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Abstract
Amplified spontaneous emission (ASE) light is the most natural optical carrier to hide a message in the existing optical networks at photonic layer. To enhance the anti-intercept ability of the ASE-carried stealth channel, a novel optical stealth communication scheme based on quantum noise stream cipher is proposed. The ASE light is intensity modulated by the cipher-text according to Y-00 protocol, and then transmitted under public optical noise after power attenuation. The expression of quantum noise stream ciphered ASE signal is derived, and numerical simulation is carried out. A proof-of-concept experiment is set up to demonstrate the feasibility of the proposed scheme. The experiment results show that the quantum noise stream ciphered stealth signals can be transmitted over a 25 km single-mode fiber span error-free.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the past decades, physical layer security has drawn much attention to deal with the serious information security threat. Owing to the quantum effect, and the immature optical information storage, securing the photonic layer provides inevitable protection after being detected. Securing the photonic layer can be realized by quantum communications [1,2], chaos laser communications [3–7], optical code division multiple access [8,9], quantum noise stream cipher [10–13], optical frequency hopping [14], and optical stealth communication (OSC) [15–19].
Different from the optical encryption method, OSC can provide imperceptibility security by hiding the existence of data transmission underneath a public transmission channel. To achieve this, amplified spontaneous emission (ASE) light is the most suitable source because it has the same signal characteristics as optical noise in the public channel. Several contributions have proposed the optical signal processing on ASE light for OSC [20,21]. However, the OSC system faces the challenge of interception. Optical code-division multiple-access [22], and temporal phase mask encryption [23] have been proposed to enhance the anti-interception capability of OSC. Due to the power limitation of the optical stealth channel, the system performance of these encryption methods is limited. Quantum noise stream cipher and OSC have the same requirement on transmitted optical power [24], therefore, quantum noise stream ciphered OSC based on ASE as the carrier is a possible solution to the above issue. In addition, ASE light can provide inevitable ASE-ASE beat noise to enhance the uncertainty [25].
In this paper, a novel optical stealth communication scheme based on quantum noise stream ciphered ASE light is proposed. The expression of quantum noise stream ciphered ASE signal is derived. Numerical simulation is carried out to analyze the bit error rate (BER) performance and the number of masked symbol (NMS). Then, to demonstrate the feasibility of the proposed scheme, a proof-of-concept experiment is set up.
2. Principle and system model
The configuration of the quantum noise stream ciphered OSC system based on ASE light is shown in Fig. 1. The public channels are the existing wavelength-division multiplexing (WDM) channels over optical fiber. The stealth channel is sent to the public channels and extracted from the public channels through optical coupler. In the stealth transmitter, the signal from the ASE source is complementary modulated by the cipher-text.The cipher-text is generated by encrypting the expanded key and data according to Y-00 protocol [26]. In the complementary modulation, the ASE light is complementary filtered by an optical filter, and the filtered signal is separated equally into two branches with same time delay. Two intensity modulators are set in each branches and modulated by conjugated cipher-text. A variable optical attenuator (VOA) is used to control the transmitting power. Figure 1(b) shows the schematic diagram of the signal waveform of the upper branch and lower branch. After the optical coupler, the combined signal shows the same waveform as the original ASE light [21]. In the stealth receiver, an optical filter with multiple notches is used to suppress the public signal and filter out one of the conjugated stealth signal. As following, another intensity modulator is modulated with deciphering key for decryption. Then, the decrypted optical signal is detected by a photodetector.
Fig. 1. The basic configuration of the proposed OSC system. ASE, amplified spontaneous emission light; OF, optical filter; IM, intensity modulator; VOA, variable optical attenuator; SMF, single-mode fiber; DCF, dispersion compensating fiber; EDFA, Erbium-doped optical fiber amplifier; PD, photodetector; TX, transmitter; RX, receiver.
Coherent light is based on stimulated emission, and its optical field is closest to coherent quantum field, so it is generally considered as coherent state. Different from coherent light, ASE photons are generated by spontaneous emission in the photon transition process. The optical field of ASE photons is desultorily, independent, and unrelated to each other. ASE photons have a random distribution of wavelength, phase and polarization, and present the incoherence.
Assume that the average output power of ASE photons at the transmitting end is ${\overline S _{ASE}}{B_o}$, where $B_o$ is optical bandwidth, $\overline S _{ASE}$ is the average power spectral density of the output signal. For uniformly intensity-modulated $M$-level ASE light, the lowest-level power of the intensity modulated signal is
where $r_{ex}$ is the extinction ratio. The power difference between the two adjacent levels isThe power of the $m$-th level is
In the public transmission channel, ASE noise will be introduced by EDFA, and the noise with the same wavelength and polarization cannot be eliminated. For the stealth receiver, there will be public residual signals and ASE noise. The ASE noise is the main optical noise, let the power of ASE noise be $\xi$ times of the transmitted power of the stealth signal, then $P_{m0}$ can be rewritten as
2.1 Detection of illegal users
The first purpose of concealment is to obtain imperceptibility and not to arouse the interest of eavesdropper (Eve). Then, the stealth channel will not be attacked by Eve. However, once the eavesdropper knows the deployment of the stealth channel in the public transmission link through intelligence, or knows the point-to-point transmission link that the stealth data must be transmitted over, then the security of stealth channel should be reevaluated. There are two layers of security, that is imperceptibility and confidentiality. And the eavesdropper’s interception is also divided into two steps. The first step is to crack the first layer of security, which emphasis on imperceptibility, to find out the stealth channel. The second step is to crack the second layer of security, which focus on the confidentiality, to intercept the quantum noise stream ciphered signal.
2.1.1 Imperceptibility
For the first layer of security, according to the different concealment strategies, it is difficult to describe the imperceptibility with a standard mathematical model. We assume the worst case, that is, the eavesdropper knows the deployment of the stealth channel through intelligence. To detect the signal in the stealth channel, Eve must scan the entire possible wavelengths, communication times and code word spaces. The probability of finding the stealth channel is the product of the probability of getting the correct wavelength, communication time and code. Then, it can be written as
where $B_s$ and $B_p$ are the bandwidth of the stealth and public channel respectively, $C$ is the codeword space, $T$ is the time length of the stealth and public data.When the complementary stealth signal is not recovered from Eve’s brute force attack, the received signals are ASE photons. The $m$-level electrical signal is covered and expressed as ${I} = \Re (\xi +1){\overline S _{ASE}}{B_o}$, where $\Re$ is the responsivity of the detector. Assuming the eavesdropper has the best receiver for extremely low thermal and dark noise, such as a superconducting nanowire single photon detector. Therefore, the noises are mainly quantum noise and beat noise, which can be expressed as [27]
As can be seen, $\Gamma$ is independent of $m$. Since stealth signal is covered, the value of the NMS has no effect on the security of the stealth channel. However, once the stealth signal is detected by Eve, the confidentiality should be evaluated for the second layer of security and the NMS should be rewritten.
2.1.2 Confidentiality
The confidentiality of the stealth channel mainly analyze the anti-interception capability of quantum noise stream ciphering, which is mainly evaluated through NMS. It is assumed that the eavesdropper has the maximum capacity to obtain a complete output signal. Since ASE photons are incoherent state with random characteristics, Eve cannot use local oscillator light for coherent detection, but can only use direct detection.
When the complementary signal is recovered, from (1), (2), (4), the corresponding $m$-level electrical signal is
Considering the various noises Eve faces, the quantum noise is unavoidable noise, so is the beat noise between ASE noise and the stealth signal. These noises will cause uncertainty of Eve detected signal. The quantum noise of the $m$-level stealth signal can be expressed as
In terms of beat noise, both the ASE noise and the $m$-level stealth ASE signal can be regarded as ASE photons, then the beat noise can be expressed as
Then, the intensity uncertainty of the signal is enhanced by beat noise, and the intensity uncertainty at $m$-level is
where the subscript $n$ denotes noise. Therefore, the average uncertainty of the stealth signal can be expressed asThus, NMS can be written as
According to the uncertainty principle, when $\Gamma$ is not less than $1$, the eavesdropper cannot accurately distinguish all signal levels.
2.2 Detection of legitimate users
The stealth receiver extends the shared seed key to obtain the corresponding operation key. To restore the multi-level intensity modulated signal into a binary signal, Bob can adjust the best decision threshold of $M$-level Y-00 signal according to the operation key. After the public transmission and optical filter, the ASE photons received by Bob are the superposition of stealth ASE photons and ASE noise introduced by EDFA in the public channel. In addition, there are residual public signals and other noises. The suppression of public signal is composed of multiple optical band-pass filters. This filtering will affect the waveform of the coherent light source, but since the optical carrier of the stealth channel is incoherent, the effect of filtering on the waveform is small. To simplify the model, only the ASE noise introduced by the public channel and the total bandpass bandwidth is considered.
In the eavesdropper detection, the most capable eavesdropper is considered. The eavesdropper obtains the same information as the legitimate user, but does not know the specific key. Therefore, the signal of the legitimate user is similar to that of the eavesdropper, and the corresponding expressions remain unchanged. For the electrical noise in the legitimate receiver, we also consider the thermal noise. The thermal noise is described as [27]
where $k_B$ is Boltzmann constant, $T$ is absolute temperature, and $R_L$ is the load resistance. The expression of the total noise isIn this way, the average Q factor of all $M/2$ basis is solved, then [28]
Thus, the BER of the stealth channel can be expressed as [28]
For the public channel, the ciphered ASE signal in the stealth channel has the same temporal and spectral characteristics with the ASE noise, so it can be treated as the ASE noise when analyzing the impact of stealth channel on the public channel. The performance analysis can be referred to our previous work [29]. The ASE light based stealth channel has little impact on the public channels, which is much less than that of coherent light based stealth channel. Therefore, it is not studied separately here.
2.3 Numerical simulation results
According to the theory above, numerical calculation results are carried out. Figure 2 shows the NMS under different $M$. $B_e$ is set to be 1.25 GHz, $\xi$ is 0.1, $r_{ex}$ is 1000, the transmitted power is -20 dBm. As can be seen, when only quantum noise is taken into consideration, NMS is less than 3.5 and NMS is affected by $B_o$. Note that the two curves overlap, and it shows that optical bandwidth has no effect on the number of masked symbol. Then, as the number of levels increases, the curve increases linearly. When considering ASE-ASE beat noise, for $B_o$ of 0.2 THz, the total NMS increases by a factor of 10 compared to considering only quantum noise. As the number of levels increases, the curve also increases linearly. It shows that the ASE-ASE beat noise, which is unavoidable noise for communication systems based on ASE light, can effectively increase the uncertainty. In addition, as $B_o$ goes down to 0.2 THz, ASE-ASE beat noise increases, and so does NMS.
Figure 3 shows the NMS and BER performance under different powers, in which $B_e$ is set to be 1.25 GHz, $M$ is set to be 256. In Figs. 3(a) and (b), the power of ASE noise is -20 dBm, which means $\xi$ is changed from 0.1 to 10. As the transmitted power increases, NMS for illegal users decreases. It shows that the transmitted power has an important influence on NMS. When $B_o$ is 2 THz, NMS is much less than that of $B_o$ at 200 GHz. For legitimate user, the BER curve for $B_o$ of 2 THz is better than that of 200 GHz. In Figs. 3(c) and (d), $\xi$ is 1 while the received power changes. In terms of quantum noise only, NMS changes in a big range. However, the variation of total NMS is small. This means that the illegal users can not effectively reduce NMS by optical amplification. For the legitimate user, there is a BER floor at $10^{-3}$ for $B_o$ of 200 GHz, and error free transmission can be achieved for $B_o$ of 2 THz.
Fig. 3. (a) NMS and (b) BER under different transmitted powers, (c) NMS and (d) BER under different received powers.
Figure 4 shows the NMS and BER performance under different $B_e$, in which $B_o$ is 200 GHz, $\xi$ is 0.1, $M$ is set to be 256. As the increasing of $B_e$, the quantum noise and ASE-ASE beat noise increases, and resulting in the enhancement of NMS. BER performance is degraded as the increase of $B_e$. Therefore, in terms of BER performance, the bit rate of the stealth channel is set to be 156.25 Mbps in the proof-of-concept experiment. To transmit a high bit rate stealth signal, $B_o$ should be large.
3. Experiment setup
A proof-of-concept experiment is set for the demonstration of the proposed OSC over public noise as shown in Fig. 5. Different from coherent OSC, the transmission performance of the incoherent OSC based on ASE photons is insensitive to the residual public signal [29]. The noise introduced by the public channel is mainly ASE noise, in addition, the interaction between the public channel and the stealth channel has been investigated in detail [29,30]. Therefore, the proof-of-concept experiment is focused on the transmission performance and security of the stealth channel over public noise. Note that the complementary modulation is simplified to be intensity modulation with temporal spreading by chromatic dispersion.
Fig. 5. Experiment setup of the proof-of-concept experiment. ASE, amplified spontaneous emission light; IM, intensity modulator; VOA, variable optical attenuator; SMF, single-mode fiber; DCF, dispersion compensating fiber; EDFA, Erbium-doped optical fiber amplifier; PD, photodetector; Osc, oscilloscope.
In the stealth transmitter, an ASE source connected with a 50:50 optical coupler is used to generate ASE light. The upper branch is sent to an intensity modulator for quantum noise stream ciphering and modulation. An AWG is used to generate the cipher-text, and the bit rate is 156.25 Mbps, $M$ is set to be 256. Then a DCF span with +423 ps/nm dispersion is used to spread the ciphered ASE light , and an VOA is used to control the transmitted power. The noise in the public channel is generated by the lower branch, and the optical path difference between the upper branch and the lower branch is much larger than the coherence length of ASE light. A VOA in the lower branch is also used to control the power of public noise. The combined signals are amplified by an EDFA, which is followed by a span of DCF and a 25 km SMF span. In the stealth receiver, the received optical signal is sent to a 25 km SMF span and then sent to a PD with bandwidth of 10 GHz. The detected signal is collected by oscilloscope with bandwidth of 0.25 GHz for off-line decryption and analysis.
4. Results and discussions
The measured optical spectra of the ASE without and with quantum noise stream ciphering are shown in Fig. 6. As can be seen, the ciphered ASE light has the same optical spectrum as the original ASE light. This means that the eavesdropper cannot find the existence of stealth communication through spectral analysis.
Figure 7 shows the waveform of the ASE light. As can be seen in Fig. 7(a), the waveform of the original ASE light is chaotic and disorderly. After quantum noise stream ciphering, the ASE light is also disorderly as shown in Fig. 7(b). Since the complementary modulation is simplified to be intensity modulation with temporal spreading, waveforms of the ASE light and the ciphered signal are different. The results show that the intensity modulated quantum noise stream cipher makes ASE light have noise-like characteristics in time domain. With the matched key, as shown in Fig. 7(c), the ciphered ASE light is successfully decrypted by off-line processing.
Fig. 7. The waveform of the ASE signal (a) before ciphering, (b) after ciphering, and (c) after deciphering.
The BER and NMS under different transmitted powers are shown in Fig. 8. The BER values are calculated numerically from the received signal by the oscilloscope. NMS is calculated according to Eq. (14), in which $B_o$ is 4.9 THz, $B_e$ is 250 MHz, and $\xi$ is 0. As can be seen, with the increase of transmitted power, the BER firstly decreases and then increases, while the NMS keeps decreasing. To ensure that the NMS is greater than 1, which means that the eavesdropper is unable to discriminate all signal levels physically without mistakes, the power must be lower than -23 dBm. Considering the BER performance and security, the transmitted power should be controlled between -30.5 dBm and -23 dBm. In addition, to get optimal BER performance and security, the transmitted power should be as low as possible under the premise of ensuring error-free transmission. According to the results of the numerical analysis in Section 2.3, the NMS can be increased by increasing $\xi$ or decreasing $B_o$. The BER curves under different received power are shown in Fig. 9. The transmitted power of the stealth channel is -18 dBm, $B_o$ and $B_e$ remain unchanged. According to Eq. (14), NMS is 2.8 for $\xi$ of 2, NMS is 4.6 for $\xi$ of 4. As can be seen, the quantum noise stream ciphered stealth channel can be transmitted over 25 km SMF with error-free. After $\xi$ is changed from 2 to 4, the receiver sensitivity decreases by about 2dB. It also shows that, the stealth signal can be transmitted with further for $\xi$ of 2. In addition, the transmission length can be enhanced by amplifying the output ciphered stealth signal and then attenuating the power to the appropriate value.
5. Conclusions
We proposed a novel optical stealth communication scheme based on quantum noise stream ciphered amplified spontaneous emission light. The expression of quantum noise stream ciphered ASE signal is derived. The numerical results show that NMS of the quantum noise stream ciphered stealth channel is enhanced by inevitable ASE-ASE beat noise. $M$, $B_e$ and $B_o$ have an important influence on the BER performance and security. The feasibility of the proposed scheme is demonstrated by a proof-of-concept experiment. The experiment results show the quantum noise stream ciphered stealth signals can be transmitted over a 25 km single-mode fiber span with error-free. This work provides a novel photonic layer security solution, and may promote convergence between photonic layer security technologies.
Funding
National Natural Science Foundation of China (61901480).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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