minor

ACNS/presentation/key_exchange.tex

@@ -2,18 +2,28 @@
 \section{Actively Secure Key Exchange}
 \begin{frame}
 	\frametitle{Measures for Active Security}
-	\begin{definition}[Zero-knowledge Proof of Knowledge in HHS \(\left(\mathcal E,\mathcal G\right)\)]
+	\begin{definition}[Zero-knowledge Proof of Knowledge in \(\left(\mathcal E,\mathcal G\right)\) \cite{DBLP:conf/pqcrypto/BeullensDPV21}]
 		A party proves knowledge of \(s\) with
 			\[  \left[s\right] E_i = E_i' \]
 		for pairs \(\left(E_i,E_i'\right) \in \mathcal E^2\), \(i=1,\ldots, m\).
 	\end{definition}
-	\begin{definition}[Piecewise Verifiable Proof]
+	\begin{definition}[Piecewise Verifiable Proof \cite{DBLP:conf/asiacrypt/BeullensKV19}]
 		A party proves knowledge of a polynomial \(f\) for a statement
 		\[x = \left(\left(E_0,E_1\right),s_1,\ldots, s_n\right),\]
 		where \(E_1 = \left[f\paren* 0\right] E_0\) and \(s_i = f\paren* i\) for \(i=1,\ldots, n\).
 	\end{definition}
 \end{frame}
 
+\begin{frame}
+	\frametitle{What to do?}
+	\begin{itemize}
+		\item Transfer PVP and ZK proof to the threshold setting
+		\item Integrate both to decapsulation protocol to achieve active security
+		\item Prove, that resulting protocol is at least as secure as original decapsulation
+	\end{itemize}
+
+\end{frame}
+
 \begin{frame}
 	\frametitle{Key Generation}
 	\begin{pchstack}[center]
@@ -75,6 +85,6 @@
 	\begin{itemize}
 		\item IND-CPA, i.e., the encapsulated key cannot be distinguished from the ciphertext, assuming the hardness of the GAIP
 		\item Simulatable (as was \cite{FeoM20})
-		\item Actively Secure, i.e., a misbehaving shareholder can be detected, if the PVP and ZK proof are sound
+		\item Actively secure, i.e., a misbehaving shareholder can be detected, if the PVP and ZK proof are sound
 	\end{itemize}
 \end{frame}

ACNS/presentation/motivation.tex

@@ -2,7 +2,7 @@
 
 \begin{frame}[allowframebreaks]
 	\frametitle{Where are we?}
-	\begin{block}{Hard Homogeneous Spaces}
+	\begin{block}{Hard Homogeneous Spaces (Couveignes \cite{DBLP:journals/iacr/Couveignes06})}
 		A hard homogeneous space \(\left(\mathcal E,\mathcal G\right)\) is
 		\begin{itemize}
 			\item a set \(\mathcal E\),