Synchronizing hyperchaos for communication

Recent work pioneered by Pecora and Carroll has considered the possibility of exploiting the phenomenon of chaos synchronization to achieve secure communication. But, theoretical and experimental models studied thus far limit to low dimensional systems with one positive Lyapunov exponent. Consequently, messages masked by such simple chaotic processes are shown to be easily extracted in some cases. In this paper we investigate high dimensional implementation of the Pecora-Carroll synchronization paradigm. In particular, in regard to potential applications to communication, we address the question of whether by transmitting just one scalar signal one can achieve synchronism in chaotic systems with two or more positive Lyapunov exponents (hyperchaos). Using both numerical and analytical examples we argue that under very general conditions the answer to the above question is affirmative