Tight Differential Privacy Blanket for Shuffle Model

With the recent bloom of focus on digital economy, the importance of personal data has seen a massive surge of late. Keeping pace with this trend, the model of data market is starting to emerge as a process to obtain high-quality personal information in exchange of incentives. To have a formal guarantee to protect the privacy of the sensitive data involved in digital economy, \emph{differential privacy (DP)} is the go-to technique, which has gained a lot of attention by the community recently. However, it is essential to optimize the privacy-utility trade-off by ensuring the highest level of privacy protection is ensured while preserving the utility of the data. In this paper, we theoretically derive sufficient and necessary conditions to have tight $(\epsilon,\,\delta)$-DP blankets for the shuffle model, which, to the best of our knowledge, have not been proven before, and, thus, characterize the best possible DP protection for shuffle models which can be implemented in data markets to ensure privacy-preserving trading of digital economy.