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diff --git a/vorlesungen/slides/a/aes/blocks.tex b/vorlesungen/slides/a/aes/blocks.tex new file mode 100644 index 0000000..9e95a86 --- /dev/null +++ b/vorlesungen/slides/a/aes/blocks.tex @@ -0,0 +1,193 @@ +% +% blocks.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\def\s{0.4} +\def\punkt#1#2{({#1*\s},{(3-#2)*\s})} +\def\feld#1#2#3{ + \fill[color=#3] \punkt{(#1-0.5)}{(#2+0.5)} + rectangle \punkt{(#1+0.5)}{(#2-0.5)}; +} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Blocks} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Blocks} +$4\times k$ Matrizen mit $k=4,\dots,8$ +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\xdef\s{0.4} +\foreach \i in {0,...,31}{ + \pgfmathparse{mod(\i,4)} + \xdef\y{\pgfmathresult} + \pgfmathparse{int(\i/4)} + \xdef\x{\pgfmathresult} + \node at \punkt{\x}{\y} {\tiny $\i$}; +} +\foreach \x in {-0.5,0.5,...,7.5}{ + \draw \punkt{\x}{-0.5} -- \punkt{\x}{3.5}; +} +\foreach \y in {-0.5,0.5,...,3.5}{ + \draw \punkt{-0.5}{\y} -- \punkt{7.5}{\y}; +} +\end{tikzpicture} +\end{center} +\uncover<2->{% +Spalten sind $4$-dimensionale $\mathbb{F}_{2^8}$-Vektoren +} +\end{block} +\uncover<3->{% +\begin{block}{Zeilenshift} +\begin{center} +\begin{tikzpicture}[>=latex,thick] + +\xdef\s{0.35} + +\begin{scope} + \feld{0}{3}{red!20} + \feld{0}{2}{red!20} + \feld{0}{1}{red!20} + \feld{0}{0}{red!20} + + \feld{1}{3}{red!10} + \feld{1}{2}{red!10} + \feld{1}{1}{red!10} + \feld{1}{0}{red!10} + + \feld{2}{3}{yellow!20} + \feld{2}{2}{yellow!20} + \feld{2}{1}{yellow!20} + \feld{2}{0}{yellow!20} + + \feld{3}{3}{yellow!10} + \feld{3}{2}{yellow!10} + \feld{3}{1}{yellow!10} + \feld{3}{0}{yellow!10} + + \feld{4}{3}{darkgreen!20} + \feld{4}{2}{darkgreen!20} + \feld{4}{1}{darkgreen!20} + \feld{4}{0}{darkgreen!20} + + \feld{5}{3}{darkgreen!10} + \feld{5}{2}{darkgreen!10} + \feld{5}{1}{darkgreen!10} + \feld{5}{0}{darkgreen!10} + + \feld{6}{3}{blue!20} + \feld{6}{2}{blue!20} + \feld{6}{1}{blue!20} + \feld{6}{0}{blue!20} + + \feld{7}{3}{blue!10} + \feld{7}{2}{blue!10} + \feld{7}{1}{blue!10} + \feld{7}{0}{blue!10} + + \foreach \x in {-0.5,0.5,...,7.5}{ + \draw \punkt{\x}{-0.5} -- \punkt{\x}{3.5}; + } + \foreach \y in {-0.5,0.5,...,3.5}{ + \draw \punkt{-0.5}{\y} -- \punkt{7.5}{\y}; + } +\end{scope} + +\begin{scope}[xshift=3.5cm] + \feld{0}{0}{red!20} + \feld{1}{1}{red!20} + \feld{2}{2}{red!20} + \feld{3}{3}{red!20} + + \feld{1}{0}{red!10} + \feld{2}{1}{red!10} + \feld{3}{2}{red!10} + \feld{4}{3}{red!10} + + \feld{2}{0}{yellow!20} + \feld{3}{1}{yellow!20} + \feld{4}{2}{yellow!20} \feld{5}{3}{yellow!20} + + \feld{3}{0}{yellow!10} + \feld{4}{1}{yellow!10} + \feld{5}{2}{yellow!10} + \feld{6}{3}{yellow!10} + + \feld{4}{0}{darkgreen!20} + \feld{5}{1}{darkgreen!20} + \feld{6}{2}{darkgreen!20} + \feld{7}{3}{darkgreen!20} + + \feld{5}{0}{darkgreen!10} + \feld{6}{1}{darkgreen!10} + \feld{7}{2}{darkgreen!10} + \feld{0}{3}{darkgreen!10} + + \feld{6}{0}{blue!20} + \feld{7}{1}{blue!20} + \feld{0}{2}{blue!20} + \feld{1}{3}{blue!20} + + \feld{7}{0}{blue!10} + \feld{0}{1}{blue!10} + \feld{1}{2}{blue!10} + \feld{2}{3}{blue!10} + + \foreach \x in {-0.5,0.5,...,7.5}{ + \draw \punkt{\x}{-0.5} -- \punkt{\x}{3.5}; + } + \foreach \y in {-0.5,0.5,...,3.5}{ + \draw \punkt{-0.5}{\y} -- \punkt{7.5}{\y}; + } + + \node at \punkt{-1.5}{1.5} {$\rightarrow$}; +\end{scope} + +\end{tikzpicture} +\end{center} +\end{block}} +\end{column} +\begin{column}{0.50\textwidth} +\uncover<4->{% +\begin{block}{Spalten mischen} +Lineare Operation auf Spaltenvektoren mit Matrix +\begin{align*} +C&=\begin{pmatrix} +\texttt{02}_{16}&\texttt{03}_{16}&\texttt{01}_{16}&\texttt{01}_{16}\\ +\texttt{01}_{16}&\texttt{02}_{16}&\texttt{03}_{16}&\texttt{01}_{16}\\ +\texttt{01}_{16}&\texttt{01}_{16}&\texttt{02}_{16}&\texttt{03}_{16}\\ +\texttt{03}_{16}&\texttt{01}_{16}&\texttt{01}_{16}&\texttt{02}_{16} +\end{pmatrix} +\\ +\uncover<5->{ +\det C +&= +\texttt{0a}_{16} +} +\uncover<6->{ +\ne 0} +\uncover<7->{ +\quad\Rightarrow\quad \exists C^{-1} +} +\end{align*} +\end{block}} +\uncover<8->{% +\begin{block}{Als Polynommultiplikation} +Spalten = Polynome in $\mathbb{F}_{2^8}[Z]/(Z^4-1)$, +\\ +\uncover<9->{% +$C=\mathstrut$ Multiplikation mit +\[ +c(Z) = \texttt{03}_{16}Z^3 + Z^2 + Z + \texttt{02}_{16} +\] +} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |