changed active security and simulatability to subsubsections, minor

ACNS/data.txt

@@ -2,6 +2,6 @@
 \author{Fabio Campos \and Philipp Muth}
 \index{Campos, Fabio}
 \index{Muth, Philipp}
-\nbpages{22}
+\nbpages{26}
 \contact{campos@sopmac.de, philipp.muth@tu-darmstadt.de}
 

ACNS/keyexchange.tex

@@ -201,7 +201,7 @@ We resolve the conflicts by amending \cite{DBLP:conf/pqcrypto/BeullensDPV21}'s P
 %\[\paren*{\left(R,R'\right),\left( L_{i,S^\ast} s_{ij}\right)_{P_j \in S^\ast}},\]
 \ifshamir
 	\[\paren*{\left(R,R'\right),\left(f_i\paren j\right)_{P_j \in S^\ast}},\]
-	for a superauthorised set \(S^\ast\), where \(R\sample\mathcal E\), \(R' = \left[L_{i,S^\ast} f_i\paren 0\right] R = \left[L_{i,S^\ast} s_i\right] R\).
+	to a superauthorised set \(S^\ast\), where \(R\sample\mathcal E\), \(R' = \left[L_{i,S^\ast} f_i\paren 0\right] R = \left[L_{i,S^\ast} s_i\right] R\).
 	The inputs of our amended proving protocol are the proving shareholder's index \(i\), the witness polynomial \(f_i\), the superauthorised set \(S^\ast \in\Gamma^+\) and the statement \(\left(\left(R,R'\right), \left( f_i\paren j\right)_{P_j\in S^\ast}\right)\). The protocol can be found in \algoref{fig.tpvpp}, in which \(\mathcal C\) denotes a commitment scheme.
 	The verifying protocol in turn has the prover's and the verifier's indices \(i\) and \(j\), respectively, a set \(S^\ast\in\Gamma^+\), a statement piece \(x_j\) and a proof piece \(\left(\pi,\pi_j\right)\) as input, where \(x_j = \left(R,R'\right)\in\mathcal E^2\) if \(j=0\) and \(x_j\in\Z_p\) otherwise. The verifying protocol is given in \algoref{fig.tpvpv}.
 \else
@@ -467,7 +467,7 @@ There are two aspects of security to consider:
 \end{itemize}
 \  
 \ifsubsection
-\subsection{Active security}
+\subsubsection{Active security}
 \else
 \noindent\textbf{\\Active security.}
 \fi
@@ -516,7 +516,7 @@ There are two aspects of security to consider:
 	\fi
 \end{proof}
 \ifsubsection
-\subsection{Simulatability}
+\subsubsection{Simulatability}
 \else
 \noindent\textbf{Simulatability.}
 \fi