more proofs

thesis/sections/security_of_eddsa/dlog'_implies_gamez.tex

@@ -6,12 +6,12 @@ This section shows that \sdlog implies \igame using the Algebraic Group Model. T
 
 \paragraph{\underline{Introducing \sdlog}}
 
-The \sdlog game is a variant of the discrete logarithm game which represents the clearing and setting of bits in the secret scalar during the EdDSA key generation. The only difference to the normal discrete logarithm game is that the secret scalars are not choosen uniformly random from $\field{L}$ with $L$ being the order of the generator but rather from the set $\{2^{n-1}, 2^{n-1} + 8, ..., 2^{n} - 8\}$. This set represents all valid private keys according to the key generation algorithm. The hardness of this version of the discrete logarithm problem is further analyzed in section \ref{sec:sdlog}. The \sdlog game is depicted in figure \ref{fig:sdlog}. 
+The \sdlog game is a variant of the discrete logarithm game which represents the clearing and setting of bits in the secret scalar during the EdDSA key generation. The only difference to the normal discrete logarithm game is that the secret scalars are not chosen uniformly random from $\field{L}$ with $L$ being the order of the generator but rather from the set $\{2^{n-1}, 2^{n-1} + 8, ..., 2^{n} - 8\}$. This set represents all valid private keys according to the key generation algorithm. The hardness of this version of the discrete logarithm problem is further analyzed in section \ref{sec:sdlog}. The \sdlog game is depicted in figure \ref{fig:sdlog}. 
 
 \begin{definition}[\sdlog]
 	For an adversary $\adversary{A}$ we define its advantage in the \sdlog game as following:
 	
-	\[ \advantage{\adversary{A}}{\sdlog}(\secparamter) \assign | \Pr[\sdlog^{\adversary{A}} \Rightarrow 1] | \].
+	\[ \advantage{\adversary{A}}{\text{\sdlog}}(\secparamter) \assign | \Pr[\text{\sdlog}^{\adversary{A}} \Rightarrow 1] | \].
 \end{definition}