From fc28b51942f790acc340664f11dd0a968867d85a Mon Sep 17 00:00:00 2001
From: Aaron Kaiser <a_kaiser@posteo.de>
Date: Wed, 1 Mar 2023 18:14:48 +0100
Subject: [PATCH] Moved captions below elements

---
 thesis/Abschlussarbeit.tex | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/thesis/Abschlussarbeit.tex b/thesis/Abschlussarbeit.tex
index b567f25..1fe5936 100644
--- a/thesis/Abschlussarbeit.tex
+++ b/thesis/Abschlussarbeit.tex
@@ -128,7 +128,6 @@ Let $SIG = (\keygen, \sign, \verify)$ be a digital signature scheme. $SIG$ is \c
 \[ \advantage{SIG,\adversary{A}}{\cma}(\secparamter) \assign \prone{\cma^{\adversary{A}}} \leq \epsilon \]
 
 \begin{figure}
-	\caption{\cma Security Game}
 	\label{game:cma}
 	\hrule
 	\begin{multicols}{2}
@@ -149,6 +148,7 @@ Let $SIG = (\keygen, \sign, \verify)$ be a digital signature scheme. $SIG$ is \c
 		\end{algorithmic}
 	\end{multicols}
 	\hrule
+	\caption{\cma Security Game}
 \end{figure}
 
 \subsection{Random Oracle Model (ROM)}
@@ -195,7 +195,6 @@ The EdDSA signature scheme is defined using a twisted Edwards curve. Twisted Edw
 % TODO: Ist das ok hier einfach zu kopieren?
 \begin{center}
 	\begin{table}[t]
-		\caption{Parameter of the EdDSA signature scheme}
 		\label{tab:parameter}
 		\centering
 		\begin{tabularx}{\textwidth}{@{}lX@{}}
@@ -212,13 +211,13 @@ The EdDSA signature scheme is defined using a twisted Edwards curve. Twisted Edw
 			$l$ & The order of the prime order subgroup. \\
 			$H'(\inp)$ & A prehash function applied to the message prior to applying the \sign or \verify procedure.
 		\end{tabularx}
+	\caption{Parameter of the EdDSA signature scheme}
 	\end{table}
 \end{center}
 
 
 
 \begin{figure}
-	\caption{Generic description of the algorithms \keygen, \sign and \verify used by the EdDSA signature scheme}
 	\label{fig:eddsa}
 	\hrule
 	\begin{multicols}{3}
@@ -252,6 +251,7 @@ The EdDSA signature scheme is defined using a twisted Edwards curve. Twisted Edw
 		\end{algorithmic}
 	\end{multicols}
 	\hrule
+	\caption{Generic description of the algorithms \keygen, \sign and \verify used by the EdDSA signature scheme}
 \end{figure}
 
 \subsection{Replacing Hash Function Calls}
@@ -290,7 +290,6 @@ To generate a signature without the knowledge of the private key the challenge a
 This section shows that \igame implies the UF-NMA security if the EdDSA signature scheme using the Algebraic Group Model. The section starts by first providing an intuition if the proof followed by the detailed security proof.
 
 \begin{figure}
-	\caption{\igame}
 	\label{game:igame}
 	\hrule
 	\begin{multicols}{2}
@@ -313,6 +312,7 @@ This section shows that \igame implies the UF-NMA security if the EdDSA signatur
 		\end{algorithmic}
 	\end{multicols}
 	\hrule
+	\caption{\igame}
 \end{figure}
 
 \subsection{\sdlog $=>$ \igame (AGM)}
@@ -324,8 +324,8 @@ This section shows that \sdlog implies \igame using the Algebraic Group Model. T
 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}. 
 
 \begin{figure}
-	\caption{\sdlog}
 	\label{fig:sdlog}
+	\hrule
 	\begin{algorithmic}[1]
 		\State \underline{\game \sdlog}
 		\State $a \randomsample \{ 2^{n-1}, 2^{n-1} + 8, ..., 2^{n} - 8 \}$
@@ -333,6 +333,8 @@ The \sdlog game is a variant of the discrete logarithm game which represents the
 		\State $a' \randomassign \adversary{A}(\groupelement{A})$
 		\State \Return $a = a'$
 	\end{algorithmic}
+	\hrule
+	\caption{\sdlog}
 \end{figure}
 
 \paragraph{\underline{Proof Overview}}
@@ -350,7 +352,6 @@ Assuming that $r_2 + 2^c c$ is invertable in $\field{L}$ (not equal to $0$) we c
 
 \begin{figure}
 	% TODO: set caption
-	\caption{\igame with aborts}
 	\label{fig:igamewithabort}
 	\hrule
 	\begin{multicols}{2}
@@ -381,6 +382,7 @@ Assuming that $r_2 + 2^c c$ is invertable in $\field{L}$ (not equal to $0$) we c
 		\end{algorithmic}
 	\end{multicols}
 	\hrule
+	\caption{\igame with aborts}
 \end{figure}
 
 \paragraph{Introducing aborts}