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20 changes: 13 additions & 7 deletions paper/protocol.tex
Original file line number Diff line number Diff line change
@@ -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.