Fixed security parameter

thesis/sections/security_of_eddsa/dlog'_implies_gamez.tex

@@ -11,7 +11,7 @@ The \sdlog game is a variant of the discrete logarithm game which represents the
 \begin{definition}[\sdlog]
 	For an adversary $\adversary{A}$ we define its advantage in the \sdlog game as following:
 	
-	\[ \advantage{\adversary{A}}{\sdlog}(k) \assign | \Pr[\sdlog^{\adversary{A}} \Rightarrow 1] | \].
+	\[ \advantage{\adversary{A}}{\sdlog}(\secparamter) \assign | \Pr[\sdlog^{\adversary{A}} \Rightarrow 1] | \].
 \end{definition}
 
 
@@ -34,7 +34,7 @@ The \sdlog game is a variant of the discrete logarithm game which represents the
 	\label{theorem:advgamez}
 	Let $\adversary{A}$ be an adversary against \igame with $\group{G}$ being a cyclic group of prime order $L$, making at most $\oraclequeries$ oracle queries. Then
 	
-	\[ \advantage{\group{G},\adversary{A}}{\igame}(k) \leq \advantage{\group{G},\adversary{B}}{\sdlog}(k) - \frac{\oraclequeries}{2^{-\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}} \].
+	\[ \advantage{\group{G},\adversary{A}}{\igame}(\secparamter) \leq \advantage{\group{G},\adversary{B}}{\sdlog}(\secparamter) - \frac{\oraclequeries}{2^{-\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}} \].
 \end{theorem}
 
 \paragraph{\underline{Proof Overview}}
@@ -97,7 +97,7 @@ The adversary has to call the \ioracle oracle with a commitment $\groupelement{R
 	
 	\item \paragraph{\underline{$G_0$:}} Let $G_0$ be defined in figure \ref{fig:igamewithabort} by excluding all boxes and $G_0$ be \igame. By definition,
 	
-	\[ \advantage{\group{G},\adversary{A}}{\igame}(k) = \Pr[\igame^{\adversary{A}} \Rightarrow 1] = \Pr[G_0^{\adversary{A}} \Rightarrow 1] \].
+	\[ \advantage{\group{G},\adversary{A}}{\igame}(\secparamter) = \Pr[\igame^{\adversary{A}} \Rightarrow 1] = \Pr[G_0^{\adversary{A}} \Rightarrow 1] \].
 	
 	\item \paragraph{\underline{$G_1$:}} Game $G_1$ is exactly the same as $G_0$ with the only change being the bad flag being set inside an if condition. The bad flag is set if $2^c \ch_i = -r_2$. This represents cases where not all solutions from the adversary $\adversary{A}$ can be used to calculate the discrete logarithm of $\groupelement{A}$. This is just a conceptual change since the behavior of the game does not change whether the flag is set or not. Hence,
 	
@@ -111,7 +111,7 @@ The adversary has to call the \ioracle oracle with a commitment $\groupelement{R
 	\item Finally, Game $G_2$ is well prepared to show that there exists an adversary $\adversary{B}$ satisfying
 	
 	\begin{align}
-		\Pr[G_2^{\adversary{A}} \Rightarrow 1] = \advantage{\group{G},\adversary{B}}{\sdlog}(k) \label{eq:advbsdlog}
+		\Pr[G_2^{\adversary{A}} \Rightarrow 1] = \advantage{\group{G},\adversary{B}}{\sdlog}(\secparamter) \label{eq:advbsdlog}
 	\end{align}.
 	
 	\begin{figure}