From eb4e301626c295e21a63aa3eb3d42a76e1a90588 Mon Sep 17 00:00:00 2001 From: couchot Date: Wed, 2 Sep 2015 11:50:57 +0200 Subject: [PATCH] modi exp prng --- 14Secrypt.tex | 146 ++++++++++++++++++++++++++++---------------------- 1 file changed, 81 insertions(+), 65 deletions(-) diff --git a/14Secrypt.tex b/14Secrypt.tex index 435e739..fd6cbaf 100644 --- a/14Secrypt.tex +++ b/14Secrypt.tex @@ -688,49 +688,66 @@ la figure~\ref{fig:markov:f*}. \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} @@ -833,12 +850,12 @@ de tests statistiques développée par le 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. @@ -851,29 +868,28 @@ 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} % -- 2.39.5