From 48bbf09e9e46adcc76a76d060c1828d130212189 Mon Sep 17 00:00:00 2001
From: Aaron Kaiser <a_kaiser@posteo.de>
Date: Fri, 24 Feb 2023 12:08:14 +0100
Subject: [PATCH] Introduced security parameter macro

---
 thesis/Abschlussarbeit.tex | 6 +++---
 thesis/macros.tex          | 1 +
 2 files changed, 4 insertions(+), 3 deletions(-)

diff --git a/thesis/Abschlussarbeit.tex b/thesis/Abschlussarbeit.tex
index 3fc4330..801f677 100644
--- a/thesis/Abschlussarbeit.tex
+++ b/thesis/Abschlussarbeit.tex
@@ -115,9 +115,9 @@ TODO
 
 \cma is a security notion for digital signature schemes. In this game the attacker is given access to a \Osign oracle, which generates valid signatures for arbitrary messages. The attacker wins the game if he is able to provide a message signature pair which is valid and was not generated by the \Osign oracle. The security game is depicted in figure \ref{game:cma}.
 
-Let $SIG = (\keygen, \sign, \verify)$ be a digital signature scheme. $SIG$ is \cma secure if for all ppt adversaries $\adversary{A}$ the $\advantage{SIG,\adversary{A}}{\cma}(k)$ is negligible in k.
+Let $SIG = (\keygen, \sign, \verify)$ be a digital signature scheme. $SIG$ is \cma secure if for all ppt adversaries $\adversary{A}$ the $\advantage{SIG,\adversary{A}}{\cma}(k)$ is negligible in $\secparamter$.
 
-\[ \advantage{SIG,\adversary{A}}{\cma}(k) \assign \prone{\cma^{\adversary{A}}} \leq \epsilon \]
+\[ \advantage{SIG,\adversary{A}}{\cma}(\secparamter) \assign \prone{\cma^{\adversary{A}}} \leq \epsilon \]
 
 \begin{figure}
 	\caption{\cma Security Game}
@@ -127,7 +127,7 @@ Let $SIG = (\keygen, \sign, \verify)$ be a digital signature scheme. $SIG$ is \c
 		\normalsize
 		\begin{algorithmic}[1] 
 			\State \underline{\game \cma}
-			\State $(\pubkey, \privkey) \randomassign \keygen(1^k)$
+			\State $(\pubkey, \privkey) \randomassign \keygen(1^\secparamter)$
 			\State $(\m^*, \signature^*) \randomassign \adversary{A}^{\sign(\cdot)}(\pubkey)$
 			\State \Return $\verify(\pubkey, \m^*, \signature^*) = 1 \wedge (\m^*, \signature^*) \notin M$
 		\end{algorithmic}
diff --git a/thesis/macros.tex b/thesis/macros.tex
index 4f36be1..5b54663 100644
--- a/thesis/macros.tex
+++ b/thesis/macros.tex
@@ -1,5 +1,6 @@
 % Games
 \newcommand{\game}{\textbf{Game} }
+\newcommand{\secparamter}{\lambda}
 \newcommand{\randomsample}{\overset{{\scriptscriptstyle\$}}{\leftarrow}}
 \newcommand{\randomassign}{\leftarrow}
 \newcommand{\assign}{:=}