Adaptive synchronization of chaotic systems based on speed gradient method and passification

Fradkov, Alexander L.; Markov, A. Yu.

doi:10.1109/81.633879

Cited by 107 publications

(47 citation statements)

References 17 publications

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“…Essentially, chaotic switching is a special type of chaotic parameter modulation: binary modulation. As a generalization of chaotic switching, the parameter involved in a parameter modulation system can be both discrete [89,38] or continuous [42,51], rather than only 0 or 1 in chaotic switching. The message-embedding technique is given different names in the literature: embedding [72,82], non autonomous modulation [112] or direct chaotic modulation [47].…”

Section: Main Problems In Chaos-based Cryptographymentioning

confidence: 99%

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

Álvarez

Amigó

Arroyo

et al. 2011

Studies in Computational Intelligence

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The idea of using chaotic transformations in cryptography is explicit in the foundational papers of Shannon on secrecy systems (e.g., [96]). Although the word "chaos" was not minted till the 1970s [71], Shannon clearly refers to this very concept when he proposes the construction of secure ciphers by means of measure-preserving, mixing maps which depend 'sensitively' on their parameters. The implementation of Shannon's intuitions had to wait till the development of Chaos Theory in the 1980s. Indeed, it was around 1990 when the first chaos-based ciphers were proposed (e.g., [78], [46]). Moreover, in 1990 chaos synchronization [91] entered the scene and shortly thereafter, the first applications to secure communications followed [56,37]. The idea is remarkably simple: mask the message with a chaotic signal and use synchronization at the receiver to filter out the chaotic signal. The realization though had to overcome the desynchronization induced by the message itself. After this initial stage, the number of proposals which exploited the properties of chaotic maps for cryptographical purposes, grew in a spectacular way.

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Section: Main Problems In Chaos-based Cryptographymentioning

confidence: 99%

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

Álvarez

Amigó

Arroyo

et al. 2011

Studies in Computational Intelligence

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“…For a passivity based adaptive approach to synchronization the reader is referred to the interesting articles by Fradkov and Markov [1997] and that by . On the other hand, a purely state estimation based approach entitles the transmission of the chaotic system output for the purpose of remotely generating the unperturbed states of the transmitting system via a properly designed asymptotic observer.…”

Section: Introductionmentioning

confidence: 99%

An Algebraic State Estimation Approach for the Recovery of Chaotically Encrypted Messages

Sira‐Ramírez

Fliesś

2006

Int. J. Bifurcation Chaos

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In this article, we use a variant of a recently introduced algebraic state estimation method obtained from a fast output signal time derivatives computation process. The fast time derivatives calculations are entirely based on the consequences of using the "algebraic approach" in linear systems description (basically; module theory and non-commutative algebra). Here, we demonstrate, through computer simulations, the effectiveness of the proposed algebraic approach in the accurate and fast (i.e. non asymptotic) estimation of the chaotic states in some of the most popular chaotic systems. The proposed state estimation method can then be used in a coding-decoding process of a secret message transmission using the message-modulated chaotic system states and the reliable transmission of the chaotic system observable output. Simulation examples, using Chen's chaotic system and the Rossler system, demonstrate the important features of the proposed fast state estimation method in the accurate extraction of a chaotically encrypted messages. In our simulation results, the proposed approach is shown to be quite robust with respect to (computer generated) transmission noise perturbations. We also propose a way to evade computational singularities associated with the local lack of observability of certain chaotic system outputs and still carry out the encrypting and decoding of secret messages in a reliable manner.

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“…When this is achieved using adaptive control type methods, the process is referred to as adaptive synchronization [John & Amritkar, 1994;Boccaletti et al, 1997;Fradkov & Markov, 1997;Dedieu & Ogorzalek, 1997]. More recently, the concept of partial synchronization between two or more similar chaotic systems has been studied [Hasler, 1998;Yanchuk et al, 2001].…”

Section: Introductionmentioning

confidence: 99%

Partial Synchronization of Nonidentical Chaotic Systems via Adaptive Control, With Applications to Modeling Coupled Nonlinear Systems

Wagg

2002

Int. J. Bifurcation Chaos

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We consider the coupling of two nonidentical dynamical systems using an adaptive feedback linearization controller to achieve partial synchronization between the two systems. In addition we consider the case where an additional feedback signal exists between the two systems, which leads to bidirectional coupling. We demonstrate the stability of the adaptive controller, and use the example of coupling a Chua system with a Lorenz system, both exhibiting chaotic motion, as an example of the coupling technique. A feedback linearization controller is used to show the difference between unidirectional and bidirectional coupling. We observe that the adaptive controller converges to the feedback linearization controller in the steady state for the ChuaLorenz example. Finally we comment on how this type of partial synchronization technique can be applied to modeling systems of coupled nonlinear subsystems. We show how such modeling can be achieved where the dynamics of one system is known only via experimental time series measurements.

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Adaptive synchronization of chaotic systems based on speed gradient method and passification

Cited by 107 publications

References 17 publications

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

An Algebraic State Estimation Approach for the Recovery of Chaotically Encrypted Messages

Partial Synchronization of Nonidentical Chaotic Systems via Adaptive Control, With Applications to Modeling Coupled Nonlinear Systems

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