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I recently read the definition of differential privacy, which is as follows:

a randomized function $K$ gives $\epsilon$-differential privacy if for all data sets $D$ and $D'$ differing in at most one row, and all output space $S$, we have $Pr[K(D) \in S] \leq \exp(\epsilon).Pr[K(D') \in S]$ where the probability space in each case is over the coin flips of $K$

Could somebody explain what it means when saying "probability is over the coin flip" ? an example would be greatly appreciated

Cheers

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the probability space in each case is over the coin flips of K

Simply put, $K$ has values in a discrete set $\mathfrak K$ with $\Pr(K=k)=p_k$ for every $k$ in $\mathfrak K$, and $$ \Pr(K(D)\in S)=\sum_{k\in\mathfrak K}p_k\cdot\mathbf 1_{k(D)\in S}. $$ Similarly for $\Pr(K(D')\in S)$.

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