Merge pull request #44 from AAU-Dat/capital

Capitalization of section titles

Author: Maltesius

report/src/sections/04-Approach.tex

@@ -29,9 +29,9 @@ \subsection{Springproofs}\label{sec:approach-springproofs}
     $N\gets 2^{\lceil\log n\rceil-1}$
     $i_h \gets \lfloor (2N-n)/2\rfloor+1$
     $i_t=\lfloor n/2\rfloor$
-    if $n\neq N$: #Not power of 2
+    if $n\neq N$: #Not power of two
         $\mathbf{\mathcal{T}}\gets\{i_h:i_t\}\cup\{N+1:n\}$
-    else if $n=N$: #Power of 2
+    else if $n=N$: #Power of two
         $\mathbf{\mathcal{T}}\gets\{1:n\}$ #Meaning S is empty
     $\mathbf{\mathcal{S}}\gets\mathbf{n}-\mathbf{\mathcal{T}}$
     \end{lstlisting}
@@ -136,7 +136,7 @@ \subsubsection*{Prover computation}
 
 At the end of the recursive round, on line 31,~$n$ is updated to the length of the concatenated vectors before starting a new round.
 
-The result of this is a proof,~$\mathbf{\pi}$, constructed in $\lceil \log n \rceil$ rounds, but with the proof size being smaller than if the shuffle size was a power of 2.
+The result of this is a proof,~$\mathbf{\pi}$, constructed in $\lceil \log n \rceil$ rounds, but with the proof size being smaller than if the shuffle size was a power of two.
 
 In step 3, lines 32--36, the folded vectors of size 1 are added to the proof as values as well as the commitments to the blinding values,~$B_C$ and~$B_D$.
 The proof, folded vectors, and updated commitment are saved for the verifier to use for verification.
@@ -223,7 +223,7 @@ \subsubsection*{Verifier computation}
 \end{theorem}
 
 
-\subsection{Shuffle security}\label{subsec:approach-shuffle-security}
+\subsection{Shuffle Security}\label{subsec:approach-shuffle-security}
 The shuffle method proposed by Larsen et al.~\cite{cryptoeprint:2022/560} that is used in Curdleproofs is based on the idea of shuffling a list of proposers over a set of slots.
 A formal definition of the shuffle is given in~\autoref{fig:shuffle}.
 
@@ -397,7 +397,7 @@ \subsubsection{Shuffle Security}
 
 By repeating this experiment for several runs, one can experimentally say when a shuffle with given parameters is secure.
 
-\subsubsection{Size reduction}
+\subsubsection{Size Reduction}
 If we reduce the shuffle size used in Whisk and still prove it secure, then we expect to see a reduction in the size overhead on the blockchain.
 
 We first set our focus on Curdleproofs, as this is the protocol we have modified directly.
@@ -413,7 +413,7 @@ \subsubsection{Size reduction}
 
 The CAAUrdleproofs modification can still reduce the overall block size overhead.
 By using the overhead calculation described by Whisk on CAAUrdleproofs, it measures a block overhead of $16.656$ KB when the shuffle size is 128~\cite{Whisk2024}.
-Note that this is the same size as Curdleproofs, as the shuffle size is a power of 2.
+Note that this is the same size as Curdleproofs, as the shuffle size is a power of two.
 The provided calculation of the block overhead is provided as the following, where $\mathbb{G}=48$ bytes and $\mathbb{F}=32$ bytes\footnote{\text{As noted in the code on the Curdleproofs GitHub repository: }\\ \href{https://github.com/asn-d6/curdleproofs/blob/main/src/whisk.rs}{https://github.com/asn-d6/curdleproofs/blob/main/src/whisk.rs}. Accessed: 26/05/2025}:
 \begin{itemize}
     \item List of shuffled trackers ($\ell\cdot96\Rightarrow\text{eg. }124\cdot96=11,904$ bytes).

report/src/sections/05-experimental-protocol.tex

@@ -11,7 +11,7 @@ \section{Experimental Protocol}\label{sec:experimental-protocol}
 The virtual machine is running Ubuntu Server 24.
 
 
-\subsection{CAAUrdleproof}\label{sec:CAAUrdleproof-experiment}
+\subsection{CAAUrdleproofs}\label{sec:CAAUrdleproof-experiment}
 In this experiment, we measure the time to run the CAAUrdleproofs protocol.
 The results will be compared to those of Curdleproofs, which we re-run on our hardware.
 As Curdleproofs already has a Rust benchmark implemented, we will be using that same benchmark for both protocols.
@@ -24,7 +24,7 @@ \subsection{CAAUrdleproof}\label{sec:CAAUrdleproof-experiment}
 
 
 
-\subsection{Shuffle security}\label{subsec:experimental-protocol-shuffle-security}
+\subsection{Shuffle Security}\label{subsec:experimental-protocol-shuffle-security}
 In this experiment, we run the shuffle protocol with varying shuffle sizes and varying numbers of adversarial tracked ciphertexts.
 The purpose of this experiment is to find the lowest possible shuffle size that is still secure against adversarial tracking.
 We, therefore, run the experiment with shuffle sizes,~$\ell$, between 32 and 512.

report/src/sections/06-results.tex

@@ -29,7 +29,7 @@ \subsection{Proving and Verifying Times}\label{subsec:results:provingverifying}
 
 
 
-\subsection{Shuffle security}\label{subsec:Shuffle-security}
+\subsection{Shuffle Security}\label{subsec:Shuffle-security}
 
 \begin{figure}[!htb]
     \centering

report/src/sections/07-discussion.tex

@@ -5,7 +5,7 @@ \section{Discussion}\label{sec:discussion}
 We will also discuss some of the limitations of the CAAUrdleproofs protocol and how it compares to Curdleproofs.
 
 
-\subsection{CAAUrdleproofs in comparison to Curdleproofs}\label{subsec:CAAUrdleproofs-vs-Curdleproofs}
+\subsection{CAAUrdleproofs in Comparison to Curdleproofs}\label{subsec:CAAUrdleproofs-vs-Curdleproofs}
 As mentioned in~\autoref{subsec:results:provingverifying}, the proving and verifying times between the two protocols are close to identical when $\ell$ is a power of two.
 This is because the added computation is negligible compared to the other computations present in the original Curdleproofs protocol.
 

report/src/sections/09-future-works.tex

@@ -1,4 +1,4 @@
-\section{Future work}\label{sec:future-works}
+\section{Future Work}\label{sec:future-works}
 In this section, we will focus on areas where the Whisk protocol still has room for improvement.
 
 The main modification from Curdleproofs to CAAUrdleproofs is the added flexibility in choosing the shuffle size for Whisk.

report/src/sections/appendix/04-shuffling-times.tex

@@ -1,5 +1,5 @@
 \clearpage
-\section{Shuffling results}\label{sec:shuffling-results}
+\section{Shuffling Results}\label{sec:shuffling-results}
 Here, we present the results of the shuffling times given different shuffling size values.
 The results can be seen in~\autoref{fig:shufflespeed}.
 \begin{figure}[!htb]