Shuffle Gaussian Mechanism for Differential Privacy
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We study Gaussian mechanism in the shuffle model of differential privacy (DP). Particularly, we characterize the mechanism's Rényi differential privacy (RDP), showing that it is of the form: ϵ(λ) ≤1/λ-1log(e^-λ/2σ^2/n^λ∑_k_1+…+k_n=λ; k_1,…,k_n≥ 0λk_1,…,k_ne^∑_i=1^nk_i^2/2σ^2) We further prove that the RDP is strictly upper-bounded by the Gaussian RDP without shuffling. The shuffle Gaussian RDP is advantageous in composing multiple DP mechanisms, where we demonstrate its improvement over the state-of-the-art approximate DP composition theorems in privacy guarantees of the shuffle model. Moreover, we extend our study to the subsampled shuffle mechanism and the recently proposed shuffled check-in mechanism, which are protocols geared towards distributed/federated learning. Finally, an empirical study of these mechanisms is given to demonstrate the efficacy of employing shuffle Gaussian mechanism under the distributed learning framework to guarantee rigorous user privacy.
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