fortify working and verifying

whitepaper/Dissertation.tex

@@ -806,6 +806,8 @@ Validating $E(m)$ is done with the proof of zero. Then it remains to prove that
 	\end{enumerate}
 \end{protocol}
 
+The downside of this proof over the BCDG proof \cite{bcdg1987} is that the time to perform and verify this proof grows linearly with $|m|$. However, in most cases $|m|$ should be small: i.e, $|m| \leq 5$.
+
 Range proof is used in points (3), (4), and (5). In (3), this is to convince other players that the number of units is sufficient for the action. In (4), this is to show that the region is not totally depleted. In (5), this is to ensure the number of units being fortified is less than the strength of the region. All of these are performed using \hyperref[protocol4]{Protocol~\ref*{protocol4}} and by using the additive homomorphic property to subtract the lower range from $m$ first.
 
 \subsection{Proving fortifications}