Discussion & results shuffling

Author: ironmand123

report/src/sections/06-results.tex

@@ -33,14 +33,22 @@ \subsection{Shuffle security}\label{subsec:Shuffle-security}
 
 \begin{figure*}[!htb]
     \centering
-    \subfloat[\centering]{{\includegraphics[width=0.45\textwidth]{figures/results/4096-256-p2} }}%
-    \qquad
-    \subfloat[\centering]{{\includegraphics[width=0.45\textwidth]{figures/results/5462-256-p2} }}%
-    \subfloat[\centering]{{\includegraphics[width=0.45\textwidth]{figures/results/8192-256-p2} }}%
+    \subfloat[\centering]{{\includegraphics[width=0.32\textwidth]{figures/results/4096-256-p2} }}%
+    \subfloat[\centering]{{\includegraphics[width=0.32\textwidth]{figures/results/5462-256-p2} }}%
+    \subfloat[\centering]{{\includegraphics[width=0.32\textwidth]{figures/results/8192-256-p2} }}%
     \caption{The results of the shuffle security experiment showing the mean amount of honest shuffles necessary with one standard deviation}%
     \label{fig:shufflesecurity}%
 \end{figure*}
 
+\begin{figure*}[!htb]
+    \centering
+    \subfloat[\centering]{{\includegraphics[width=0.32\textwidth]{figures/results/violin-4096} }}%
+    \subfloat[\centering]{{\includegraphics[width=0.32\textwidth]{figures/results/violin-5462} }}%
+    \subfloat[\centering]{{\includegraphics[width=0.32\textwidth]{figures/results/violin-8192} }}%
+    \caption{The results of the shuffle security experiment showing the spread of nessecary shuffle need for the shuffle to be secure}%
+    \label{fig:shufflesecurityviolin}%
+\end{figure*}
+
 The results of the shuffle security experiment are shown in \autoref{fig:shufflesecurity}.
 
 \autoref{fig:shufflesecurity} shows the mean of the 1000 runs of each shuffle size $\ell$ and the standard deviation.
@@ -64,15 +72,7 @@ \subsection{Shuffle security}\label{subsec:Shuffle-security}
 Another thing that differs between the experiments is that they all have a sudden dip in higher $\ell$ values in the experiment.
 Here we see a trend that the lower the~$\alpha$ is, the earlier the dip happens.
 
-\begin{figure*}[!htb]
-    \centering
-    \subfloat[\centering]{{\includegraphics[width=0.45\textwidth]{figures/results/violin-4096} }}%
-    \qquad
-    \subfloat[\centering]{{\includegraphics[width=0.45\textwidth]{figures/results/violin-5462} }}%
-    \subfloat[\centering]{{\includegraphics[width=0.45\textwidth]{figures/results/violin-8192} }}%
-    \caption{The results of the shuffle security experiment showing the spread of nessecary shuffle need for the shuffle to be secure}%
-    \label{fig:shufflesecurityviolin}%
-\end{figure*}
+
 
 The results in \autoref{fig:shufflesecurityviolin} show that for all three $\alpha$ values, the spread of the necessary honest shuffles tightens the larger the shuffle size $\ell$ gets.
 Like the results in \autoref{fig:shufflesecurity}, \autoref{fig:shufflesecurityviolin} also shows that the bigger a shuffle size $\ell$, the less honest shuffles on average are necessary to make the shuffle secure.

report/src/sections/07-discussion.tex

@@ -55,4 +55,8 @@ \subsection{Shuffle Security}\label{subsec:Discution-Shuffle-security}
 Some nodes contain multiple validators, and this means that during the shuffling phase, when selecting the 16384 possible proposers, there is a chance that a single node controls multiple of the chosen validators.
 This is also possible during the selecting of the shufflers.
 
-
+From the results we see that the mean starts higher and ends lower for the experiments with a higher $\alpha$.
+One of the reasons for the could be the relationship between the number of adversarial tracked cups and the threshold necessary before the shuffle is secure.
+Since the threshold is $2/(n-\alpha)$ the higher $\alpha$ is, the higher the threshold for the amount of water allowed in any cup.
+Therefore, the higher $\alpha$ is, the less the water needs to be divided be the harder it is to get the initial 1 unit of water divided.
+And opposite to this the lower $\alpha$ is, the more evenly the water needs to be divided, and therefore the harder it is to get the every cup below the lower threshold.