RDP_Sampled_Shuffle

Here, we give local and central differential privacy definitions that we use throughout this work. Now, we prove Theorem 5. Our proof is an adaptation of the proof of [ 's are disjoint for all We present a proof of Lemma 4 in Appendix C.2. From Lemma 3 and Lemma 4, we get E By substituting from (27) into (25) completes the proof of Theorem 5. C.2 Proof of Lemma 4 We only show (22); (23) and (24) can be shown similarly. Let x, y 2 R be any two real numbers. From Lemma 6, we get the following corollary. Remark 3. Observe that the proof of Corollary 1 does not require This is what we do in the lemma below.