<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/7e1869395799899be33ae9c59d7ddf936d3d5907..d509acd9cc478541bd9cf2f33686e60f3b77cce5:/main.tex

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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
+
+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.
+A upper bound of the 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.
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