This chapter deals with the statistical description of chaotic signals and systems. Although chaotic systems are purely deterministic they can be modelled, analysed and designed by using probability measures and statistical characteristics, such as probability density functions and correlation functions, widely used in signal theory and in engineering applications. The chapter describes the problem of statistical analysis, the performance evaluation of chaotic signal processing schemes. This requires the introduction of an extended calculus because random processes interact with chaotic signals. The chapter examines the solution of inverse problem, the synthesis and design of chaotic systems from prescribed statistical characteristics of signals to be generated. Chaos communication schemes are analysed and the results are presented in terms of performance criteria commonly used in communication engineering. The fundamentals of statistical analysis of chaotic systems are explained systematically. The theory is mainly developed for multidimensional systems and illustrated with examples for one-dimensional case. The chapter presents and develops tools for the statistical analysis.

In this paper, the authors present their opinion and research results collected during the last ten years on the conjunction of chaos and cryptography. Special consideration is taken to show some general critical points and limitations of this approach and to provide some pointers to a comprehensive and careful evaluation of the cryptographical properties of chaotic systems.

Nonlinear Dynamics of Electronic Systems, pp. 66-70 (2000) No AccessDiscrete Versus Continuous Maps – A Cryptographical ComparisonFrank Dachselt and Wolfgang SchwarzFrank DachseltTechnical University of Dresden, Institute for Fundamentals of Electrical Engineering and Electronics, Mommsenstraße 13, 01062 Dresden, Germany and Wolfgang SchwarzTechnical University of Dresden, Institute for Fundamentals of Electrical Engineering and Electronics, Mommsenstraße 13, 01062 Dresden, Germanyhttps://doi.org/10.1142/9789812792662_0014Cited by:1 (Source: Crossref) PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: Discrete-value and continuous-value maps are compared with respect to their cryptographical properties. In order to provide a more rigid evaluation of nonlinear chaotic encryption systems information-theoretic measures are derived that allow a comparison with classical discrete-value systems in relevant practical situations. Furthermore the consideration gives some insight about the general limitations of continuous-value operations in cryptographic applications. The application of these evaluation measures is illustrated by some examples. FiguresReferencesRelatedDetailsCited By 1Cited by lists all citing articles based on Crossref citation.Chaos and cryptographyF. Dachselt and W. Schwarz1 Dec 2001 | IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 48, No. 12 Recommended Nonlinear Dynamics of Electronic SystemsMetrics History PDF download

Chaotic and classical (binary) stream ciphers are compared with respect to their cryptographical properties. Possible synchronization schemes, algebraic and analytical properties as well as design and implementation aspects are discussed. For two example classes with similar system structures it is shown that chaotic stream ciphers can achieve a higher level of complexity than classical binary systems due to the algebraic properties of the system structure.

For pt. 2 see Proc. Workshop Nonlinear Dynamic Electron. Syst.., Seville, p. 27-32 (1996). This work deals with the cryptographical analysis of a class of discrete-time continuous-value encryption systems. The design of these systems has been treated in Part I. Here, approaches and criteria used in applied cryptography are adopted for continuous-value systems. Two different ciphertext-only attacks on the encryption system are presented in detail. Based on the analysis, improvements of the coder system are suggested

This paper deals with principles of hiding information by chaotic coders and methods of attacking these encryption systems (cryptoanalysis). After a survey of working principles and cryptographical assumptions the attention is focused on public channel chaotic coding systems where principles of the cryptographical analysis are discussed. Finally a discrete-time chaotic encryption system which has been designed on the condition of public channel and unknown coder structure is treated and two ciphertext-only, public structure attacks are performed.