Message Authentication Code is a function of the message and a secret key that produces a fixed-length value that serves as the authenticator. MAC provides authentication and confidentiality. This authentication technique does not include measures to counter repudiation by the source i.e. it does not provide digital signature. We propose a new Message authentication Image (MAI) Algorithm that provides confidentiality, authentication and digital signature. It uses Cryptographic and Steganographic ideas to conceal the data in the image. MAI is generated by using fractals. This approach explores the main feature of fractal image generated by Iterated Function System (IFS) techniques.

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.

On the base of the estimator variance analysis we present a classification for a number digital chaos communication schemes and conventional spread spectrum techniques, which allows the qualitative comparison of the behaviour of the systems under the presence of additive white Gaussian noise on the channel. The classification results in a ranking and shows that the conventional stored-reference technique outperforms all analyzed chaotic schemes, which reach at most the characteristics of transmitted-reference techniques.

In this paper the modeling of a signal by a chaotic generator with respect to a specified signal statistic will be considered. To accomplish that, the considered class of n-dimensional piecewise linear Markov generators will first be analyzed analytically, yielding an algebraic expression for the statistical quantity in question. Based on this analytical result an optimal set of parameters minimizing the modeling error with respect to the considered statistical quantity will be calculated.

This paper demonstrates the application of cumulant equations to the analysis of non-recursive systems with polynomial characteristics, as they are often found in the baseband equivalents of communication systems. The described method leads to an analytical characterization of the systems, which is not known so far for many chaos communication systems. We use the DPSK and DCSK communication schemes under the influence of white Gaussian channel noise as examples for the derivation of first- and second-order cumulants. This allows us to find the qualitative differences between the two systems which are very similar in structure. Furthermore it provides criteria for optimum selection of signals to be used in DCSK. This demonstrates the usefulness and power of cumulant analysis

| In this paper we compare the chaotic Diierential Chaos Shift Keying (DPSK) communication scheme with the conventional Diierential Phase Shift Keying (DPSK). The two methods are similar in both, structure and function. However, the existing diierences in the schemes lead to qualitatively diier-ent behaviour under the innuence of additive white Gaussian noise on the channel. In DPSK a transmission power decrease is compensated by a proportional bitlength increase, whereas in DCSK it is not. As a consequence, DCSK is not robust against noise.

This paper deals with the generation of chaotic signals which have a uniform probability distribution up to nth-order. First a generator structure containing a static nonlinearity and a dynamical subsystem is deduced and the system characteristics are specified. Then conditions for the generation of continuous-value signals with nth-order uniform distribution are derived. For the special case of digital filter structures with chaotic behaviour the condition is simply that one specified parameter has to be an integer. Finally problems of continuous-value and discrete-value analysis and realisation are discussed. Some simulation results are provided