28 lines
1.7 KiB
TeX
28 lines
1.7 KiB
TeX
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\subsection{Problem definition}
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\label{subsec:lmdk-sel-prob}
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The problem setting is similar to the one that we described in detail in Section~\ref{subsec:lmdk-set}.
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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.
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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:
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\begin{enumerate}
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\item Selecting a set of options (Section~\ref{subsec:lmdk-set-opts}) consisting of different possible versions of $\{l_k\}$.
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\mk{`option' or `candidate'?}
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This could be:
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\begin{itemize}
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\item either a random set of $k$ other timestamps similar to the actual {\thething} timestamps (Section~\ref{subsec:lmdk-rnd}),
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\item or a set including $\{l_k\}$ and $x \in [1, n - k]$ additional dummy timestamps (Section~\ref{subsec:lmdk-dum-gen}).
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\end{itemize}
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\item Releasing a privacy-preserving version of the {\thething} timestamps (Section~\ref{subsec:priv-opt-sel}).
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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.
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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.
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\end{enumerate}
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Following this process allows the release, and thereafter processing, of {\thething} timestamps.
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Thus, we provide an extra layer of privacy protection when we separate {\thethings} from regular events.
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