A Note on Differential Privacy: Defining Resistance to Arbitrary Side Information

In this note we give a precise formulation of "resistance to arbitrary side information" and show that several relaxations of differential privacy imply it. The formulation follows the ideas originally due to Dwork and McSherry, stated implicitly in [Dw06]. This is, to our knowledge, the first place such a formulation appears explicitly. The proof that relaxed definitions satisfy the Bayesian formulation is new.