Generalized Synchronization Theorem for Non-Autonomous Differential Equation with Application in Encryption Scheme

Abstract

This paper introduces a constructive theorem for design- ing a non-autonomous driven system, which can achieve generalized chaos synchronization (GCS) to a driving sys- tem. As a first application, a encryption scheme is established based on GCS non-autonomous systems. This scheme has the functions of the datum authentication and one-time-pad. As a second application, the non-autonomous Driven van der Pol oscillator is selected as a driving system. A invertible transform H is introduced to design a driven sys- tem such that the two systems are in GS with respect to H. Based on the GCS systems and the scheme one can en- crypt and decrypt original information without any loss. The analysis of the key space and sensitivity of key param- eters show that this scheme has sound security. The key space of the scheme is larger that 2148. It can be expected that our theorem provides a new tool for studying and understanding the GS phenomena and the scheme offers a new method for information encryption.