Open Access
Add to BibSonomy
Abstract
Protecting confidential high speed optical signal transmission at the lowest physical layer is a critical challenge for modern fiber-optic communication systems. In this paper, we experimentally demonstrate a novel synchronous privacy enhanced chaotic temporal phase en/decryption scheme for high-speed physical layer secure optical communication. A remote chaos synchronization architecture relying on common source signal driving and private response hardware modules comprising of dispersive components and slave lasers is employed to generate synchronized private chaotic en/decryption signals, and simultaneously suppress residual driving-response correlation for enhancing the security. A proof-of-principle demonstration by secure transmission of a 28 Gb/s on-off-keying modulated confidential signal over 100 km single mode fiber link based on the private chaotic temporal phase en/decryption scheme is successfully achieved. The demonstrated hardware optical en/decryption approach may provide a promising way towards future ultra-high speed physical layer secure optical communication systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the tremendous growth of big data traffic over optical networks, network security is emerging as a worldwide challenge in recent years [1]. Achieving physical layer security has been paid increasing attention, due to its striking advantages of providing network security at the lowest physical layer and unique capability of complementing with the upper layer digital cryptography [2]. It is extremely desirable to realize high speed physical secure optical communication based on commercial fiber-optic components and transmission architectures for modern optical fiber communication systems.
Chaotic optical communication based on chaos synchronization, has been recognized as an effective solution for physical layer secure optical communication [3,4]. The noise-like temporal waveform of optical chaos with large amplitude fluctuation naturally provides an optical carrier that is particularly suitable to conceal a confidential message [3]. Various chaotic optical communication systems relying on either all-optical external feedback [5–11] or electro-optic modulator based chaotic transmitters [12–16] have been demonstrated in the past years. Nevertheless, in conventional chaotic communication systems, since the chaotic signal is employed as an optical carrier, the limited bandwidth of optical chaos in the order of several gigahertz imposes great restriction for transmission of high bit-rate confidential messages [4–9]. Although many approaches have been proposed to generate wideband optical chaos, high quality chaos synchronization for the wideband chaos is difficult to be achieved [14,17]. Moreover, as another important aspect, the power ratio between the confidential message and the optical chaos carrier has to be controlled sufficiently low in order to avoid direct low pass filtering attack and guarantee the security [5–8,14], which inevitably sacrifices the transmission performance.
On the other hand, providing physical layer security based on hardware optical encryption, is another much promising way for secure optical communication, which has the potential for achieving high-speed transmission [18,19]. Optical encryption and decryption based on hardware components have been already demonstrated for achieving 10 Gb/s secure communication, including specially designed super-structured fiber-Bragg-grating (SSFBGs) [20], multi-port arrayed waveguide grating encoder [21], or utilizing nonlinear effects including cross-gain modulation in a semiconductor optical amplifier [22] and stimulated Brillouin scattering effect in optical fiber [23], etc. To enable the encryption flexibility and high bit rate operation, we have previously proposed a novel temporal stretched optical phase en/decryption scheme for encrypting confidential optical signals based on hardware dispersive optical components and an optical phase modulator [24]. A 10 Gb/s secure optical communication system with differential-phase-shift-keying (DPSK) modulation format has been successfully achieved [25]. Secure transmission of 25 Gb/s on-off-keying (OOK) confidential data has also been recently demonstrated [26]. However, in order to validate the encryption and decryption, a high-speed digital key sequence was employed, where the problem of remotely distributing such a high-speed digital key has not been resolved for a long time. It was until recently that an innovative solution using remotely synchronized optical chaos instead of a digital key was proposed and numerically demonstrated to perform chaotic spectral phase en/decryption for physical secure optical communication [27]. Unfortunately, a common chaotic signal driving and external cavity chaotic lasers response scheme was employed for generating the encryption and decryption chaotic signals based on chaos synchronization, which has a high residual driving-response cross-correlation and relatively simple response hardware structure, inducing potential security risks of malicious attack by directly intercepting the driving signal that exposes in the public channel and attempting to reproduce the decryption signal [27,28]. To the best of our knowledge, the feasibility of employing remotely synchronized chaotic signals in our proposed temporal stretched optical phase en/decryption scheme for high-speed physical secure optical communication in a single fiber transmission link has not been experimentally demonstrated yet.
In this paper, we propose and experimentally demonstrate a synchronous privacy-enhanced chaotic temporal phase encryption and decryption scheme by private hardware encryption modules for high-speed physical layer secure optical communication. Unlike conventional chaotic communication systems that employs the chaotic signal as an optical carrier to conceal a confidential message, which limits the achievable bit rate due to the limited chaos bandwidth, the generated optical chaos by the hardware encryption modules is instead used as a chaotic encryption key to perform temporal phase en/decryption in our system, enabling high bit-rate and secure optical signal transmission even if the chaos bandwidth is lower than the bandwidth of a confidential signal. As a proof-of-principle demonstration, a 28 Gb/s confidential signal has been temporally phase encrypted by a 7.8 GHz chaotic signal, transmitted over 100 km single mode fiber and successfully decrypted by remotely synchronized private optical chaos. The proposed scheme is fully compatible with commercial fiber-optic components, exhibiting great potential to accommodate advanced optical modulation formats and multiplexing technologies for future ultra-high speed physical secure optical communication.
2. Principle and experimental setup
Figure 1 illustrates the experimental setup of the proposed synchronous private chaotic phase en/decryption scheme for high-speed physical secure optical communication. At the transmitter side, a commercial external-cavity-laser (ECL) with an output power of 10 dBm and a center wavelength of 1550.92 nm is used as the optical source. A 40 GHz Mach-Zehnder modulator (MZM, FTM-7937) driven by a 231-1 pseudo-random bit sequence (PRBS) from a pattern generator (Anritsu MP2110A) with a maximum bit rate of 28.2 Gb/s is used to modulate the optical carrier to generate a 28 Gb/s non-return-to-zero (NRZ) on-off-keying (OOK) signal. The generated signal to be confidentially transmitted is then directed into a hardware encryption module, which consists of a dispersive fiber (D1) with a chromatic dispersion value of ∼1000 ps/nm for temporal spreading and a high-speed optical phase modulator (PM1) with a half-wave voltage of ∼6 V for temporal phase encryption. The 28 Gb/s confidential optical signal is firstly spreading in the time domain and distorted by the chromatic dispersion, so that the adjacent confidential symbols are temporally overlapped. The temporal stretched signal is then phase encrypted by a chaotic signal generated by a private hardware encryption module, which includes another dispersion element (D3) followed by an open-loop distributed feedback slave semiconductor laser (SL1) with the inner optical isolator removed to enable external injection. The dispersion value of D3 is 2322 ps/nm and the center wavelength of SL2 is 1550.3 nm in the setup.
Fig. 1. Experimental setup of the high-speed chaotic en/decryption secure optical communication system. ECL, external-cavity laser; PC, polarization controller; MZM, Mach-Zehnder modulator; SMF, single mode fiber; DCF, dispersion compensation fiber; ISO: isolator; D, dispersive component; OC, optical circulator; PM, phase modulator; DL, driving laser; SL, slave laser; PD: photodetector; FC: fiber coupler; Amp, amplifier; VOA: variable optical attenuator; EDFA, erbium-doped fiber amplifier; WDM, wavelength division multiplexer.
Then, a separate encryption channel is used to provide a common external driving signal at a different wavelength of 1550.12 nm, which is injected into the private hardware module to output the response chaotic optical signal that has a rather low cross-correlation with the common driving signal. An external feedback chaotic driving laser (DL) is employed to generate the source chaotic driving optical signal. By employing such a response hardware structure, the cross-correlation between the common driving signal exposing in the public transmission channel and the response output signal that is used for private temporal phase encryption of the confidential signal is greatly suppressed. It is worth noting that the driving-response architecture is transparent to the source optical signal, which can be also extended to a common broadband optical noise signal or other types of advanced optical driving signals. The chaotic driving signal is taken as an example for proof-of-principle demonstration. The dispersion value of the dispersion component and the physical parameters of the response laser both contribute to enhance the privacy of the encryption signal, which acts as the temporal phase encryption key. More importantly, thanks to the unpredictable and non-reproducible features of laser chaos, the temporal stretched confidential signal is temporally phase encrypted with time-varying phase profiles by the private chaotic signal, which is quite beneficial to greatly enhance the security of the confidential signal.
After that, the encrypted confidential signal and the common driving signal are multiplexed by a wavelength division multiplexer (WDM), and then launched into a span of single mode fiber (SMF) with a length of ∼100 km for transmission. In line erbium-doped fiber amplifiers (EDFA) are used to compensate the transmission loss. A piece of ∼12 km dispersion compensation fiber (DCF) is used for compensating the dispersion of SMF. At the receiver side, a wavelength division demultiplexer is used to separate the encrypted confidential signal and the common driving signal into two paths. The separated signal to be decrypted is directed into the decryption module which has symmetrical configuration to the encryption part, where the PM is driven by the inverse private synchronized chaotic signal for temporal phase decryption and the dispersion value of the dispersive element (-D2) is opposite to that of the encryption module for temporal compression. As for the common driving signal, it is injected into the private hardware decryption pair module, which also includes a dispersion component (D4) followed by another response DFB slave laser (SL2) at 1550.3 nm to generate the remote synchronized private chaotic decryption signal. The dispersion value of D4 is identical to D3 to ensure high quality synchronization. Finally, after temporal phase decryption by the synchronized chaotic signal, the confidential signal is temporally compressed by the dispersive element (-D2) and detected by a 40 GHz photo-detector (PD) to recover the original confidential data for further bit-error-rate (BER) analysis. Note that without the matched hardware components for proper decryption and synchronized chaotic decryption signal generation, an eavesdropper attempting to intercept the encrypted confidential signal by simply using a tunable dispersion compensator can only obtain an intensity seriously scrambled signal due to the chaotic encrypted phase to intensity conversion, let alone without any private hardware for decryption, which sufficiently enhance the security of confidential signal in the physical layer.
3. Experimental results and discussions
3.1 Encryption and decryption performances
Figures 2(a)–2(f) show the experimental results for encryption and decryption performances. Compared with the original 28 Gb/s optical signal in Figs. 2(a) and 2(b), the encrypted signal is seriously scrambled in the temporal domain, and the corresponding eye diagram is fully closed, as shown in Figs. 2(c) and 2(d), indicating that a malicious eavesdropper without the private decryption hardware is extremely difficult to intercept the confidential data. To successfully decrypt the signal, a legal user firstly has to generate the synchronized chaotic decryption signal and then perform the temporal decryption. Figure 2(e) shows the waveform of the properly decrypted signal, which resembles the original optical signal in Fig. 2(a). The corresponding eye diagram for the properly decrypted 28 Gb/s OOK confidential signal has clear eye opening, as shown in Fig. 2(f).
Fig. 2. (a),(b) Waveform and eye diagram of the original 28 Gb/s confidential signals; (c),(d) and (e),(f) are the waveforms and eye diagrams of the encrypted and decrypted signals.
Figure 3 illustrates the optical spectra for the original confidential signal, encrypted and decrypted signals, respectively. It can be seen that the optical spectrum of the encrypted signal is significantly expanded compared with that of the original signal due to the chaotic optical phase encryption induced spectrum broadening. The recovered spectrum after signal decryption almost coincides with that of the original unencrypted optical spectrum, showing excellent decryption performance.
Figures 4(a1)–4(a3) show the measured temporal waveforms of the response laser output from SL1 of Alice, SL2 of Bob and the common DL source. It is clear that the generated chaotic waveforms from the response SL1 and SL2 lasers are highly correlated and exhibit similar temporal profiles. The correlation coefficient between the output chaotic signals from the two slave lasers reaches up to 0.97 in the experiment, as shown in Fig. 4(b), indicating that high quality synchronization has been achieved to guarantee the performance of temporal phase decryption. In contrast, the chaotic waveforms of the response laser output are obviously distinct from the output of the DL. The cross-correlation coefficient between the driving and response signals is as low as ∼0.21, which is mainly ascribed to the response architecture employing a private dispersion component and a slave laser. It is extremely difficult for an eavesdropper to obtain the private chaotic encryption signal by simply intercepting the public driving signal.
Fig. 4. Measured temporal waveforms of the chaotic signals generated by (a1) SL1, (a2) SL2 and (a3) DL, and the cross-correlation plots of (b) SL1-SL2 and (c) DL-SL1.
Figure 5(a) shows the measured cross-correlation coefficient between the driving and response signals versus the dispersion value D3 in the private hardware encryption modules. It is found that the driving-response cross-correlation coefficient monotonically decreases with the increase of the dispersion value. Compared to the traditional chaotic common driving-response configuration that has a relatively high residual cross-correlation up to ∼0.7 [28], the introduction of the private dispersion component in front of slave response lasers substantially suppresses the residual correlation to ∼0.21 when D3 is ∼2333 ps/nm in the experiment. Further reduction of the driving-response residual correlation could be expected when larger dispersion value is employed. The effect of dispersion mismatch between D3 and D4 of the encryption and decryption hardware modules on the synchronization coefficient of the response output signals from SL1 and SL2 is also depicted in Fig. 5(b), from which it is evident that the synchronization coefficient is degraded when the dispersion mismatch is increased. A dispersion mismatch of ∼ ±40 ps/nm could be tolerated when the synchronization coefficient is degraded to ∼ 0.87, which is the minimum requirement for the synchronization coefficient to guarantee the decryption performance and ensure the BER lower than the hard-decision forward error-correction (HD-FEC) limit in the system.
Fig. 5. (a) The driving-response cross-correlation versus the dispersion value of D3. (b) The cross-correlation between two response lasers versus the dispersion mismatch.
3.2 Hardware parameter requirements and BER performances
Having examined the en/decryption performances and chaos synchronization coefficient, attention is now turned into the requirement of physical hardware parameters for chaotic temporal en/decryption. Figure 6 depicts the impact of phase modulation depth (MD) for the temporal phase en/decryption on BER for the legal user (Bob) and an eavesdropper (Eve). In the case of direct detection attack without any chaotic decryption modules for Eve, the measured BER far exceeds the HD-FEC threshold of 3.8×10−3 no matter how the MD changes, indicating high security against malicious attack. However, an Eve may be sophisticated enough and attempts to attack the system by using a tunable dispersion compensator even if the private temporal phase decryption module is not available. As shown by the green circular line in Fig. 6, the measured BER for Eve gradually increases with the MD in this case. It is found that when the MD is less than 0.37, the measured BER for Eve can be lower than the HD-FEC threshold, indicating potential security vulnerability for low modulation depth due to the negligible temporal phase encryption imposed onto the time spreading confidential signal. On the contrary, when the MD is higher than 0.37, the BER for Eve is always kept above the HD-FEC threshold, showing strong security against eavesdropping. On the other hand, the measured BER for the legal user is still below the HD-FEC threshold when the MD surpasses 0.37. Increasing the MD could enhance the security but leads to a deteriorated BER for the legal user. When the MD is gradually increased to an upper bound of ∼0.84, the measured BER for legal user approaches the HD-FEC threshold accordingly, which is mainly caused by the imperfect decryption by the private hardware. Hence, a phase modulation depth ranging between 0.37 and 0.84 for the temporal phase encryption is required to guarantee the tradeoff between security and BER performance in the system.
Fig. 6. BER performances versus phase modulation depth for different eavesdropping attack scenarios and legitimate user’s decryption.
The eavesdropped BER performance versus the dispersion value of D1 for hardware encryption is also illustrated in Fig. 7 with three typical different phase MD values, where it is assumed that an eavesdropper attempts to attack the system with a matched dispersion compensation module of -D2 but without the chaotic phase decryption. It is clear that higher phase MD requires lower dispersion of D1 for temporal encryption. A minimum dispersion of ∼320 ps/nm corresponding to a standard SMF length of ∼20 km is required to prevent the eavesdropper from extracting the confidential data by dispersion compensation only attack in the 28 Gb/s secure optical communication system. If D1 is lower than the minimum required value, it is possible for an eavesdropper to intercept the confidential data and obtain an eavesdropped BER lower than the HD-FEC limit by simply applying the opposite dispersive element -D2 without any phase decryption, inducing serious security risks. Hence, a standard SMF with a fiber length of ∼60 km is employed to guarantee the system security against eavesdropper’s attack in the experiment. Furthermore, as one of the critical key hardware parameters, the impact of dispersion mismatch between the encryption and decryption dispersive components (D1, D2) on BER is also evaluated, which is shown in Fig. 8(a). A maximum dispersion mismatch tolerance of around ±160 ps/nm at the HD-FEC threshold is obtained for the MD of 0.37, which is reduced to around ±80 ps/nm when increasing the MD to 0.75. The dependence of the transmission fiber dispersion mismatch with the BER for different MD values exhibits similar tendency as the en/decryption parts, as shown in Fig. 8(b). Increasing the MD causes the reduction of dispersion mismatch tolerance due to the increased sensitivity of decryption performance on the dispersion mismatch.
Fig. 8. Measured BER curves versus phase modulation depth for the legal user and eavesdropper with different detection schemes.
Figure 9 shows the effect of synchronization delay time mismatch between the encrypted confidential signal and the synchronous chaotic decryption signal on the measured BER. The synchronization delay time mismatch will lead to the misalignment between the chaotic decryption channel and the confidential signal channel, deteriorating the decryption performance. The measured maximum delay time mismatch tolerance is around ±35 ps at the HD-FEC threshold for a MD of 0.37, which shrinks to around ±18 ps when the MD is increased to 0.75. A tunable delay line with a high resolution of 1 ps is thus employed in the experiment to minimize the delay time mismatch to guarantee the decryption performance.
Fig. 9. BER versus the delay time mismatch between the encryption and confidential signal transmission channels.
Finally, the BER performances of the 28 Gb/s confidential optical signal for back-to-back (B2B) and 100 km transmission scenarios are also measured, as plotted in Fig. 10. Compared to the case of without phase en/decryption, despite of the BER degradation has been introduced by the non-ideal en/decryption due to the imperfect matching of the private hardware en/decryption modules, BER lower than the HD-FEC threshold has been achieved successfully for all different phase modulation depths after transmission. Higher phase modulation depth for temporal encryption provides enhanced security, but leads to a deteriorated BER. It is also worth noting that the bit rate in current demonstrated system is mainly limited by the pattern generator, which has great potential to be improved based on the proposed scheme. Although the bandwidth of the private chaotic encryption signal is lower than the bit rate of the confidential signal, it is efficient to scramble the temporal waveform of the confidential signal to resist against malicious eavesdropper’s attack thanks to the temporal stretching then chaotic phase encryption scheme. To scramble a 28 Gb/s confidential OOK signal against eavesdropper’s dispersion compensation only attack, it has been found that only ∼5.1 GHz bandwidth of chaotic signal is required in the system. Increasing the transmission bit rate could enhance the system security against eavesdropping due to the increased temporal scrambling of the confidential signal in the time domain, but inevitably sacrificing the BER performance for the legal user due to increased sensitivity and reduced tolerance to hardware parameters mismatch. Therefore, it is desirable to minimize the hardware parameters mismatch by employing identical pairs of hardware en/decryption components to further improve the transmission bit rate and BER performance whilst ensuring the system security in future.
Fig. 10. BER performances for B2B and 100 km fiber transmission with different phase modulation depths.
4. Conclusions
In conclusion, we propose and experimentally demonstrate a privacy enhanced synchronous chaotic temporal phase en/decryption scheme for high-speed physical layer secure optical communication. Private hardware encryption and decryption modules composed of dispersion elements and response slave lasers are employed to generate synchronous chaotic en/decryption signals as well as greatly suppressing residual driving-response correlation to enhance the system security. In the experiment, a 28 Gb/s confidential optical signal is temporally encrypted by the chaotic signal generated by the private hardware en/decryption modules and successfully transmitted over 100 km optical fiber link. The demonstrated system has great potential to be upgraded to higher order modulation formats such as four-level pulse amplitude modulation (PAM4) or quadrature phase shift keying (QPSK), and accommodate advanced multiplexing technologies for achieving higher capacity.
Funding
National Key Research and Development Program of China (2020YFB1806401); National Natural Science Foundation of China (11904057, 62004047, U2001601); Basic and applied basic research project of Guangzhou basic research program (202102020506); Guangdong Introducing Innovative and Entrepreneurial Teams of “The Pearl River Talent Recruitment Program” (2019ZT08X340).
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.
References
1. O. Spitz, A. Herdt, J. Wu, G. Maisons, M. Carras, C. W. Wong, W. Elsäßer, and F. Grillot, “Private communication with quantum cascade laser photonic chaos,” Nat. Commun. 12(1), 3327 (2021). [CrossRef]
2. M. P. Fok, Z. Wang, Y. Deng, and P. R. Prucnal, “Optical layer security in fiber-optic networks,” IEEE Trans. Inf. Forensic Secur. 6(3), 725–736 (2011). [CrossRef]
3. M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015). [CrossRef]
4. A. Argyris, D. Syvridis, L. Larger, V. A. Lodi, P. Colet, I. Fischer, J. G. Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005). [CrossRef]
5. L. Wang, Y. Guo, D. Wang, Y. Wang, and A. Wang, “Experiment on 10-Gb/s message transmission using an all-optical chaotic secure communication system,” Opt. Commun. 453, 124350 (2019). [CrossRef]
6. J. Wu, Z. Wu, X. Tang, F. Li, W. Deng, and G. Xia, “Experimental demonstration of LD-based bidirectional fiber-optic chaos communication,” IEEE Photonics Technol. Lett. 25(6), 587–590 (2013). [CrossRef]
7. X. Dou, H. Yin, H. Yue, and Y. Jin, “Experimental demonstration of polarization-division multiplexing of chaotic laser secure communications,” Appl. Opt. 54(14), 4509–4513 (2015). [CrossRef]
8. Q. Zhao, H. Yin, and X. Chen, “Long-haul dense wavelength division multiplexing between a chaotic optical secure channel and a conventional fiber-optic channel,” Appl. Opt. 51(22), 5585–5590 (2012). [CrossRef]
9. J. Zhang, A. Wang, J. Wang, and Y. Wang, “Wavelength division multiplexing of chaotic secure and fiber-optic communications,” Opt. Express 17(8), 6357–6367 (2009). [CrossRef]
10. C. Hu, G. Xia, D. Yue, Z. Jiang, B. Cui, Y. Zheng, G. Lin, and Z. Wu, “Experimental demonstration of a chaotic communication system with a switchable chaotic carrier wavelength based on two weak-resonant-cavity Fabry–Perot laser diodes,” Appl. Opt. 60(9), 2745–2750 (2021). [CrossRef]
11. A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010). [CrossRef]
12. N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electrooptical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004). [CrossRef]
13. R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 1430–1435 (2010). [CrossRef]
14. J. Ke, L. Yi, G. Xia, and W. Hu, “Chaotic optical communications over 100-km fiber transmission at 30-Gb/s bit rate,” Opt. Lett. 43(6), 1323–1326 (2018). [CrossRef]
15. J. Ai, L. Wang, and J. Wang, “Secure communications of CAP-4 and OOK signals over MMF based on electro-optic chaos,” Opt. Lett. 42(18), 3662–3665 (2017). [CrossRef]
16. L. Jiang, Y. Pan, A. Yi, J. Feng, W. Pan, L. Yi, W. Hu, A. Wang, Y. Wang, Y. Qin, and L. Yan, “Trading off security and practicability to explore high-speed and long-haul chaotic optical communication,” Opt. Express 29(8), 12750–12762 (2021). [CrossRef]
17. J. Ke, L. Yi, G. Xia, and W. Hu, “Key technologies in chaotic optical communications,” Front. Optoelectron. 9(3), 508–517 (2016). [CrossRef]
18. E. Wohlgemuth, Y. Yoffe, T. Yeminy, Z. Zalevsky, and D. Sadot, “Photonic-layer encryption and steganography over IM/DD communication system,” Opt. Express 26(25), 32691–32703 (2018). [CrossRef]
19. M. L. F. Abbade, M. Cvijetic, C. A. Messani, C. J. Alves, and S. Tenenbaum, “All-optical cryptography of M-QAM formats by using two-dimensional spectrally sliced keys,” Appl. Opt. 54(14), 4359–4365 (2015). [CrossRef]
20. X. Wang, K. Matsushima, A. Nishiki, N. Wada, and K. Kitayama, “High reflectivity superstructured FBG for coherent optical code generation and recognition,” Opt. Express 12(22), 5457–5468 (2004). [CrossRef]
21. T. Kodama, N. Nakagawa, N. Kataoka, N. Wada, G. Cincotti, X. Wang, T. Miyazaki, and K.-I. Kitayama, “Secure 2.5 Gbit/s, 16-Ary OCDM block-ciphering with XOR using a single multi-port en/decoder,” J. Lightwave Technol. 28(1), 181–187 (2010). [CrossRef]
22. Y. J. Jung, C. W. Son, S. Lee, S. K. Gil, H. S. Kim, and N. Park, “Demonstration of 10 Gbps, all-optical encryption and decryption system utilizing SOA XOR logic gates,” Opt. Quant. Electron. 40(5-6), 425–430 (2008). [CrossRef]
23. L. Yi, T. Zhang, Z. Li, J. Zhou, Y. Dong, and W. Hu, “Secure optical communication using stimulated Brillouin scattering in optical fiber,” Opt. Commun. 290, 146–151 (2013). [CrossRef]
24. X. Wang, Z. Gao, X. H. Wang, N. Kataoka, and N. Wada, “Bit-by-bit optical code scrambling technique for secure optical communication,” Opt. Express 19(4), 3503–3512 (2011). [CrossRef]
25. Z. Gao, B. Dai, X. Wang, N. Kataoka, and N. Wada, “Rapid programmable/code-length-variable, time-domain bit-by-bit code shifting for high-speed secure optical communication,” Opt. Lett. 36(9), 1623–1625 (2011). [CrossRef]
26. Z. Gao, Q. Wu, X. Gao, Q. Li, Z. Ma, X. Wang, and Y. Qin, “25 Gb/s physical secure communication based on temporal spreading-then-random phase encryption,” IEEE Photonics Technol. Lett. 33(24), 1363–1366 (2021). [CrossRef]
27. N. Jiang, A. Zhao, C. Xue, J. Tang, and K. Qiu, “Physical secure optical communication based on private chaotic spectral phase encryption/ decryption,” Opt. Lett. 44(7), 1536–1539 (2019). [CrossRef]
28. T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007). [CrossRef]
