1. Introduction

With the everlasting pursuits for large-capacity communications, an increasing amount of personal information and confidential information are transmitted over optical fiber networks. Thus, secure fiber transmission has attracted considerable attention. Although quantum key distribution (QKD) together with one-time pad (OTP) encryption should have been a perfect secrecy communication system [1], the key generation rate is too limited (eg., 2.38Mb/s [2]) to support high-speed data stream with OTP, which needs key stream as long as data. This has led to the seeking of efficient physical-layer encryption technologies that provide data security ensured by physical principles, instead of the large computation complexity of traditional mathematical cipher.

Quantum-noise randomized cipher (QNRC) is an emerging physical-layer encryption method based on Heisenberg’s uncertainty principle [3], which can realize high-speed and long-distance secure transmission [4]. Yuen 2000 (Y-00), the basic QNRC protocol [5], exploits the quantum noise of multiphoton coherent states (i.e., uncertainty of phase [6] or intensity [7]) to mask M-ary signals so as to protect both the key and data in safe. Employing multi-level modulation, QNRC is well compatible with the currently existing optical network infrastructure. So far, QNRC realization with data rate up to single-channel 40Gb/s over 480-km fiber has been reported [8]. Recently, a QNRC system with 70Gb/s single-channel transmission over 100km is realized, whose secret key is on-line generated by continuous variable QKD [9].

According to the previous studies [5,8,10,11], the security level of QNRC is particularly dependent on the number of masked signals (NMS), which means the larger NMS contributes to a safer system. Generally, there are two ways to enlarge NMS, namely, diminishing the adjacent signal distance and enhancing the quantum noise effect. A sophisticated scheme was proposed [11], which further divides the basic state divisions of Y-00 into many regions, whereas two independent key streams were needed. And the former way may be limited by the hardware circuits. The latter one usually resorts to the amplified spontaneous emission (ASE) noise, which is common in optical fiber channel, so as to assist quantum shot noise to mask more states. The previous schemes of the latter method adopt the ordinary laser sources for fiber communications and introduce ASE noise by employing erbium-doped fiber amplifiers (EDFA) [3, 8, 10]. Because ASE is much bigger than the quantum shot noise of coherent state of laser light, the NMS can be quite large.

However, the ASE noise is still a kind of additive noise with broad spectrum in contrast to the coherent-state signal, which can be greatly reduced by optical filtering without damaging the signal. In this paper, we propose and investigate a Y-00 encryption system based on ASE light source, that is, the information is carried on ASE light [13]. Therefore, if eavesdroppers try suppressing the classical ASE, the useful signals will be impaired inevitably, and information will still be unavailable to them. We believe our scheme based on ASE source can provide an improved security with larger NMS than the previous ASE-assisted schemes under the same conditions. This paper is organized as follows. In Section 2, the theoretical model of our scheme is described and investigated. A proof-of-principle experiment is demonstrated in Section 3, which is followed by the discussion and conclusion in Section 4.

2. System model of QNRC based on ASE light source

2.1 System model

As a noise optical source, ASE light with random phase, polarization and wavelength is not the pure coherent state but an incoherent collection of a series of basic coherent states, which also has certain quantum uncertainty. In this paper, we discuss the ASE source based Y-00 system of M-ary intensity modulation (ISK), as shown in Fig. 1. A polarizer is placed after ASE source to ensure only one polarization will be modulated, aiming at reducing the polarization-dependent noise. The modulating signal is the M-ary ciphertext generated according to Y-00 protocol. The optical bandwidth and power spectral density (PSD) of ASE signal are adjusted by optical band-pass filter (OBPF) and variable optical attenuator (VOA), respectively. Suppose the average output power from transmitter (Alice) to be ${\overline{P}}_{ASE,0}={\overline{S}}_{ASE}{B}_o$, with optical bandwidth B_o and average PSD ${\overline{S}}_{ASE}$. And the M-ary modulated signal power P_0m, m = 1~M, gives

 

Fig. 1 Schematic of ISK semi-QNRC based on ASE source. PRNG: pseudo-random number generator.

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First, consider eavesdropper Eve. She is assumed to be extremely powerful, who can acquire the original output signals. Because ASE light is incoherent with random characteristics, coherent detection is basically impossible for eavesdroppers. Thus only direct photoelectric detection can be performed in our scheme, through which the corresponding M-level electrical signals will be

Meanwhile, Eve is confronted with various kinds of noise, including quantum shot noise, beat noise, thermal noise and other noise sources. Among them, shot noise and self-beating noise of ASE signals can never be eliminated, which both are the uncertainties unavoidable in any case, despite the technical development. Hereinto, the shot noise is originated from quantum noise and the signal self-beating noise is classical, so this scheme is a semi-QNRC in the rigorous sense. Specifically, the quantum shot noise and signal ASE-ASE beat noise can be derived as [14]

Now focus on the legitimate transmission to receiver Bob. For long-haul transmission, several relay amplifiers will be employed. The average output power of each relaying EDFA can be expressed as [15]

By regulating the decision threshold as the running key generated from shared seed key, the M-ary ISK signal can be recovered into binary. Bob only need make a decision between a pair of basis states $\left\{I_m^B,I_{m+M/2}^B\right\}$. After channel transmission, the received ASE spectrum is the superposition of source ASE signal and noise ASE from EDFA. Thus, we consider the received PSD of the m-th level ASE light as

As for the electrical noise at Bob, we take into account thermal noise, shot noise and ASE-ASE beat noise, which are, respectively,

2.2 Numerical results

Based on the theoretical model above, we investigate the security and transmission performances of this ASE-based semi-QNRC in terms of NMS and Q-factor, respectively. Some general parameters are configured in Table 1.

Table 1. Simulation parameters.

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Figure 2 illustrates the impact of number of signal levels on security, with ${\overline{P}}_{ASE,0}=6dBm$, B_o = 200GHz, and for Eve B_e = R/2 = 1.25GHz. It seems that NMS increases exponentially with the length of symbol, l = log₂M. Meanwhile, the average symbol error rate of Eve based on Gaussian distribution with mean I_m and standard deviation $\Delta I_m$ rises with the growth of ${\Gamma }_{ASE}^E$. To compare with the former ASE-assisted scheme, we also present the case, where an inner EDFA is adopted to boost ${\overline{P}}_{ASE,0}$ from −24dBm to 6dBm. The NMS of ASE noise assisted ISK schemes, ${\Gamma }_{LD}^E$, is calculated based on homodyne coherent detection under the same settings, where the coherent-state light is attenuated to be mesoscopic and then amplified with ASE noise added. The gain of EDFA is G_in = 30dB that saturates its impact on security [10] and outputs are all 6dBm. And the NMS of quadrature amplitude modulation (QAM) QNRC is nearly a square multiple of ISK NMS [12], so ${({\Gamma }_{LD}^E)}^2$ is presented to approximate ${\Gamma }_{QAM}$. In comparison, obviously, ${\Gamma }_{ASE}^E$ is always much larger than ${\Gamma }_{LD}^E$, which shows the better security of this scheme. For small M, ${\Gamma }_{ASE}^E$ is superior to ${({\Gamma }_{LD}^E)}^2$, and the NMS of 2-D modulation surpasses that of our ASE scheme for big M. For NMS, here 1335-level ASE scheme is equivalent to a 1335 × 1335 QAM scheme. Further, the adoption of G_in brings a little influence on ${\Gamma }_{ASE}^E$ with the same output power here, since there is already sufficient ASE from source.

 

Fig. 2 NMS and symbol error rate versus the number of signal levels M = 2^l, with η = 1 for Eve.

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We evaluate the NMS, ${\Gamma }_{ASE}^E$ as well as ${\Gamma }_{LD}^E$, as a function of the output power from transmitter for the case of B_o = {50GHz, 200GHz} and EDFA gain of ${\Gamma }_{LD}^E$ at 30dB, as shown in Fig. 3(a). ${\Gamma }_{LD}^E$ is evidently getting smaller with the growth of output power, while the decrease of ${\Gamma }_{ASE}^E$ with larger power is very tiny, which is almost insensitive to output power (PSD, actually). Thus, to achieve NMS large enough, the former needs to make output not too strong. In contrast, the latter can send out more powerful signal, which resists more fiber loss. Moreover, for the same power, the NMS ${\Gamma }_{ASE}^E$ with narrow optical bandwidth is much bigger apparently. It implies the security of this ASE-based Y-00 realization can be guaranteed by mainly setting the output B_o. Note that too small B_o affects the legitimate Q-factor (see Fig. 4 below).

 

Fig. 3 (a) NMS versus output power, with B_e = R/2; (b) NMS versus B_e of eavesdropper receiver/bit rate, with average output PSD ${\overline{S}}_{ASE}$ = −107dBm/Hz. M = 128 and η = 1 for both (a)(b).

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Fig. 4 (a) Q-factor versus optical bandwidth; (b) Q-factor versus average output PSD, ${\overline{S}}_{ASE}$, with 20 relay EDFAs. For both, M = 128, B_e = 2.7GHz, G₀ = 30dB and $\Re \text{=}0.9$.

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Further, NMS ${\Gamma }_{ASE}^E$ versus the electrical bandwidth of Eve’s receiver normalized to bit rate is shown in Fig. 3(b), for different B_o and the same PSD. It indicates the eavesdropper will reduce B_e as far as possible in order to weaken the intrinsic noise masking effect. However, according to the first Nyquist criteria, there is a lower bound for the low-pass bandwidth, i.e., B_e≥R/2. Below the Nyquist criteria, severe intersymbol interference (ISI) will occur, so NMS can’t be decreased infinitely by electrical filtering. Additionally, for the same PSD, narrow B_o also benefits the increase of NMS. Without doubt, Eve cannot diminish NMS by optical filtering, too.

When analyzing transmission performance, we take G_i = 1/L_i = G₀ for simplicity, implying that the relay EDFAs are deployed at uniformly-spaced positions with equal gains.

The impacts of optical bandwidth and PSD on Q-factor are analyzed in Fig. 4, for different numbers of relay EDFAs. Figure 4(a) focuses on how to set B_o to get optimal Q-factor for certain number of relays and output power. It indicates when there is no ASE noise from relays, Q-factor is better with broader bandwidth. However, as the increase of transmission distance, the accumulative ASE noise from channel gradually becomes the dominant noise, which is more serious with bigger B_o. Therefore, for certain output power, there is an optimal B_o maximizing the Q-factor. And the more ASE noise is accumulated, the smaller the optimal B_o will be. Besides, when output signal power decreases, the optimal B_o also goes narrow. Furthermore, the Q-factor gets better with the growth of output PSD with B_o fixed, as shown in Fig. 4(b). And for the same PSD, although the broader optical bandwidth brings more noise in, the signal power is also larger, which enlarges the Q-factor as a result, even with enough ASE noise (20 EDFAs). Thus, it is no good for Bob adopting a narrower OBPF than Alice, and he had better use the same OBPF.

Figure 5 investigates the Q-factor as a function of the number of EDFA stages, which corresponds to transmission distance, for different values of receiver electrical bandwidth and output power. Here EDFA with G₀ = 30dB is deployed every 150-km fiber with loss coefficient of 0.2 dB/km, that is, every stage of EDFA implies a distance of 150km. Normally, Q-factor becomes worse with the accumulation of ASE from relay EDFAs. And the impacts of different power values are increasingly different for longer distance. Importantly, Q-factor can be greatly improved by appropriate electrical filtering, which reduces much noise. For example, an extra 1650km or 750km can be transmitted at Q = 6 (bit-error rate, BER = 10⁻⁹) by filtering B_e to 0.75R (1.875GHz) from 2.7GHz, as shown in Fig. 5.

 

Fig. 5 Q-factor versus optical amplifier stages corresponding to transmission distance, with M = 128, B_o = 500GHz, G₀ = 30dB and $\Re \text{=}0.9$.

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3. Experiment of ISK-QNRC based on ASE source

3.1 Experimental Setup

Based on the equipment available to us, we perform a proof-of-principle experiment for the proposed scheme. And a 128-ISK ASE-based semi-QNRC is demonstrated at 2.5Gb/s over 100-km optically amplified links.

The experimental setup is presented in Fig. 6. The spectrum of ASE source is centered at 1547.5nm with a 10dB bandwidth of 5THz spanning from 1527.5nm to 1567.5nm, as shown in Fig. 7(a). A polarization beam splitter (PBS) splits the ASE light into two polarization modes, and only one polarization is utilized. Then the polarized ASE is modulated by Mach-Zehnder modulator (MZM), of which the modulating signal is the M-ary electrical signal generated by Arbitrary Waveform Generator (AWG) according to ciphertext symbols. Note that the M-ary ciphertext is mapped from binary data bit and M/2-ary running key symbol according to the Y-00 protocol. The data bit sequence pattern is set by pseudo-random binary sequence (PRBS) with the length of 2¹¹-1, and the running key symbol is randomized following uniform distribution. The AWG is running at 2.5Gsymbol/s with a 10-bit resolution, implying a data rate of 2.5Gb/s. The commercial wavelength selective switch (WSS) works as a tunable OBPF to adjust B_o, and VOA₁ is to control the output PSD. ${\overline{P}}_{ASE,0}={\overline{S}}_{ASE}{B}_o$ is monitored by an optical power meter (OPM) at the weak branch of a 1:9 optical coupler (OC).

 

Fig. 6 Experimental setup of ISK-QNRC based on ASE source. PC, polarization controller.

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Fig. 7 (a) Full spectrum of ASE source; (b) different spectra of WSS filtering.

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The transmission line is a 100-km optically amplified links over 2 × 50.4 km standard single-mode fiber (SSMF) spans and the corresponding dispersion compensation fiber (DCF) as well as two EDFAs with gain at 16.9dB. The stability of AWG clock is enhanced by introducing a 10MHz external reference (X72 Rubidium frequency standard), because we find the clock of ciphertext channel becomes unstable after 100-km transmission.

At receiver, a local light source, tunable laser (TLD), is adopted, which is modulated by the MZM driven by the running key signals from a second channel of AWG synchronously. This key-modulated local light is to be applied as the deciphering signal. To match the received encrypted optical signal, the modulated local light will pass the optical tunable delay line (OTDL) and VOA₃, where time delay and power levels must be properly adjusted, respectively. Then the received ASE signal carrying ciphertext symbol and the matched local light modulated by corresponding running key symbol are detected by a balanced photodetector (BPD) simultaneously. As a result of balanced detection, the binary signal can be recovered from the M-ary encrypted signal after clock data recovery (CDR). The low-pass filter (LPF) is employed after BPD to restrict the electrical bandwidth, B_e. The oscilloscope (OSCP) is to monitor the adjusting results of OTDL and VOA₃. At last, the transmission performance is measured by a BER tester.

3.2 Results and Analyses

We perform several experimental tests for back-to-back (B2B) transmission and 100-km transmission, and for different system parameters, so as to investigate the proposed semi-QNRC based on ASE source. Figure 8 presents some visualized results. In contrast, the M-ISK signals of ASE source (Figs. 8(c) and 8(d)) are harder to distinguish than those of coherent laser diode (Figs. 8(a) and 8(b)). Note that the power for the first row is larger to display their difference. Due to the unavoidable quantum noise, the eye-openings of Y-00 encrypted signals can’t be observed fundamentally (Figs. 8(e), 8(g), 8(q) and 8(s)), which are measured directly or with unmatched key and may be regarded as what the eavesdroppers obtain. It implies the security, since Eve cannot acquire the correct Y-00 signals, not to mention the plaintext. However, the eye-openings after decrypted by the running key are clearly measured. Comparing Figs. 8(f) and 8(j), and Figs. 8(h) and 8(l) for the same PSD (−126.3dBm/Hz), we see the eye-openings with larger B_o are better, which conforms to Fig. 4(b). Comparing Figs. 8(n) and 8(p), and Figs. 8(r) and 8(t) for the same M, we find the eye-openings with a properly smaller B_e are clearer, which conforms to the results of Fig. 5.

 

Fig. 8 Measured eye diagrams and waveforms. (a)-(d) measured directly by optical port of OSCP. (e)-(t) results of BPD: (e)(g)(q)(s) Y-00 encrypted signals and (f) (h)-(p) (r)(t) corresponding decrypted signals. (e)-(h) B_o = 2.5T, B2B, B_e = 2.7G; (i)-(n) B_o = 5T, B2B, B_e = 2.7G; (o)(p) B_o = 5T, B2B, B_e = 27G; (q)(r) B_o = 5T, 100km, B_e = 2.7G; (s)(t) B_o = 5T, 100km, B_e = 27G. 132ps/div for all eye diagrams.

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We further measure the BER curves as functions of M = 2^l and B_o in B2B tests, respectively, as shown in Fig. 9. In Fig. 9(a), it shows M becomes a less influential factor on BER for M large enough. And BER with LPF is better than that without LPF by about two orders of magnitude. The dotted line, representing the corresponding theoretical result for B_e = 27GHz, agrees with the tendency of experiment result. Despite the similar tendency, system performance in theory can be greatly improved with B_e = 2.7GHz, whose BER is far bellow the corresponding experiment result. In Fig. 9(b), the impact of B_o is experimentally (Exp.) tested with the fixed output power for M = 4 and M = 128, where the values of B_o are set by WSS as Fig. 7(b) shows. It is in accordance with the Q-factor trend of Fig. 4(a), but the BER performance is worse than the theoretical results, which is simulated by following the experiment setup with 2 EDFAs of 16.9dB for 100km and M = 128. We attribute these degradations of experiment performances to the lack of a typical QNRC receiver, and some concrete causes will be discussed in Section 4. After all, the theoretical model only considers the main noise sources.

 

Fig. 9 Measured BER curves. (a) BER versus the number of signal levels M = 2^l, with B_o = 2.5THz; (b) BER versus B_o, with B_e = 2.7G. For both, ${\overline{P}}_{ASE,0}\text{=-}2.67dBm$ and $\Re =0.75$ of BPD .

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Figure 10 presents the measured BER as a function of average received power for B2B and 100-km transmission (configured as Fig. 6) at 2.5Gb/s, with M = 128, B_o = 5THz and output power 6.25dBm. In this case with ext = 22.89, for Eve of B_e = R/2 and η = 1, NMS of the intrinsic noise is calculated to be NMS = 1.097 as Eq. (6), implying certain guaranteed security. It indicates a BER below the forward error correction (FEC) threshold is achieved after 100-km transmission. The power penalty of our system between B2B and 100km is about 1.545dB and 0.762dB for BER = 10⁻⁶ and FEC threshold of 2 × 10⁻³ [8], respectively. The feasibility of the theoretical scheme is experimentally demonstrated, though, the system performance is worse than the theoretical results in Section 2. And we will discuss the reasons in next part.

 

Fig. 10 Measured BER versus the average received power. M = 128, B_o = 5THz and B_e = 2.7GHz.

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4. Discussion and Conclusion

The receiver of the proposed scheme follows the general QNRC receiver [4], which changes the decision threshold as the running key. However, we don’t have such a sophisticated receiver, so this experimental system based on standard components is a substitute for proof of principle. Although the performance seems not as good as that in theory, it does demonstrate the validity and feasibility of this scheme. The causes of degradations may be described as follows. The receiver lacks a proper OBPF, leading to the extra out-band noise into BPD. The BPD with two photodetectors may double some basic electrical noise, such as shot noise, dark current and so on. And DCF is not perfectly matched with the SSMF and there are some residues of chromatic dispersion, which broadens the transmitted waveform and results in ISI. Moreover, the M-ary ciphertext and M/2-ary running key are best to be uniformly-spaced. However, because the driver of MZM could have some nonlinearity, the output signals driving the MZM may be not uniformly-spaced, so will the modulated optical signals, correspondingly. These causes mainly result from the substitute of QNRC receiver, as well as dispersion residue. We believe this ASE source based scheme should have desirable performance, when employing typical QNRC receiver.

In addition, the NMS in this paper is obtained by theoretical calculation, which only considers the unavoidable intrinsic noise and imagines Eve of the strongest ability, i.e., she has access to the original output signals and has ideal receiver with $\eta \text{=}1$ and B_e = R/2. However, NMS in [8], Yoshida et al, and [12], Nakazawa et al, are obtained from the measurement results of B2B test, which can be quite large. From the comparison under equal conditions (Fig. 2), we believe the NMS of our scheme by practical measurement can be considerably large, too.

In conclusion, we propose and experimentally demonstrate the semi-QNRC based on ASE light source employing ISK Y-00 protocol. This scheme can provide a larger NMS by incorporating the quantum shot noise and beat noise of ASE signals, which are both fundamentally inevitable. The improvement of security and the feasibility for transmission are investigated in terms of NMS and Q-factor, respectively. A proof-of-principle experiment is performed to verify the proposed scheme. Specifically, a BPD is adopted as the optical comparator to decode the M-ary Y-00 encrypted signals with the M/2-ary key-modulated local light as optical threshold signals, correspondingly. The experimental results basically agree with the theory, and a 128-level Y-00 realization based on ASE source is realized at 2.5Gb/s over 100-km optically amplified links. This ASE-based semi-QNRC is believed to be a promising scheme for secrecy communications, and we will work on the quantitative principle of setting parameters for optimal system performance in the next step.