simplified equations

thesis/sections/mu_security_of_eddsa/mu-gamez_implies_mu-uf-nma.tex

@@ -7,7 +7,7 @@ This section shows that MU-\igame implies MU-EUF-NMA security of the EdDSA signa
 \begin{definition}[MU-\igame]
 	Let $n$ and $N$ be positive integers. For an adversary $\adversary{A}$, receiving $N$ public keys as input, we define its advantage in the MU-\igame as following:
 	
-	\[ \advantage{\adversary{A}}{\text{MU-\igame}}(\secparamter) \assign | \Pr[\text{MU-\igame}^{\adversary{A}} \Rightarrow 1] |. \]
+	\[ \advantage{\adversary{A}}{\text{$N$-MU-\igame}}(\secparamter) \assign | \Pr[\text{MU-\igame}^{\adversary{A}} \Rightarrow 1] |. \]
 \end{definition}
 
 \begin{figure}[h]
@@ -15,7 +15,7 @@ This section shows that MU-\igame implies MU-EUF-NMA security of the EdDSA signa
 	\vspace{1mm}
 	\large
 	\begin{algorithmic}
-		\Statex \underline{\game \igame}
+		\Statex \underline{\game $N$-MU-\igame}
 		\State \textbf{for} $i \in \{1,2,...,N\}$
 		\State \quad $a_i \randomsample \{2^{n-1}, 2^{n-1} + 2^c, ..., 2^n - 2^c\}$
 		\State \quad $\groupelement{A_i} \assign a_i \groupelement{B}$
@@ -30,7 +30,7 @@ This section shows that MU-\igame implies MU-EUF-NMA security of the EdDSA signa
 		\State \Return $\ch_i$
 	\end{algorithmic}
 	\hrule
-	\caption{MU-\igame}
+	\caption{$N$-MU-\igame}
 	\label{game:mu-igame}
 \end{figure}