## Abstract

A Quantum Stream Cipher (QSC) using Quadrature Amplitude Modulation (QAM) is presented to greatly increase the secure degree compared with ASK or PSK/QSC. We propose encoding multi-bit data in one symbol with a multi-bit basis state, resulting in QAM/QSC, which employs amplitude and phase encryption of the light beam simultaneously. A 16 QAM/QSC experiment at 10 Gbit/s was successfully carried out over 160 km using a digital coherent optical transmission technique, where 16 QAM data were encrypted in a constellation with 32 × 32~4096 × 4096 symbols. We show experimentally that the Number of Masked Signals (NMS) in the quantum noise Γ_{QAM} for QAM/QSC becomes a square multiple larger than Γ_{ASK} for ASK/QSC. Γ_{QAM} exceeds 10,000. This result indicates that the QSC technique is more robust against eavesdroppers than ASK or PSK/QSC.

© 2014 Optical Society of America

## 1. Introduction

With the advances made on the Internet, wireless phones, and data communication, the need for information capacity has been increasing at 40% every year. Driven by the rapid growth in data traffic, serious attempts are being made to achieve a high capacity and high-speed optical network on both in long-haul and local area networks. Of the various attempts, QAM and Orthogonal Frequency Division Multiplexing (OFDM) are receiving a lot of attention because of their high spectral efficiencies (SEs) [1–3]. We have achieved a 1024 QAM digital coherent optical transmission over 150 km by using an Optical Phase-Locked Loop (OPLL), Frequency Domain Equalization (FDE), and Digital Back Propagation (DBP). This made it possible to realize a SE exceeding 14 bit/s/Hz [4].

A high-capacity network carries personal and confidential information, and therefore, a secure optical communication network is indispensable to the ICT community. As regards the application of the cipher technique to optical communication, there are two methods, one is one-time pad encryption with Quantum Key Distribution (QKD) using a single-photon [5–7] and the other is Quantum Stream Cipher (QSC) using quantum noises [8–11]. The QSC is very interesting since we can encrypt secret data at a very high speed matching that of a conventional optical transmission system. The principle of this stream cipher protocol is to hide the data signal in quantum phase noise or amplitude noise in the receiver of the eavesdropper. PSK/QSC and ASK/QSC transmission experiments over a few hundred kilometers have already been successfully reported in the Giga bit/s region by several authors [12–14].

To construct a more robust QSC protocol, it is interesting to introduce multi-level PSK and ASK simultaneously under quantum phase noise and Amplified Spontaneous Emission (ASE) noise, which we call this QAM/QSC. The QAM like QSC was proposed theoretically in 2005 and its security against a cipher text-only attack and a known/chosen plaintext attack have been theoretically investigated [15]. However, in the paper, only one bit data was considered on a two-dimensional basis state using IQ mapping. A multi-bit encoded QSC scheme employing Quadrature Phase Shift Keying (QPSK) has been proposed in a wireless system [16]. However, it is a simple multi-bit extension of the basis state of one-dimensional PSK/QSC along a ring-type encrypted constellation, which is useful for increasing the bit-rate but does not lead to a fundamental enhancement of secureness. No actual encryption and decryption schemes that can send encrypted data consisting of multi-bit and multi-dimensional data and a basis state have yet been proposed.

In this paper, we report the first 10 Gbit/s QAM/QSC transmission over 160 km, where we adopted 2.5 Gsymbol/s, 16 QAM. We show experimentally that the QSC technique enables much higher degree of security when we introduce a QAM encryption and decryption technique. The QAM/QSC can be classified as a two-dimensional cipher encryption.

## 2. Principle of QAM/QSC

When we use a QAM technique for QSC with a data length of *n* bits and a basis state length of *m* bits per dimension (or axis), we prepare a multi-level modulation signal with a total constellation size of 2^{2(}^{n}^{+}^{m}^{)}, in which one 2^{(}^{n}^{+}^{m}^{)} is for the In-phase (I) channel and the other 2^{(}^{n}^{+}^{m}^{)} is for the Quadrature-phase (Q) channel. Hence, the strength of the secure level as a cipher system would become a square multiplication of that of a one-dimensional QSC system, provided that I and Q are independent. In addition, by increasing the QAM multiplicity, we can easily increase the transmission speed to over 10 Gbit/s per channel. Furthermore, in a QAM system, all the information from both the amplitude and phase of the electric field of the light beam must be measured with high precision. To realize this detection, we prepared an optical local oscillator (LO), which is precisely phase-controlled to a data signal with an OPLL circuit, and its homodyne detection is indispensable [4]. This process also makes it difficult to decrypt the true data since a simple tapping of the light signal from the fiber system may be insufficient to guarantee a successful OPLL operation for Eve because of a low Optical Signal to Noise Ratio (OSNR).

A constellation of 16 QAM/QSC is shown in Fig. 1, where 16 QAM (2 bits for I and Q, respectively) data is encrypted by using 64 basis states (3 bits for I and Q, respectively). That is, I or Q has 2 bit data (*n* = 2) with a 3 bit basis state (*m* = 3), and a 5 bit encrypted signal in total. Therefore, we hide 4 bit (I + Q) information in the constellation of 1024 (2^{5} × 2^{5} = 32 × 32) encrypted symbols and the decision level for Eve is covered with ASE noise. As for the I data, each 8 symbol from the left to the right corresponds to 00, 01, 10, and 11 and for the Q data each 8 symbol from the bottom to the top corresponds to 00, 01, 10, and 11 in this case. Here, I and Q data are given by *S _{I}*

*R*and

_{I}*S*

_{Q}*R*, respectively, where

_{Q}*S*and

_{I}*S*are the information bits and

_{Q}*R*and

_{I}*R*are the random key bits. The XOR operation enables

_{Q}*S*and

_{I}*S*to be randomly distributed over the entire constellation map. Hence, for example, a combination of (

_{Q}*I*,

*Q*)

_{data}= (11,01) and a basis state (

*B*,

_{I}*B*) = (001,010) generates (

_{Q}*I*,

*Q*)

_{encrypted}= (

*I*+

_{data}*B*,

_{I}*Q*+

_{data}*B*) = (11001, 01010). In each time slot, the 16 QAM constellation is moving with a different basis state.

_{Q}Figure 2 shows a scheme for generating encrypted 16 QAM/QSC. Alice and Bob share the same secret seed key. At the transmitter, the secret seed key for Alice drives pattern generators 1 and 2 using Linear Feedback Shift Registers (LFSRs); one is for Random bit pattern *R _{I}* (Upper 2 bits) and

*R*(Lower 2 bits) for first XOR operation of the I and Q data, and the other is a Random pattern for basis states

_{Q}*B*(Upper

_{I}*m*bits) and

*B*(Lower

_{Q}*m*bits) for I and Q, respectively. In both cases, a Serial-to-Parallel (S/P) conversion technique is used for the I and Q data. 16 QAM data (4 bit/symbol) are separated into

*S*(Upper 2 bits) and

_{I}*S*(Lower 2 bits). As we mentioned earlier, XOR operations between

_{Q}*S*and

_{I}*R*and between

_{I}*S*and

_{Q}*R*are carried out and denoted by

_{Q}*S*

_{I}*R*and

_{I}*S*

_{Q}*R*, respectively. Then,

_{Q}*S*

_{I}*R*and

_{I}*B*, and

_{I}*S*

_{Q}*R*and

_{Q}*B*are combined with a Parallel-to-Serial (P/S) converter, where the encrypted I and Q data are given by (

_{Q}*I*,

*Q*)

_{Encrypted}= (

*S*

_{I}*R*+

_{I}*B*,

_{I}*S*

_{Q}*R*+

_{Q}*B*). To drive the IQ modulator, the encrypted analogue data

_{Q}*E*and

_{I,DEC}*E*between 0~2

_{Q,DEC}

^{m}^{+2}−1, which here we call the decimal E unit, are changed to new decimal data

*D*and

_{I}*D*between −2

_{Q}

^{m}^{+2}+ 1~2

^{m}^{+2}−1 because the electric field of the light beam has positive and negative values, which does not occur in a one dimensional QSC case. That is,

*D*= 2 ×

_{I}*E*− (2

_{I,DEC}

^{m}^{+2}−1) and

*D*= 2 ×

_{Q}*E*− (2

_{Q,DEC}

^{m}^{+2}−1), which here we call the decimal D unit.

In the QAM/QSC decryption process at the receiver, we apply a reverse encryption process using the same key and obtain the original data. We have 2-bit data under a wide 4-level decision width of *W* = 2* ^{m}* for Bob, where the 3 decision levels in the E unit for I data are given by

*E*

_{I,DEC}_{1}=

*W*/2 = 2

^{m}^{−1},

*E*

_{I,DEC}_{2}= 3

*W*/2 = 3 × 2

^{m}^{−1}, and

*E*

_{I,DEC}_{3}= 5

*W*/2 = 5 × 2

^{m}^{−1}. When

*m*= 3 in Fig. 1, the decision levels in the E unit are 4, 12, and 20, corresponding to −23, −7, and + 9 in the D unit. In the binary expression, where the E unit is normalized with 2

^{m}^{−1}, they become 00100, 01100, 10100, respectively, where the lower 2 bits of “00” come from the decrypted basis state. These binary decision levels are used for Bit Error Rate (BER) measurements.

Constellations of encrypted electrical data are shown in Fig. 3, where (a) is the original 16 QAM data before encryption and (b) is encrypted 2^{2(2+}^{m}^{)} QAM data after encryption. The blue, yellow, and green squares indicate three examples with different 6-bit basis states. The position of 16 QAM changes every time slot within *M* × *M* symbols, resulting in a noisy constellation for Eve, but it becomes like Fig. 3(a) with a small noise distribution for Bob by using the shared basis state information.

## 3. Experimental set-up for 10 Gbit/s 16 QAM/QSC digital coherent transmission over 160 km

The experimental set-up for 16 QAM/QSC digital coherent transmission over 160 km is shown in Fig. 4. The symbol rate is 2.5 Gsymbol/s and the multiplicity for the original data is 2^{4} (16 QAM), resulting in a 10 Gbit/s transmission. The multiplicity *M* of the encrypted data in bits is equal to 2 bits (data) + *m* bits (basis state), where *m* is set between 3 and 10. The lengths of random patterns 1 and 2 (register size) are set at *R* = 2^{7}−1 and *B* = 2^{15}−1, respectively. The data length is given by a PRBS of 2^{15}−1.

The optical source for the transmitter is a CW, C_{2}H_{2} frequency-stabilized fiber laser with a linewidth of 4 kHz [17]. The signal passes through an EDFA and is coupled to an IQ modulator, where the coherent light is modulated with a 2.5 Gsymbol/s, encrypted 16 QAM signal and a tone signal generated by an Arbitrary Waveform Generator (AWG) running at 10 Gsample/s with a 12-bit resolution. The multiplicity of the encrypted I and Q signals, *M*, can be arbitrarily set between 32 and 4096. We adopt a Nyquist filter [18] with a roll-off factor α of 0.3 at the AWG, which enables us to reduce the bandwidth of the encrypted QAM signal. The bandwidth is 3.3 GHz, which is given by Symbol-rate × (1 + α), resulting in an SE of 3 bit/s/Hz. This is the highest SE for QSC transmission yet reported. The tone signal is used to track the optical phase of an LO under OPLL operation [19]. The optical power ratio between the encrypted QAM data and the tone signal is set at 4: 1. The power of the encrypted QAM data, *P _{out}*, at the transmitter is decreased with an attenuator to increase the level of data security against Eve. That is, we set

*P*at the lowest power level where 16 QAM data can be transmitted perfectly over 160 km in an error-free condition. After amplifying the total power of the encrypted QAM and the tone signals to 0 dBm with an EDFA, these signals are coupled into a 160 km-long transmission fiber composed of two 80 km spans of Standard Single-Mode Fiber (SSMF) and an EDFA repeater.

_{out}At the receiver, which is followed by an EDFA, the transmitted signal is combined with an LO and detected by balanced photodiodes after passing through a 90-degree optical hybrid. The detected I and Q data signals are then A/D-converted at 20 Gsamples/s with an 8-bit resolution and processed with an offline Digital Signal Processor (DSP). The demodulation bandwidth is set at 3.3 GHz by adopting a Nyquist filter. In the DSP, we first compensate for the fiber dispersion by FDE and Self Phase Modulation (SPM) impairment by time domain phase compensation. Then, the compensated *M* × *M* QAM signal is decrypted to a 16 QAM signal with a shared secret seed key. Finally, the decrypted 16 QAM signal is demodulated into binary data, and the BER is evaluated. For comparison, we also evaluate the BER performance of a one-dimensionally-encrypted 4 ASK transmission as a conventional ASK/QSC, where only I data is amplitude-modulated at the transmitter.

The Intermediate Frequency (IF) phase noise, which is estimated from the power spectrum of the Single-Side Band (SSB) phase noise of the IF signal, is 1.55 deg., whereas it is 1.50 deg. before transmission. The phase noise tolerance for 16 QAM, which is determined by the phase difference between the two nearest symbols, is as large as ± 13.3 degrees. This indicates that the OPLL operates successfully within the tolerance of phase errors for 16 QAM error-free operation.

## 4. Experimental results of 10 Gbit/s 16 QAM/QSC digital coherent transmission over 160 km

Figure 5 compares QAM/QSC (case 1) and ASK/QSC (case 2) before and after decryption. With QAM (case 1), we adopted a multiplicity *M* of 256 levels, so that the true information is hidden in a constellation of 256 × 256 symbols, which are covered with ASE noise. The normalized minimum decision level, Δ, is defined by Δ = 2/(*M*−1), where the I and Q levels are normalized to ± 1. Here, the output power from the transmitter, *P _{out}*, which is not the transmission power through the fiber, was reduced to – 35 dBm to decrease the OSNR against Eve. After the decryption with the secret seed keys, we can obtain the original data as clear 16 QAM data as shown on the right. Case 2 is shown below and the corresponding decrypted 4 ASK data are shown on the right, where

*P*was reduced by 3 dB to – 38 dBm to match the OSNR of the QAM transmission.

_{out}We observed error-free transmissions at *P _{out}* above –38 dBm for 16 QAM and at

*P*above −41 dBm for 4-ASK. Here, the error-free condition is defined as a BER below 3 × 10

_{out}^{−5}, which was the minimum BER value that could be measured in our system with a data length of 2

^{15}−1. Therefore,

*P*of −38 dBm, which is equivalent to an OSNR of 12 dB in our experiment, is the optimum operation power for QAM/QSC. The transmission power in the fiber is kept at 0 dBm in all the transmission experiments. A 3 dB difference between the

_{out}*P*of 4-ASK and 16 QAM comes from the fact that the I and Q components were set at −41 dBm (equivalent to that of 4 ASK) resulting in a total

_{out}*P*of −38 dBm in the QAM signal.

_{out}We estimate the noise distribution values, ${\overline{\sigma}}_{16\text{QAM}}$ and ${\overline{\sigma}}_{\text{4ASK}}$, around the symbols for the decrypted 16 QAM and 4 ASK signals, which arise from a degradation of OSNR. We define the average noise distributions, ${\overline{\sigma}}_{16\text{QAM}}$ and ${\overline{\sigma}}_{\text{4ASK}}$, in each case as follows:

It is important to discuss how the Number of Masked Signals (NMS) of QAM/QSC, Γ_{QAM}, is related to Γ_{ASK} (NMS of ASK/QSC). We can calculate Γ_{QAM} and Γ_{ASK} from our experiments. In our experimental results as seen in Fig. 5, we have 256 encrypted levels normalized to ± 1. Hence, we have Δ = 2/(256−1). Γ_{QAM} and Γ_{ASK} are given by

_{QAM}is nearly a square multiple of Γ

_{ASK}. Figure 6 shows Γ

_{QAM}and Γ

_{ASK}as a function of the output power

*P*from the transmitter. Here,

_{out}*M*is 256 levels (2 bit data + 6 bit basis states). For a

*P*of − 38 dBm, Γ

_{out}_{ASK}is approximately 11.3 as shown with a solid red line and Γ

_{ASK}

^{2}shown with a dashed line is 128. On the other hand, Γ

_{QAM}for a

*P*of − 35 dBm is 133. This means that Γ

_{out}_{ASK}

^{2}agrees well with Γ

_{QAM}, resulting in each I and Q axis having almost the same Γ

_{ASK}. It is also important to note that there is a 3 dB difference between QAM/QSC and ASK/QSC.

The experimental results of the demodulation performance for the eavesdropper are shown in Fig. 7, where the Detection Failure Probability (DFP) is given as a function of *M*. Here, DFP is defined as the probability that the encrypted constellation point is shifted to a different constellation point. The DFP is measured by comparing the *M* × *M* (32 × 32~4096 × 4096) QAM data pattern at the receiver with the original *M* × *M* QAM electrical data pattern at the transmitter. In addition, the DFP is detected under a back-to-back (b-b) condition without transmission fibers because the highest OSNR can be obtained for Eve. When Eve detects the encrypted data from the transmission fiber, the DFP increases. When the transmitted signal is outside the area of Δ^{2}, it becomes an error. In both figures, we kept *P _{out}* = −38 dBm for ASK and

*P*= −35 dBm for QAM to ensure the same OSNR. It is clearly seen that the DFP reaches unity much faster in

_{out}*M*×

*M*QAM than

*M*-ASK. Since each symbol point for Eve has a DFP close to unity, it is very difficult to find the secret seed key because such a DFP continues for a time given by the shared key length divided by the basis state length (

*m*bits). This means that much better performance as an encryption protocol can be obtained in QAM/QSC.

Γ_{QAM} and Γ_{ASK} as a function of multiplicity *M* are summarized in Fig. 8. Γ_{ASK} reported in ref [20]. is also plotted, which completely overlaps our experimental result plotted with closed squares. On the other hand, the closed circle shows our experimental data for Γ_{QAM}. It is very important to note that Γ_{QAM} becomes a square multiple of Γ_{ASK}. That is, the dotted line showing (Γ_{ASK})^{2} is in good agreement with Γ_{QAM}. It is important to note in Fig. 8 that Γ_{QAM} can easily exceed 10,000. It has been pointed out by several authors that a larger Γ in any modulation format introduces an increase in the brute-force search complexity for the shared key that follows ${\Gamma}^{k/{\mathrm{log}}_{2}M}$, where *k* is the key length [21]. Specifically, the search complexity for *M*-ary ASK/QSC is given by

*M*>>1 and used the relationship Δ = 2/(

*M*− 1) and ${M}^{1/{\mathrm{log}}_{2}M}=2$. For QAM/QSC, we have

*M*− 1), only increases to σ(2

*M*− 1) for ASK while it increases to σ

^{2}(

*M*− 1)

^{2}for QAM when the AWG resources are doubled. In this respect, a larger

*M*is advantageous for increasing the magnitude of Γ.

## 5. Summary

We have proposed a QAM/QSC and successfully demonstrated a 16 QAM/QSC transmission at 10 Gbit/s over 160 km. We showed experimentally that the strength of the secureness of the QAM/QSC becomes a square multiple compared with that of the ASK/QSC. Since we can increase the total secure capacity by increasing the multiplicity as we did in the 1024 QAM transmission, it is very promising to send 160 Gbit/s QAM/QSC data over 100 km at 10 Gsymbol/s, in a 256 QAM, and polarization-multiplexed system. If we also introduce a WDM technique, it will be possible to realize a Tbit/s secure communication system simply in the near future.

## Acknowledgment

This work is supported by a grant from the National Institute of Information and Communications Technology (NICT).

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