Abstract

We investigate the secret key rates for the recently proposed intensity-modulated dual-threshold key distribution [T. Ikuta and K. Inoue, New J. Phys. 18, 013018 (2016) [CrossRef]  ] under beam splitting attacks. We show that previous assumptions on an eavesdropper that performs hard decision measurements on the channel, overestimates the secret key rate. We discuss the impact of an eavesdropper that can measure full soft information and give the secret key rates under forward and reverse reconciliation. Further, we perform simulations for different system assumptions and show the optimal modulation depths for these systems. We also outline an attack on this protocol based on photon counting that prohibits secret key generation.

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

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References

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2018 (2)

E. Wohlgemuth, Y. Yoffe, T. Yeminy, Z. Zalevsky, and D. Sadot, “Demonstration of coherent stealthy and encrypted transmission for data center interconnection,” Opt. Express 26(6), 7638–7645 (2018).
[Crossref] [PubMed]

P. V. Trinh, T. V. Pham, N. T. Dang, H. V. Nguyen, S. X. Ng, and A. T. Pham, “Design and security analysis of quantum key distribution protocol over free-space optics using dual-threshold direct-detection receiver,” IEEE Access 6, 4159–4175 (2018).
[Crossref]

2016 (3)

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]

E. Diamanti, H-K. Lo, B. Qi, and Z. Yua, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).
[Crossref]

T. Ikuta and K. Inoue, “Intensity modulation and direct detection quantum key distribution based on quantum noise,” New Journal of Physics 18, 013018 (2016).
[Crossref]

2015 (2)

M. Bloch, M. Hayashi, and A. Thangaraj, “Error-control coding for physical-layer secrecy,” Proc. of the IEEE 103(10), 1725–1746 (2015).
[Crossref]

J. F. 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]

2014 (2)

S. Goorden, M. Horstmann, A. Mosk, B. Škorić, and P. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1(6), 421–424 (2014).
[Crossref]

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[Crossref]

2011 (2)

2005 (1)

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 fibre-optic links,” Nature 438(17), 343–346, (2005).
[Crossref] [PubMed]

2003 (1)

R. Namiki and T. Hirano, “Security of quantum cryptography using balanced homodyne detection,” Phys. Rev. A 67(2), 022308 (2003).
[Crossref]

2002 (1)

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[Crossref] [PubMed]

1993 (1)

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

1984 (1)

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Int. Conf. on Computer System and Signal Processing 560, 175–179 (1984).

1975 (1)

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

Ahlswede, R.

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

Allacher, A.

Alléaume, R.

R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Alléaumea, R.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[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 fibre-optic links,” Nature 438(17), 343–346, (2005).
[Crossref] [PubMed]

Aoki, T.

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 fibre-optic links,” Nature 438(17), 343–346, (2005).
[Crossref] [PubMed]

Asai, T.

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Int. Conf. on Computer System and Signal Processing 560, 175–179 (1984).

Bloch, M.

M. Bloch, M. Hayashi, and A. Thangaraj, “Error-control coding for physical-layer secrecy,” Proc. of the IEEE 103(10), 1725–1746 (2015).
[Crossref]

M. Bloch and J. B. Matthieu, Physical-layer security: From information theory to security engineering(Cambridge University Press, 2011).
[Crossref]

Bouda, J.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[Crossref]

R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Branciard, C.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[Crossref]

R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Int. Conf. on Computer System and Signal Processing 560, 175–179 (1984).

Chandrasekhar, S.

J. Cho, K. Guan, S. Chandrasekhar, and P. J. Winzer, “Experimental demonstration of physical-layer security in a fiber-optic link by information scramblings,” Proc. European Conference on Optical Communication (ECOC), paper W.4.P 1.SC5.55, (2016).

Cho, J.

J. Cho, K. Guan, S. Chandrasekhar, and P. J. Winzer, “Experimental demonstration of physical-layer security in a fiber-optic link by information scramblings,” Proc. European Conference on Optical Communication (ECOC), paper W.4.P 1.SC5.55, (2016).

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 fibre-optic links,” Nature 438(17), 343–346, (2005).
[Crossref] [PubMed]

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2 ed. (Wiley, New York, NY, USA2006).

Csiszár, I.

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

Dang, N. T.

P. V. Trinh, T. V. Pham, N. T. Dang, H. V. Nguyen, S. X. Ng, and A. T. Pham, “Design and security analysis of quantum key distribution protocol over free-space optics using dual-threshold direct-detection receiver,” IEEE Access 6, 4159–4175 (2018).
[Crossref]

Debuisschert, T.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[Crossref]

R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Deng, Y.

M. P. Fok, Z. Wang, Y. Deng, and P. R. Prucnal, “Optical layer security in fiber-optic networks,” IEEE Trans. Inf. Forensics Security 6(3), 725–736 (2011).
[Crossref]

Diamanti, E.

E. Diamanti, H-K. Lo, B. Qi, and Z. Yua, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).
[Crossref]

Dianati, M.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[Crossref]

R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Dixon, A. R.

Domeki, T.

Dynes, J. F.

Elschner, R.

V. Forutan, R. Elschner, C. Schmidt-Langhorst, C. Schubert, and R. F. H. Fischer, “Towards information-theoretic security in optical networks,” Photonic Networks; 18. ITG-Symposium, 64–70 (2017).

Endo, H.

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 fibre-optic links,” Nature 438(17), 343–346, (2005).
[Crossref] [PubMed]

Fischer, R. F. H.

V. Forutan, R. Elschner, C. Schmidt-Langhorst, C. Schubert, and R. F. H. Fischer, “Towards information-theoretic security in optical networks,” Photonic Networks; 18. ITG-Symposium, 64–70 (2017).

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 Security 6(3), 725–736 (2011).
[Crossref]

Forutan, V.

V. Forutan, R. Elschner, C. Schmidt-Langhorst, C. Schubert, and R. F. H. Fischer, “Towards information-theoretic security in optical networks,” Photonic Networks; 18. ITG-Symposium, 64–70 (2017).

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 fibre-optic links,” Nature 438(17), 343–346, (2005).
[Crossref] [PubMed]

Garrido-Balsells, J. M.

J. F. 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]

Gisin, N.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[Crossref]

R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Godfrey, M.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[Crossref]

R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Gomez, G.

J. F. 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]

Goorden, S.

Grangier, P.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
[Crossref]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[Crossref] [PubMed]

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Nguyen, H. V.

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P. V. Trinh, T. V. Pham, H. V. Nguyen, S. X. Ng, and A. T. Pham, “Performance of free-space QKD systems using SIM/BPSK and dual-threshold/direct-detection,” IEEE Globecom, Workshop on Quantum Communications and Information Technology, (2016).

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Painchault, P.

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Pham, T. V.

P. V. Trinh, T. V. Pham, N. T. Dang, H. V. Nguyen, S. X. Ng, and A. T. Pham, “Design and security analysis of quantum key distribution protocol over free-space optics using dual-threshold direct-detection receiver,” IEEE Access 6, 4159–4175 (2018).
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P. V. Trinh, T. V. Pham, H. V. Nguyen, S. X. Ng, and A. T. Pham, “Performance of free-space QKD systems using SIM/BPSK and dual-threshold/direct-detection,” IEEE Globecom, Workshop on Quantum Communications and Information Technology, (2016).

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Poppe, A.

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R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
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R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

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Qi, B.

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Rarity, J.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
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R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Renner, R.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
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R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Ribordy, G.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
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Riguidel, M.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
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R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

Robyr, S.

Sadot, D.

Sakai, Y.

Salvail, L.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
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Sharpe, A. W.

Shields, A.

R. Alléaumea, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, N. Lütkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “Using quantum key distribution for cryptographic purposes: A survey,” Theoretical Computer Science 560, 62–81 (2014).
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Shields, A. J.

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M. Bloch, M. Hayashi, and A. Thangaraj, “Error-control coding for physical-layer secrecy,” Proc. of the IEEE 103(10), 1725–1746 (2015).
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Theoretical Computer Science (1)

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Other (8)

R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC white paper on quantum key distribution and cryptography,” White Paper Secoqc-WP-v5, (2007).

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P. V. Trinh, T. V. Pham, H. V. Nguyen, S. X. Ng, and A. T. Pham, “Performance of free-space QKD systems using SIM/BPSK and dual-threshold/direct-detection,” IEEE Globecom, Workshop on Quantum Communications and Information Technology, (2016).

P. V. Trinh and A. T. Pham, “Design and secrecy performance of novel two-way free-space QKD protocol using standard FSO systems,” Proc. IEEE International Conference on Communications (ICC), 929–934 (2017).

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Figures (10)

Fig. 1
Fig. 1 Conceptual sketch of the modulation scheme used in IMDTD-KD. δ is the modulation depth, d the symmetric threshold chosen by Bob, and µ is the mean intensity.
Fig. 2
Fig. 2 Beam splitting channel. All the loss of the channel is assumed to be accessible to Eve.
Fig. 3
Fig. 3 Bob’s hard-decision channel modeled as a binary symmetric channel with erasures.
Fig. 4
Fig. 4 Eve’s hard-decision channel modeled as a binary symmetric channel.
Fig. 5
Fig. 5 Secret key rate (SKR) as a function of modulation depth δ. The threshold d is optimized for each value of δ. The channel transmittance is T = 0.65 and the bandwidth is RB = 1 GHz.
Fig. 6
Fig. 6 Secret key rate (SKR) as a function of modulation depth δ. The threshold d is optimized for each value of δ. The channel transmittance is T = 0.40 and the bandwidth is RB = 1 GHz.
Fig. 7
Fig. 7 Secret key rate (SKR) as a function of bandwidth and modulation depth δ. For each point, the threshold d is optimized. Channel transmittance is Tch = 0.65.
Fig. 8
Fig. 8 Variance as a function of launched optical power for Tch = 0.40 (solid lines) and Tch = 0.65 (dashed lines) and Tch = 0.80 (dotted lines) for Bob (black) and Eve (orange).
Fig. 9
Fig. 9 Optimal modulation depth δ as a function of Alice’s transmitted power for reverse reconciliation showing the case when Bob has an ideal receiver (dashed black line) and a realistic receiver (green solid line). Channel transmittance is Tch = 0.65.
Fig. 10
Fig. 10 Maximum secret key rate as a function of Alice’s transmitted Power for forward reconciliation (yellow lines) and reverse reconciliation (pink lines) shown when Bob’s receiver is deal (dotted lines) or realistic (solid lines). Channel transmittance is Tch = 0.65.

Tables (1)

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Table 1 Simulation Parameters

Equations (14)

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x = μ + δ b ,
y Bob = x P Bob + N ( 0 , σ Bob 2 ) ,
σ Bob 2 = σ T 2 + σ shot , Bob 2 ,
y Eve = x P Eve + N ( 0 , σ Eve 2 ) ,
I HD ( A ; B ) = ( 1 q ) ( 1 q ) log 2 ( 1 q ) + ( 1 q p ) log 2 ( 1 q p ) + p log 2 ( p ) ,
I HD ( A ; E ) = ( 1 q ) [ 1 + p E log 2 ( p E ) + ( 1 p E ) log 2 ( 1 p E ) ] ,
I SD ( A ; E ) = ( 1 q ) E [ log 2 p y E | x ( y E | x ) p y E ( y E ) ] ,
I SD ( B HD ; E ) = ( 1 q ) E [ log 2 p y E | x ( y E | x ^ Bob ) p y E ( y E ) ] ,
I SD ( A ; E ) = ( 1 q ) E [ log 2 p y B | x ( y B | x ) p y B ( y E ) ] ,
SKR FR | Bob-HD , Eve-HD = I HD ( A ; B ) I HD ( A ; E ) .
SKR FR | Bob-HD , Eve-SD = I HD ( A ; B ) I SD ( A ; E ) .
SKR FR | Bob-HD , Eve-SD SKR FR | Bob HD , Eve HD
SKR FR | Bob-SD , Eve-SD = I SD ( A ; B ) I SD ( A ; E ) .
SKR RR | Bob-HD , Eve-SD = I HD ( A ; B ) I SD ( B HD ; E ) .

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