Abstract

An external-cavity laser (ECL) operating in a chaotic state is usually used in a chaotic optical secure communication system and its feedback length (FL) is often regarded as an additional key. Our analyses show that an eavesdropper’s (Eve) laser can synchronize with a transmitter (Alice) without any knowledge of the FL by simply increasing the injection strength. A sequence of a 1  Gbit/s nonreturn-to-zero message encoded by the FL as the key is successfully eavesdropped. The reason for the synchronization deviation between Alice’s and Eve’s lasers is given. Our results indicate that the FL as a key cannot enhance the security of chaotic optical communication using long-ECLs.

© 2009 Optical Society of America

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References

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  1. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821-824 (1990).
    [CrossRef] [PubMed]
  2. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems & Signal Processing (IEEE, 1984), pp. 175-179.
  3. K.-W. Wong, “A combined chaotic cryptographic and hashing scheme,” Phys. Lett. A 307, 292-298 (2003).
    [CrossRef]
  4. C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299-301 (1996).
    [CrossRef]
  5. G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279, 1198-1200 (1998).
    [CrossRef] [PubMed]
  6. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
    [CrossRef]
  7. S. Sivaprakasam and K. A. Shore, “Signal masking for chaotic optical communication using external-cavity diode lasers,” Opt. Lett. 24, 1200-1202 (1999).
    [CrossRef]
  8. S. Tang and J. M. Liu, “Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers,” Opt. Lett. 26, 1843-1845 (2001).
    [CrossRef]
  9. J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, “Optically modulated chaotic communication scheme with external-cavity length as a key to security,” J. Opt. Soc. Am. B 20, 497-503 (2003).
    [CrossRef]
  10. M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photonics Technol. Lett. 21, 426-428 (2009).
    [CrossRef]
  11. A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119-124 (2008).
    [CrossRef]
  12. D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32, 2960-2962(2007).
    [CrossRef] [PubMed]
  13. Y. Li, Y. Wang, and A. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656-2662 (2008).
    [CrossRef]
  14. J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. 38, 1141-1154 (2002).
    [CrossRef]
  15. V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72, 373-377 (2005).
    [CrossRef]
  16. 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, 1197-1204 (2002).
    [CrossRef]

2009 (1)

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photonics Technol. Lett. 21, 426-428 (2009).
[CrossRef]

2008 (2)

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119-124 (2008).
[CrossRef]

Y. Li, Y. Wang, and A. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656-2662 (2008).
[CrossRef]

2007 (1)

2005 (2)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72, 373-377 (2005).
[CrossRef]

2003 (2)

2002 (2)

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. 38, 1141-1154 (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, 1197-1204 (2002).
[CrossRef]

2001 (1)

1999 (1)

1998 (1)

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279, 1198-1200 (1998).
[CrossRef] [PubMed]

1996 (1)

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299-301 (1996).
[CrossRef]

1990 (1)

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

Argyris, A.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119-124 (2008).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems & Signal Processing (IEEE, 1984), pp. 175-179.

Bogris, A.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119-124 (2008).
[CrossRef]

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems & Signal Processing (IEEE, 1984), pp. 175-179.

Carroll, T. L.

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Chlouverakis, K. E.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119-124 (2008).
[CrossRef]

Citrin, D. S.

Colet, P.

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photonics Technol. Lett. 21, 426-428 (2009).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299-301 (1996).
[CrossRef]

Fisher, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

García-Fernández, P.

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299-301 (1996).
[CrossRef]

García-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

Goedgebuer, J. P.

Larger, L.

V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72, 373-377 (2005).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

Li, Y.

Y. Li, Y. Wang, and A. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656-2662 (2008).
[CrossRef]

Liu, J. M.

Locquet, A.

Mirasso, C. R.

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photonics Technol. Lett. 21, 426-428 (2009).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[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, 1197-1204 (2002).
[CrossRef]

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299-301 (1996).
[CrossRef]

Ohtsubo, J.

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. 38, 1141-1154 (2002).
[CrossRef]

Paul, J.

Pecora, L. M.

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

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, 1197-1204 (2002).
[CrossRef]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

Rizomiliotis, P.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119-124 (2008).
[CrossRef]

Rontani, D.

Roy, R.

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279, 1198-1200 (1998).
[CrossRef] [PubMed]

Sciamanna, M.

Shore, K. A.

Sivaprakasam, S.

Soriano, M. C.

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photonics Technol. Lett. 21, 426-428 (2009).
[CrossRef]

Spencer, P. S.

Syvridis, D.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119-124 (2008).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

Tang, S.

Udaltsov, V. S.

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279, 1198-1200 (1998).
[CrossRef] [PubMed]

Vicente, R.

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, 1197-1204 (2002).
[CrossRef]

Wang, A.

Y. Li, Y. Wang, and A. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656-2662 (2008).
[CrossRef]

Wang, Y.

Y. Li, Y. Wang, and A. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656-2662 (2008).
[CrossRef]

Wong, K.-W.

K.-W. Wong, “A combined chaotic cryptographic and hashing scheme,” Phys. Lett. A 307, 292-298 (2003).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119-124 (2008).
[CrossRef]

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. 38, 1141-1154 (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, 1197-1204 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photonics Technol. Lett. 21, 426-428 (2009).
[CrossRef]

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299-301 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Opt. Technol. (1)

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fisher, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343-346 (2005).
[CrossRef]

Opt. Commun. (1)

Y. Li, Y. Wang, and A. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656-2662 (2008).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

K.-W. Wong, “A combined chaotic cryptographic and hashing scheme,” Phys. Lett. A 307, 292-298 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Science (1)

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279, 1198-1200 (1998).
[CrossRef] [PubMed]

Other (1)

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems & Signal Processing (IEEE, 1984), pp. 175-179.

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Figures (8)

Fig. 1
Fig. 1

Schematic setup for chaotic optical communication and message eavesdropping using the FL as a static key.

Fig. 2
Fig. 2

Generated chaotic carrier with the Alice’s FL of 0.6 m and corresponding time delay of 4 ns . (a) Time series. (b) Power spectrum. (c) Autocorrelation function (ACF). (d) Average mutual information (AMI) function.

Fig. 3
Fig. 3

Correlation coefficient between Alice’s and Eve’s laser outputs.

Fig. 4
Fig. 4

1   Gbit / s NRZ message transmission and eavesdropping using the static key. (a) Time series of Alice’s laser output. (b) Power spectrum of Alice’s laser output. (c) From the top to bottom panel: original message, recovered message at the authorized Bob’s side after filtering, and eavesdropped message at Eve’s side after filtering. (d) AMI curves. Solid line, AMI between the eavesdropped message and the message recovered by Bob; dotted line, the message recovered by Bob and the original message; dashed line: the eavesdropped message and the original message.

Fig. 5
Fig. 5

Schematic setup for chaotic optical communication and message eavesdropping using the FL as a dynamic key. OS: optical switch. VDL: variable delay line.

Fig. 6
Fig. 6

Correlation coefficient between Alice’s and Eve’s laser outputs.

Fig. 7
Fig. 7

1   Gbit / s NRZ message transmission and eavesdropping using the dynamic key. (a) Time series of Alice’s laser output; (b) Power spectrum of Alice’s laser output. (c) From the top to bottom panel: original message, recovered message at the authorized Bob’s side after filtering, and eavesdropped message at Eve’s side after filtering. (d) AMI curves. Solid line, AMI between the eavesdropped message and the message recovered by Bob; dotted line, the message recovered by Bob and the original message; dashed line, the eavesdropped message and the original message.

Fig. 8
Fig. 8

RF spectra. (a) Output power of Alice’s laser. (b) Output power of Eve’s laser.

Tables (1)

Tables Icon

Table 1 Parameter Values Used in the Numerical Simulation

Equations (6)

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

d E A ( t ) d t = 1 2 ( 1 + i α ) { g [ N A ( t ) N 0 ] 1 τ P } E A ( t ) + k A E A ( t τ A ) exp ( i ω A τ A ) ,
d E E ( t ) d t = 1 2 ( 1 + i α ) { g [ N E ( t ) N 0 ] 1 τ P } E E ( t ) + k E E E ( t τ E ) exp ( i ω E τ E ) + k inj E A ( t τ inj ) exp ( i ω A τ inj ) ,
d N A , E d t = I A , E ( t ) q V 1 τ N N A , E ( t ) g [ N A , E ( t ) N 0 ] | E A , E ( t ) | 2 ,
k A , E = 1 τ in ( 1 r 0 ) 2 r A , E r 0 ,
k inj = 1 τ in ( 1 r 0 ) 2 r inj r 0 ,
ρ = [ A ( t ) A ( t ) ] [ E ( t ) E ( t ) ] | [ A ( t ) A ( t ) ] | 2 | [ E ( t ) E ( t ) ] | 2 ,

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