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+% 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. diff --git a/prng.tex b/prng.tex index b4f2059..8acfce7 100644 --- a/prng.tex +++ b/prng.tex @@ -186,7 +186,7 @@ achieve to pass the NIST battery of tests. -\begin{table} +\begin{table*} \renewcommand{\arraystretch}{1.3} \begin{center} \begin{scriptsize} @@ -217,7 +217,7 @@ Linear Complexity& 0.719 (1.0)& 0.739 (0.99)& 0.759 (0.98)& 0.122 (0.97)& 0.514 \end{center} \caption{NIST SP 800-22 test results ($\mathbb{P}_T$)} \label{The passing rate} -\end{table} +\end{table*} %%% Local Variables: -- 2.39.5