Merge pull request #14 from AAU-Dat/Related-work

Related work

Author: ironmand123

report/src/bib/main.bib

@@ -139,4 +139,29 @@ @inproceedings{10.1145/3419614.3423258
     keywords = {Secret Leader Election, Proof of Stake, Blockchain},
     location = {New York, NY, USA},
     series = {AFT '20}
+}
+
+@article{haastad2006square,
+    title={The square lattice shuffle},
+    author={H{\aa}stad, Johan},
+    journal={Random Structures and Algorithms},
+    volume={29},
+    number={4},
+    pages={466--474},
+    year={2006},
+    publisher={New York: J. Wiley, c1990-}
+}
+
+@article{Feistle,
+    title        = {Privacy Analysis of Whisk},
+    author       = {The Ethereum Foundation Cryptography Research Team},
+    note         = {Accessed: 15-05-2025},
+    url = {https://github.com/khovratovich/whisk-analysis/blob/ba6a4b1374efe56ebbde692c7fc3b549d1eb0133/WhiskAnalysis.pdf}
+}
+
+@article{safrole,
+    title        = {-safrole},
+    author       = {Polkadot Web3 Foundation},
+    note         = {Accessed: 16-05-2025},
+    url = {https://wiki.polkadot.network/learn/learn-safrole/}
 }

report/src/sections/01-introduction.tex

@@ -3,5 +3,4 @@
 \section{Introduction}\label{sec:introduction}
 This is the introduction
 
-\subsection*{Related Work}\label{subsec:related-work}
-This is related work
+

report/src/sections/02-related-work.tex

@@ -4,21 +4,27 @@ \section{Related Work}\label{sec:related-work}
 
 
 \subsection{Single Secret Leader Election}\label{sec:related-work-SSLE}
+A~\gls{ssle} is a protocol where a group of participants randomly elects only one leader from the group.
+The identity of the leader is kept secret from all other participants so only the leader themselves know that they have been chosen.
+The elected leader can then later publicly prove that they have been elected~\cite{10.1145/3419614.3423258}.
+One of the use cases of~\gls{ssle} is to make~\gls{pos} cryptocurrencies more secure due to the added privacy that the proposer has.
 
+One~\gls{pos} cryptocurrency that uses an~\gls{ssle} is Polkadot which uses Safrole as their~\gls{ssle} protocol~\cite{safrole}.
 
 
 
 \subsection{Shuffling algorithm}\label{sec:related-work-Shuffling-algorithm}
-The shuffling algorithm used in curdleproofs has gone though many iterations and improvements in order to increase speed and reduce the size the proof.
-This is because the proposer has a limited amount of time to propose a block in each slot, and the addition of the proof to the protocol increases the size of the block the proposers have to create.
-This is the reason why the current implementation of curdleproofs has chosen the shuffling algorithm~\cite{cryptoeprint:2022/560} proposed by Larsen et al.
 
-The way the shuffle works is by selecting 2 days' worth of proposers, and then shuffling the proposers over one day's worth of slots to create a new list of proposers for the following day.
-In each slot a subset of the proposers are shuffled, and the rest are left unchanged.
+The Håstad square shuffle~\cite{haastad2006square} is one of the proposed ways of integrating an~\gls{ssle}.
+The Håstad square shuffle is a shuffling algorithm that shuffles a $n$ long vector with a shuffle size of $\sqrt {n}$.
+The algorithm works by splitting the vector into $\sqrt {n}$ times $\sqrt {n}$ square matrix and for each step in the algorithm it switches between shuffling a row and a column.
+The Håstad shuffle is more rigid than the shuffling algorithm used in curdleproofs~\cite{cryptoeprint:2022/560} because of the fixed size of the shuffle being $\sqrt {n}$.
+
+The Feistel shuffle~\cite{Feistle} is the previous shuffle method used in the Whisk protocol~\cite{Whisk2024}.
+The Feistel shuffle is a shuffling algorithm that works by taking $n$ number of trackers and arranging them in a $k$ times $k$ matrix.
+Each round the $i$-th proposer selects the $i$-th row of the created matrix and shuffles it in the form $F(x,y)=(y,x+y^3 mod k)$.
+The Feistel shuffle was then later replaced by the shuffle proposed be Larsen et al.~\cite{cryptoeprint:2022/560} because of the Feistel shuffle being too slow to shuffle the list of proposers.
 
-Though experiments Larsen et al. has shown that after enough shuffles becomes secrue even in adversarial environments.
-They also surgests that their may be room to lower the size of the subsets chosen in each lot without losing the security of the shuffle.
-Thereby increasing the speed of the shuffle and reducing the size of the proof being added to the blockchain.
 
 \subsection{Bulletproofs}\label{sec:related-work-bulletproofs}
 A big inspiration for the curdleproofs protocol is the use of bulletproofs~\cite{bunz2018bulletproofs}.