Proceedings of Topical Meeting on Optoinformatics (pdf-format, 1.21 ...

6 OPTOINFORMATICS’05
We applied and analyzed five published methods for the identification <strong>of</strong> the time
delay from time series generated by a few different types <strong>of</strong> chaos-generating emitters.
These methods are:
1. Analysis <strong>of</strong> the return maps <strong>of</strong> the transmitted signal,
2. Analysis <strong>of</strong> the autocorrelation function (ACF) <strong>of</strong> the transmitted signal,
3. Application <strong>of</strong> the average mutual information technique (the AMI-technique),
4. Recovery <strong>of</strong> T by local linear fits in a low-dimensional space [6] ,
5. Analysis <strong>of</strong> the time-distribution <strong>of</strong> extrema [7] .
We used the numerical models describing a few modifications <strong>of</strong> a communication
system based on a DDE-circuit. These are:
1. A system with two feedback loops, one <strong>of</strong> them controlling the source and another
one controlling the nonlinearity,
2. A system with two parallel time delays,
3. A system with two parallel time delays and two different filters,
4. A system with two parallel nonlinearities and two time delays,
5. A system with two switching time delays,
6. A system with modulated time delays.
We integrated the numerical models with the Runge-Kutta procedure for different
sets <strong>of</strong> parameters in the feedback loops. Next, chaotic time series generated by the
aforementioned systems were analyzed from the point <strong>of</strong> view <strong>of</strong> the possibility to identify
the time delay T.
In brief, the main results obtained can be summarized as follows:
1. The communication system based on the chaos-generating circuit with a single
feedback containing a time delay and a nonlinearity can be successfully attacked and
reconstructed by an eavesdropper, despite the possibility <strong>of</strong> generating hyperchaotic
signals.
2. Numerical results obtained show that it is possible to find system architectures that
increase the security <strong>of</strong> the cryptosystem up to the necessary level.
3. A simple addition <strong>of</strong> a second feedback loop is not the universal remedy against
breaking; the system becomes more secure only with specific choices <strong>of</strong> system
architectures and parameters.
Acknowledgements: The participation <strong>of</strong> V. S. Udaltsov was supported by the Centre
National de la Recherche Scientifique (CNRS), France.
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