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Optica Publishing Group
  • CLEO/Europe and IQEC 2007 Conference Digest
  • (Optica Publishing Group, 2007),
  • paper JSI1_3

Nonlinear dynamics reconstruction of chaotic cryptosystems based on delayed optoelectronic feedback

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Abstract

Recent results provide a convincing proof-of-practical-concept for optical chaos communications technology [1]. However, security of these systems remains the key issue to be addressed. Since the dynamics generated by delay systems can be high dimensional, many optical chaotic cryptosystems are based on delayed optical or optoelectronic feedback [1]. We consider a system based on encrypting the signal within the high dimensional chaotic fluctuations of the wavelength from a delayed feedback tunable laser diode [2]. In this work we show that the nonlinear dynamics of the chaotic carrier can be reconstructed from experimental data. Then it is possible to extract the message by using the nonlinear model as a receiver. The transmitter consists of a DBR laser with a feedback loop formed by a delay line and an optical device with a nonlinearity in wavelength of the form β sin2 [2]. The number of oscillations of the nonlinear function depends on β that can be changed with the gain of an amplifier in the loop. The response time of the loop τ is adjusted by using a low-pass filter. Data acquisition is performed with a 8 bits resolution oscilloscope. The data set corresponds to a time interval of 2s. The first step to extract the nonlinear dynamics is the estimation of the delay time T. Then a new type of modular neural network (NN) is used to obtain the transmitter nonlinear dynamics. According to the structure of the system, the NN has two modules: one for the non-feedback part with input data delayed by the embedding time A and a second one for the feedback part with input data, Xj=(x(t−Δ−T)), x(t−T)), x(t+A−T)) delayed by the feedback time. A feed-forward NN is used for each of the modules with one neuron for the non-feedback part, and a 4:2 topology for the feedback module. The value given by the NN is xnn(t)=g(x(t−Δ))+f(Xf) where g and f correspond to the non-feedback and feedback modules, respectively. We use 1300 points to train the NN.

© 2007 IEEE

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