This work tests the level of security in secure communication systems based on nonlinear dynamics (NLD), or chaos. In these systems, a chaotic carrier signal is used in a type of spread-spectrum signaling system, with the added benefit that the hidden information signal is buried at something of the order of −30 dB with respect to the chaotic carrier. To investigate the level of security in such systems, an examination was conducted on a test set of chaotic carriers and hidden information signals prepared by the NLD research group at the Naval Research Lab. The hidden signals included a triangle wave, a period doubled signal, and a chaotic signal that was different from the chaotic carrier. The analysis process was to use NLD forecasting to predict the carrier dynamics, and then subtract away the predicted values to reveal the hidden signal or at least increase its signal-to-noise ratio with respect to the carrier. In each case, it was a simple task to determine the power spectrum of the hidden signal once the prediction of the carrier was removed. This was then used to create a “comb” filter to extract the correct frequencies from the FFT of the first two signals. When this was done, the hidden signals were recreated with almost perfect accuracy. In the third case, the hidden chaotic signal had a broadband component, so the spectrum was used to develop a Weiner filter which enabled the hidden signal to be reconstructed with only moderate accuracy, where the overall structure of the hidden chaotic signal was preserved, but the fine structure was lost. As a further test, the processing approach was applied to a voice signal hidden in one-dimensional Lorenz data at −35 dB. After subtracting away the carrier model, the voice signal was reconstructed with reasonable accuracy, and had the same characteristic structure. In this case, no secondary filtering was applied. The forecasting approach was then extended to allow for dynamic signal estimation using threshold detection, so that whenever a signal was detected, multiple predictions of the carrier behavior were made into the future. This was tested on a square wave embedded at −42 dB in Lorenz data. The extended approach was able to reveal the square wave with almost perfect precision, except in a few regions where it temporarily lost synchrony with the carrier. This allowed for the elimination of the secondary filtering requirement entirely. The final conclusion is that the secure communications systems based on chaotic carriers may be useful to increase privacy, but are not yet capable of providing a high level of security. The paper concludes with a discussion of measures which may be taken to improve the security of such systems so that they may be applicable to areas where higher security is required.

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This paper will address the problem of unmasking a new chaotic communication scheme using synchronizing circuits, where the Lorenz system is modulated by the message and the x-coordinate of the modulated system is added to the message and transmitted to the receiver. The receiver is driven into perfect synchrony with the transmitter even in the presence of the message, and since the message becomes part of the dynamics it provides very little distortion to the phase space of the dynamical system. However, this paper will demonstrate that it is still possible to extract a sinusoidal message from the transmitted signal. It will also be shown that it is possible to extract the sinusoidal signal solely from the x-coordinate, without secondarily adding back the message sinusoid before transmission. The message extraction is also shown to work for simple frequency-modulated and phase-modulated message signals. The modulated communication scheme does effectively nullify a multi-step unmasking technique which had been somewhat successful when applied to chaotic communication schemes which employed additive message signals.

This paper will consider the use of nonlinear dynamic forecasting techniques to extract message signals from a six-dimensional, message-modulated hyperchaotic communication scheme. It will be shown that a variety of messages can be successfully extracted using only a three-dimensional reconstruction. Further, the robustness of the signal extraction is demonstrated by extracting a speech message with the speech amplitude varied by over an order of magnitude. In all cases intelligible speech was extracted, so security was not greatly improved by going to a hyperchaotic system or larger amplitude signals. ͓S1063-651X͑98͒12207-9͔ PACS number͑s͒: 05.45.ϩb, 89.70.ϩc FIG. 4. Extracted speech.

No abstract