## QAM quantum stream cipher using digital coherent optical transmission |

Optics Express, Vol. 22, Issue 4, pp. 4098-4107 (2014)

http://dx.doi.org/10.1364/OE.22.004098

Acrobat PDF (1107 KB)

### 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

4. Y. Koizumi, K. Toyoda, M. Yoshida, and M. Nakazawa, “1024 QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km,” Opt. Express **20**(11), 12508–12514 (2012). [CrossRef] [PubMed]

16. D. Reilly and G. S. Kanter, “Noise-enhanced encryption for physical layer security in an OFDM radio,” IEEE Radio and Wireless Symposium (RWS ’09), TU2P–28. [CrossRef]

## 2. Principle of QAM/QSC

*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

4. Y. Koizumi, K. Toyoda, M. Yoshida, and M. Nakazawa, “1024 QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km,” Opt. Express **20**(11), 12508–12514 (2012). [CrossRef] [PubMed]

*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}*W*= 2

*for Bob, where the 3 decision levels in the E unit for I data are given by*

^{m}*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.

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

^{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.

_{2}H

_{2}frequency-stabilized fiber laser with a linewidth of 4 kHz [17

17. K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C_{2}H_{2}) frequency-stabilized fiber laser,” IEICE Electron. Express **3**(22), 487–492 (2006). [CrossRef]

*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

19. 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]

*P*, at the transmitter is decreased with an attenuator to increase the level of data security against Eve. That is, we set

_{out}*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}## 4. Experimental results of 10 Gbit/s 16 QAM/QSC digital coherent transmission over 160 km

*P*above –38 dBm for 16 QAM and at

_{out}*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}## 5. Summary

## Acknowledgment

## References and links

1. | M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds., |

2. | A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long-haul WDM systems,” in Proceedings of OFC2006 (Anaheim, USA) PDP39. |

3. | Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” in Proceedings of OFC2008 (San Diego, USA) PDP7. |

4. | Y. Koizumi, K. Toyoda, M. Yoshida, and M. Nakazawa, “1024 QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km,” Opt. Express |

5. | C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. Int. Conf. Comput., Syst., Signal Process. (Bangalore, India, 2011) 175–179. [CrossRef] |

6. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. |

7. | T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. |

8. | G. A. Barbosa, E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. |

9. | 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 |

10. | C. Liang, G. S. Kanter, E. Corndorf, and P. Kumar, “Quantum noise protected data encryption in a WDM network,” IEEE Photon. Technol. Lett. |

11. | O. Hirota, M. Sohma, M. Fuse, and K. Kato, “Quantum stream cipher by Yuen 2000 protocol: Design and experiment by intensity modulation scheme,” Phys. Rev. A |

12. | G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. |

13. | 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. |

14. | F. Futami and O. Hirota, “40 Gbit/s (4 x 10 Gbit/s) Y-00 protocol for secure optical communication and its transmission over 120 km,” in Proceedings of OFC2012 (Los Angeles, USA) OTu1H.6. |

15. | K. Kato and O. Hirota, “Quantum quadrature amplitude modulation system and its applicability to coherent state quantum cryptography,” SPIE 5893, Quantum Communications and Quantum Imaging III (Bellingham, USA, 2005) 589303. |

16. | D. Reilly and G. S. Kanter, “Noise-enhanced encryption for physical layer security in an OFDM radio,” IEEE Radio and Wireless Symposium (RWS ’09), TU2P–28. [CrossRef] |

17. | K. Kasai, A. Suzuki, M. Yoshida, and M. Nakazawa, “Performance improvement of an acetylene (C |

18. | H. Nyquist, “Certain topics in telegraph transmission theory,” Transact. Am. Inst. Elec. Eng. |

19. | 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 |

20. | F. Futami and O. Hirota, “Masking of 4096-level intensity modulation signals by noises for secure communication employing Y-00 cipher protocol,” in Proceedings of ECOC2011 (Geneva, Switzerland) Tu.6.C.4. |

21. | O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.4080) Fiber optics and optical communications : Modulation

(060.4785) Fiber optics and optical communications : Optical security and encryption

(060.5565) Fiber optics and optical communications : Quantum communications

**ToC Category:**

Optical Communications

**History**

Original Manuscript: December 27, 2013

Revised Manuscript: February 10, 2014

Manuscript Accepted: February 11, 2014

Published: February 13, 2014

**Citation**

Masataka Nakazawa, Masato Yoshida, Toshihiko Hirooka, and Keisuke Kasai, "QAM quantum stream cipher using digital coherent optical transmission," Opt. Express **22**, 4098-4107 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4098

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### References

- M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds., High Spectral Density Optical Transmission Technologies, Springer (2010).
- A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long-haul WDM systems,” in Proceedings of OFC2006 (Anaheim, USA) PDP39.
- Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” in Proceedings of OFC2008 (San Diego, USA) PDP7.
- Y. Koizumi, K. Toyoda, M. Yoshida, M. Nakazawa, “1024 QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km,” Opt. Express 20(11), 12508–12514 (2012). [CrossRef] [PubMed]
- C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. Int. Conf. Comput., Syst., Signal Process. (Bangalore, India, 2011) 175–179. [CrossRef]
- A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991). [CrossRef] [PubMed]
- T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84(20), 4729–4732 (2000). [CrossRef] [PubMed]
- G. A. Barbosa, E. Corndorf, P. Kumar, H. P. Yuen, “Secure communication using mesoscopic coherent states,” Phys. Rev. Lett. 90(22), 227901 (2003). [CrossRef] [PubMed]
- E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, H. P. Yuen, “Quantum noise randomized data encryption for wavelength division multiplexed fiber optic network,” Phys. Rev. A 71(6), 062326 (2005). [CrossRef]
- C. Liang, G. S. Kanter, E. Corndorf, P. Kumar, “Quantum noise protected data encryption in a WDM network,” IEEE Photon. Technol. Lett. 17(7), 1573–1575 (2005). [CrossRef]
- O. Hirota, M. Sohma, M. Fuse, K. Kato, “Quantum stream cipher by Yuen 2000 protocol: Design and experiment by intensity modulation scheme,” Phys. Rev. A 72(2), 022335 (2005). [CrossRef]
- G. S. Kanter, D. Reilly, N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009). [CrossRef]
- K. Harasawa, O. Hirota, K. Yamashita, M. Honda, K. Ohhata, S. Akutsu, T. Hosoi, 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]
- F. Futami and O. Hirota, “40 Gbit/s (4 x 10 Gbit/s) Y-00 protocol for secure optical communication and its transmission over 120 km,” in Proceedings of OFC2012 (Los Angeles, USA) OTu1H.6.
- K. Kato and O. Hirota, “Quantum quadrature amplitude modulation system and its applicability to coherent state quantum cryptography,” SPIE 5893, Quantum Communications and Quantum Imaging III (Bellingham, USA, 2005) 589303.
- D. Reilly and G. S. Kanter, “Noise-enhanced encryption for physical layer security in an OFDM radio,” IEEE Radio and Wireless Symposium (RWS ’09), TU2P–28. [CrossRef]
- K. Kasai, A. Suzuki, M. Yoshida, M. Nakazawa, “Performance improvement of an acetylene (C2H2) frequency-stabilized fiber laser,” IEICE Electron. Express 3(22), 487–492 (2006). [CrossRef]
- H. Nyquist, “Certain topics in telegraph transmission theory,” Transact. Am. Inst. Elec. Eng. 47, 617–644 (1928).
- K. Kasai, J. Hongo, M. Yoshida, 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]
- F. Futami and O. Hirota, “Masking of 4096-level intensity modulation signals by noises for secure communication employing Y-00 cipher protocol,” in Proceedings of ECOC2011 (Geneva, Switzerland) Tu.6.C.4.
- O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007). [CrossRef]

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