Shuffle Gaussian Mechanism for Differential Privacy

2022/06/20 by Liew, Seng Pei, Takahashi, Tsubasa
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2206.09569

Abstract

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-1)log(\frace^-λ/2σ2n^λ ∑_\substackk₁+\dotsc+k_n = λ;
k₁,\dotsc,k_n≥ 0\binomλk₁,\dotsc,k_ne^∑_i=1ⁿk_i²/2σ²) 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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