A Other properties of differential privacy and RDP

RDP inherits and generalizes the information-theoretic properties of DP . This composition rule, together with Lemma 3, often allows for tighter calculations of (null,δ)-DP for the composed mechanism than directly invoking the strong composition theorem below. Also w.l.o.g., we assume thresholds Substituting the above expression to the definition of RDP and apply Jensen's inequality (6) = The inequality applies Jensen's inequality to bivariate function We use a trick due to [Bun and Steinke, 2016] with some modifications. Now we are ready to prove the three claims of Theorem 8. 13 The claim (3): Substitute the the above bound into Lemma 17, we get: E In the last line, we applied the "indistinguishability" property of an RDP mechanism in Lemma 15 The issue is how to proceed. The proof follows a similar sequence of arguments to that we presented for c = 1 .