From ca9bfefc866eb4c590905fd1c187f8cb3a82dc9c Mon Sep 17 00:00:00 2001
From: Fabio Campos <campos@sopmac.de>
Date: Tue, 13 Sep 2022 11:49:28 +0200
Subject: [PATCH] typo and titles

---
 ACNS/presentation/key_exchange.tex | 4 ++--
 ACNS/presentation/motivation.tex   | 7 ++++---
 2 files changed, 6 insertions(+), 5 deletions(-)

diff --git a/ACNS/presentation/key_exchange.tex b/ACNS/presentation/key_exchange.tex
index ea7cd14..7464e00 100644
--- a/ACNS/presentation/key_exchange.tex
+++ b/ACNS/presentation/key_exchange.tex
@@ -58,10 +58,10 @@
 \end{frame}
 
 \begin{frame}[allowframebreaks]
-	\frametitle{A Shareholder \(P_i\)'s Turn in the Decapsulation Protocol}
+	\frametitle{Shareholder \(P_i\)'s Turn in the Decapsulation}
 	Let \(S^\ast\) be a superauthorised set of shareholders executing the decapsulation protocol.
 	\begin{enumerate}
-		\item Ascertain \(E^{k-1} \in \mathcal E\), where \(E^{k-1}\) is previous shareholder's output of \(E^0 = c\)
+		\item Ascertain \(E^{k-1} \in \mathcal E\), where \(E^{k-1}\) is previous shareholder's output or \(E^0 = c\)
 		\item Sample \(R_k \sample \mathcal E\), compute \(R_k'\gets \left[L_{i,S^\ast}s_i\right] R_k\).
 		\item Compute and publish
 			\begin{align*}
diff --git a/ACNS/presentation/motivation.tex b/ACNS/presentation/motivation.tex
index f276bb2..e5db780 100644
--- a/ACNS/presentation/motivation.tex
+++ b/ACNS/presentation/motivation.tex
@@ -88,7 +88,8 @@
 
 \begin{frame}
 	\frametitle{Key Exchange Mechanisms in a HHS}
-	\begin{pchstack}[center,space=2em]
+    \begin{center}
+	\begin{pchstack}[center,space=3em]
 	\procedure[space=auto]{$\keygen()$}{
 		\sk \sample \ZZ_p\\
 		\pk \gets \left[\sk\right] E_0\\
@@ -107,11 +108,11 @@
 		\pcreturn \key
 		}
 	\end{pchstack}
-
+\end{center}
 \end{frame}
 
 \begin{frame}
-	\frametitle{A Decapsulation Protocol with Shared Secret Key \cite{FeoM20}}
+	\frametitle{Decapsulation w/ Shared Secret \cite{FeoM20}}
 
 	\begin{center}
 	\begin{tikzpicture}
-- 
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