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Aligns formal adversary model with the rest
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paper/.gitignore

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base-identity-cause-adversary.tikz
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base-identity-location-adversary.tikz
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base-adversary.tikz
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Jacobs-method.jpg
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anon.bib

paper/Makefile

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FIGS+= proofshare.tikz
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proofshare.tikz: ../fig/proofshare.tikz
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FIGS+= base-identity-proof-share-adversary.tikz
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base-identity-proof-share-adversary.tikz: ../fig/base-identity-proof-share-adversary.tikz
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FIGS+= base-adversary.tikz
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base-adversary.tikz: ../fig/base-adversary.tikz
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${FIGS}:
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${LN} $< $@

paper/adversary-model.tex

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\subsection{Privacy adversary}%
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\label{adversary-model-different-levels}
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\subsection{Adversary model}%
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\label{formal-adversary-model}
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We provide one system model with two possible adversaries: one who tries to link a protester's real identity (\(P\)) to a protest proof-share (\(\cid\)) and one
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that aims at linking a protester's or a witness's real identity (\(P\), respectively \(W\)), to a location (\(l\)).
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We also define varying strengths of each adversary.
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We now provide a concretely defined system and adversary model.
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We give three definitions, each defines an adversary with increasingly stronger
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capabilities (\ie more auxiliary information).
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\paragraph{The identity--proof share linking adversary}
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There are three players: the protest participant (with identity) \(P\), a witness (with identity) \(W\) and the storage \(S\).
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There are three players: the protest participant (with identity) \(P\), a
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witness (with identity) \(W\) and the storage \(S\).
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The adversary \(A\) controls \(W\) and \(S\).
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This is illustrated in \cref{fig:base-adversary}.
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\begin{figure}
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\centering
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\includegraphics{base-adversary.tikz}
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\caption{\label{fig:base-adversary}%
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An overview of the base adversary model.
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The protester with real identity \(P\) and witness with real identity \(W\)
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communicate.
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They exchange protocol data, \(d_{P,W}(\cid, P)\), and record the time it
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happened, \(t_{P,W}\).
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The protester submits \(f(d_{P,W}(\cid, P))\), for some function \(f\), to
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the storage \(S\), who records the time it happened, \(t_{P,S}\).
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Both the witness \(W\) and storage \(S\) are controlled by the adversary
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\(A\).
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}
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\end{figure}
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\begin{definition}[Base identity--proof share adversary]%
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\label{base-identity-proof-share-adversary}
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\begin{definition}[Base adversary]%
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\label{base-adversary}
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The protester \(P\) and the witness \(W\) communicate.
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Each learns only the protocol data \(d_{P,W}(\cid, P)\) and when it happened
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\(t_{P,W}\)\footnote{%
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Each learns only the protocol data \(d_{P,W}(\cid, P)\) and when the
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communication occurred \(t_{P,W}\)\footnote{%
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Specifically, they do \emph{not} learn the real identities \(P\) and \(W\)
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directly, only if those appear in the data \(d_{P,W}(\cid, P)\).
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directly from the communication medium, only if those appear in the data
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\(d_{P,W}(\cid, P)\).
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}.
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The protester \(P\) communicates with \(S\), in which \(S\) only learns
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\(f(d_{P,W}(\cid, P))\), for some function \(f\), and the time of the
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do, but can additionally correlate what he learns from \(W\) and \(S\).
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\end{definition}
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This definition is illustrated in \cref{fig:identity-proof-share-adversary}.
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\begin{figure}
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\centering
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\includegraphics{base-identity-proof-share-adversary.tikz}
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\caption{\label{fig:identity-proof-share-adversary}%
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An overview of the base identity--proof share adversary model.
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The protester with real identity \(P\) and witness with real identity \(W\)
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communicate and each learn only the protocol data, \(d_{P,W}(\cid, P)\),
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and the time it happened, \(t_{P,W}\).
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The protester submits \(f(d_{P,W}(\cid, P))\), for some function \(f\), to
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the storage \(S\), who learns only that and the time it happened,
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\(t_{P,S}\).
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Both the witness \(W\) and storage \(S\) are controlled by the adversary
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\(A\).
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}
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\end{figure}
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The base adversary (\cref{base-adversary}) represents an adversary that has no
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access to auxiliary information, \eg inferences that can be done from the
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communication layer, which means that it has only the protocol data at its
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disposal.
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We find \cref{base-identity-proof-share-adversary} suitable when the protester and witness both move in a crowd and there is no way for the witness to decide exactly with whom he or she communicates with.
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However, in some situations this might not be the case, \eg the crowd is not dense.
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In these situations the witness will likely see the face of the protester.
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We capture this by the following definition.
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We find \cref{base-adversary} suitable when the protester and witness both move
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in a crowd and there is no way for the witness to decide exactly with whom he
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or she communicates with.
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However, in some situations this might not be the case: \Eg if the crowd is not
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dense the witness will likely see the face of the protester.
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If the witness is controlled by the adversary, then it is likely that the
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witness can capture a picture of the face, which can be turned into an identity
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through face recognition.
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There are various such scenarios leading to the adversary learning the
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protester's identity, we capture this by the following definition.
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\begin{definition}[Stronger identity--proof share adversary]%
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\label{stronger-identity-proof-share-adversary}
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The situation is the same as in \cref{base-identity-proof-share-adversary}, but now the
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witness \(W\) learns the protester \(P\)'s identity.
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\begin{definition}[Deanonymizing-witness adversary]%
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\label{deanonymizing-witness-adversary}
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The situation is the same as in \cref{base-adversary}, but now the witness
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\(W\) learns the protester \(P\)'s identity from an auxiliary channel.
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(\(P\) will also learn \(W\)'s identity.)
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However, \(S\) still does not learn \(P\)'s identity.
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\end{definition}
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However, given a strong enough adversary, such anonymous communication might not be possible.
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We capture such a strong adversary in the following definition.
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\begin{definition}[Strongest identity--proof share adversary]%
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\label{strongest-identity-proof-share-adversary}
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Everything is the same as in \cref{stronger-identity-proof-share-adversary}, except that now \(S\) also learns \(P\)'s identity.
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\begin{definition}[Deanonymizing adversary]%
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\label{deanonymizing-adversary}
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Everything is the same as in \cref{deanonymizing-witness-adversary}, except
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that now \(S\) also learns \(P\)'s identity from an auxiliary channel.
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\end{definition}
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paper/definitions.tex

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We first present an abstraction of a protest and how to count the
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participation (\cref{protest-model}). Then, we formulate the desired
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verifiability (\cref{verifiability-properties}) and privacy properties
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(\cref{privacy-properties}) \sonja{add? as well as the adversary model (\cref{formal-adversary-model})}.
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(\cref{privacy-properties}).
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Finally, we define a more concrete adversary model
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(\cref{formal-adversary-model}).
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\include*{protest-model}
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\include*{verifiability-properties}

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