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 \section{Objectifs de le thÃ¨se}
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+During my research studies, the quantization effects on the dynamics of the chaotic maps have been investigated. It is noticed that most of the maps will experience the problems such as short periodic cycle length, high correlation of data, and the problem of the existence of fixed points will become significant. Therefore, a new scheme based on chaotic iterations is proposed. It is found that the statistical properties of a sequence can be greatly improved by applying this newly designed chaotic iterations function. This hence can also serve as the major building block for the design of chaos-based random number generators.
 
 \section{Organisation du manuscrit}
 
+The organization of this thesis is as follows.
+
+In Chapter 2, serving as the background of this thesis, the fundamental views and definitions of random number are summarized, and an overview of the classification and explanation of different types of RNGs are provided. We present the definitions that will be used in this thesis. The use of chaos for random number generators will be summarized. Some techniques to generate random number, based on chaos, will be revisited. 
+
+In Chapter 3, beginning with an brief review of the combinatorial objects used in the design of CIs PRNG and a theoretical proof of chaotic iterations, it outlines two novel approaches for generating random number sequences based on chaotic iterations techniques. The design of CIs for random number generators will be summarized. Some typical examples of chaos-based random number generators are described.
+
+
+ 
+In Chapter 4, a detailed study is undergone, how a PRNG can be tested is described and the details of Diehard, NIST, comparative test parameters and TestU01 statistical test suites are presented. A comparative study on the quality of two novel approaches for CIs PRNGs and the associated random number generators are reported. The approach for combining two generators based on chaotic iterations would give better properties than the individual components alone. The comparison of the speed and  statistical tests results allow us to consider that our new CIs generator has better pseudo-random characteristics
+
+
+in Chapter 5. The performance of these newly designed PRNG based on chaotic iterations will be analyzed and compared with some common PRNGs. Finally, the criteria, such as uniformity, correlations, sequence patterns and complexity, and so on, which are commonly used to verify the randomness of a sequence, are also introduced.
+
+In Chapter 6, In prior literature, the iterate function is just the vectorial boolean negation.  
+In this Chapter, we propose a method using Graph with strongly connected components as a selection criterion for chaotic iterate function. 
+In order to face the challenge of using the proposed chaotic iterate functions in PRNG, these PRNGs are subjected to the above statistical batteries of tests.
+
+
+In Chapter 7, a potential use of above PRNGs in some Internet security field is presented, namely in information hiding. Such generators can strongly improve the confidence put in any information hiding scheme and in cryptography in general: due to their properties of unpredictability, the possibilities offered to an attacker to achieve his goal are drastically reduced in that context. 
+
+
+We conclude this thesis in Chapter 8 by summarizing the significance of our work  and discussing the possible future work in this area.
+
 
 \section{AbrÃ©viations}
 \begin{tabular}{ll}\toprule
