diff --git a/thesis/Abschlussarbeit.tex b/thesis/Abschlussarbeit.tex
index 47eb640..c7c7296 100644
--- a/thesis/Abschlussarbeit.tex
+++ b/thesis/Abschlussarbeit.tex
@@ -352,7 +352,6 @@ The adversary has to call the \ioracle oracle with a commitment $\groupelement{R
 Assuming that $r_2 + 2^c c$ is invertable in $\field{L}$ (not equal to $0$) we can use both equations to calculate the discrete logarithm of $\groupelement{A}$. To ensure that $r_2 + 2^c c$ is invertable the reduction has to abort if $-r_2$ equals $2^c c$ with $c$ being randomly choosen in the \ioracle oracle.
 
 \begin{figure}
-	% TODO: set caption
 	\hrule
 	\begin{multicols}{2}
 		\large
@@ -398,11 +397,9 @@ Game $G_0$ is defined in Figure \ref{fig:igamewithabort} by ignoring all boxes.
 	
 	% TODO: hard bezüglich ggen
 	% TODO: min entropy von {0,1}^{2b} mod L?
-	\[ \advantage{\igame}{\adversary{A}} \leq \advantage{\sdlog}{\adversary{B}} - \frac{\oraclequeries}{L} \]
+	\[ \advantage{\igame}{\adversary{A}} \leq \advantage{\sdlog}{\adversary{B}} - \frac{\oraclequeries}{2^{\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}} \]
 \end{theorem}
 
-TODO: vielleicht doch eher $\oraclequeries$  durch min entropy von $\{0,1\}^{2b} \pmod L$?
-
 \begin{proof}
 	\item \paragraph{\underline{$G_0$:}} Let $G_0 \assign \igame$ be \igame. By definition,
 	
@@ -413,9 +410,9 @@ TODO: vielleicht doch eher $\oraclequeries$  durch min entropy von $\{0,1\}^{2b}
 	\[ \Pr[G_0^{\adversary{A}} \Rightarrow 1] = \Pr[G_1^{\adversary{A}} \Rightarrow 1] \]
 	
 	% TODO: wählen von 
-	\item \paragraph{\underline{$G_2:$}} Game $G_2$ aborts if the flag bad is set. For each individual \ioracle query the bad flag is set with probability at most $\frac{1}{L}$, since $c$ is chosen from $\field{L}$ uniformly at random. By the Union bound over all $\oraclequeries$ queries we obtain $\Pr[bad] = \frac{\oraclequeries}{L}$. Since $G_1$ and $G_2$ are identical-until-bad games, we have
+	\item \paragraph{\underline{$G_2:$}} Game $G_2$ aborts if the flag bad is set. For each individual \ioracle query the bad flag is set with probability at most $\frac{1}{2^{\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}}$, since $c$ is chosen from $\{0,1\}^{2b}$ uniformly at random and then reduced modulo $L$. By the Union bound over all $\oraclequeries$ queries we obtain $\Pr[bad] = \frac{\oraclequeries}{2^{\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}}$. Since $G_1$ and $G_2$ are identical-until-bad games, we have
 	
-	\[ |\Pr[G_1^{\adversary{A}} \Rightarrow 1] - \Pr[G_2^{\adversary{A}} \Rightarrow 1]| \leq \Pr[bad] \leq \frac{\oraclequeries}{L} \]
+	\[ |\Pr[G_1^{\adversary{A}} \Rightarrow 1] - \Pr[G_2^{\adversary{A}} \Rightarrow 1]| \leq \Pr[bad] \leq \frac{\oraclequeries}{2^{\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}} \]
 	
 	\item Finally, Game $G_2$ is well prepared to show that there exists an adversary $\adversary{B}$ satisfying