X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/14b55657fe448a88441d16d87e11398351dfb4ab..e536269e382351ff7272f843e08c414f492fc437:/prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 807f6df..26460b3 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -177,8 +177,8 @@ Pseudorandom numbers are generated at a rate of 20GSamples/s, which is faster
 than in~\cite{conf/fpga/ThomasHL09,Marsaglia2003} (and with a better
 statistical behavior). Experiments are also provided using BBS as the initial
 random generator. The generation speed is significantly weaker.
-Note also that an original qualitative comparison between topological chaotic
-properties and statistical tests is also proposed.
+%Note also that an original qualitative comparison between topological chaotic
+%properties and statistical tests is also proposed.
 
 
 
@@ -1786,14 +1786,7 @@ Let $\varepsilon > 0$.
 $\mathcal{D}$ is called a $(T,\varepsilon)-$distinguishing attack on pseudorandom
 generator $G$ if
 
-\begin{flushleft}
-$\left| Pr[\mathcal{D}(G(k)) = 1 \mid k \in_R \{0,1\}^\ell ]\right.$
-\end{flushleft}
-
-\begin{flushright}
-$ - \left. Pr[\mathcal{D}(s) = 1 \mid s \in_R \mathds{B}^M ]\right| \geqslant \varepsilon,$
-\end{flushright}
-
+$$\left| Pr[\mathcal{D}(G(k)) = 1 \mid k \in_R \{0,1\}^\ell ]\right. - \left. Pr[\mathcal{D}(s) = 1 \mid s \in_R \mathds{B}^M ]\right| \geqslant \varepsilon,$$
 \noindent where the probability is taken over the internal coin flips of $\mathcal{D}$, and the notation
 ``$\in_R$'' indicates the process of selecting an element at random and uniformly over the
 corresponding set.