Nonlinear Analysis: Real World Applications 8 (2007) 1003 – 1012 www.elsevier.com/locate/na Secure communication by chaotic synchronization: Robustness under noisy conditions Amalia N. Miliou a , ∗ , Ioannis P. Antoniades a , Stavros G. Stavrinides b , Antonios N. Anagnostopoulos b a Department of Informatics, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece b Physics Department, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece Received 28 March 2006; accepted 3 May 2006 Abstract In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a drive- response configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical imple- mentation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous second order non-linear oscillator system presented by G. Mycolaitis et al. in Proceed- ings of Seventh International Workshop on Nonlinear Dynamics of Electronic Systems [Globally synchronizable non-autonomous chaotic oscillator, Denmark, July 1999, pp. 277–280], which is particularly suitable for digital communications. Binary information is encoded by combining square pulses of two different frequencies selected so that the system is always in the chaotic regime independent of the encoded message.  2006 Elsevier Ltd. All rights reserved. Keywords: Chaos; Non-linear circuits; Synchronization; Communication system security 1. Introduction Computer networks are inherently insecure for Internet communication. Data transmission is not safe unless it is assured that the packets will never pass through a router or a computer, over which there is no control.Traditionally, software techniques were used for data encoding. However, the ever-increasing computer power threatens Internet communication security. The simplicity of chaos generators, the rich structure of chaotic signals and the fact that chaotic signals can be synchronized caused a significant interest in possible utilization of chaos for secure Internet communications [3,6,9]. The use of synchronized chaotic systems for communications usually relies on the robustness of the synchronization within the transmitter and receiver pair [6,13,11,2,10,8,4,5]. However, if the communication channel is imperfect and/or there is internal noise at the electronic circuitry the distorted signal at the receiver input might cause considerable synchronization mismatch between the transmitter–receiver pair [12,7,14,1,15]. ∗ Corresponding author. Tel.: +30 2310 998407; fax: +30 2310 998419. E-mail address: amiliou@csd.auth.gr (A.N. Miliou). 1468-1218/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.nonrwa.2006.05.004