Hide cid in ppk

paper/protocol.tex

@@ -2,7 +2,7 @@ \section{\CROCUS:\@ A protocol for crowd counting estimation}%
 \label{Protocol}
 
 
-We now present \CROCUS, a protocol for privately verifyiable crowd counts.
+We now present \CROCUS, a protocol for privately verifiable crowd counts.
 The protocol consists of five phases: setup (in \cref{ProtocolSetup}),
 join, participation, submission (all in in \cref{ProtocolDuring}) and
 verification (in \cref{ProtocolVerification}).
@@ -121,7 +121,7 @@ \subsection{Creation, join and participation in a protest and submission of proo
       P\to W\colon & \pid \\
       P\leftrightarrow W\colon &
         \PPK\mleft\{ (\sk_P) : \mright. \\
-        & \qquad \pid = \ACprf[_{\sk_P}][\cid], \\
+        & \qquad \pid = \ACprf[_{\sk_P}][\cid] \quad \land \\
         & \qquad \mleft. \sigma_P' = \ACblind[\ACsign[_{\ssk}][\sk_P]] \mright\} 
         \\
       W\colon & \wid\gets \ACprf[_{\sk_W}][\pid] \\
@@ -136,14 +136,14 @@ \subsection{Creation, join and participation in a protest and submission of proo
       W\to S\colon & (\cid, \pid, \wid, t_s, t_s', t_e, l, \pi_{\wid}),\quad 
       \text{where} \\
         & \pi_{\wid} = \SPK\mleft\{ (\sk_W) : \mright. \\
-        & \qquad \wid = \ACprf[_{\sk_W}][\pid], \\
+        & \qquad \wid = \ACprf[_{\sk_W}][\pid] \quad \land \\
         & \qquad \mleft. \sigma_W' = \ACblind[\ACsign[_{\ssk}][\sk_W]]\mright\} 
         \\
         & \qquad\qquad (\cid, \pid, \wid, t_s, t_s', l) \\
       P\to S\colon & (\cid, \pid, \wid, t_s, t_s', t_e, l, \pi_{\pid}),\quad 
       \text{where}\\
         & \pi_{\pid} = \SPK\mleft\{ (\sk_P) : \mright. \\
-        & \qquad \pid = \ACprf[_{\sk_P}][\cid], \\
+        & \qquad \pid = \ACprf[_{\sk_P}][\cid] \quad \land \\
         & \qquad \mleft. \sigma_P' = \ACblind[\ACsign[_{\ssk}][\sk_P]] \mright\} 
         \\
         & \qquad\qquad (\cid, \pid, \wid, t_s, t_s', l)
@@ -172,9 +172,15 @@ \subsection{Creation, join and participation in a protest and submission of proo
 the witness construct the proof share of the protester (\cref{fig:ProofFig}).
 
 The protester sends \(\pid\) to the witness.
-Then they run the protocol \[
-  \Proto{\ACproveSig[\spk, k, r, \sigma]}{\ACverifySig[\spk, \ssk]}
-\] (see \cref{ACacAlg}).
+Then they run the protocol
+\begin{multline*}
+  \PK\left\{ (\sk_P, \sigma_P, \cid): \right.\\
+    \pid = \ACprf[\sk_P, \cid] \land \sigma' = \ACblind[\sigma_P] \land \\
+    \cid' = \ACcommit[\cid]
+  \left.\right\},
+\end{multline*}
+where \(\sigma_P = \ACsign[\spk, \ssk, \sk_P]\).
+(See \cref{ACacAlg}.)
 Note that the \ac{PK} in \cref{ACacAlg} must be run as \iac{PPK}.
 If the protocol succeeds, the witness will compute \(\wid \gets 
   \ACprf[_{\sk_W}][\pid]\) and send \((\wid, t_s', l)\) to the protester.