X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/7f294da7c47bc256747d5453c1f8ef17183020fe..a57f211cb3b73d523ff516e65f2559b296775c11:/prng.tex?ds=sidebyside

diff --git a/prng.tex b/prng.tex
index 4ad9989..8acfce7 100644
--- a/prng.tex
+++ b/prng.tex
@@ -54,7 +54,7 @@ it preserves this property.
 
 For each number $\mathsf{N}=4,5,6,7,8$ of bits, we have generated 
 the functions according to the method 
-given in Sect.~\ref{sec:hamilton}.
+given in Sect.~\ref{sec:SCCfunc} and~\ref{sec:hamilton}. 
 % MENTION FILTRAGE POSSIBLE LORS DE CONSTRUCTION... (SCV) 
 For each $\mathsf{N}$, we have then restricted this evaluation to the function 
 whose Markov Matrix (issued from Eq.~(\ref{eq:Markov:rairo})) 
@@ -126,100 +126,45 @@ $\textcircled{d}$&70, 75, 82, 64, 0, 127, 54, 53, 62, 51, 59, 56, 60, 39, 52, 37
 &&\\
 &22, 83, 2, 16, 80, 13, 78, 9, 14, 3, 11, 73, 12, 23, 4, 21, 20, 
 &&\\
-&67, 66, 5, 1]
-
-
-
-
-
-
-
-[111, 94, 93, 116, 122, 90, 125, 88, 115, 126, 119, 84, 123, 98,
-&&\\
-&
- 81, 120, 109, 106, 105, 110, 99, 107, 104, 72, 71, 118,  117, 
- &&\\
-&
-96, 103, 102, 113, 64, 79, 86, 95, 124, 83, 91, 121, 24, 85, 22, 
-&&\\
-69, 20, 19, 114, 17, 112, 77, 76, 13, 108, 74, 10, 9, 73, 67, 66,
-&7 & 99\\
-
-& 
- 101, 100, 75, 82, 97, 0, 127, 54, 57, 62, 51, 59, 56, 48, 53, 38,
-&&\\
-&
- 37, 60, 55, 58, 33, 49, 63, 44, 47, 40, 42, 46, 45, 41, 35, 34, 
-&&\\
-&
-39, 52, 43, 50, 32, 36, 29, 28, 61, 92, 26, 18, 89, 25, 87, 30, 
-&&\\
-&
-23, 4, 27, 2, 16, 80, 31, 78, 15, 14, 3, 11, 8, 12, 5, 70, 21, 
-&&\\
-&
-68, 7, 6, 65, 1]
-&&\\
-
-
+&67, 66, 5, 1] &&\\
 %%%%%n=8
 \hline
 &
-[223, 190, 249, 254, 187, 251, 233, 232, 183, 230, 247, 180, 227, 
+[223, 238, 249, 254, 243, 251, 233, 252, 183, 244, 229, 245, 227, 
 &&\\
-&
-178, 240, 248, 237, 236, 253, 172, 203, 170, 201, 168, 229, 166, 
+&246, 240, 176, 175, 174, 253, 204, 203, 170, 169, 248, 247, 226, 
 &&\\
-&
-165, 244, 163, 242, 241, 192, 215, 220, 205, 216, 218, 222, 221, 
+&228, 164, 163, 162, 161, 192, 215, 220, 205, 216, 155, 222, 221, 
 &&\\
-&
-208, 213, 210, 212, 214, 219, 211, 217, 209, 239, 202, 207, 140, 
+&208, 213, 150, 212, 214, 219, 211, 145, 209, 239, 202, 207, 140, 
 &&\\
-&
-139, 234, 193, 204, 135, 196, 199, 132, 194, 130, 225, 200, 159, 
+&195, 234, 193, 136, 231, 230, 199, 197, 131, 198, 225, 200, 63, 
 &&\\
-&
-62, 185, 252, 59, 250, 169, 56, 191, 246, 245, 52, 243, 50, 176, 
+&188, 173, 184, 186, 250, 57, 168, 191, 178, 180, 52, 187, 242, 
 &&\\
-&
-48, 173, 238, 189, 44, 235, 42, 137, 184, 231, 38, 37, 228, 35,
+&241, 48, 143, 46, 237, 236, 235, 138, 185, 232, 135, 38, 181, 165, 
 &&\\
-&
-226, 177, 224, 151, 156, 141, 152, 154, 158, 157, 144, 149, 146,
+&35, 166, 33, 224, 31, 30, 153, 158, 147, 218, 217, 156, 159, 148, 
 &&\\
-&
-148, 150, 155, 147, 153, 145, 175, 206, 143, 136, 11, 142, 129,
+$\textcircled{e}$&151, 149, 19, 210, 144, 152, 141, 206, 13, 12, 171, 10, 201, 128, 
+&8&109\\
+&133, 130, 132, 196, 3, 194, 137, 0, 255, 124, 109, 120, 122, 106, 
 &&\\
-$\textcircled{e}$&
-8, 7, 198, 197, 4, 195, 2, 161, 160, 255, 124, 109, 108, 122,
-&8&110\\
-&
- 126, 125, 112, 117, 114, 116, 100, 123, 98, 97, 113, 79, 106,
+&125, 104, 103, 114, 116, 118, 123, 98, 97, 113, 79, 126, 111, 110, 
 &&\\
-&
- 111, 110, 99, 74, 121, 120, 71, 118, 103, 101, 115, 66, 65, 
+&99, 74, 121, 72, 71, 70, 117, 101, 115, 102, 65, 112, 127, 90, 89, 
 &&\\
-&
-104, 127, 90, 89, 94, 83, 91, 81, 92, 95, 84, 87, 85, 82, 86,
+&94, 83, 91, 81, 92, 95, 84, 87, 85, 82, 86, 80, 88, 77, 76, 93, 
 &&\\
-&
-80, 88, 77, 76, 93, 72, 107, 78, 105, 64, 69, 102, 68, 70, 75,
-&&\\
-&
-67, 73, 96, 55, 58, 45, 188, 51, 186, 61, 40, 119, 182, 181, 
+&108, 107, 78, 105, 64, 69, 66, 68, 100, 75, 67, 73, 96, 55, 190, 
 &&\\
-&
-53, 179, 54, 33, 49, 15, 174, 47, 60, 171, 46, 57, 32, 167, 6,
+&189, 62, 51, 59, 41, 60, 119, 182, 37, 53, 179, 54, 177, 32, 45, 
 &&\\
-&
- 36, 164, 43, 162, 1, 0, 63, 26, 25, 30, 19, 27, 17, 28, 31, 
+&44, 61, 172, 11, 58, 9, 56, 167, 34, 36, 4, 43, 50, 49, 160, 23, 
 &&\\
-&
-20, 23, 21, 18, 22, 16, 24, 13, 10, 29, 14, 3, 138, 41, 12, 
+&28, 157, 24, 26, 154, 29, 16, 21, 18, 20, 22, 27, 146, 25, 17, 47, 
 &&\\
-&
-39, 134, 133, 5, 131, 34, 9, 128]
+&142, 15, 14, 139, 42, 1, 40, 39, 134, 7, 5, 2, 6, 129, 8]
 &&\\
 \hline
 \end{tabular}
@@ -241,7 +186,7 @@ achieve to pass the NIST battery of tests.
 
 
 
-\begin{table} 
+\begin{table*} 
 \renewcommand{\arraystretch}{1.3}
 \begin{center}
 \begin{scriptsize}
@@ -272,7 +217,7 @@ Linear Complexity& 0.719 (1.0)& 0.739 (0.99)& 0.759 (0.98)& 0.122 (0.97)& 0.514
 \end{center}
 \caption{NIST SP 800-22 test results ($\mathbb{P}_T$)}
 \label{The passing rate}
-\end{table}
+\end{table*}
 
 
 %%% Local Variables: