From 2447fce0b509054a83ba7656933a6bf148551217 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 4 Apr 2024 15:03:37 +0200
Subject: [PATCH] Langzahl-Arithmetik

---
 20230316/ad-20240404.pdf | Bin 230695 -> 233443 bytes
 20230316/ad-20240404.tex |  64 +++++++++++++++++++++++++++++++++++----
 2 files changed, 58 insertions(+), 6 deletions(-)

diff --git a/20230316/ad-20240404.pdf b/20230316/ad-20240404.pdf
index 86ebb433fe74a2ca5e0936c529b07abd8b8e9e9e..6cb1790f76c9d38a386efb8ce360a6e2b45d67c7 100644
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diff --git a/20230316/ad-20240404.tex b/20230316/ad-20240404.tex
index 0f54184..73338a5 100644
--- a/20230316/ad-20240404.tex
+++ b/20230316/ad-20240404.tex
@@ -86,7 +86,7 @@
 
   \begin{itemize}
     \item[\textbf{1}] \textbf{Einführung}
-      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp.git}}}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
     \item[\textbf{2}] \textbf{Einführung in C}
     \item[\textbf{3}] \textbf{Bibliotheken}
     \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
@@ -117,7 +117,7 @@
   \begin{itemize}
     \color{gray}
     \item[\textbf{1}] \textbf{Einführung}
-      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp.git}}}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
     \item[\textbf{2}] \textbf{Einführung in C}
     \item[\textbf{3}] \textbf{Bibliotheken}
     \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
@@ -374,7 +374,7 @@
 
     \pause[4]
     \smallskip
-    \hspace*{2.29cm}\textcolor{magenta}{\textbf{Mit Quantencomputer: \boldmath$\mathcal{O}\bigl((\log n)^3\bigr)$}}
+    \hspace*{2.29cm}\textcolor{red}{\textbf{Mit Quantencomputer: \boldmath$\mathcal{O}\bigl((\log n)^3\bigr)$}}
 
   \end{onlyenv}
 
@@ -390,7 +390,7 @@
 
   \begin{itemize}
     \item[\textbf{1}] \textbf{Einführung}
-      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/ad.git}}}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/ad}}}
     \item[\textbf{2}] \textbf{\dots}
   \end{itemize}
 
@@ -431,7 +431,7 @@
   \begin{itemize}
     \item[\textbf{1}] \textbf{Einführung}
       \underconstruction
-      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/ad.git}}}
+      \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}
@@ -724,6 +724,58 @@
 
 \end{frame}
 
+\fi
+
+\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}
+  \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}
+
+\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
+      binäre Exponentiation:\\
+      Basis fortlaufend quadrieren, ggf.\ damit multiplizieren\\
+      Beispiel: $x^9 = ((x^2)^2)^2 \cdot x$
+    \item
+      Suche nach $d$ mit $d\cdot e\,\text{mod}\,N = 1$:\\
+      erweiterter Euklidischer Algorithmus
+    \smallskip
+    \arrowitem
+      RSA
+  \end{itemize}
+
+\end{frame}
+
+\iffalse
+
 \nosectionnonumber{\inserttitle}
 
 \begin{frame}
@@ -733,7 +785,7 @@
   \begin{itemize}
     \item[\textbf{1}] \textbf{Einführung}
       \underconstruction
-      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/ad.git}}}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/ad}}}
 %    \item[\textbf{i}] \textbf{Gesellschaftliche Auswirkungen\\
 %                              von Algorithmen und Datenstrukturen}
     \item[\textbf{2}] \textbf{Datenorganisation}
-- 
GitLab