From: cguyeux Date: Thu, 30 Aug 2012 12:01:05 +0000 (+0200) Subject: lfkdjslkjfsd X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/commitdiff_plain/c471dd052c6b541bcbc3712b5c3cad2e0f0df08b?ds=inline lfkdjslkjfsd --- diff --git a/prng_gpu.tex b/prng_gpu.tex index bf74539..c7853b2 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -565,7 +565,7 @@ This new generator is designed by the following process. First of all, some chaotic iterations have to be done to generate a sequence $\left(x^n\right)_{n\in\mathds{N}} \in \left(\mathds{B}^{32}\right)^\mathds{N}$ of Boolean vectors, which are the successive states of the iterated system. -Some of these vectors will be randomly extracted and our pseudo-random bit +Some of these vectors will be randomly extracted and our pseudorandom bit flow will be constituted by their components. Such chaotic iterations are realized as follows. Initial state $x^0 \in \mathds{B}^{32}$ is a Boolean vector taken as a seed and chaotic strategy $\left(S^n\right)_{n\in\mathds{N}}\in @@ -578,7 +578,7 @@ updated, as follows: $x_i^n = x_i^{n-1}$ if $i \neq S^n$, else $x_i^n = \overlin Such a procedure is equivalent to achieve chaotic iterations with the Boolean vectorial negation $f_0$ and some well-chosen strategies. Finally, some $x^n$ are selected -by a sequence $m^n$ as the pseudo-random bit sequence of our generator. +by a sequence $m^n$ as the pseudorandom bit sequence of our generator. $(m^n)_{n \in \mathds{N}} \in \mathcal{M}^\mathds{N}$ is computed from $PRNG_1$, where $\mathcal{M}\subset \mathds{N}^*$ is a finite nonempty set of integers. The basic design procedure of the New CI generator is summarized in Algorithm~\ref{Chaotic iteration1}. @@ -611,8 +611,7 @@ N \text{ if }\sum_{i=0}^{N-1}{C^i_{32}}\leqslant{y^n}<1.\\ } \ENDFOR \STATE$a\leftarrow{PRNG_1()}$\; -\STATE$m\leftarrow{g(a)}$\; -\STATE$k\leftarrow{m}$\; +\STATE$k\leftarrow{g(a)}$\; \WHILE{$i=0,\dots,k$} \STATE$b\leftarrow{PRNG_2()~mod~\mathsf{N}}$\; @@ -944,7 +943,7 @@ have $d((S,E),(\tilde S,E))<\epsilon$. \begin{color}{red} \section{Statistical Improvements Using Chaotic Iterations} -\label{The generation of pseudo-random sequence} +\label{The generation of pseudorandom sequence} Let us now explain why we are reasonable grounds to believe that chaos