From d6c2d5955a6fc13ec5863a894aa15b36fdf74d59 Mon Sep 17 00:00:00 2001
From: Manos Katsomallos <manos@delkappa.com>
Date: Sun, 10 Oct 2021 19:48:54 +0200
Subject: [PATCH] theotherthing: Problem

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+\subsection{Problem definition}
+\label{subsec:lmdk-sel-prob}
+
+The problem setting is similar to the one that we described in detail in Section~\ref{subsec:lmdk-set}.
+The main difference in this case lies in our threat model where we consider, in addition to the values of the regular and {\thething} events, the {\thething} timestamps $L$ privacy-sensitive as well.
+
+Given a set of {\thethings} at respective timestamps $\{l_k\}$ in a series of events at $\{t_n\}$, such that $\{l_k\} \subseteq \{t_n\}$, a data publisher might release this information by:
+
+\begin{enumerate}
+  \item Selecting a set of options (Section~\ref{subsec:lmdk-set-opts}) consisting of different possible versions of $\{l_k\}$.
+  
+  \mk{`option' or `candidate'?}
+
+  This could be:
+
+  \begin{itemize}
+    \item either a random set of $k$ other timestamps similar to the actual {\thething} timestamps (Section~\ref{subsec:lmdk-rnd}),
+    \item or a set including $\{l_k\}$ and $x \in [1, n - k]$ additional dummy timestamps (Section~\ref{subsec:lmdk-dum-gen}).
+  \end{itemize}
+
+  \item Releasing a privacy-preserving version of the {\thething} timestamps (Section~\ref{subsec:priv-opt-sel}).
+  We utilize the exponential mechanism with a utility function that calculates an indicator for each of the options in the set that we selected in the previous step.
+  The utility depends on the positioning of the {\thething} timestamps of an option in the series, e.g.,~the distance from the previous/next {\thething}, the distance from the start/end of the series, etc.
+\end{enumerate}
+
+Following this process allows the release, and thereafter processing, of {\thething} timestamps.
+Thus, we provide an extra layer of privacy protection when we separate {\thethings} from regular events.