Abstract

We demonstrate the first 40 Gbit/s single-channel polarization-multiplexed, 5 Gsymbol/s, 16 QAM quantum noise stream cipher (QNSC) transmission over 480 km by incorporating ASE quantum noise from EDFAs as well as the quantum shot noise of the coherent state with multiple photons for the random masking of data. By using a multi-bit encoded scheme and digital coherent transmission techniques, secure optical communication with a record data capacity and transmission distance has been successfully realized. In this system, the signal level received by Eve is hidden by both the amplitude and the phase noise. The highest number of masked signals, 7.5 x 104, was achieved by using a QAM scheme with FEC, which makes it possible to reduce the output power from the transmitter while maintaining an error free condition for Bob. We have newly measured the noise distribution around I and Q encrypted data and shown experimentally with a data size of as large as 225 that the noise has a Gaussian distribution with no correlations. This distribution is suitable for the random masking of data.

© 2016 Optical Society of America

1. Introduction

A high-capacity network carries personal and confidential information, and therefore, a secure optical communication network is indispensable to the Information and Communication Technologies (ICT) community. Recently, a physical layer encryption technique using quantum shot noise has attracted a lot of attention with a view to realizing a high-speed and long-distance secure optical transmission system [1–4]. In this scheme, a streamed data signal is hidden in quantum phase noise or amplitude noise; hence we refer to this as a “quantum noise stream cipher (QNSC)”. A 100 Gbit/s 10 WDM (in total 100 Gbit/s) transmission over 120 km has been reported that uses this scheme [5].

The basic security concept of QNSC relies on the fact that the probability of data being eavesdropped can ultimately be made close to zero. This is entirely different from quantum key distribution (QKD), with which perfect security is theoretically guaranteed. The degree of security of QNSC, which is defined by the detection failure probability, can be made extremely high up to a practically sufficient level. The quantity measurement of the security of the QNSC scheme depends in part on the amount of noise on the data, which corresponds to the number of masked signals (NMS). Therefore, to improve the strength of the system security, it is important to increase the NMS. To satisfy this demand, a QNSC using quadrature amplitude modulation (QAM), which employs the amplitude and phase encryption of the light beam simultaneously, has also been proposed theoretically, where the data was one bit [6]. On the other hand, we have proposed and demonstrated a real QAM/QNSC, in which the data consist of multi bit I and Q data, and have realized a 10 Gbit/s 16 QAM/QNSC transmission over 160 km [7]. In our QAM/QNSC system, the amplified spontaneous emission (ASE) noise from an erbium doped fiber amplifier (EDFA) is used for masking data as well as the quantum shot noise of the coherent state of laser light. Since the ASE occurs in a completely random process, it provides a very convenient way for our QAM/QNSC system to enhance security since EDFA repeaters are installed in the optical fiber transmission line and act as random noise sources. The ASE quantum noise is indistinguishable from the quantum shot noise of the coherent state of the lasers because they have Gaussian distributions for a large number of photons.

In this paper, we report the first single-channel 40 Gbit/s QNSC transmission over 480 km by using a polarization-multiplexed 5 Gsymbol/s, 16 QAM data format and digital coherent transmission techniques. By using I and Q encrypted signals with 4096 levels, a bit error rate (BER) below the forward error correction (FEC) threshold of 2 x 10−3 was achieved for the legitimate receiver after a 480 km transmission. Here, we could obtain a detection failure probability (DFP) of 99.9987% for the eavesdropper with the highest NMS yet realized of 7.5 x 104. We also show that even at 40 Gbit/s the NMS is increased in proportion to the square of the multiplicity of the I or Q encrypted signal, which is the same as the performance reported for 10 Gbit/s in [7]. This indicates that the masking performance is bit-rate free as long as the OSNR remains the same after the transmission. Furthermore, we have newly measured the noise distribution around the I and Q encrypted data and shown experimentally with a data size of as large as 225 that the noise has a Gaussian distribution. This distribution is suitable for the random masking of data.

2. Experimental preparation of single-channel 40 Gbit/s digital coherent QAM/QNSC transmission over 480 km

Figure 1 shows our experimental setup for 40 Gbit/s digital coherent QAM/QNSC transmission over 480 km. For comparison with our previous study [7], we increased the symbol rate of the 16 QAM original data from 2.5 to 5 Gsymbol/s and newly adopted apolarization-multiplexing scheme, resulting in a 40 Gbit/s transmission in a single channel. Furthermore, we employed an automatic polarization controller for polarization demultiplexing and digital compensation for the distortion (back-propagation method [8]) caused by the cross phase modulation between the two orthogonally polarized data at the receiver. In this scheme, 2-bit I and Q data were encrypted by using m-bit basis states. As a result, the multiplicity M of the encrypted I or Q data was equal to 2(2 + m), where m was set between 3 and 10. The lengths of the QAM data and the random pattern for the basis state were set at 215−1 and 231−1, respectively. By using a digital oscilloscope with a memory size of more than 200 Msamples, the data size for demodulation was increased to as large as 225 symbols, which was larger than the multiplicity of the encrypted M x M QAM signal. Therefore, a large number of noise measurements were guaranteed to enable us to evaluate the masking effect on the encrypted signal even when M was set at 4096.

 

Fig. 1 Experimental setup for single-channel 40 Gbit/s digital coherent QAM/QNSC transmission over 480 km.

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The optical source for the transmitter was a CW, C2H2 frequency-stabilized fiber laser with a linewidth of 4 kHz [9]. The signal was coupled to an IQ modulator, where the coherent light was modulated with a 5 Gsymbol/s, encrypted M x M QAM signal and a tone signal generated by an arbitrary waveform generator (AWG) running at 10 Gsample/s with a 12-bit resolution. We adopted a Nyquist filter [10] with a roll-off α of 0.2 at the AWG, which enabled us to reduce the bandwidth of the encrypted QAM signal to 6 GHz. A 3.33 GHz-shifted single sideband from the carrier frequency was used as a tone signal to track the optical phase of a local oscillator (LO) under optical phase-locked loop (OPLL) operation [11]. The optical power ratio between the encrypted QAM data and the tone signal was set at 4: 1. These signals were coupled to a polarization-multiplexer to double the data rate. The power of the encrypted QAM data, Pout, at the transmitter was reduced with an attenuator to increase the level of data security against Eve. By setting the signal level sufficiently low, a large shot noise, which originates from quantum noise caused by amplified spontaneous emission (ASE), is intentionally added to the received signal during the course of transmission with EDFAs. We call this a “quantum noise stream cipher (QNSC)”. That is, we set Pout at the lowest power level at which 16 QAM data can be transmitted with a BER below an FEC threshold over 480 km. After amplifying the encrypted QAM and the tone signals with an EDFA, we coupled these signals into a transmission fiber link. Part of the laser output was divided in front of the IQ modulator, and its frequency was downshifted by 3.2 GHz against the carrier frequency. This signal was used as a second tone signal for polarization demultiplexing at the receiver. The polarization and power of the second tone signal were set at the Y-axis of the encrypted QAM signal and –10 dB lower than the encrypted QAM signal, respectively. The transmission link was composed of six 80 km spans of standard single-mode fiber and an EDFA repeater.

At the receiver, the transmitted signal was combined with an LO and detected by balanced photodiodes after passing through a 90-degree optical hybrid. Since the second tone signal was set with a Y-polarization, the encrypted QAM signal could be polarization demultiplexed with an automatic polarization controller by minimizing the second tone signal level at 3.2 GHz detected at the X-polarization port. The detected I and Q data signals were then A/D-converted at 20 Gsamples/s with an 8-bit resolution and processed with an offline DSP. In the DSP, we first compensated for nonlinearities and dispersion simultaneously with a digital back-propagation method [8]. Then, the compensated M × M QAM signal was decrypted to a 16 QAM signal with a shared secret seed key. Finally, the decrypted 16 QAM signal was demodulated into binary data, and the bit error rate (BER) was evaluated.

Figures 2(a) and 2(b) show the optical spectra of the encrypted QAM signal before and after a 480 km transmission, respectively, and 2(c) shows the electrical spectrum of the demodulated signal (X-polarization) at the DSP, where Pout and the fiber launched power were set at –35 and 0 dBm, respectively. The optical signal to noise ratios (OSNRs) before and after transmission were reduced to 20.2 and 19.3 dB, respectively, due to the accumulation of ASE noise. The demodulation bandwidth was set at 6 GHz by employing a Nyquist filter as shown in Fig. 2(c). We used an additional bandwidth of 0.33 GHz to set a tone signal for the OPLL. Therefore, 40 Gbit/s data were transmitted with an optical bandwidth of 6.33 GHz, resulting in a spectral efficiency (SE) of as high as 5.9 bit/s/Hz even when taking account of the 7% FEC overhead, which is the largest yet reported in QNSC experiments. In our previous work, the SE was 2.5 bit/s/Hz and therefore we more than doubled the SE thanks to the adoption of a polarization-multiplexing scheme and the reduction of the bandwidth for a tone signal from 0.87 GHz (10 Gbit/s system) to 0.33 GHz.

 

Fig. 2 Optical spectra of the QAM/QNSC signal before (a) and after (b) 480 km transmission, and electrical spectrum of the demodulated signal at the DSP (c).

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Figure 3 shows the single sideband (SSB) noise power spectrum of a heterodyne beat note between the LO and the pilot tone after a 480 km transmission, where Pout was set at –35 dBm. By integrating this spectrum, the phase noise was estimated to be 1.43 degrees. 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 phase error tolerance for 16 QAM error-free operation.

 

Fig. 3 SSB noise power spectrum of a heterodyne beat note between the LO and the pilot tone for an OPLL after 480 km transmission.

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3. Experimental results of 40 Gbit/s 16 QAM/QNSC digital coherent transmission over 480 km

Figures 4(a) and 4(b) show the constellations of a QAM/QNSC signal after 480 km transmissions without and with decryption, respectively. In these figures, 225 symbol data are plotted by using a digital oscilloscope with a memory size of 200 Msamples. In Fig. 4(b), the original 16 QAM signal is decrypted by subtracting the basis state level from the received encrypted QAM signal level shown in Fig. 4(a). It appears as if new data were generated in the decryption process, but this is simply the result of the subtraction of the basis state offset. The transmission distance of 480 km is the largest yet reported for a QNSC experiment. We adopted a multiplicity M of 256 levels so that the true information is hidden in a constellation of 256 × 256 symbols, which is covered with ASE noise. We used standard A/D and D/A converters with an 8-bit resolution, which is compatible with a real system. 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, Pout, was reduced to –35 dBm to reduce the OSNR against Eve. Here, the electrical noise from the AWG is negligible compared with the optical noise such as the quantum noise of the laser light and the ASE noise from the EDFA. For example, QAM multiplicity up to 2048 (11 bits) can be detected without errors when the electrical data from the AWG are directly detected with a digital oscilloscope. After decryption with the secret seed keys, we can obtain the original data as clear 16 QAM data with a BER below an FEC (7% overhead) threshold of 2 x 10−3 as shown in Fig. 4(b).

 

Fig. 4 Constellation of QAM/QNSC signal after 480 km transmission without (a) and with decryption (b).

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Figure 5 shows the BER for Bob after a 480 km transmission for various powers launched into each span, where Pout was set at –35 dBm. From this result, the launched power was optimally set at 0 dBm. Figure 6 shows the BER performance after a 480 km transmission as a function of Pout. Error free operation defined by a BER of 1 x 10−9 and a BER below the FEC threshold (2 x 10−3) were obtained at Pout values above – 27.5 and – 36.5 dBm, respectively. By using FEC, the Pout value was reduced by as much as 8 dB, which can greatly increase system security.

 

Fig. 5 BER for Bob after 480 km transmission as a function of fiber launched power (Pout = –35 dBm).

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Fig. 6 BER for Bob after 480 km transmission as a function of Pout.

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On the other hand, the demodulation performance for Eve is measured under a back-to-back condition without transmission fibers because the highest OSNR can be obtained for Eve. Figure 7(a) shows the constellation of a QAM/QNSC signal with decryption under a back-to-back condition for a Pout of – 35 dBm, where a BER below the FEC threshold was achieved for Bob after a 480 km transmission. The ASE noise and the shot noise on the detected signal appeared on the decrypted 16 QAM data. Figures 7(b) and 7(c), which were measured with a data size of 225, show the noise distributions ΔI and ΔQ around the I and Q data in the constellation of the decrypted 16 QAM data. These figures show that the noise has a Gaussian distribution, which is suitable for masking data as random noise. This is quite plausible since the shot noise or Poisson noise for a large photon number approaches a Gaussian distribution.

 

Fig. 7 Constellation of QAM/QNSC signal under back-to-back condition with decryption (a) and the noise distribution around the I and Q data (b)(c).

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To evaluate the correlations in the noise around the I and Q data, we estimated the autocorrelation coefficients of the noise signals, which are defined by the following equations.

CI(τ)=nΔI(nT)ΔI(nTτ)nΔI(nT)ΔI(nT),CQ(τ)=nΔQ(nT)ΔQ(nTτ)nΔQ(nT)ΔQ(nT)
Here, τ is the time delay for the autocorrelation. Figure 8 shows calculated results for the autocorrelation coefficients. The coefficients were as small as 0.01 and almost constant as a function of τ. These results indicate that there is no measurable autocorrelation, which means that the total noise consisting of the ASE noise from the EDFA and the quantum noise from the light source can be treated as a random Gaussian noise without any correlations. This is the best condition for data masking in a QAM/QNSC system.

 

Fig. 8 Autocorrelation coefficients of the noise signals around I and Q data.

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When the received signal is outside the area of Δ2, it becomes an error. The detection failure probability (DFP) for Eve as a function of Pout is shown in Fig. 9. Here, DFP is defined as the probability that the encrypted constellation point is shifted to a different constellation point. The DFP was measured by comparing the 256 × 256 QAM data pattern at the receiver with the original 256 × 256 QAM electrical data pattern at the transmitter. A theoretical curve, which is determined solely by the OSNR of the QAM/QNSC signal in Fig. 9. There is difference between the experimental result and the theoretical curve for Pout values exceeding −30 dBm, where the resolution limit of the digital oscilloscope caused a detection error in the experiment. On the other hand, such a resolution limit is negligible for Pout values below −35 dBm, where the ASE noise from the EDFA becomes dominant. The DFP was as high as 99.7% for a Pout of –35 dBm. Figure 10 shows the DFP as a function of the multiplicity M, where Pout was set at –35 dBm. The DFP reached more than 99.998% when the multiplicity M was set at 4096.

 

Fig. 9 DFP for Eve under a back-to-back condition as a function of Pout.

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Fig. 10 DFP for Eve under a back-to-back condition as a function of the multiplicity M of an I, Q encrypted signal.

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We estimated the number of masked signals (NMS) of QAM/QNSC [7], ΓQAM, which is given by

ΓQAM=(2σ¯I/Δ)(2σ¯Q/Δ)
This value is one of the metrics for security estimation. Since the NMS is inversely proportional to the detection “success” probability (1–DFP), thus NMS = 1/(1–DFP), the NMS and DFP represent the same information as regards system security. In our experimental results, as seen in Fig. 7, 2σ¯Iand 2σ¯Iare 0.14, and Δ = 2/(256-1), resulting in ΓQAM = 319. Figure 11 shows ΓQAM as a function of multiplicity M. In the performance estimation of our system in Fig. 11, the demodulation data size of 225 is sufficient to estimate the system performance with an M of 4096. The NMS reached as high as 7.5 x 104 when the multiplicity M was increased to 4096. It is very important to note that ΓQAM becomes more than a square multiple of the NMS for intensity modulation QNSC (ΓIM = 196 for M of 4096) reported in [12] by using a QAM scheme and reducing Pout with FEC. 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 Γk/log2M, where k is the key length [13].

 

Fig. 11 NMS of QAM/QNSC ΓQAM as a function of multiplicity M.

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Here we compare the NMS performance with that of our previous 10 Gbit/s work [7]. To compensate for the OSNR degradation induced by fiber transmission, the OSNR of the output signal from the transmitter should be increased by increasing Pout. This enables Eve to detect the signal with the higher OSNR, resulting in a reduction of Γ. In our experiment, however, we compensated for the nonlinear effect in the fiber transmission line by using a digital back-propagation method. Thus, the OSNR degradation after a 480 km transmission was suppressed by only 0.9 dB as shown in Fig. 2. Therefore, we were able to obtain almost the same NMS performance as that obtained in our previous 160 km transmission experiment [7]. It is important to note that the NMS performance is bit-rate free as long as the OSNR remains the same after the transmission.

4. Summary

We have demonstrated a 16 QAM/QNSC transmission at 40 Gbit/s over 480 km for the first time under polarization-multiplexed and 5 Gsymbol/s conditions. The SE reached as high as 5.9 bit/s/Hz even when we took account of the extra bandwidth needed for the tones and the 7% FEC overhead. This system achieved a record data speed and a transmission distance with the highest SE in a QNSC transmission. The noise used in our QAM/QNSC has a Gaussian distribution with no correlations, and thus plays a very important role in data masking under complete randomization. Furthermore, the highest NMS of 7.5 x 104 was successfully achieved by using both amplitude and a phase noise masking scheme and reducing Pout with FEC. In future work, a Tera-bit/s QNSC transmission can be expected by adopting a WDM scheme.

Acknowledgment

This work was supported by the National Institute of Information and Communications Technology (NICT), Japan under “Development of secure photonic network technologies”.

References and links

1. G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003). [CrossRef]   [PubMed]  

2. E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005). [CrossRef]  

3. G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009). [CrossRef]  

4. K. Harasawa, O. Hirota, K. Yamashita, M. Honda, K. Ohhata, S. Akutsu, T. Hosoi, and Y. Doi, “Quantum encryption communication over a 192-km 2.5-Gbit/s line with optical transceivers employing Yuen-2000 protocol based on intensity modulation,” J. Lightwave Technol. 29(3), 316–323 (2011). [CrossRef]  

5. F. Futami and O. Hirota, “100 Gbit/s (10 x 10 Gbit/s) Y-00 cipher transmission over 120 km for secure optical fiber communication between data centers,” in OECC/ACOFT (2014), paper MO1A–2.

6. K. Kato and O. Hirota, “Quantum quadrature amplitude modulation system and its applicability to coherent state quantum cryptography,” Proc. SPIE 5893, 589303 (2005). [CrossRef]  

7. M. Nakazawa, M. Yoshida, T. Hirooka, and K. Kasai, “QAM quantum stream cipher using digital coherent optical transmission,” Opt. Express 22(4), 4098–4107 (2014). [CrossRef]   [PubMed]  

8. C. Paré, A. Villeneuve, P.-A. Bélanger, and N. J. Doran, “Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,” Opt. Lett. 21(7), 459–461 (1996). [CrossRef]   [PubMed]  

9. K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006). [CrossRef]  

10. H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928). [CrossRef]  

11. K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007). [CrossRef]  

12. F. Futami and O. Hirota, “Masking of 4096-level intensity modulation signals by noises for secure communication employing Y-00 cipher protocol,” in ECOC (2011), paper Tu.6.C.4.

13. O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007). [CrossRef]  

References

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  1. G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003).
    [Crossref] [PubMed]
  2. E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005).
    [Crossref]
  3. G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
    [Crossref]
  4. K. Harasawa, O. Hirota, K. Yamashita, M. Honda, K. Ohhata, S. Akutsu, T. Hosoi, and Y. Doi, “Quantum encryption communication over a 192-km 2.5-Gbit/s line with optical transceivers employing Yuen-2000 protocol based on intensity modulation,” J. Lightwave Technol. 29(3), 316–323 (2011).
    [Crossref]
  5. F. Futami and O. Hirota, “100 Gbit/s (10 x 10 Gbit/s) Y-00 cipher transmission over 120 km for secure optical fiber communication between data centers,” in OECC/ACOFT (2014), paper MO1A–2.
  6. K. Kato and O. Hirota, “Quantum quadrature amplitude modulation system and its applicability to coherent state quantum cryptography,” Proc. SPIE 5893, 589303 (2005).
    [Crossref]
  7. M. Nakazawa, M. Yoshida, T. Hirooka, and K. Kasai, “QAM quantum stream cipher using digital coherent optical transmission,” Opt. Express 22(4), 4098–4107 (2014).
    [Crossref] [PubMed]
  8. C. Paré, A. Villeneuve, P.-A. Bélanger, and N. J. Doran, “Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,” Opt. Lett. 21(7), 459–461 (1996).
    [Crossref] [PubMed]
  9. K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006).
    [Crossref]
  10. H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
    [Crossref]
  11. K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
    [Crossref]
  12. F. Futami and O. Hirota, “Masking of 4096-level intensity modulation signals by noises for secure communication employing Y-00 cipher protocol,” in ECOC (2011), paper Tu.6.C.4.
  13. O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007).
    [Crossref]

2014 (1)

2011 (1)

2009 (1)

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

2007 (2)

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007).
[Crossref]

2006 (1)

K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006).
[Crossref]

2005 (2)

K. Kato and O. Hirota, “Quantum quadrature amplitude modulation system and its applicability to coherent state quantum cryptography,” Proc. SPIE 5893, 589303 (2005).
[Crossref]

E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005).
[Crossref]

2003 (1)

G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003).
[Crossref] [PubMed]

1996 (1)

1928 (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Akutsu, S.

Barbosa, G. A.

G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003).
[Crossref] [PubMed]

Bélanger, P.-A.

Corndorf, E.

E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005).
[Crossref]

G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003).
[Crossref] [PubMed]

Doi, Y.

Doran, N. J.

Futami, F.

F. Futami and O. Hirota, “100 Gbit/s (10 x 10 Gbit/s) Y-00 cipher transmission over 120 km for secure optical fiber communication between data centers,” in OECC/ACOFT (2014), paper MO1A–2.

F. Futami and O. Hirota, “Masking of 4096-level intensity modulation signals by noises for secure communication employing Y-00 cipher protocol,” in ECOC (2011), paper Tu.6.C.4.

Harasawa, K.

Hirooka, T.

Hirota, O.

K. Harasawa, O. Hirota, K. Yamashita, M. Honda, K. Ohhata, S. Akutsu, T. Hosoi, and Y. Doi, “Quantum encryption communication over a 192-km 2.5-Gbit/s line with optical transceivers employing Yuen-2000 protocol based on intensity modulation,” J. Lightwave Technol. 29(3), 316–323 (2011).
[Crossref]

O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007).
[Crossref]

K. Kato and O. Hirota, “Quantum quadrature amplitude modulation system and its applicability to coherent state quantum cryptography,” Proc. SPIE 5893, 589303 (2005).
[Crossref]

F. Futami and O. Hirota, “100 Gbit/s (10 x 10 Gbit/s) Y-00 cipher transmission over 120 km for secure optical fiber communication between data centers,” in OECC/ACOFT (2014), paper MO1A–2.

F. Futami and O. Hirota, “Masking of 4096-level intensity modulation signals by noises for secure communication employing Y-00 cipher protocol,” in ECOC (2011), paper Tu.6.C.4.

Honda, M.

Hongo, J.

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

Hosoi, T.

Kanter, G. S.

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005).
[Crossref]

Kasai, K.

M. Nakazawa, M. Yoshida, T. Hirooka, and K. Kasai, “QAM quantum stream cipher using digital coherent optical transmission,” Opt. Express 22(4), 4098–4107 (2014).
[Crossref] [PubMed]

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006).
[Crossref]

Kato, K.

K. Kato and O. Hirota, “Quantum quadrature amplitude modulation system and its applicability to coherent state quantum cryptography,” Proc. SPIE 5893, 589303 (2005).
[Crossref]

Kumar, P.

E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005).
[Crossref]

G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003).
[Crossref] [PubMed]

Liang, C.

E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005).
[Crossref]

Nakazawa, M.

M. Nakazawa, M. Yoshida, T. Hirooka, and K. Kasai, “QAM quantum stream cipher using digital coherent optical transmission,” Opt. Express 22(4), 4098–4107 (2014).
[Crossref] [PubMed]

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006).
[Crossref]

Nyquist, H.

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Ohhata, K.

Paré, C.

Reilly, D.

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

Smith, N.

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

Suzuki, A.

K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006).
[Crossref]

Villeneuve, A.

Yamashita, K.

Yoshida, M.

M. Nakazawa, M. Yoshida, T. Hirooka, and K. Kasai, “QAM quantum stream cipher using digital coherent optical transmission,” Opt. Express 22(4), 4098–4107 (2014).
[Crossref] [PubMed]

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006).
[Crossref]

Yuen, H. P.

E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005).
[Crossref]

G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003).
[Crossref] [PubMed]

IEEE Commun. Mag. (1)

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

IEICE Electron. Express (2)

K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006).
[Crossref]

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005).
[Crossref]

O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007).
[Crossref]

Phys. Rev. Lett. (1)

G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003).
[Crossref] [PubMed]

Proc. SPIE (1)

K. Kato and O. Hirota, “Quantum quadrature amplitude modulation system and its applicability to coherent state quantum cryptography,” Proc. SPIE 5893, 589303 (2005).
[Crossref]

Trans. Am. Inst. Electr. Eng. (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Other (2)

F. Futami and O. Hirota, “100 Gbit/s (10 x 10 Gbit/s) Y-00 cipher transmission over 120 km for secure optical fiber communication between data centers,” in OECC/ACOFT (2014), paper MO1A–2.

F. Futami and O. Hirota, “Masking of 4096-level intensity modulation signals by noises for secure communication employing Y-00 cipher protocol,” in ECOC (2011), paper Tu.6.C.4.

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Figures (11)

Fig. 1
Fig. 1 Experimental setup for single-channel 40 Gbit/s digital coherent QAM/QNSC transmission over 480 km.
Fig. 2
Fig. 2 Optical spectra of the QAM/QNSC signal before (a) and after (b) 480 km transmission, and electrical spectrum of the demodulated signal at the DSP (c).
Fig. 3
Fig. 3 SSB noise power spectrum of a heterodyne beat note between the LO and the pilot tone for an OPLL after 480 km transmission.
Fig. 4
Fig. 4 Constellation of QAM/QNSC signal after 480 km transmission without (a) and with decryption (b).
Fig. 5
Fig. 5 BER for Bob after 480 km transmission as a function of fiber launched power (Pout = –35 dBm).
Fig. 6
Fig. 6 BER for Bob after 480 km transmission as a function of Pout.
Fig. 7
Fig. 7 Constellation of QAM/QNSC signal under back-to-back condition with decryption (a) and the noise distribution around the I and Q data (b)(c).
Fig. 8
Fig. 8 Autocorrelation coefficients of the noise signals around I and Q data.
Fig. 9
Fig. 9 DFP for Eve under a back-to-back condition as a function of Pout.
Fig. 10
Fig. 10 DFP for Eve under a back-to-back condition as a function of the multiplicity M of an I, Q encrypted signal.
Fig. 11
Fig. 11 NMS of QAM/QNSC ΓQAM as a function of multiplicity M.

Equations (2)

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C I (τ)= n ΔI(nT)ΔI(nTτ) n ΔI(nT)ΔI(nT) , C Q (τ)= n ΔQ(nT)ΔQ(nTτ) n ΔQ(nT)ΔQ(nT)
Γ QAM =(2 σ ¯ I /Δ)(2 σ ¯ Q /Δ)

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