From 9be5824b4b2a291e04a694196044231ecb607174 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 2 May 2024 11:13:31 +0200
Subject: [PATCH] Vorbereitung 2.5.2024

---
 20240418/ad-20240418.pdf                     | Bin 149777 -> 149792 bytes
 20240418/ad-20240418.tex                     |   4 +-
 20240418/landau-symbols-2.pdf                |   1 -
 20240418/landau-symbols-3.pdf                |   1 -
 20240418/landau-symbols.pdf                  |   1 -
 20240502/Zeichen_123.pdf                     |   1 +
 20240502/ad-20240502.pdf                     | Bin 0 -> 149663 bytes
 20240502/ad-20240502.tex                     | 318 +++++++++++++++++++
 20240502/ad-20240502.txt                     |  21 ++
 20240502/logo-hochschule-bochum-cvh-text.pdf |   1 +
 20240502/logo-hochschule-bochum.pdf          |   1 +
 20240502/pgslides.sty                        |   1 +
 12 files changed, 345 insertions(+), 5 deletions(-)
 delete mode 120000 20240418/landau-symbols-2.pdf
 delete mode 120000 20240418/landau-symbols-3.pdf
 delete mode 120000 20240418/landau-symbols.pdf
 create mode 120000 20240502/Zeichen_123.pdf
 create mode 100644 20240502/ad-20240502.pdf
 create mode 100644 20240502/ad-20240502.tex
 create mode 100644 20240502/ad-20240502.txt
 create mode 120000 20240502/logo-hochschule-bochum-cvh-text.pdf
 create mode 120000 20240502/logo-hochschule-bochum.pdf
 create mode 120000 20240502/pgslides.sty

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diff --git a/20240418/ad-20240418.tex b/20240418/ad-20240418.tex
index f65f5cd..47e0061 100644
--- a/20240418/ad-20240418.tex
+++ b/20240418/ad-20240418.tex
@@ -140,7 +140,7 @@
       Verwenden Sie den Datentyp \lstinline{uint64_t}
       (oder Langzahl-Arithmetik)
     \item
-      Für Details siehe: \file{hp-20240411.txt}
+      Für Details siehe: \file{ad-20240411.txt}
   \end{itemize}
 
 \end{frame}
@@ -301,7 +301,7 @@
       und daß bestimmte Operationen mit Zirkel und Lineal unmöglich sind.
     \item
       asymmetrische Verschlüsselung, Signaturen:\\
-      RSA, ElGamal, elliptische Kurven
+      RSA, ElGamal\color{gray}, elliptische Kurven
     \item
       symmetrische Verschlüsselung: AES
     \item
diff --git a/20240418/landau-symbols-2.pdf b/20240418/landau-symbols-2.pdf
deleted file mode 120000
index 6b458b6..0000000
--- a/20240418/landau-symbols-2.pdf
+++ /dev/null
@@ -1 +0,0 @@
-../common/landau-symbols-2.pdf
\ No newline at end of file
diff --git a/20240418/landau-symbols-3.pdf b/20240418/landau-symbols-3.pdf
deleted file mode 120000
index 46efa40..0000000
--- a/20240418/landau-symbols-3.pdf
+++ /dev/null
@@ -1 +0,0 @@
-../common/landau-symbols-3.pdf
\ No newline at end of file
diff --git a/20240418/landau-symbols.pdf b/20240418/landau-symbols.pdf
deleted file mode 120000
index ca14542..0000000
--- a/20240418/landau-symbols.pdf
+++ /dev/null
@@ -1 +0,0 @@
-../common/landau-symbols.pdf
\ No newline at end of file
diff --git a/20240502/Zeichen_123.pdf b/20240502/Zeichen_123.pdf
new file mode 120000
index 0000000..fdbc897
--- /dev/null
+++ b/20240502/Zeichen_123.pdf
@@ -0,0 +1 @@
+../common/Zeichen_123.pdf
\ No newline at end of file
diff --git a/20240502/ad-20240502.pdf b/20240502/ad-20240502.pdf
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diff --git a/20240502/ad-20240502.tex b/20240502/ad-20240502.tex
new file mode 100644
index 0000000..0e994df
--- /dev/null
+++ b/20240502/ad-20240502.tex
@@ -0,0 +1,318 @@
+% ad-20240502.pdf - Lecture Slides on Algorithms and Data Structures in C/C++
+% Copyright (C) 2018, 2019, 2020, 2021, 2022, 2023, 2024  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Diskrete Mathematik: Anwendungen
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{tikz}
+%\usepackage{rotating}
+
+\newcommand{\underconstruction}{%
+  \begin{picture}(0,0)
+    \color{black}
+    \put(6,-2.2){\makebox(0,0)[b]{\includegraphics[width=1.5cm]{Zeichen_123.pdf}}}
+    \put(6,-2.5){\makebox(0,0)[t]{\shortstack{Änderungen\\vorbehalten}}}
+  \end{picture}}
+
+\title{Algorithmen und Datenstrukturen in C/C++}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{2.\ Mai 2024}
+
+\begin{document}
+
+\maketitleframe
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \underconstruction
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/ad}}}
+%    \item[\textbf{\color{red}i}] {\color{red}Online-Werkzeuge für Home Office, Lehre\\
+%                                             und Kommunikation mit Unterdrückten}
+    \item[\textbf{2}] \textbf{Arrays und Zeiger für Fortgeschrittene}
+    \item[\textbf{3}] \textbf{\color{medgreen}Langzahl-Arithmetik}
+    \item[\textbf{4}] \textbf{\color{orange}Kryptographie}
+    \item[\color{red}\textbf{5}] \textbf{\color{orange}Datenkompression}
+    \item[\textbf{6}] \textbf{C++}
+    \item[\textbf{7}] \textbf{Datenorganisation}
+    \vspace{-\smallskipamount}
+    \item[\textbf{\dots}]
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{2}
+\section{Langzahl-Arithmetik}
+
+\begin{frame}
+
+  \showsection
+
+  Problem: Rechnen mit ganzen Zahlen, die größer sind als das,\\
+  was der Rechner normalerweise verarbeiten kann
+
+  \bigskip
+
+  {\large\textbf{Aufgabe: Addition langer Zahlen}\par}
+  \smallskip
+  \begin{itemize}
+    \item[(a)]
+      Überlegen Sie sich eine Datenstruktur, um eine lange Zahl zu speichern.
+    \item[(b)]
+      Schreiben Sie eine Funktion, die zwei lange Zahlen addiert.
+  \end{itemize}
+
+  \bigskip
+
+  {\large\textbf{Lösungsansätze}\par}
+  \smallskip
+  \begin{itemize}
+    \item
+      ziffernweise (z.\,B.\ Zahlen als Strings abspeichern)
+    \item
+      zu einer Zehnerpotenz-Basis (z.\,B.\ 1\,000\,000\,000)
+    \item
+      zu einer Zweierpotenz-Basis (z.\,B.\ $2^{32}$)\\
+    \item
+      speziell: Registerbreite \textarrow\ Hardware-Unterstützung (in Assembler)
+  \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+  \showsection
+
+  Problem: Rechnen mit ganzen Zahlen, die größer sind als das,\\
+  was der Rechner normalerweise verarbeiten kann
+
+  \medskip
+
+  \begin{itemize}
+    \item
+      Grundrechenarten (einschließlich "`modulo"'):\\
+      "`schriftlich"' rechnen
+    \item
+      \href{https://de.wikipedia.org/wiki/Binäre_Exponentiation}%
+           {binäre Exponentiation}:\\
+      Basis fortlaufend quadrieren, ggf.\ damit multiplizieren\\
+      Beispiel: $x^9 = ((x^2)^2)^2 \cdot x$
+    \item
+      Suche nach $d$ mit $d\cdot e~\text{mod}~N = 1$:\\
+      \href{https://de.wikipedia.org/wiki/Erweiterter_euklidischer_Algorithmus}%
+           {erweiterter euklidischer Algorithmus}
+    \smallskip
+    \arrowitem
+      RSA
+  \end{itemize}
+
+  \bigskip
+
+  {\large\textbf{Aufgabe: RSA effizient implementieren}\par}
+  \smallskip
+  \begin{itemize}
+    \item
+      Verwenden Sie den Datentyp \lstinline{uint64_t}
+      (oder Langzahl-Arithmetik)
+    \item
+      Für Details siehe: \file{hp-20240411.txt}
+  \end{itemize}
+
+\end{frame}
+
+\section{Kryptographie}
+\subsectionnonumber{\boldmath 4.$(x^2 - 1)$\quad Der Herr der Ringe: Manchmal ist $1 + 1 = 0$.}
+\subsubsectionnonumber{\boldmath 4.$(x^2 - 1).x$\quad Motivation}
+
+\begin{frame}
+
+  \showsection
+%  \pause
+  \showsubsectionnonumber
+%  \pause
+  \showsubsubsectionnonumber
+
+  Man kann auch mit sehr merkwürdigen Objekten\\
+  wie mit "`ganz normalen"' Zahlen rechnen.
+
+%  \pause
+  \bigskip
+  
+  Anwendungen:
+  \begin{itemize}
+    \item Funktionsweise von Computern (\textarrow\ Rechnertechnik)
+    \item Fehlererkennung
+    \item Fehlerkorrektur
+    \item Verschlüsselung
+    \item Digitale Signaturen
+  \end{itemize}
+
+\end{frame}
+
+\subsubsectionnonumber{\boldmath 4.$(x^2 - 1).(x + 1)$\quad Gruppen}
+
+\begin{frame}
+
+  \showsection
+  \showsubsectionnonumber
+  \showsubsubsectionnonumber
+
+  \textbf{Definition:}
+  Sei $G$ eine Menge, $*$ eine Verknüpfung auf $G$.
+  Wenn
+  \begin{itemize}
+    \item
+      $\forall a, b, c \in G$: $(a * b) * c = a * (b * c)$ \quad (Assoziativgesetz),
+    \item
+      $\exists e \in G$: $\forall a \in G$: $a * e = e * a = a$ \quad (neutrales Element),
+    \item
+      $\forall a \in G$: $\exists a^{-1} \in G$: $a * a^{-1} = a^{-1} * a = e$ \quad (inverses Element),
+  \end{itemize}
+  dann heißt $(G,*)$ eine \newterm{Gruppe}.
+
+%  \pause
+  \bigskip
+
+  \textbf{Definition:}
+  Sei $(G,*)$ eine Gruppe.
+  Wenn zusätzlich
+  \begin{itemize}
+    \item
+      $\forall a, b \in G$: $a * b = b * a$ \quad (Kommutativgesetz),
+  \end{itemize}
+  dann heißt $(G,*)$ eine \newterm{kommutative Gruppe}.
+
+\end{frame}
+
+\subsubsectionnonumber{\boldmath 4.$(x^2 - 1).(x + 2)$\quad Ringe}
+
+\begin{frame}
+
+%  \showsection
+  \showsubsectionnonumber
+  \showsubsubsectionnonumber
+
+  \textbf{Definition:}
+  Sei $R$ eine Menge; seien $+$ und $\cdot$ Verknüpfungen auf $R$.
+  Wenn
+  \begin{itemize}
+    \item
+      $(R,+)$ eine kommutative Gruppe ist,
+    \item
+      $\forall a, b, c \in R$: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$ \quad (Assoziativgesetz),
+    \item
+      $\forall a, b, c \in R$: $(a + b)\cdot c = a\cdot c + b\cdot c$
+      und $a\cdot(b + c) = a\cdot b + a\cdot c$ \quad (Distributivgesetze),
+  \end{itemize}
+  dann heißt $(R,+,\cdot)$ ein \newterm{Ring}.
+
+%  \pause
+  \bigskip
+
+  \textbf{Definition:}
+  Sei $(R,+,\cdot)$ ein Ring.
+  Wenn zusätzlich
+  \begin{itemize}
+    \item
+      $\forall a, b \in R$: $a \cdot b = b \cdot a$ \quad (Kommutativgesetz),
+  \end{itemize}
+  dann heißt $(R,+,\cdot)$ ein \newterm{kommutativer Ring}.
+
+%  \pause
+  \bigskip
+
+  \textbf{Definition:}
+  Sei $(R,+,\cdot)$ ein (kommutativer) Ring.
+  Wenn zusätzlich
+  \begin{itemize}
+    \item
+      ein $e \in R$ existiert, so daß für alle $a \in R$ gilt: $a \cdot e = e \cdot a = a$\\
+      (neutrales Element),
+  \end{itemize}
+  dann heißt $(R,+,\cdot)$ ein \newterm{(kommutativer) Ring mit 1}.
+
+  \vspace*{-1cm}
+
+\end{frame}
+
+\subsubsectionnonumber{\boldmath 4.$(x^2 - 1).(x + 3)$\quad Körper}
+
+\begin{frame}
+
+%  \showsection
+  \showsubsectionnonumber
+  \showsubsubsectionnonumber
+
+  \textbf{Definition:}
+  Sei $K$ eine Menge; seien $+$ und $\cdot$ Verknüpfungen auf $K$.
+  Wenn
+  \begin{itemize}
+    \item
+      $(K,+,\cdot)$ ein Ring mit 1 ist und
+    \item
+      $(K \backslash \{0\},\cdot)$ eine kommutative Gruppe ist,
+  \end{itemize}
+  dann heißt $(K,+,\cdot)$ ein \newterm{Körper}.
+
+\end{frame}
+
+\subsubsectionnonumber{\boldmath 4.$(x^2 - 1).(x + 4)$\quad Anwendungen}
+
+\begin{frame}
+
+%  \showsection
+  \showsubsectionnonumber
+  \showsubsubsectionnonumber
+
+  Man kann auch mit sehr merkwürdigen Objekten\\
+  wie mit "`ganz normalen"' Zahlen rechnen.
+
+  \bigskip
+  
+  \begin{itemize}
+    \item
+      innermathematisch: Man kann beweisen,\\
+      daß es ab $x^5$ keine "`$p$-$q$-Formel"' mehr gibt\\
+      und daß bestimmte Operationen mit Zirkel und Lineal unmöglich sind.
+    \item
+      asymmetrische Verschlüsselung, Signaturen:\\
+      RSA, ElGamal\color{red}, elliptische Kurven
+    \item
+      symmetrische Verschlüsselung: AES
+    \item
+      Fehlererkennung: Parität, CRC\\
+      Anwendungen: Datenübertragung, RAID
+    \item
+      Fehlerkorrektur: Reed-Solomon\\
+      Anwendungen: Raumsonden, optische Datenträger, ECC-RAM
+  \end{itemize}
+
+\end{frame}
+
+\end{document}
diff --git a/20240502/ad-20240502.txt b/20240502/ad-20240502.txt
new file mode 100644
index 0000000..5aa8b80
--- /dev/null
+++ b/20240502/ad-20240502.txt
@@ -0,0 +1,21 @@
+18.04.2024
+~~~~~~~~~~
+ - Erweiterter euklidischer Algorithmus
+ - Nutzung von ChatGPT für die Fehlersuche
+ - diskreter Logarithmus: Diffie-Hellman, ElGamal
+   --> gruppen-ringe-koerper-2-05-elgamal-und-diffie-hellman.png
+
+25.04.2024
+~~~~~~~~~~
+ - Kompression am Beispiel RDP (VNC, RFC 6143, yesVNC)
+ - Lasttest für PULT (Mumble, VNC, CVHCamera)
+ - Sicherheitsüberlegunen zu PULT:
+   https://www.bsi.bund.de/SharedDocs/Downloads/DE/BSI/Grundschutz/Kompendium_Einzel_PDFs/03_CON_Konzepte_und_Vorgehensweisen/CON_5_Entwicklung_Einsatz_von_Individualsoftware_Edition_2020.pdf?__blob=publicationFile&v=2
+
+02.05.2024
+~~~~~~~~~~
+ - yesVNC (Fortsetzung)
+ - Skripte zur allgemeinen Nutzung von Online-Plattformen
+   (s, mic, Weiterentwicklung: VNC Vollbild)
+ - weitere Anwendungen diskreter Mathematik:
+   elliptische Kurven, AES, Fehlererkennung und -korrektur
diff --git a/20240502/logo-hochschule-bochum-cvh-text.pdf b/20240502/logo-hochschule-bochum-cvh-text.pdf
new file mode 120000
index 0000000..a059461
--- /dev/null
+++ b/20240502/logo-hochschule-bochum-cvh-text.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum-cvh-text.pdf
\ No newline at end of file
diff --git a/20240502/logo-hochschule-bochum.pdf b/20240502/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20240502/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20240502/pgslides.sty b/20240502/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20240502/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
-- 
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