diff options
Diffstat (limited to 'vorlesungen')
| -rw-r--r-- | vorlesungen/slides/4/schieberegister.tex | 38 |
1 files changed, 30 insertions, 8 deletions
diff --git a/vorlesungen/slides/4/schieberegister.tex b/vorlesungen/slides/4/schieberegister.tex index 6914c79..f349337 100644 --- a/vorlesungen/slides/4/schieberegister.tex +++ b/vorlesungen/slides/4/schieberegister.tex @@ -5,6 +5,7 @@ % \bgroup \def\ds{0.7} +\definecolor{darkgreen}{rgb}{0,0.6,0} \def\punkt#1#2{({(#1)*\ds},{(#2)*\ds})} \def\rahmen{ \draw ({-0.5*\ds},{-0.5*\ds}) rectangle ({7.5*\ds},{0.5*\ds}); @@ -23,17 +24,25 @@ \node at \punkt{7}{0} {$#8$}; } \begin{frame}[t] -\frametitle{Schieberegister} -Rechnen mit Polynomen in $\mathbb{F}_2(\alpha)$ ist speziell einfach +\frametitle{Implementation der Multiplikation in $\mathbb{F}_2(\alpha)$\uncover<10->{: Schieberegister}} +Rechnen in $\mathbb{F}_2[X]$\only<5->{ und $\mathbb{F}_2(\alpha)$} +ist speziell einfach \\ -Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard) +Minimalpolynom von $\alpha$: ${\color{darkgreen}m(X) = X^8 + X^4+X^3+X+1}$ +(aus dem AES Standard) \begin{center} \begin{tikzpicture}[>=latex,thick] +\uncover<4->{ + \fill[color=blue!20] + \punkt{-0.5}{-0.5} rectangle \punkt{7.5}{0.5}; +} + \uncover<2->{ \begin{scope} \rahmen + \node at \punkt{-0.5}{1} [left] {$p(X)=\mathstrut$}; \node at \punkt{0}{1} {$X^7$\strut}; \node at \punkt{2.5}{1}{$+$\strut}; \node at \punkt{3}{1} {$X^4$\strut}; @@ -48,10 +57,20 @@ Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard) \draw[->] ({7.7*\ds},-0.2) to[out=-45,in=45] ({7.7*\ds},-1.8); \node at ({8*\ds},-1) [right] {$\mathstrut\cdot X = \text{Shift}$}; } +\uncover<4->{ + \foreach \x in {0,...,7}{ + \draw[->,color=blue!40] + ({\x*\ds},{-0.6*\ds}) -- ({(\x-1)*\ds},{-2+0.6*\ds}); + } +} + +\fill[color=white] (-4.65,0) circle[radius=0.01]; \uncover<3->{ \begin{scope}[yshift=-2cm] \uncover<4->{ + \fill[color=blue!20] + \punkt{-1.5}{-0.5} rectangle \punkt{6.5}{0.5}; \rahmen \polynom00101010 } @@ -62,7 +81,7 @@ Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard) \node at \punkt{6}{1} {$X$\strut}; \begin{scope}[xshift=0.4cm] \node at \punkt{-1}{1} [left] - {$\uncover<5->{X^4+X^3+X+1=}X^8$\strut}; + {$\uncover<5->{{\color{darkgreen}\alpha^4+\alpha^3+\alpha+1=\alpha^8}}\only<-4>{X^8}$\strut}; \end{scope} \node at \punkt{-1}{0} {$1$\strut}; \end{scope} @@ -70,11 +89,13 @@ Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard) \uncover<6->{ {\color<8->{red} - \draw[->] (-3,-1.5) to[out=-90,in=180] (-0.5,-2.7); + \draw[->] (-2.5,-1.5) to[out=-90,in=180] (-0.5,-2.7); } \begin{scope}[yshift=-2.7cm] \rahmen - \polynom00011011 + {\color{darkgreen} + \polynom00011011 + } \end{scope} } @@ -83,12 +104,13 @@ Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard) \begin{scope}[yshift=-4.2cm] \rahmen - \polynom00110111 + \polynom00110001 + \node at \punkt{7.6}{0} [right] {$\mathstrut=\alpha\cdot p(\alpha)$}; \end{scope} } \uncover<8->{ - \node[color=red] at (-3.5,-2.7) {Feedback}; + \node[color=red] at (-3.0,-2.5) {Feedback}; } \end{tikzpicture} |