## Abstract

A record-large product of data rate and transmission distance in quantum-noise-assisted cipher systems for physical layer security of fiber-optic transmission was demonstrated. The cipher system is based on symmetric-key direct-data encryption utilizing signal masking by quantum (shot) noise. The encryption is achieved by 2^{16}-level phase randomization of quadrature phase-shift keying data signal, resulting in 48-Gbit/s dual polarization Y-00 cipher with 2^{18} phase levels. Successful transmission of the Y-00 cipher over 400- and 800-km standard single-mode fibers was achieved without significant negative impact on transmission quality. The product of the data rate and distance was 40 Gbit/s (net rate) × 800 km = 32,000 Gbit/s·km. The system achieves masking of 217 phase levels by shot noise, which promises irreducible and unchanged security based on the quantum nature of coherent light.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Fiber tapping is a potential security risk in the physical layer of optical transmission systems. Even though conventional ciphers based on computational complexity are implemented in the higher layers, such vulnerability should be reduced for absolute security of the transmission systems. Encryption techniques for the physical layer security are categorized into key-distribution systems as represented by quantum key distribution [1] and direct-data encryption systems. The direct data encryption systems are achievable based on the unique physical nature of light. A promising approach applicable to the current high-data-rate systems is symmetric-key direct-data encryption utilizing signal masking by quantum (shot) noise [2]. This cipher system was originally demonstrated as AlphaEta [3] or Y-00 quantum stream cipher [4]. To encrypt data (plain text), first, mathematical encryption with a preshared seed key is employed, where the binary plain text is combined with pseudorandom bits. Then, high-order optical phase and/or amplitude modulation is performed using the combined bits. The modulation order or the number of signal levels is set at an extremely large value such that uncertainty caused by shot noise is larger than the signal distance of the high-order modulation. Then, correct measurement of the high-order signal by an eavesdropper without the key is disrupted by the inevitable effect of shot noise, while a legitimate receiver can detect the cipher as lower-order data modulation after decryption using the key. This secrecy effect is called quantum-noise masking. The cipher system utilizing the effect promises irreducible and unchanged security, because the shot noise is truly random and is inherently inevitable. Moreover, the system is practical because the cipher can be used in the current dense wavelength division multiplexing (WDM) systems with optical amplification [5].

Here, a phase-shift keying (PSK)-based cipher in which *M*-ary PSK data modulation is encrypted only by phase randomization is focused on in particular. In the early research, AlphaEta systems based on binary PSK (BPSK) data modulation were demonstrated at 622 Mbit/s and 2.66 Gbit/s [6,7]. Recently, we have proposed coarse-to-fine phase randomization that realizes quantum-noise masking at a high bit rate and have demonstrated a 10-Gbit/s digital coherent PSK Y-00 cipher based on BPSK data modulation [8]. Then, to increase the bit rate, a polarization-division multiplexing technique was introduced, and a 20-Gbit/s dual-polarization (DP) Y-00 cipher was demonstrated [9]. Another prospective approach for a higher bit rate per channel is to increase the order of data modulation. This approach has been demonstrated for quadrature amplitude modulation (QAM)-based cipher systems where both the amplitude and phase of QAM data modulation are randomized. The highest line rate of 70 Gbit/s was demonstrated employing 128-QAM data modulation [10].

Here, a DP PSK Y-00 cipher based on quadrature PSK (QPSK) data modulation is reported. The baud rate of the cipher is 12 Gbaud, and polarization multiplexing is emulated. Hence, the line rate is 48 Gbit/s. The coarse-to-fine phase randomization is employed for the encryption, and a Y-00 cipher with 2^{18} (=262,144) phase levels is achieved. Transmission of the Y-00 cipher over 400- and 800-km standard single-mode fiber (SSMF) is demonstrated. Experimental results show that the cipher transmission was achieved with a small optical signal-to-noise ratio (OSNR) penalty. The number of phase levels masked by shot noise was 338 and 217 for the transmission distances of 400 and 800 km, respectively, at a net rate of 40 Gbit/s, when soft-decision forward error correction (SD-FEC) with an overhead of 20% was employed. An important measure of single-channel transmission systems is the product of bit rate and distance. This demonstration achieved a record-large product of 32,000 Gbit/s·km in the cipher transmission system, which is approximately 1.7 times larger than the record in previous research [11] (line rate of 40 Gbit/s and distance of 480 km). Although this demonstration was single-channel transmission, Y-00 cipher is straightforwardly scalable to multiterabits-per-second WDM systems.

## 2. Operating principles

#### 2.1 PSK Y-00 cipher based on QPSK data modulation

Encryption in PSK Y-00 cipher is achieved by randomizing the phase of *M*-ary PSK data modulation. The operation when the data modulation is QPSK (*M* = 4) is shown in Fig. 1. As shown in Fig. 1(a), a basis phase of the QPSK data modulation, which is indicated by the black allowed line on the *I*-axis, is rotated by *θ*_{basis} for the encryption of one symbol. The angle is between −π/4 and π/4 and is determined randomly using a seed key and pseudorandom number generators (PRNGs) for extending the key. The seed key must be shared securely between legitimate users before starting the cipher transmission. The key length is short, e.g., 256 bits. The basis phase is rotated in a symbol-by-symbol manner, and the QPSK data modulation is converted to a high-order PSK signal. When 2* ^{m}* phase levels (

*m*-bit resolution) between −π/4 and π/4 are prepared for the phase randomization, PSK Y-00 cipher based on QPSK data modulation (

*M*= 4) becomes 2

^{(m+2)}PSK signal. As shown in Fig. 1(b),

*m*is set to be a large number, e.g., >10, such that adjacent signal phase levels are difficult to discriminate because of noises. Provided that

*m*is particularly large, shot noise masks adjacent phase levels (see the magnified image). The masking effect by shot noise is irreducible and unchanged, because the shot noise is truly random and is inherently inevitable at optical detection. The masking by shot noise for secrecy is only effective for an eavesdropper who has to measure the high-order PSK signals without the seed key. A legitimate receiver can subtract the symbol-by-symbol phase rotation by using the key and detects the cipher as a QPSK signal.

#### 2.2 Signal masking by quantum noise

A quantum-noise masking number Γ is introduced to discuss quantitatively the masking effect for secrecy. The masking number for PSK Y-00 cipher has been defined when the data modulation is binary PSK (*M* = 2) [8]. Here, the definition is modified for *M*-ary PSK data modulation. The masking number is defined as the number of signal phase levels covered by shot noise. A higher masking number is better for secrecy. As shown in the magnified image of Fig. 1(b), the spread of shot noise is approximated by twice the standard deviation of shot noise 2*σ*_{shot} supposing that shot noise has a Gaussian distribution when the number of photons is large. The masking number for a single polarization PSK Y-00 cipher based on *M*-ary data modulation is calculated as the ratio of Δ*ϕ*_{shot} and Δ*θ*_{basis}:

*P*

_{0},

*R*,

*h*,

*ν*

_{0}, and

*m*are the average power per polarization, baud rate, Planck constant, signal frequency, and bit number of the bases, respectively. The masking number is proportional to 2

*and is inversely proportional to the square root of the average optical power. When a target masking number is set to be 100 for 12-Gbaud DP PSK Y-00 cipher based on QPSK data modulation (*

^{m}*M*= 4), the bit resolution

*m*should be 16 at optical average power (sum of both polarizations) of −9 dBm. Thus, high bit resolution

*m*is important to achieve a high masking number.

The masking number is related to uncertainty when an eavesdropper tries to measure encrypted high-order signals. One can estimate the success probability of guessing one symbol via ideal measurement by an eavesdropper. The probability is approximately obtained as 1/Γ for a large Γ. In practical eavesdropping attacks, consecutive symbols must be discriminated, and the success probability becomes (1/Γ)* ^{n}* for

*n*consecutive symbols. Thus, overall security of the Y-00 cipher depends not only on the masking number Γ but also consecutive symbol length

*n*. The symbol length required to deduce a seed key or to decipher messages is related to the mathematical encryption part in which the symbol-by-symbol phase rotation angles are determined using the seed key. The symbol length

*n*is typically large, and the success probability (1/Γ)

*is very small in practice. Detailed discussion regarding the practical overall security is provided elsewhere [12].*

^{n}#### 2.3 Coarse-to-fine phase randomization for encryption

In PSK Y-00 cipher, encryption is achieved by 2* ^{m}*-level random phase modulation. The bit number of bases

*m*is practically limited by bit resolution of a digital-to-analog converter for driving a phase modulator (PM). Coarse-to-fine phase randomization using cascaded PMs is utilized to break the limit. The technique was demonstrated for PSK Y-00 cipher based on BPSK data modulation [8]. Here, the technique is modified for the encryption of QPSK data modulation (

*M*= 4). Figure 2 shows the configuration and operating principle of the encryption. First, QPSK data modulation is achieved with an IQ modulator, and then phase randomization with 2

*levels is achieved using two cascaded PMs. The first PM (PM-1) is used for coarse phase adjustment with 2*

^{m}*levels, and the second one (PM-2) for fine adjustment with 2*

^{K}*levels.*

^{L}*K*and

*L*are set to satisfy

*m*=

*K*+

*L*. To achieve 2

*-level phase randomization by the two phase adjustments, peak-to-peak phase modulation angles at PM-1 and PM-2 must be precisely adjusted according to the following equations.*

^{K+L}These equations are generalized for the encryption of *M*-ary PSK data modulation. An example of operation when *K* = 1 and *L* = 2 is shown in Fig. 2. After the QPSK modulation, 2^{1}-level phase modulation with a peak-to-peak rotation angle *θ*_{pp_PM-1} of π/4 is performed at PM-1, and the constellation becomes 8 (=2^{(2+1)}) PSK signal. Then, fine 2^{2}-level modulation with *θ*_{pp_PM-2} of 3π/16 is performed at PM-2, resulting in the constellation of 32 (=2^{(2+1+2)}) PSK signal. This example is a simple case. *K* and *L* were set to 6 and 10, respectively, for a target *m* of 16 in the following experiments. This technique requires two additional PMs. Photonics integration will be a key to reduce the cost.

## 3. Experiments

We experimentally demonstrate transmission of 12-Gbaud DP-PSK Y-00 cipher based on QPSK data modulation over 400- and 800-km SSMF. The line rate is 48 Gbit/s, and the net rate is 40 Gbit/s when the 20% overhead of SD-FEC is considered. Figure 3(a) shows the experimental setup. A pseudorandom binary sequence (PRBS) for a data stream and a preshared seed key are put into a Y-00 mathematical encryption box. The encryption box consists of PRNGs and a mapper. The PRNG extends the seed key to a key stream that is a very long pseudorandom binary sequence to determine angles of random phase rotation for each symbol. Here, *m* was set to 16 such that 16 bits of the key stream are consumed for the encryption of one symbol. For the mathematical encryption, the random 16 bits are combined with 2 bits of QPSK data, and the 18-bit encrypted data are mapped on an IQ plane as 2^{18} PSK. Additionally, the polarity of the data is randomized before combining the bits. These mathematical processes are implemented offline. A 12 Gsample/s arbitrary waveform generator (AWG) is driven using the encrypted data. To achieve coarse-to-fine phase randomization, the 18-bit data for one-symbol modulation are divided into polarity-randomized 2-bit data for IQ modulation and coarse 6- and fine 10-bit data for the phase randomization. An IQ modulator and two cascaded PMs are driven by the three AWG outputs after adjusting voltages with amplifiers and attenuators. The three modulations are synchronously performed, and coherent light at 1550.12 nm from a tunable laser diode (TLD) is modulated as Y-00 cipher with 2^{18} phase levels. Then, Y-00 cipher is launched into a polarization-division multiplexing emulator (PMDE), and DP-PSK Y-00 cipher at a line rate of 48 Gbit/s is generated.

After adjusting the optical power (2*P*_{0}) with a variable attenuator, Y-00 cipher is launched into the transmission line. Each fiber span consists of 100-km SSMF and an erbium-doped fiber amplifier to compensate the loss of the fiber. The transmission was tested over 400- and 800-km fibers. Then, Y-00 cipher was received by conventional intradyne coherent detection. A free-running local oscillator (LO), a polarization-diversity 90° optical hybrid circuit, and balance photodetectors were used. Analog-to-digital conversion was achieved with a real-time oscilloscope (OSC) with a bandwidth of 13 GHz. After the digitization, Y-00 cipher was decrypted and demodulated by offline digital signal processing (DSP), as shown in Fig. 3(b). First, chromatic dispersion was compensated by a finite impulse response filter [13]. Next, polarizations were demultiplexed using a multiple-input and multiple-output equalizer optimized by constant modulus algorithm [13]. These two processes work properly for the encrypted high-order PSK without special modification. Then, the cipher was decrypted by subtracting the phase in a symbol-by-symbol manner. A phase rotation angle *θ*_{basis} for each symbol was obtained by putting the seed key into the same encryption box, and exp(−j*θ*_{basis}) was multiplied by the complex amplitude of each symbol of the cipher. Timing synchronization between the transmitter and receiver for the decryption was achieved by adding preamble bits in the offline processing. In a real-time DSP, synchronization protocol is implemented prior to the start of communication and no overhead is necessary. The decryption process is simple, and real-time implementation is feasible. Finally, carrier phase was recovered by feed-forward carrier phase estimation, and binary data were demodulated.

Figures 4(a) and 4(b) show the constellation diagrams of Y-00 cipher after the transmission over 400- and 800-km SSMF, respectively. When the dispersion compensation and polarization demultiplexing were performed, the constellation diagrams became shapes like a donut. The constellations of QPSK data modulation were successfully recovered by the decryption and carrier phase recovery. Figure 4(c) shows the bit error ratio (BER) characteristics. The span-launch signal power 2*P*_{0} was changed, and the received OSNR was changed accordingly. A reference curve of noncipher DP-QPSK signal and three curves of DP-PSK Y-00 cipher in a back-to-back condition and after 400- and 800-km transmission were plotted. The three curves of DP-PSK Y-00 cipher are similar. Hence, the penalty caused by the transmission was negligibly small. The OSNR penalty caused by the encryption and decryption, which is the difference between the curves of DP QPSK signal and DP-PSK Y-00 cipher, was approximately 0.5 dB at a BER of SD-FEC threshold. Physical-layer security was achievable at the small cost of 0.5 dB.

Figure 5 shows the Q factors and quantum-noise masking number when the span-launch signal power changed. The masking number is defined at the input of the transmission line, which is considered to be the best case for an eavesdropper. One can see the tradeoffs between the Q factor and masking number in this figure: higher span-launch power improves signal quality while the masking number decreases. For higher security, the span-launch power should be reduced to the extent that the signal quality is greater than an FEC threshold. The Q factors of the SD-FEC threshold (7.3 dB) were achieved at a masking number of 338 and 217 for the transmission distances of 400 and 800 km, respectively. One can estimate from the masking number of 217 that a success probability of guessing 32 consecutive symbols by an eavesdropper is (1/217)^{32} = 1.7 × 10^{−75}. The probability is small, and practical physical layer security is achieved at the net rate of 40 Gbit/s while keeping generally required transmission quality. The maximum reach is not limited to 800 km. A cipher transmission system for a longer distance can be designed in consideration of the relation between the masking number and span-launch optical power (black curve) shown in Fig. 5. Moreover, Y-00 cipher is applicable to conventional dense WDM systems, because the occupied bandwidth fits with a typical channel spacing of 50 or 100 GHz. It is confirmed that optical spectrum of the cipher is comparable with that of noncipher signals at the same baud rate when Nyquist filtering is not applied [14].

## 4. Summary

We have experimentally demonstrated transmission of 48-Gbit/s DP PSK Y-00 cipher with 2^{18} phase levels over 400- and 800-km SSMF. To increase the bit rate without increasing the baud rate, QPSK data modulation was employed. Successful transmission of the cipher was achieved with a small OSNR penalty of 0.5 dB from reference noncipher QPSK signals. Provided that the net rate is 40 Gbit/s by employing SD-FEC, the quantum-noise masking numbers, which indicate a primal measure of security of the cipher system, are 338 and 217 for transmission distances of 400 and 800 km, respectively. The largest product of the data rate and distance of 32,000 Gbit/s·km was achieved. The transmission quality required for typical communication systems and security based on the inherent effect of signal masking by shot noise were simultaneously achieved in the quantum-noise-assisted cipher system.

## Funding

Japan Society for the Promotion of Science (JP18K04290); Telecommunications Advancement Foundation.

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