1. Introduction

Eavesdropping is a potential security risk in the current fiber-optic transmission system. A typical attack comprises two steps: 1) fiber tapping and demodulating optical signals into digital data, and 2) cryptanalyzing the data with computational resources. The digital-layer cipher implemented in layer two or higher, such as the advanced encryption standard, prevents step 2) because of the high computational complexity involved. To achieve higher security, step 1) should be prevented as well. Such techniques are known as physical layer encryption (PLE). In PLE, a short seed key is used and data are directly hidden using unique optical encoding or scrambling techniques. Before PLE, the short seed key must be shared securely, e.g., through quantum key distribution [1] and post quantum cryptography [2]; however, it is noteworthy that such key exchange methods are beyond the scope of this study. PLE has been extensively studied as an application of chaotic lasers [3], where chaotic synchronization is utilized to achieve secrecy. Secure fiber transmissions at gigabit/second data rates were experimentally demonstrated [4–8]. Furthermore, physical layer security enhancement by exploiting optical code-division multiplexing access (CDMA) has been investigated [9,10]. Fiber transmission experiments with enhanced security have been reported [11–13].

In this study, we focused on PLE based on signal masking by quantum (shot) noise [14], originally known as AlphaEta [15] or Y-00 quantum stream cipher [16]. Low-order data signals are converted into extremely high-order intensity modulation/phase-shift-keying (PSK)/ quadrature amplitude modulation signals, e.g., 2¹⁷ PSK [17], utilizing a prescribed conversion protocol with a seed key. In such cases, the correct detection of extremely high-order signals without the key is disrupted by shot noise. Signal masking by shot noise provides irreducible security because shot noise is inherently inevitable and random. The true randomness of shot noise, which is the consequence of Born’s rule, contributes to irreducibility in the strict sense of cryptology. In the Y-00 cipher system, a legitimate receiver converts extremely high-order signals back into low-order data signals using the key. Ideally, the encryption and decryption processes should not negatively affect the signal quality. This feature indicates that the system can achieve highly secure fiber transmission without sacrificing the data rate and reach.

 Figure 1 shows the transmission distance and single-channel line rate of secure fiber transmission experiments with PLE based on signal masking by shot noise (AlphaEta and Y-00 cipher) [18–26], chaotic synchronization [4–8], and optical CDMA [11–13]. The maximum reach reported was 1,000 km in 1.5 and 2.5 Gbit/s cipher systems based on signal masking by shot noise [19,21]. Recently, digital coherent technologies have been introduced to the approach based on the signal masking, and a few hundred kilometer fiber transmissions at a line rate exceeding 10 Gbit/s have been demonstrated [23–25,27]. Our recent study showed that the optical signal-to-noise ratio (OSNR) penalty of the digital-coherent PSK Y-00 cipher system was less than 0.5 dB when compared with that of a noncipher conventional system [24]. This result suggests that transmission over a much longer fiber is possible. Meanwhile, the reach and line rates of cipher systems based on chaotic synchronization and optical CDMA are limited to 150 km and 32 Gbit/s, respectively. In both approaches, precise optical chromatic dispersion compensation is required for fiber transmission, which limits the reach and line rate in modern fiber-optic transmission systems without optical dispersion management. Hence, the Y-00 cipher can provide enhanced security at the physical layer in high-capacity and long-reach fiber-optic transmission systems. Moreover, the cipher occupies a bandwidth comparable with noncipher signals and is applicable to wavelength-division multiplexing systems [15,18,25,28,29].

 

Fig. 1. Transmission distances and single-channel line rates in previous experimental demonstrations of secure fiber-optic transmission with PLE.

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This paper reports a digital coherent PSK Y-00 cipher system for ultra-long-haul fiber transmission exceeding 10,000 km. Comprehensive study of system design and details of our experimental demonstration of 10,118-km cipher transmission [30] are presented. In the PSK Y-00 cipher system, tradeoffs exist between the transmission reach and security. This may hinder the ultra-long-haul transmission of the cipher. We studied the tradeoffs theoretically and derived an equation that describes the relationship among the reach, number of phase levels after encryption, and quantum-noise masking number. The quantum-noise masking number, which indicates the number of phase levels covered by the shot noise after encryption, is a primary measure of security. Numerical analysis using the equation shows that the tradeoff can be mitigated by increasing the number of phase levels or the PSK order after the encryption. A transmission reach exceeding 10,000 km while maintaining sufficient signal masking by shot noise is achievable, provided that the number of phase levels is 2¹⁸. We experimentally demonstrated the fiber transmission of a single-channel 48-Gbit/s line-rate digital coherent PSK Y-00 cipher with 2¹⁸ levels. A record-long transmission reach of 10,118 km, which is a 10-fold increase as shown in Fig. 1, was demonstrated at a single channel net rate of 40 Gbit/s. The quantum-noise masking number reached 231, and a high symbol error ratio (SER) of 0.9965 for an eavesdropper without the key information was achieved by irreducible signal masking by shot noise. Thus the first experimental demonstration of ultra-long-haul, transoceanic-distance, physical-layer secure fiber transmission was demonstrated.

2. Operating principles

2.1 Signal masking by quantum (shot) noise

Encryption in the PSK Y-00 cipher was achieved by randomizing the phase of M-ary PSK data modulation. Figure 2 shows the operating principle when the data modulation was quadrature PSK (QPSK) with M = 4. As shown in Fig. 2(a), the basis phase of the QPSK data modulation, which is indicated by the black arrow on the I-axis, was rotated by θ_basis(i) for the encryption of one symbol with identification i. The angle was between −π/4 and π/4 and was determined randomly using a seed key and pseudorandom number generators (PRNGs). The seed key must be shared securely between legitimate users before starting cipher transmission. Details of the procedure to determine the angle for each symbol θ_basis(i) is shown in Section 2.3. The basis phase was rotated in a symbol-by-symbol manner, and the QPSK data modulation was converted to a high-order PSK signal. When 2^m phase levels (m-bit resolution) were prepared for the phase randomization, the PSK Y-00 cipher based on the QPSK data modulation (M = 4) corresponded to a 2^(m+2) PSK signal. As shown in Fig. 1(b), m was set to a large number, e.g., >12; as such, adjacent signal phase levels could not be discriminated easily because of noise. Provided that m is particularly large, the shot noise will mask adjacent phase levels, as shown in the magnified image. The masking effect by shot noise is irreducible and unchanged because the shot noise is truly random and inherently inevitable in optical detection. Masking by shot noise for secrecy is only effective for an eavesdropper who must measure the high-order PSK signals without the seed key. A legitimate receiver can subtract the symbol-by-symbol phase rotation using the seed key and detect the cipher as a QPSK signal.

 

Fig. 2. Operating principle of PSK Y-00 cipher based on QPSK data modulation: (a) phase rotation of symbol for encryption and (b) constellation diagram after encryption.

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A quantum-noise masking number Γ_Q is introduced to quantitatively discuss the masking effect for secrecy. The masking number is defined as the number of signal phase levels covered by the shot noise and is calculated as the ratio of Δϕ_shot and Δθ_basis which are shown in the magnified image of Fig. 2(b). A higher masking number is better for secrecy because a larger uncertainty is imposed during the signal detection of an eavesdropper. In our previous studies [17,24], the masking number of the PSK Y-00 cipher was defined assuming an ideal simultaneous phase and amplitude detection, which were considered impossible in practice. In this study, the masking number was defined assuming ideal heterodyne detection. This definition is more practical as the ideal heterodyne detection, which provides the standard quantum limit, is considered to be the best implementable strategy for signal detection. The quantum-noise masking number is expressed as

2.2 Security realized by quantum-noise masking

Signal masking by shot noise disrupts the eavesdropper’s measurement of the cipher or high-order signals, which have M·2^m phase levels. The quantum-noise masking number Γ_Q is related to the uncertainty of the measurement. One can estimate the SER when an eavesdropper performs an ideal heterodyne measurement of the cipher. As the purpose of this cipher system is to prevent signal interception, the SER is a security measure which indicates the difficulty of the successful interception. The SER is obtained from the masking number Γ_Q as follows (see Supplement 1, Section 2 for details):

Using Eqs. (1) and (2), we calculated the SERs for various values of the optical power of the cipher per polarization P_S. The order of data modulation M, signal bandwidth B, signal frequency ν₀, and quantum efficiency η_q were 4 (QPSK), 12 GHz (12 Gbaud), 193.55 THz (1550 nm), and 1, respectively. Figure 3 shows the results. The right vertical axis denotes the quantum-noise masking numbers corresponding to the SERs. As P_S is an optical power at the input of the fiber link, a typical power range to maintain the best transmission performance in a long-haul fiber link is approximately −10 to −3 dBm. The bit resolution of phase randomization m should be 16 or more for SER > 0.99 in the power range. In eavesdropping attacks, if long consecutive symbols should be discriminated without errors, the risk of correctly deducing the seed key by subsequent cryptanalysis would increase. The success probability of correctly discriminating l consecutive symbols is (1 − P_{SER_eve})^l, depending not only on the masking effect, but also on the consecutive symbol length l. The symbol length required to deduce a seed key or to decipher meaningful messages is related to the mathematical encryption part, in which the symbol-by-symbol phase rotation angles are determined using the seed key. The length is typically long, and the success probability is small enough to be ignored. In the following pages, the SER an eavesdropper can reach with ideal heterodyne detection P_{SER_eve} and the quantum-noise masking number Γ_Q are mainly used for simplified assessment of security. However, as shown partly in this paragraph, the overall security of a Y-00 cipher system is also related to other factors, such as the length of a seed key and configuration of the mathematical encryption part, and is more complicated.

 

Fig. 3. SER of detection of PSK Y-00 cipher at line rate per polarization of 24 Gbit/s (M = 4 and B = 12 GHz) without seed key for various optical powers.

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An important feature of the Y-00 cipher is that P_{SER_eve} cannot be reduced because the quantum-noise masking number Γ_Q is defined for an ideal heterodyne detection only in the presence of inevitable shot noise. It is assumed that an eavesdropper can tap all powers of the cipher at the input of the fiber link; any restriction will not be imposed to the interception. In the strict sense of cryptology, it is also important that shot noise is proven to be truly random, because there is no statistical weakness in the signal masking. In other words, P_{SER_eve} defined under such conditions is a lower bound, and the security of the cipher system cannot be broken down unless the standard quantum limit of signal detection or the shot-noise limit is surpassed. Detailed discussions regarding the practical overall security are provided elsewhere [31].

2.3 Encryption and decryption

 Figure 4 shows the flow of encryption process in a PSK Y-00 cipher system based on QPSK data modulation (M = 4). The inputs are binary data of plain text and seed key. The key length |K| is typically 256 bits. The seed key is extended to the key stream, which is a practically nonrepeated pseudorandom binary sequence (PRBS), using a PRNG. Subsequently, m bits are extracted to determine the phase rotation angle of a symbol. Here, i denotes the identification number of a symbol. An irregular mapper is used to convert the m-bit sequence into a rotation angle θ_basis(i). The mapping is designed such that the effect of shot noise on the key stream is random [32], with which the cipher becomes robust against attacks on the seed key. In addition, bitwise exclusive OR (XOR) operation on the data bits and key stream, which is known as overlap selection keying [33], is performed. Subsequently, the data bits are mapped to the QPSK signals, where encoding for each time slot is changed based on the last two bits of the m-bit sequence. The relationship between the data bits and the phase angle of QPSK modulation, [XX] = [θ_data(i)], is as follows: [11, 01, 00, 10] = [π/4, 3π/4, 5π/4, 7π/4] for the last two bits of 00; [10, 11, 01, 00] = [π/4, 3π/4, 5π/4, 7π/4] for the last two bits of 01; [00, 10, 11, 01] = [π/4, 3π/4, 5π/4, 7π/4] for the last two bits of 10; [01, 00, 10, 11] = [π/4, 3π/4, 5π/4, 7π/4] for the last two bits of 11. This cyclic shift of gray coding is necessary to hide the data bits by shot noise. Hence, a pair comprising θ_basis(i) and θ_data(i) is obtained for each time slot. Finally, coherent light is modulated such that the phase angle becomes θ_basis(i) + θ_data(i). The process described herein is the basic process. Additional randomization techniques to further enhance security, such as deliberate signal randomization and deliberate error randomization, are discussed elsewhere [34].

 

Fig. 4. Signal processing for the encryption in a PSK Y-00 cipher system based on QPSK data modulation.

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The summation of θ_basis(i) and θ_data(i) is achieved in the electrical or optical domain. The simplest approach is to combine the angles in the electrical domain. Subsequently, the phase of the light is modulated using an IQ modulator and a digital-to-analog converter (DAC) with a bit resolution of m + 2 (M = 4) or higher. The bit resolution for the phase randomization m, which is related to the security of the cipher system, is limited by the resolution of the DAC, although the setup is relatively simple. The limitation is strict at high baud rates conventionally used in modern optical transmission systems. For instance, m + 2 must be 12 or less at a baud rate of 10 Gbaud or more, whereas m = 16 is required to achieve sufficient masking by shot noise. Another approach is summation in the optical domain. The QPSK modulation and phase rotation of θ_basis(i) are achieved using an IQ modulator and a phase modulator (PM), respectively. This setup will relax the requirement for the bit resolution of the DAC by 2 bits. However, we still need to achieve m = 16. Therefore, a coarse-to-fine phase randomization technique was proposed and demonstrated [17]. The phase rotation angle θ_basis(i) was segmented into coarse and fine angles, θ_{basis_C}(i) and θ_{basis_F}(i), and two cascaded PMs were synchronously driven by two DACs. The nominal resolution became twice the bit resolution of a single DAC. We previously demonstrated a 12-Gbaud PSK Y-00 cipher with m = 16 using this technique [24].

A legitimate receiver comprises a seed key, PRNG, and mapper; hence, the θ_basis(i) for each time slot is shared. At the receiver side, the phase of the light is inversely rotated by θ_basis(i) in a symbol-by-symbol manner for decryption. This process is achieved in the optical or electrical domains. An optical phase modulator is used to perform inverse-phase rotation in the optical domain [15,18]. Meanwhile, an electrical decryption is achieved by multiplying exp(-jθ_basis(i)) by the received phase in the digital domain after coherent detection. A self-coherent technique with a one-bit delay interferometer was first employed for decryption [35]. Recently, digital coherent detection with a free-running local oscillator (LO) was employed, where multiplying the inverse phase was incorporated straightforwardly into a standard digital signal processing (DSP) for intradyne coherent detection [24]. In both the optical and electrical approaches, timing synchronization between the received cipher and key stream is necessary. A synchronization protocol can be implemented prior to the start of communication.

3. Systematic design

3.1 Tradeoffs between masking number and transmission reach

Assuming a simple long-haul fiber link in which each constant span loss is fully compensated by an Er-doped fiber amplifier (EDFA), we theoretically investigated the quantum-noise masking number Γ_Q and transmission reach in the cipher system. Figure 5 shows the model of the fiber link and power diagram. The link comprises L-km fiber spans and EDFAs, and the loss and gain are repeated regularly. The number of spans is N, and the span loss is equivalent to the amplifier gain G. When the signal power launched into each fiber span is P_in, the OSNR of the output signal OSNR_out is calculated as

 

Fig. 5. Simple model of optical fiber link.

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As the number of spans is an integer, the floor function is used. The maximum reach is obtained by multiplying N_max by L. In the PSK Y-00 cipher system, the signal power and quantum-noise masking number are correlated as shown in Eq. (1). Hence, tradeoffs between the masking number and the maximum number of spans are obtained using Eqs. (1) and (4).

Next, we discuss the theoretical limit of the tradeoff. OSNR_req and E_b/N₀, which is a bit energy to the noise power density ratio or SNR per bit, are related as follows [37]:

3.2 Numerical analysis of long-haul cipher transmission systems

 

Fig. 6. Theoretical tradeoff between quantum-noise masking number and transmission reach in the transmission system of PSK Y-00 cipher based on QPSK data modulation (M = 4).

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Using Eq. (7), we numerically investigated the ultra-long haul transmission of the PSK Y-00 cipher. The target reach was set to 10,000 km for a transoceanic submarine cable system. The practical choices of data modulation for such a long reach were BPSK (M = 2) or QPSK (M = 4). We here chose QPSK data modulation because Eq. (7) indicated that the tradeoff was effectively mitigated for the QPSK provided that a bit resolution for the phase randomization m was fixed. Table 1 summarizes the specifications of the cipher and fiber link. Soft decision forward error correction (SD-FEC) with an overhead of 20% (r = 5/6) was employed, and a typical BER threshold of 1.8 × 10⁻² was assumed [38]. The fiber link comprised a low-loss pure-silica-core fiber with a loss of 0.154 dB/km [39]. When M = 4, a SNR per bit required to achieve the BER threshold, (E_b/N₀)_req, is 3.42 dB (see Supplement 1, Section 3 for details). The relation between the quantum-noise masking number Γ_Q and transmission reach N_{Y-00_limit} × L is calculated by substituting (E_b/N₀)_req and other parameters shown in Table 1 into Eq. (7). Figure 6 shows the results for various bit resolutions of phase randomization m. The right vertical axis denotes the SER of an eavesdropper P_{SER_eve}, which is calculated using Eq. (2). The masking number on the left axis corresponds to the SER on the right one. Note that the scale of the right axis is irregular to maintain the consistency. When m = 16, a masking number exceeding 650, corresponding to P_{SER_eve} > 0.9987, is achieved in the transmission over 10,000-km fiber. As this tradeoff is independent of the baud rate of the cipher, such secure long-reach transmission is achievable at a high baud of a few tens of gigabaud. Although linear transmission is assumed in this calculation, this theoretical investigation indicates that the tradeoff can be mitigated using phase randomization with a bit resolution m of 16 or higher. Hence, the PSK Y-00 cipher can achieve high-speed ultra-long-haul transmissions with security realized by quantum-noise masking.

Table 1. Parameters of Numerical Analysis of Ultra-long-haul Cipher Transmission

View Table

4. Experiments

4.1 Back-to-back condition

First, experimental demonstrations of the encryption and decryption of the dual-polarization (DP) PSK Y-00 cipher with 2¹⁸ phase levels (M = 4 and m = 16) are reported. Figure 7 shows the experimental setup. A data stream comprising a PRBS with a length of 2²³-1 and a pre-shared seed key were placed into a Y-00 mathematical encryption box. The prescribed process detailed in Section 2.3 was performed, and θ_data(i) and θ_basis(i), which correspond to 2-bit data with randomization and 16 bits for phase randomization, respectively, were obtained for each symbol. They were combined in the optical domain. First, coherent light at 1550.12 nm was modulated with an IQ modulator at 12 Gbaud by the 2-bit data corresponding to θ_data(i). Subsequently, two cascaded PMs were synchronously driven for the phase rotation of θ_basis(i). The nominal bit resolution of the phase randomization was 16 bits, and a PSK Y-00 cipher with nominal 2¹⁸ phase levels was generated. Next, polarization-division multiplexing was emulated using a coupler and a polarization beam combiner, and a DP-PSK Y-00 cipher at a line rate of 48 Gbit/s was generated.

 

Fig. 7. Experimental setup of 48-Gbit/s (line rate) DP PSK Y-00 cipher transmission.

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In a back-to-back condition, which is shown as (i) in Fig. 7, a variable optical attenuator (VOA) and an EDFA were used to adjust the OSNR at the receiver. Subsequently, the Y-00 cipher was received using a conventional intradyne coherent detection setup. A free-running LO, a polarization-diversity 90° optical hybrid circuit, and balance photodetectors were used. Digitization was achieved using a real-time oscilloscope with a bandwidth of 13 GHz. Finally, offline DSP for polarization demultiplexing, decryption, and carrier phase recovery was performed. The decryption, which is a symbol-by-symbol inverse phase rotation, is a unique process for the cipher. The phase rotation angle θ_basis(i) for each symbol was obtained by placing the same seed key into the same encryption box, and exp(−jθ_basis(i)) was multiplied by the detected complex amplitude of each symbol of the cipher. Timing synchronization between the transmitter and receiver for decryption was achieved by adding preamble bits in the offline processing.

 Figure 8 shows the constellation diagrams and Q factors in the back-to-back condition. As shown in Fig. 8(a), the phase of the cipher was randomized, and the constellation was donut-shaped. After decryption, QPSK data modulations were recovered for both polarizations, as shown in Fig. 8(b). Figure 8(c) shows the Q factors for various OSNRs at the receiver. A measured reference curve of the noncipher DP QPSK was co-plotted. More than 1.1 million (>2²⁰) symbols were processed to measure the BER, and the Q factor was calculated from the BER using the relation Q [dB] = 20 × log₁₀[√2erfc^-1(2 × BER)]. An SD-FEC Q-threshold of 6.4 dB was achieved at an OSNR of 7.4 dB for the cipher. The Q-penalty caused by the encryption and decryption, which is the difference between the curves of the cipher and reference at the same OSNR, was approximately 0.3 dB. Although this penalty was sufficiently small, it can be ideally zero in this cipher system.

 

Fig. 8. Experimental results of encryption and decryption of 48-Gbit/s DP PSK Y-00 cipher: (a) constellation diagram of the cipher, (b) constellation diagram of decrypted QPSK, (c) Q-value characteristics.

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4.2 Ultra-long-haul transmission

Ultra-long-haul transmissions of the DP-PSK Y-00 cipher were demonstrated using a recirculating loop system shown as (ii) in Fig. 7. The recirculating loop system comprised two acousto–optic modulators and a 50.59 km × 5 standard SMF link with EDFAs. A mode field diameter of SMF was 9.2 μm. The average span loss was 9.6 dB. The signal power launched into each span P_in was adjusted to be consistent with the EDFA and VOA. Chromatic dispersion compensation was additionally implemented in the DSP for a long fiber transmission. Figure 9 shows the Q-factors of the decrypted QPSK signal when the transmission distance was 10,118 km (after 40 loops). The Q-factors were calculated from the measured BER. The span-launch power P_in was changed from −10 to −4 dBm. The maximum Q-factor, which is higher than the Q-threshold of the SD-FEC, was achieved at an input power P_in of −7 dBm. The effect of self-phase modulation limited the maximum input power. The inset constellation diagrams show that the DP QPSK data signals had recovered successfully after the decryption. The black solid curve in Fig. 9 shows the SER of the ideal heterodyne detection of the cipher (2¹⁸ PSK) by an eavesdropper, P_{SER_eve}. When P_in = −7 dBm, P_{SER_eve} was 0.9965 (Γ_Q = 231). This high SER at the highest optical power in the link means that detection without a seed key results in inevitable many errors even if all powers of the cipher are tapped at the input of the fiber link and are detected by an ideal heterodyne receiver without any additive noise.

 

Fig. 9. Q-factors and SER of ideal heterodyne detection of cipher P_{SER_eve} for various input powers P_in and transmission distance of 10,118 km.

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For intuitive understanding of high security, we estimate the probability that an eavesdropper correctly detects symbols containing the full information of a seed key. Here we assume that an eavesdropper uses an ideal heterodyne receiver and discriminates symbols straightforwardly. As discussed in Section 2.2, the probability of discriminating l consecutive symbols without errors is (1 − P_{SER_eve})^l. The symbol length in which the full information of a seed key is contained is the length of the seed key divided by the bit resolution of phase randomization, |K|/m. Since m is the denominator, to reduce the success probability by simply increasing m becomes less effective at some point. The value of m = 16 in this experiment is a good point of compromise. By substituting |K|/m = 16 for |K| = 256 bits into l, the probability is estimated to be 3.87 × 10⁻⁴⁰, which is small. It is noteworthy that this probability is the higher bound guaranteed from masking by shot noise. If the cipher is tapped at the fiber link after amplification, accumulated amplified spontaneous emission noise from EDFAs will function effectively for signal masking. If only a part of the optical power is tapped, then the masking number increases. These practical factors will significantly reduce the probability in real situations, and high practical security with irreducible security bounds based on shot noise will be achieved.

 Figure 10 shows the Q-factors of the cipher and reference DP QPSK as the transmission distance varied from 3,035 to 10,118 km. The signal input power P_in was set to −10 and −7 dBm. The maximum reach defined by the typical Q-threshold of the SD-FEC (6.4 dB) was 8,094 and 10,118 km for P_in of −10 and −7 dBm, respectively. When P_in was −10 dBm, the SER of the ideal heterodyne detection without a seed key P_{SER_eve} was 0.9975, whereas the reach decreased by approximately 20%. The difference in the Q-factors between the cipher and reference was 0.4 dB on average. The Q-penalty of 0.3 dB caused by encryption and decryption, as discussed in the previous subsection, was dominant. The cipher had a large Q margin when the transmission distance was shorter. This indicates that a higher masking number or a higher P_{SER_eve} is achievable for a shorter transmission distance by appropriately reducing the input power P_in of the cipher. The penalty for the secure transmission is small; hence, ultra-long haul transmissions (e.g., transoceanic distance transmission) with enhanced security at the physical layer can be achieved without significantly sacrificing the signal quality in the coherent PSK Y-00 cipher system.

 

Fig. 10. Q-factors of cipher and DP-QPSK reference signal for various transmission distances.

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5. Summary

The system design and experimental demonstrations of a digital coherent PSK Y-00 quantum stream cipher for security-enhanced ultra-long-haul fiber transmission were reported. A theoretical study showed that the tradeoff between transmission performance and security based on signal masking by shot noise was mitigated by increasing the number of phase levels after encryption. It was numerically demonstrated that fiber transmission exceeding 10,000 km with sufficient signal masking for secrecy was achievable provided that the PSK Y-00 cipher based on QPSK data modulation had 2¹⁸ phase levels. A single-channel 48-Gbit/s DP PSK Y-00 cipher transmission over a 10,118-km standard SMF was experimentally demonstrated. A Q-factor exceeding the threshold of the SD-FEC was achieved at a span-launch optical power of −7 dBm, resulting in a single-channel net data rate of 40 Gbit/s. The PSK Y-00 cipher had 2¹⁸ phase levels, and the quantum-noise masking number was 231 at the optical power. This number corresponded to an extremely high SER of 0.9965 when an eavesdropper detected all the powers of the cipher at the input of the fiber link using an ideal heterodyne receiver. Hence, transmission performance sufficient for transoceanic-distance fiber transmission and security enhancement at the physical layer were simultaneously achieved in the PSK Y-00 cipher system.