Discontinuity, Nonlinearity, and Complexity 4(1) (2015) 1–9 Discontinuity, Nonlinearity, and Complexity https://lhscientificpublishing.com/Journals/DNC-Default.aspx How to Resist Synchronization Attacks A.N. Pisarchik 1,2† , M. Jim´ enez-Rodr´ ıguez 3 , and R. Jaimes-Re´ ategui 4 1 Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, Leon, Guanajuato, Mexico 2 Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid, Spain 3 Centro Universitario de la Ci´ enega, Universidad de Guadalajara, Av. Universidad 1115, Lindavista, Ocotl´ an, Jalisco, Mexico 4 Centro Universitario de Los Lagos, Universidad de Guadalajara, Enrique D´ ıaz de Le ´ on 1144, Paseo de la Monta˜ na, Lagos de Moreno, Jalisco, Mexico Submission Info Communicated by Valentin Afraimovich Received 16 February 2014 Accepted 17 June 2014 Available online 1 April 2015 Keywords Communication, security, cipher Encryption, chaos, synchronization R¨ ossler oscillator, logistic map Abstract Conventional synchronization-based chaotic communication is vulnerable to synchronization attacks enable to recuperate system parameters. How- ever, it is possible to make these attacks inefficient. The simple way to resist synchronization attacks is to change a parameter of the master sys- tem faster than the time needed for the system to synchronize. To verify this idea we construct a hybrid communication system composed of two chaotic R¨ ossler oscillators and the chaotic logistic map. The latter is used for fast variation of the most sensitive system parameter when the R¨ ossler oscilla- tors synchronize. The algorithm is robust to noise in the communication channel. ©2015 L&H Scientific Publishing, LLC. All rights reserved. 1 Introduction Chaos communication is attracted much attention because of intrinsic properties of chaotic systems, such as pseudorandom behavior and spread spectrum [1–4]. Since chaos is a deterministic motion, it can be easily decoded. In recent years a growing interest in applications of chaos in communications has been motivated by the fact that chaotic systems can be synchronized [5] that allows information transmission using a wide band chaotic signal [6]. The main advantage of a synchronization-based communication system over a traditional one is that the former makes implementation of coherent receivers feasible, i.e., the received chaotic waveform contains all possible sample functions, while by incoherent detection only one or several characteristics of the sample functions are estimated. Moreover, chaotic modulation has better performance under multi path propagation conditions, because the cross correlation between segments of chaotic time series is lower than between periodic ones. In the first scientific paper on chaotic cryptography that appeared in 1989, Matthews [7] came up with the idea of a stream cipher based on a one-dimensional chaotic map. One year later, Pecora and Caroll [5] † Corresponding author. Email address: apisarch@cio.mx ISSN 2164 - 6376, eISSN 2164 - 6414/$-see front materials © 2015 L&H Scientific Publishing, LLC. All rights reserved. DOI : 10.5890/DNC.2015.03.001