An Optimal chaotic bidirectional communicator for hidden information, based on synchronized lorenz circuits

 

R. Núñez

 

Centro de Investigación Científica y de Educación Superior de Ensenada, B.C. División de Física Aplicada, Km. 107, Carretera Tijuana-Ensenada, Ensenada, B.C., México 22860. Tel. (646) 175-0555. E-Mail: rnunez@cicese.mx

 

Received: September 13^th, 2001.
Accepted: September 11^th, 2003.

 

Abstract

An Optimal Chaotic Bidirectional Communicator for Hidden Information (OCBCHI) is presented. Its realization is based on a Standard Chaotic Bidirectional Communicator for Hidden Information (SCBCHI), that uses two Lorenz synchronized circuits with an open-loop explicit method. All the chaotic dynamics of the circuits were studied and analysed using DSP techniques. Regarding to our real-time application, -on bidirectional audio communications field-, the optimum conclusion was to make the synchronization and the hidden communication of the private information by the lower chaotic dynamic variable and the most higher chaotic dynamics variables, respectively. By the complete characterization of the bidirectional channels, we got the minimum parameters (i.e., time and spectrum magnitude) of the private information that it must have just to make a confidential and robust communication.

Keywords: Encrypted communication, Synchronization, Lorenz circuits.

 

Resumen

En este trabajo se presenta un Comunicador Bidireccional Caótico Estandar de Información Oculta (CBCEIO), el cual utiliza dos Circuitos Sincronizados de Lorenz con un método explícito open-loop. Todas las dinámicas caóticas del circuito fueron estudiadas y analizadas usando Técnicas DSP. Por lo que se refiere a nuestra aplicación de tiempo real —en el campo de audio de la Comunicación Bidireccional—, la conclusión óptima fue hacer la sincronización y la comunicación oculta de la información privada, por medio de la variable baja de la dinámica caótica y de la variable alta de la dinámica caótica respectivamente. Por medio de la completa caracterización de los canales Bidireccionales, obtuvimos los parámetros mínimos (ejem: tiempo y magnitud de espectro) de la información privada que debe tener para hacer una comunicación confidencial y robusta.

 

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Acknowledgement

This work was supported by CONACYT, México, under Research Grant 31874-1.

 

References

[1] Núñez P., R., "Implementation and testing of one Chaotic Bidirectional Communicator for Hidden Information, based on two Synchronized Circuits of Lorenz", Technical Report: UET588, DET-CICESE, September, 2000.         [ Links ]

[2] Lorenz E. N., "Deterministic nonperiodic flow", J. Atmospheric Sci., vol. 20, pp. 130-141. Mar., 1963.         [ Links ]

[3] Márquez, A. and Alvarez G., J., "Circuit of Lorenz". Technical Report. CICESE, 1996.         [ Links ]

[4] Núñez P., R., "The Labview (Generator/Dynamic Analyzer) and Dadisp ATS's". Confidential Technical Reports, DET-CICESE, 1998.         [ Links ]

[5] Núñez P., R., "Applications of the DSP in the modern instrumentation using the Dadisp and Labview programs". DSP Institutional course Notes-EP631, DET-CICESE, 1998.         [ Links ]

[6] Cuomo, K.M., Oppenheim, A.V. and Strogatz, S.H., "Synchronization of Lorenz-Based Chaotic Circuits with Applications to Communications". IEEE Trans. on Circuits and Systems-II: Analog/ Digital and Signal Processing, vol. 40, N. - 10, October, 1993.         [ Links ]

[7] Carroll, T.L. and Pecora, L.M., "Synchronizing chaotic circuits", IEEE Trans. on Circuits and Systems, vol. 38, pp. 4536, Apr., 1991.         [ Links ]

 

Note

A partial version of this work was presented as a poster in the 6 ^th Experimental Chaos Conference Postdam, Germany, July 22-26, 2001.