Update report/src/sections/07-discussion.tex

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

Author: Maltesius

report/src/sections/07-discussion.tex

@@ -47,8 +47,8 @@ \subsection{Shuffle Security}\label{subsec:Discution-Shuffle-security}
 Only 72.33\% of the currently calculated size for Curdleproofs.
 This would result in saving $\sim 12.11GB$ of space on the blockchain each year.
 Some other things to keep in mind when deciding on how many honest shuffles should be necessary to make the shuffle secure is that there are other factors that can affect the security of the blockchain.
-One of such factors is some of the known attacks that takes advantage of controlling a large number of validators.
-Attacks like the $\geq50\%$ stake attack and the $33\%$ finality attack~\cite{EthereumAttackDefense2024} takes advantage of controlling a large number of validators in order to negatively effect the blockchain system.
+One of such factors is some of the known attacks that take advantage of controlling a large number of validators.
+Attacks like the $\geq50\%$ stake attack and the $33\%$ finality attack~\cite{EthereumAttackDefense2024} take advantage of controlling a large number of validators in order to negatively effect the blockchain system.
 Because of attacks like these, which rely on controlling a large number of validators, we would recommend, when evaluating how many honest shuffles are necessary to make the shuffle secure; one should also take into account how many honest validators are necessary to make the blockchain secure.
 
 Another thing to keep in mind is that within the Ethereum system not every validator is owned by a different person.