Shuffle Gaussian Mechanism for Differential Privacy

• URL: http://arxiv.org/abs/2206.09569v1
• Date: Mon, 20 Jun 2022 04:54:16 GMT
• Title: Shuffle Gaussian Mechanism for Differential Privacy
• Authors: Seng Pei Liew, Tsubasa Takahashi
• Abstract summary: We study the mechanism's R'enyi differential privacy (RDP), showing that it is of the form: $$ epsilon(lambda) leq frac1lambda-1logleft(frace-da/2sigma2ndasum_substackk_+dotsc+k_n=lambda;k_nlambda!k_nlambda!k_nlambda!k_nlambda!
• Score: 2.7564955518050693
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study Gaussian mechanism in the shuffle model of differential privacy (DP). Particularly, we characterize the mechanism's R\'enyi differential privacy (RDP), showing that it is of the form: $$ \epsilon(\lambda) \leq \frac{1}{\lambda-1}\log\left(\frac{e^{-\lambda/2\sigma^2}}{n^\lambda}\sum_{\substack{k_1+\dotsc+k_n=\lambda;\\k_1,\dotsc,k_n\geq 0}}\binom{\lambda!}{k_1,\dotsc,k_n}e^{\sum_{i=1}^nk_i^2/2\sigma^2}\right) $$ 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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