Open Access
Add to BibSonomy
Abstract
In this paper, we experimentally demonstrate a secure 100 Gb/s 214-level intensity modulation and direct detection transmission over a 50 km standard single-mode fiber (SSMF) using a quantum noise stream cipher (QNSC) technique and 8-bit digital to analog converters. Optical coarse-to-fine modulation (CTFM) has been proposed to simultaneously enhance the security and overcome the weakness of low modulation depth in the traditional CTFM scheme. The optical power instead of the radio-frequency signal power is adjusted to satisfy the required peak-to-peak relation for CTFM, and thus the coarse and fine modulation has the same modulation depth. Two optical CTFM schemes based on an optical coupler and a polarizing beam combiner (PBC) are proposed and their pros and cons are analyzed and compared. Considering the trade-off of transmission performance and security performance, the optical CTFM scheme based on PBC is preferred in our experiment. 214-level pulse amplitude modulation (PAM) is achieved using two dual-drive Mach-Zehnder modulators (DD-MZM). Simultaneously, each DD-MZM is also used to achieve single-sideband (SSB) modulation to eliminate the power fading induced by fiber dispersion. By these means, 100 Gb/s 214-level PAM-QNSC signal transmission over 50 km SSMF with the bit error rate below the 7% overhead hard-decision forward error correction threshold of 3.8×10−3 is achieved. The results validate that the proposed scheme is effective to realize low-cost, high-speed, and highly secure optical transmission in the data center.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As five-generation (5G) mobile communication continues to roll out, more and more data centers have been built to support various network services. The intensity modulation and direct detection (IMDD) technique is a promising scheme in data centers for its low cost and high reliability [1]. To be specific, pulse amplitude modulation (PAM), especially PAM-4, becomes the hottest signal transmission technology for IMDD-based high-speed optical interconnect [2]. On the other hand, to safeguard the security of data centers, multifarious encryption algorithms at the media access control (MAC) layer or higher layers are applied [3], but these schemes are limited by the electronic bottleneck and are vulnerable to quantum computer technology. What’s more, the physical layer of the optical link is more susceptible to malicious attacks because the fiber is easy to eavesdrop on. And encryption at the physical layer has many advantages such as minimum latency and zero overhead. Therefore, physical-layer encryption technologies are getting more and more attention.
There are lots of physical-layer encryption approaches reported recently [4–8]. For example, thanks to quantum mechanical properties, quantum key distribution (QKD) can provide information-theoretic security [4], and the typical bit-rate is several Kb/s [5]. Based on the space-time duality, a temporal cloak could open and suture a time gap to hide events which is also useful for secure communication [6]. Moreover, optical chaotic encryption is another promising scheme, and it utilizes the intrinsic nonlinearities in communication devices, contributing to high security and high robustness [7]. So far, the highest bit-rate of the reported optical chaotic encryption system is 40 Gb/s [8]. To support >100 Gb/s transmission speed in the data center, the quantum noise stream cipher (QNSC) [9–14] is an appropriate candidate. Different from the common stream cipher communication system, it doesn’t need additional optical devices and is compatible with the existing optical network. In particular, QNSC utilizes inevitable quantum noise such as amplified spontaneous emission (ASE) noise and shot noise to mask adjacent signals to realize high security. There are mainly three methods to realize optical QNSC encryption. One is the intensity shift keying (ISK) with multi-level mapping, the second is the phase-shift keying (PSK) with phase rotation, and the other is quadrature amplitude modulation (QAM) with both phase and intensity modulation. Rely on the benefits of coherent optical communication techniques, PSK-QNSC and QAM-QNSC can both achieve high speed (Tb/s) and long-distance transmission (800 km) [9,10]. However, IMDD is preferred in data centers due to its simple structure and low cost, and thus ISK-QNSC is attracting more and more attention [12–14]. Due to the server inter-symbol interference (ISI) induced by bandwidth-limited components, most of the reported ISK-QNSC schemes are limited by the bitrate. With the help of a sparse Volterra equalizer, the highest bitrate of the reported ISK-QNSC system is realized in our previous work [14], and 100 Gb/s PAM8-QNSC signals are transmitted over 100 km standard single-mode fiber (SSMF).
Actually, the security performance of the QNSC system relies on the fact that the quantum noise can mask these adjacent signal levels, which makes information recovery impossible without the shared seed key. A crucial design parameter is the encrypted PAM size in the ISK-QNSC system. The higher the ciphertext level is chosen, the higher security the system can provide. However, the order of the ultra-dense modulation is limited by the resolution of digital to analog converter (DAC). Generally, the operating bandwidth of DAC is inversely proportional to its resolution, and this is the reason why only a 256-level ISK-QNSC signal is achieved in our previous work [14]. Fortunately, a coarse-to-fine modulation (CTFM) scheme using dual-drive Mach-Zehnder modulator (DD-MZM) proposed in [13] is a promising approach to overcome the resolution limitation of DACs. The only fly in the ointment is that the electrical power of the radio frequency (RF) signal should be precisely adjusted to satisfy the condition of CTFM. This leads to a huge modulation depth difference between coarse and fine modulation, and thus the transmission performance is significantly decreased in a high-speed application scenario. Moreover, the proof-of-concept experiment in [13] only considers the optical back-to-back transmission, and no electrical amplifier and Erbium-doped fiber amplifier (EDFA) is used. It is worth investigating the impact of ASE noise on the CTFM scheme for a long transmission distance application.
In this paper, by extending our previous work in [14], we have proposed and experimentally demonstrated a secure 100 Gb/s 214-level PAM4-QNSC signal transmission over 50 km SSMF. Optical coarse-to-fine modulation is proposed to realize ultra-high level pulse amplitude modulation using 8-bit DACs. Instead of the RF signal power, the optical power is controlled for coarse-to-fine modulation, and thus the weakness of low modulation depth in the traditional CTFM technique is resolved. Two optical CTFM schemes based on an optical coupler (OC) and a polarizing beam combiner (PBC) are proposed. Considering the trade-off of transmission performance and security performance, the optical CTFM scheme based on PBC is preferred in our proof-of-concept experiment. In the proposed scheme, DD-MZM could be adopted to take place of MZM for optical SSB modulation. In our test, secure 100 Gb/s 214 PAM-QNSC signal transmission over 50 km SSMF with the bit error rate (BER) below the 7% overhead hard-decision forward error correction (HD-FEC) threshold of 3.8×10−3 is achieved.
2. Principle
2.1 ISK-QNSC using the traditional coarse-to-fine modulation technique
As shown in Fig. 1(a), in a traditional cipher encryption system, the plaintext is mapped to the ciphertext by the secret keystream which is extended by the secret seed key. Therefore, the plaintext has the same modulation format as the ciphertext. It is easy for an eavesdropper to record the ciphertext and decipher the ciphertext, due to the growing development of attacking techniques and more powerful computer technique. To cope with this issue, the QNSC technique utilizes the inevitable quantum noise mask adjacent signals to achieve higher security. As shown in Fig. 1(b), each plaintext data bit is mapped to a ciphertext data bit with the help of a set of bases and the secret keystream. Therefore, the original PAM4 data bit is mapped to an M-level data sequence randomly. When M is large enough, adjacent signal levels are very close and masked by the quantum noise as shown in Fig. 1(b), resulting in a wrong M-level decision for the eavesdropper. Note that quantum noise such as ASE noise induced by EDFA and the shot noise of the photodetector (PD) is unavoidable and ineradicable in the transmission link. The legitimate receiver can combine the secret keystream with the known basis to recover the plaintext with the help of the shared secret seed key from the transmitter. Therefore, it needs only to distinguish 4-level ciphertext data instead of M-level. Precise security analysis has proven that the QNSC scheme has good security performance even under algebraic attacks, fast correlation, and known-plaintext attacks [15–17].
Fig. 1. The principle of the traditional PAM4 signal stream cipher (a), and the PAM4-based quantum noise stream cipher (b).
The security performance relies on the mechanism that the quantum noise can mask these adjacent signal levels as much as possible. However, the maximum signal level number is limited by the resolution of DACs. Fortunately, the coarse-to-fine modulation technique using a single DD-MZM is a good solution [13]. As shown in Fig. 2(a), one arm of this DD-MZM is driven for coarse modulation, and another arm is driven for fine modulation. The output optical field of this DD-MZM could be expressed as
Fig. 2. The structure of the traditional coarse-to-fine modulation technique (a) and the proposed optical coarse-to-fine modulation technique based on optical coupler (b).
As described in [13], to reduce the peak-to-peak voltage (Vpp) difference between the coarse-modulation and fine-modulation arms, Eq. (1) could be approximated as
This approximation leads to non-uniform PAM modulation with unequal Euclidean distance among levels, but it has little impact on QNSC. As shown in Fig. 2(a), it can be observed that there is a significant Vpp disparity between the coarse and the fine modulation, and f is defined as the Vpp ratio. Table 1 shows the typical value of f when different high-level PAM is used. Obviously, the Vpp of the driven signal at the fine-modulation arm is too small and the signal-to-noise ratio is limited. This also leads to a small intensity modulation index, making the generated optical signal very sensitive to ASE noise.
Table 1. The typical value of f using different high-level PAM
2.2 ISK-QNSC using the optical coarse-to-fine modulation technique
To improve the modulation depth in the fine-modulation arm, an optical coarse-to-fine modulation technique is proposed as shown in Fig. 2(b). In this scheme, two single-drive MZMs with a variable optical attenuator (VOA) are used to control the optical power instead of the RF signal power for coarse-to-fine modulation. The output optical field of each MZM could be expressed as
where S is the input electrical signal of this MZM. After an optical coupler (OC), the output optical field can be written asUnder stable conditions such as using an integrated optical chip, the optical path delay difference $\varphi$ is time-invariant and a fixed optical delay could be used to make $\varphi \textrm{ = }{\pi / 2}$. In this case, the optical power of these two optical paths can be adjusted for the coarse-to-fine modulation, and there is no need to adjust the Vpp of the driven RF signals, contributing to no modulation depth loss. As shown in Table 1, the required Vpp ratio of 1 can be achieved in the proposed CTFM method, and the optical power difference between the two arms is 12 dB, 10.7 dB, and 10.8 dB for 216-level PAM, 214-level PAM, and 212-level PAM, respectively.
However, in a proof-of-concept experiment based on discrete optical components, the optical path delay difference $\varphi$ in Fig. 2(b) is going to change in time, leading to unstable transmission performance. To address this issue, another scheme based on a polarization beam combiner (PBC) is proposed and used in the following experiment as shown in Fig. 3(a), and the polarization scrambler is used to randomize the instantaneous polarization state of output light. The received signal at the output of PD can be expressed as
It is a remarkable fact that the received signal in Eq. (7) is a superposition of light intensity and doesn’t have the coupling term caused by the time-varying optical delay difference $\varphi$. Furthermore, DD-MZM could be adopted to take place of MZM for optical SSB modulation as shown in Fig. 3(b), and the power fading effect induced by fiber dispersion can be effectively eliminated, contributing to a longer transmission distance. In this case, the driven signal at the input of each DD-MZM can be described as ${I_t} = \hat{S} + S,{Q_t} = \hat{S} - S,$ here S and $\hat{S}$ is the input transmitted signal and its Hilbert transform, respectively.
Outwardly, despite using a high-speed polarization scrambler in the proposed PBC-based CTFM scheme, the coarse and fine channel have the risk of being separated by powerful polarization tracking and demultiplexing algorithms, leading to reduced security. Actually, the optical power difference between these two arms is too larger (>10 dB), and the polarization rotates very quickly (>50 Mrad/s). Therefore, it is very hard to separate these two orthogonal polarization states even powerful algorithms are used [19]. Furthermore, assuming that Eve could perfectly track and demultiplex these two polarization signals, Fig. 4 shows the theoretical voltage interval of the adjacent level in different QNSC schemes. It could be seen that the proposed 214-level PAM-QNSC scheme using PBC has better security performance than the 28-level PAM-QNSC scheme without coarse-to-fine modulation. The measured voltage intervals of 214-level PAM-QNSC schemes based on PBC and OC are the same order of magnitude. From the above analysis, we know that the proposed PBC-based CTFM scheme has good security.
3. Experimental setup
Figure 5 shows the proof-of-concept experiment of a high-speed secure optical fiber transmission system based on the proposed optical CTFM scheme. At the transmitter, the PAM4 signals are generated by pseudorandom bit sequences (PRBS) with a length of 215-1. The secret keystream is extended by the pre-shared secret seed key both in the transmitter and the receiver using the same rule. The shared basis table consists of a set of different bases, and there are 214/4 kinds of basis in the basis table for the PAM4 signal. Therefore, all levels of the 214-level ISK-QNSC signal can be covered. Each bit of the plaintext is mapped to the ciphertext using the secret keystream, and then the 214-level encrypted data sequence is produced. Subsequently, 214 intensity levels are divided into 26 coarse and 28 fine levels. After pulse-shaped by a root-raised cosine filter with the Nyquist factor of 0.1, the 50 Gbaud PAM signal has a 3-dB bandwidth of 27.5 GHz. The ciphertext is resampled to loaded into an arbitrary waveform generator (AWG, Keysight M8195A) with 3-dB bandwidth of 25 GHz and resolution of 8-bits. The sampling rate of this AWG is set to 64 GSa/s, and thus the data rate of the generated PAM-QNSC signal is 100 Gb/s.
Fig. 5. The experimental setup of a high-speed secure optical transmission system based on the proposed PBC-based CTFM technique.
A 100 kHz linewidth tunable laser (TL) with a wavelength of 1550.1 nm is used as the optical source, and two DD-MZMs with a half-wave voltage of 1.8 V are used to realize the proposed optical coarse-to-fine modulation and SSB modulation simultaneously. The driving voltage of each DD-MZM is set to 1 V which is the optimized value by consideration of both modulation index and nonlinearity in our experiment. Two polarization controllers (PC) and a PBC are placed at the output of two DD-MZMs for polarization multiplexing. The output optical power of these two arms is -3.52 dBm and -14.2 dBm, respectively. Note that a proof-of-concept experiment is demonstrated in our laboratory without the polarization scrambler, but a high-speed polarization scrambler such as Novoptel EPS1000 (>50 Mrad/s) could be used in practice. It can utilize high-speed and random control signal to further disturb the polarization of signal light and make the input and output polarization state uncorrelated. After 50 km SSMF propagation, an EDFA with the noise figure of 5 dB is placed to compensate for the power loss and introduce the ASE noise to mask the adjacent level of the encrypted optical signal. After that, a tunable optical filter (TOF) is used to filter out the out-of-band noise and the residual sideband caused by the imperfect SSB modulation. A variable optical attenuator (VOA) is adopted to adjust the received optical power at the PD, and the encrypted optical signal is detected by a PD with a 3-dB bandwidth of 31 GHz. Note that not only the ASE noise in the fiber link but also the shot noise of the PD could mask the encrypted signals. In our experiment, the EDFA is placed after the transmission fiber for proof-of-concept, and it could be placed at the transmitter in practice for reducing the probability of interception.
Subsequently, the received electrical signal is captured and sampled by a digital sampling oscilloscope (DSO, Tektronix DPO70000SX) operating at 100 GSa/s with a 3-dB bandwidth of 33 GHz. At the receiver, the electrical signal is resampled and then filtered by the matched filter. A third-order Volterra equalizer is used for linear and nonlinear effect equalization, and a sparse ${\ell _1}$ regularization based on recursive least square (RLS) algorithm is used in this Volterra equalizer for minimizing the algorithm complexity [20]. Finally, the legitimate receiver can decrypt the encrypted signal with the help of the shared secret seed key, and the eavesdropper must demodulate the 214-level encrypted data in case of knowing no information about the secret seed key. About 3×105 symbols are loaded into the AWG to cyclically generate the frame symbols, and 2-3 frame symbols (6-9×105) in DSO is captured for BER calculation in our experiment.
4. Results and discussion
To verify the advantages of the proposed scheme, 214-level PAM-QNSC signal using the optical CTFM technique and 210-level PAM-QNSC signal using the traditional CTFM technique mentioned in Fig. 2(a) are both tested and analyzed. In each case, 20 Gbaud and 50 Gbaud PAM-QNSC signals are both tested. As shown in Table 1, the modulation-index ratio f is 0.0852 for 214-level PAM-QNSC signal in the traditional CTFM scheme, and the fine arm has too small modulation index and the signal-to-noise ratio is limited. Therefore, the modulation level for the conventional CTFM scheme is limited to 210 ($f\textrm{ = }0.3125$) in our experiment. In the proposed CTFM scheme, the limiting factor to further improve the modulation level is the optical power difference between the coarse and fine arm, and 100 Gb/s 214-level PAM-QNSC signal transmission can be successfully achieved in our experiment.
Figures 6(a) and 6(b) shows the optical spectrum of the transmitted 100 Gb/s 214-level PAM-QNSC signals using the proposed CTFM scheme with and without optical SSB modulation, respectively. It can be seen that the fine arm still has high modulation depth even 214 intensity levels are used, and more than 20 dB sideband suppression ratio could be achieved. Thanks to the optical SSB modulation, the power fading effect can be effectively mitigated and the transmission distance is extended to 50 km. Figure 6(c) presents the electrical spectrum of the received 50 GBaud 214-level PAM-QNSC signals after 50 km SSMF transmission.
Fig. 6. The optical spectra of 100 Gb/s 214-level PAM-QNSC signal after the proposed PBC-based optical CTFM scheme using DD-MZM (a) and MZM (b), and the electric spectrum of the received 100 Gb/s 214-level PAM-QNSC signals after 50 km SSMF transmission (c).
To investigate the impact of ASE noise on the CTFM scheme, we have built up an experiment of 40 Gb/s PAM-QNSC signal transmission. Only optical back-to-back (OBTB) transmission is considered in this test, and no electrical amplifier is used. Both the proposed 214-level CTFM scheme and the traditional 210-level CTFM scheme are tested. Besides, a regular 40 Gb/s PAM4 signal without QNSC encryption is tested for comparison. Figure 7 presents the measured BER performance of 40 Gb/s PAM-QNSC signals using different CTFM schemes as a function of the received optical power (ROP) after OBTB transmission. In each measurement, the cases with and without EDFA after the transmitter are tested to evaluate the impact of ASE noise on the security and transmission performance. Note that the received optical power at the PD is set to the same value by using a tunable optical attenuator under these two test conditions. When EDFA is not used, the proposed CTFM scheme and the conventional CTFM scheme have very close BER performance, and it means there is not much noise in the link. But this small noise still leads to a 2 dB power penalty, compared to the regular 40 Gb/s PAM4 signal without QNSC encryption. When EDFA is used, the BER performances of these two schemes are both deteriorated due to the increased quantum noise. The power penalty induced by EDFA is 2 dB and 7 dB for the proposed CTFM scheme and the traditional CTFM scheme, respectively. This means that the proposed CTFM scheme is also susceptible to ASE noise due to the 10.7 dB optical power difference between the coarse and fine arms for 214-level modulation. However, it could be clearly observed in Fig. 7 that the proposed CTFM scheme has higher channel noise tolerance than the traditional CTFM scheme because of the higher intensity modulation index. Note that it needs to balance the security and transmission performance when more EDFAs are used for longer transmission distance applications in practice. In the following experiments, EDFA is used in all cases for higher security.
Fig. 7. The measured BER performance of 40 Gb/s PAM-QNSC signals using different CTFM schemes with and without EDFA after OBTB transmission.
Figures 8(a) and 8(b) show the measured BER performance of 40 Gb/s and 100 Gb/s PAM-QNSC signals as a function of ROP after OBTB and 50 km SSMF transmission, respectively. The proposed optical CTFM and the traditional CTFM schemes are both tested and compared. Thanks to the optical SSB in the transmitter, the dispersion induced by 50 km SSMF has little impact on the BER performance in these two CTFM schemes as shown in Fig. 8(a). However, a 5 dB power penalty is observed between the proposed CTFM scheme and the traditional CTFM scheme after 50 km SSMF transmission, which is consistent with the results in Fig. 7. In the case of 100 Gb/s PAM-QNSC signal transmission in Fig. 8(b), only the BER value of 214-level PAM-QNSC signal using the proposed CTFM scheme can reach the HD-FEC threshold, here 0.5 dB power penalty induced by 50 km SSMF can be attributed to the imperfect SSB modulation. This further proves that the lower modulation index at the fine arm in the traditional CTFM scheme has a serious impact on the transmission performance.
Fig. 8. The measured BER performance of 40 Gb/s (a) and 100 Gb/s (b) PAM-QNSC signals using different CTFM schemes after OBTB and 50 km SSMF transmission.
Figure 9(a) present the measured BER performance of 40 Gb/s PAM signals as a function of ROP with and without the proposed 214-level QNSC encryption. 4 dB power penalty is induced by the proposed QNSC encryption after both OBTB and 50 km SSMF transmission, and this reason could be explained by large optical power difference (10.7 dB) between the coarse and fine arm leads to the different optical signal to noise ratio. When the data rate is improved to 100 Gb/s, it still has a 4 dB power penalty caused by the coarse-to-fine modulation as shown in Fig. 9(b). Besides, the power penalty induced by 50 km SSMF transmission is increased to 0.7 dB in both PAM4 and 214-level PAM-QNSC cases, and this could be attributed to the imperfect SSB modulation. However, secure 100 Gb/s 214-level PAM-QNSC signal transmission over 50 km SSMF with the BER below HD-FEC threshold is achieved just using 8-bit DACs. With the help of a high-speed polarization scrambler and large optical power difference between the two arms, the proposed 214-level PAM-QNSC scheme using PBC will have better security performance as described in Section 2. Figures 9(a) and 9(b) also present the BER performance for the illegitimate receiver who doesn’t know the secret key, and the BER value is close to 0.5. Figure 10 shows the noise-masking number (NMS) [13,21] of the 210-level and 214-level PAM4-QNSC signal in terms of the average optical power, and the maximum to minimum intensity ratio is set to 9 in our experiments. The NMS of the 214-level PAM4-QNSC signal is approximately 60 at an average optical power of -5 dBm and 40 at an average optical power of -2 dBm, which means that the detection failure probability (DFP) ($DFP = 1 - 1/NMS$) [14] for an eavesdropper is about 98.33% and 97.5%, respectively. Therefore, it is scarcely possible to recover a correct intensity level without the secret key.
Fig. 9. The measured BER performance of 40 Gb/s (a) and 100 Gb/s (b) PAM signals with and without the proposed 214-level QNSC encryption after OBTB and 50 km SSMF transmission.
Fig. 10. Noise masking number of 214-level and 210-level PAM4-QNSC signal versus the average optical power.
5. Conclusions
In this paper, we have experimentally demonstrated a secure 100 Gb/s 214-level PAM-QNSC signal transmission over 50 km SSMF using 8-bit DACs. To overcome the weakness of low modulation depth in the traditional CTFM scheme, a novel optical CTFM scheme is proposed to adjust the optical power instead of RF signal power. Two optical CTFM schemes based on an OC and a PBC are proposed, and the PBC-based scheme is proven to balance the security performance and the practicality. To eliminate the power fading induced by fiber CD, DD-MZM-based SSB modulation is also used. 210-level PAM-QNSC signal using the traditional CTFM scheme and 214-level PAM-QNSC signal using the proposed CTFM scheme are both tested and compared. The experimental results show that after 50 km SSMF transmission, 40 Gb/s 214-level PAM-QNSC signal using the proposed CTFM scheme has 5 dB power gain compared to 40 Gb/s 210-level PAM-QNSC signals using the traditional CTFM scheme. Only the BER value of the 214-level PAM-QNSC signal using the proposed CTFM scheme can reach the HD-FEC threshold in the case of 100 Gb/s signal transmission. The experimental results indicate that the ISK-QNSC system with optical CTFM has great potential to achieve high speed, long-distance, and high-security optical transmission in the data center.
Funding
National Key Research and Development Program of China (2018YFB1800904); National Natural Science Foundation of China (61675083); Fundamental Research Funds for the Central Universities (2019kfyXMBZ033); State Key Laboratory of Advanced Optical Communication Systems and Networks. (2019GZKF7).
Disclosures
The authors declare no conflicts of interest.
References
1. K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. Lau, “Digital signal processing for short-reach optical communications: A review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018). [CrossRef]
2. D. Sadot, G. Dorman, A. Gorshtein, E. Sonkin, and O. Vidal, “Single channel 112Gb/s PAM4 at 56Gbaud with digital signal processing for data centers applications,” Opt. Express 23(2), 991–997 (2015). [CrossRef]
3. M. E. Smid and D. K. Branstad, “Data encryption standard: past and future,” Proc. IEEE 76(5), 550–559 (1988). [CrossRef]
4. M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557(7705), 400–403 (2018). [CrossRef]
5. J. Yin, Y. Li, S. Liao, M. Yang, Y. Cao, L. Zhang, J. Ren, W. Cai, W. Liu, S. Li, R. Shu, Y. Huang, L. Deng, L. Li, Q. Zhang, N. Liu, Y. Chen, C. Lu, X. Wang, F. Xu, J. Wang, C. Peng, A. K. Ekert, and J. Pan, “Entanglement-based secure quantum cryptography over 1,120 kilometers,” Nature 582(7813), 501–505 (2020). [CrossRef]
6. J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498(7453), 205–208 (2013). [CrossRef]
7. A. Kiani-B, K. Fallahi, N. Pariz, and H. Leung, “A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter,” Commun. Nonlinear Sci. Numer. Simul. 14(3), 863–879 (2009). [CrossRef]
8. L. Wang, X. Mao, A. Wang, Y. Wang, Z. Gao, S. Li, and L. Yan, “Scheme of coherent optical chaos communication,” Opt. Lett. 45(17), 4762–4765 (2020). [CrossRef]
9. K. Tanizawa and F. Futami, “Single-channel 48-Gbit/s DP PSK Y-00 quantum stream cipher transmission over 400- and 800-km SSMF,” Opt. Express 27(18), 25357–25363 (2019). [CrossRef]
10. M. Yoshida, T. Kan, K. Kasai, T. Hirooka, and M. Nakazawa, “10 Tbit/s QAM quantum noise stream cipher coherent transmission over 160 km,” in Optical Fiber Communication Conference (OFC), (Optical Society of America, 2020), paper T3D.2.
11. X. Chen, K. Tanizawa, P. Winzer, P. Dong, J. Cho, F. Futami, K. Kato, A. Melikyan, and K. Kim. “Experimental demonstration of 4,294,967,296-QAM based Y-00 quantum stream cipher carrying 160-Gb/s 16-QAM signals,” arXiv: 2009.11412 (2020).
12. F. Futami and O. Hirota, “Masking of 4096-level intensity modulation signals by noises for secure communication employing Y-00 cipher protocol,” in Proceedings of IEEE European Conference on Optical Communication, (IEEE, 2011), 1–3 (2011).
13. K. Tanizawa and F. Futami, “214 intensity-level 10-Gbaud Y-00 quantum stream cipher enabled by coarse-to-fine modulation,” IEEE Photonics Technol. Lett. 30(22), 1987–1990 (2018). [CrossRef]
14. Q. Yu, Y. Wang, D. Li, H. Song, Y. Fu, X. Jiang, L. Huang, M. Cheng, D. Liu, and L. Deng, “Secure 100 Gb/s IMDD transmission over 100 km SSMF enabled by quantum noise stream cipher and sparse RLS-Volterra equalizer,” IEEE Access 8, 63585–63594 (2020). [CrossRef]
15. S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006). [CrossRef]
16. O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007). [CrossRef]
17. H. Jiao, T. Pu, J. Zheng, P. Xiang, and T. Fan, “Physical-layer security analysis of a quantum-noise randomized cipher based on the wire-tap channel model,” Opt. Express 25(10), 10947–10960 (2017). [CrossRef]
18. Y. Jiang, W. Ding, P. Liang, L. Fu, and C. Wang, “Phase-shifted white-light interferometry for the absolute measurement of fiber optic Mach-Zehnder interferometers,” J. Lightwave Technol. 28(22), 3294–3299 (2010).
19. N. Cui, X. Zhang, N. Zhang, X. Tang, and L. Xi, “True equalization of PDL in presence of fast RSOP,” in Optical Fiber Communication Conference, (Optical Society of America, 2020), paper Th1I.3.
20. D. Li, L. Deng, Y. Ye, Y. Zhang, H. Song, M. Cheng, S. Fu, M. Tang, and D. Liu, “Amplifier-free 4×96Gb/s PAM8 transmission enabled by modified Volterra equalizer for short-reach applications using directly modulated lasers,” Opt. Express 27(13), 17927–17939 (2019). [CrossRef]
21. H. Jiao, T. Pu, J. Zheng, H. Zhou, L. Lu, P. Xiang, J. Zhao, and W. Wang, “Semi-quantum noise randomized data encryption based on an amplified spontaneous emission light source,” Opt. Express 26(9), 11587–11598 (2018). [CrossRef]
