1. Introduction

It is the 5th Generation Fixed networks (F5G) with the features of Full-Fiber Connection (FFC), enhanced Fixed BroadBand (eFBB), and Guaranteed Reliable Experience (GRE) that have witnessed the optical networks turning into the most widely deployed and crucial infrastructure. The most demanding applications such as Ultra/Super High-Definition Video streaming (4K/8K video), Internet of Things (IoT), Virtual/Augmented Reality (VR/AR) gaming, and telemedicine [1,2] can greatly benefit from the FFC optical networks. Inevitably, more sensitive information such as financial transactions, medical records, and confidential intellectual property [3] will be transmitted on them. Although various security mechanisms are used to protect the confidentiality, integrity, and availability triad supported by modern cryptographies in the application layer (e.g. Secure Shell, SSH), transport layer (e.g. Transport Layer Security, TLS), network layer (e.g. Internet Protocol Security, IPSec), and datalink layer (e.g. Tri-element peer architecture-based Local area network Security, TLSec), security protection in the photonic layer has not been attracting much attention. However, the photonic layer is also vulnerable to attack by tapping [3–5] or listening to the residual adjacent channel crosstalk [4] without any destruction of the communication systems. Meanwhile, some security threats like the exposed project Tempora [6] which eavesdrops the information directly from the optical cables are increasing in the modern information era. As a supplement to those modern cryptographies [7,8], the two abovementioned reasons have facilitated more and more technologies such as optical cryptography using all-optical Exclusive OR (XOR) logic gates [9] and optical steganography [10] to cope with the security threats of the photonic layer.

As a promising encryption method to guarantee security, Young et al. [11] started the research on all-optical XOR cryptography. That era was merely in the 3rd Generation Fixed networks (F3G) when the fiber had just begun to replace the copper cables [12]. Only the On-Off Keying (OOK) or Intensity Modulation (IM) was supported for the all-optical XOR. In the current F5G era, the feature of efficient eFBB requires advanced modulation formats, e.g., (Differential) Quadrature Phase Shift Keying [(D)QPSK], (Differential) 8-Phase Shift Keying [(D)8PSK], or 16-Quadrature Amplitude Modulation (16QAM). Indubitably, the researchers never stopped. Kong et al. [13] have taken the lead in charging toward all-optical XOR gates for QPSK signals based on the Degenerate Four-Wave Mixing (DFWM). According to their XOR gates, Zhang et al. [14] designed corresponding all-optical encryption/decryption systems for 8PSK signals. Nevertheless, there are still issues that need to be addressed. The output phases of both systems subtract the other input phase from twice one of the input phases. When the encrypted signals are eavesdropped on, the quadrature tributary may be extracted by only operating a DFWM without any other prior information according to some special constellation mapping in [15] or [16], causing some potential photonic layer security hazards. To transmit QPSK or 8PSK more securely, all-optical XOR gates employing Non-degenerate Four-Wave Mixing (NFWM) appear. Cui et al. [17] and Wang et al. [18] proposed the NFWM encryption/decryption systems by inputting three QPSK signals but transmitting their NFWM results or executing two-stage NFWM of a pair of different $m$PSK signals such as QPSK and BPSK signals, respectively. One flaw is that coherent receivers must be employed to demodulate the signals, which may be too expensive to satisfy the greener evolution direction of F5G advanced [19]. To reduce the cost of coherent receivers, Yang et al. [20] achieved a differential direct-detection (DD) receiver for the DFWM/NFWM encryption/decryption system of D8PSK and DQPSK signals. Among all the systems abovementioned, three or four wavelengths will be occupied to execute the encryption/decryption in the DFWM/NFWM processes, which can either be cost- or power-consuming or reduce the wavelength utilization for multi-wavelength systems. Also, all the key used for encryption has not been specially treated, which may be eavesdropped on when transmitted. Therefore, a requirement for the wavelength-efficient and key-security-enhanced system should be satisfied as well for future all-optical encryption/decryption systems.

To address the abovementioned technical challenges, especially for the all-optical encryption/decryption system within manageable costs supporting different advanced modulation formats for the photonic layer security of F5G, in this work, a novel all-optical encryption/decryption system for D$m$PSK signals occupying only a single wavelength with key steganography is proposed and simulated. The proposed system consists of two parallel parts: an encryption/decryption part for the data security guarantee employed by the generalized XOR (GXOR) and a steganography part for the key security enhancement implemented by the Equvilent-Phase-Shifted Super-Structured Fiber Bragg Grating (EPS-SSFBG). The GXOR dominates the encryption/decryption part, which has the same security as NFWM. Thus, we first define the specific meaning of the GXOR as an expanded concept of XOR and dramatically find that the GXOR is equivalent to the conjugate multiplication. Then, according to the equivalence, we implement GXOR by employing the cascaded IQ Mach-Zehnder Modulators (IQMZMs) occupying only a single wavelength. Detailed operating principles of the cascaded IQMZMs implementation are theoretically derived. Next, we analyze the operating principles of the EPS-SSFBG to implement the key steganography. Finally, after applying the two parts to complete the proposed system, the numerical simulation results demonstrate that the proposed system is reconfigurable for DQPSK and D8PSK signals merely with a single wavelength participating in the encryption/decryption part. With the key steganography based on the $\pm \pi /2$-phase-shifted EPS-SSFBG, the proposed system can greatly improve the photonic layer security with a recorded bit rate of up to 260Gbps. The employment of a differential DD receiver and EPS method to fabricate the SSFBGs further improves the cost-effectiveness of the proposed system over all the existing systems, which can be applied to enhance the photonic layer security in F5G and beyond.

The rest of this paper is organized as follows. In section 2, elaborate theoretical derivations for the operating principles of the proposed system are analyzed. We configure the simulation setup and parameters and then discuss some simulation results in section 3 before concluding this paper in section 4.

2. Operating principle

In this section, we first introduce the general architecture of our proposed system. Then an expansion of XOR, named GXOR, is defined. The implementation architecture of the cascaded IQMZMs is designed and the theoretical derivations are given next. We elaborate on the operating principles of the EPS-SSFBG at the end.

Figure 1 illustrates the general architecture of our proposed system. It consists of two parallel parts: one is the reconfigurable all-optical encryption/decryption part employing GXOR of the data signal and key signal to guarantee the security of data, and the other is the all-optical steganography part implemented by the EPS-SSFBG to enhance the security of the key.

 

Fig. 1. General architecture of the reconfigurable all-optical encryption/decryption and key steganography system.

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2.1 Reconfigurable all-optical encryption/decryption

In the encryption/decryption part, the source data is first modulated as the D$m$PSK format through an IQMZM. Then the modulated signal and the source key are input to achieve the GXOR of the data signal and the key signal.

2.1.1 Generalized XOR definition

Before defining the GXOR, let us start according to the truth table of the conventional XOR displayed as Table 1. For simplicity, assume the data and key signals are both in DBPSK modulation format, with the phase $\varphi _{DBPSKd}$ and $\varphi _{DBPSKk}$, respectively. $\varphi _{DBPSKd}=0$ or $\varphi _{DBPSKk}=0$ describes the information bit 0 while $\varphi _{DBPSKd}=\pi$ or $\varphi _{DBPSKk}=\pi$ describes the information bit 1. The XOR result is also in DBPSK modulation format and the phase describes the same information bit as the data and key. In terms of the DBPSK phase, we define two types of phases that will be used multiple times in the following description. The first one is called the reference phase, described as $\varphi _{ref}$, which is a selected constant phase. The second one is named the rotated phase, described as $\varphi _{rot}$, which is the phase rotated from the data phase to $\varphi _{ref}$. Based on the definition of two types of phases and Table 1, we can reinterpret the logic XOR as follows:

After the reinterpretation, the concept of XOR can be expanded similarly for the DQPSK modulation format, only $\varphi _{ref}$ and $\varphi _{rot}$ may be a little different. For simplicity again, assume $\varphi _{DQPSKd}$ or $\varphi _{DQPSKk}$ is the data or key phase of the Gray-code DQPSK modulation format signal, respectively. $\varphi _{DQPSKd}=\pi /4$ or $\varphi _{QPSKk}=\pi /4$ describes the information bits 00, $\varphi _{DQPSKd}=3\pi /4$ or $\varphi _{DQPSKk}=3\pi /4$ describes the information bits 01, $\varphi _{DQPSKd}=-3\pi /4$ or $\varphi _{DQPSKk}=-3\pi /4$ describes the information bits 11, and $\varphi _{DQPSKd}=-\pi /4$ or $\varphi _{DQPSKk}=-\pi /4$ describes the information bits 10. The XOR for the DQPSK modulation format can be expanded as follows:

Table 1. XOR truth table

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The analogous truth table of the above XOR is displayed in Table 2. For a DQPSK signal, although the different data phases from the key phase are rotated through the same rotated phase $\varphi _{rot}$, they are totally different from the reference phase $\varphi _{ref}$, which could be considered an expansion of the concept of XOR, defined as GXOR here. Similarly, the GXOR can be applied to other D$m$PSK modulation formats by merely changing $\varphi _{rot}$ to $2n\pi /m$, $n\in \left \{m, m-1, m-2, \ldots, 1\right \}$ when $\varphi _{ref}$ is selected to be $\pi /m$, $m\ge 4$.

Table 2. Analogous XOR truth table

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For the D$m$PSK modulation, by further considering the key phase input $\varphi _{DmPSKk}$ and $\varphi _{rot}$, we dramatically found that they are associated with a linear relationship expressed as

When operating the GXOR, the D$m$PSK data phase is rotated through the phase $\varphi _{rot}$ and obtained the GXOR phase $\varphi _{GXOR}$ given by

In Eq. (2), the amplitudes of both data and key D$m$PSK signals are omitted due to their constant power. Compared to Eqs. (1$\sim$3) in [17], the phase operation of the GXOR is the same as NFWM. Therefore, they should have the same security. When the reference phase $\varphi _{ref}$ is selected, $\exp \left (j\varphi _{ref}\right )$ is a constant as well. Therefore, the GXOR can be achieved by conjugately multiplying the data and key D$m$PSK signals. Obviously, implementing the GXOR will be the most challenging and innovative process of the encryption/decryption part. We will design an implementation architecture of the GXOR based on the fact that it is equivalent to conjugate multiplication.

2.1.2 Cascaded IQMZMs-based GXOR theoretical derivation

The implementation architecture employs two cascaded IQMZMs, as Fig. 2 illustrates. For a push-pull IQMZM, the field transfer function $h\left (t\right )$ to transform the input signal $E_{in}\left (t\right )$ can be defined as

 

Fig. 2. Reconfigurable all-optical encryption structure.

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A D$m$PSK modulation format signal is usually modulated by setting $V_1=(k-1/2)V_{\pi DC1}$, $V_2=(k-1/2)V_{\pi DC2}$, (null point) and $V_{p}=(k/2-1/4)V_{\pi DCp}$ (quadrature point), $k\in \mathcal {Z}$, where $\mathcal {Z}$ is the set of all integers. To simplify the analysis, we suppose an ideal linewidth, i.e. $\text {0Hz}$, of the output of the Laser Diode (LD), leading $E_{in}\left (t\right )=\sqrt {P_0}$, where $P_0$ is the output power of the LD, an ideal insertion loss, i.e., $\alpha =1$, and infinite extinction ratios, resulting in $a=b=\sqrt {2}/2$. As a result, the output of the first IQMZM $D\left (t\right )$ can be formulated as

The encrypted signal is then transmitted on the optical fiber channel. As for the decryption, the GXOR is a little different from XOR. The encrypted signal should be multiplied by the conventional modulated key, i.e., modified $\overline {K\left (t\right )}$ with the same form of Eq. (4) as $K\left (t\right )$. The decryption, named inverse GXOR in Fig. 1, can be described as

2.2 All-optical steganography

The encryption/decryption part guarantees the security of data during transmission, while the steganography part enhances the security of the key. The key is first modulated in a low-duty-cycle IM format to approximate short pulses. Then these short pulses input an EPS-SSFBG to achieve the steganography. For a conventional SSFBG, each input pulse is coded in Direct-Sequence Optical Code-Division Multiple-Access (DS-OCDMA) [22]. For the IM modulated key signal $K'\left (t\right )$, the output DS-OCDMA signal can be described as

$\Lambda \left (z\right )$ is around $500\text {nm}$, thus, accurate phase movement requires the fabrication platform to have a control precision of nanometers or even below when fabricating an SSFBG, which is obviously cost-consuming and difficult to control. Fortunately, the EPS method addresses the dilemma [23]. Considering the total phase of the cosine function in Eq. (11), if $z$ is attached to a fixed $\Delta z$, the formula without $\varphi \left (z\right )$ is modified as

Finally, Dai et al. [24] found that conventional $0/\pi$-phase-shifted SSFBG allows the eavesdroppers to extract code sequences straightforwardly through the dips when the adjacent phases change $\pi$ of the coded signals. Therefore, $\pm \pi /2$-phase-shifted SSFBG [24] is proposed to improve security. Here, we adopt the solution as well in EPS-SSFBG by configuring $\Lambda \left (z\right )$ as $4$ or $4/3$ times $\Delta z$, i.e.,

Figure 3 illustrates an example of the spatial refractive index modulation of code $\left \{\pi /2,\pi /2,\pi /2,\right.$

 

Fig. 3. An example of the spatial refractive index modulation of code $\left \{\pi /2,\pi /2,\pi /2,-\pi /2\right \}$, resulting in phase $\left \{\pi /2,\pi,-\pi /2,\pi \right \}$ in an EPS-SSFBG.

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$\left.-\pi /2\right \}$ (representing the perfect sequence $\left \{+1,+1,+1,-1\right \}$ in bipolar code) in an EPS-SSFBG. For a certain usual segment of the EPS-SSFBG, it includes four grating periods, i.e., $z=4\Lambda$. As for the transition segment $\Delta z$ with a sudden $\pi /2$ phase shift (the 5th and 10th period in Fig. 3), the grating period is modified as $\Lambda '=4\Delta z$ while $\Lambda '=4\Delta z/3$ with a sudden $-\pi /2$ phase shift (the 15th period in Fig. 3). In a word, employing the $\pm \pi /2$-phase-shifted EPS-SSFBG can not only be a cost-efficient method to achieve the key steganography part but also improve the security of the key when it is transmitted on the optical fiber channel.

3. Simulation setup and results analysis

Having defined and theoretically derived the two parallel parts, in this section, the simulation setup of our proposed system is illustrated first. Then the configurations of its parameters are introduced in detail. Finally, the performance of each part is demonstrated.

We use VPITransmissionMaker 9.5 to simulate the performance of the proposed system at the recorded bit rate of $260\text {Gbps}$. This bit rate value stems from the highest record baud rate $260\text {GBaud}$ of the current commercial electro-optic modulators [25] and photodetectors [26,27]. However, the key steganography part of the proposed system must input binary IM signals, i.e., the highest bit rate of this part can only achieve $260\text {Gbps}$. The transmission baud rate of data must be divided by corresponding bits of the modulation format to make sure the key can be received in the same time window as the data. As a result, the baud rate of DQPSK signals should be $260/2=130\text {GBaud}$ and that of D8PSK signals should be $260/3\approx 86.67\text {GBaud}$, respectively. The complete schematic of the proposed system is illustrated in Fig. 4.

 

Fig. 4. Setup of the proposed system.

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3.1 Performance of the data encryption/decryption part

The performance of the data encryption/decryption part is first demonstrated by assuming that the key is perfectly received, i.e., the bit error rate (BER) of the key transmission is zero. In Fig. 4, after the source data bits are mapped into D$m$PSK phases, their I and Q tributaries [$v_1\left (t\right )$ and $v_2\left (t\right )$, respectively] are fed into MZM-I and MZM-Q of the first IQMZM, respectively. With the optical source of LD1 input and the null and quadrature point configuration of the IQMZM, $D\left (t\right )$ will be generated. In the second IQMZM to encrypt the data as $D\left (t\right )\overline {K\left (t\right )}$, the source key bits are mapped into the same type of D$m$PSK phases. The I tributaries $v_1'\left (t\right )$ and Q tributaries $v_2'\left (t\right )$ are fed into MZM-I and MZM-Q, respectively. At this time, the null point is maintained while the quadrature point should be configured differently from the first IQMZM as Eq. (5). To simulate a real transmission scenario, we add EDFAs (EDFA1 and EDFA2 as boosters, EDFA3 and EDFA4 as in-line amplifiers), Standard Single-Mode Fiber (SSMF), and Dispersion Compensation Fiber (DCF) between the second and third IQMZM. The dispersion of SSMF will distort $D\left (t\right )\overline {K\left (t\right )}$ severely, which must be compensated before the third IQMZM for decryption. For an all-optical system, we simply employ the DCF here, and other all-optical technologies such as chirped fiber Bragg grating, Gires-Tournois filter, and optical phase conjugation can also be adopted. In the third IQMZM to decrypt the signal, the sink key bits (the same as source key bits in fact in this subsection) are mapped into D$m$PSK phases as well and subsequently fed into the IQMZM with the same points configuration of the first IQMZM. As a consequence, the output result of the third IQMZM $D\left (t\right )\overline {K\left (t\right )}K\left (t\right )$ is achieved. In the end, $D\left (t\right )\overline {K\left (t\right )}K\left (t\right )$ is demodulated as the sink data by a cost-efficient differential DD receiver compared to a coherent receiver like [28] or [29].

3.1.1 Parameters configuration

For the I or Q tributaries of the source data, source key, and sink key, a square-root raised cosine filter with the roll-off factor of $0.6$ and the truncated symbols of $64$ is applied as the shaping filter to limit the bandwidth and reduce the Inter Symbol Interference (ISI) during the transmission. We adopt the center frequency $f_1=189.5145\text {THz}$, the linewidth of $100\text {kHz}$, and the output power of $10\text {mW}$ with the initial phase of $\pi /4$ (to compensate the phase rotation caused by $V_p$) for the LD1. For three IQMZMs, they are all push-pull IQMZMs with $40\text {dB}$ extinction ratio, i.e., $ER_c=ER_p=40\text {dB}$, $3\text {dB}$ insertion loss, $V_{\pi RF1}=V_{\pi DC1}=V_{\pi RF2}=V_{\pi RF2}=1\text {V}$ [30], and driver voltage of $62.5\text {mV}$ of I or Q tributary. EDFA1-EDFA4 in Fig. 4 are all set to power-controlled mode with the same Noise Figure (NF) $5.5\text {dB}$ and Noise Tilt (NT) $0\text {dB/Hz}$ according to [31]. The center frequency and bandwidth of the four EDFAs are all set to the same as the LD’s center frequency i.e., $189.5145\text {THz}$ and I or Q tributary’s bandwidth, i.e., $130\text {GHz}$ for DQPSK and $86.67\text {GHz}$ for D8PSK, respectively. The bandwidth setting here is equivalent to assuming an optical filter after each EDFA to remove the out-of-band amplified spontaneous emission (ASE) noise. The output power of the four EDFAs is all set to $2\text {mW}$.

As for the differential DD receiver, the phase shift for DQPSK of the lower arm in the Mach-Zehnder Interferometer (MZI) is $-\pi /4$ and $\pi /4$ for I and Q tributary while the phase shift for D8PSK is $-5\pi /8$ and $-\pi /8$, respectively. The balanced PDs after the I and Q tributary MZIs are both PIN-model as [26] defines. The bandwidth is $105\text {GHz}$ and the responsivity is $0.25\text {A}/\text {W}$. Detection currents of them will be influenced by the sum of the dark current of $5\text {nA}$, the thermal noise of $10\text {pA}/\sqrt {\text {Hz}}$, and shot noise. After the direct detection by balanced PDs, Trans-Impedance Amplifiers (TIAs) with the trans-impedance of $1\text {k}\Omega$ and equivalent noise of $1.1\mu \text {A}$ are employed to amplify the detecting currents as output voltages. Some Digital Signal Processing (DSP) steps including IQ imbalance compensation, matched filter with the same parameters as the shaping filter, Gardner time recovery, channel equalization, and preamble synchronization are applied before the sink data can be demonstrated at the end.

A summary of the parameters abovementioned is displayed in Table 3.

Table 3. Parameters in encryption/decryption part setup

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3.1.2 Results analysis

For the random source data, we first assign fixed bits ($00$ for DQPSK and $000$ for D8PSK) in the first symbol of the data sequence due to the D$m$PSK modulation. Next, two segments of $13$-bit Barker code [32] are assigned after the first symbol to achieve the preamble synchronization in the DSP process. The total number of source data symbols is $2048$. The first $27$ symbols will not be taken into account when calculating the BER. As for the random source key, in order to maintain the Barker code after the encryption, the fixed bits $01$ for DQPSK and $001$ for D8PSK are assigned with the same length of Barker code symbol, which can maintain the D$m$PSK phase as the previous symbol. Here, this assignment is designed to achieve preamble synchronization when estimating the eavesdropper’s performance. In a certain real scenario, the source key can be entirely random so that the Barker code symbol can be encrypted as well to further guarantee transmission security. Then, the BER performance of the all-optical encryption/decryption part can be illustrated in Fig. 5 according to the parameters configuration abovementioned.

 

Fig. 5. BER performance of the all-optical encryption/decryption part.

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In Fig. 5, for DQPSK and D8PSK modulation formats, we suppose that the eavesdropper located after EDFA3 in Fig. 4 can eavesdrop on the signals with sufficient power. Some distortions can be optically compensated by the DCF, i.e., we have ruled out the distortions caused by the transmission of the eavesdropped signals. However, the dotted lines indicating the eavesdroppers’ signals in Fig. 5 still illustrate high BER values, which proves the photonic layer security of the proposed all-optical encryption/decryption part. The dash-dotted lines illustrate the usual transmission performance in a $100\text {km}$ optical fiber channel without any encryption/decryption operation. While the solid lines illustrate the performance after the proposed all-optical encryption/decryption part. For the DQPSK format, their BER performance is almost the same, which reveals the proposed all-optical encryption/decryption part can not only guarantee the photonic layer security but also require almost no additional power cost. As for the D8PSK format, by contrast, the encryption/decryption operation introduces about $1.5\text {dB}$ power penalty at the threshold of $7{\% }$ Hard Decision-Forward Error Correction (HD-FEC), i.e. $BER\approx 3.8\times 10^{-3}$ or about $0.5\text {dB}$ power penalty at the threshold of $20{\% }$ Soft Decision-Forward Error Correction (SD-FEC), i.e. $BER\approx 2\times 10^{-2}$. Considering the guarantee of transmission security, the power penalty can be acceptable as well.

To demonstrate the encryption/decryption effect, we select point A in Fig. 5 just below the HD-FEC threshold when the received optical power is $-11\text {dBm}$ for DQPSK and point B when the received optical power is $-7\text {dB}$ for D8PSK, respectively. Their demodulated constellations after EDFA1 in Fig. 4 to demonstrate the source data, after EDFA3 to demonstrate the encrypted data, and after EDFA4 to demonstrate the decrypted data are all illustrated in Fig. 6. Apparently, the encryption operation scrambles the constellations of the source data and the encryption operation descrambles them, which improve the photonic layer security.

 

Fig. 6. Constellations of source data, encrypted data, and decrypted data.

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Note that the phases of a D$m$PSK are scrambled by the GXOR, some distortions caused by the phase noise of LD1’s linewidth or the Self-Phase Modulation(SPM) of the fiber may affect the encryption/decryption performance. Therefore, we illustrate the BER performance in Fig. 7 and Fig. 8 when the linewidth and fiber length are changed, respectively.

 

Fig. 7. BER performance of the all-optical encryption/decryption part along with the laser linewidth.

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Fig. 8. BER performance of the all-optical encryption/decryption part along with the fiber length.

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The linewidth starts from $100\text {kHz}$ and gradually increases to $30\text {MHz}$ in Fig. 7, we can find that there is little influence on the BER performance of DQPSK while the BER is increased at $10\text {MHz}$ and $30\text {MHz}$ for D8PSK, and the linewidth under $1\text {MHz}$ has almost no impact on the D8PSK BER performance. The reason should be that the discrete constellation points of D$m$PSK provide a certain resistance to the phase noise. The farther distance the constellation points are, the better their resistance could be. As a result, the DQPSK is almost unaffected and the D8PSK can resist the phase noise within the linewidth $1\text {MHz}$. For wider linewidth, the power penalty will be increased to about $2\text {dB}$ at the HD-FEC threshold until $30\text {MHz}$. The linewidth wider than $30\text {MHz}$ may cause the BER being always higher than the HD-FEC threshold, which blocks the transmission. Obviously, the system requires the LDs with linewidth under $30\text {MHz}$ to maintain the effectiveness of the GXOR encryption/decryption.

Similar results will be obtained when the fiber length increases. We consider that the SSMF and DCF in Fig. 4 is only one span of the transmission. Increasing the span should add an EDFA in each span to compensate for the attenuation. Then the BER performance is illustrated in Fig. 8. Due to the increasing SPM effect and accumulated noise of EDFAs, they can also be regarded as phase noise. Therefore, Fig. 8 illustrates a similar phenomenon as Fig. 7. There is little influence on the BER performance of DQPSK while the BER is increased longer than $200\text {km}$ for D8PSK. The power penalty is increased to about $2\text {-}2.5\text {dB}$. For the fiber length shorter than $200\text {km}$, the BER performance is almost constant, which reveals the resistance within $200\text {km}$.

3.2 Performance of the key steganography part

The performance of the key steganography part is then demonstrated by assuming that the BER of data transmission is acceptable, i.e., the received optical power of the data transmission is larger than $-11\text {dBm}$ for DQPSK and $-7\text {dBm}$ for D8PSK according to Fig. 5, respectively. In Fig. 4, after the source key bits are mapped into Return-to-Zero (RZ) symbols with a small enough duty cycle, the mapped symbols are directed fed into an MZM. With the other optical source of LD2 input and the quadrature point configuration of the MZM, the IM modulated source key signal with short pulses during each symbol $K'\left (t\right )$ will be generated. Then $K'\left (t\right )$ is input into the EPS-SSFBG to obtain the reflected DS-OCDMA signal $DSOCDMAK\left (t\right )$. Similar to the all-optical encryption/decryption part, we also add EDFAs (EDFA5 as a booster, and EDFA6 as an in-line amplifier), SSMF, and DCF between the EPS-SSFBG of the transmitter and the flipped EPS-SSFBG of the receiver. Obviously, the transmission of the key steganography can be multiplexed with the data transmission, which is implemented by a multiplexer (MUX) and a demultiplexer (DEMUX). Note that the power of the output signal $K'\left (t\right )$ should be usually small enough, even hidden under the out-of-band noise level of the encrypted data, the center frequency $f_2$ of LD2 should be away from $f_1$ of LD1 to avoid the influence of $D\left (t\right )\overline {K\left (t\right )}$ with high power. In the end, after the reflected output $K''\left (t\right )$ of the flipped EPS-SSFBG of the receiver, $K''\left (t\right )$ is DD demodulated through a single PD without the TIA as the sink key.

3.2.1 Parameters configuration

For the source key with RZ symbols, the duty cycle of $0.1$ is applied. We adopt $f_2=193.4145\text {THz}$($1550\text {nm}$) for the LD2. The linewidth and output power are both the same as the LD1. The difference is that the initial phase has nothing to do with an IM system, therefore, it can be set any value here. For simplicity, $0$ is selected. For the MZM, a child MZM model of the IQMZM in [30] is employed here to support the key baud rate up to $260\text {GBaud}$. Thus, the MZM is push-pull with $40\text {dB}$ extinction ratio, $3\text {dB}$ insertion loss, and $V_{\pi RF}=V_{\pi DC}=1\text {V}$ according to [30]. To simulate the RZ signals as pulses as much as possible, the driver voltage should be large enough, that the limit value $250\text {mV}$ is configured here. For EDFA5, the base configuration is the same as EDFA1-EDFA4, only the center frequency and bandwidth should be modified as $f_2$ and $260\text {GHz}$ to match the baud rate of the source key. For EDFA6, since $K''\left (t\right )$ is obtained after two reflections of EPS-SSFBGs, its power is too small indeed. To ensure the right DD of the following PD, its noise is neglected here. In practice, EDFA6 can be replaced with a Raman amplifier as [33] to achieve this assumption. For the single PD, a PIN-model PD as [27] defines is adopted. The TIA is left out here to avoid introducing additional noise. The bandwidth is $100\text {GHz}$ and the responsivity is $0.6\text {A}/\text {W}$. The detection current will be also influenced by the sum of the dark current of $5\text {nA}$, the thermal noise of $10\text {pA}/\sqrt {\text {Hz}}$, and shot noise.

As for the EPS-SSFBG, in the weak grating limit, the amplitude $\delta _n\left (z\right )$ of the spatial refractive index modulation $\Delta n$ is assigned a constant $10^{-4}$. According to Eq. (12), the phase $\varphi \left (z\right )$ of $\Delta n$ for the EPS-SSFBG is proportional to the impulse response $h_{SSFBG}\left (t\right )$. And $h_{SSFBG}\left (t\right )$ must have a good autocorrelation characteristic. Considering the eavesdropping situation by other receivers, $h_{SSFBG}\left (t\right )$ should also have a good cross-correlation characteristic to improve security. One of the sequences that satisfy the good autocorrelation and cross-correlation characteristics is Hadamard code [34]. Here, we employ the $7$th row of the $128$-order Hadamard matrix as the Hadamard code for $h_{SSFBG}\left (t\right )$. In addition, in order to avoid the broadened pulses overflowing one-symbol time window, the length of an EPS-SSFBG segment [described as an integer multiple $n$ of $\Lambda \left (z\right )$] of $\varphi \left (z\right )$ should satisfy

A summary of the parameters abovementioned is displayed in Table 4.

Table 4. Parameters in steganography part setup

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3.2.2 Results analysis

Based on the parameters configuration abovementioned, let us start with $K'\left (t\right )$ and its broadened signal $DSOCDMAK\left (t\right )$ illustrated in Fig. 9. DQPSK format is taken as the example in Fig. 9. We only list the $55$th-$59$th symbol among the total $2048\times 2=4096$ symbols. Compared to the only short pulse of $K'\left (t\right )$ (the dash-dotted line) in each symbol, the output $DSOCDMAK\left (t\right )$ of the EPS-SSFBG is definitely broadened to some short pulses and greatly reduced the power amplitude (from about $40\text {mW}$ to about $16\text {nW}$), which proves the DS-OCDMA of the EPS-SSFBG. The power reduction extent of the broadened signal $DSOCDMAK\left (t\right )$ can be demonstrated by its spectrum illustrated in Fig. 10. The solid line of the broadened key’s spectrum is almost under the out-of-band data noise level. Fig. 10 reveals that the DS-OCDMA of the EPS-SSFBG can even hide the source key under the system noise level, which brings great improvement to the photonic layer security.

Then, we still demonstrate the BER performance of the key steganography part and its influence on the all-optical encryption/decryption part for both D$m$PSK formats, respectively. For the DQPSK format, the BER performance of the sink key demodulation is illustrated in Fig. 11. Except for the legally flipped EPS-SSFBG with the same Hadamard code as the transmitter, we added two additional situations in the receiver to compare. One is directly demodulating $DSOCDMAK\left (t\right )$ without any EPS-SSFBGs, which can simulate any eavesdroppers who do not know the existence of key steganography. The other one is employing an illegally flipped EPS-SSFBG with a different Hadamard code from the transmitter to demodulate $DSOCDMAK\left (t\right )$, which can simulate the eavesdroppers who try to recover $DSOCDMAK\left (t\right )$. The different Hadamard code is selected to be the $8$th row of the $128$-order Hadamard matrix. In Fig. 11, the marked hexagram BER performance demonstrates the correctness of the key steganography. Only the legally flipped EPS-SSFBG can correctly demodulate the sink key.

 

Fig. 9. Steganography $K'\left (t\right )$ and $DSOCDMAK\left (t\right )$.

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Fig. 10. Spectrum of encrypted data and broadened key.

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Fig. 11. DQPSK BER performance of the key steganography part.

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To demonstrate the key recovery effect, point C in Fig. 11 when the received optical power is $-10\text {dBm}$ is selected. Three eye diagrams of the three situations are all illustrated in Fig. 12. We can find that the eyes of another two eavesdropping situations are still closed even if their time clock is aligned with the source key at the optimal judgment moment. The eyes are only open when employing the legally flipped EPS-SSFBG to demodulate the sink key, which can prove the key security enhancement of the steganography part.

 

Fig. 12. DQPSK eye diagram of legal, no, and illegal EPS-SSFBG.

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Finally, let us analyze the influence on the data decryption when the key steganography has some bit errors. The BER performance of the decrypted data under the three situations is still illustrated in Fig. 11. We can see that they demonstrate almost the same performance as the key steganography. It is easy to understand this phenomenon because the all-optical GXOR is executed parallelly for each symbol without any relationship with the adjacent symbols. When the key of a certain symbol is wrong, it will only affect the corresponding data symbol. Therefore, the BER performance of the decrypted data is similar to the key steganography.

As for the D8PSK format, we illustrate similar figures in Figs. 13–14. Obviously, we can find the same results as the DQPSK format, which will not repeat here.

 

Fig. 13. D8PSK BER performance of the key steganography part.

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Fig. 14. D8PSK eye diagram of legal, no, and illegal EPS-SSFBG.

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In addition, except for the illegally flipped EPS-SSFBG, parameter mismatch caused by the fabrication error may affect the key steganography BER performance. According to Eq. (10), simple delay of $h_{SSFBG}\left (t\right )$ has no impact on the condition of Eq. (10). As a consequence, changing the initial phase of the spatial refractive index in Fig. 3 should also make no difference. Only the Errors in the sudden phase shift period(such as the 5th, 10th, and 15th period in Fig. 3) may cause the mismatch. Suppose the error is $\theta \Delta z$, which is equivalent to $\theta \Delta z/4\Delta z\times 2\pi =\theta \pi /2$ phase error of the $\pi /2$ phase shift. When the mismatch $\theta \pi /2$ changes from $-0.5^\circ$ to $+0.6^\circ$ ($\theta$ changes from $-1/180$ to $1/150$), the key steganography BER performance is illustrated in Fig. 15. It reveals that the mismatch smaller than $-0.2^\circ$ or larger than $+0.6^\circ$ may cause high BER (over the threshold of HD-FEC) of the key steganography and then cause high data BER according to Fig. 11 and Fig. 13. The strict tolerance when the key steganography BER is small enough is between $-0.1^\circ$ and $+0.2^\circ$.

 

Fig. 15. BER of the parameter mismatch between the EPS-SSFBG and its flipped EPS-SSFBG.

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4. Conclusion

To summarize, our proposed system employing the all-optical GXOR encryption/decryption part implemented by two cascaded IQMZMs and key steganography part implemented by a legal pair of EPS-SSFBGs can reconfigurable handle both D$m$PSK such as DQPSK and D8PSK modulation formats with acceptable power penalty compared to usual optical fiber transmission. Only the legal pair of EPS-SSFBGs can demodulate the sink key and further decrypt the encrypted data. The attainable bit rate of 260Gbps shows the potentiality of our proposed system to improve the photonic layer security in future F5G and beyond. The performance of the proposed all-optical encryption/decryption depends on a high extinction ratio of the IQMZMs. Further improving the data bandwidth may need a high extinction ratio over $40\text {dB}$ in the future. Additionally, the data and key signals should be aligned at the beginning of the signals, therefore, a precise all-optical synchronization technology may be required for real application scenarios in the future.