\begin{table}[ht]
\begin{center}
\begin{scriptsize}
- \begin{tabular}{|c|l|c|c|}
+ \begin{tabular}{|c|c|l|c|c|}
\hline
- fonction & $f(x)$, $f(x)$ pour $x \in [0,1,2,\hdots,2^n-1]$ & $b$ & $b'$ \\
+ $n$ & fonction & $f(x)$, $f(x)$ pour $x \in [0,1,2,\hdots,2^n-1]$ & $b$ & $b'$ \\
\hline
- $f^{*4}$ & [13,10,9,14,3,11,1,12,15,4,7,5,2,6,0,8] & 17 & 38 \\
+ 4 & $f^{*4}$ & [13,10,9,14,3,11,1,12,15,4,7,5,2,6,0,8] & \textbf{17} & \textbf{38} \\
\hline
- $f^{*5}$ & [29, 22, 25, 30, 19, 27, 24, 16, 21, 6, 5, 28, 23, 26, 1, & 13 & 48 \\
- & 17, 31, 12, 15, 8, 10, 14, 13, 9, 3, 2, 7, 20, 11, 18, 0, 4] & & \\
+ \multirow{4}{0.5cm}{5}& $f^{*5}$ & [29, 22, 25, 30, 19, 27, 24, 16, 21, 6, 5, 28, 23, 26, 1, & \textbf{13} & 48 \\
+ & & 17, 31, 12, 15, 8, 10, 14, 13, 9, 3, 2, 7, 20, 11, 18, 0, 4] & & \\
+ \cline{2-5}
+ & $g^{*5}$ & [29, 22, 21, 30, 19, 27, 24, 28, 7, 20, 5, 4, 23, 26, 25, & 15 & \textbf{47} \\
+ & & 17, 31, 12, 15, 8, 10, 14, 13, 9, 3, 2, 1, 6, 11, 18, 0, 16
+ & & \\
+
\hline
- $f^{*6}$ & [55, 60, 45, 44, 58, 62, 61, 48, 53, 50, 52, 36, 59, 34, 33, & 11 & 55 \\
- & 49, 15, 42, 47, 46, 35, 10, 57, 56, 7, 54, 39, 37, 51, 2, 1, & & \\
- & 40, 63, 26, 25, 30, 19, 27, 17, 28, 31, 20, 23, 21, 18, 22, & & \\
- & 16, 24, 13, 12, 29, 8, 43, 14, 41, 0, 5, 38, 4, 6, 11, 3, 9, 32] & & \\
- \hline
- $f^{*7}$ & [111, 94, 93, 116, 122, 114, 125, 88, 87, 126, 119, 84, 123, & 10 & 63 \\
- & 98, 81, 120, 109, 106, 105, 110, 99, 107, 104, 108, 101, 70, & & \\
- & 117, 96, 67, 102, 113, 64, 79, 30, 95, 124, 83, 91, 121, 24, & & \\
- & 23, 118, 69, 20, 115, 90, 17, 112, 77, 14, 73, 78, 74, 10, 72, & & \\
- & 76, 103, 6, 71, 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, 19, 86, 85, 4, 27, 2, 16, 80, 31, 12, 15, 8, & & \\
- & 3, 11, 13, 9, 5, 22, 21, 68, 7, 66, 65, 1] & & \\
+ \multirow{8}{0.5cm}{6}& $f^{*6}$ &
+ [55, 60, 45, 56, 58, 42, 61, 40, 53, 50, 52, 54, 59, 34, 33, & \multirow{4}{0.5cm}{\textbf{11}}& \multirow{4}{0.5cm}{55}\\
+& & 49, 39, 62, 47, 46, 11, 43, 57, 8, 37, 6, 36, 4, 51, 38, 1, & & \\
+& & 48, 63, 26, 25, 30, 19, 27, 17, 28, 31, 20, 23, 21, 18, 22, & & \\
+& & 16, 24, 13, 12, 29, 44, 10, 14, 41, 0, 15, 2, 7, 5, 35, 3, 9, 32] & &\\
+ \cline{2-5}
+&$g^{*6}$ & [55, 60, 45, 44, 43, 62, 61, 48, 53, 50, 52, 36, 59, 51, 33, & \multirow{4}{0.5cm}{12}& \multirow{4}{0.5cm}{\textbf{54}}\\
+ & & 49, 15, 14, 47, 46, 35, 58, 57, 56, 7, 54, 39, 37, 3, 38, 1, & & \\
+ & & 40, 63, 26, 25, 30, 19, 27, 17, 28, 31, 20, 23, 21, 18, 22, & & \\
+ & & 16, 24, 13, 12, 29, 8, 10, 42, 41, 0, 5, 2, 4, 6, 11, 34, 9, 32] & & \\
+ \hline
+
+
+
+
+
+
+ &$f^{*7}$ & [111, 94, 93, 116, 122, 114, 125, 88, 87, 126, 119, 84, 123, & 10 & 63 \\
+ & & 98, 81, 120, 109, 106, 105, 110, 99, 107, 104, 108, 101, 70, & & \\
+ & & 117, 96, 67, 102, 113, 64, 79, 30, 95, 124, 83, 91, 121, 24, & & \\
+ & & 23, 118, 69, 20, 115, 90, 17, 112, 77, 14, 73, 78, 74, 10, 72, & & \\
+ & & 76, 103, 6, 71, 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, 19, 86, 85, 4, 27, 2, 16, 80, 31, 12, 15, 8, & & \\
+ & & 3, 11, 13, 9, 5, 22, 21, 68, 7, 66, 65, 1] & & \\
\hline
- $f^{*8}$ &[223, 190, 249, 254, 187, 251, 233, 232, 183, 230, 247, 180,& 9 & 72 \\
- & 227, 178, 240, 248, 237, 236, 253, 172, 203, 170, 201, 168, &&\\
- & 229, 166, 165, 244, 163, 242, 241, 192, 215, 220, 205, 216, &&\\
- & 218, 222, 221, 208, 213, 210, 212, 214, 219, 211, 217, 209, &&\\
- & 239, 202, 207, 140, 139, 234, 193, 204, 135, 196, 199, 132, &&\\
- & 194, 130, 225, 200, 159, 62, 185, 252, 59, 250, 169, 56, 191,&&\\
- & 246, 245, 52, 243, 50, 176, 48, 173, 238, 189, 44, 235, 42, &&\\
- & 137, 184, 231, 38, 37, 228, 35, 226, 177, 224, 151, 156, 141,&&\\
- & 152, 154, 158, 157, 144, 149, 146, 148, 150, 155, 147, 153, &&\\
- & 145, 175, 206, 143, 136, 11, 142, 129, 8, 7, 198, 197, 4, 195, &&\\
- & 2, 161, 160, 255, 124, 109, 108, 122, 126, 125, 112, 117, 114, &&\\
- & 116, 100, 123, 98, 97, 113, 79, 106, 111, 110, 99, 74, 121, 120,&&\\
- & 71, 118, 103, 101, 115, 66, 65, 104, 127, 90, 89, 94, 83, 91, 81,&&\\
- & 92, 95, 84, 87, 85, 82, 86, 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, 53, 179, 54, 33, 49, 15, 174, 47, 60, 171, && \\
- & 46, 57, 32, 167, 6, 36, 164, 43, 162, 1, 0, 63, 26, 25, 30, 19,&&\\
- & 27, 17, 28, 31, 20, 23, 21, 18, 22, 16, 24, 13, 10, 29, 14, 3, &&\\
- &138, 41, 12, 39, 134, 133, 5, 131, 34, 9, 128]&&\\
+ & $f^{*8}$ &[223, 190, 249, 254, 187, 251, 233, 232, 183, 230, 247, 180,& 9 & 72 \\
+ & & 227, 178, 240, 248, 237, 236, 253, 172, 203, 170, 201, 168, &&\\
+ & & 229, 166, 165, 244, 163, 242, 241, 192, 215, 220, 205, 216, &&\\
+ & & 218, 222, 221, 208, 213, 210, 212, 214, 219, 211, 217, 209, &&\\
+ & & 239, 202, 207, 140, 139, 234, 193, 204, 135, 196, 199, 132, &&\\
+ & & 194, 130, 225, 200, 159, 62, 185, 252, 59, 250, 169, 56, 191,&&\\
+ & & 246, 245, 52, 243, 50, 176, 48, 173, 238, 189, 44, 235, 42, &&\\
+ & & 137, 184, 231, 38, 37, 228, 35, 226, 177, 224, 151, 156, 141,&&\\
+ & & 152, 154, 158, 157, 144, 149, 146, 148, 150, 155, 147, 153, &&\\
+ & & 145, 175, 206, 143, 136, 11, 142, 129, 8, 7, 198, 197, 4, 195, &&\\
+ & & 2, 161, 160, 255, 124, 109, 108, 122, 126, 125, 112, 117, 114, &&\\
+ & & 116, 100, 123, 98, 97, 113, 79, 106, 111, 110, 99, 74, 121, 120,&&\\
+ & & 71, 118, 103, 101, 115, 66, 65, 104, 127, 90, 89, 94, 83, 91, 81,&&\\
+ & & 92, 95, 84, 87, 85, 82, 86, 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, 53, 179, 54, 33, 49, 15, 174, 47, 60, 171, && \\
+ & & 46, 57, 32, 167, 6, 36, 164, 43, 162, 1, 0, 63, 26, 25, 30, 19,&&\\
+ & & 27, 17, 28, 31, 20, 23, 21, 18, 22, 16, 24, 13, 10, 29, 14, 3, &&\\
+ & &138, 41, 12, 39, 134, 133, 5, 131, 34, 9, 128]&&\\
\hline
\end{tabular}
\end{scriptsize}
que la chaîne est considérée comme aléatoire avec une confiance de $99\%$.
-
-
- Le tableau~\ref{fig:TEST} donne une vision synthétique de toutes
- ces expérimentations.
-L'expérience a montré notamment que toutes ces fonctions
-passent avec succès cette batterie de tests.
+Le tableau~\ref{fig:TEST} donne une vision synthétique de ces expérimentations.
+Nous avons évalué les fonctions préfixées par
+$f$ (respecitvement $g$) avec le générateur issu des itérations
+généralisées (resp. unaires).
+%L'expérience a montré notamment que toutes ces fonctions
+%passent avec succès cette batterie de tests.
\begin{table}[ht]
\centering
\begin{scriptsize}
- \begin{tabular}{|*{5}{c|}}
- \hline
-Test & $f^{*4}$ & $f^{*5}$ & $f^{*6}$ & $f^{*7}$ \\ \hline
-Fréquence (Monobit) & 0.025 (0.99) & 0.066 (1.0) & 0.319 (0.99) & 0.001 (1.0) \\ \hline
-Fréquence / bloc & 0.401 (0.99) & 0.867 (1.0) & 0.045 (0.99) & 0.085 (0.99) \\ \hline
-Somme Cumulé* & 0.219 (0.995) & 0.633 (1.0) & 0.635 (1.0) & 0.386 (0.99) \\ \hline
-Exécution & 0.964 (0.98) & 0.699 (0.99) & 0.181 (0.99) & 0.911 (0.98) \\ \hline
-Longue exécution dans un bloc & 0.137 (0.99) & 0.964 (1.0) & 0.145 (0.99) & 0.162 (0.98) \\ \hline
-Rang & 0.616 (0.99) & 0.678 (1.0) & 0.004 (1.0) & 0.816 (1.0) \\ \hline
-Fourier rapide & 0.048 (0.99) & 0.637 (0.97) & 0.366 (0.99) & 0.162 (0.99) \\ \hline
-Patron sans superposition* & 0.479 (0.988) & 0.465 (0.989) & 0.535 (0.989) & 0.499 (0.989) \\ \hline
-Patron avec superposition & 0.897 (1.0) & 0.657 (0.97) & 0.897 (0.98) & 0.236 (0.99) \\ \hline
-Statistiques universelles & 0.991 (0.98) & 0.657 (0.98) & 0.102 (0.98) & 0.719 (0.98) \\ \hline
-Entropie approchée (m=10) & 0.455 (1.0) & 0.964 (1.0) & 0.162 (1.0) & 0.897 (0.98) \\ \hline
-Suite aléatoire * & 0.372 (0.993) & 0.494 (0.986) & 0.243 (0.992) & 0.258 (0.993) \\ \hline
-Suite aléatoire variante * & 0.496 (0.989) & 0.498 (0.992) & 0.308 (0.983) & 0.310 (0.999) \\ \hline
-Série* (m=10) & 0.595 (0.995) & 0.289 (0.975) & 0.660 (0.995) & 0.544 (0.99) \\ \hline
-Complexité linaire & 0.816 (1.0) & 0.897 (0.98) & 0.080 (0.98) & 0.798 (1.0) \\ \hline
- \end{tabular}
+
+
+
+ \end{scriptsize}
+
+\label{fig:TEST:generalise}
+\caption{Test de NIST pour les fonctions
+ du tableau~\ref{table:functions} selon les itérations généralisées}
+\end{table}
+
+
+\begin{table}[ht]
+ \centering
+ \begin{scriptsize}
+
+
+
\end{scriptsize}
-\label{fig:TEST}
-\caption{Test de NIST réalisé sur les fonctions $f^*$ détaillées au tableau~\label{table:functions}}
+\label{fig:TEST:unaire}
+\caption{Test de NIST pour les fonctions
+ du tableau~\ref{table:functions} selon les itérations unaires}
\end{table}
%
