Output Choice of a Chaotic Jerk Circuit Used as Transmitter in Data Secure Communications

Abstract

Usually, when analyzing a data series, dynamical systems theory is used to reconstruct the state space of the original system. This work aims to determine which of a chaotic system's states is best suited as output when transmitting secret messages. This is the first step prior to designing an actual communication scheme. As an example, the three states of Sprott's jerk circuit are analyzed in terms of the local observability they ensure for the original dynamics when transmitted as a scalar data series. Results show that its first two states enable accurate estimation of the transmitter's dynamics at the receiving end. However, its third state generates, in some regions of the state space, a non-invertible transformation between the original state space and the one the receiver sees. This is due to the exponential nonlinearities present in this state's derivatives. Given that these nonlinearities remain inaccessible to the receiver, they are neglected in order to allow the partial reconstruction of the dynamics of the transmitter. But, since these nonlinearities are essential for the chaotic behavior, this makes the third state unusable for cryptographic purposes. This analysis may be applied to any bipolar junction transistor or diode based chaotic circuit.

Keywords

• chaotic communication
• nonlinear dynamical systems
• observers
• signals analysis
• sliding mode control