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Binary files a/doc/report.pdf and b/doc/report.pdf differ
diff --git a/doc/report.tex b/doc/report.tex
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--- a/doc/report.tex
+++ b/doc/report.tex
@@ -54,6 +54,8 @@ line/.style={-latex}   % the lesser the width the greater will be the diagram wi
 \section{Simple combinatorics}
 
 \section{XOR cipher}
+Following the rule $a \oplus b = c \Leftrightarrow b = a \oplus c$ these calculations can be made:
+
 \begin{figure}[h]
     \centering
 \begin{tikzpicture}  
@@ -84,7 +86,7 @@ line/.style={-latex}   % the lesser the width the greater will be the diagram wi
 \caption{This Diagram shows how an attacker can calculate the key $K$ and the message $M_1$. \newline
     $C_x$, $C_y$ and $M_2$ are known to the attacker.}
 \end{figure}
-A few requirements must be satisfied in order to get hold of the $K$ and the $M_1$:
+A few requirements must be satisfied in order to get hold of $K$ and $M_1$:
 \begin{itemize}
     \item $M_2$ must be longer than $M_1$ or $K$, so that the key can be calculated in at least the needed length.
     \item A successfully decoded message must be distinguishable from an unsuccessfully decoded message, so that the