the good synchronization performance of the wideband physical sources enables the proposed scheme to encrypt the message with a bit rate up to 10 Gb/s. By contrast, the BER for the intercepted message is much higher than that of the legal recovered message, and the message cannot be recovered by the DDLF attack with a BER over 10−2, when the bit rate is larger than 4 Gb/s.
Fig. 7. Experimental BER performances of the encrypted message (black), the recovered message (red) and the intercepted message under DDLF attack (blue), as a function of (a) the message rate and (b) the message modulation amplitude at 5 Gb/s bit rate. The green dashed line is the threshold of HD-FEC.
In our communication system, since the message is superposed to the carrier through the intensity modulator, the message modulation amplitude is an important parameter for the efficiency of the encryption process [31]. In Fig. 7(b), the BER performance of the encrypted, the decrypted and the intercepted messages versus the message modulation amplitude, is presented in the 5 Gb/s transmission case. The BER results for both of the intercepted message and the recovered message show similar developing trends: gradually decreasing with increasing the message modulation amplitude. For the legal recovered message, the BER is always smaller than 3.8 × 10−3. By contrast, the BER for the encrypted and intercepted message is always larger than 3.8 × 10−3 when the modulation amplitude is less than 20%. Here the message modulation amplitude is controlled in a range of 10% to 20%, which is determined by the adjustable amplitude range of the AWG used in the experiment. On the one hand, the above results show that the message modulation amplitude range of 10% to 20% is sufficient for efficient encryption and decryption. On the other hand, when the modulation amplitude further increases beyond 20%, it can be deduced from the decreasing curve of the intercepted message that the BER may further decrease and be lower than 3.8 × 10−3. In practical application, the message modulation amplitude should be sufficiently small to prevent being recovered by DDLF attack [31]. Therefore, it is reasonable to set the message modulation amplitude in a range of 10% to 20%. In addition, since the encryption of the proposed scheme is implemented at the optical layer, it can also be combined with all-optical logic [33]. The above results indicate that by properly setting the bit rate and the modulation amplitude, message can be efficiently hidden in the carrier and be robust against eavesdropping.
3.3 Theoretical model and numerical results
In order to further verify the correctness of the experimental results and the feasibility of the proposed scheme, numerical investigations are also performed and compared with the experimental results. The dynamics of the ECSLs in the proposed scheme are described by the modified Lang-Kobayashi rate equations [9,11,22]. The rate equations of the slowly-varying complex electric field E and the corresponding carrier number N in the active region of the ECSLs can be written as
The values of the intrinsic parameters of the ECSLs are set as [20]: the linewidth enhancement factor α=5, the gain saturation coefficient ε=5×10−7, the photon lifetime τp=2 ps, the carrier lifetime τe=2 ns, the differential gain parameter g=1.5×10−8 ps−1, the transparent carrier number N0=1.5×108, the feedback delay time τf = 5 ns, the feedback strength k=15 ns−1, and the spontaneous emission rate β=1.5×10−6 ns−1. The operation current of the SLs is set as I=1.5Ith, where Ith=14.7 mA is the threshold current. Einj(t) is the injected signal of the SLs, which is obtained from PM1. The injection strength σ is set as 50 ns−1. The unity-variance and zero-mean Gaussian noise source χ(t) is used to model the spontaneous emission noise. The phase modulation can be mathematically described as
where Ein and Eout are the input and output of phase modulators, respectively. KPM is the PM modulation depth, N[|E(t)|2] denotes the normalized electronic driving signal. The dispersive components are also constructed with SMFs [5,29]. For consistency, the PM modulation depth of the PMs, the dispersion of the dispersive components and the frequency detuning between the DL and SLs in the simulation are set as the same with those in the experiment.Figure 8 presents the numerical results of temporal waveforms, power spectra and ACF traces of the initial chaos generated from ECSL1 and the wideband carrier measured at position A. It is seen that the power spectrum of the generated wideband carrier as shown in Fig. 8(e) is significantly broadened and becomes flat within a wide frequency range in comparison with that of the initial chaos as shown in Fig. 8(b). Compared to the initial chaos, the effective bandwidth of generated wideband carrier is greatly improved from 11.2 GHz to 22.3 GHz. Moreover, the comparison between the ACF traces of these two signals as shown in Figs. 8(c) and 8(f) shows that, the TDS at the position of feedback delay time can be completely suppressed. The numerical results in Fig. 8 are well in line with the experimental results in Fig. 2, which verify the correctness and feasibility of wideband complex carrier generation in the proposed scheme.
Fig. 8. Numerical temporal waveforms (first column), power spectra (second column) and ACF traces (third column) of the initial chaos generated by ECSL1 (first row) and the output signal measured at position A in Fig. 1 (second row).
Figures 9(a) and 9(b) present the influence of PM modulation depth on the effective bandwidth and the TDS value of the generated wideband carrier, respectively. With the increase of modulation depth, the effective bandwidth gradually increases from 12.6 GHz to 26 GHz, and the TDS value gradually decreases to an indistinguishable level (lower than 0.02). Moreover, Fig. 9(c) shows the influence of modulation depth mismatch between PM2 and PM3 on the synchronization performance. It can be observed that, the CC degrades as the increase of mismatch value. High-quality synchronization with a CC value of 0.97 can be achieved when the PM modulation depths are matched with each other. The simulation results in Fig. 9 agree well with the experimental results in Fig. 4, which further indicate that the wideband TDS-suppressed carriers can be easily obtained in the proposed scheme, by properly setting the PM modulation depth.
Fig. 9. The influence of PM modulation depth on (a) the effective bandwidth and (b) the TDS value in the ACF traces of the output signal measured at position A. (c) The influence of modulation depth mismatch on CC value.
Figure 10(a) illustrates the numerical BER performances of the encrypted, the decrypted and the intercepted messages as a function of the message bit rate. Here the BER performances are quantified by the Q-factor [31,32]. The message modulation amplitude in the simulation is set as the same with that in the experiment. For the legal recovered message, the BER gradually increases and is always lower than the threshold of 3.8 × 10−3. While for the encrypted message, the BER maintains at a high level larger than 0.1. The BER of the intercepted message also gradually increases, but the values are much higher than that of the legal recovered message. When the bit rate is larger than 4 Gb/s, the message cannot be recovered by the DDLF attack with a BER higher than 3.8 × 10−3. Moreover, the eye diagrams of the encrypted message, the intercepted message of DDLF attack scenario and the recovered message in the 5 Gb/s transmission case are also presented in Fig. 10. The numerical communication performances in Fig. 10 are consistent with the experimental results as shown in Fig. 6 and Fig. 7(a). Therefore, the above simulation results further prove the proposed secure optical communication scheme.
Fig. 10. (a) Numerical BER performances of the encrypted message (black), the recovered message (red) and the intercepted message under DDLF attack (blue), as a function of the message bit rate. The eye diagrams of (b) the encrypted message, (c) the intercepted message and (d) the recovered message in the 5 Gb/s transmission case.
4. Conclusions
In conclusion, a novel scheme for achieving high-speed secure optical communication has been proposed and demonstrated, based on two synchronized wideband complex carriers. In the proposed scheme, the wideband complex carriers are independently generated from two private chaotic driving signals in two communication parties, with the combined effects of phase-modulation induced spectrum expansion and phase-to-intensity conversion of dispersive components. The results of the experiment and the numerical simulation are highly consistent, which demonstrate that the proposed scheme can produce wideband carriers with an effective bandwidth over 20 GHz. Moreover, the TDS of the chaotic driving signal can be considerably suppressed to an undistinguished level, thus the complexity is greatly enhanced. Furthermore, high-quality synchronization with a large CC value of 0.94 is achieved, which enables the generated wideband complex carriers to encode and decode the message signal for achieving secure transmission. The communication performance indicates that the message with a bit rate over Gb/s can be efficiently hidden into the carrier, and correctly recovered at the receiver with a satisfactory BER performance.
Funding
National Natural Science Foundation of China (61671119); Fundamental Research Funds for the Central Universities (ZYGX2019J003).
Disclosures
The authors declare no conflicts of interest.
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