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

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  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).
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    [Crossref]
  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]
  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 438, 343–346 (2005).
    [Crossref] [PubMed]
  27. R. Pappu, R. Recht, J. Taylor, and N, Gershenfeld, “Physical one way functions,” Science 297, 2026–2030 (2002).
    [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]
  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]
  31. G. A. Barbosa, “Fast and secure key distribution using mesoscopic coherence states of light,” Phys. Rev. A  68, 052307 (2003).
    [Crossref]
  32. B. Alpern and F. B. Schneider, “Key exchange using keyless cryptography,” Info. Proc. Lett. 16, 79–81 (1983).
    [Crossref]
  33. J. R. Barry, E. A. Lee, and D. G. Messerschmitt, Digital Communication (Kluwer Academic Publisher, 3rd Ed. 2004).
  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]
  36. A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54, 1355–1387 (1975).
  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).

2008 (2)

2007 (1)

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]

2006 (1)

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]

2005 (5)

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

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

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 438, 343–346 (2005).
[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]

2004 (2)

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]

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]

2003 (3)

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

G. A. Barbosa, “Fast and secure key distribution using mesoscopic coherence states of light,” Phys. Rev. A  68, 052307 (2003).
[Crossref]

2002 (2)

R. Pappu, R. Recht, J. Taylor, and N, Gershenfeld, “Physical one way functions,” Science 297, 2026–2030 (2002).
[Crossref] [PubMed]

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

2001 (1)

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]

2000 (3)

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).

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]

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

1999 (2)

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]

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

1998 (1)

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]

1997 (1)

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

1996 (1)

C. K. Madsen and J. H. Zhao, “A general planar waveguide autoregressive optical filter,” IEEE J. Lightwave Technol. 14, 437–447 (1996).
[Crossref]

1995 (1)

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]

1993 (1)

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]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

1985 (1)

C. H. Bennett and G. Brassard, “Quantum public key distribution system,” IBM Tech. Discl. Bull. 28, 3153– 3163 (1985).

1983 (1)

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

1979 (1)

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

1978 (1)

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]

1975 (1)

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54, 1355–1387 (1975).

1926 (1)

G. Vernam, “Cipher printing telegraph systems for secret wire and radio telegraphic communications,” J. Am. Inst. Electr. Eng. 45, 109–116 (1926).

Adleman, L. M.

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]

Alpern, B.

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

Anand, M.

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).

Andonovich, I.

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]

Annovazzi-Lodi, V.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Argyris, A.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Aspelmeyer, M.

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]

Baek, B.

Barbosa, G. A.

G. A. Barbosa, “Fast and secure key distribution using mesoscopic coherence states of light,” Phys. Rev. A  68, 052307 (2003).
[Crossref]

Barry, J. R.

J. R. Barry, E. A. Lee, and D. G. Messerschmitt, Digital Communication (Kluwer Academic Publisher, 3rd Ed. 2004).

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum public key distribution system,” IBM Tech. Discl. Bull. 28, 3153– 3163 (1985).

Blaze, M. A.

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).

Bohm, H. R.

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]

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum public key distribution system,” IBM Tech. Discl. Bull. 28, 3153– 3163 (1985).

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

Brendel, J.

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]

Budin, J.

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]

Chen, K.

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Chiao, R. Y.

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]

Cirac, J. I.

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]

Colet, P.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Cronin, E.

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).

de Riedmatten, H.

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]

Dixon, A. R.

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]

Duan, L.-M.

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]

Dynes, J. F.

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]

Eberhard, P. H.

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]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Fischer, I.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Fujiwara, M.

Garcia-Ojalvo, J.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Gershenfeld, N,

R. Pappu, R. Recht, J. Taylor, and N, Gershenfeld, “Physical one way functions,” Science 297, 2026–2030 (2002).
[Crossref] [PubMed]

Gisin, N.

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]

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

Gobby, C.

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]

Goedgebuer, J.-P.

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]

Griffin, R. A.

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

Gyasto, T.

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]

Hadfield, R. H.

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]

Honjo, T.

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]

Hughes, R. J.

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).

Hwang, W.-Y.

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

Jennewein, T.

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]

Kaltenbaek, R.

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]

Kannan, S.

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).

Kwiat, P. G.

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]

Larger, L.

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 438, 343–346 (2005).
[Crossref] [PubMed]

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]

Lee, E. A.

J. R. Barry, E. A. Lee, and D. G. Messerschmitt, Digital Communication (Kluwer Academic Publisher, 3rd Ed. 2004).

Legre, M.

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]

Lindenthal, M.

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]

Lo, H.-K.

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Lukin, M. D.

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]

Lutkenhaus, N.

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

Ma, X.

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Madsen, C. K.

C. K. Madsen and J. H. Zhao, “A general planar waveguide autoregressive optical filter,” IEEE J. Lightwave Technol. 14, 437–447 (1996).
[Crossref]

Maeda, W.

Marcikic, I.

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]

Messerschmitt, D. G.

J. R. Barry, E. A. Lee, and D. G. Messerschmitt, Digital Communication (Kluwer Academic Publisher, 3rd Ed. 2004).

Miki, S.

Mirasso, C. R.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Molina-Terriza, G.

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]

Morgan, G. L.

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).

Nam, S. W.

Nambu, Y.

Pappu, R.

R. Pappu, R. Recht, J. Taylor, and N, Gershenfeld, “Physical one way functions,” Science 297, 2026–2030 (2002).
[Crossref] [PubMed]

Pendock, G.

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

Pesquera, L.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Peterson, C. G.

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).

Petroff, M. D.

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]

Poppe, A.

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]

Porte, H.

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]

Preskill, J.

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]

Recht, R.

R. Pappu, R. Recht, J. Taylor, and N, Gershenfeld, “Physical one way functions,” Science 297, 2026–2030 (2002).
[Crossref] [PubMed]

Resch, K.

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]

Ribordy, G.

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

Rivest, R. L.

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]

Sampson, D. D.

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

Sasaki, M.

Scheuer, J.

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]

Schneider, F. B.

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

Shake, T. H.

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

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

Shamir, A.

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]

Sharpe, A. W.

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]

Sherr, M.

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).

Shields, A. J.

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]

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]

Shor, P. W.

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]

Shore, K. A.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Singh, S.

S. Singh, The Code Book: The science of secrecy from ancient Egypt to quantum cryptography (Fourth Estate, 1999).

Steinberg, A. M.

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]

Syvridis, D.

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 438, 343–346 (2005).
[Crossref] [PubMed]

Tajima, A.

Takahashi, S.

Takesue, H.

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]

Tamaki, K.

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]

Tanaka, A.

Tancevski, L.

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]

Taraba, M.

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]

Taylor, J.

R. Pappu, R. Recht, J. Taylor, and N, Gershenfeld, “Physical one way functions,” Science 297, 2026–2030 (2002).
[Crossref] [PubMed]

Tittel, W.

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]

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

Tomita, A.

Ursin, R.

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]

Vernam, G.

G. Vernam, “Cipher printing telegraph systems for secret wire and radio telegraphic communications,” J. Am. Inst. Electr. Eng. 45, 109–116 (1926).

Walther, P.

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]

Wang, X.-B.

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

Wang, Z.

Wolf, S.

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

Wyner, A. D.

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54, 1355–1387 (1975).

Yamamoto, Y.

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]

Yariv, J. and A.

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]

Yoshino, K.-I.

Yuan, Z. L.

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]

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]

Zbinden, H.

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]

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

Zeilinger, A.

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]

Zhang, Q.

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]

Zhao, J. H.

C. K. Madsen and J. H. Zhao, “A general planar waveguide autoregressive optical filter,” IEEE J. Lightwave Technol. 14, 437–447 (1996).
[Crossref]

Zoller, P.

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]

Appl. Phys. Lett. (2)

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]

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]

Bell Syst. Tech. J. (1)

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54, 1355–1387 (1975).

Commun. ACM (1)

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]

Fiber Integr. Opt. (1)

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

IBM Tech. Discl. Bull. (1)

C. H. Bennett and G. Brassard, “Quantum public key distribution system,” IBM Tech. Discl. Bull. 28, 3153– 3163 (1985).

IEEE J. Lightwave Technol. (3)

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

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

C. K. Madsen and J. H. Zhao, “A general planar waveguide autoregressive optical filter,” IEEE J. Lightwave Technol. 14, 437–447 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (1)

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]

IEEE Trans. Inf. Theory (1)

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

Info. Proc. Lett. (1)

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

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

G. Vernam, “Cipher printing telegraph systems for secret wire and radio telegraphic communications,” J. Am. Inst. Electr. Eng. 45, 109–116 (1926).

J. Mod. Opt. (1)

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).

Lectures on data security (1)

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

Nat. Photon. (1)

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]

Nature (2)

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 438, 343–346 (2005).
[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]

Opt. Express (1)

Phys. Rev. A (4)

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]

G. A. Barbosa, “Fast and secure key distribution using mesoscopic coherence states of light,” Phys. Rev. A  68, 052307 (2003).
[Crossref]

Phys. Rev. Lett. (8)

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]

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]

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]

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]

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]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

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

Science (2)

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]

R. Pappu, R. Recht, J. Taylor, and N, Gershenfeld, “Physical one way functions,” Science 297, 2026–2030 (2002).
[Crossref] [PubMed]

Other (3)

J. R. Barry, E. A. Lee, and D. G. Messerschmitt, Digital Communication (Kluwer Academic Publisher, 3rd Ed. 2004).

S. Singh, The Code Book: The science of secrecy from ancient Egypt to quantum cryptography (Fourth Estate, 1999).

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).

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Figures (6)

Fig. 1.
Fig. 1. (a). Schematic of the UFL system. (b). Top: simulated steady state UFL spectra for the four possible combinations of mirror choices by Alice and Bob. The spectra for (0,1) and (1,0) mirror choices are distinguishable only in their weak spectral side lobes. Bottom: reflectivity profiles |r 0(ω)|2, |r 1(ω)|2 of ‘0’ and ‘1’ mirrors used in simulations: r 0(ω)=0.75°sinc2(ω/Δω), r 1(ω)=0.75°sinc2[(ω-ω sep )Δω], with a spectral width of Δω=2π°7GHz, and a frequency separation of ω sep ≡2π(f 1-f 0)=2π°5 GHz. The EDFAs small signal gain, saturation power and noise figure are: 10log10 G 0=17dB above transparency, Psat =13dBm and NF=3dB.

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Fig. 2.
Fig. 2. (a). Simulated time resolved spectra of the UFL signal, with mirrors choice of (0,1) corresponding to a ‘0’ bit. The spectra were calculated after 3 (red), 6 (magenta) and 10 (blue) one-way propagation cycles following the UFL switch-on. (b). Simulated histograms of the difference between the power in the left hand side lobe and that of the right hand side-lobe, 3 ms following switch-on of a 25 km long UFL. Using such time-resolved spectral measurements, Eve can recover 95% of the key.

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Fig. 3.
Fig. 3. Simulated histograms of the difference between the power in the left hand side lobe and that of the right hand side-lobe, 3 ms following the switch-on of a 25 km long UFL. The terminals include intermediate narrowband filters, with a 3 dB full width of 2.5 GHz and a 20 dB full width of 3.75 GHz. The small signal gain of the EDFAs was reduced to 10log10 G 0=7 dB. In addition, the peak reflectivity frequencies of the mirrors were randomly varied between bits, within a range of 2.5 GHz surrounding the nominal values. (a). One filter included in each terminal. (b). Two filters cascaded in each terminal

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Fig. 4.
Fig. 4. (a). Experimental setup. (b). Detection scheme for calculating Alice, Bob, and Eve’s decision variables. Black solid lines indicate optical signals. Blue dashed lines indicate RF electrical signals. The red line indicated off-line software processing of the sampled data. (c). Measured steady state spectra of the UFL subject to all four combinations of mirror choices.

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Fig. 5.
Fig. 5. (a). Alice and Bob’s decision variable VAB (t), versus time following switch-on. Significant signal power is observed when Alice and Bob share a secure key bit (blue, complementary mirror choices), no signal is observed when information represented by mirror choices is non-secure (green, identical mirror choices). (b). Histogram of the RMS value of VAB (t), taken 3 ms after the switch-on of the UFL. Blue: the decision variable distribution for secure bits, (1,0) and (0,1) mirror choices. Red: the distribution for non-secure bits, (1,1) and (0,0) choices. Setting a threshold value for VAB (t), 994 out of 1000 bits are properly categorized.

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Fig. 6.
Fig. 6. Histogram of the RMS value of Eve’s decision variable VE (t=3 ms), with a spectral detuning of Δf=600 MHz Blue: 500 different ‘0’ bits. Red: 500 different ‘1’ bits.

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Equations (4)

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E + 1 + l ( ω ) = E − l ( ω ) ( − j β L ) r A ( ω ) exp ( G + l / 2 ) + E s ( ω )
E − l + 1 ( ω ) = E + l ( ω ) exp ( − j β L ) r B ( ω ) exp ( G − l / 2 ) + E s ( ω )
G ± l = G 0 1 + ∫ ∣ E ∓ l ( ω ) ∣ 2 d ω / P sat
∣ E s ( ω ) ∣ 2 d ω = h v · NF [ exp ( G ± ) − 1 ] · d ω

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