X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/7e1869395799899be33ae9c59d7ddf936d3d5907..c9d6a79d174af327059607a3e0a1f23ab7921a49:/main.tex?ds=inline

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 % in the abstract or keywords.
 
 
+% \begin{abstract}
+% This paper is dedicated to the design of chaotic random generators
+% and extends previous works proposed by some of the authors.
+% We propose a theoretical framework proving both the chaotic properties and
+% that the limit distribution is uniform.
+% A theoretical bound on the stationary time is given and
+% practical experiments show that the generators successfully pass
+% the classical statistical tests.
+% \end{abstract}
+
 \begin{abstract}
-This paper is dedicated to the design of chaotic random generators
-and extends previous works proposed by some of the authors.
-We propose a theoretical framework proving both the chaotic properties and
-that the limit distribution is uniform.
-A theoretical bound on the stationary time is given and
-practical experiments show that the generators successfully pass
-the classical statistical tests.
+
+Designing a pseudorandom number generator (PRNG) is a hard and complex task.
+Many recent works have consider chaotic functions as the basis of built 
+PRNGs:
+the quality of the output would be an obvious consequence of some chaos 
+properties.  
+However, there is no direct reasoning that goes from chaotic functions to 
+uniform distribution of the output. 
+Moreover, it is not clear that embedding such kind of functions into a PRNG
+allows to get a chaotic output, which could be required for simulating 
+some chaotic behaviours.
+
+In a previous work, some of the authors have proposed the idea of walking
+into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle have been
+removed as the basis of a chaotic PRNG. In this article,  all the difficult
+issues observed in the previous work have been tackled. The chaotic behavior
+of the whole PRNG is proven. The construction of the balanced Hamiltonian
+cycle is theoretically and practically solved. An upper bound of the
+expected length of the walk to obtain a uniform distribution is calculated.
+Finally practical experiments show that the generators successfully pass the
+classical statistical tests.
+
+
 \end{abstract}
 
+
+
+
 % Note that keywords are not normally used for peerreview papers.
 % \begin{IEEEkeywords}
 % IEEE, IEEEtran, journal, \LaTeX, paper, template.