Chaotic Synchronization Signal Shape Alteration as Seen by a Higher-Order Sliding-Mode Observer

Abstract

A method to overcome a correlation function based cryptanalytic attack in the case of chaos-based cryptography was proposed in the literature. The output of the transmitter, the synchronization message, was digitized and the weights of the bits of its binary representation were changed with a secret key consisting in a permutation only known by the two communication partners. The receiver was evolving according to the same equations as the transmitter. The present paper tests the feasibility of such an alteration of the synchronization signal, when the receiver does not have the same structure as the transmitter, being represented by a high-order sliding-mode observer. Simulation results are given for a chaotic Sprott's jerk circuit. Conclusions are drawn with respect to a physical implementation of such a schematic and the steps of the modified algorithm are summarized.Key Words: chaotic synchronization, sliding-mode observer, cryptography, shape alteration. INTRODUCTIONApplications of chaos theory are found in many domains as true random number generators (Creț, 2012;Ilyas, 2013), economy (Scarlat, 2006), physics (Stan, 2008), management (Scarlat, 2010), communications (Sterian, 2010Vlădeanu, 2004), symmetric and asymmetric cryptography (Zoghabi, 2013). A survey of existing chaos-based data encryption techniques and their application areas is presented in (Shukla, 2015). Research in the chaos-based field has occasioned its counterpart, cryptanalysis of such ciphers (a survey in (Li, 2007), enabling the formulation of a common framework for the designing of chaos based cryptosystems in (Alvarez, 2006). (Teodorescu, 2012) reviews several methods of determining features of the attractors, characterizing chaotic systems that are suitable in engineering and medical applications, such as control, measurement, and pattern recognition, based on chaotic dynamics.The present work aims to contribute to the area of symmetric cryptography based on chaotic synchronization (Boccaletti, 2002). The Colpitts oscillator, considered in (DeFeo, 2000) as a paradigm for sinusoidal oscillation, was used as chaotic transmitter and receiver in (Tauleigne, 2014). A countermeasure to autocorrelation function based attacks (see, for example, (Sobhy, 2001) was proposed, by digitizing the synchronization signal, transmitted over the unsecure communication channel, and by changing the weight of the bits in its binary representation. The secret-key was constituted by the bit permutation, the scheme showing good results, even if the parameters and the initial conditions of the transmitter were known by the hacker. This paper tests the feasibility of such a binary alteration of the synchronization signal, when the two communication partners do not possess the same structure, as in (Tauleigne, 2014). The synchronization between the transmitter and the receiver is achieved, this time, by using a higher-order sliding-mode observer. The fundamental nature of sliding mode control is described in (Spurgeon, 2014). Another difference from th...