Two mutually coupled chaotic diode lasers with individual external feedback, are shown to establish chaos synchronization in the low-frequency fluctuations regime. A third laser with identical external feedback but coupled unidirectionally to one of the pair does not synchronize. Both experiments and simulations reveal the existence of a window of parameters for which synchronization by mutual coupling is possible but synchronization by unidirectional coupling is not. This parameter space forms the basis of a proposed public-channel cryptographic scheme and is robust to various possible attacks.
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