Add crypto exercise

school/intro-crypto/uebung/05/05.tex

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+\documentclass[12pt,a4paper,german]{article}
+\usepackage{url}
+%\usepackage{graphics}
+\usepackage{times}
+\usepackage[T1]{fontenc}
+\usepackage{pifont}
+\usepackage{ngerman}
+\usepackage{float}
+\usepackage{diagbox}
+\usepackage[latin1]{inputenc}
+\usepackage{geometry}
+\usepackage{amsfonts}
+\usepackage{amsmath}
+\usepackage{delarray}
+% \usepackage{minted}
+\usepackage{csquotes}
+\usepackage{graphicx}
+\usepackage{epsfig}
+\usepackage{longtable}
+\usepackage{paralist}
+\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
+
+\graphicspath{.}
+
+%%%%%%%%%% Fill out the the definitions %%%%%%%%%
+\def \name {Valentin Brandl}					%
+\def \matrikel {108018274494}				%
+% \def \pname {Vorname2 Nachname2}				%
+% \def \pmatrikel {Matrikelnummer2}				%
+\def \gruppe {Gruppe 193}					%
+\def \uebung {5}								%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ % DO NOT MODIFY THIS HEADER
+\newcommand{\hwsol}{
+\vspace*{-2cm}
+\noindent \matrikel \quad \name \hfill Gruppe:\gruppe \\
+% \noindent \pmatrikel \quad \pname \\
+\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
+}
+
+\newcommand{\cmark}{\ding{51}}%
+\newcommand{\xmark}{\ding{55}}%
+\newcommand{\csquare}{\text{\rlap{$\checkmark$}}\square}%
+
+\begin{document}
+%Import header
+\hwsol
+
+
+\section*{Aufgabe 1}
+
+\begin{enumerate}[a)]
+
+    \item Das National Bureau of Standards (NBS) (heute National Institute of Standards and Technology (NIST)) hat die
+        Entwicklung des DES ausgeschrieben.
+
+    \item DES wurde 1977 standardisiert.
+
+    \item Die National Security Agency (NSA) hat an der Entwicklung des DES mitgewirkt.
+
+    \item Die Kryptographen, die den Kandidaten eingereicht haben, geh<65>rten IBM an.
+
+    \item Auf einen Feistel Netz mit einer Blockgr<67><72>e von 64 bit und einer Schl<68>ssell<6C>nge von 128 bit
+
+    \item Die Schl<68>ssell<6C>nge von Lucifer ist 128 bit
+
+    \item Die Schl<68>ssell<6C>nge des DES ist 56 bit und das Sicherheitsniveau ist 56 bit.
+
+    \item Es werden 64 bit in einer DES Operation verschl<68>sselt.
+
+    \item Abbildung \ref{feist_alg} und \ref{feist_round}
+
+        \begin{figure}[h!]
+            \centering
+            \includegraphics[scale=0.5]{./build/school/intro-crypto/uebung/05/a1i.png}
+            \caption{Allgemeine Struktur eines Feistel Netzes}
+            \label{feist_alg}
+        \end{figure}
+        \begin{figure}[h!]
+            \centering
+            \includegraphics[width=\textwidth]{school/intro-crypto/uebung/05/a1i2.jpg}
+            \caption{Struktur einer Feistel Runde}
+            \label{feist_round}
+        \end{figure}
+
+\end{enumerate}
+
+\section*{Aufgabe 2}
+
+\begin{enumerate}[a)]
+
+    \item
+        \begin{tabular}{|c|ccccc|}
+            \hline
+            $S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline
+            0 & 07 & 13 & 14 & 03 & 00 \\\hline
+            1 & 13 & 08 & 11 & 05 & 06 \\\hline
+        \end{tabular}
+
+        \begin{tabular}{|c|ccccc|}
+            \hline
+            & 0 & 1 & 2 & 3 & 4 \\\hline
+            $(y_1,y_2,y_3,y_4)$ & 0111 & 1101 & 1110 & 0011 & 0000 \\\hline
+            $(y_2,y_1,y_4,y_3)$ & 1011 & 1110 & 1101 & 0011 & 0000 \\\hline
+            $(y_2,y_1,y_4,y_3) \oplus (0,1,1,0)$ & 1101 & 1000 & 1011 & 0101 & 0110 \\\hline
+            Dezimal & 13 & 8 & 11 & 5 & 6 \\\hline
+        \end{tabular}
+
+        Das Ergebnis entspricht genau der 1. Zeile in der S-Box $S_4$.
+
+    \item
+        \begin{tabular}{|c|ccccc|}
+            \hline
+            $S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline
+            2 & 10 & 06 & 09 & 00 & 12 \\\hline
+            3 & 03 & 15 & 00 & 06 & 10 \\\hline
+        \end{tabular}
+
+        Tabelle in bin<69>r:
+
+        \begin{tabular}{|c|ccccc|}
+            \hline
+            $S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline
+            2 & 1010 & 0110 & 1001 & 0000 & 1100 \\\hline
+            3 & 0011 & 1111 & 0000 & 0110 & 1010 \\\hline
+        \end{tabular}
+
+        Gesucht:
+
+        \begin{itemize}
+            \item Permutationsfunktion $f : (y_1,y_2,y_3,y_4) \to (y_1',y_2',y_3',y_4')$
+            \item xor Parameter $x = (x_1,x_2,x_3,x_4)$
+    \end{itemize}
+
+    Der Ausgangswert von Spalte 3 (0000) bleibt von der Permutationsfunktion unver<65>ndert: $f(0000) = 0000 \Rightarrow x
+    = 0000 \oplus 0110 = 0110$
+
+        \begin{tabular}{|c|ccccc|}
+            \hline
+            $S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline
+            3 & 0011 & 1111 & 0000 & 0110 & 1010 \\\hline
+            Zeile $3 \oplus 0110$ & 0101 & 1001 & 0110 & 0000 & 1100 \\\hline
+            2 & 1010 & 0110 & 1001 & 0000 & 1100 \\\hline
+        \end{tabular}
+
+        Man kann sehen, dass wieder $y_1$ mit $y_2$ und $y_3$ mit $y_4$ vertauscht werden.
+
+        $\Rightarrow$ Ableitung von Zeile 2 zu 3:
+
+        \begin{align*}
+            (y_1,y_2,y_3,y_4) \to (y_2,y_1,y_4,y_3) \oplus (0,1,1,0)
+        \end{align*}
+
+
+\end{enumerate}
+
+\section*{Aufgabe 3}
+
+
+\begin{tabular}{|c|ccccccccc|}
+    \hline
+    & $x_1$ & $x_2$ & ... & $x_{56}$ & $x_{57}$ & $x_{58}$ & ... & $x_{63}$ & $x_{64}$ \\\hline
+    Eingabe $x$ & 1 & 1 & ... & 1 & 0 & 1 & ... & 1 & 1 \\\hline
+    $IP(x)$     & 1 & 1 & ... & 1 & 1 & 1 & ... & 0 & 1 \\\hline
+\end{tabular}
+
+$L_0 = 11111111111111111111111111111111$
+
+$R_0 = 11111111111111111111111111111101 = L_1$
+
+Das zu beobachtende Bit steht an Position $31$.
+
+$E(R_0) = 111111111111111111111111111111111111111111111011$
+
+
+\begin{enumerate}[a)]
+
+    \item Auswirkungen:
+
+        $S_1\ \square$
+        $S_2\ \square$
+        $S_3\ \square$
+        $S_4\ \square$
+        $S_5\ \square$
+        $S_6\ \square$
+        $S_7\ \square$
+        $S_8\ \csquare$
+
+        Eingangsbits: $E(R_0) \oplus 111111111111111111111111111111111111111111111111$
+
+        S-Box $S_1$: $000000$
+
+        S-Box $S_2$: $000000$
+
+        S-Box $S_3$: $000000$
+
+        S-Box $S_4$: $000000$
+
+        S-Box $S_5$: $000000$
+
+        S-Box $S_6$: $000000$
+
+        S-Box $S_7$: $000000$
+
+        S-Box $S_8$: $000100$
+
+    \item
+        Ausgabe der S-Boxen:
+
+        S-Box $S_1$: $14 = 1110$
+
+        S-Box $S_2$: $15 = 1111$
+
+        S-Box $S_3$: $10 = 1010$
+
+        S-Box $S_4$: $07 = 0111$
+
+        S-Box $S_5$: $02 = 0010$
+
+        S-Box $S_6$: $12 = 1100$
+
+        S-Box $S_7$: $04 = 0100$
+
+        S-Box $S_8$: $08 = 1000$
+
+        Ausgabe nach allen S-Boxen: $s = 11101111101001110010110001001000$
+
+        $P(s) = 10000010010110011101011100111011$ (berechnet mit Code im Anhang)
+
+        $P(s) \oplus L_0 = 01111101101001100010100011000100 = R_1$
+
+        \begin{align*}
+            L_1 = R_0:\\
+            11111111111111111111111111111101 \\
+            R_1:\\
+            01111101101001100010100011000100
+        \end{align*}
+
+    \item
+
+        \begin{align*}
+            L_1:\\
+            R_1:\\
+        \end{align*}
+
+\end{enumerate}
+
+\section*{Aufgabe 4}
+
+\end{document}
+

school/intro-crypto/uebung/05/a1i.dot

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+digraph {
+    {
+        rank=same;
+        0 [ style="invisible" shape="point" width=0 ];
+        3 [ style="invisible" shape="point" width=0 ];
+    }
+
+    {
+        rank=same;
+        1 [ style="invisible" shape="point" width=0 ];
+        4 [ style="invisible" shape="point" width=0 ];
+    }
+
+    {
+        rank=same;
+        2 [ style="invisible" shape="point" width=0 ];
+        5 [ style="invisible" shape="point" width=0 ];
+    }
+
+    {
+        rank=same;
+        r1 [ label="Runde 1" shape="box" ];
+        s1 [ label="" shape="box" ];
+    }
+
+    {
+        rank=same;
+        rn [ label="Runde n" shape="box" ];
+        sn [ label="" shape="box" ];
+    }
+
+
+
+    3 -> s1 [ label="K" ];
+
+    s1 -> r1 [ label="K1" ];
+
+    s1 -> 4;
+    4 -> sn [ style="dotted" ];
+    sn -> rn [ label="Kn" ];
+
+    0 -> r1 [ label="x" ];
+    r1 -> 1;
+    1 -> rn [ style="dotted" ];
+    rn -> 2 [ label="y" ];
+}

school/intro-crypto/uebung/05/p/Cargo.lock

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+[[package]]
+name = "p"
+version = "0.1.0"
+

school/intro-crypto/uebung/05/p/Cargo.toml

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+[package]
+name = "p"
+version = "0.1.0"
+authors = ["Valentin Brandl <vbrandl@riseup.net>"]
+
+[dependencies]

school/intro-crypto/uebung/05/p/src/main.rs

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+const P: [usize; 32] = [
+    16, 7, 20, 21, 29, 12, 28, 17, 1, 15, 23, 26, 5, 18, 31, 10, 2, 8, 24, 14, 32, 27, 3, 9, 19,
+    13, 30, 6, 22, 11, 4, 25,
+];
+
+fn p<T: Copy + Default>(i: [T; 32]) -> [T; 32] {
+    let mut res: [T; 32] = [T::default(); 32];
+    for (i, p) in i.iter().zip(P.iter()) {
+        res[*p - 1] = *i;
+    }
+    res
+}
+
+fn main() {
+    let i: [u8; 32] = [
+        1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0,
+        0, 0,
+    ];
+    p(i).iter().for_each(|i| print!("{}", i));
+    println!();
+
+    let p = &[
+        true, false, false, false, false, false, true, false, false, true, false, true, true,
+        false, false, true, true, true, false, true, false, true, true, true, false, false, true,
+        true, true, false, true, true,
+    ];
+    let l0 = &[
+        true, true, true, true, true, true, true, true, true, true, true, true, true, true, true,
+        true, true, true, true, true, true, true, true, true, true, true, true, true, true, true,
+        true, true,
+    ];
+
+    p.iter()
+        .zip(l0.iter())
+        .map(|(a, b)| a ^ b)
+        .map(|x| if x { '1' } else { '0' })
+        .for_each(|x| print!("{}", x));
+    println!();
+}

school/intro-crypto/uebung/05/p/target/.rustc_info.json

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+{"rustc_fingerprint":1996615077234892980,"outputs":{"15337506775154344876":["___\nlib___.rlib\nlib___.so\nlib___.so\nlib___.a\nlib___.so\n/home/me/.rustup/toolchains/stable-x86_64-unknown-linux-gnu\ndebug_assertions\nproc_macro\ntarget_arch=\"x86_64\"\ntarget_endian=\"little\"\ntarget_env=\"gnu\"\ntarget_family=\"unix\"\ntarget_feature=\"fxsr\"\ntarget_feature=\"sse\"\ntarget_feature=\"sse2\"\ntarget_os=\"linux\"\ntarget_pointer_width=\"64\"\nunix\n",""],"1617349019360157463":["___\nlib___.rlib\nlib___.so\nlib___.so\nlib___.a\nlib___.so\n/home/me/.rustup/toolchains/stable-x86_64-unknown-linux-gnu\ndebug_assertions\nproc_macro\ntarget_arch=\"x86_64\"\ntarget_endian=\"little\"\ntarget_env=\"gnu\"\ntarget_family=\"unix\"\ntarget_feature=\"fxsr\"\ntarget_feature=\"sse\"\ntarget_feature=\"sse2\"\ntarget_os=\"linux\"\ntarget_pointer_width=\"64\"\nunix\n",""],"1164083562126845933":["rustc 1.30.1 (1433507eb 2018-11-07)\nbinary: rustc\ncommit-hash: 1433507eba7d1a114e4c6f27ae0e1a74f60f20de\ncommit-date: 2018-11-07\nhost: x86_64-unknown-linux-gnu\nrelease: 1.30.1\nLLVM version: 8.0\n",""]},"successes":{}}

school/intro-crypto/uebung/05/p/target/debug/.fingerprint/p-317830ef682f5c46/bin-p-317830ef682f5c46

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+0727989ce1aa1e48

school/intro-crypto/uebung/05/p/target/debug/.fingerprint/p-317830ef682f5c46/bin-p-317830ef682f5c46.json

@@ -0,0 +1 @@
+{"rustc":3409524444662720818,"features":"[]","target":6265867820755230167,"profile":8404152588981882898,"path":1036222786711178230,"deps":[],"local":[{"MtimeBased":[[1543354048,10023042],".fingerprint/p-317830ef682f5c46/dep-bin-p-317830ef682f5c46"]}],"rustflags":[],"edition":"Edition2015"}

school/intro-crypto/uebung/05/p/target/debug/.fingerprint/p-a8d68fe4b06c3a8a/bin-p-a8d68fe4b06c3a8a

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+5e32215f8f612020

school/intro-crypto/uebung/05/p/target/debug/.fingerprint/p-a8d68fe4b06c3a8a/bin-p-a8d68fe4b06c3a8a.json

@@ -0,0 +1 @@
+{"rustc":3409524444662720818,"features":"[]","target":6265867820755230167,"profile":256579555595379356,"path":1036222786711178230,"deps":[],"local":[{"MtimeBased":[[1543354051,669476378],".fingerprint/p-a8d68fe4b06c3a8a/dep-bin-p-a8d68fe4b06c3a8a"]}],"rustflags":[],"edition":"Edition2015"}

school/intro-crypto/uebung/05/p/target/debug/deps/p-317830ef682f5c46.d

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+/home/me/Dokumente/notes/school/intro-crypto/uebung/05/p/target/debug/deps/p-317830ef682f5c46.rmeta: src/main.rs
+
+/home/me/Dokumente/notes/school/intro-crypto/uebung/05/p/target/debug/deps/p-317830ef682f5c46.d: src/main.rs
+
+src/main.rs:

school/intro-crypto/uebung/05/p/target/debug/deps/p-a8d68fe4b06c3a8a.d

@@ -0,0 +1,5 @@
+/home/me/Dokumente/notes/school/intro-crypto/uebung/05/p/target/debug/deps/p-a8d68fe4b06c3a8a: src/main.rs
+
+/home/me/Dokumente/notes/school/intro-crypto/uebung/05/p/target/debug/deps/p-a8d68fe4b06c3a8a.d: src/main.rs
+
+src/main.rs:

school/intro-crypto/uebung/05/p/target/debug/libp.d

@@ -0,0 +1 @@
+/home/me/Dokumente/notes/school/intro-crypto/uebung/05/p/target/debug/libp.rmeta: /home/me/Dokumente/notes/school/intro-crypto/uebung/05/p/src/main.rs

school/intro-crypto/uebung/05/p/target/debug/p.d

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+/home/me/Dokumente/notes/school/intro-crypto/uebung/05/p/target/debug/p: /home/me/Dokumente/notes/school/intro-crypto/uebung/05/p/src/main.rs