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

SAINT-PETERSBURG, October 17 – 20, 2005 5
SOME ASPECTS OF SECURITY OF CHAOS-BASED
COMMUNICATIONS
V. S. Udaltsov a , A. Locquet a,b , L. Larger a , J. P. Goedgebuer a , and D. S. Citrin a,b
a GTL-CNRS TELECOM, UMR FEMTO-ST 6174, Georgia Tech Lorraine, 2-3 rue
Marconi, 57070 Metz, France
b School <strong>of</strong> Electrical and Computer Engineering, Georgia Institute <strong>of</strong> Technology,
Atlanta, Georgia 30332-0250, USA
E-mail: udaltsov@georgiatech-metz.fr
Chaotic dynamics ruled by delay-differential equations (DDE) and chaos-based
communication systems are explored from the point <strong>of</strong> view <strong>of</strong> security. The
problem <strong>of</strong> the identification <strong>of</strong> the time-delay is the main security aspect
considered here. It is shown that carefully chosen architectures <strong>of</strong> the chaotic
transmitter can increase the degree <strong>of</strong> security.
The idea to use a chaotic carrier and synchronized chaotic waveforms for secure
communications proposed originally in the beginning <strong>of</strong> the nineties was revised precisely
in conjunction with security issues. Several papers dedicated to the security <strong>of</strong> chaotic
cryptosystems have been published in the last years. In the very beginning, systems using
low-dimensional chaotic carriers have been explored and broken successfully. Then, it was
shown that even a high chaos complexity characterized by a large number <strong>of</strong> positive
Lyapunov exponents, is not sufficient to ensure a high degree <strong>of</strong> security. This means that
hyperchaotic cryptosystems can also be broken, as it was is shown in our paper [1] .
We consider here optoelectronic cryptosystems ruled by delay-differential equations
(a DDE in its simplest normalized form is known as Ikeda’s equation [2] ). They are <strong>of</strong>
particular interest because they can produce highly complex chaos and, at the same time,
are relatively easy to realize [3] . Message encoding is performed by a chaotic modulation
technique [3] . Actually, the DDE-emitter represents a circuit with the feedback loop that
includes a controlled source (for example, a tunable laser diode), a nonlinear element (for
example, a birefringent plate placed between two polarizers or an interferometer), and a
detecting photodiode that converts optical signals to electrical ones and also limits the
bandwidth <strong>of</strong> chaotic oscillations. In numerical models such a limitation can be modeled
by low- or band-pass filters [4] .
If the topology <strong>of</strong> the system (the block-diagrams and the equations describing the
dynamics <strong>of</strong> the system) is known to an eavesdropper (this assumption is usual for
cryptanalysis), the reconstruction <strong>of</strong> the parameters <strong>of</strong> the system allows decoding <strong>of</strong> the
transmitted information. The eavesdropper’s attack can be fulfilled with a real receiver that
should be synchronized with the chaotic emitter [5] , or by numerical modeling <strong>of</strong> this
receiver.
In our previous article [1] , we have shown that the reconstruction <strong>of</strong> all the parameters
characterizing a hyperchaotic system with a single feedback loop containing a strong
nonlinearity is possible, when the value <strong>of</strong> the time delay T is known or recovered. When
there is no way to identify the time delay, the chaos-based communication system becomes
difficult to break using the cryptanalysis techniques published in the literature. In that
sense, the main problem for an eavesdropper is to recover T. Thus, we have concentrated
our attention on the problem <strong>of</strong> identifying the value <strong>of</strong> the time delay T.