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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-06-14 07:26:10 +0200 |
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committer | GitHub <noreply@github.com> | 2021-06-14 07:26:10 +0200 |
commit | 114633b43a0f1ebedbc5dfd85f75ede9841f26fd (patch) | |
tree | 18e61c7d69883a1c9b69098b7d36856abaed5c1e /vorlesungen/slides/a/aes/bytes.tex | |
parent | Delete buch.pdf (diff) | |
parent | Fix references.bib (diff) | |
download | SeminarMatrizen-114633b43a0f1ebedbc5dfd85f75ede9841f26fd.tar.gz SeminarMatrizen-114633b43a0f1ebedbc5dfd85f75ede9841f26fd.zip |
Merge branch 'master' into master
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-rw-r--r-- | vorlesungen/slides/a/aes/bytes.tex | 96 |
1 files changed, 96 insertions, 0 deletions
diff --git a/vorlesungen/slides/a/aes/bytes.tex b/vorlesungen/slides/a/aes/bytes.tex new file mode 100644 index 0000000..e873e9a --- /dev/null +++ b/vorlesungen/slides/a/aes/bytes.tex @@ -0,0 +1,96 @@ +% +% bytes.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Bytes} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Endlicher Körper} +1 Byte = 8 bits: $\mathbb{F}_{2^8}$ +mit Minimalpolynom: +\[ +m(X) = X^8+X^4+X^3+X+1 +\] +\end{block} +\vspace{-10pt} +\uncover<2->{% +\begin{block}{Inverse $a^{-1}$} +Mit dem euklidischen Algorithmus +\[ +\begin{aligned} +sa+tm&=1 +&&\Rightarrow& +\uncover<3->{ +a^{-1} &= s} +\\ +& +&&& +\uncover<4->{ +\overline{a} +&= +\begin{cases} +a^{-1}&\; a\ne 0\\ +0 &\; a = 0 +\end{cases}} +\end{aligned} +\] +\end{block}} +\vspace{-10pt} +\uncover<5->{% +\begin{block}{Vektorraum} +$\mathbb{R}_{2^8}$ +ist ein $8$-dimensionaler $\mathbb{F}_2$-Vektorraum +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<6->{% +\begin{block}{S-Box} +$S\colon a\mapsto A\overline{a}+q$ mit +\begin{align*} +\only<1-7>{\phantom{\mathstrut^{-1}}A} +\ifthenelse{\boolean{presentation}}{}{\only<8>{A^{-1}}} +&=\only<1-7>{\begin{pmatrix} +1&0&0&0&1&1&1&1\\ +1&1&0&0&0&1&1&1\\ +1&1&1&0&0&0&1&1\\ +1&1&1&1&0&0&0&1\\ +1&1&1&1&1&0&0&0\\ +0&1&1&1&1&1&0&0\\ +0&0&1&1&1&1&1&0\\ +0&0&0&1&1&1&1&1 +\end{pmatrix}} +\ifthenelse{\boolean{presentation}}{}{ +\only<8->{ +\begin{pmatrix} +0&0&1&0&0&1&0&1\\ +1&0&0&1&0&0&1&0\\ +0&1&0&0&1&0&0&1\\ +1&0&1&0&0&1&0&0\\ +0&1&0&1&0&0&1&0\\ +0&0&1&0&1&0&0&1\\ +1&0&0&1&0&1&0&0\\ +0&1&0&0&1&0&1&0 +\end{pmatrix}} +} +\\ +q&=X^7+X^6+X+1 +\end{align*} +\end{block}} +\vspace{-10pt} +\uncover<7->{% +\begin{block}{Inverse $S$-Box} +\vspace{-10pt} +\[ +S^{-1}(b) = \overline{A^{-1}(b-q)} +\] +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |