## Abstract

We report a 10-Gbaud fiber-optic cipher transmission system by using a phase-shift keying (PSK) Y-00 quantum stream cipher. The PSK Y-00 cipher is a symmetric-key direct data encryption technique based on extremely high-order random phase modulation using a pre-shared short key. Neighboring signal phases following encryption are masked by quantum (shot) noise, which provides security based on shot noise’s inherent effects. To implement such a system, we utilize coarse-to-fine phase modulation with two cascaded phase modulators and digital decryption incorporated into digital signal processing (DSP) for intra-dyne coherent detection. We demonstrate 10-Gbaud PSK Y-00 cipher transmission over a 400-km standard single-mode fiber (SSMF). The coarse-to-fine phase modulation achieves 2^{17} phase levels for signal masking by shot noise. The DSP with decryption realizes detection of the cipher without penalties. Masking 167 signal phase levels by shot noise is achieved at a bit-error ratio defined by a hard-decision forward-error correction threshold (3.8 × 10^{−3}) in the transmissions over the 400-km SSMF.

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

## 1. Introduction

The expanding Internet of things (IoT) has created various challenges in communication systems. One important challenge is communication security. Fiber-optic transmissions are no exception because installed fiber cables suffer from potential tapping risks. Introducing cipher technology is an effective countermeasure to this risk. High security has potential value beyond the capacity and reach of fiber-optic transmissions. One promising approach that can operate at a high data rate is the use of symmetric-key direct data encryption systems, where legitimate users exchange data encrypted using a pre-shared short key. In fiber-optic transmissions, such encryption systems are implemented physically based on signal masking by noise. While conventional encryption systems based on mathematical complexity is implemented on data link layer (Layer 2 in the Open Systems Interconnection model) or higher layers, the physical encryption directly protects optical data signals from being intercepted. One particularly promising approach is the Y-00 quantum stream cipher, where signals are masked by “quantum (shot)” noise [1]. Because shot noise is truly random and inevitable in optical detection, security is enhanced significantly by such masking. This masking is achieved in two steps. First, multilevel data for high-order modulation are generated from original data (plain text) and a short key shared preliminarily between legitimate users. Next, the phase and/or amplitude of coherent light is modulated with the multilevel data. As the modulation order increases, the distance between adjacent optical signals decreases to an extent less than the variance of the shot noise. Hence, the signals are inherently masked by the shot noise when detected. This masking effect counteracts eavesdropping attempts to extract data and/or keys by discriminating high-order modulation. On the other hand, a legitimate receiver can convert the high-order modulation into original data modulation by utilizing the key information. Additionally, the Y-00 cipher is compatible with existing wavelength-division multiplexing transmission systems because it occupies the classical channel bandwidth corresponding to the baud rate of high-order modulation [2,3].

A phase-shift keying (PSK) Y-00 cipher is the implementation in which binary PSK (BPSK) signals are encrypted only by phase rotation. The phase encryption was originally proposed as AlphaEta [4], which is a different name for the Y-00 cipher. Differential BPSK signals at an OC-12 data rate (622 Mbit/s) are mapped to 2^{14} phase levels in the range of 0–2π for encryption. Demodulation with decryption following transmission over a 250-km single mode fiber (SMF) was demonstrated using a one-bit delay interferometer and phase modulator (PM) [5]. Next, a 2.66-Gbit/s PSK AlphaEta system with 2^{8} phase levels was achieved based on an electronic decryption process following differential in-phase/quadrature (I/Q) detection [6]. Recently, we proposed introducing decryption processes into conventional digital signal processing (DSP) for intra-dyne coherent detection using a free-running local oscillator. Numerical simulation results demonstrated that the penalty imposed by the decryption was negligible [7]. Another approach for signal randomization in Y-00 cipher is utilizing both phase and amplitude, called quadrature amplitude modulation (QAM) Y-00 cipher [8]. 10- and 40-Gbit/s coherent QAM Y-00 cipher systems in which 16-QAM data modulation was converted to 2^{8} × 2^{8}-level QAM for encryption were demonstrated [9], [10]. When the two modulations are compared, the PSK Y-00 cipher based on BPSK data is advantageous for long reach transmission because a signal-to-noise ratio per bit (E_{b}/N_{0}) required for a target BER is the lowest, while the QAM Y-00 cipher based on 16 QAM data achieves higher spectral efficiency. Theoretical analysis and comparison of security based on the masking by shot noise are provided in [11].

This paper reports the experimental demonstration of a 10-Gbaud digital coherent PSK Y-00 quantum stream cipher with 2^{17} phase levels. The proposed cipher system achieves security based on the inherent effects of shot noise with no negative impact on transmission performance. First, we discuss the operating principles of the PSK Y-00 cipher and introduce a quantum-noise masking number Γ as a primal measure of security. The masking number Γ indicates how many signal phase levels are masked by shot noise. A higher Γ is better for security. A challenge for the PSK Y-00 cipher at a high baud rate is to achieve extremely high-order modulation to realize a high masking number. A digital-to-analog converter (DAC) for the high-order modulation has tradeoffs between resolution and operating bandwidth, and practically limits the order of phase modulation at a high baud rate. To overcome this limitation, we have proposed coarse-to-fine phase modulation that multiplexes two DAC outputs in an optical domain using two cascaded PMs [12]. We show operating principle of the technique for cipher generation, and then describe the flow of DSP for intra-dyne coherent detection of the cipher. Decryption is achieved in the digital domain prior to carrier phase recovery (CPR). In addition to proof-of-concept back-to-back experiments for coarse-to-fine phase modulation [12], we experimentally verified that signal quality following decryption is independent of the signal phase levels for encryption. We then demonstrate 10-Gbaud PSK Y-00 cipher transmission over a 400-km standard SMF (SSMF). Chromatic dispersion compensation, decryption, and CPR are successfully achieved in the DSP and the OSNR penalty imposed by cipher transmission is negligible. The quantum-noise masking number is 167, provided that a bit-error ratio (BER) less than a given hard-decision forward-error correction (HD-FEC) threshold (3.8 × 10^{−3}) is achieved.

## 2. Operating principles

#### 2.1 PSK Y-00 quantum stream cipher

Encryption for PSK Y-00 cipher is achieved by converting data modulation into *M*-ary PSK modulation with a high modulation order *M*. Figure 1 shows this operating principle when BPSK is employed for data modulation. A signal of conventional BPSK is mapped to 0 or π in an I/Q plane. As shown in the left diagram in Fig. 1, in the Y-00 cipher, the reference phase for BPSK modulation is rotated by *θ*_{basis} in a bit-by-bit manner. The rotation angle *θ*_{basis} ranges from 0–π and is determined randomly utilizing a short key that is pre-shared between legitimate users. A pair of signals representing 0 and 1 with an angle *θ*_{basis} is called a basis. The middle diagram in the figure shows the mapping of bases when the number of bases is eight as an intuitive example. The bases are allocated evenly across the I/Q plane. The angle between two adjacent bases Δ*θ*_{basis} is π/8 and the values of the angle *θ*_{basis} are 0, π/8, π/4, 3π/8, π/2, 5π/8, 3π/4, or 7π/8 for one-bit modulation. Therefore, a 16-PSK constellation diagram is achieved following encryption. The assignments of 0 and 1 are flipped between adjacent signals.

In the Y-00 cipher, the number of bases must be large enough that the constellation cannot be discriminated as an *M*-ary PSK, as shown in the right diagram in Fig. 1. If the bit number of bases is *m*, the angle between two adjacent bases Δ*θ*_{basis} is π/2* ^{m}*. To guarantee security, the masking of signals by shot noise is important because shot noise is inherent in optical detection and is truly random. As shown in the inset magnified image, when shot noise masks adjacent signal phase levels, an eavesdropping attempt to discriminate the Y-00 cipher as an

*M*-ary PSK for deducing data and/or a shared key is prevented by the inherent effect of shot noise. In contrast, a legitimate receiver with the key knows the bases of each BPSK modulation, meaning they can detect the Y-00 cipher in a manner similar to the BPSK case by subtracting the angles in bit-by-bit fashion.

As a measure of security in the Y-00 cipher, we define a quantum-noise masking number Γ as a ratio of the standard deviation under the Gaussian probability density approximation for the phase uncertainty derived from shot noise Δ*ϕ*_{shot} divided by Δ*θ*_{basis}.

*P*

_{0},

*R*,

*h*, and

*ν*

_{0}are the average power, baud rate, Planck constant, and signal frequency, respectively. The masking number Γ indicates the number of signal phase levels covered by the shot noise. The success probability of guessing one bit via ideal measurement is approximately obtained as 1/Γ. In practical eavesdropping attacks, consecutive bits must be discriminated and the success probability is (1/Γ)

*for*

^{n}*n*consecutive bits. The overall security of the Y-00 cipher depends not only on the masking effect, but also on mathematical encryption, in which the bit-by-bit phase rotation angle is determined randomly based on the pre-shared short key. Detailed discussion regarding this issue is provided in [13].

Figure 2 shows the relationship between the quantum-noise masking number Γ and bit number of bases *m* for baud rates of 10, 25, and 50 Gbaud, given that the optical average power of the cipher *P*_{0} is −10 dBm. The baud rates are equivalent to bit rates for the Y-00 cipher based on BPSK data modulation. A masking number of more than 1 (Γ > 1) is achieved when *m* ≥ 11. We set the target bit number of bases *m* to 16, which achieves a masking number of more than 35 at 10 Gbaud. As shown in Eq. (1), the masking number is inversely proportional to the square root of the optical power. Therefore, in practical cases, a higher masking number can be achieved by minimizing the power to the extent that the target transmission quality is satisfied.

#### 2.2 Coarse-to-fine phase modulation

To achieve the 2^{17}-level phase modulation corresponding to the target 16-bit bases, we have proposed coarse-to-fine phase modulation using cascaded PMs. Figure 3 presents the system configuration and main operating principle when the technique is utilized for the generation of PSK Y-00 cipher. Three-stage phase modulation is performed by using a Mach-Zehnder modulator (MZM) for BPSK data modulation and two PMs for basis modulation. The first PM (PM-1) is utilized for coarse phase adjustment and the second (PM-2) is utilized for fine adjustment. The Y-00 mathematical encryption box mainly consists of pseudorandom number generators (PRNGs) and a signal mapper. The PRNGs extend the shared short key into the key stream, which determines the bit-by-bit random bases. By putting data and the key into the box, random bases and binary data with bit flipping are generated. The bases are divided into 2* ^{K}*-coarse and 2

*-fine levels for coarse-to-fine modulation. PM-1 and PM-2 are driven by the coarse and fine levels, respectively.*

^{L}This operation is explained in Fig. 3 with a simple example of (*K*, *L*) = (1, 2). First, BPSK data modulation is achieved using the MZM biased to the null point. The phase of the BPSK signal is then rotated by the coarse 2^{1} levels at PM-1. The peak-to-peak angle of the phase rotation *θ*_{pp_PM-1} is π/2 and the constellation becomes quadrature PSK. Next, in PM-2, the fine 2^{2}-level modulation is performed with a peak-to-peak angle *θ*_{pp_PM-2} of 3π/8, resulting in a 16-PSK constellation. The peak-to-peak angles of the phase modulation, *θ*_{pp_PM-1} and *θ*_{pp_PM-2}, can be generalized for *K* and *L* as follows:

^{K}^{+}

*level phase modulation is achieved with*

^{L}*K*- and

*L*-bit DACs. This modulation method with large

*K*and

*L*values is utilized for the basis modulation of the PSK Y-00 cipher.

#### 2.3 Digital-coherent detection with decryption

Intra-dyne coherent detection using a conventional 90° hybrid circuit and free-running local oscillator is employed for reception of the PSK Y-00 cipher. DSP is performed for equalization, decryption, and demodulation. Figure 4 presents the flow of DSP following intra-dyne detection. The inputs are the digitized I and Q components of two (X and Y) polarizations. First, fixed chromatic dispersion compensation is achieved by utilizing a finite-impulse-response filter [14]. Next, the polarizations are aligned in the Stokes space [15]. An additional step for demodulating the Y-00 cipher is decryption, where the angle of phase rotation *θ*_{basis} is subtracted in bit-by-bit fashion from the measured signal phase via multiplexing as exp(−*jθ*_{basis}). The angle *θ*_{basis} for each bit is determined by placing a shared key into the same Y-00 mathematical encryption box as that utilized by the transmitter. Timing synchronization between the transmitter and receiver is also necessary for decryption. We add preamble bits for synchronization in the offline processing. In a practical Y-00 cipher system with real-time DSP, synchronization is performed as a preliminary process prior to the start of communication and no overhead is necessary. Following decryption, the carrier phase of the decrypted signal is recovered based on the calculation of a power of the received phase [16]. Finally, data demodulation is achieved.

## 3. Experiments

#### 3.1 Back-to-back measurements

We first tested coarse-to-fine phase modulation for a small number of bases to verify the operation via constellation measurement. The coarse and fine bits (*K*, *L*) were set to (1, 1) and (1, 2) for four and eight bases, respectively. Figure 5 shows the experimental setup. A pseudorandom binary sequence as data and a shared key were placed into the Y-00 mathematical encryption box (offline). The outputs of binary data with bit flipping and coarse 2* ^{K}*- and fine 2

*- level electrical signals for basis modulation were used to drive a 10-Gsample/s arbitrary waveform generator (AWG). Coherent light with a wavelength of 1550.12 nm from a tunable laser diode (TLD) with a linewidth of 100 kHz was launched into the three-stage modulators. BPSK data modulation at 10 Gbaud was performed by the MZM. Next, the phase of the BPSK signal was rotated in bit-by-bit fashion to perform encryption in the cascaded PMs. Coarse*

^{L}*K*- and fine

*L*-bit phase modulations were synchronously achieved. After adjusting the signal power with a variable optical attenuator (VOA), the cipher was launched into an erbium-doped fiber amplifier (EDFA) for back-to-back measurements orinto a 400-km transmission line consisting of 100-km spans of SSMFs and EDFAs. At the receiver side, out-of-band noise is suppressed by a band-pass filter (BPF) with a 3-nm pass bandwidth. Next, the Y-00 cipher is launched into a coherent receiver front-end circuit with a free-running local oscillator. The four outputs, which correspond to the I and Q components of the X and Y polarizations, are detected by four balance photo detectors (BPDs) and digitized by a real-time oscilloscope (OSC) with an electrical bandwidth of 12 GHz. Finally, the received Y-00 cipher is decrypted and demodulated by the offline DSP. During detection, the OSNR is monitored by an optical spectrum analyzer (OSA).

We measured constellation diagrams when the number of bases was set to a low value to verify the operation of coarse-to-fine modulation. Figure 6 shows the results of (a) 2-bit bases or 2^{3} = 8 levels (*K* = 1, *L* = 1), and (b) 3-bit bases or 2^{4} = 16 levels (*K* = 1, *L* = 2). The constellation diagrams of the signals before and after decryption were measured at an OSNR of 20 dB. The signal prior to decryption was intentionally demodulated as *M*-ary PSK (*M* = 2^{K}^{+}^{L}^{+1}) for verification purposes. As shown in the left constellations of Figs. 6(a) and 6(b), 8-PSK and 16-PSK constellations were observed. Following decryption, the random basis modulation was stripped out and a clear BPSK constellation was recovered. No error was observed at an OSNR of 20 dB. Thus, coarse-to-fine phase modulation was successfully applied to the basis modulation. Next, we measured the Q factors of the decrypted cipher at an OSNR of 7 dB as the number of bases varied. Figure 7 shows the results. The Q factors were obtained from measured BERs based on the relationship of Q [dB] = 20 × log_{10}[√2*erfc*^{−1}(2 × BER)]. The bit numbers of bases were 2, 3, 12, 14, and 16, corresponding to 2^{3}, 2^{4}, 2^{13}, 2^{15}, and 2^{17} phase levels after encryption. The coarse and fine bit numbers (*K*, *L*) were set to (1, 1), (1, 2), (6, 6), (6, 8), and (6, 10) for the bit numbers of bases of 2, 3, 12, 14, and 16, respectively. For reference, the results with bit numbers of bases of 6 and 10 achieved by conventional modulation with a single DAC are also plotted. The dotted lines in the figure present another reference Q factor for BPSK signals at the same baud rate. The measured Q factors were approximately 10.15 dB in all cases, which indicates that the Q penalty imposed by coarse-to-fine modulation is negligible.

#### 3.2 Transmission over 400-km SSMF

We performed PSK Y-00 cipher transmission over a 400-km SSMF. The experimental setup was the same as that shown in Fig. 5 and a 400-km transmission line consisting of four spans of 100-km SSMFs with EDFAs was used. We changed the signal power launched into span *P*_{0} to vary the received OSNR following transmission. In the DSP, a chromatic dispersion of 6625 ps/nm is compensated. Figures 8(a) and 8(b) present constellation diagrams of the PSK Y-00 cipher under back-to-back conditions and after 400-km transmission, respectively, when the OSNR was approximately 9 dB. The constellation diagrams prior to decryption are shaped like a donut, which is caused by both the random phase rotation for encryption and carrier phase fluctuation. Following decryption and CPR, both of these effects are removed and clear BPSK constellations are obtained. CPR cannot function properly without decryption because phase continuity is lost in the encryption. Figure 8(c) shows BER characteristics of the PSK Y-00 cipher and BPSK (reference). There are no noticeable differences between the curves, which indicates that the OSNR penalty imposed by Y-00 encryption and transmission over a 400-km SSMF is negligible.

Next, we discuss security of the system. A BER less than the HD-FEC threshold ( = 3.8 × 10^{−3}) was achieved at an OSNR of approximately 5.5 dB, corresponding to a signal power of approximately −23 dBm launched into the span. By substituting this signal power into Eq. (1), one can obtain a masking number of 167. This number is defined at the output of the transmitter which is considered to be the best place for eavesdropping. The first step in eavesdropping is to measure the correct signal phase levels of consecutive bits for subsequent mathematical analysis. As an example, the success probability for correctly measuring 32 consecutive bits via ideal measurement limited only by shot noise is estimated to be a very small value of (1/167)^{32} = 7.5 × 10^{−72} in the Y-00 cipher transmission system with 2^{16} bases. Discriminating the phase levels of larger numbers of consecutive bits is virtually impossible. Provided that the number of bases is 2^{12}, which could be achieved by conventional phase modulation using a single state-of-the-art DAC, the success probability is calculated as (1/10)^{32} = 1.0 × 10^{−32}. Thus, the large number of bases realized by the coarse-to-fine modulation significantly improves security, and secure 10-Gbaud transmission over a 400-km SSMF link can be achieved by the PSK Y-00 cipher with 2^{16} bases. The transmission reach in this demonstration was limited by our equipment. Since the BER of the HD-FEC threshold is achieved at a low OSNR of 5.5 dB, significantly longer reach, e.g. more than a few thousands of kilometers, is expected by adjusting signal power launched into the fiber link. The tradeoff between the signal power and masking number in Eq. (1) should be considered carefully when designing such long-reach PSK Y-00 cipher systems.

## 4. Summary

We demonstrated 10-Gbaud PSK Y-00 quantum stream cipher transmission over a 400-km SSMF. Coarse-to-fine phase modulation using two cascaded PMs was utilized for encryption. The PSK Y-00 cipher has 2^{16} bases or 2^{17} signal phase levels, enabling signal masking by quantum (shot) noise at practical optical powers for transmission. For detection with decryption, we employed intra-dyne coherent detection with DSP. The decryption process was incorporated into DSP. Decryption without penalty and independent of the number of bases was achieved. Finally, cipher transmission over a 400-km SSMF was successfully achieved with negligible OSNR penalties. The quantum-noise masking number was 167 at a BER of 3.8 × 10^{−3} (HD-FEC threshold). Thus, enhanced security provided by the inherent effects of shot noise and transmission performance comparable to classical modulation were simultaneously achieved. The baud rate and reach we experimentally demonstrated were limited by our equipment. A higher baud rate and longer reach should be achievable for the PSK Y-00 cipher because the degradation of transmission performance caused by encryption and decryption is negligibly small.

## Funding

JSPS KAKENHI (Grant Number JP18K04290) and Telecommunications Advancement Foundation.

## Acknowledgments

The authors thank K. Kato for fruitful discussions.

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