Abstract

We propose and experimentally demonstrate a method for generating and sharing a secret key using phase fluctuations in fiber optical links. The obtained key can be readily used to support secure communication between the parties. The security of our approach is based on a fundamental asymmetry associated with the optical physical layer: the sophistication of tools needed by an eavesdropping adversary to subvert the key establishment is significantly greater and more costly than the complexity needed by the legitimate parties to implement the scheme. In this sense, the method is similar to the classical asymmetric algorithms (Diffie-Hellman, RSA, etc.)

© 2013 Optical Society of America

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2011 (6)

K. Ren, H. Su, and Q. Wang, “Secret key generation exploiting channel characteristics in wireless communications,” IEEE Wireless Communications18, 6–12 (2011).
[CrossRef]

M. P. Fok, Z. Wang, Y. Deng, and P. R. Prucnal, “Optical layer security in fiber-optic networks,” IEEE Trans. Inf. Forensics Security6, 725–736 (2011).
[CrossRef]

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightwav. Technol.29, 3210–3222 (2011).
[CrossRef]

G. B. Xavier and J. P. von der Weid, “Stable single-photon interference in a 1 km fiber-optic Mach-Zehnder interferometer with continuous phase adjustment,” Opt. Lett.36, 1764–1766 (2011).
[CrossRef] [PubMed]

G. Xavier, T. da Silva, G. Tempora, and J. von der Weid, “Polarisation drift compensation in 8 km-long Mach-Zehnder fibre-optical interferometer for quantum communication,” Electron. Lett47, 608–609 (2011).
[CrossRef]

M. Sasaki, M. Fujiwara, H. Ishizuka, and , “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19, 10387 (2011).
[CrossRef] [PubMed]

2010 (7)

M. Amemiya, M. Imae, Y. Fujii, T. Suzuyama, F.-L. Hong, and M. Takamoto, “Precise frequency comparison system using bidirectional optical amplifiers,” IEEE Trans. Instr. Meas.59, 631–640 (2010).
[CrossRef]

F. Xu, B. Qi, and H.-K. Lo, “Experimental demonstration of phase-remapping attack in a practical quantum key distribution system,” New J. Phys.12, 113026 (2010).
[CrossRef]

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nature Photon.4, 686–689 (2010).
[CrossRef]

N. Patwari, J. Croft, S. Jana, and S. K. Kasera, “High-rate uncorrelated bit extraction for shared secret key generation from channel measurements,” IEEE Trans. Mobile Computing9, 17–30 (2010).
[CrossRef]

C. Ye, S. Mathur, A. Reznik, Y. Shah, W. Trappe, and N. B. Mandayam, “Information-theoretically secret key generation for fading wireless channels,” IEEE Trans. Inf. Forensics Security5, 240–254 (2010).
[CrossRef]

P.-L. Liu, “Key exchange using random signals and feedback-statistical analysis,” J. Lightwav. Technol.28, 65–70 (2010).
[CrossRef]

L. L. Kish, B. Zhang, and L. B. Kish, “Cracking the Liu key exchange protocol in its most secure state with lorentzian spectra,” Fluct. and noise lett.9, 37–45 (2010).
[CrossRef]

2009 (4)

P.-L. Liu, “A key agreement protocol using band-limited random signals and feedback,” J. Lightwav. Technol.27, 5230–5234 (2009).
[CrossRef]

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in fiber laser key distribution systems,” Phys. Lett. A373, 4287–4296 (2009).
[CrossRef]

S.-B. Cho and T.-G. Noh, “Stabilization of a long-armed fiber-optic single-photon interferometer,” Opt. Express17, 19027–19032 (2009).
[CrossRef]

G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146 km fiber link with 10−19relative accuracy,” Opt. Lett.34, 2270–2272 (2009).
[CrossRef] [PubMed]

2008 (4)

J. Minář, H. de Riedmatten, C. Simon, H. Zbinden, and N. Gisin, “Phase-noise measurements in long-fiber interferometers for quantum-repeater applications,” Phys. Rev. A77, 052325 (2008).
[CrossRef]

P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B25, 1284–1293 (2008).
[CrossRef]

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A78, 042333 (2008).
[CrossRef]

A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express16, 16680–16690 (2008).
[CrossRef] [PubMed]

2007 (5)

I. Glesk, Y.-K. Huang, C. S. Brès, and P. R. Prucnal, “Design and demonstration of a novel optical CDMA platform for use in avionics applications,” Opt. Commun.271, 65–70 (2007).
[CrossRef]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nature Photon.1, 283–287 (2007).
[CrossRef]

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum.78, 021101 (2007).
[CrossRef] [PubMed]

C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum-key-distribution systems,” Phys. Rev. A75, 032314 (2007).
[CrossRef]

S. M. Foreman, A. D. Ludlow, M. H. G. de Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1 s instability at 10−17,” Phys. Rev. Lett.99, 153601 (2007).
[CrossRef]

2006 (2)

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

B. B. Wu and E. E. Narimanov, “A method for secure communications over a public fiber-optical network,” Opt. Express14, 3738–3751 (2006).
[CrossRef] [PubMed]

2005 (1)

E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum-noise randomized data encryption for wavelength-division-multiplexed fiber-optic networks,” Phys. Rev. A71, 062326 (2005).
[CrossRef]

2004 (2)

O. Hirota, K. Katob, M. Shomac, and T. S. Usuda, “Quantum key distribution with unconditional security for all optical fiber network,” Proc. SPIE5161, 320–331 (2004).
[CrossRef]

A. Kraskov, H. Stögbauer, and P. Grassberger, “Estimating mutual information,” Phys. Rev. E69, 066138 (2004).
[CrossRef]

2003 (1)

H. Hodara, E. Miles, J. Menders, and W. Wells, “Secure fiberoptic communications,” Fiber and Integrated Optics22, 47–61 (2003).

2002 (1)

W. Wells, J. Menders, E. Miles, B. Loginov, and H. Hodara, “Another alternative to quantum cryptography,” Quant. Inform. Processing1, 91–106 (2002).
[CrossRef]

2001 (1)

J. Menders, C. Diamond, and E. Miles, “Interferometric generation of random binary keys for secure optical communication,” Proc. SPIE4471, 208–213 (2001).
[CrossRef]

1996 (1)

E. Udd, “Secure fiber optic communication system based on the Sagnac interferometer,” Proc. SPIE2837, 172–176 (1996).
[CrossRef]

1994 (1)

1993 (1)

W. Wells, R. Stone, and E. Miles, “Secure communications by optical homodyne,” IEEE J. Sel. Areas Commun.11, 770–777 (1993).
[CrossRef]

1986 (1)

A. M. Fraser and H. L. Swinney, “Independent coordinates or strange attractors from mutual information,” Phys. Rev. A33, 1134–1140 (1986).
[CrossRef] [PubMed]

Aggelos, K.

A.-S. Babak, K. Aggelos, M. Alejandra, and Y. Bulent, “Robust key generation from signal envelopes in wireless networks,” in “CCS ’07 Proceedings of the 14th ACM conference on Computer and communications security,” (2007), pp. 401–410.

Alejandra, M.

A.-S. Babak, K. Aggelos, M. Alejandra, and Y. Bulent, “Robust key generation from signal envelopes in wireless networks,” in “CCS ’07 Proceedings of the 14th ACM conference on Computer and communications security,” (2007), pp. 401–410.

Amemiya, M.

M. Amemiya, M. Imae, Y. Fujii, T. Suzuyama, F.-L. Hong, and M. Takamoto, “Precise frequency comparison system using bidirectional optical amplifiers,” IEEE Trans. Instr. Meas.59, 631–640 (2010).
[CrossRef]

Araki, S.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightwav. Technol.29, 3210–3222 (2011).
[CrossRef]

Babak, A.-S.

A.-S. Babak, K. Aggelos, M. Alejandra, and Y. Bulent, “Robust key generation from signal envelopes in wireless networks,” in “CCS ’07 Proceedings of the 14th ACM conference on Computer and communications security,” (2007), pp. 401–410.

Bar-Lev, D.

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in fiber laser key distribution systems,” Phys. Lett. A373, 4287–4296 (2009).
[CrossRef]

Bergquist, J. C.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nature Photon.1, 283–287 (2007).
[CrossRef]

Brassard, G.

G. Brassard and L. Salvail, “Secret-key reconciliation by public discussion,” in “EUROCRYPT ’93: Workshop on the theory and application of cryptographic techniques on Advances in cryptology,” (Secaucus, NJ, USA, 1994), pp. 410–423.

Brès, C. S.

I. Glesk, Y.-K. Huang, C. S. Brès, and P. R. Prucnal, “Design and demonstration of a novel optical CDMA platform for use in avionics applications,” Opt. Commun.271, 65–70 (2007).
[CrossRef]

Bulent, Y.

A.-S. Babak, K. Aggelos, M. Alejandra, and Y. Bulent, “Robust key generation from signal envelopes in wireless networks,” in “CCS ’07 Proceedings of the 14th ACM conference on Computer and communications security,” (2007), pp. 401–410.

Chen, C.

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A78, 042333 (2008).
[CrossRef]

Cho, S.-B.

Coddington, I.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nature Photon.1, 283–287 (2007).
[CrossRef]

Coq, Y. L.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nature Photon.1, 283–287 (2007).
[CrossRef]

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 networks,” Phys. Rev. A71, 062326 (2005).
[CrossRef]

Croft, J.

N. Patwari, J. Croft, S. Jana, and S. K. Kasera, “High-rate uncorrelated bit extraction for shared secret key generation from channel measurements,” IEEE Trans. Mobile Computing9, 17–30 (2010).
[CrossRef]

da Silva, T.

G. Xavier, T. da Silva, G. Tempora, and J. von der Weid, “Polarisation drift compensation in 8 km-long Mach-Zehnder fibre-optical interferometer for quantum communication,” Electron. Lett47, 608–609 (2011).
[CrossRef]

de Miranda, M. H. G.

S. M. Foreman, A. D. Ludlow, M. H. G. de Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1 s instability at 10−17,” Phys. Rev. Lett.99, 153601 (2007).
[CrossRef]

de Riedmatten, H.

J. Minář, H. de Riedmatten, C. Simon, H. Zbinden, and N. Gisin, “Phase-noise measurements in long-fiber interferometers for quantum-repeater applications,” Phys. Rev. A77, 052325 (2008).
[CrossRef]

Deng, Y.

M. P. Fok, Z. Wang, Y. Deng, and P. R. Prucnal, “Optical layer security in fiber-optic networks,” IEEE Trans. Inf. Forensics Security6, 725–736 (2011).
[CrossRef]

Diamond, C.

J. Menders, C. Diamond, and E. Miles, “Interferometric generation of random binary keys for secure optical communication,” Proc. SPIE4471, 208–213 (2001).
[CrossRef]

Diddams, S. A.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nature Photon.1, 283–287 (2007).
[CrossRef]

S. M. Foreman, A. D. Ludlow, M. H. G. de Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1 s instability at 10−17,” Phys. Rev. Lett.99, 153601 (2007).
[CrossRef]

Elser, D.

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nature Photon.4, 686–689 (2010).
[CrossRef]

Feder, K. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nature Photon.1, 283–287 (2007).
[CrossRef]

Fok, M. P.

M. P. Fok, Z. Wang, Y. Deng, and P. R. Prucnal, “Optical layer security in fiber-optic networks,” IEEE Trans. Inf. Forensics Security6, 725–736 (2011).
[CrossRef]

Foreman, S. M.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum.78, 021101 (2007).
[CrossRef] [PubMed]

S. M. Foreman, A. D. Ludlow, M. H. G. de Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1 s instability at 10−17,” Phys. Rev. Lett.99, 153601 (2007).
[CrossRef]

Fraser, A. M.

A. M. Fraser and H. L. Swinney, “Independent coordinates or strange attractors from mutual information,” Phys. Rev. A33, 1134–1140 (1986).
[CrossRef] [PubMed]

Fujii, Y.

M. Amemiya, M. Imae, Y. Fujii, T. Suzuyama, F.-L. Hong, and M. Takamoto, “Precise frequency comparison system using bidirectional optical amplifiers,” IEEE Trans. Instr. Meas.59, 631–640 (2010).
[CrossRef]

Fujiwara, M.

Fung, C.-H. F.

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A78, 042333 (2008).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Scheme of the proposed key sharing method.

Fig. 2
Fig. 2

Interference waveforms due to phase fluctuations in the Mach-Zehnder interferometer for different lengths of its arms: a. 2 m; b. 100 m; c. 26 km. The waveforms are normalized such that the in-phase (Δφ = 0) interference corresponds to 1.4 and the out-of-phase (Δφ = π) to −1.4.

Fig. 3
Fig. 3

FFT spectra of phase fluctuations in the Mach-Zehnder interferometer: a. 2 m long arms; b. 100 m long arms; c. 26 km long arms.

Fig. 4
Fig. 4

Eavesdropper tapped into the system.

Fig. 5
Fig. 5

System with added delays and physical separation between the arms of interferometer.

Fig. 6
Fig. 6

Experimental setup. ASE – broadband amplified spontaneous emission source; PD – photodiode; 2×2 – 50/50 fiber coupler; SMF – single-mode fiber; PC – polarization controller; T – variable delay line.

Fig. 7
Fig. 7

Characteristics of the broadband optical signal used in the experiments: a. optical spectrum of the signal; b. measured visibility of interference vs. time delay (length change) and the Fourier transform of the signal spectrum.

Fig. 8
Fig. 8

An example of the waveforms measured by Alice and Bob at the two ends of the 26 km long Mach-Zehnder interferometer. The signals are highly correlated, however, they have noticeable differences due to a finite time of light propagation in the interferometer.

Fig. 9
Fig. 9

FFT power spectrum of a single channel and a difference between the two channels. The power suppression of the channel difference at frequencies below 400 Hz is due to high correlation of the waveforms at low frequencies.

Fig. 10
Fig. 10

Autocorrelation functions for the two signals measured by Alice and Bob and cross-correlation between them. The inset shows the same correlation functions for a larger time span, which confirms full decorrelation for time periods larger 2 ms.

Equations (1)

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x = | 1 2 E 0 e i φ 1 + 1 2 E 0 e i φ 2 | 2 E 0 2 = 1 + cos ( φ 1 φ 2 ) 2 = 1 + cos Δ φ 2 .

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