ajout espace bib

[rairo15.git] / prng.tex

diff --git a/prng.tex b/prng.tex
index 3776d09ef95fe98f1968ee88c0d8829068eea25b..5025b4eca7a9d1115ab01749ab0afe33f06660bf 100644 (file)
--- a/prng.tex
+++ b/prng.tex
@@ -10,7 +10,7 @@ a random choice of which edge to follow, and traverses this edge
 provided it is allowed to do so, \textit{i.e.}, 
 when $\textit{Random}(1)$ is not null. 
 The final configuration is thus outputted.
 provided it is allowed to do so, \textit{i.e.}, 
 when $\textit{Random}(1)$ is not null. 
 The final configuration is thus outputted.

-This PRNG is formalized in Algorithm~\ref{CI Algorithm}.
+This PRNG is formalized in Algorithm~\ref{CI Algorithm:2}.

 
 
 
 
 
 


@@ -29,7 +29,7 @@ $x\leftarrow{F_f(s,x)}$\;
 return $x$\;
 %\end{scriptsize}
 \caption{Pseudo Code of the $\chi_{\textit{15Rairo}}$ PRNG}
 return $x$\;
 %\end{scriptsize}
 \caption{Pseudo Code of the $\chi_{\textit{15Rairo}}$ PRNG}

-\label{CI Algorithm}
+\label{CI Algorithm:2}

 \end{algorithm}
 
 
 \end{algorithm}
 
 


@@ -86,11 +86,11 @@ Function $f$ & $f(x)$, for $x$ in $(0,1,2,\hdots,2^n-1)$ & $\mathsf{N}$ & $b$
 &$E[\tau]$\\ 
 \hline
 %%%%% n= 4
 &$E[\tau]$\\ 
 \hline
 %%%%% n= 4

-$\textcircled{a}$&[13,10,9,14,3,11,1,12,15,4,7,5,2,6,0,8]&4&64&\\
+$\textcircled{a}$&[13,10,9,14,3,11,1,12,15,4,7,5,2,6,0,8]&4&64&154\\

 \hline
 %%%%% n= 5
 $\textcircled{b}$& 
 \hline
 %%%%% n= 5
 $\textcircled{b}$& 

-[29, 22, 25, 30, 19, 27, 24, 16, 21, 6, 5, 28, 23, 26, 1, 17, & 5 & 78 & \\
+[29, 22, 25, 30, 19, 27, 24, 16, 21, 6, 5, 28, 23, 26, 1, 17, & 5 & 78 & 236\\

 &
  31, 12, 15, 8, 10, 14, 13, 9, 3, 2, 7, 20, 11, 18, 0, 4]
 &&&\\
 &
  31, 12, 15, 8, 10, 14, 13, 9, 3, 2, 7, 20, 11, 18, 0, 4]
 &&&\\


@@ -104,7 +104,7 @@ $\textcircled{b}$&
 &&&\\
 $\textcircled{c}$&
  26, 25, 30, 19, 27, 17, 28, 31, 20, 23, 21, 18, 22, 16, 24, 13, 
 &&&\\
 $\textcircled{c}$&
  26, 25, 30, 19, 27, 17, 28, 31, 20, 23, 21, 18, 22, 16, 24, 13, 

-&6&88&\\
+&6&88&335\\

 &
 12, 29, 8, 43, 14, 41, 0, 5, 38, 4, 6, 11, 3, 9, 32]
 &&&\\
 &
 12, 29, 8, 43, 14, 41, 0, 5, 38, 4, 6, 11, 3, 9, 32]
 &&&\\


@@ -121,7 +121,7 @@ $\textcircled{c}$&
 &&&\\
 $\textcircled{d}$& 
 69, 20, 19, 114, 17, 112, 77, 76, 13, 108, 74, 10, 9, 73, 67, 66,
 &&&\\
 $\textcircled{d}$& 
 69, 20, 19, 114, 17, 112, 77, 76, 13, 108, 74, 10, 9, 73, 67, 66,

-&7 & 99&\\
+&7 & 99&450\\

 
 & 
  101, 100, 75, 82, 97, 0, 127, 54, 57, 62, 51, 59, 56, 48, 53, 38,
 
 & 
  101, 100, 75, 82, 97, 0, 127, 54, 57, 62, 51, 59, 56, 48, 53, 38,


@@ -171,7 +171,7 @@ $\textcircled{d}$&
 &&&\\
 $\textcircled{e}$&
 8, 7, 198, 197, 4, 195, 2, 161, 160, 255, 124, 109, 108, 122,
 &&&\\
 $\textcircled{e}$&
 8, 7, 198, 197, 4, 195, 2, 161, 160, 255, 124, 109, 108, 122,

-&8&110&\\
+&8&110&582\\

 &
  126, 125, 112, 117, 114, 116, 100, 123, 98, 97, 113, 79, 106,
 &&&\\
 &
  126, 125, 112, 117, 114, 116, 100, 123, 98, 97, 113, 79, 106,
 &&&\\


@@ -226,6 +226,26 @@ achieve to pass the NIST battery of tests.
 \setlength{\tabcolsep}{2pt}
 
 
 \setlength{\tabcolsep}{2pt}
 
 

+\begin{tabular}{|l|l|l|l|l|l|}
+\hline
+Method &$\textcircled{a}$& $\textcircled{b}$ & $\textcircled{c}$ & $\textcircled{d}$ & $\textcircled{e}$   \\ \hline\hline
+Frequency (Monobit)& 0.851 (0.98)& 0.719 (0.99)& 0.699 (0.99)& 0.514 (1.0)& 0.798 (0.99)\\ \hline 
+Frequency (Monobit)& 0.851 (0.98)& 0.719 (0.99)& 0.699 (0.99)& 0.514 (1.0)& 0.798 (0.99)\\ \hline 
+Frequency  within a Block& 0.262 (0.98)& 0.699 (0.98)& 0.867 (0.99)& 0.145 (1.0)& 0.455 (0.99)\\ \hline 
+Cumulative Sums (Cusum) *& 0.301 (0.98)& 0.521 (0.99)& 0.688 (0.99)& 0.888 (1.0)& 0.598 (1.0)\\ \hline 
+Runs& 0.224 (0.97)& 0.383 (0.97)& 0.108 (0.96)& 0.213 (0.99)& 0.616 (0.99)\\ \hline 
+Longest Run of 1s & 0.383 (1.0)& 0.474 (1.0)& 0.983 (0.99)& 0.699 (0.98)& 0.897 (0.96)\\ \hline 
+Binary Matrix Rank& 0.213 (1.0)& 0.867 (0.99)& 0.494 (0.98)& 0.162 (0.99)& 0.924 (0.99)\\ \hline 
+Disc. Fourier Transf. (Spect.)& 0.474 (1.0)& 0.739 (0.99)& 0.012 (1.0)& 0.678 (0.98)& 0.437 (0.99)\\ \hline 
+Unoverlapping Templ. Match.*& 0.505 (0.990)& 0.521 (0.990)& 0.510 (0.989)& 0.511 (0.990)& 0.499 (0.990)\\ \hline 
+Overlapping Temp. Match.& 0.574 (0.98)& 0.304 (0.99)& 0.437 (0.97)& 0.759 (0.98)& 0.275 (0.99)\\ \hline 
+Maurer's Universal Statistical& 0.759 (0.96)& 0.699 (0.97)& 0.191 (0.98)& 0.699 (1.0)& 0.798 (0.97)\\ \hline 
+Approximate Entropy (m=10)& 0.759 (0.99)& 0.162 (0.99)& 0.867 (0.99)& 0.534 (1.0)& 0.616 (0.99)\\ \hline 
+Random Excursions *& 0.666 (0.994)& 0.410 (0.962)& 0.287 (0.998)& 0.365 (0.994)& 0.480 (0.985)\\ \hline 
+Random Excursions Variant *& 0.337 (0.988)& 0.519 (0.984)& 0.549 (0.994)& 0.225 (0.995)& 0.533 (0.993)\\ \hline 
+Serial* (m=10)& 0.630 (0.99)& 0.529 (0.99)& 0.460 (0.99)& 0.302 (0.995)& 0.360 (0.985)\\ \hline 
+Linear Complexity& 0.719 (1.0)& 0.739 (0.99)& 0.759 (0.98)& 0.122 (0.97)& 0.514 (0.99)\\ \hline 
+\end{tabular}

 \end{scriptsize}
 \end{center}
 \caption{NIST SP 800-22 test results ($\mathbb{P}_T$)}
 \end{scriptsize}
 \end{center}
 \caption{NIST SP 800-22 test results ($\mathbb{P}_T$)}