\chapter{{\Thething} privacy}
\label{ch:lmdk-prv}

% Crowdsensing applications
The plethora of sensors currently embedded in personal devices and other infrastructures have paved the way for the development of numerous \emph{crowdsensing services} (e.g.,~Ring~\cite{ring}, TousAntiCovid~\cite{tousanticovid}, Waze~\cite{waze}, etc.) based on the collected personal, and usually geotagged and timestamped data.
% Continuously user-generated data
User--service interactions gather personal event-like data, that are data items comprised of pairs of an identifying attribute of an individual and the---possibly sensitive---information at a timestamp (including contextual information), e.g.,~(\emph{`Bob', `dining', `Canal Saint-Martin', $17{:}00$}).
When the interactions are performed in a continuous manner, we obtain ~\emph{time series} of events.
% Observation/interaction duration
Depending on the duration, we distinguish the interaction/observation into \emph{finite}, when taking place during a predefined time interval, and \emph{infinite}, when taking place in an uninterrupted fashion.
Example~\ref{ex:scenario} shows the result of user--LBS interaction while retrieving location-based information or reporting user-state at various locations.
 
\begin{example}
  \label{ex:scenario}

  Consider a finite sequence of spatiotemporal data generated by Bob during an interval of $8$ timestamps, as shown in Figure~\ref{fig:scenario}.
  Events in a shade correspond to privacy-sensitive events that Bob has defined beforehand. For instance his home is around {\'E}lys{\'e}e, his workplace is around the Louvre, and his hangout is around Canal Saint-Martin.

  \begin{figure}[htp]
    \centering
    \includegraphics[width=\linewidth]{problem/lmdk-scenario}
    \caption{A time series with {\thethings} (highlighted in gray).
    }
    \label{fig:scenario}
  \end{figure}

\end{example}

% Privacy-preserving data processing
The services collect and further process the time series in order to give useful feedback to the involved users or to provide valuable insight to various internal/external analytical services.
The regulation regarding the processing of user-generated data sets~\cite{tankard2016gdpr} requires the provision of privacy guarantees to the users. 
At the same time, it is essential to provide utility metrics to the final consumers of the privacy-preserving process output. 
To accomplish this, various privacy techniques perturb the original data or the processing output at the expense of the overall utility of the final output.
A widely recognized tool that introduces probabilistic randomness to the original data, while quantifying with a parameter $\varepsilon$ (`privacy budget'~\cite{mcsherry2009privacy}) the privacy/utility ratio is \emph{$\varepsilon$-differential privacy}~\cite{dwork2006calibrating}.
Due to its \emph{composition} property, i.e.,~the combination of differentially private outputs satisfies differential privacy as well, differential privacy is suitable for privacy-preserving time series publishing.
\emph{Event}, \emph{user}~\cite{dwork2010differential, dwork2010pan}, and \emph{$w$-event}~\cite{kellaris2014differentially} comprise the possible levels of privacy protection.
Event-level limits the privacy protection to \emph{any single event}, user-level protects \emph{all the events} of any user, and $w$-event provides privacy protection to \emph{any sequence of $w$ events}.

In this chapter, we propose a novel configurable privacy scheme, \emph{\thething} privacy, which takes into account significant events (\emph{\thethings}) in the time series and allocates the available privacy budget accordingly.
We propose three privacy models that guarantee {\thething} privacy.
To further enhance our privacy method, and protect the {\thethings} position in the time series, we propose techniques to perturb the initial {\thethings} set (Section~\ref{sec:theotherthing}).

\input{problem/thething/main}
\input{problem/theotherthing/main}

\input{problem/summary}
