Synchronization of Unified Chaotic Systems Using Sliding Mode Controller

This paper presents a method for synchronizing the unified chaotic systems via a sliding mode controller (SMC). The unified chaotic system and problem formulation are described. Two identical unified chaotic systems can be synchronized using the SMC technique. The switching surface and its controller design are developed in detail. Simulation results show the feasibility of a chaotic secure communication system based on the synchronization of the Lorenz circuits via the proposed SMC

Esquema de sincronização adaptativa de sistemas caóticos com aplicação à comunicação com segurança

Monografia (graduação)—Universidade de Brasília, Faculdade de Tecnologia, 2013.Neste trabalho estudam-se esquemas de comunicação com segurança baseados no mascaramento caótico da mensagem a ser transmitida. Para tanto, uma revisão sobre sistemas caóticos e sua participação nos esquemas de comunicação com segurança é apresentada. Na sequência, dois esquemas conhecidos na literatura são analisados. No primeiro esquema é utilizada uma sincronização por sinal comum. No segundo esquema é empregada uma sincronização usando um controlador de modos deslizantes. Objetivando-se suprir as deficiências dos esquemas analisados, é proposto um esquema para comunicação com segurança baseado em sincronização adaptativa de sistemas caóticos unificados em combinação com uma criptografia caótica. O esquema de sincronização é baseado na teoria de estabilidade de Lyapunov, para assegurar limitação e convergência assintótica do erro de sincronização para zero, mesmo na presença de distúrbios limitados e parâmetros incertos. Um exemplo é apresentado objetivando-se mostrar a aplicação do esquema proposto e seu desempenho quando comparado com os dois esquemas analisados previamente. Como esperado da análise teórica, sob as condições propostas, o desempenho do esquema proposto é superior. ___________________________________________________________________________ ABSTRACTThe present work studies secure communication schemes based on chaotic masking of the transmitted signal. Therefore, a brief review of chaotic systems and their importance to secure communication schemes is presented. In the sequel, two known, by the engineering community, schemes are analyzed. On the first one, a drive-signal synchronization is proposed, whereas on the second, a sliding-mode control synchronization is proposed. To extinguish the deficiencies of the analyzed schemes, a new scheme is proposed based on adaptive synchronization of unified chaotic systems in combination with chaotic cryptography. The scheme is based on the Lyapunov Stability Theory, so that ultimately, the asymptotic convergence of the error to zero is proven, even in the presence of limited disturbances e uncertain parameters. An example is presented so that the applications and performance of the proposed scheme can be shown in comparison to the two already analyzed schemes. As expected, the proposed scheme shows an improvement in the synchronization and security of the communications scheme

Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption

Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which adds enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.Comment: 20 pages, 11 figures; Article in press, Optics Communications (2011

On synchronization of chaotic systems

This paper deals with the problem of synchronization, or observer design, of chaotic dynamical systems. It is argued that the complex nature of the transmitter dynamics may provide additional tools for finding a suitable observer. A number of characteristic examples illustrate the idea, and reveal some challenging open problems in this contex