Skip to main content

Chaos-Based Secure Optical Communications Using Semiconductor Lasers

  • Chapter

Abstract

The advent of chaos theory in the last decade has definitively separated the notions of determinism and predictability. A nonlinear dynamical system that displays a chaotic steady-state behavior is purely deterministic, but its long-term behavior cannot be predicted because of the property of sensitivity to initial conditions (SIC). This property of chaotic systems implies that two states, initially very close to each other, become very different as time elapses. Since it is impossible to know the state of a system with arbitrarily high precision, the SIC property also implies that, in practice, it is impossible to predict the long-term evolution of a chaotic system. One of the most promising applications of chaos theory, which exploits both the deterministic and unpredictable aspects of chaotic behavior, is chaos-based secure communications.

Keywords

  • Chaotic System
  • Semiconductor Laser
  • Optical Feedback
  • Chaotic Signal
  • Slave Laser

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-04117-4_24
  • Chapter length: 28 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   349.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-04117-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   449.99
Price excludes VAT (USA)
Hardcover Book
USD   599.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Fujisaka, T. Yamada: Stability theory of synchronized motion in coupled-oscillator systems, Prog. Theor. Phys. 69, 32–47 (1983)

    MATH  CrossRef  MathSciNet  Google Scholar 

  2. H. Fujisaka, T. Yamada: Stability theory of synchronized motion in coupled-oscillator systems. II. The mapping approach, Prog. Theor. Phys. 70, 1240–1248 (1983)

    MATH  CrossRef  MathSciNet  Google Scholar 

  3. T. Yamada, H. Fujisaka: Stability theory of synchronized motion in coupled-oscillator systems. III. Mapping model for continuous system, Prog. Theor. Phys. 72, 885–894 (1984)

    CrossRef  Google Scholar 

  4. L.M. Pecora, T.L. Carroll: Synchronization in chaotic systems, Phys. Rev. Lett. 64, 821–824 (1990)

    CrossRef  MathSciNet  Google Scholar 

  5. L.M. Pecora, T.L. Carroll: Synchronizing chaotic circuits, IEEE Trans. Circ. Syst. 38, 453–456 (1991)

    CrossRef  Google Scholar 

  6. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, H.D.I. Abarbanel: Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E 51, 980–994 (1995)

    CrossRef  Google Scholar 

  7. A. Pikovsky, M. Rosenblum, J. Kurths: Synchronization – a Universal Concept in Nonlinear Science (Cambridge Univ. Press, Cambridge 2003)

    Google Scholar 

  8. S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladeres, C.S. Zhou: The synchronization of chaotic systems, Phys. Rep. 366, 1–101 (2002)

    MATH  CrossRef  MathSciNet  Google Scholar 

  9. A.V. Oppenheim, G.W. Wornell, S.H. Isabelle, K.M. Cuomo: Signal processing in the context of chaotic signals, Proc. ICASSP (1992) pp. 117–120

    Google Scholar 

  10. L. Kocarev, K.S. Halle, K. Eckert, L.O. Chua, U. Parlitz: Experimental demonstration of secure communications via chaotic synchronization, Int. J. Bifurc. Chaos 2, 709–713 (1992)

    MATH  CrossRef  Google Scholar 

  11. K.M. Cuomo, A.V. Oppenheim: Circuit implementation of synchronized chaos with applications to communications, Phys. Rev. Lett. 71, 65–68 (1993)

    CrossRef  Google Scholar 

  12. H. Dedieu, M.P. Kennedy, M. Hasler: Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits, IEEE Trans. Circ. Syst. II 40, 634–642 (1993)

    CrossRef  Google Scholar 

  13. G.P. Agrawal, N.K. Dutta: Semiconductor lasers, 2nd edn. (Van Nostrand Reinhold, New York 1993)

    Google Scholar 

  14. F.T. Arecchi, G.L. Lippi, G.P. Puccioni, J.R. Tredicce: Deterministic chaos in lasers with injected signal, Opt. Commun. 51, 308–314 (1984)

    CrossRef  Google Scholar 

  15. K.T. Alligood, T.D. Sauer, J.A. Yorke: CHAOS. An Introduction to Dynamical Systems (Springer, New York 1996)

    MATH  Google Scholar 

  16. F.T. Arecchi, R. Meucci, G. Puccioni, J.R. Tredicce: Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser, Phys. Rev. Lett. 49, 1217–1220 (1982)

    CrossRef  Google Scholar 

  17. J. Ohtsubo: Semiconductor Lasers, Stability, Instability and Chaos (Springer, Berlin Heidelberg 2006)

    Google Scholar 

  18. R. Lang: Injection locking properties of a semiconductor laser, IEEE J. Quantum Electron. 18, 976–983 (1982)

    CrossRef  Google Scholar 

  19. J.K. Hale, S.M. Verduyn Lunel: Introduction to Functional Differential Equations (Springer, New York 1993)

    MATH  Google Scholar 

  20. S. Tang, J.M. Liu: Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback, IEEE J. Quantum Electron. 37, 329–336 (2001)

    CrossRef  Google Scholar 

  21. R. Lang, K. Kobayashi: External optical feedback effects on semiconductor injection laser properties, IEEE J. Quantum Electron. 16, 347–355 (1980)

    CrossRef  Google Scholar 

  22. G.H.M. van Tartwijk, G.P. Agrawal: Laser instabilities: a modern perspective, Prog. Quantum Electron. 22, 43–122 (1998)

    CrossRef  Google Scholar 

  23. D. Lenstra, B.H. Verbeek, A.J. Den Boef: Coherence collapse in single-mode semiconductor lasers due to optical feedback, IEEE J. Quantum Electron. 21, 674–679 (1985)

    CrossRef  Google Scholar 

  24. V. Ahlers, U. Parlitz, W. Lauterborn: Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers, Phys. Rev. A 58, 7208–7213 (1998)

    Google Scholar 

  25. R. Vicente, J. Daudén, P. Colet, R. Toral: Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop, IEEE J. Quantum Electron. 41, 541–548 (2005)

    CrossRef  Google Scholar 

  26. A.P.A. Fischer, M. Yousefi, D. Lenstra, M.W. Carter, G. Vemuri: Experimental and theoretical study of semiconductor laser dynamics due to filtered optical feedback, IEEE J. Sel. Top. Quantum Electron. 10, 944–954 (2004)

    CrossRef  Google Scholar 

  27. P. Celka: Chaotic synchronization and modulation of nonlinear time-delayed feedback optical systems, IEEE Trans. Circ. Syst. I 42, 455–463 (1995)

    CrossRef  Google Scholar 

  28. N. Gastaud, S. Poinsot, L. Larger, J.M. Merolla, M. Hanna, J.-P. Goedgeuer, F. Malassenet: Electro-optical chaos for multi-10 Gbit/s optical transmissions, Electron. Lett. 40, 898–899 (2004)

    CrossRef  Google Scholar 

  29. J.-P. Goedgebuer, P. Lévy, L. Larger, C.C. Chen, W.T. Rhodes: Optical communication with synchronized hyperchaos generated electrooptically, IEEE J. Quantum Electron. 38, 1178–1183 (2002)

    CrossRef  Google Scholar 

  30. L. Larger, J.P. Goedgebuer, J.M. Merolla: Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics, IEEE J. Quantum Electron. 34, 594–601 (1998)

    CrossRef  Google Scholar 

  31. E. Genin, L. Larger, J.P. Goedgebuer, M.W. Lee, R. Ferriere, X. Bavard: Chaotic oscillations of the optical phase for multigigahertz-bandwidth secure communications, IEEE J. Quantum Electron. 40, 294–298 (2004)

    CrossRef  Google Scholar 

  32. L. Larger, M.W. Lee, J.-P. Goedgebuer, W. Elflein, T. Erneux: Chaos in coherence modulation: bifurcations of an oscillator generating optical delay fluctuations, J. Opt. Soc. Am. B 18, 1063–1068 (2001)

    CrossRef  Google Scholar 

  33. R. Roy, K.S. Thornburg: Experimental synchronization of chaotic lasers, Phys. Rev. Lett. 72, 2009–2012 (1994)

    CrossRef  Google Scholar 

  34. T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu: Observation of synchronization in laser chaos, Phys. Rev. Lett. 72, 3502–3505 (1994)

    CrossRef  Google Scholar 

  35. P. Celka: Synchronization of chaotic optical dynamical systems through 700 m of single mode fiber, IEEE Trans. Circ. Syst. I 43, 869–872 (1996)

    CrossRef  Google Scholar 

  36. J.P. Goedgebuer, L. Larger, H. Porte: Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode, Phys. Rev. Lett. 80, 2249–2252 (1998)

    CrossRef  Google Scholar 

  37. S. Sivaprakasam, K.A. Shore: Demonstration of optical synchronization of chaotic external-cavity laser diodes, Opt. Lett. 24, 466–468 (1999)

    CrossRef  Google Scholar 

  38. H. Fujino, J. Ohtsubo: Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers, Opt. Lett. 25, 625–627 (2000)

    CrossRef  Google Scholar 

  39. I. Fischer, Y. Liu, P. Davis: Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication, Phys. Rev. A 62, 011801R-1–011801R-4 (2000)

    CrossRef  Google Scholar 

  40. J.M. Liu, H.F. Chen, S. Tang: Optical-communication systems based on chaos in semiconductor lasers, IEEE Trans. Circ. Syst. I 48, 1475–1483 (2001)

    CrossRef  Google Scholar 

  41. S. Tang, J.M. Liu: Synchronization of high-frequency chaotic optical pulses, Opt. Lett. 26, 596–598 (2001)

    CrossRef  Google Scholar 

  42. P. Colet, R. Roy: Digital communication with synchronized chaotic lasers, Opt. Lett. 19, 2056–2058 (1994)

    CrossRef  Google Scholar 

  43. G.D. VanWiggeren, R. Roy: Optical communication with chaotic waveforms, Phys. Rev. Lett. 81, 3547–3550 (1998)

    CrossRef  Google Scholar 

  44. G.D. VanWiggeren, R. Roy: Communication with chaotic lasers, Science 279, 1198–1200 (1998)

    CrossRef  Google Scholar 

  45. S. Sivaprakasam, K.A. Shore: Signal masking for chaotic optical communication using external-cavity diode lasers, Opt. Lett. 24, 1200–1202 (2000)

    CrossRef  Google Scholar 

  46. H.U. Voss: Anticipating chaotic synchronization, Phys. Rev. E. 61, 5115–5119 (2000)

    CrossRef  Google Scholar 

  47. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, K.A. Shore: Chaos-based communications at high bit rates using commercial fibre-optic links, Nature 438, 343–346 (2005)

    CrossRef  Google Scholar 

  48. S. Tang, J.M. Liu: Message-encoding at 2.5 Gbit/s through synchronization of chaotic pulsing semiconductor lasers, Opt. Lett. 26, 1843–1845 (2001)

    CrossRef  Google Scholar 

  49. S. Tang, H.F. Chen, S.K. Hwang, J.M. Liu: Message encoding and decoding through chaos modulation in chaotic optical communications, IEEE Trans. Circ. Syst. I 49, 163–169 (2001)

    CrossRef  Google Scholar 

  50. H.F. Chen, J.M. Liu: Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation, IEEE J. Quantum Electron. 36, 27–34 (2000)

    CrossRef  Google Scholar 

  51. J.M. Liu, H.F. Chen, S. Tang: Synchronized chaotic optical communications at high bit rates, IEEE J. Quantum Electron. 38, 1184–1196 (2002)

    CrossRef  Google Scholar 

  52. V. Annovazzi-Lodi, S. Donati, A. Scirè: Synchronization of chaotic injected-laser systems and its application to optical cryptography, IEEE J. Quantum Electron. 32, 953–959 (1996)

    CrossRef  Google Scholar 

  53. A. Locquet, F. Rogister, M. Sciamanna, P. Mégret, M. Blondel: Two types of synchronization in unidirectionally coupled chaotic external-cavity semiconductor lasers, Phys. Rev. E 64, 045203-1–045203-4 (2001)

    CrossRef  Google Scholar 

  54. A. Locquet, C. Masoller, C.R. Mirasso: Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers, Phys. Rev. E 65, 056205-1–056205-4 (2002)

    CrossRef  Google Scholar 

  55. A. Murakami, J. Ohtsubo: Synchronization of feedback-induced chaos in semiconductor lasers by optical injection, Phys. Rev. A 65, 033826-1–033826-7 (2002)

    CrossRef  Google Scholar 

  56. Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, J.M. Liu: Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers, IEEE J. Quantum Electron. 39, 269–278 (2003)

    CrossRef  Google Scholar 

  57. J. Revuelta, C.R. Mirasso, P. Colet, L. Pesquera: Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers, IEEE Photon. Technol. Lett. 14, 140–142 (2002)

    CrossRef  Google Scholar 

  58. H. Kantz, T. Schreiber: Nonlinear Time Series Analysis, 2nd edn. (Cambridge Univ. Press, Cambridge 2004)

    MATH  Google Scholar 

  59. U. Parlitz, L. Kocarev, A. Tstojanovski, H. Preckel: Encoding messages using chaotic synchronization, Phys. Rev. E 53, 4351–4361 (1996)

    CrossRef  Google Scholar 

  60. M.W. Lee, L. Larger, V. Udaltsov, E. Genin, J.P. Goedgebuer: Demonstration of a chaos generator with two time delays, Opt. Lett. 29, 325–327 (2004)

    CrossRef  Google Scholar 

  61. R. Hegger, M.J. Bünner, H. Kantz, A. Giaquinta: Identifying and modeling delay feedback systems, Phys. Rev. Lett. 81, 558–561 (1998)

    CrossRef  Google Scholar 

  62. M.J. Bünner, M. Ciofini, A. Giaquinta, R. Hegger, H. Kantz, A. Politi: Reconstruction of systems with delayed feedback: I. Theory, Eur. Phys. J. D 10, 165–176 (2000)

    CrossRef  Google Scholar 

  63. M.J. Bünner, M. Ciofini, A. Giaquinta, R. Hegger, H. Kantz, R. Meucci, A. Politi: Reconstruction of systems with delayed feedback: II. Application, Eur. Phys. J. D 10, 177–187 (2000)

    CrossRef  Google Scholar 

  64. D. Rontani, A. Locquet, M. Sciamanna, D.S. Citrin, S. Ortin: Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view, IEEE J. Quantum Electron. 45, 879–891 (2009)

    CrossRef  Google Scholar 

  65. C. Zhou, C.H. Lai: Extracting messages masked by chaotic signals of time-delay systems, Phys. Rev. E 60, 320–323 (1999)

    CrossRef  Google Scholar 

  66. V.S. Udaltsov, J.P. Goedgebuer, L. Larger, J.B. Cuenot, P. Levy, W.T. Rhodes: Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations, Phys. Lett. A 308, 54–60 (2003)

    MATH  CrossRef  MathSciNet  Google Scholar 

  67. G. Alvarez, S. Li: Some basic cryptographic requirements for chaos-based cryptosystems, Int. J. Bifurc. Chaos 16, 2129–2151 (2006)

    CrossRef  MathSciNet  Google Scholar 

  68. B. Schneier: Applied Cryptography, 2nd edn. (John Wiley and Sons, New York 1996)

    Google Scholar 

  69. K.M. Short: Steps toward unmasking secure communications, Int. J. Bifurc. Chaos 4, 959–977 (1994)

    MATH  CrossRef  Google Scholar 

  70. K.M. Short: Unmasking a modulated chaotic communications scheme, Int. J. Bifurc. Chaos 6, 367–375 (1996)

    MATH  CrossRef  Google Scholar 

  71. K.M. Short, A.T. Parker: Unmasking a hyperchaotic modulated scheme, Phys. Rev. E 58, 1159–1162 (1998)

    CrossRef  Google Scholar 

  72. Y. Takiguchi, K. Ohyagi, J. Ohtsubo: Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback, Opt. Lett. 28, 319–321 (2003)

    CrossRef  Google Scholar 

  73. L. Kocarev, U. Parlitz: General approach for chaotic synchronization with applications to communication, Phys. Rev. Lett. 74, 5028–5031 (1995)

    CrossRef  Google Scholar 

  74. A. Sánchez-Díaz, C.R. Mirasso, P. Colet, P. García-Fernández: Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers, IEEE J. Quantum Electron. 35, 292–297 (1999)

    CrossRef  Google Scholar 

  75. A. Locquet, C. Masoller, P. Mégret, M. Blondel: Comparison of two types of synchronization of external-cavity semiconductor lasers, Opt. Lett. 27, 31–33 (2002)

    CrossRef  Google Scholar 

  76. A. Bogris, A. Argyris, D. Syvridis: Analysis of the optical amplifier noise effect on electrooptically generated hyperchaos, IEEE J. Quantum Electron. 43, 552–559 (2007)

    CrossRef  Google Scholar 

  77. M. Yousefi, Y. Barbarin, S. Beri, E.A.J.M. Bente, M.K. Smith, R. Nötzel, D. Lenstra: New role for nonlinear dynamics and chaos in integrated semiconductor laser technology, Phys. Rev. Lett. 98, 044101-1–044101-4 (2007)

    CrossRef  Google Scholar 

  78. A. Argyris, M. Hamacher, K.E. Chlouverakis, A. Bogris, D. Syvridis: Photonic integrated device for chaos application in communications, Phys. Rev. Lett. 100, 194101-1–194101-4 (2008)

    CrossRef  Google Scholar 

  79. L.S. Tsimring, M.M. Sushchik: Multiplexing chaotic signals using synchronization, Phys. Lett. A 213, 155–166 (1996)

    CrossRef  Google Scholar 

  80. Y. Liu, P. Davis: Dual synchronization of chaos, Phys. Rev. E 61, R2176–R2179 (2000)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Locquet, A. (2010). Chaos-Based Secure Optical Communications Using Semiconductor Lasers. In: Stavroulakis, P., Stamp, M. (eds) Handbook of Information and Communication Security. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04117-4_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04117-4_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04116-7

  • Online ISBN: 978-3-642-04117-4

  • eBook Packages: EngineeringEngineering (R0)