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The shuffle model of local differential privacy is an advanced method ofprivacy amplification designed to enhance privacy protection with high utility.It achieves this by randomly shuffling sensitive data, making linkingindividual data points to specific individuals more challenging. However, mostexisting studies have focused on the shuffle model based on$(\epsilon_0,0)$-Locally Differentially Private (LDP) randomizers, with limitedconsideration for complex scenarios such as $(\epsilon_0,\delta_0)$-LDP orpersonalized LDP (PLDP). This hinders a comprehensive understanding of theshuffle model's potential and limits its application in various settings. Tobridge this research gap, we propose a generalized shuffle framework that canbe applied to any $(\epsilon_i,\delta_i)$-PLDP setting with personalizedprivacy parameters. This generalization allows for a broader exploration of theprivacy-utility trade-off and facilitates the design of privacy-preservinganalyses in diverse contexts. We prove that shuffled$(\epsilon_i,\delta_i)$-PLDP process approximately preserves $\mu$-GaussianDifferential Privacy with \mu = \sqrt{\frac{2}{\sum_{i=1}^{n}\frac{1-\delta_i}{1+e^{\epsilon_i}}-\max_{i}{\frac{1-\delta_{i}}{1+e^{\epsilon_{i.$  This approach allows us to avoid the limitations and potential inaccuraciesassociated with inequality estimations. To strengthen the privacy guarantee, weimprove the lower bound by utilizing hypothesis testing} instead of relying onrough estimations like the Chernoff bound or Hoeffding's inequality.Furthermore, extensive comparative evaluations clearly show that our approachoutperforms existing methods in achieving strong central privacy guaranteeswhile preserving the utility of the global model. We have also carefullydesigned corresponding algorithms for average function, frequency estimation,and stochastic gradient descent.

A Generalized Shuffle Framework for Privacy Amplification: Strengthening Privacy Guarantees and Enhancing Utility