Public Channel Cryptography: Chaos Synchronization and Hilbert’s Tenth Problem

Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang

doi:10.1103/physrevlett.101.084102

Cited by 61 publications

(35 citation statements)

References 22 publications

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“…Even if the delay time is extremely large, complete (zero-lag) synchronization is possible [12][13][14]. Chaos synchronization has been discussed in the context of secure communication [15,16].…”

Section: Introductionmentioning

confidence: 99%

Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings

et al. 2013

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Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question of whether strong and weak chaos can be identified from the shape of the intensity trace, the autocorrelations, and the external cavity modes. The concept of the sub-Lyapunov exponent λ 0 is generalized to the case of two time-scale-separated delays in the system. We give experimental evidence of strong and weak chaos in a network of lasers, which supports the sequence of weak to strong to weak chaos upon monotonically increasing the coupling strength. Finally, we discuss strong and weak chaos for networks with several distinct sub-Lyapunov exponents and comment on the dependence of the sub-Lyapunov exponent on the number of a laser's inputs in a network.

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Section: Introductionmentioning

confidence: 99%

Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings

et al. 2013

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“…Many proposed applications of chaos, including secure communication systems, sensor networks and data assimilation and prediction, rely on this phenomenon of synchronization between chaotic oscillators (Argyris et al 2005;Golubitsky et al 2005;Boccaletti et al 2006;Arenas et al 2008;Kanter et al 2008). There have been some analytical studies of the coupling threshold required for synchronization in delayed-feedback systems (Bünner & Just 1998;Pyragas 1998).…”

Section: Coupled Systems and Synchronizationmentioning

confidence: 99%

Complex dynamics and synchronization of delayed-feedback nonlinear oscillators

Murphy

Cohen

Ravoori

et al. 2010

Phil. Trans. R. Soc. A.

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We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electro-optic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.

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“…The synchronization process of two mutually delay-coupled deterministic chaotic maps was demonstrated both analytically and numerically by Kanter, Kopelowitz, and Kinzel (2008). The mutually transmitted signals were concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals.…”

Section: Chaos Communication and Chaos Key Distributionmentioning

confidence: 99%

Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

et al. 2013

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Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing.

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Public Channel Cryptography: Chaos Synchronization and Hilbert’s Tenth Problem

Cited by 61 publications

References 22 publications

Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings

Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings

Complex dynamics and synchronization of delayed-feedback nonlinear oscillators

Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

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