Abstract
We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations.
Highlights
Since it was found that chaotic waveforms can be used to encrypt signals for secure communications [1], many attempts to break the key of chaotic cryptosystems and to retrieve the information have been reported
This Letter considers a specific class of chaotic systems, the delayed nonlinear feedback (DNLF) systems, i.e., systems ruled by nonlinear time-delay differential equation (DDE) whose dynamics can exhibit high-dimensional attractors with many positive Lyapunov exponents
The same features were used in another system we reported later in the radiofrequency domain [7,8] to enhance the security level. Security of these systems is still an open issue chaotic communications based on simpler encryption schemes have been shown to be susceptible to be cracked mainly in two cases: (i) it was shown that the information transmitted by a DNLF-system with a weak nonlinearity introduced by an erbium optical amplifier in the feedback loop [9] could be successfully unmasked by considering the chaotic waveform as a convolution of the original laser pulses with an “echo”-function associated with the delayed feedback loop [10]; (ii) a second type of attacks was proposed from time-series analysis in the case of Mackey–Glass systems, which feature a nonlinear function with only one extremum [11,12,13]
Summary
Since it was found that chaotic waveforms can be used to encrypt signals for secure communications [1], many attempts to break the key of chaotic cryptosystems and to retrieve the information have been reported. This Letter considers a specific class of chaotic systems, the delayed nonlinear feedback (DNLF) systems, i.e., systems ruled by nonlinear time-delay differential equation (DDE) whose dynamics can exhibit high-dimensional attractors with many positive Lyapunov exponents Those few last years, researchers have focused on the use of synchronized chaos to achieve secure communication systems. The same features were used in another system we reported later in the radiofrequency domain [7,8] to enhance the security level Security of these systems is still an open issue chaotic communications based on simpler encryption schemes have been shown to be susceptible to be cracked mainly in two cases: (i) it was shown that the information transmitted by a DNLF-system with a weak nonlinearity introduced by an erbium optical amplifier in the feedback loop [9] could be successfully unmasked by considering the chaotic waveform as a convolution of the original laser pulses with an “echo”-function associated with the delayed feedback loop [10]; (ii) a second type of attacks was proposed from time-series analysis in the case of Mackey–Glass systems, which feature a nonlinear function with only one extremum [11,12,13]. In order to evaluate the security we used experimental data sets obtained from the setup reported in [6]
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