Deciphering Secure Chaotic Communication

A simple technique for decoding an unknown modulated chaotic time-series is presented. We point out that, by fitting a polynomial model to the modulated chaotic signal, the error in the fit gives sufficient information to decode the modulating signal. For analog implementation, a lowpass filter can be used for fitting. This method is simple and easy to implement in hardware. Indexing terms: chaotic time-series, secure communication (PACS: 05.45). Secure communication using chaos has received much attention recently. Various methods for modulating and demodulating a chaotic oscillator have been proposed (see [1] and references cited in [2]). There are two ways to hide the modulating signal inside the chaotic carrier signal. One way is to add a small modulating signal to the chaotic carrier signal whose amplitude is much larger. This is called chaotic masking. In this case, power is wasted in the carrier. Another way to encode the modulating signal is to modulate the parameters of the carrier chaotic oscillator. This method has been demonstrated experimentally by many groups[2]. However, it has also been pointed out that secure communication using chaos can be broken ([3],[4]). The first method in [3] is specific to the Lorenz oscillator case. The second method by Short[4] is more general. In this approach by Short, the modulating signal is ∗e-mail address: [email protected]