From 38aa2ef568547b954ca0e578860dd9c69cbccebe Mon Sep 17 00:00:00 2001
From: Philipp Muth <muth@seceng.informatik.tu-darmstadt.de>
Date: Thu, 28 Jul 2022 11:14:21 +0200
Subject: [PATCH] fixed two-lvl sharing reference in 'amending the pvp'
---
ACNS/keyexchange.tex | 10 +++++++---
1 file changed, 7 insertions(+), 3 deletions(-)
diff --git a/ACNS/keyexchange.tex b/ACNS/keyexchange.tex
index 4ddf8e9..20c6c7b 100644
--- a/ACNS/keyexchange.tex
+++ b/ACNS/keyexchange.tex
@@ -21,7 +21,7 @@ We fix the following publically known parameters.
We give our key exchange mechanism in the context of Shamir's secret sharing scheme and elaborate possible extensions to other, more general secret sharing schemes in \secref{sec.generalsss}.
\ifsubsection
-\subsection{Key Generation}
+\subsection{Key Generation}\label{subsec.keygen}
\else
\noindent\textbf{\\Key Generation.}
\fi
@@ -211,8 +211,12 @@ We resolve the conflicts by amending \cite{DBLP:conf/pqcrypto/BeullensDPV21}'s P
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}.
\fi
-It is here, that the two-level sharing we introduced in \secref{sec.keygen} in the key generation protocol comes into play. We will have each shareholder \(P_i\) engaged in an execution of \(\decaps\) provide a PVP with respect to its share \(s_i\) of the secret key \(\sk\), that is then verified by each other participating shareholder with its respective share of \(s_i\).
-\todo{fix this line}
+\ifsubsection
+It is here, that the two-level sharing we introduced in \secref{subsec.keygen} comes into play. We will have each shareholder \(P_i\) engaged in an execution of \(\decaps\) provide a PVP with respect to its share \(s_i\) of the secret key \(\sk\), that is then verified by each other participating shareholder with its respective share of \(s_i\).
+\else
+It is here, that the two-level sharing we introduced in the key generation protocol comes into play. We will have each shareholder \(P_i\) engaged in an execution of \(\decaps\) provide a PVP with respect to its share \(s_i\) of the secret key \(\sk\), that is then verified by each other participating shareholder with its respective share of \(s_i\).
+\fi
+%\todo{fix this line}
The definitions of soundness and zero-knowledge for a threshold PVP scheme carry over from the non-threshold setting in \secref{sec.prelim} intuitively, yet we restate the completeness definition for the threshold setting.
\begin{definition}[Completeness in the threshold setting]
--
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