Luis Pesquera(1), S. Ortín(1), M. Jacquot(2), M. Peil(2),L. Larger(2)
(1)    Instituto de Física de Cantabria (CSIC-UC), Santander, Spain.
(2)    UMR CNRS FEMTO-ST 6174/Optics Dpt, Université de Franche-Comté, Besançon, France

Nonlinear dynamics reconstruction of chaotic cryptosystems based on a laser diode subject to optoelectronic feedback with fixed and variable delay

Chaotic communication is a promising technique to complement quantum or software cryptography. However, security of these systems remains the key issue to be addressed. In this talk we consider a chaotic communication system with a transmitter based on a DBR laser subject to optoelectronic feedback with fixed and variable delay. The signal is encrypted within the high dimensional chaotic fluctuations of the wavelength of the tunable laser diode. It is shown that the nonlinear dynamics of the chaotic carrier can be reconstructed from experimental time series when the time delay is fixed. The transmitter nonlinear dynamics is reconstructed by using a modular neural network. It is found that the required number of neurons to achieve similar training errors does not increase with the delay time, even though the system is high dimensional. However, the training error increases with the feedback strength. The nonlinear model is used as the receiver to extract the message. Therefore these systems are vulnerable when the time delay is fixed. It has been proposed to use a variable time delay to enhance the security. A first step to break the system is the extraction of the time delay. It is shown that the periodic time delay can be extracted from experimental data. Different periodic functions are considered for the time delay. The period of the time delay is obtained from the mutual information. Applying a modified filling factor method the periodic time delay function is recovered for different periods and modulation depths.