Abstract

The physical-layer security of a quantum-noise randomized cipher (QNRC) system is, for the first time, quantitatively evaluated with secrecy capacity employed as the performance metric. Considering quantum noise as a channel advantage for legitimate parties over eavesdroppers, the specific wire-tap models for both channels of the key and data are built with channel outputs yielded by quantum heterodyne measurement; the general expressions of secrecy capacities for both channels are derived, where the matching codes are proved to be uniformly distributed. The maximal achievable secrecy rate of the system is proposed, under which secrecy of both the key and data is guaranteed. The influences of various system parameters on secrecy capacities are assessed in detail. The results indicate that QNRC combined with proper channel codes is a promising framework of secure communication for long distance with high speed, which can be orders of magnitude higher than the perfect secrecy rates of other encryption systems. Even if the eavesdropper intercepts more signal power than the legitimate receiver, secure communication (up to Gb/s) can still be achievable. Moreover, the secrecy of running key is found to be the main constraint to the systemic maximal secrecy rate.

© 2017 Optical Society of America

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References

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2015 (1)

K. Guan, A. Tulino, P. Winzer, and E. Soljanin, “Secrecy capacities in space-division multiplexed fiber optic communication systems,” IEEE T Inf. Foren. Sec 10(7), 1325–1335 (2015).

2014 (1)

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

2013 (1)

W. K. Harrison, J. Almeida, M. R. Bloch, S. W. McLaughlin, and J. Barros, “Coding for secrecy: an overview of error-control coding techniques for physical-layer security,” IEEE Signal Process. Mag. 30(5), 41–50 (2013).
[Crossref]

2011 (1)

H. Mahdavifar and A. Vardy, “Achieving the secrecy capacity of wiretap channels using polar codes,” IEEE Trans. Inf. Theory 57(10), 6428–6443 (2011).
[Crossref]

2009 (2)

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

2007 (3)

A. Thangaraj, D. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J. M. Merolla, “Applications of LDPC codes to the wiretap channel,” IEEE Trans. Inf. Theory 53(8), 2933–2945 (2007).
[Crossref]

O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007).
[Crossref]

M. J. Mihaljević, “Generic framework for the secure Yuen 2000 quantum-encryption protocol employing the wire-tap channel approach,” Phys. Rev. A 75(5), 052334 (2007).
[Crossref]

2006 (2)

S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. M. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006).
[Crossref]

R. Nair, H. P. Yuen, E. Corndorf, T. Eguchi, and P. Kumar, “Quantum-noise randomized ciphers,” Phys. Rev. A 74(5), 052309 (2006).
[Crossref]

2005 (4)

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “Reply to: Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 7–16 (2005).
[Crossref]

Z. L. Yuan and A. J. Shields, “Comment on “Secure Communication using Mesoscopic coherent states”,” Phys. Rev. Lett. 94(4), 048901 (2005).
[Crossref] [PubMed]

H. P. Yuen, P. Kumar, E. Corndorf, and R. Nair, “Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 1–6 (2005).
[Crossref]

H. Yuen, E. Corndorf, G. Barbosa, and P. Kumar, “Reply to Comment on Secure Communication using mesoscopic coherent states,” Phys. Rev. Lett. 94(4), 048902 (2005).
[Crossref]

2004 (1)

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “How much security does Y-00 protocol provide us?” Phys. Lett. A 327(1), 28–32 (2004).
[Crossref]

1997 (1)

P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIMA. J. Comput. (Taipei) 26(5), 1484–1509 (1997).

1975 (1)

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54(8), 1355–1387 (1975).
[Crossref]

1973 (1)

A. D. Wyner and J. Ziv, “A theorem on the entropy of certain binary sequences and applications: part I,” IEEE Trans. Inf. Theory IT-19(6), 769–772 (1973).
[Crossref]

Almeida, J.

W. K. Harrison, J. Almeida, M. R. Bloch, S. W. McLaughlin, and J. Barros, “Coding for secrecy: an overview of error-control coding techniques for physical-layer security,” IEEE Signal Process. Mag. 30(5), 41–50 (2013).
[Crossref]

Barbosa, G.

H. Yuen, E. Corndorf, G. Barbosa, and P. Kumar, “Reply to Comment on Secure Communication using mesoscopic coherent states,” Phys. Rev. Lett. 94(4), 048902 (2005).
[Crossref]

Barros, J.

W. K. Harrison, J. Almeida, M. R. Bloch, S. W. McLaughlin, and J. Barros, “Coding for secrecy: an overview of error-control coding techniques for physical-layer security,” IEEE Signal Process. Mag. 30(5), 41–50 (2013).
[Crossref]

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Bloch, M.

S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. M. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006).
[Crossref]

Bloch, M. R.

W. K. Harrison, J. Almeida, M. R. Bloch, S. W. McLaughlin, and J. Barros, “Coding for secrecy: an overview of error-control coding techniques for physical-layer security,” IEEE Signal Process. Mag. 30(5), 41–50 (2013).
[Crossref]

Calderbank, A. R.

A. Thangaraj, D. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J. M. Merolla, “Applications of LDPC codes to the wiretap channel,” IEEE Trans. Inf. Theory 53(8), 2933–2945 (2007).
[Crossref]

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Choi, I.

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Corndorf, E.

R. Nair, H. P. Yuen, E. Corndorf, T. Eguchi, and P. Kumar, “Quantum-noise randomized ciphers,” Phys. Rev. A 74(5), 052309 (2006).
[Crossref]

H. Yuen, E. Corndorf, G. Barbosa, and P. Kumar, “Reply to Comment on Secure Communication using mesoscopic coherent states,” Phys. Rev. Lett. 94(4), 048902 (2005).
[Crossref]

H. P. Yuen, P. Kumar, E. Corndorf, and R. Nair, “Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 1–6 (2005).
[Crossref]

Cussey, J.

S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. M. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006).
[Crossref]

Dihidar, D.

A. Thangaraj, D. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J. M. Merolla, “Applications of LDPC codes to the wiretap channel,” IEEE Trans. Inf. Theory 53(8), 2933–2945 (2007).
[Crossref]

Donnet, S.

S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. M. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006).
[Crossref]

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Dynes, J.

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Eguchi, T.

R. Nair, H. P. Yuen, E. Corndorf, T. Eguchi, and P. Kumar, “Quantum-noise randomized ciphers,” Phys. Rev. A 74(5), 052309 (2006).
[Crossref]

Gray, S.

K. Shaneman and S. Gray, “Optical network security: Technical analysis of fiber tapping mechanisms and methods for detection prevention,” in Proc. IEEE MILCOM (IEEE, 2004), pp. 711–716.
[Crossref]

Guan, K.

K. Guan, A. Tulino, P. Winzer, and E. Soljanin, “Secrecy capacities in space-division multiplexed fiber optic communication systems,” IEEE T Inf. Foren. Sec 10(7), 1325–1335 (2015).

Harrison, W. K.

W. K. Harrison, J. Almeida, M. R. Bloch, S. W. McLaughlin, and J. Barros, “Coding for secrecy: an overview of error-control coding techniques for physical-layer security,” IEEE Signal Process. Mag. 30(5), 41–50 (2013).
[Crossref]

Hasegawa, T.

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “Reply to: Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 7–16 (2005).
[Crossref]

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “How much security does Y-00 protocol provide us?” Phys. Lett. A 327(1), 28–32 (2004).
[Crossref]

Hirota, O.

O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007).
[Crossref]

Imafuku, K.

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “Reply to: Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 7–16 (2005).
[Crossref]

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “How much security does Y-00 protocol provide us?” Phys. Lett. A 327(1), 28–32 (2004).
[Crossref]

Imai, H.

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “Reply to: Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 7–16 (2005).
[Crossref]

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “How much security does Y-00 protocol provide us?” Phys. Lett. A 327(1), 28–32 (2004).
[Crossref]

Ishizuka, H.

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “Reply to: Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 7–16 (2005).
[Crossref]

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “How much security does Y-00 protocol provide us?” Phys. Lett. A 327(1), 28–32 (2004).
[Crossref]

Kanter, G. S.

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

Kumar, P.

R. Nair, H. P. Yuen, E. Corndorf, T. Eguchi, and P. Kumar, “Quantum-noise randomized ciphers,” Phys. Rev. A 74(5), 052309 (2006).
[Crossref]

H. P. Yuen, P. Kumar, E. Corndorf, and R. Nair, “Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 1–6 (2005).
[Crossref]

H. Yuen, E. Corndorf, G. Barbosa, and P. Kumar, “Reply to Comment on Secure Communication using mesoscopic coherent states,” Phys. Rev. Lett. 94(4), 048902 (2005).
[Crossref]

Larger, L.

S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. M. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006).
[Crossref]

Lucamarini, M.

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Lütkenhaus, N.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Mahdavifar, H.

H. Mahdavifar and A. Vardy, “Achieving the secrecy capacity of wiretap channels using polar codes,” IEEE Trans. Inf. Theory 57(10), 6428–6443 (2011).
[Crossref]

McLaughlin, S. W.

W. K. Harrison, J. Almeida, M. R. Bloch, S. W. McLaughlin, and J. Barros, “Coding for secrecy: an overview of error-control coding techniques for physical-layer security,” IEEE Signal Process. Mag. 30(5), 41–50 (2013).
[Crossref]

A. Thangaraj, D. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J. M. Merolla, “Applications of LDPC codes to the wiretap channel,” IEEE Trans. Inf. Theory 53(8), 2933–2945 (2007).
[Crossref]

Merolla, J. M.

A. Thangaraj, D. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J. M. Merolla, “Applications of LDPC codes to the wiretap channel,” IEEE Trans. Inf. Theory 53(8), 2933–2945 (2007).
[Crossref]

S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. M. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006).
[Crossref]

Mihaljevic, M. J.

M. J. Mihaljević, “Generic framework for the secure Yuen 2000 quantum-encryption protocol employing the wire-tap channel approach,” Phys. Rev. A 75(5), 052334 (2007).
[Crossref]

Nair, R.

R. Nair, H. P. Yuen, E. Corndorf, T. Eguchi, and P. Kumar, “Quantum-noise randomized ciphers,” Phys. Rev. A 74(5), 052309 (2006).
[Crossref]

H. P. Yuen, P. Kumar, E. Corndorf, and R. Nair, “Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 1–6 (2005).
[Crossref]

Nishioka, T.

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “Reply to: Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 7–16 (2005).
[Crossref]

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “How much security does Y-00 protocol provide us?” Phys. Lett. A 327(1), 28–32 (2004).
[Crossref]

Patel, K.

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Peev, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Penty, R.

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Reilly, D.

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

Scarani, V.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Shaneman, K.

K. Shaneman and S. Gray, “Optical network security: Technical analysis of fiber tapping mechanisms and methods for detection prevention,” in Proc. IEEE MILCOM (IEEE, 2004), pp. 711–716.
[Crossref]

Sharpe, A.

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Shields, A.

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Shields, A. J.

Z. L. Yuan and A. J. Shields, “Comment on “Secure Communication using Mesoscopic coherent states”,” Phys. Rev. Lett. 94(4), 048901 (2005).
[Crossref] [PubMed]

Shor, P. W.

P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIMA. J. Comput. (Taipei) 26(5), 1484–1509 (1997).

Smith, N.

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

Soljanin, E.

K. Guan, A. Tulino, P. Winzer, and E. Soljanin, “Secrecy capacities in space-division multiplexed fiber optic communication systems,” IEEE T Inf. Foren. Sec 10(7), 1325–1335 (2015).

Thangaraj, A.

A. Thangaraj, D. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J. M. Merolla, “Applications of LDPC codes to the wiretap channel,” IEEE Trans. Inf. Theory 53(8), 2933–2945 (2007).
[Crossref]

S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. M. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006).
[Crossref]

Tulino, A.

K. Guan, A. Tulino, P. Winzer, and E. Soljanin, “Secrecy capacities in space-division multiplexed fiber optic communication systems,” IEEE T Inf. Foren. Sec 10(7), 1325–1335 (2015).

Vardy, A.

H. Mahdavifar and A. Vardy, “Achieving the secrecy capacity of wiretap channels using polar codes,” IEEE Trans. Inf. Theory 57(10), 6428–6443 (2011).
[Crossref]

Winzer, P.

K. Guan, A. Tulino, P. Winzer, and E. Soljanin, “Secrecy capacities in space-division multiplexed fiber optic communication systems,” IEEE T Inf. Foren. Sec 10(7), 1325–1335 (2015).

Wyner, A. D.

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54(8), 1355–1387 (1975).
[Crossref]

A. D. Wyner and J. Ziv, “A theorem on the entropy of certain binary sequences and applications: part I,” IEEE Trans. Inf. Theory IT-19(6), 769–772 (1973).
[Crossref]

Yuan, Z. L.

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Z. L. Yuan and A. J. Shields, “Comment on “Secure Communication using Mesoscopic coherent states”,” Phys. Rev. Lett. 94(4), 048901 (2005).
[Crossref] [PubMed]

Yuen, H.

H. Yuen, E. Corndorf, G. Barbosa, and P. Kumar, “Reply to Comment on Secure Communication using mesoscopic coherent states,” Phys. Rev. Lett. 94(4), 048902 (2005).
[Crossref]

Yuen, H. P.

R. Nair, H. P. Yuen, E. Corndorf, T. Eguchi, and P. Kumar, “Quantum-noise randomized ciphers,” Phys. Rev. A 74(5), 052309 (2006).
[Crossref]

H. P. Yuen, P. Kumar, E. Corndorf, and R. Nair, “Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 1–6 (2005).
[Crossref]

Ziv, J.

A. D. Wyner and J. Ziv, “A theorem on the entropy of certain binary sequences and applications: part I,” IEEE Trans. Inf. Theory IT-19(6), 769–772 (1973).
[Crossref]

Appl. Phys. Lett. (1)

K. Patel, J. Dynes, M. Lucamarini, I. Choi, A. Sharpe, Z. L. Yuan, R. Penty, and A. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104(5), 051123 (2014).
[Crossref]

Bell Syst. Tech. J. (1)

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J. 54(8), 1355–1387 (1975).
[Crossref]

IEEE Commun. Mag. (1)

G. S. Kanter, D. Reilly, and N. Smith, “Practical physical-layer encryption: The marriage of optical noise with traditional cryptography,” IEEE Commun. Mag. 47(11), 74–81 (2009).
[Crossref]

IEEE Signal Process. Mag. (1)

W. K. Harrison, J. Almeida, M. R. Bloch, S. W. McLaughlin, and J. Barros, “Coding for secrecy: an overview of error-control coding techniques for physical-layer security,” IEEE Signal Process. Mag. 30(5), 41–50 (2013).
[Crossref]

IEEE T Inf. Foren. Sec (1)

K. Guan, A. Tulino, P. Winzer, and E. Soljanin, “Secrecy capacities in space-division multiplexed fiber optic communication systems,” IEEE T Inf. Foren. Sec 10(7), 1325–1335 (2015).

IEEE Trans. Inf. Theory (3)

A. Thangaraj, D. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J. M. Merolla, “Applications of LDPC codes to the wiretap channel,” IEEE Trans. Inf. Theory 53(8), 2933–2945 (2007).
[Crossref]

H. Mahdavifar and A. Vardy, “Achieving the secrecy capacity of wiretap channels using polar codes,” IEEE Trans. Inf. Theory 57(10), 6428–6443 (2011).
[Crossref]

A. D. Wyner and J. Ziv, “A theorem on the entropy of certain binary sequences and applications: part I,” IEEE Trans. Inf. Theory IT-19(6), 769–772 (1973).
[Crossref]

Phys. Lett. A (4)

S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J. M. Merolla, and L. Larger, “Security of Y-00 under heterodyne measurement and fast correlation attack,” Phys. Lett. A 356(6), 406–410 (2006).
[Crossref]

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “How much security does Y-00 protocol provide us?” Phys. Lett. A 327(1), 28–32 (2004).
[Crossref]

T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, and H. Imai, “Reply to: Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 7–16 (2005).
[Crossref]

H. P. Yuen, P. Kumar, E. Corndorf, and R. Nair, “Comment on: How much security does Y-00 protocol provide us?” Phys. Lett. A 346(1–3), 1–6 (2005).
[Crossref]

Phys. Rev. A (3)

R. Nair, H. P. Yuen, E. Corndorf, T. Eguchi, and P. Kumar, “Quantum-noise randomized ciphers,” Phys. Rev. A 74(5), 052309 (2006).
[Crossref]

O. Hirota, “Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol,” Phys. Rev. A 76(3), 032307 (2007).
[Crossref]

M. J. Mihaljević, “Generic framework for the secure Yuen 2000 quantum-encryption protocol employing the wire-tap channel approach,” Phys. Rev. A 75(5), 052334 (2007).
[Crossref]

Phys. Rev. Lett. (2)

H. Yuen, E. Corndorf, G. Barbosa, and P. Kumar, “Reply to Comment on Secure Communication using mesoscopic coherent states,” Phys. Rev. Lett. 94(4), 048902 (2005).
[Crossref]

Z. L. Yuan and A. J. Shields, “Comment on “Secure Communication using Mesoscopic coherent states”,” Phys. Rev. Lett. 94(4), 048901 (2005).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
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SIMA. J. Comput. (Taipei) (1)

P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIMA. J. Comput. (Taipei) 26(5), 1484–1509 (1997).

Other (3)

K. Shaneman and S. Gray, “Optical network security: Technical analysis of fiber tapping mechanisms and methods for detection prevention,” in Proc. IEEE MILCOM (IEEE, 2004), pp. 711–716.
[Crossref]

F. Futami and O. Hirota, “100 Gbit/s (10 x 10 Gbit/s) Y-00 cipher transmission over 120 km for secure optical communication between data centers,” in Proc. OECC/ACOFT2014, pp.4–6.

R. Nair, H. P. Yuen, E. Corndorf, and P. Kumar, “Reply to: Reply to: Comment on: How much security does Y-00 protocol provide us?” arXiv preprint quant-ph/ 0509092.

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Figures (10)

Fig. 1
Fig. 1

General case of wire tapping in OFC system.

Fig. 2
Fig. 2

Wire-tap channel model of the running key.

Fig. 3
Fig. 3

Wire-tap channel model of the data.

Fig. 4
Fig. 4

Secrecy capacity of the running key vs. LE, with Mb = 127, |α| = 13.5 and μ = 0.2 dB/km.

Fig. 5
Fig. 5

Secrecy capacity of running key (normalized to CMu) vs. Mb = 2l-1. Smart Eve (LE = 0) with strongest ability (r = t = 1).

Fig. 6
Fig. 6

Secrecy capacity of running key (normalized to CMu) vs. Nσ, assuming LE = 0 and r = t = 1.

Fig. 7
Fig. 7

Secrecy capacity of data vs. LB, with Nσ = 3. Smart wiretapper (LE = 0) and Mb = 127.

Fig. 8
Fig. 8

(a) Secrecy capacity of data, CSx vs. |α|, with Eve of normal ability (r = 0.01, t = 0.99); (b) CSx vs. |α|, with Eve of strongest power (r = t = 1); (c) Data capacity of main channel, CM and data capacity of wire-tap channel, CW vs. |α|, with r = 0.01, t = 0.99; (d) CM and CW vs. |α|, with r = t = 1. LB = 100km and LE = 0 for all (a)~(d).

Fig. 9
Fig. 9

Secrecy capacity of data vs. Nσ, with optimal wiretapper (r = t = 1, LE = 0), and LB = 100km.

Fig. 10
Fig. 10

Comparisons between secrecy capacities of data and running key per bit as function of |α|. Parameter values: (a) Mb = 63, LB = 100km, (b) Mb = 127, LB = 100km, (c) Mb = 255, LB = 100km, (d) Mb = 127, LB = 200km, (e) Mb = 255, LB = 200km, (f) Mb = 1023, LB = 200km, with optimal Eve (r = t = 1 and LE = 0) for all (a)~(f).

Equations (24)

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m = f ( x , u ) = u + [ x P o l ( u ) ] M b
| ϕ ( m ) = | α e i m π M b , m { 0 , 1 , , 2 M b 1 }
{ | α B | 2 = t | α | 2 e μ L B | α E | 2 = r | α | 2 e μ L E
p ( r , θ | m ) = r 2 π σ 2 exp ( | α x | 2 r 2 + 2 | α x | r cos ( θ m θ ) 2 σ 2 )
D m = { ( r , θ ) | 0 r < , θ m ' π / 2 M b θ < θ m ' + π / 2 M b } , m = 0 , 1 , , M 1
P ( m | m ) = D m p ( r , θ | m ) d r d θ
D m = { ( r , θ ) | 0 r < , θ m π / 2 θ < θ m + π / 2 } , m = m or m + M b
P ( m | m ) = D m p ( r , θ | m ) d r d θ
P ( U ^ c | U c ) = i = 1 n P ( u ^ c i | u c i ) P ( u ^ c i | u c i ) = m i m ^ i P ( u ^ c i | m ^ i ) P ( m ^ i | m i ) P ( m i | u c i )
P ( u ^ c i | u c i ) = ( P ( m ^ u ^ c i + M b | m u c i + M b ) + P ( m ^ u ^ c i | m u c i + M b ) ) P ( m u c i + M b | u c i ) + ( P ( m ^ u ^ c i | m u c i ) + P ( m ^ u ^ c i + M b | m u c i ) ) P ( m u c i | u c i )
P ( u ^ c | u c ) = ( P ( m ^ u ^ c | m u c ) + P ( m ^ u ^ c + M b | m u c ) ) ( P ( m u c i | u c i ) + P ( m u c i + M b | u c i ) ) = P ( m ^ u ^ c | m u c ) + P ( m ^ u ^ c + M b | m u c )
C S u = max P ( u c ) { I ( u c , u c ) I ( u c , u ^ c ) } = max P ( u c ) { [ H ( u c ) H ( u c | u c ) ] [ H ( u c ) H ( u c | u ^ c ) ] } = max P ( u c ) { H ( u c | u ^ c ) }
C S u = j = 0 M b 1 P ( u ^ c = j | u c = i ) log 2 P ( u ^ c = j | u c = i ) , 0 i < M b
P ( Y n | X c n ) = i = 1 n P ( y i | x c i ) , P ( Z n | X c n ) = i = 1 n P ( z i | x c i ) , P ( y i | x c i ) = m i m ^ i P ( y i | m ^ B i ) P ( m ^ B i | m i ) P ( m i | x c i ) , P ( z i | x c i ) = m i m ^ i P ( z i | m ^ E i ) P ( m ^ E i | m i ) P ( m i | x c i )
P ( m | x c ) = P ( u c )
P ( y | m ^ B ) = { 1 , m ^ B = f ( y , u c ) 0 , e l s e , P ( z | m ^ E ) = { 1 , m ^ E = f ( z , u ^ c ) 0 , e l s e
P ( z | x c ) = u c u ^ c P ( m ^ E = f ( z , u ^ c ) | m = f ( x c , u c ) ) P ( u c ) ( a ) ¯ ¯ u c P ( u c ) u ^ c P ( m ^ E = f ( z , u ^ c ) | m = f ( x c , 0 ) ) = u ^ c P ( m ^ E = f ( z , u ^ c ) | m = f ( x c , 0 ) )
P ( y | x c ) = u ^ c P ( m ^ B = f ( y , u ^ c ) | m = f ( x c , 0 ) ) ( b ) ¯ ¯ P ( m ^ B = f ( y , 0 ) | m = f ( x c , 0 ) )
P B e = P ( m ^ B = M b | m = 0 )
P E e = u ^ c P ( m ^ E = f ( 1 , u ^ c ) | m = 0 ) ( c ) ¯ ¯ i = 1 M b P ( m ^ E = 2 i 1 | m = 0 )
C S x = max P ( x c ) { I ( x c , y ) I ( x c , z ) } = max P ( x c ) { [ H ( y ) H ( y | x c ) ] [ H ( z ) H ( z | x c ) ] } = max P ( x c ) { H ( y ) H ( z ) } + H ( z | x c ) H ( y | x c ) ( d ) H ( z | x c ) H ( y | x c )
C S x = h ( P E e ) h ( P B e )
{ R x C S x l R x C S u R x min { C S x , C S u l } = min { C S x , C S u 0 }
{ | α B | | α B 0 | M b π | α E | > 1 | α B 0 | 10 β L B 20 | α | < M b π r

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