Abstract

It has been proposed that a secure key distribution scheme using correlated random bit sequences can be implemented using common random-signal induced synchronization of semiconductor laser systems. In this scheme it is necessary to use laser systems consisting of multiple cascaded lasers to be secure against a powerful eavesdropper. In this paper, we report the results of an experimental study that demonstrate that the common random-signal induced synchronization is possible in cascaded semiconductor laser systems. We also show that the correlated random bit sequences generated in the synchronized cascaded laser systems can be used to create an information-theoretically secure key between two legitimate users.

©2013 Optical Society of America

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    [Crossref]
  3. A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
    [Crossref]
  4. J. Scheuer and A. Yariv, “Giant Fiber Lasers: A New Paradigm for Secure Key Distribution,” Phys. Rev. Lett. 97(14), 140502 (2006).
    [Crossref] [PubMed]
  5. A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008).
    [Crossref] [PubMed]
  6. D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in Fiber Laser Key Distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
    [Crossref]
  7. E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
    [Crossref] [PubMed]
  8. I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
    [Crossref] [PubMed]
  9. R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
    [Crossref] [PubMed]
  10. W. Diffie and M. Hellman, “New Directions in cryptography,” IEEE Trans. Inf. Theory 22(6), 644–654 (1976).
    [Crossref]
  11. C. E. Shannon, “Communication theory of secret system,” Bell Syst. Tech. J. 28, 656–715 (1949).
  12. U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39(3), 733–742 (1993).
    [Crossref]
  13. J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
    [Crossref]
  14. K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
    [Crossref] [PubMed]
  15. H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
    [Crossref] [PubMed]
  16. T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
    [Crossref] [PubMed]
  17. I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
    [Crossref] [PubMed]
  18. R. Vicente, T. Pérez, and C. R. Mirasso, “Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
    [Crossref]
  19. J. Muramatsu, “Secret key agreement from correlated source outputs using low density parity check matrices,” IEICE Trans. Fundamentals E89-A(7), 2036–2046 (2006).
    [Crossref]
  20. A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization, (Wiley-VCH, Weinheim, 2012).
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    [Crossref]
  22. J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Secret key capacity for optimally correlated sources under sampling attack,” IEEE Trans. Inf. Theory 52(11), 5140–5151 (2006).
    [Crossref]
  23. T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
    [Crossref]
  24. A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, “Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056201 (2004).
    [Crossref] [PubMed]
  25. A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
    [Crossref] [PubMed]
  26. A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
    [Crossref] [PubMed]
  27. A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
    [Crossref] [PubMed]
  28. T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).
  29. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [Crossref]
  30. K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
    [Crossref] [PubMed]

2012 (2)

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

2011 (1)

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).

2010 (4)

2009 (2)

2008 (3)

A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

2007 (3)

2006 (4)

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

J. Scheuer and A. Yariv, “Giant Fiber Lasers: A New Paradigm for Secure Key Distribution,” Phys. Rev. Lett. 97(14), 140502 (2006).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Secret key capacity for optimally correlated sources under sampling attack,” IEEE Trans. Inf. Theory 52(11), 5140–5151 (2006).
[Crossref]

J. Muramatsu, “Secret key agreement from correlated source outputs using low density parity check matrices,” IEICE Trans. Fundamentals E89-A(7), 2036–2046 (2006).
[Crossref]

2004 (1)

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, “Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056201 (2004).
[Crossref] [PubMed]

2003 (1)

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

2002 (3)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

R. Vicente, T. Pérez, and C. R. Mirasso, “Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[Crossref]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

1993 (1)

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

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

1976 (1)

W. Diffie and M. Hellman, “New Directions in cryptography,” IEEE Trans. Inf. Theory 22(6), 644–654 (1976).
[Crossref]

1949 (1)

C. E. Shannon, “Communication theory of secret system,” Bell Syst. Tech. J. 28, 656–715 (1949).

Aida, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Arahata, M.

Arai, K.

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Secret key capacity for optimally correlated sources under sampling attack,” IEEE Trans. Inf. Theory 52(11), 5140–5151 (2006).
[Crossref]

Argyris, A.

Ariizumi, H.

Aviad, Y.

Bar-Lev, D.

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in Fiber Laser Key Distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
[Crossref]

Bogris, A.

Butkovski, M.

Chlouverakis, K. E.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

Colet, P.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

Davis, P.

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[Crossref] [PubMed]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Secret key capacity for optimally correlated sources under sampling attack,” IEEE Trans. Inf. Theory 52(11), 5140–5151 (2006).
[Crossref]

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

Deligiannidis, S.

Diffie, W.

W. Diffie and M. Hellman, “New Directions in cryptography,” IEEE Trans. Inf. Theory 22(6), 644–654 (1976).
[Crossref]

Elsäßer, W.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

Fischer, I.

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[Crossref] [PubMed]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Goto, S. I.

Grivas, E.

Gross, N.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

Hamacher, M.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
[Crossref] [PubMed]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

Harayama, T.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).

Heil, T.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

Hellman, M.

W. Diffie and M. Hellman, “New Directions in cryptography,” IEEE Trans. Inf. Theory 22(6), 644–654 (1976).
[Crossref]

Hirano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Itaya, S.

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

Kanter, I.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

Khaykovich, L.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

Kinzel, W.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

Klein, E.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Koizumi, H.

Kopelowitz, E.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Li, M.

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]

Mirasso, C. R.

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[Crossref] [PubMed]

R. Vicente, T. Pérez, and C. R. Mirasso, “Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[Crossref]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

Morikatsu, S.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

Mulet, J.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

Muramatsu, J.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

J. Muramatsu, “Secret key agreement from correlated source outputs using low density parity check matrices,” IEICE Trans. Fundamentals E89-A(7), 2036–2046 (2006).
[Crossref]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Secret key capacity for optimally correlated sources under sampling attack,” IEEE Trans. Inf. Theory 52(11), 5140–5151 (2006).
[Crossref]

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Nogawa, S.

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, “Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056201 (2004).
[Crossref] [PubMed]

Okumura, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

Oowada, I.

Peil, M.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

Peleg, Y.

Pérez, T.

R. Vicente, T. Pérez, and C. R. Mirasso, “Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[Crossref]

Pikasis, E.

Reidler, I.

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Rosenbluh, M.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

Scheuer, J.

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in Fiber Laser Key Distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
[Crossref]

A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008).
[Crossref] [PubMed]

J. Scheuer and A. Yariv, “Giant Fiber Lasers: A New Paradigm for Secure Key Distribution,” Phys. Rev. Lett. 97(14), 140502 (2006).
[Crossref] [PubMed]

Sendowski, J.

Shannon, C. E.

C. E. Shannon, “Communication theory of secret system,” Bell Syst. Tech. J. 28, 656–715 (1949).

Shibasaki, N.

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, “Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056201 (2004).
[Crossref] [PubMed]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Sunada, S.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).

Syvridis, D.

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Tsuzuki, K.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).

Uchida, A.

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, “Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056201 (2004).
[Crossref] [PubMed]

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

Valiusaityte, I.

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[Crossref] [PubMed]

Vicente, R.

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[Crossref] [PubMed]

R. Vicente, T. Pérez, and C. R. Mirasso, “Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[Crossref]

Yamamoto, T.

Yariv, A.

Yip, H.

Yoshimori, S.

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, “Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056201 (2004).
[Crossref] [PubMed]

Yoshimura, K.

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[Crossref] [PubMed]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Secret key capacity for optimally correlated sources under sampling attack,” IEEE Trans. Inf. Theory 52(11), 5140–5151 (2006).
[Crossref]

Zadok, A.

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Zigzag, M.

Appl. Phys. Lett. (1)

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

Bell Syst. Tech. J. (1)

C. E. Shannon, “Communication theory of secret system,” Bell Syst. Tech. J. 28, 656–715 (1949).

Fast nondeterministic random-bit generation using on-chip chaos lasers (1)

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803(R) (2011).

IEEE J. Quantum Electron. (3)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[Crossref]

R. Vicente, T. Pérez, and C. R. Mirasso, “Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[Crossref]

IEEE Trans. Inf. Theory (3)

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

W. Diffie and M. Hellman, “New Directions in cryptography,” IEEE Trans. Inf. Theory 22(6), 644–654 (1976).
[Crossref]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Secret key capacity for optimally correlated sources under sampling attack,” IEEE Trans. Inf. Theory 52(11), 5140–5151 (2006).
[Crossref]

IEICE Trans. Fundamentals (1)

J. Muramatsu, “Secret key agreement from correlated source outputs using low density parity check matrices,” IEICE Trans. Fundamentals E89-A(7), 2036–2046 (2006).
[Crossref]

Lect. Notes Comput. Sci. (1)

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

Nat. Photonics (1)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Opt. Express (7)

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
[Crossref] [PubMed]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[Crossref] [PubMed]

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008).
[Crossref] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Lett. A (1)

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in Fiber Laser Key Distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (3)

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046201 (2006).
[Crossref] [PubMed]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[Crossref] [PubMed]

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, “Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056201 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

J. Scheuer and A. Yariv, “Giant Fiber Lasers: A New Paradigm for Secure Key Distribution,” Phys. Rev. Lett. 97(14), 140502 (2006).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Other (2)

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, Bangalore, India,1984), 175–179.

A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization, (Wiley-VCH, Weinheim, 2012).

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Figures (14)

Fig. 1
Fig. 1

Configuration of cascaded laser system.

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Fig. 2
Fig. 2

Configuration of the cascaded laser system driven by a common random light.

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Fig. 3
Fig. 3

Schematic diagram of the secure key distribution scheme based on correlated randomness phenomena. In the example, random switching of the binary (0 or π) phase shift parameter and one bit sampling of the corresponding waveform is repeated eight times. The parameter settings and sampled bits of Alice and Bob match in two of the eight instances.

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Fig. 4
Fig. 4

Experimental setup for the synchronization of semiconductor lasers subject to a common constant-amplitude random-phase (CARP) light. Amp, electronic amplifier; ATT, optical attenuator; DSF, dispersion-shifted fiber; EDFA, erbium-doped fiber amplifier; FC, fiber coupler; ISO, optical isolator; M, mirror; PC, polarization controller; PD, photodetector; PM, phase modulator; SL, semiconductor laser; WL Filter, wavelength filter.

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Fig. 5
Fig. 5

Experimental results of (a) temporal waveforms and (b) corresponding correlation plots for the outputs of the Response A-1 and B-1 lasers, (c) temporal waveforms and (d) corresponding correlation plots for the outputs of the Response A-2 and B-2 lasers. The feedback phases are matched at each stage.

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Fig. 6
Fig. 6

Experimental results of (a) temporal waveforms and (b) corresponding correlation plots for the outputs of the Drive and Response A-2 lasers.

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Fig. 7
Fig. 7

Experimental results of correlation plots for the outputs of the Response A-2 and Response B-2 lasers when the feedback phases θA,j and θB,j are matched at (a) both the first (Response A-1 and B-1) and second (Response A-2 and B-2) stages (i.e., θA,1 = θB,1 and θA,2 = θB,2), (b) only the first stage (θA,1 = θB,1 and θA,2 ≠ θB,2), (c) only the second stage (θA,1 ≠ θB,1 and θA,2 = θB,2), and (d) no stages (θA,1 ≠ θB,1 and θA,2 ≠ θB,2).

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Fig. 8
Fig. 8

Experimental result of RF spectra for (a) Drive, (b) Response A-1, (c) Response A-2, (d) Response B-1, and (e) Response B-2 lasers. Experimental parameter is the same as shown in Figs. 5 and 6.

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Fig. 9
Fig. 9

Time evolutions of randomly-selected parameter shifts of the optical feedback phases for the four Response lasers (RZ format) and the corresponding short-term cross-correlation values (the bottom trace) between the Response A-2 and B-2 lasers. The dashed boxes indicate that the phase-shift parameters are matched at each stage (θA,1 = θB,1 and θA,2 = θB,2) and high cross-correlation values are obtained.

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Fig. 10
Fig. 10

Example of the robust sampling method with two threshold values. (a) Temporal waveforms and (b) corresponding correlation plot. (b) The two bits indicate Alice’s and Bob’s bits. 11 and 00 indicate that the same bit can be shared, whereas 10 and 01 indicate that different bits are generated.

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Fig. 11
Fig. 11

(a) Bit generation rate Rgen and (b) bit error rate Rfail as functions of two threshold coefficients C+ and C-. (b) Bit error rate is plotted with a logarithmic scale.

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Fig. 12
Fig. 12

(a) Final key generation rate Rfinal as functions of two threshold coefficients, C+ and C-. The black line indicates a set of the threshold coefficients by which the probability of the occurrence of 0 for generated bits is within 0.500 ± 0.003. The white dotted circle indicates the maximum value on the black line. (b) Final key generation rate Rfinal along with the black line shown in (a).

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Fig. 13
Fig. 13

The maximum final key generation rate Rfinal and the final key generation speed as a function of the number of laser units (stages) N when the parameter frequency is 2 MHz. Three types of Eve are assumed. Weak Eve only has one cascaded Response laser system, i.e., ME = 1. Moderate Eve has half of the total number of cascaded Response laser systems that are required to produce all possible sets of parameter values, i.e., ME = 2N−1. Strong Eve has ME = 2N - 1 cascaded laser systems, just one less than necessary to make it impossible for key generation to be secure against sampling attack.

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Fig. 14
Fig. 14

Final key generation rate Rfinal as a function of N for a fixed ME = 210 obtained from Eq. (5).

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Tables (6)

Tables Icon

Table 1 Statistical evaluation on the generated bit stream. The thresholds for the robust sampling are set to C+ = 0.640 and C- = 0.495.

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Table 2 Analog cross correlation CA and mutual information I(A;E) between Alice and Eve when Eve samples the Response signal at stage 2 with parameter values mismatched at stage 1 and/or 2.

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Table 3 Analog cross correlation CA and mutual information I(A;E) between Alice and Eve when Eve samples the Response signal at stage 1 with parameter values mismatched at stage 1 and/or 2.

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Tables Icon

Table 4 Numerical result of statistical evaluation of the analog cross correlation CA and mutual information I(A;E) between Alice and Eve. Eve samples the Response signal of the stage 1 or 2, when the parameter values are mismatched at the stage 1 and/or 2. The number in () is the stage number of Eve’s sampling.

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Table 5 Experimental values of bit generation rate by robust sampling Rgen and the bit error rate Rfail for the cascaded laser systems with one laser unit (N = 1) and two laser units (N = 2).

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Table A1 Example of CH and CL for different N.

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Equations (15)

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

C A = 〈 ( I x ( t )− I ¯ x )( I y ( t )− I ¯ y ) 〉 σ x ⋅ σ y
R final = 1 M [ ( 1− M E M )( 1− I E )−h( R fail ) ]
I th,u =m+ C + σ
I th,l =m− C − σ
R final = R gen 1 M [ ( 1− M E M )( 1− I E )−h( R fail ) ]
R final = 1 M ( 1− M E M )
R gen = N gen N sample
R fail = N diff N gen
I( X;Y )= ∑ a=0 1 ∑ b=0 1 p X,Y ( a,b ) log 2 p X,Y ( a,b ) p X ( a ) p Y ( b )
E ˙ j (t)= 1 2 ( 1+iα ) G N ( N j (t)− N th ) E j (t)+ κ r,j τ in E j (t− τ j )exp[i θ j ]+ κ inj,j τ in E inj,j ,
N ˙ j (t)= J j − 1 τ s N j (t)− G N ( N j (t)− N 0 )⋅ | E j (t)  | 2 ,
E inj,j ={ E 0 exp[i (Δ ω j t+ϕ(t))] for j=1, E j−1 (t)exp[i Δ ω j t] for j≥2,
ϕ ˙ (t)=− 1 τ m ϕ(t)+ 2 τ m σ⋅ξ(t),
C H = min v=v' C (v,v') A
C L = max v≠v' C A (v,v')

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