A Graph Symmetrisation Bound on Channel Information Leakage under Blowfish Privacy. (arXiv:2007.05975v2 [cs.IT] UPDATED)

Blowfish privacy is a recent generalisation of differential privacy that
enables improved utility while maintaining privacy policies with semantic
guarantees, a factor that has driven the popularity of differential privacy in
computer science. This paper relates Blowfish privacy to an important measure
of privacy loss of information channels from the communications theory
community: min-entropy leakage. Symmetry in an input data neighbouring relation
is central to known connections between differential privacy and min-entropy
leakage. But while differential privacy exhibits strong symmetry, Blowfish
neighbouring relations correspond to arbitrary simple graphs owing to the
framework’s flexible privacy policies. To bound the min-entropy leakage of
Blowfish-private mechanisms we organise our analysis over symmetrical
partitions corresponding to orbits of graph automorphism groups. A construction
meeting our bound with asymptotic equality demonstrates tightness.