Extracting messages masked by chaotic signals of time-delay systems

We show how to extract messages masked by a chaotic signal of a time-delay system with very high dimensions and many positive Lyapunov exponents. Using a special embedding coordinate, the infinite-dimensional phase space of the time-delay system is projected onto a special three-dimensional space, which enables us to identify the time delay of the system from the transmitted signal and reconstruct the chaotic dynamics to unmask the hidden message successfully. The message extraction procedure is illustrated by simulations with the Mackey-Glass time-delay system for two types of masking schemes and different kinds of messages.