Extracting Messages Masked by Chaotic Signals of Time-delay Systems

Abstract

We show how to extract messages masked by a chaotic signal of a time-delay system with very high dimension and many positive Lyapunov exponents. Using a special embedding coordinate, the infinite dimensional phase space of the time-delay system is projected to 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 Mackey-Glass time-delay system for two type of masking schemes and different kinds of messages.