X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/d509acd9cc478541bd9cf2f33686e60f3b77cce5..a57f211cb3b73d523ff516e65f2559b296775c11:/main.tex?ds=sidebyside diff --git a/main.tex b/main.tex index f49eef6..6225751 100644 --- a/main.tex +++ b/main.tex @@ -551,15 +551,15 @@ 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. +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}