## Secure key generation using an ultra-long fiber laser: transient analysis and experiment

Optics Express, Vol. 16, Issue 21, pp. 16680-16690 (2008)

http://dx.doi.org/10.1364/OE.16.016680

Acrobat PDF (246 KB)

### Abstract

The secure distribution of a secret key is the weakest point of shared-key encryption protocols. While quantum key distribution schemes could theoretically provide unconditional security, their practical implementation remains technologically challenging. Here we provide an extended analysis and present an experimental support of a concept for a classical key generation system, based on establishing laser oscillation between two parties, which is realized using standard fiber-optic components. In our *Ultra-long Fiber Laser* (UFL) system, each user places a randomly chosen, spectrally selective mirror at his/her end of a fiber laser, with the two-mirror choice representing a key bit. We demonstrate the ability of each user to extract the mirror choice of the other using a simple analysis of the UFL signal, while an adversary can only reconstruct a small fraction of the key. The simplicity of this system renders it a promising alternative for practical key distribution in the optical domain.

© 2008 Optical Society of America

## 1. Introduction

20. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-dB channel loss using superconducting single photon detectors,” Nat. Photon. **1**, 343– 348 (2007). [CrossRef]

7. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature **414**, 413–424 (2001). [CrossRef] [PubMed]

11. C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. **84**, 3762–3764 (2004). [CrossRef]

5. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002). [CrossRef]

16. N. Lutkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A **61**, 052304 (2000). [CrossRef]

17. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A **59**, 4150–4163, (1999). [CrossRef]

5. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002). [CrossRef]

5. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002). [CrossRef]

18. P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High efficiency single photon detectors,” Phys. Rev. A **48**, R867–870 (1993). [CrossRef] [PubMed]

20. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-dB channel loss using superconducting single photon detectors,” Nat. Photon. **1**, 343– 348 (2007). [CrossRef]

**74**, 145–195 (2002). [CrossRef]

12. W.-Y. Hwang, “Quantum key distribution with high loss: towards global secure communication,” Phys. Rev. Lett. **91**, 057901 (2003). [CrossRef] [PubMed]

14. X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. **94**, 230503 (2005). [CrossRef] [PubMed]

15. Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. **92**, 201104 (2008). [CrossRef]

15. Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. **92**, 201104 (2008). [CrossRef]

19. A. Tanaka, M. Fujiwara, S. W. Nam, Y. Nambu, S. Takahashi, W. Maeda, K.-I. Yoshino, S. Miki, B. Baek, Z. Wang, A. Tajima, M. Sasaki, and A. Tomita, “Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization,” Opt. Express **16**, 11354–11360 (2008). [CrossRef] [PubMed]

20. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-dB channel loss using superconducting single photon detectors,” Nat. Photon. **1**, 343– 348 (2007). [CrossRef]

21. L. Tancevski, I. Andonovich, and J. Budin, “Secure optical network architecture utilizing wavelength hopping/time spreading codes,” IEEE Photon. Technol. Lett. **7**, 573–575 (1995). [CrossRef]

22. D. D. Sampson, G. Pendock, and R. A. Griffin, “Photonic code-division multiple-access communications,” Fiber Integr. Opt. **16**, 129–157 (1997). [CrossRef]

23. T. H. Shake, “Security performance of optical CDMA against eavesdropping,” IEEE J. Lightwave Technol. **23**, 655–670 (2005). [CrossRef]

24. T. H. Shake, “Confidentiality performance of spectral-phase-encoded optical CDMA,” IEEE J. Lightwave Technol. **23**, 1652–1663 (2005). [CrossRef]

23. T. H. Shake, “Security performance of optical CDMA against eavesdropping,” IEEE J. Lightwave Technol. **23**, 655–670 (2005). [CrossRef]

23. T. H. Shake, “Security performance of optical CDMA against eavesdropping,” IEEE J. Lightwave Technol. **23**, 655–670 (2005). [CrossRef]

**23**, 655–670 (2005). [CrossRef]

24. T. H. Shake, “Confidentiality performance of spectral-phase-encoded optical CDMA,” IEEE J. Lightwave Technol. **23**, 1652–1663 (2005). [CrossRef]

**23**, 655–670 (2005). [CrossRef]

24. T. H. Shake, “Confidentiality performance of spectral-phase-encoded optical CDMA,” IEEE J. Lightwave Technol. **23**, 1652–1663 (2005). [CrossRef]

**23**, 655–670 (2005). [CrossRef]

**23**, 1652–1663 (2005). [CrossRef]

28. J. Scheuer and J. and A. Yariv, “Giant fiber lasers: a new paradigm for secure key distribution,” Phys. Rev. Lett. **97**, 140502 (2006). [CrossRef] [PubMed]

28. J. Scheuer and J. and A. Yariv, “Giant fiber lasers: a new paradigm for secure key distribution,” Phys. Rev. Lett. **97**, 140502 (2006). [CrossRef] [PubMed]

## 3. Numerical simulations

*E*

_{+}(ω), ω denoting the optical frequency, and to the field propagating from Bob to Alice is

*E*-(ω). The fields are normalized so that the integral ∫|

*E*±(ω)|

^{2}dω represents optical power. The EDFAs used in both terminals are assumed to be identical, characterized by their small signal gain coefficient

*G*

_{0}, saturation output power

*P*and noise figure

_{sat}*NF*.

*r*(ω) and

_{A}*r*(ω) are the spectral reflectance profiles of the mirrors chosen by Alice and Bob, respectively. The fiber spans connecting the two terminals are both of length

_{B}*L*, and have the same propagation constant β.

28. J. Scheuer and J. and A. Yariv, “Giant fiber lasers: a new paradigm for secure key distribution,” Phys. Rev. Lett. **97**, 140502 (2006). [CrossRef] [PubMed]

*E*

^{l}_{±}(ω) denote the optical fields in both directions of propagation, following

*l*one way trips within the UFL. The gain coefficients

*G*

^{l}_{±}are determined by the overall input power of the EDFAs:

*E*(ω) in Eq. (1) represents the random phase optical field of the Amplified Spontaneous Emission (ASE) of the EDFAs. The power of the ASE field within a frequency window of width dω is assumed to be independent of ω:

_{s}*hν*is the energy of a single photon, and

*G*

^{l}_{±}are used in the evaluation of

*E*

^{l}_{±}(ω).

*P*

_{+}(ω)≡(ω)|

*E*

^{l}_{+}(ω)|

^{2}

*d*ω,

*l*≫1, for the four possible combinations of mirror choices. When the choices of mirrors are (0,0) or (1,1), the central lasing frequency is

*f*

_{0}or

*f*

_{1}, correspondingly. The spectra obtained for (1,0) and (0,1) mirror choices, representing ‘1’ and ‘0’ bits, are both centered at

*f*and their main lobes are identical. In order to distinguish between the two, Eve must examine the spectral side lobes, whose steady state power is 60 dB lower than that of the main lobe. The difference in the available signal power sets an inherent imbalance between the task of Alice and Bob and that of Eve, as one-way functions do in public key, data encoding schemes [29

_{c}29. R. L. Rivest, A. Shamir, and L. M. Adleman, “A method for of obtaining digital signatures and public key cryptosystems,” Commun. ACM **21**, 120–126 (1978). [CrossRef]

30. G. Brassard, “A note on the complexity of cryptography,” IEEE Trans. Inf. Theory -**IT25**, 232–233 (1979). [CrossRef]

**97**, 140502 (2006). [CrossRef] [PubMed]

*E*

^{l}_{+}(ω)|

^{2}dω for (0,1) mirror choice, generating a ‘0’ bit, for different values of

*l*following the UFL switch-on. During the few initial propagation cycles, these spectra bear a residual signature of Alice’s choice of mirror, and hence the key bit. This signature decreases gradually as the UFL approaches steady state. Even though these spectrally asymmetric transient signals are weak, they could disclose the key to Eve, and care must be taken to conceal them.

*V*. Figure 2(b) shows simulated probability distribution functions of

_{E}*V*, taken 3 ms following the switch-on of a 25 km long UFL, for (0,1) and (1,0) mirror choices. Let us denote these functions as

_{E}*P*

_{01}(

*V*) and

_{E}*P*

_{10}(

*V*), respectively. Here,

_{E}*V*is normalized by the mean side lobe power. In order to quantify the performance of Eve’s attack, we assume that Eve has a prior knowledge of the distributions in Fig. 2(b). For each reading of her variable, Eve would guess that the particular bit was ‘0’ if

_{E}*P*

_{01}(

*V*)>

_{E}*P*

_{10}(

*V*), and vice versa. This decision criterion was shown to be optimal for binary data in the presence of noise [33]. In the ideal case of equal histograms, Eve would guess correctly only 50% of the bits, whereas if the histograms are entirely non-overlapping she can obtain 100% of the bits. In Fig. 2(b),

_{E}*P*

_{01}(

*V*) and

_{E}*P*

_{10}(

*V*) overlap only minimally, and Eve can correctly identify 95% of the bits.

_{E}*V*| is 20 dB above the shot noise equivalent power, and 30 dB above the level of the beat noise among the multiple UFL modes and the amplified spontaneous emission of the EDFAs. Therefore, an attack strategy based on the asymmetry of time resolved spectra is feasible and poses a relevant threat.

_{E}*P*

_{01}(

*V*) and

_{E}*P*

_{10}(

*V*) (Fig. 3(a)). Due to the mirror frequencies variations, Eve can only recover 75% of the key bits. In addition, the ratio of mean |

_{E}*V*| to the shot noise equivalent power is reduced to 7 dB, and the ratio of mean |

_{E}*V*| to the optical beat noise is lowered to 6 dB. Eve can try to reduce her error ratio by moving her spectral filters further away from the main lobe, making

_{E}*V*less susceptible to mirror frequency variations. However, in doing so Eve’s measurement SNR would deteriorate even further. Eve’s partial knowledge can be reduced further with cascading several intermediate filters inside the terminals. For example, Eve can only recover 60% of the key if two filters are used (Fig. 3(b)).

_{E}34. C. K. Madsen and J. H. Zhao, “A general planar waveguide autoregressive optical filter,” IEEE J. Lightwave Technol. **14**, 437–447 (1996). [CrossRef]

35. S. Wolf, “Unconditional security in cryptography,” Lectures on data security **1561**, 217–250 (1999). [CrossRef]

## 4. Experiment

*f*

_{0}or

*f*

_{1}. The frequency separation on

*f*

_{1}-

*f*

_{0}is 3 GHz. The terminals are connected by two 25 km long spans of standard single-mode fiber. Eve’s tapping coupler is placed at the very beginning of the fiber span connected to Alice’s terminal output port. Each terminal is buffered from the fiber spans by a 2X2 voltage controlled optical switch. When the switches are set to reflection mode, the UFL is effectively split into two local loops at the terminals, with no light transmitted outside the terminals. This mode of operation is used for individually tuning the peak reflectivity frequencies of the FBGs to

*f*

_{0}or

*f*

_{1}, while literally leaving Eve “in the dark”. Once the tuning is completed, the two switches are simultaneously set to transmission mode and the UFL is re-established. Light from a 30 nm wide, external noise source is coupled to the input of each EDFA, and the UFL is set to operate close to the lasing threshold. The peak reflectivity frequencies of both FBGs are randomly varied in between bits, within a range of ±500 MHz around either

*f*

_{0}or

*f*

_{1}. The small signal gain, saturation power and noise figure of the terminals’ EDFAs are 20 dB, 13 dBm and 4.5 dB, respectively. The nominal peak reflection wavelength, peak power reflectivity and full width at half maximum of the FBG mirrors are 1549.9 nm, 0.75 and 6 GHz, respectively.

*V*(

_{AB}*t*) for Alice and Bob, and

*V*(

_{E}*t*) for Eve. The UFL signal, emerging from either the analysis output ports of the terminals or from the eavesdropping coupler, is initially down-converted to the Radio Frequency (RF) domain through heterodyne beating with an external tunable laser of optical frequency

*f*

*. The difference in frequencies*

_{lo}*f*-

_{lo}*f*is set to fall within the bandwidth of a broadband detector. The detected photo-current is observed using an electrical RF spectrum analyzer, or processed further.

_{c}*V*(

_{AB}*t*),

*f*is tuned to satisfy

_{lo}*f*+

_{lo}*f*=

_{VCO}*f*. Figure 5(a) shows

_{c}*V*(

_{AB}*t*) for two different key bits, one with complementary mirror choices by Alice and Bob, and the other with identical choices. When the mirror choices of Alice and Bob are complementary, the UFL central frequency is close to

*f*and the magnitude of

_{c}*V*(

_{AB}*t*) increases following the UFL switch-on. This build-up of the signal power is an indication of the secure generation of a single key bit. On the other hand, when Alice and Bob choose identical mirrors, the lasing frequency of either

*f*

_{0}or

*f*

_{1}is detuned from

*f*+

_{lo}*f*by approximately 1.5 GHz, and no build-up is observed in

_{VCO}*V*(

_{AB}*t*). Figure 5(b) shows the histograms of the root-mean-square (RMS) values of

*V*(

_{AB}*t*=3 ms), for 1000 random bits. As seen in the figure, a clear distinction between securely generated bits and those who should be discarded is established. The probability of Alice or Bob making a wrong decision is 0.006.

*V*(

_{E}*t*) is calculated by detuning the local oscillator from

*f*-

_{c}*f*by a frequency offset Δ

_{VCO}*f*, in attempt to recover residual spectral asymmetries. Figure 6 shows the histograms of the RMS value of

*V*(

_{E}*t*=3 ms) for 1000 bits. As seen in the figure, the ranges of Eve’s decision variable for (1,0) and (0,1) choice bits overlap almost entirely. Eve’s error probability was 30–40% for all examined values of Δ

*f*and

*t*. The range of Δ

*f*was restricted to ±1 GHz by the noise floor of our detection scheme.

## 5. Summary

19. A. Tanaka, M. Fujiwara, S. W. Nam, Y. Nambu, S. Takahashi, W. Maeda, K.-I. Yoshino, S. Miki, B. Baek, Z. Wang, A. Tajima, M. Sasaki, and A. Tomita, “Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization,” Opt. Express **16**, 11354–11360 (2008). [CrossRef] [PubMed]

**1**, 343– 348 (2007). [CrossRef]

**97**, 140502 (2006). [CrossRef] [PubMed]

**97**, 140502 (2006). [CrossRef] [PubMed]

25. J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. **80**, 2249–2252 (1998). [CrossRef]

32. B. Alpern and F. B. Schneider, “Key exchange using keyless cryptography,” Info. Proc. Lett. **16**, 79–81 (1983). [CrossRef]

## Acknowledgments

## References and links

1. | S. Singh, |

2. | G. Vernam, “Cipher printing telegraph systems for secret wire and radio telegraphic communications,” J. Am. Inst. Electr. Eng. |

3. | C. H. Bennett and G. Brassard, “Quantum public key distribution system,” IBM Tech. Discl. Bull. |

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

5. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. |

6. | P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. |

7. | L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature |

8. | M. Aspelmeyer, H. R. Bohm, T. Gyasto, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long distance free space distribution of quantum entanglement,” Science |

9. | I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legre, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett. |

10. | R. J. Hughes, G. L. Morgan, and C. G. Peterson, “Quantum key distribution over a 48-km optical fiber network,” J. Mod. Opt. |

11. | C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. |

12. | W.-Y. Hwang, “Quantum key distribution with high loss: towards global secure communication,” Phys. Rev. Lett. |

13. | H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. |

14. | X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. |

15. | Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. |

16. | N. Lutkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A |

17. | W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A |

18. | P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High efficiency single photon detectors,” Phys. Rev. A |

19. | A. Tanaka, M. Fujiwara, S. W. Nam, Y. Nambu, S. Takahashi, W. Maeda, K.-I. Yoshino, S. Miki, B. Baek, Z. Wang, A. Tajima, M. Sasaki, and A. Tomita, “Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization,” Opt. Express |

20. | H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-dB channel loss using superconducting single photon detectors,” Nat. Photon. |

21. | L. Tancevski, I. Andonovich, and J. Budin, “Secure optical network architecture utilizing wavelength hopping/time spreading codes,” IEEE Photon. Technol. Lett. |

22. | D. D. Sampson, G. Pendock, and R. A. Griffin, “Photonic code-division multiple-access communications,” Fiber Integr. Opt. |

23. | T. H. Shake, “Security performance of optical CDMA against eavesdropping,” IEEE J. Lightwave Technol. |

24. | T. H. Shake, “Confidentiality performance of spectral-phase-encoded optical CDMA,” IEEE J. Lightwave Technol. |

25. | J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. |

26. | A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature |

27. | R. Pappu, R. Recht, J. Taylor, and N, Gershenfeld, “Physical one way functions,” Science |

28. | J. Scheuer and J. and A. Yariv, “Giant fiber lasers: a new paradigm for secure key distribution,” Phys. Rev. Lett. |

29. | R. L. Rivest, A. Shamir, and L. M. Adleman, “A method for of obtaining digital signatures and public key cryptosystems,” Commun. ACM |

30. | G. Brassard, “A note on the complexity of cryptography,” IEEE Trans. Inf. Theory - |

31. | G. A. Barbosa, “Fast and secure key distribution using mesoscopic coherence states of light,” Phys. Rev. A |

32. | B. Alpern and F. B. Schneider, “Key exchange using keyless cryptography,” Info. Proc. Lett. |

33. | J. R. Barry, E. A. Lee, and D. G. Messerschmitt, |

34. | C. K. Madsen and J. H. Zhao, “A general planar waveguide autoregressive optical filter,” IEEE J. Lightwave Technol. |

35. | S. Wolf, “Unconditional security in cryptography,” Lectures on data security |

36. | A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. |

37. | M. Anand, E. Cronin, M. Sherr, M. A. Blaze, and S. Kannan, “Security protocols with isotropic channels,” Technical report MS-CIS-06-18, Department of Computer and Information Science, University of Pennsylvania (2006). |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(140.3510) Lasers and laser optics : Lasers, fiber

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

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 15, 2008

Revised Manuscript: September 15, 2008

Manuscript Accepted: October 1, 2008

Published: October 3, 2008

**Citation**

Avi Zadok, Jacob Scheuer, Jacob Sendowski, and Amnon Yariv, "Secure key generation using an ultra-long fiber laser: transient analysis and experiment," Opt. Express **16**, 16680-16690 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16680

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### References

- S. Singh, The Code Book: The science of secrecy from ancient Egypt to quantum cryptography (Fourth Estate, 1999).
- G. Vernam, "Cipher printing telegraph systems for secret wire and radio telegraphic communications," J. Am. Inst. Electr. Eng. 45, 109-116 (1926).
- C. H. Bennett, and G. Brassard, "Quantum public key distribution system," IBM Tech. Discl. Bull. 28, 3153-3163 (1985).
- A. K. Ekert, "Quantum cryptography based on Bell�??s theorem," Phys. Rev. Lett. 67, 661-663 (1991). [CrossRef] [PubMed]
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- P. W. Shor, and J. Preskill, "Simple proof of security of the BB84 quantum key distribution protocol," Phys. Rev. Lett. 85, 441-444 (2000). [CrossRef] [PubMed]
- L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature 414, 413-424 (2001). [CrossRef] [PubMed]
- M. Aspelmeyer, H. R. Bohm, T. Gyasto, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long distance free space distribution of quantum entanglement," Science 301, 621-623 (2003). [CrossRef] [PubMed]
- I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legre, and N. Gisin, "Distribution of time-bin entangled qubits over 50 km of optical fiber," Phys. Rev. Lett. 93, 180502 (2004). [CrossRef] [PubMed]
- R. J. Hughes, G. L. Morgan, and C. G. Peterson, "Quantum key distribution over a 48-km optical fiber network," J. Mod. Opt. 47, 533-547 (2000).
- C. Gobby, Z. L. Yuan, and A. J. Shields, "Quantum key distribution over 122 km of standard telecom fiber," Appl. Phys. Lett. 84, 3762-3764 (2004). [CrossRef]
- W.-Y. Hwang, "Quantum key distribution with high loss: towards global secure communication," Phys. Rev. Lett. 91, 057901 (2003). [CrossRef] [PubMed]
- H.-K. Lo, X. Ma, and K. Chen, "Decoy state quantum key distribution," Phys. Rev. Lett. 94, 230504 (2005). [CrossRef] [PubMed]
- X.-B. Wang, "Beating the photon-number-splitting attack in practical quantum cryptography," Phys. Rev. Lett. 94, 230503 (2005). [CrossRef] [PubMed]
- Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, "Gigahertz quantum key distribution with InGaAs avalanche photodiodes," Appl. Phys. Lett. 92, 201104 (2008). [CrossRef]
- N. Lutkenhaus, "Security against individual attacks for realistic quantum key distribution," Phys. Rev. A 61, 052304 (2000). [CrossRef]
- W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Long-distance Bell-type tests using energy-time entangled photons," Phys. Rev. A 59, 4150-4163, (1999). [CrossRef]
- P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, "High efficiency single photon detectors," Phys. Rev. A 48, R867-870 (1993). [CrossRef] [PubMed]
- A. Tanaka, M. Fujiwara, S. W. Nam, Y. Nambu, S. Takahashi, W. Maeda, K.-I. Yoshino, S. Miki, B. Baek, Z. Wang, A. Tajima, M. Sasaki, and A. Tomita, "Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization," Opt. Express 16, 11354-11360 (2008). [CrossRef] [PubMed]
- H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single photon detectors," Nat. Photon. 1, 343-348 (2007). [CrossRef]
- L. Tancevski, I. Andonovich, and J. Budin, "Secure optical network architecture utilizing wavelength hopping / time spreading codes," IEEE Photon. Technol. Lett. 7, 573-575 (1995). [CrossRef]
- D. D. Sampson, G. Pendock, and R. A. Griffin, "Photonic code-division multiple-access communications," Fiber Integr. Opt. 16, 129-157 (1997). [CrossRef]
- T. H. Shake, "Security performance of optical CDMA against eavesdropping," IEEE J. Lightwave Technol. 23, 655-670 (2005). [CrossRef]
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