Abstract

Common randomness arising from turbulence-induced signal fading in reciprocal optical wireless channels is a beneficial resource that can be used to generate secret keys shared by two legitimate parties. The concept of optical wireless channels using common-transverse-spatial-mode coupling (CTSMC) that can maintain perfect fading reciprocity in atmospheric turbulence is first developed in a general manner. Subsequently, by performing Monte Carlo simulations, the Johnson SB probability distribution is demonstrated to be appropriate for statistical description of turbulence-induced signal fading in an optical wireless channel constructed by use of two identical CTSMC transceivers, and the nature of correlation between signal fadings detected by two contiguous reception spatial modes is further quantitatively characterized, revealing that rapid spatial decorrelation between signal fadings observed by a legitimate party and an eavesdropper holds for scenarios of practical interest. Finally, the information theoretic capacity for generating secret keys from CTSMC-based optical wireless channels is theoretically formulated and quantitatively examined under different conditions, manifesting that the turbulence strength and average electrical signal-to-noise ratio have a noticeable combined impact on the secret key capacity, especially in the far-field case.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

D. Zou, C. Gong, and Z. Xu, “Secrecy rate of MISO optical wireless scattering communications,” IEEE Trans. Commun. 66(1), 225–238 (2018).
[Crossref]

2017 (4)

2016 (6)

2015 (3)

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photon. J. 7(2), 7901014 (2015).
[Crossref]

M. F. Haroun and T. A. Gulliver, “Secret key generation using chaotic signals over frequency selective fading channels,” IEEE Trans. Inf. Forensics Security 10(8), 1764–1775 (2015).
[Crossref]

C. Chen, H. Yang, S. Tong, and Y. Lou, “Mean-square angle-of-arrival difference between two counter-propagating spherical waves in the presence of atmospheric turbulence,” Opt. Express 23(19), 24657–24668 (2015).
[Crossref] [PubMed]

2014 (4)

N. Chandrasekaran and J. H. Shapiro, “Photon information efficient communication through atmospheric turbulence–part I: Channel model and propagation statistics,” J. Lightwave Technol. 32(6), 1075–1087 (2014).
[Crossref]

N. Wang, X. Song, J. Cheng, and V. C. Leung, “Enhancing the security of free-space optical communications with secret sharing and key agreement”, J. Opt. Commun. Netw. 6(12), 1072–1081 (2014).
[Crossref]

H. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photon. 8(8), 595–604 (2014).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

2013 (3)

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15(2), 022401 (2013).
[Crossref]

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[Crossref]

2012 (4)

L. Lai, Y. Liang, and H. V. Poor, “A unified framework for key agreement over wireless fading channels,” IEEE Trans. Inf. Forensics Security 7(2), 480–490 (2012).
[Crossref]

Y. Liu, S. C. Draper, and A. M. Sayeed, “Exploiting channel diversity in secret key generation from multipath fading randomness,” IEEE Trans. Inf. Forensics Security 7(5), 1484–1497 (2012).
[Crossref]

N. Perlot and D. Giggenbach, “Scintillation correlation between forward and return spherical waves,” Appl. Opt. 51(15), 2888–2893 (2012).
[Crossref] [PubMed]

J. H. Shapiro and A. L. Puryear, “Reciprocity-enhanced optical communication through atmospheric turbulence–Part I: Reciprocity proofs and far-field power transfer optimization,” J. Opt. Commun. Netw. 4(12), 947–954 (2012).
[Crossref]

2010 (3)

A. Belmonte, “Statistical model for fading return signals in coherent lidars,” Appl. Opt. 49, (35)6737–6748 (2010).
[Crossref] [PubMed]

J. W. Wallace and R. K. Sharma, “Automatic secret keys from reciprocal MIMO wireless channels: Measurement and analysis,” IEEE Trans. Inf. Forensics Security 5(3), 381–392 (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 Comput. 9(1), 17–30 (2010).
[Crossref]

2007 (2)

R. Wilson, D. Tse, and R. A. Scholtz, “Channel identification: Secret sharing using reciprocity in ultrawideband channels,” IEEE Trans. Inf. Forensics Security 2(3), 364–375 (2007).
[Crossref]

F. S. Vetelino, C. Young, L. Andrews, and J. Recolons, “Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence,” Appl. Opt. 46(11), 2099–2108 (2007).
[Crossref] [PubMed]

2003 (1)

J. H. Shapiro, “Near-field turbulence effects on quantum-key distribution,” Phys. Rev. A 67(2), 022309 (2003).
[Crossref]

1998 (1)

1993 (2)

U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39(3), 733–742 (1993).
[Crossref]

R. Ahlswede and I. Csiszár, “Common randomness in information theory and cryptography–part I: Secret sharing,” IEEE Trans. Inf. Theory 39(4), 1121–1132 (1993).
[Crossref]

1987 (1)

1982 (1)

V. P. Lukin and M. I. Charnotskii, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12(5), 602–605 (1982).
[Crossref]

1974 (1)

1971 (2)

Ahlswede, R.

R. Ahlswede and I. Csiszár, “Common randomness in information theory and cryptography–part I: Secret sharing,” IEEE Trans. Inf. Theory 39(4), 1121–1132 (1993).
[Crossref]

Andrews, L.

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

Aoki, T.

Bas, C. F.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Bayraktar, Ö.

Belmonte, A.

Ben, S. T.

S. T. Ben, J. B. Pierrot, and C. Castelluccia, #x0201C;An adaptive quantization algorithm for secret key generation using radio channel measurements,” in proceedings of the 3rd International Conference on New Technologies, Mobility and Security, Dec.2009, pp. 1–5.

Boche, H.

N. Tavangaran, H. Boche, and R. F. Schaefer, “Secret-key generation using compound sources and one-way public communication,” IEEE Trans. Inf. Forensics Security 12(1), 227–241 (2017).

Castelluccia, C.

S. T. Ben, J. B. Pierrot, and C. Castelluccia, #x0201C;An adaptive quantization algorithm for secret key generation using radio channel measurements,” in proceedings of the 3rd International Conference on New Technologies, Mobility and Security, Dec.2009, pp. 1–5.

Chandrasekaran, N.

Charnotskii, M. I.

V. P. Lukin and M. I. Charnotskii, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12(5), 602–605 (1982).
[Crossref]

Chen, C.

Cheng, J.

Cheung, D.

C. Prettie, D. Cheung, L. Rusch, and M. Ho, “Spatial correlation of UWB signals in a home environment,” in proceedings of 2002 IEEE Conference on Ultra Wideband Systems and Technologies, May2002, pp. 65–69.

Clark, M.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[Crossref]

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley, 2006).

Croft, J.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[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 Comput. 9(1), 17–30 (2010).
[Crossref]

Csiszár, I.

R. Ahlswede and I. Csiszár, “Common randomness in information theory and cryptography–part I: Secret sharing,” IEEE Trans. Inf. Theory 39(4), 1121–1132 (1993).
[Crossref]

Curty, M.

H. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photon. 8(8), 595–604 (2014).
[Crossref]

D’Ambrosio, V.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

DeGroot, M. H.

M. H. DeGroot and M. J. Schervish, Probability and Statistics, 4th ed. (Pearson Education, 2012).

Djordjevic, I. B.

X. Sun and I. B. Djordjevic, “Physical-layer security in orbital angular momentum multiplexing free-space optical communications,” IEEE Photon. J. 8(1), 7901110 (2016).
[Crossref]

Dolfi, D.

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15(2), 022401 (2013).
[Crossref]

Donnangelo, N. C.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Drake, M. D.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Draper, S. C.

Y. Liu, S. C. Draper, and A. M. Sayeed, “Exploiting channel diversity in secret key generation from multipath fading randomness,” IEEE Trans. Inf. Forensics Security 7(5), 1484–1497 (2012).
[Crossref]

Duplys, P.

C. Huth, R. Guillaume, T. Strohm, P. Duplys, I. A. Samuel, and T. Güneysu, “Information reconciliation schemes in physical-layer security: A survey,” Comput. Netw. 109(P1), 84–104 (2016).
[Crossref]

Elser, D.

Endo, H.

Francoeur, J.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Fujiwara, M.

Garrido-Balsells, J. M.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photon. J. 7(2), 7901014 (2015).
[Crossref]

Gervais, D. R.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Giggenbach, D.

Gomez, G.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photon. J. 7(2), 7901014 (2015).
[Crossref]

Gong, C.

Gowda, P. L.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[Crossref]

Greulich, P.

Guillaume, R.

C. Huth, R. Guillaume, T. Strohm, P. Duplys, I. A. Samuel, and T. Güneysu, “Information reconciliation schemes in physical-layer security: A survey,” Comput. Netw. 109(P1), 84–104 (2016).
[Crossref]

Gulliver, T. A.

M. F. Haroun and T. A. Gulliver, “Secret key generation using chaotic signals over frequency selective fading channels,” IEEE Trans. Inf. Forensics Security 10(8), 1764–1775 (2015).
[Crossref]

Güneysu, T.

C. Huth, R. Guillaume, T. Strohm, P. Duplys, I. A. Samuel, and T. Güneysu, “Information reconciliation schemes in physical-layer security: A survey,” Comput. Netw. 109(P1), 84–104 (2016).
[Crossref]

Günthner, K.

Gütlich, B.

Hanson, S. G.

Haroun, M. F.

M. F. Haroun and T. A. Gulliver, “Secret key generation using chaotic signals over frequency selective fading channels,” IEEE Trans. Inf. Forensics Security 10(8), 1764–1775 (2015).
[Crossref]

Heine, F.

Ho, M.

C. Prettie, D. Cheung, L. Rusch, and M. Ho, “Spatial correlation of UWB signals in a home environment,” in proceedings of 2002 IEEE Conference on Ultra Wideband Systems and Technologies, May2002, pp. 65–69.

Huang, B.

Huth, C.

C. Huth, R. Guillaume, T. Strohm, P. Duplys, I. A. Samuel, and T. Güneysu, “Information reconciliation schemes in physical-layer security: A survey,” Comput. Netw. 109(P1), 84–104 (2016).
[Crossref]

Ito, T.

Jana, S.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[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 Comput. 9(1), 17–30 (2010).
[Crossref]

Kasera, S. K.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[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 Comput. 9(1), 17–30 (2010).
[Crossref]

Khan, I.

Kitamura, M.

Kotz, S.

S. Kotz and J. R. van Dorp, Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications (World Scientific Publishing Company, 2004).
[Crossref]

Krishnamurthy, S. V.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[Crossref]

Lai, L.

L. Lai, Y. Liang, and H. V. Poor, “A unified framework for key agreement over wireless fading channels,” IEEE Trans. Inf. Forensics Security 7(2), 480–490 (2012).
[Crossref]

Laurenti, N.

Leeb, W. R.

Leuchs, G.

Leung, V. C.

Liang, Y.

L. Lai, Y. Liang, and H. V. Poor, “A unified framework for key agreement over wireless fading channels,” IEEE Trans. Inf. Forensics Security 7(2), 480–490 (2012).
[Crossref]

Liu, Y.

Y. Liu, S. C. Draper, and A. M. Sayeed, “Exploiting channel diversity in secret key generation from multipath fading randomness,” IEEE Trans. Inf. Forensics Security 7(5), 1484–1497 (2012).
[Crossref]

Lo, H.

H. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photon. 8(8), 595–604 (2014).
[Crossref]

Lopez-Martinez, F. J.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photon. J. 7(2), 7901014 (2015).
[Crossref]

Lou, Y.

Lukin, V. P.

V. P. Lukin and M. I. Charnotskii, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12(5), 602–605 (1982).
[Crossref]

Lutomirski, R. F.

Marquardt, C.

Marrucci, L.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Maurer, U. M.

U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39(3), 733–742 (1993).
[Crossref]

Minet, J.

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15(2), 022401 (2013).
[Crossref]

Müller, C. R.

Patwari, N.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[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 Comput. 9(1), 17–30 (2010).
[Crossref]

Perlot, N.

Philipp-May, S.

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

Pierrot, J. B.

S. T. Ben, J. B. Pierrot, and C. Castelluccia, #x0201C;An adaptive quantization algorithm for secret key generation using radio channel measurements,” in proceedings of the 3rd International Conference on New Technologies, Mobility and Security, Dec.2009, pp. 1–5.

Polnau, E.

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15(2), 022401 (2013).
[Crossref]

Poor, H. V.

L. Lai, Y. Liang, and H. V. Poor, “A unified framework for key agreement over wireless fading channels,” IEEE Trans. Inf. Forensics Security 7(2), 480–490 (2012).
[Crossref]

Premnath, S. N.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[Crossref]

Prettie, C.

C. Prettie, D. Cheung, L. Rusch, and M. Ho, “Spatial correlation of UWB signals in a home environment,” in proceedings of 2002 IEEE Conference on Ultra Wideband Systems and Technologies, May2002, pp. 65–69.

Puryear, A. L.

Recolons, J.

Renda, P. F.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Rusch, L.

C. Prettie, D. Cheung, L. Rusch, and M. Ho, “Spatial correlation of UWB signals in a home environment,” in proceedings of 2002 IEEE Conference on Ultra Wideband Systems and Technologies, May2002, pp. 65–69.

Rushanan, J. J.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Samuel, I. A.

C. Huth, R. Guillaume, T. Strohm, P. Duplys, I. A. Samuel, and T. Güneysu, “Information reconciliation schemes in physical-layer security: A survey,” Comput. Netw. 109(P1), 84–104 (2016).
[Crossref]

Sasaki, M.

Saucke, K.

Sayeed, A. M.

Y. Liu, S. C. Draper, and A. M. Sayeed, “Exploiting channel diversity in secret key generation from multipath fading randomness,” IEEE Trans. Inf. Forensics Security 7(5), 1484–1497 (2012).
[Crossref]

Schaefer, R. F.

N. Tavangaran, H. Boche, and R. F. Schaefer, “Secret-key generation using compound sources and one-way public communication,” IEEE Trans. Inf. Forensics Security 12(1), 227–241 (2017).

Schervish, M. J.

M. H. DeGroot and M. J. Schervish, Probability and Statistics, 4th ed. (Pearson Education, 2012).

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in Matlab (SPIE, 2010).

Scholtz, R. A.

R. Wilson, D. Tse, and R. A. Scholtz, “Channel identification: Secret sharing using reciprocity in ultrawideband channels,” IEEE Trans. Inf. Forensics Security 2(3), 364–375 (2007).
[Crossref]

Sciarrino, F.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Seel, S.

Shapiro, J. H.

Sharma, R. K.

J. W. Wallace and R. K. Sharma, “Automatic secret keys from reciprocal MIMO wireless channels: Measurement and analysis,” IEEE Trans. Inf. Forensics Security 5(3), 381–392 (2010).
[Crossref]

Shimizu, R.

Slussarenko, S.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Song, X.

Sponselli, A.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Stenner, M. D.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Stiller, B.

Strohm, T.

C. Huth, R. Guillaume, T. Strohm, P. Duplys, I. A. Samuel, and T. Güneysu, “Information reconciliation schemes in physical-layer security: A survey,” Comput. Netw. 109(P1), 84–104 (2016).
[Crossref]

Sun, X.

X. Sun and I. B. Djordjevic, “Physical-layer security in orbital angular momentum multiplexing free-space optical communications,” IEEE Photon. J. 8(1), 7901110 (2016).
[Crossref]

Takayama, Y.

Takenaka, H.

Tamaki, K.

H. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photon. 8(8), 595–604 (2014).
[Crossref]

Tavangaran, N.

N. Tavangaran, H. Boche, and R. F. Schaefer, “Secret-key generation using compound sources and one-way public communication,” IEEE Trans. Inf. Forensics Security 12(1), 227–241 (2017).

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley, 2006).

Tong, S.

Townsend, D.

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Toyoshima, M.

Tröndle, D.

Tse, D.

R. Wilson, D. Tse, and R. A. Scholtz, “Channel identification: Secret sharing using reciprocity in ultrawideband channels,” IEEE Trans. Inf. Forensics Security 2(3), 364–375 (2007).
[Crossref]

Vallone, G.

H. Endo, M. Fujiwara, M. Kitamura, T. Ito, M. Toyoshima, Y. Takayama, H. Takenaka, R. Shimizu, N. Laurenti, G. Vallone, P. Villoresi, T. Aoki, and M. Sasaki, “Free-space optical channel estimation for physical layer security,” Opt. Express 24(8), 8940–8955 (2016).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

van Dorp, J. R.

S. Kotz and J. R. van Dorp, Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications (World Scientific Publishing Company, 2004).
[Crossref]

Vetelino, F. S.

Villoresi, P.

H. Endo, M. Fujiwara, M. Kitamura, T. Ito, M. Toyoshima, Y. Takayama, H. Takenaka, R. Shimizu, N. Laurenti, G. Vallone, P. Villoresi, T. Aoki, and M. Sasaki, “Free-space optical channel estimation for physical layer security,” Opt. Express 24(8), 8940–8955 (2016).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Vorontsov, M. A.

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15(2), 022401 (2013).
[Crossref]

Wallace, J. W.

J. W. Wallace and R. K. Sharma, “Automatic secret keys from reciprocal MIMO wireless channels: Measurement and analysis,” IEEE Trans. Inf. Forensics Security 5(3), 381–392 (2010).
[Crossref]

Wang, N.

Wilson, R.

R. Wilson, D. Tse, and R. A. Scholtz, “Channel identification: Secret sharing using reciprocity in ultrawideband channels,” IEEE Trans. Inf. Forensics Security 2(3), 364–375 (2007).
[Crossref]

Winzer, P. J.

Xu, Z.

Yang, H.

Young, C.

Yura, H. T.

Zech, H.

Zou, D.

D. Zou, C. Gong, and Z. Xu, “Secrecy rate of MISO optical wireless scattering communications,” IEEE Trans. Commun. 66(1), 225–238 (2018).
[Crossref]

Appl. Opt. (5)

Comput. Netw. (1)

C. Huth, R. Guillaume, T. Strohm, P. Duplys, I. A. Samuel, and T. Güneysu, “Information reconciliation schemes in physical-layer security: A survey,” Comput. Netw. 109(P1), 84–104 (2016).
[Crossref]

IEEE Photon. J. (2)

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photon. J. 7(2), 7901014 (2015).
[Crossref]

X. Sun and I. B. Djordjevic, “Physical-layer security in orbital angular momentum multiplexing free-space optical communications,” IEEE Photon. J. 8(1), 7901110 (2016).
[Crossref]

IEEE Trans. Commun. (1)

D. Zou, C. Gong, and Z. Xu, “Secrecy rate of MISO optical wireless scattering communications,” IEEE Trans. Commun. 66(1), 225–238 (2018).
[Crossref]

IEEE Trans. Inf. Forensics Security (6)

N. Tavangaran, H. Boche, and R. F. Schaefer, “Secret-key generation using compound sources and one-way public communication,” IEEE Trans. Inf. Forensics Security 12(1), 227–241 (2017).

J. W. Wallace and R. K. Sharma, “Automatic secret keys from reciprocal MIMO wireless channels: Measurement and analysis,” IEEE Trans. Inf. Forensics Security 5(3), 381–392 (2010).
[Crossref]

L. Lai, Y. Liang, and H. V. Poor, “A unified framework for key agreement over wireless fading channels,” IEEE Trans. Inf. Forensics Security 7(2), 480–490 (2012).
[Crossref]

Y. Liu, S. C. Draper, and A. M. Sayeed, “Exploiting channel diversity in secret key generation from multipath fading randomness,” IEEE Trans. Inf. Forensics Security 7(5), 1484–1497 (2012).
[Crossref]

R. Wilson, D. Tse, and R. A. Scholtz, “Channel identification: Secret sharing using reciprocity in ultrawideband channels,” IEEE Trans. Inf. Forensics Security 2(3), 364–375 (2007).
[Crossref]

M. F. Haroun and T. A. Gulliver, “Secret key generation using chaotic signals over frequency selective fading channels,” IEEE Trans. Inf. Forensics Security 10(8), 1764–1775 (2015).
[Crossref]

IEEE Trans. Inf. Theory (2)

U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39(3), 733–742 (1993).
[Crossref]

R. Ahlswede and I. Csiszár, “Common randomness in information theory and cryptography–part I: Secret sharing,” IEEE Trans. Inf. Theory 39(4), 1121–1132 (1993).
[Crossref]

IEEE Trans. Mobile Comput. (2)

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 Comput. 9(1), 17–30 (2010).
[Crossref]

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mobile Comput. 12(5), 917–930 (2013).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. (1)

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15(2), 022401 (2013).
[Crossref]

J. Opt. Commun. Netw. (3)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nat. Photon. (1)

H. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photon. 8(8), 595–604 (2014).
[Crossref]

Opt. Eng. (1)

M. D. Drake, C. F. Bas, D. R. Gervais, P. F. Renda, D. Townsend, J. J. Rushanan, J. Francoeur, N. C. Donnangelo, and M. D. Stenner, “Optical key distribution system using atmospheric turbulence as the randomness generating function: Classical optical protocol for information assurance,” Opt. Eng. 52(5), 055008 (2013).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Optica (1)

Phys. Rev. A (1)

J. H. Shapiro, “Near-field turbulence effects on quantum-key distribution,” Phys. Rev. A 67(2), 022309 (2003).
[Crossref]

Phys. Rev. Lett. (1)

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

V. P. Lukin and M. I. Charnotskii, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12(5), 602–605 (1982).
[Crossref]

Other (7)

S. Kotz and J. R. van Dorp, Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications (World Scientific Publishing Company, 2004).
[Crossref]

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in Matlab (SPIE, 2010).

M. H. DeGroot and M. J. Schervish, Probability and Statistics, 4th ed. (Pearson Education, 2012).

C. Prettie, D. Cheung, L. Rusch, and M. Ho, “Spatial correlation of UWB signals in a home environment,” in proceedings of 2002 IEEE Conference on Ultra Wideband Systems and Technologies, May2002, pp. 65–69.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

S. T. Ben, J. B. Pierrot, and C. Castelluccia, #x0201C;An adaptive quantization algorithm for secret key generation using radio channel measurements,” in proceedings of the 3rd International Conference on New Technologies, Mobility and Security, Dec.2009, pp. 1–5.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley, 2006).

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Figures (4)

Fig. 1
Fig. 1 Schematic diagram of a bidirectional optical wireless channel with each terminal transmitting and receiving wave fields in a common transverse spatial mode; ΨA(rA) and ΨB(rB) therein are the common transverse spatial modes used by Alice’s and Bob’s terminals, respectively, which are not necessarily identical; rA and rB represent a two-dimensional point in the transverse planes at z = 0 and z = L, respectively. An eavesdropper called Eve separated from Alice by distance d is equipped with a receiving aperture centered at point rE; α is the angle that the z-axis makes with the line from point o′ to point rE.
Fig. 2
Fig. 2 Probability density function of the instantaneous signal fading ζA with different qc and L, where the plus-marks, x-marks, asterisks, triangles, circles and squares denote values determined according to numerical simulation results, and the dotted and solid curves represent the fit of a Johnson SB probability density function to the values obtained from the numerical simulation results. (a) the far-field case with qw ≡ 0.2; (b) the transition case with qw ≡ 2; (c) the near-field case with qw ≡ 20.
Fig. 3
Fig. 3 Scaled spatial correlation distance as a function of log10 (qc) with qw ≡ 0.2 and different L. The asterisks and circles denote values calculated according to numerical simulation results and the curves represent the fit of a smoothing spline to the values obtained from the numerical simulation results.
Fig. 4
Fig. 4 Secret key capacity in terms of the base-10 logarithm of the average electrical SNR with different qc. The noise variances at Alice’s and Bob’s terminals take the same value. ϑAϑB = ϑ. (a) the far-field case with qw ≡ 0.2; (b) the transition case with qw ≡ 2; (c) the near-field case with qw ≡ 20.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

U B A ( r A ) = P t , B 1 / 2 B d 2 r B Ψ B ( r B ) G B A ( r B , r A ) ,
P r , A = P t , B | A d 2 r A Ψ A * ( r A ) U B A ( r A ) | 2 = P t , B | c B A | 2
c B A = A d 2 r A B d 2 r B Ψ B ( r B ) G B A ( r B , r A ) Ψ A * ( r A ) .
P r , B = P t , A | c A B | 2
c A B = B d 2 r B A d 2 r A Ψ A ( r A ) G A B ( r A , r B ) Ψ B * ( r B ) ,
Ψ ˜ A ( r ˜ A ) = A d 2 r A Ψ A ( r A ) G A D ( r A , r ˜ A ) ,
Ψ ˜ A ( r ^ A ) = A d 2 r A Ψ A ( r A ) G A S * ( r A , r ^ A ) ,
Ψ ˜ B ( r ˜ B ) = B d 2 r B Ψ B ( r B ) G B D ( r B , r ˜ B ) ,
Ψ ^ B ( r ^ B ) = B d 2 r B Ψ B ( r B ) G B S * ( r B , r ^ B ) ,
p ζ A ( ζ A ) = δ 2 π 1 ζ A ( 1 ζ A ) exp { 1 2 [ γ + δ ln ( ζ A 1 ζ A ) ] 2 } ,
ζ ¯ A = ζ A 1
σ ζ A 2 = ζ A 2 ζ A 1 2 ,
ζ A n = 0 1 ζ A n p ζ A ( ζ A ) d ζ A
Ψ A ( r ) = Ψ B ( r ) = 2 π w 0 2 exp ( | r | 2 w 0 2 ) ,
ζ E = P r , E / P t , B = | A d 2 r A Ψ E * ( r A ) U B A ( r A ) | 2 ,
μ = ( ζ A ζ ¯ A ) ( ζ E ζ ¯ E ) ( ζ A ζ ¯ A ) 2 ( ζ E ζ ¯ E ) 2 ,
ζ ^ A = η ζ A + n A ,
ζ ^ B = η ζ B + n B ,
C k = I ( ζ ^ A ; ζ ^ B ) = h ( ζ ^ A ) h ( ζ ^ A | ζ ^ B ) = h ( ζ ^ A ) + h ( ζ ^ B ) h ( ζ ^ A , ζ ^ B ) ,
h ( ζ ^ v ) = d ζ ^ v p ζ ^ v ( ζ ^ v ) log 2 [ p ζ ^ v ( ζ ^ v ) ] ,
p ζ ^ v ( ζ ^ v ) = 1 2 π σ n , v 2 0 1 d ζ v p ζ v ( ζ v ) exp [ ( ζ ^ v η ζ v ) 2 2 σ n , 2 2 ] .
p ζ ^ v ( ζ ^ v ) = δ ϑ v 1 / 2 2 π η 0 ζ ¯ v 1 d t ( t ζ ¯ v ) 1 ( 1 t ζ ¯ v ) 1 exp [ ϑ v 2 ( ζ ^ v η ζ ^ v t ) 2 ] × exp { 1 2 [ γ + δ ln ( t ζ ¯ v 1 t ζ ¯ v ) ] 2 } ,
p ζ ^ A , ζ ^ B ( ζ ^ A , ζ ^ B ) = 1 ( 2 π ) 3 / 2 δ η 2 ζ ¯ v ϑ A 1 / 2 ϑ B 1 / 2 0 ζ ¯ v 1 d t exp { 1 2 [ γ + δ ln ( t ζ ¯ v 1 t ζ ¯ v ) ] 2 } × 1 t ζ ¯ v ( 1 t ζ ¯ v ) exp [ ϑ A 2 ( ζ ^ A η ζ ¯ v t ) 2 ϑ B 2 ( ζ ^ B η ζ ¯ v t ) 2 ] .
p ζ ^ A ( ζ ^ A ) = p ζ ^ A , ζ ^ B ( ζ ^ A , ζ ^ B ) d ζ ^ B .
h ( ζ ^ A , ζ ^ B ) = d ζ ^ A d ζ ^ B p ζ ^ A , ζ ^ B ( ζ ^ A , ζ ^ B ) log 2 [ p ζ ^ A , ζ ^ B ( ζ ^ A , ζ ^ B ) ] .