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Blowfish privacy is a recent generalisation of differential privacy thatenables improved utility while maintaining privacy policies with semanticguarantees, a factor that has driven the popularity of differential privacy incomputer science. This paper relates Blowfish privacy to an important measureof privacy loss of information channels from the communications theorycommunity: min-entropy leakage. Symmetry in an input data neighbouring relationis central to known connections between differential privacy and min-entropyleakage. But while differential privacy exhibits strong symmetry, Blowfishneighbouring relations correspond to arbitrary simple graphs owing to theframework's flexible privacy policies. To bound the min-entropy leakage ofBlowfish-private mechanisms we organise our analysis over symmetricalpartitions corresponding to orbits of graph automorphism groups. A constructionmeeting our bound with asymptotic equality demonstrates tightness.

A Graph Symmetrisation Bound on Channel Information Leakage under Blowfish Privacy