Abstract

We introduce a chaos-based communication scheme allowing for bidirectional exchange of information. By coupling two semiconductor lasers through a partially transparent optical mirror, delay dynamics is induced in both lasers. We numerically demonstrate that this dynamics can be identically synchronized, and moreover, information introduced on both ends of the link can be simultaneously transmitted. This scheme allows one to negotiate a key through a public channel.

© 2007 Optical Society of America

Full Article  |  PDF Article

Corrections

Raúl Vicente, Claudio R. Mirasso, and Ingo Fischer, "Simultaneous bidirectional message transmission in a chaos-based communication scheme: erratum," Opt. Lett. 32, 1271-1271 (2007)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-32-10-1271

References

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  1. S. Donati and C. R. Mirasso, eds., 'Feature section on optical chaos and applications to cryptography,' IEEE J. Quantum Electron. 38, 1138-1205 (2002).
    [CrossRef]
  2. L. Larger and J. P. Goedgebuer, eds., 'Cryptography using optical chaos,' C. R. Phys. 5, 609-681 (2004).
    [CrossRef]
  3. A. Uchida, F. Rogister, J. Garcia-Ojalvo, and R. Roy, Prog. Opt. 48, 203 (2005).
    [CrossRef]
  4. I. Fischer, Y. Liu, and P. Davis, Phys. Rev. A 62, 011801R (2000).
    [CrossRef]
  5. 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, Nature 238, 343 (2005).
    [CrossRef]
  6. T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
    [CrossRef] [PubMed]
  7. H. Fujino and J. Ohtsubo, Opt. Rev. 8, 351 (2001).
    [CrossRef]
  8. I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
    [CrossRef] [PubMed]
  9. E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
    [CrossRef]
  10. J. Mulet, C. Masoller, and C. R. Mirasso, Phys. Rev. A 65, 063815 (2002).
    [CrossRef]
  11. C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).
    [CrossRef] [PubMed]
  12. R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, Phys. Rev. Lett. 91, 118701 (2003).
    [CrossRef] [PubMed]

2006 (2)

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
[CrossRef]

2005 (2)

A. Uchida, F. Rogister, J. Garcia-Ojalvo, and R. Roy, Prog. Opt. 48, 203 (2005).
[CrossRef]

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, Nature 238, 343 (2005).
[CrossRef]

2004 (1)

L. Larger and J. P. Goedgebuer, eds., 'Cryptography using optical chaos,' C. R. Phys. 5, 609-681 (2004).
[CrossRef]

2003 (1)

R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, Phys. Rev. Lett. 91, 118701 (2003).
[CrossRef] [PubMed]

2002 (2)

S. Donati and C. R. Mirasso, eds., 'Feature section on optical chaos and applications to cryptography,' IEEE J. Quantum Electron. 38, 1138-1205 (2002).
[CrossRef]

J. Mulet, C. Masoller, and C. R. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

2001 (2)

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

H. Fujino and J. Ohtsubo, Opt. Rev. 8, 351 (2001).
[CrossRef]

2000 (1)

I. Fischer, Y. Liu, and P. Davis, Phys. Rev. A 62, 011801R (2000).
[CrossRef]

1992 (1)

C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).
[CrossRef] [PubMed]

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, Nature 238, 343 (2005).
[CrossRef]

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, Nature 238, 343 (2005).
[CrossRef]

Bennett, C. H.

C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).
[CrossRef] [PubMed]

Buldú, J. M.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

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, Nature 238, 343 (2005).
[CrossRef]

Davis, P.

I. Fischer, Y. Liu, and P. Davis, Phys. Rev. A 62, 011801R (2000).
[CrossRef]

Donati, S.

S. Donati and C. R. Mirasso, eds., 'Feature section on optical chaos and applications to cryptography,' IEEE J. Quantum Electron. 38, 1138-1205 (2002).
[CrossRef]

Elsäßer, W.

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Fischer, I.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

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, Nature 238, 343 (2005).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

I. Fischer, Y. Liu, and P. Davis, Phys. Rev. A 62, 011801R (2000).
[CrossRef]

Fujino, H.

H. Fujino and J. Ohtsubo, Opt. Rev. 8, 351 (2001).
[CrossRef]

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, Nature 238, 343 (2005).
[CrossRef]

A. Uchida, F. Rogister, J. Garcia-Ojalvo, and R. Roy, Prog. Opt. 48, 203 (2005).
[CrossRef]

García-Ojalvo, J.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

Goedgebuer, J. P.

L. Larger and J. P. Goedgebuer, eds., 'Cryptography using optical chaos,' C. R. Phys. 5, 609-681 (2004).
[CrossRef]

Gross, N.

E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Kanter, I.

E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
[CrossRef]

R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, Phys. Rev. Lett. 91, 118701 (2003).
[CrossRef] [PubMed]

Khaykovich, L.

E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Kinsel, W.

E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Kinzel, W.

R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, Phys. Rev. Lett. 91, 118701 (2003).
[CrossRef] [PubMed]

Klein, E.

E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
[CrossRef]

R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, Phys. Rev. Lett. 91, 118701 (2003).
[CrossRef] [PubMed]

Larger, L.

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, Nature 238, 343 (2005).
[CrossRef]

L. Larger and J. P. Goedgebuer, eds., 'Cryptography using optical chaos,' C. R. Phys. 5, 609-681 (2004).
[CrossRef]

Liu, Y.

I. Fischer, Y. Liu, and P. Davis, Phys. Rev. A 62, 011801R (2000).
[CrossRef]

Masoller, C.

J. Mulet, C. Masoller, and C. R. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

Mirasso, C. R.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

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, Nature 238, 343 (2005).
[CrossRef]

S. Donati and C. R. Mirasso, eds., 'Feature section on optical chaos and applications to cryptography,' IEEE J. Quantum Electron. 38, 1138-1205 (2002).
[CrossRef]

J. Mulet, C. Masoller, and C. R. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Mislovaty, R.

R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, Phys. Rev. Lett. 91, 118701 (2003).
[CrossRef] [PubMed]

Mulet, J.

J. Mulet, C. Masoller, and C. R. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Ohtsubo, J.

H. Fujino and J. Ohtsubo, Opt. Rev. 8, 351 (2001).
[CrossRef]

Peil, M.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

Pesquera, L.

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, Nature 238, 343 (2005).
[CrossRef]

Rogister, F.

A. Uchida, F. Rogister, J. Garcia-Ojalvo, and R. Roy, Prog. Opt. 48, 203 (2005).
[CrossRef]

Rosenbluh, N.

E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Roy, R.

A. Uchida, F. Rogister, J. Garcia-Ojalvo, and R. Roy, Prog. Opt. 48, 203 (2005).
[CrossRef]

Shore, K. 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, Nature 238, 343 (2005).
[CrossRef]

Syvridis, D.

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, Nature 238, 343 (2005).
[CrossRef]

Torrent, M. C.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

Uchida, A.

A. Uchida, F. Rogister, J. Garcia-Ojalvo, and R. Roy, Prog. Opt. 48, 203 (2005).
[CrossRef]

Vicente, R.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

C. R. Phys. (1)

L. Larger and J. P. Goedgebuer, eds., 'Cryptography using optical chaos,' C. R. Phys. 5, 609-681 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Donati and C. R. Mirasso, eds., 'Feature section on optical chaos and applications to cryptography,' IEEE J. Quantum Electron. 38, 1138-1205 (2002).
[CrossRef]

Nature (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, Nature 238, 343 (2005).
[CrossRef]

Opt. Rev. (1)

H. Fujino and J. Ohtsubo, Opt. Rev. 8, 351 (2001).
[CrossRef]

Phys. Rev. A (2)

I. Fischer, Y. Liu, and P. Davis, Phys. Rev. A 62, 011801R (2000).
[CrossRef]

J. Mulet, C. Masoller, and C. R. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

Phys. Rev. E (1)

E. Klein, N. Gross, N. Rosenbluh, L. Khaykovich, W. Kinsel, and I. Kanter, Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).
[CrossRef] [PubMed]

R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, Phys. Rev. Lett. 91, 118701 (2003).
[CrossRef] [PubMed]

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Prog. Opt. (1)

A. Uchida, F. Rogister, J. Garcia-Ojalvo, and R. Roy, Prog. Opt. 48, 203 (2005).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Scheme of two semiconductor lasers coupled through a partially transparent mirror: PD, photodiode; m 1 , 2 , encoding messages.

Fig. 2
Fig. 2

Temporal traces of the optical power of SL1 (black) and SL2 (gray, red online) once the proper lag has been compensated for. The trace of SL2 has also been shifted vertically to distinguish it from that of SL1. The inset shows the cross-correlation function between the two laser outputs.

Fig. 3
Fig. 3

(a), (b) Temporal traces of SL1 and SL2, respectively, under the injection of a current pulse shown in (c). (d) Evolution of the synchronization error.

Fig. 4
Fig. 4

Illustration of the message decryption process. (a) and (b) Original messages encoded by SL1 and SL2, respectively. (c) Subtraction of messages [ m 1 ( t ) m 2 ( t + Δ t ) ] with a given time lag, which is reconstructed by the synchronization error [ P 1 ( t ) P 2 ( t + Δ t ) ] . This difference, (d), has been filtered with a fifth-order Butterworth filter with a cutoff frequency of 0.8 GHz .

Equations (3)

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

E ̇ 1 = i Δ ω 1 E 1 + 1 2 ( 1 + i α ) G ( N 1 , E 1 ) E 1 + κ 2 , 1 exp ( i ϕ 2 , 1 ) E 2 ( t τ m , 1 τ m , 2 ) + κ f , 1 exp ( i ϕ m , 1 ) E 1 ( t 2 τ m , 1 ) ,
N ̇ 1 = I 1 e γ e N 1 G ( N 1 , E 1 2 ) E 1 2 ,
G ( N i , E i 2 ) = g ( N i N 0 ) 1 + s E i 2 γ .

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