lfkdjslkjfsd

[prng_gpu.git] / prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index bf745396e5de1554ae158241292cc6c1b56293eb..c7853b230ce4ab04aab4605b483b5b54a42afeb7 100644 (file)
--- 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. 
 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 
 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
 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}.
 $(m^n)_{n \in \mathds{N}} \in \mathcal{M}^\mathds{N}$ 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$a\leftarrow{PRNG_1()}$\;
 }
 \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$b\leftarrow{PRNG_2()~mod~\mathsf{N}}$\;
 \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}
 
 \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 
 
 
 Let us now explain why we are reasonable grounds to believe that chaos