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I can't give an example illustrating why leakage must be non-negligible for the utility of the mechanism, but I can give a proof of why leakage must be non-negligible for the utility of the mechanism. Let $\;\; U \: = \: \left\{\langle D,D'\rangle : D,D' \text{ differ in one element}\right\} \;\;\;$. By the triangle inequality, for all $D$ and $D'$, for ...

Differential privacy has been "invented" for a completely different use case scenario than indistinguishability for data privacy. The scenario is that you outsource your data into an untrusted party with that amount of noise that when the untrusted party applies some operations on data , individual data privacy is protected but the aggregate operation is in ...

The two primary techniques I'm familiar with is structuring a cryptographic primitive as a sequence of games and the universally composable security framework. Sequence of Games The idea here is to represent a protocol/primitive as a game played between an attacker and a challenger. You define a bad event and show through the game that the event happens ...